MOLECULAR DYNAMICS SIMULATIONS ON PHOSPHOLIPID MEMBRANES

MARJAHYVÖNEN

Department of Physical Sciences,University of Oulu

Wihuri Research Institute

OULU 2001

MARJA HYVÖNEN

MOLECULAR DYNAMICS SIMULATIONS ON PHOSPHOLIPID MEMBRANES

Academic Dissertation to be presented with the assent ofthe Faculty of Science, University of Oulu, for publicdiscussion in Auditorium GO101, Linnanmaa, on April20th, 2001, at 12 noon.

OULUN YLIOPISTO, OULU 2001

Copyright © 2001University of Oulu, 2001

Manuscript received 20 March 2001Manuscript accepted 21 March 2001

Communicated byDocent Pentti SomerharjuProfessor Olle Edholm

ISBN 951-42-5943-2 (URL: http://herkules.oulu.fi/isbn9514259432/)

ALSO AVAILABLE IN PRINTED FORMATISBN 951-42-5942-4ISSN 0355-3191 (URL: http://herkules.oulu.fi/issn03553191/)

OULU UNIVERSITY PRESSOULU 2001

Hyvönen, Marja, Molecular dynamics simulations on phospholipid membranes Department of Physical Sciences, University of Oulu, P.O.Box 3000, FIN-90014 University ofOulu, Finland, Wihuri Research Institute, Kalliolinnantie 4, FIN-00140 Helsinki, Finland 2001Oulu, Finland(Manuscript received 20 March 2001)

Abstract

Phospholipids are the main components of cell membranes, lipoproteins and other membranestructures in living organisms. Properties of lipid molecules are important to the overall behaviourand interactions of membranes. Furthermore, characteristics of the biological membranes act asimportant regulators of membrane functions. Molecular dynamics (MD) simulations were applied inthis thesis to study properties of biological membranes. A certain degree of acyl chainpolyunsaturation is essential for the proper functioning of membranes, but earlier MD simulationshad not addressed the effects of polyunsaturation. Therefore a solvated all-atom bilayer modelconsisting of diunsaturated 1-palmitoyl-2-linoleoyl-3-phosphatidylcholine (PLPC) molecules wassimulated. The analysis of the simulation data was focused on the effects of double bonds on amembrane structure.

Self-organising neural networks were applied to the analysis of the conformational data from the1-ns simulation of PLPC membrane. Mapping of 1.44 million molecular conformations to a two-dimensional array of neurons revealed, without human intervention or requirement of a prioriknowledge, the main conformational features. This method provides a powerful tool for gaininginsight into the main molecular conformations of any simulated molecular assembly.

Furthermore, an application of MD simulations in the comparative analysis of the effects of lipidhydrolysis products on the membrane structure was introduced. The hydrolysis products of thephospholipase A2 (PLA2) enzyme are known to have a role in a variety of physiological processesand the membrane itself acts as an important regulator of this enzyme. The simulations revealeddifferences in the bilayer properties between the original and hydrolysed phospholipid membranes.This study provides further evidence that MD simulations on biomembranes are able to provideinformation on the properties of biologically and biochemically important lipid systems at themolecular level.

Keywords: unsaturation, self-organizing map, conformational analysis, phospholipase A2

5

Acknowledgements

This work took place in the NMR Research Group at the Department of Physical Sciences of the University of Oulu, and, during the last year, in the Wihuri Research Institute, Helsinki. I would like to thank the former head of the Department of Physical Sciences, Prof. Rauno Anttila, his successor Prof. Jukka Jokisaari, and Prof. Petri Kovanen, the head of the Wihuri Research Institute, for providing the facilities at my disposal.

I am grateful to Docent Mika Ala-Korpela and Prof. Tapio Rantala, my supervisors. Tapio introduced me to the world of computer simulations and offered his expert physical insight. I wish to thank Mika for pushing me into the world of lipids, for his scientific attitude, never-ending positivism, and patient, continuous support.

In addition to Professors Jukka Jokisaari, Petri Kovanen and my supervisors, I have had the privilege to work with Doctors Wael El-Deredy, Yrjö Hiltunen, Timo Ojala, Juha Vaara, and Katariina Öörni. The academic, technical and secretarial staff in both places provided both expert help and a pleasant working atmosphere.

I wish to thank Docent Pentti Somerharju and Professor Olle Edholm for reviewing and commenting the thesis, and Mr. Gordon Roberts for checking the language of the thesis.

This work has been financially supported by the Jenny and Antti Wihuri Foundation, the A. I. Virtanen Institute for Molecular Sciences, the Finnish Cultural Foundation, the Research Foundation of Orion Corporation, The Vilho, Yrjö, and Kalle Väisälä Foundation, the University of Oulu and Neuroproduction Ltd. The computer simulations of this work were possible with the computer facilities and support from the CSC Center for Scientific Computing (Espoo). Especially, I wish to thank Docent Leif Laaksonen, at an early stage of this work, and Kimmo Mattila for their patient answers to my foolish questions.

I would like to thank the members of the NMR group and the people at Wihuri for enjoyable moments during both the hard days of work and numerous unofficial parties.

I want to thank my parents Esa and Pirkko, brothers Panu, Topi and Pekka, and parents-in-law Maija and Hannu, for loving care and support, the happy days together and for being there. I am grateful for the precious time with my mother Taimi, little sister Hanna and with my grandparents. My dear friends, some of them all the way from

6

childhood and teenage years, and some appearing into my life during the course of my studies and work, are very precious.

I am privilidged to have a loving husband, Juha, whom I thank for patience and encouragement during these years. He was also ready for coauthorship when his expertise was needed. I am grateful of our charming little son Pyry, my everyday joy.

Helsinki, March 2001 Marja Hyvönen

7

Abbreviations

DLPE dilauroylphosphatidylcholine DMPC dimyristoylphosphatidylcholine DOPC dioleoylphosphatidylcholine DPPC dipalmitoylphosphatidylcholine DPPS dipalmitoylphosphatidylserine g-, g+, t gauche-, gauche+, trans Lα liquid-crystalline phase Lβ gel phase L

- linoleate

LH linoleic acid PPC 1-palmitoyl-3-phosphatidylcholine lysoPC lysophosphatidylcholine MD molecular dynamics NMR nuclear magnetic resonance NVE constant number of particles, volume, and energy NVT constant number of particles, temperature, and energy NPT constant number of particles, pressure, and temperature NγT constant number of particles, surface tension, and temperature PBC periodic boundary conditions PC phosphatidylcholine PE phosphatidylethanolamine PiLPC 1-palmitoyl-2-isolinoleoyl-3-phosphatidylcholine PLA2 phospholipase A2 PLPC 1-palmitoyl-2-linoleoyl-3-phosphatidylcholine POPC 1-palmitoyl-2-oleoyl-3-phosphatidylcholine PS phosphatidylserine SEM standard error of mean SOM self-organising map SM sphingomyelin Å Ångström = 0.1 nm

8

9

List of original papers

The present thesis consists of an introductory part and the following five papers, which are refered to in the text by their Roman numerals:

I Hyvönen M, Ala-Korpela M, Vaara J, Rantala TT & Jokisaari J (1995) Effects of

the two double bonds on the hydrocarbon interior of a phospholipid bilayer. Chemical Physics Letters 246: 300-306.

II Hyvönen M, Ala-Korpela M, Vaara J, Rantala TT & Jokisaari J (1997)

Inequivalence of single CHa and CHb methylene bonds in the interior of a diunsaturated lipid bilayer from a molecular dynamics simulation. Chemical Physics Letters 268: 55-60.

III Hyvönen MT, Rantala TT & Ala-Korpela M (1997) Structure and dynamic

properties of a diunsaturated PLPC lipid bilayer from a molecular dynamics simulation. Biophysical Journal 73: 2907-2923.

IV Hyvönen MT, Hiltunen Y, El-Deredy W, Ojala T, Vaara J, Kovanen PT & Ala-

Korpela M (2001) Application of self-organising maps in conformational analysis of lipids. Journal of the American Chemical Society 123: 810-816.

V Hyvönen MT, Öörni K, Kovanen PT & Ala-Korpela M (2001) Changes in a

phospholipid bilayer induced by the hydrolysis of a phospholipase A2 enzyme: a molecular dynamics simulation study. Biophysical Journal 80: 565-578.

The model construction, simulations and analysis required for papers I, II, III, and V together with the preparation of the data for the SOM analysis and subsequent handling of the results for paper IV have been performed by the present author. Also, the present author has been involved in the planning of all the presented studies and has written the first versions of the manuscripts, whereas the subsequent paper preparation has been teamwork.

10

11

Contents

Abstract Acknowledgements Abbreviations List of original papers Contents 1 Introduction................................................................................................................... 13 2 Lipid molecules and membrane systems....................................................................... 15

2.1 Lipid molecules...................................................................................................... 15 2.2 Lipid assembly ....................................................................................................... 16 2.3 Lipid hydrolysis ..................................................................................................... 19 2.4 Spatial and temporal scales in lipid molecular systems ......................................... 19

3 Molecular dynamics methodology on lipid systems ..................................................... 21 3.1 Basics of the molecular dynamics method............................................................. 21 3.2 Overview of methodology...................................................................................... 23

3.2.1 Force field parameters..................................................................................... 23 3.2.2 System size and boundary conditions ............................................................. 24 3.2.3 Treatment of electrostatic interactions ............................................................ 25 3.2.4 Time step and simulation length...................................................................... 27 3.2.5 Ensembles ....................................................................................................... 28 3.2.6 Initial configuration and equilibration............................................................. 29

3.3 Analysis of trajectories........................................................................................... 30 3.3.1 Self-organising maps in analysis of lipid conformations ................................ 31

4 Review of literature....................................................................................................... 33 4.1 Simulation studies on model membranes............................................................... 33

4.1.1 General characteristics of saturated phospholipid membranes........................ 33 4.1.2 Hydrophilic parts of PC lipids......................................................................... 35 4.1.3 Hydrophobic parts of saturated PC lipids........................................................ 36 4.1.4 Lipid and membrane dynamics ....................................................................... 37 4.1.5 Water structure and dynamics ......................................................................... 38 4.1.6 Electrostatics ................................................................................................... 39 4.1.7 Effects of different headgroups ....................................................................... 39

12

4.1.8 Effects of cholesterol....................................................................................... 41 4.2 Unsaturated membranes ......................................................................................... 42

4.2.1 Monounsaturated PC membranes.................................................................... 43 4.2.2 Polyunsaturated PC membranes...................................................................... 44

4.3 The relationship between membrane structure and PLA2 function ........................ 46 5 Applications .................................................................................................................. 48

5.1 Modelling and simulations..................................................................................... 48 5.2 Data analysis .......................................................................................................... 53

5.2.1 Traditional analysis tools................................................................................. 53 5.2.2 SOM based conformational analysis............................................................... 55

5.3 Structural characteristics of PLPC bilayer ............................................................. 56 5.3.1 Main conformations and conformational dynamics ........................................ 60

5.4 Structural differences between PLPC bilayer and its PLA2 modified counterpart . 63 6 Conclusions................................................................................................................... 68 7 Future perspectives........................................................................................................ 69 8 References..................................................................................................................... 70 9 Original Papers.............................................................................................................. 85

13

1 Introduction

The early model of biological membranes, the so called “fluid-mosaic model” was proposed in 1972 giving an idea that the lipid membrane could be considered as a two dimensional fluid where the proteins can diffuse around [1]. Although this model has been continuously presented as a simple perspective to biological membranes, it has become evident that, instead of acting just as a solvent for proteins, the lipid molecules have particular importance for the functioning of living organisms. This is underlined by the impressive diversity of the chemical structures of lipids, which is actively maintained by cells [2]. Thus, molecular systems consisting of different lipid molecules are increasingly studied using various experimental and computational methods [3] to explore the characteristics of these systems and the relations between the structural and dynamic properties and different functions in the membranes. By now, it is clear that the properties of the lipid membranes act as important regulators of membrane functions.

Experimental methods, such as nuclear magnetic resonance (NMR), infrared (IR), and fluorescence spectroscopies together with X-ray and neutron diffraction, are able to provide molecular level information on biological membranes. However, already since the 70's [4] there has been an interest in approaching the lipid structure in a membrane environment by means of computer simulation, which can help in the interpretation of the experimental data and in obtaining experimentally inaccessible information. However, in practice the pioneering study of applying the molecular dynamics (MD) simulation method on a lipid bilayer including explicit solvent was that by Egberts in 1988 [5,6]. Since that time, the advances in the methodology and computational resources have allowed increasing impact on the field of membrane simulations.

This thesis was started at the time when up to twenty publications on explicit lipid membrane simulations existed in the literature [7] and thus, no tradition in this field yet existed. The first goal of this thesis was to model a membrane consisting of physiologically relevant lipids, and thus to give an impact for bringing membrane simulations closer to reality. As the computational resources were relatively limited, paper I reports the preliminary results for a lipid membrane consisting of 1-palmitoyl-2-linoleoyl-3-phosphatidylcholine (PLPC) molecules, from a trajectory of 180 ps simulation. Although such a short simulation may not have yet converged, it gave the first glance at the molecular level structural characteristics of a polyunsaturated membrane. As

14

the computer resources increased during the course of this work, the simulation was continued to 1 ns to provide converged structural results. The goal of paper II was to concentrate in the origins of the experimentally observed inequivalence of single CHa and CHb bonds in some chain segments of the lipid fatty acyl chains. The importance of this phenomenon for the interpretation of the simulations was discussed. Paper III was prepared to thoroughly report on the structural features observed in the 1 ns MD simulation on a PLPC membrane and on the relation of the results obtained to the experimentally observed behavior for polyunsaturated systems. The analysis of this simulation raised an idea to more efficiently analyze the large amount of lipid conformations by applying the self-organizing map (SOM) methodology. Thus, paper IV reports the first application of SOM in the analysis of the trajectories of membrane simulations. Although SOM provides various possibilities for the analysis, the goal was to keep the approach as simple as possible and to show that the initial application of SOM will neither require any a priori knowledge of SOM, nor advanced information on the possible conformations of the lipid molecules. To move into the area of functional aspects of biomembranes, three 1-ns simulations were performed to introduce the first application of the MD simulations in the comparative analysis of the effects of lipid hydrolysis products on the membrane structure. The hydrolysis products of the phospholipase A2 (PLA2) enzyme are known to have a role in a variety of physiological processes, such as host defense and signal transduction [8]. The membrane itself acts as an important regulator of this enzyme [9,10]. The goal of paper V was to elucidate the structural changes in the membrane consisting of PLA2 hydrolysis products as compared to a neat lipid membrane, and to explore the relation of these findings to the experimental observations.

The first five chapters of this thesis will give the background for the work presented in the papers and will describe the methodology used and results obtained in the studies of this thesis. To begin with, basic information on lipid molecules and membrane systems is briefly presented, followed by a review of the methodological background with an emphasis on practical aspects of applying MD methodology to biological membranes. Subsequently, a review of the literature is presented, in which the membrane characteristics are reviewed focusing on the subjects of major importance for this thesis. There, the core of the MD simulations on lipid systems, namely the numerous studies considering the characteristics of saturated lipid species and the effects of varying headgroups or cholesterol on these membranes are first presented. Secondly, both experimental and the few simulation studies on the unsaturated model membranes are reviewed. Thirdly, the literature on the relationship between the membrane structure and activity of the PLA2 enzyme is discussed to provide background for the comparative simulations of intact and PLA2 hydrolysed membranes in this thesis. Finally, the applications of this thesis are presented.

2 Lipid molecules and membrane systems

2.1 Lipid molecules

Chemically, lipids are considered as substances that are soluble in organic solvents but little or not at all in water [11]. Lipid molecules are the main constituents of the biological membranes. They appear in numerous structural forms, of which the glycerophospholipids (or phosphoglycerides) are the most abundant lipids in eucariotic membranes.

Glycerophospholipids are named firstly after their glycerol backbone, to which two fatty acid chains are attached at positions sn-1 and sn-2, and secondly, after the phosphoric acid that is attached at position sn-3. The group attached to the phosphoric acid is called the headgroup and is most often choline, ethanolamine, serine, glycerol or inositol. The two fatty acid chains may vary in length and saturation state, but usually the chain at the sn-1 position is a saturated palmitic (16:0)1 or stearic (18:0) acid. The sn-2 chain is often 16 to 20 carbons in length and unsaturated, and e.g. oleic (18:1∆9) and linoleic (18:2 ∆9,12) acid are common. Figure 1 presents the 1-palmitoyl-2-linoleoyl-3-phosphatidylcholine (PLPC, 16:0/18:2 ∆9,12) glycerophospholipid used in the studies of this thesis. For instance, in human erythrocytes the PLPC molecule is one of the most abundant phosphatidylcholines (PCs) [12] and can be considered as biologically representative. Dimyristoylphosphatidylcholine (DMPC, 14:0/14:0) and dipalmitoyl-phosphatidylcholine (DPPC, 16:0/16:0) are common lipid species in the sense that they have served as a constituent of model membranes in numerous experimental and computational studies aiming at methodological advances and an understanding of membrane structure. These kinds of saturated lipids also occur in biological membranes, albeit as minor species.

1 Expression 16:0 defines the composition of the fatty acyl chain, giving the number of the carbon units (16) and the number of double bonds (0). The position of the double bonds can be given in superscript by, for instance, ∆9,12. There, ∆ defines the numbering of carbons to start from the carbonyl end and 9,12 identifies two double bonds from carbons 9 to 10 and 12 to 13.

16

In addition to glycerophospholipids, the main components in eucariotic cell membranes are sphingolipids and cholesterol. The most significant sphingolipid in this context is sphingomyelin (SM), a phosphate-containing sphingolipid that together with glycerophospholipids forms the group of phospholipids. The PLPC, cholesterol and SM (16:0) molecules are shown in Fig. 1.

Fig. 1. Molecular structure of the PLPC molecule (left) together with the molecular graphics of typical lipid species in biological membranes (right): PLPC, cholesterol and sphingomyelin. Color coding of the atoms is as follows: green for carbon, red for oxygen, yellow for phosphorus, blue for nitrogen, and white for hydrogen.

Lipids with long aliphatic chains present great conformational freedom. This is due to the multiple equilibrium states for each bond. For instance, each single bond may appear in three different states, trans, gauche+, and gauche-, corresponding to dihedral angle values of 180°, -60°, and 60°, respectively. The chain conformation of the PLPC molecule in Fig.1 shows bent conformation due to gauche states, whereas the chains of the SM molecule represent straight all-trans conformations.

2.2 Lipid assembly

Amphiphilic lipid molecules, which contain both hydrophilic and hydrophobic parts, have an intrinsic tendency to assemble in a water environment. The assembly results from the tendency of water molecules to exclude the hydrophobic parts of the molecules. In phospholipids, hydrophilic headgroups tend to interact with water molecules and the hydrophobic acyl chains prefer each other and hydrophobic molecular species in general as surroundings.

17

The specific form of lipid assembly is determined by the physicochemical properties of lipid molecules. The molecular shape of a lipid can induce a specific assembly: the cone-shaped lipids form inverted hexagonal structures, the cylindrical shaped ones form bilayers and the inverted cone-shaped lipids form micelles (Fig. 2). In all of these structures, the chains are hidden from the water environment. It is important to note that the effective molecular shape and the resulting polymorphic phases are affected by temperature, hydration, and counterions, among other things [2,13]. Hydrated phospholipids in the physiological temperature form mostly a bilayer structure, which is the basis for cell membranes, for example.

Fig. 2. Phospholipid assemblies: bilayer (left top), micellar (left bottom) and inverted hexagonal (right) structures.

The temperature-dependent phase behavior of phospholipids affects the properties of

membranes. At low temperatures, a pure phospholipid bilayer is in a gel (Lβ) phase, which is characterized by a high chain order, i.e. the chains tend to orient parallel to each other. Consequently, the lipids are closely packed, which results in a small surface area per lipid. In the case of PC, also a collective chain tilt with respect to the bilayer normal is observed. As the temperature rises, phase transition to a liquid-crystalline (Lα) phase occurs. The Lα phase is characterized by the decreased order of chains and increased surface area per lipid. The Lβ to Lα phase transition of the saturated DPPC (16:0,16:0), monounsaturated POPC (16:0,18:1∆9) and diunsaturated PLPC (16:0,18:2∆9,12) membranes takes place in temperatures of approximately 41.5°C [14,15], 5°C [16], and -15°C [17], respectively. As the temperature increases, the volume requirements at the chain region further increase and a transition to the inverted hexagonal phase takes place. At the physiological temperature, the most abundant phospholipid species form the Lα phase, which is considered to be the most relevant phase for biological membranes. However, biological membranes also include significant amounts of lipids that are prone to exist in a gel phase at the physiological temperature (e.g. DPPC) or in a non-bilayer phase (e.g. cone shaped lipids). The non-bilayer forming lipids are able to produce stress in the

18

bilayer plane due to their cone shaped structure and to form a so-called frustrated state [18]. This has been suggested to be important as a regulator of various functions, such as membrane fusion [19] and membrane-protein interaction [18].

The phase behavior of phospholipid membranes is strongly affected by the cholesterol, which is, together with phospholipids, a major lipid component of eucariotic membranes [20,21]. The incorporation of cholesterol broadens the cooperative phase transition from a gel to a liquid-crystalline state, i.e. the transition is not sharp but takes place over a broader temperature range. At high concentrations, cholesterol even eliminates this transition. Cholesterol is able to induce a liquid-ordered phase where the orientational order of the hydrocarbon chains is increased [22]. Mostly due to that, the surface area per phospholipid is decreased. The OH group of cholesterol has been suggested to reside at the height of ester carbonyl oxygens of PCs but not to form any tight complex with PC molecules [20,21]. Also, due to tighter packing of the hydrocarbon chains, the passive permeability across the membrane decreases in the presence of cholesterol [23]. The tight packing of PC and cholesterol molecules has been suggested to lead to the formation of stoichiometry-dependent superlattices [24]. Interestingly, cholesterol molecules have been found to favor interaction with SM as compared to PC [25]. SM is, on average, more saturated than PC. It has been suggested that this enhances hydrophobic interactions between the aliphatic chains of SM and the rings of cholesterol. Also the possibility of enhanced hydrogen bonding has been proposed [25,26].

All biological membranes include a variety of both integral and peripheral proteins, which are the main functional units of membranes. However, the lipid composition of biological membranes varies, depending on the functional properties of a membrane, and induced changes in the lipid composition are known to disturb or even damage the membrane functions [2,13]. Thus, the properties of the lipids, such as the effective molecular shape, are prone to dramatically affect the function of the membrane proteins. There is evidence suggesting the existence of two-dimensional structures such as domains and superstructures in membranes consisting of a mixture of lipids [2,27]. These structures may form due to preference of interactions or repulsion between lipid species. An example of this is the lateral segregation of lipids due to different chain length in a so-called hydrophobic mismatch [28,29]. The properties of the domains vary due to different composition, and even different phases may exist. The domains could be important in the regulation of the function of membrane proteins and also of the enzymes interacting with membranes [30]. Also, the existence of variability in the lipid lateral organisation is prone to be important in complicated bilayer systems such as the endoplasmic reticulum and Golgi apparatus, in which high local curvature of the membrane is observed.

In addition to bilayer structures, pulmonary surfactant monolayers at the water-air interface as well as lipoprotein particles are examples of biologically relevant non-bilayer lipid assemblies. Spherically shaped lipoprotein particles have a surface monolayer consisting of a mixture of phospholipids, cholesterol, and protein. The separation of hydrophobic lipids of triacylglyceride and cholesteryl ester molecules from the aqueous environment of blood plasma is stabilised by the surface monolayer. Recent reviews indicate increasing interest in the molecular structure of these transport particles [31-33]. In the case of low density lipoprotein (LDL) particles, the existence of lateral domains has also been suggested.

19

2.3 Lipid hydrolysis

During lipid hydrolysis the molecules are cleaved by specific enzymes called lipases. Fig. 3. shows the cleavage sites in a PLPC molecule for the phospholipases, i.e., the lipases that are able to hydrolyse PCs [34]. The hydrolysis products can either stay in the lipid membrane or can be released into the aqueous phase. Lipid hydrolysis is an important biological process, as the hydrolysis products are known to act as second messenger molecules that play important regulatory roles in cellular activation.

Fig. 3. The sites of phospholipase A1 (PLA1), A2, (PLA2), C (PLC), and D (PLD) cleavage on a PLPC molecule. Adapted from [34].

A common feature of lipases is interfacial activation, i.e., their preference for

aggregated substrates in contrast to monomeric substrates in the aqueous phase [34]. As they act on the lipid-water interface, they can be considered peripheral membrane proteins.

2.4 Spatial and temporal scales in lipid molecular systems

The average length of a red blood cell is 7 µm. Thus, if membranes of cellular systems need to be investigated at the molecular level of nanometers (nm) and Ångströms (Å = 0.1 nm), model membranes have to be designed, which represent only minor parts of a real biological membrane. Experimental and computational results of well-focused studies on model membranes give piecewise molecular level information on the huge real life molecular systems, such as the cell membrane. Knowledge of the relevant length and time scales is essential information for the application and interpretation of the results from various experiments and MD simulations [35].

The length of a phospholipid molecule in liquid crystalline membrane is in the order of 20 Å. The length varies depending on the acyl chain and headgroup composition but, importantly, also depending on the conformation of the molecule. Although the basic characteristics of the DPPC phospholipids in a liquid crystalline membrane have been investigated in numerous experimental studies, only recent high resolution X-ray studies have provided the accurate surface area per lipid, 62.9 Å2, the lamellar spacing, 67.2 Å, and the number of water molecules per lipid at full hydration, 29.1, in the temperature of

20

323 K [36]. Accurate experimental values are available also for DOPC (18:1/18:1) and DMPC bilayers [37,38].

The fastest motion of these molecules is the vibration of hydrogen atoms involving their bonds and bond angles, which occurs at the time scale of 0.5 femtoseconds. The vibration of other atoms happens at a scale up to a few picoseconds. This vibration is reflected in the small-scale vibration in the corresponding bond lengths, bond angles and dihedral angles. However, the dihedral angle isomerisation, i.e., the changes between the trans and gauche conformations takes place in single bonds of the acyl chains at the scale of tens of picoseconds. This movement becomes slower towards the headgroups as the membrane is tighter packed at that region.

The motion of molecular fragments is a sum of many changes in the conformational states of the covalent bonds and is often of particular interest. For instance, the motion of the headgroup with respect to the plane of the surface is quite fast, as several significant changes in the headgroup orientation may take place within a nanosecond. The movement of the whole molecule is significantly slower: the rotation of the lipid around its long molecular axis may even take a few nanoseconds. Furthermore, lipid translational diffusion, e.g. interchange of location of two lipid molecules, requires already tens of nanoseconds. At this time scale also bilayer undulations and thickness fluctuations take place. However, very short range movement of the lipid molecules both in the direction of the membrane normal (protrusion) and in-plane directions, can be observed at the nanosecond time scale. The lipid molecules may move from one leaflet to another in a bilayer, which is called the flip-flop movement. This is, however, an extremely rare process, having a typical time scale from minutes to tens of hours [12]. This is due to the demand that the polar headgroup crosses through the nonpolar hydrocarbon chain region.

Fig. 4. Approximate length and time scales in biological membranes.

3 Molecular dynamics methodology on lipid systems

3.1 Basics of the molecular dynamics method

In the classical MD method [39,40] the positions and velocities of the atoms are allowed to evolve according to the Newtonian equation of motion that can be presented for a group of N atoms as

,,...,1,),...,,( 2

2

21pot Nidtd

mE iiNi ==∇−

rrrr (1)

where Epot is the potential energy, ri the position and mi the mass of an atom. The total energy of the system is the sum of the potential and the kinetic energies. The average kinetic energy of the atoms determines the temperature of the system. The differential equations of motion are integrated using some MD algorithm according to which the particle positions or both positions and velocities are updated. The Verlet algorithm and its modifications are commonly applied [39,40]. For instance, the leap-frog Verlet uses the following relationships between the atomic positions r, velocities v, and accelerations a:

)()21()

21(

)21()()(

tttttt

tttttt

avv

vrr

δδδ

δδδ

+−=+

++=+ (2)

The force acting on each atom is determined from the gradient of the potential function, which is a function of particle positions.

In order to define the physical model of an atomic system, the interaction between all atoms has to be known or approximated, i.e., the so-called force field has to be defined. In practice, this means the determination of the potential function. The potential energy

22

function used in the biomolecular simulations to approximate the real potential energy consists of several terms, typically

vdWelbpot EEEEEE ++++= φθ , (3)

which describes the different contributors to the total interaction energy [35,41]. The energy terms related to covalent bonds are the bond energy Eb, the bond angle energy Eθ and the dihedral angle energy Eφ. The last two terms are the non-bonded interactions, namely electrostatic Eel and van der Waals EvdW interactions. The potential energy of the system could, in principle, be solved from the electronic structure of the atoms [39,40]. However, in the case of complex molecular systems this is not common at the moment. Instead, the Born-Oppenheimer approximation is applied, i.e., electronic motions are ignored and the potential energy is calculated only as a function of nuclear positions, as described here.

The bonds and angles are typically described as harmonic oscillators. Thus, the bond and bond angle energy terms are

∑ −= ,)(21 20

bb ijij rrkE (4)

and

∑ −= ,)(21 20

ijkijkkE θθθθ (5)

where rij is the distance between atoms i and j, θijk is the angle between atoms i, j, and k, r0

ij and θ 0

ijk are the equilibrium values; and kb and kθ are the force constants for bonds and angles, respectively. The dihedral angle energy is represented as a cosine expansion

( )( )( ) ,cos1 0∑ −+= φφφφ nkE (6)

where φ is the value of the dihedral angle, φ 0 the equilibrium value, kφ the force constant affecting the barrier height and n the multiplicity giving the number of minimum points in the function as the bond is rotated through 360°. The electrostatic interaction is described by the Coulombic term

,4 0

el ∑=ij

ji

rqq

Eπε

(7)

where qi and qj are the partial charges of the atoms i and j, and ε0 is the vacuum permittivity. The van der Waals interaction term describes the repulsion and the dispersion between the atoms and is often given by the Lennard-Jones formula

23

,612vdW ∑

−=

ij

ij

ij

ij

r

B

r

AE (8)

where Aij and Bij are the strength parameters for repulsion and dispersion, respectively.

Depending on the special demands of each system and study, the precise form of the potential function has countless options, as the forms or the parameters of the energy terms may be varied, and extra terms added e.g. for constraints. Beside the variation in the potential function, there are plenty of other technical issues concerning the application of the MD for lipid systems, some of which are briefly reviewed in the following section.

3.2 Overview of methodology

Practical MD methodology for biological systems is intrinsically full of trade-offs and, therefore, technical issues mostly deal with different approximations or varying levels of approximations. Some of them arise from the fact that the MD methodology is computationally heavy. Consequently, technical tricks are used to reduce the need of the computational power. The variety of approximations naturally leads to discussion about the most appropriate methodology for the specific problem under consideration. In all, tolerance for compromises is needed to design a simulation study. A variety of methodological aspects has been discussed in recent reviews [7,35,42-45].

3.2.1 Force field parameters

The force field is determined by the potential function with the specific parameter set. As the potential function formula is surveyed, it becomes evident that the determination of all the parameters is a demanding task. The parameters are based on varying experiments (therefore the force field is often called "empirical"), but also on ab initio2 calculation of different properties of the molecules under consideration. Even small biomolecules, such as lipids, are demanding for the ab initio methods. Thus, the molecules often need to be divided into functional groups for which model compounds are defined to be used in the parameterisation. The strategies on defining parameters and the resulting parameter sets for lipid molecules has been reported by various research groups [6,46-50]. In addition, it is usual that some modifications are introduced, especially the charge definition is often modified. Sometimes modifications are aimed to avoid unfavourable behaviour. For instance, scaling of charges has been applied at avoiding exaggeration of the Coulombic

2 A method of calculating atomic and molecular structure directly from the first principles of quantum mechanics, without using quantities derived from the experiment.

24

forces and to ensure the fluid phase for the lipid bilayer [6]. The multitude of parameter sets for lipid molecules has been listed by Berendsen and Tieleman [44]. The existence of multiple force fields for lipid molecules has naturally led to comparative studies testing the accuracy of the properties produced by different parameter sets in relation to other methodological aspects [51-56]. However, the number of choices is large and complete testing would thus require extraordinary effort. Therefore, the choice of parameters is still a difficult task that has to be made keeping in mind the specific purpose of the simulation and the available simulation tools.

Although the parameters are often determined on an all-atom basis, i.e. all atoms are treated separately, one way of making simulation computationally more feasible is to treat a group of atoms as one "united atom". In phospholipids, usually the methylene and methyl groups of the chains are considered as united atoms, thus avoiding the treatment of most hydrogens. In fact, some of the lipid parameter sets have been purely based on united atoms. Some criticism has been presented about their tendency to affect the packing of the acyl chains of the lipids [57] and to produce too dense a bilayer model [44].

The existence of the lipid membrane intrinsically requires the polar solvent. Various theoretical methods exist for the description of solvent effects in biomolecular systems [58], of which explicit modelling of each water molecule is commonly applied in the MD simulations of membranes. Thus, the parameterisation of water molecules has to be considered together with the lipid parameters. Several water models exist, such as single point charge (SPC) [59] and TIP3P [60]. As in the case of lipid parameters, comparative studies testing the suitability of varying water models has been performed [53,60,61].

There exist two general limitations related to parameter sets. Firstly, although it would be tempting to combine the parameters from different sets to end up with a more complete set, the mixed set may not be successful if the parameters are originally not designed to fit together. Secondly, the parameter set has often been tested to function with a certain set or sets of methodological aspects and thus, variation in methodology may require reparameterisation.

3.2.2 System size and boundary conditions

In the case of biological membranes, the size of the molecular system treatable with MD simulation is very limited, usually from tens to hundreds of lipid molecules, which corresponds to the dimensions of tens to a few hundred Ångströms. Thus, this type of simulation is, at best, able to represent a small fragment of a biological membrane. The system size defines the maximum length scale for the phenomena that can be addressed by the modelling.

In order to diminish the so-called finite size effects, i.e., abnormal behavior of the particles at the boundaries, periodic boundary conditions (PBC) are often used. The periodicity is obtained by treating the simulation cell as surrounded by its own images [39]. A particle leaving the simulation cell through one side re-enters through the opposite face. The minimum image convention is usually applied for short-range potential energy

25

[39]. Thus, the interactions of one particle are taken into account only with the surrounding particles or images of particles that lie at the maximum distance of half the cell size. Usually, a cubic or rectangular simulation cell is used in the membrane simulations. Furthermore, the bilayer is either positioned at the middle of the cell and surrounded by water on both surfaces, or two monolayers are placed at the opposite faces of the cell and separated by the water region. In both cases, the application of PBC leads to infinite multilamellar layers, which can be used in the studies aiming at detailed characteristics of both the bilayers and the water layers between them.

The treatment used in simulation A of this thesis (papers I-III) presents a method which is different from the ordinary PBC for bilayers. The primary simulation box is rectangular but does not consist of a bilayer but a monolayer. Then, in the direction of the membrane normal a combination of a reflection and a rotation is used. This implicit bilayer modeling was motivated by the limited computational resources in the early stage of this study. Although this approach appeared to be quite successful, conventional PBC have been used in our latter simulations. This "rotary-reflection" approach could be applied in the case of studies, in which, for example, properties of different headgroups or a surface peptide are investigated. There, possible effects at the acyl chain region would not be significant.

Bilayer modelling has also been performed by surrounding the lipid bilayer slab by water layers and using stochastic boundary conditions for the molecules at the edges of the system [62]. As the stochastic boundaries were considered too restrictive for the boundary molecules, harmonic potential was used for the molecules trying to escape the desired volume [57]. Exceptions from the ordinary bilayer simulations are studies of monolayers at the air/water interface (i.e., Langmuir films) [51,63,64].

3.2.3 Treatment of electrostatic interactions

Currently, in the MD methodology on biomolecules the electrostatic interactions between the atoms are taken into account by using atomic point partial charges, which are treated as fixed parameters for Coulombic interaction (equation 7). Naturally, the partial charges should vary according to the changes in the atom surroundings, for example, when changes in the molecular conformations and system configuration take place. As this polarization of molecules is currently not taken into account in MD simulations of lipid membranes, it is one aspect of methodology that is waiting for improvement. It is not a readily solvable question, as the determination of partial charges even once can be a demanding task. For water, such polarizable force fields have already been developed [65].

In principle, the electrostatic interactions should be calculated between all point charges of the molecular system as described in equation 7. The number of atoms, N, leads to a computational complexity that grows as N2. Since N is often large, various methods, such as truncation, the Ewald summation [39] and its variations, or a method based on the fast multipole algorithm (FMA) [66] are used to make the treatment of electrostatic interactions computationally feasible.

26

The principle of the truncation methods is to calculate the interactions only between the atoms that reside closer to each other than a defined cut-off distance. This treatment is called an atom-based cut-off. However, this may lead to a substantial distortion if, for instance, only one of the covalently bonded atoms of opposite charge is inside the cut-off and is accounted for the total electostatic energy. Therefore it is usual to apply group-based or residue-based cut-off [63,64] where the group of atoms or a whole molecule is taken into consideration if just one of the atoms is inside the cut-off range. This leads to an increased effective cut-off distance and to higher computational costs. Many other variations have been introduced such as a gradual cut-off with shifting functions [67], cylindrical cut-off [6] and twin-range cut-off [51]. With truncation the need of computational power can be affected by the definition of the update frequency for neighbour lists, which contain the information on which atoms have been close enough to be possibly entering the volume inside the cut-off radius. In principle, the update step can be increased unless too large changes in atomic positions occur. A failure to detect an approaching atom before it is well inside the cut-off radius causes non-conservation of energy.

Although truncation has been a very popular way of treating electrostatic interactions, it is naturally a rough approximation and has thus often been criticised. For instance, the effect of truncation on the properties of water molecules at the DMPC membrane−water interface has been studied using cut-off lengths varying from 10 to 30 Å [63,64]. Significant difference in water properties, especially in water movement, was observed between 14 Å and effective 30 Å cut-offs. Still the difference in forces between these cut-offs was only in the order of 1%. The comparison of the water properties between the 8 Å cut-off scheme and FMA method has been performed at the surface of a DLPE membrane [57]. The water polarisation was affected and caused overestimation of the membrane dipole potential upon truncation. Especially the use of truncation is warned with charged species like ions [39], although shifting of the potential is expected to reduce the artifacts. Still, truncation has been used in some bilayer simulations with ions and charged lipids [51,68-70] and in the present paper V. In our study (paper V), the actual simulation of the system with ions and charged lipid species with 13 Å shifted cut-off was compared to a simulation with 18 Å shifted cut-off. The results were similar with both cut-offs and, furthermore, the radial distribution functions of charged species were similar compared with the corresponding distributions in an MD simulation using the Ewald method [71]. Thus, the truncation approximation was considered sufficient for this particular application.

In the Ewald summation method, all electrostatic interactions are included in the infinite array of periodic replicas of the central simulation cell by using the Ewald sum. This avoids the problem of infinite-ranged interactions by summing over screened short-ranged interactions and eliminating the effect of screening by summing the canceling distributions in the reciprocal space [39]. The Ewald method as such was introduced in lipid bilayer simulations by Tu et al. [72]. The original method has been considered computationally heavy, but its modifications, such as the particle-mesh Ewald (PME) method [73,74], are more efficient. The first application of the PME method in membrane simulations was done by Essmann et al. [75]. The main criticism of the Ewald method has arisen from the fact that the Ewald method might enhance artificial periodicity [39]. Also, as the parameter sets may be sensitive to methodological aspects, the utilization of

27

the Ewald method is prone to require reparameterisation in some cases [35], as has been observed in the case of TIP3P water model [61]. Although methods based on Ewald summation are increasingly used in membrane simulations, competing opinion regards the cut-offs of 18 to 20 Å long enough to accurately reproduce the electrostatic interactions.

The FMA method [66] was introduced to MD methods by Board et al. [76], and has also been applied in lipid bilayer studies [57]. The basis for this method comes, firstly, from the idea that a single atom interacts with a distant group of atoms as it would be interacting with a single charge residing in the center of mass of the atom group. Secondly, it is based on the hierarchical "tree" treatment of particles: the atoms are assigned to cells at the finest level of the tree. At the lower level reside the extended particles presenting a group of atoms from each cell. Further, the information of these extended particles can be united to even lower level of the tree. As electrostatic interactions are considered, the treatment of the extended particles as mere point charges would lead to a loss of accuracy. This is avoided by forming multiple expansions for extended particles at lower levels. Some minor inaccuracy arises from the truncation of the multiple expansion [76]. With an appropriate number of terms in the expansion the FMA algorithm reduces the computational complexity to scale as N. However, this method has been criticised for not being usable with PBC [57,77]. While PBC are preferably used in membrane studies, the FMA method has only been employed in membrane simulation with stochastic boundaries.

3.2.4 Time step and simulation length

The time step of MD simulation affects inversely the real time needed to perform the simulation and is thus usually to be determined to be as long as possible. However, it has to be chosen to be short enough to ensure the conservation of the energy and large enough to effectively sample the phase space. In practice, time steps from one to a few femtoseconds are used. Recently, multiple time step integrators have been introduced [78], which allow the use of different time steps for the different parts of the system, depending of the time scale relevant for dynamics in these parts. This saves computational resources, since the slowly moving molecular fragments can be sampled at a lower frequency than the parts with fast changes.

The early membrane simulations lasted from tens to hundreds of picoseconds, but nowadays the simulation lengths are at the scale of nanoseconds. With an appropriate amount of lipid molecules in the simulated membrane (usually from tens of lipids to one thousand) the lipid conformations are considered to be well sampled in the time of 1 ns. At this time scale lipid protrusion is observed as well as rotational movement in the plane of the membrane. Adequate sampling for the headgroup interactions has been achieved lately in a 5 ns simulation [79]. Lipid translation in the plane of the membrane is not well sampled within the nanosecond time scale, and thus the analysis of lateral diffusion was performed only recently from the 10 ns trajectory [80]. The simulation length of 60 ns reported by Lindahl and Edholm [81] indicates that many important phenomena of

28

biological membranes that have been far out of the range of most MD simulations can be approached in the future. However, Chiu et al. [82] warn that methodological aspects need to be carefully optimised for long simulations because cumulative errors can lead to serious artefacts.

3.2.5 Ensembles

The choice of the statistical ensemble is one of the fundamental issues to consider when a simulation is planned, and it has therefore gained a lot of attention. A standard MD simulation produces the trajectory in the microcanonical ensemble, which is characterized by a constant number of particles, constant volume and energy (NVE). However, although this apprach has been used in membrane simulations, it is more common to apply temperature control, and thus to aim at producing an NVT ensemble. The requirement for constant volume in NVE and NVT ensembles is problematic in the case of various lipid species due to the lack of accurate data for the surface area per lipid molecule and the thickness of a membrane. This may lead to unnatural system dimensions. Also, inflexible boundaries can be considered unphysical, as they prohibit such large-scale phenomena that would require thickness fluctuations of the system. Therefore the constant pressure and temperature (NPT) ensemble has been considered favorable in membrane studies [35,42]. The main NPT methods for membrane simulations are the scaling algorithm of Berendsen et al. [83], which, in fact does not produce an NPT ensemble, and the Nose-Hoover method [84,85], which produces the NPT ensemble by coupling the system to an external pressure and temperature bath. In addition to flexible dimensions of the primary simulation cell, even the shape of the cell can be flexible by allowing also angles not equal to 90° between the walls [78,86,87]. It has also been questioned whether lipid-water systems are mechanically stable in constant volume simulations [88]. However, it was recently concluded from a 10-ns constant volume simulation that with a reasonable choice of box dimensions, stable trajectories are produced [80].

The first constant pressure simulations on biomembranes were performed for DPPC bilayers applying isotropic pressure [6,72,86]. However, the choice of isotropic pressure was considered questionable due to the experimental observations of surface tension γ for lipid monolayer systems at the air-water interface, and consequently simulations applying an anisotropic pressure in the NγT ensemble were performed for DPPC and DMPC bilayers [55,89]. This led to a discussion as to whether or not a non-zero surface tension should be used, and if it should, what values would be appropriate and which conditions would require its application [90-92]. Jähnig reviewed earlier studies pointing out that the surface tension is zero for unstressed membranes although for monolayers it is significant due to hydrocarbon-air interface. However, Feller and Pastor claimed that due to the absence of long wavelength undulations in a small sized simulated bilayer system, the non-zero surface tension is required to correct for finite-size effects. Tieleman and Berendsen [53]compared the application of constant pressure, surface tension and volume ensembles (NPT, NγT and NVT, respectively) in the simulations of DPPC bilayer. They

29

found little differences between the surface tension and isotropic pressure simulations, but warned about serious artifacts in the application of constant volume. Berger et al. have claimed that the constant isotropic pressure is the most appropriate macroscopic boundary condition for lipid bilayers, and optimized the Lennard-Jones parameters for DPPC hydrocarbon chains for NPT bilayer simulations to obtain the experimental density and heat of vaporization [56]. Although presently the constant-pressure ensemble is often chosen, the methodological aspects are still not clear. Firstly, discussion on the surface tension seems not to have settled [35,42,44,80,93,94]. Secondly, the different methods for constant pressure simulations may lead to surprisingly different areas per lipid molecule, as has been indicated by the recent comparison of two commonly applied methods, namely the Berendsen method [83] and Nose-Hoover method [84,85] that resulted in an approximately 10% difference in the areas per lipid [95].

3.2.6 Initial configuration and equilibration

Although the construction of the initial configuration and the subsequent equilibration can be performed in various ways, still some common outlines have evolved [44,77]. Most importantly, the construction and the equilibration of the system have to be performed with care, as the production simulation should not be affected by the initial configuration. Often the first step of the construction, the building of the phospholipid molecule itself, is performed using some of the modelling tools available. The conformation of the chains may be extended at this point, as the isomerisation of the chain bonds is known to be fast enough for equilibration to be gained in a reasonable time scale. The headgroup and glycerol backbone conformation is also more or less arbitrary in the beginning, although also the crystal structure of phospholipids has been used as the starting structure [96]. Since most often the liquid-crystalline phase is desired, the building of the bilayer system is designed to produce some disorder, i.e., the lipid molecules are variably rotated in the bilayer plane and the lipid molecules may also be shifted in the direction of the bilayer normal to produce some surface roughness. In order to minimise the length of the equilibration period of the whole system the building can be done stepwise by performing some energy minimisation and dynamic equilibration for smaller blocks of molecules and adding them together, as performed in our first simulation of the PLPC lipid bilayer (papers I-III, see chapter 5.1) and suggested by Jakobsson [77]. Usually, the subsystem of water molecules is pre-equilibrated before it is added to the system. In all, the construction of the bilayer model often resembles handwork, although also more sophisticated methods have been developed to produce varying lipid conformations for the initial construction [97]. Approaches, such as stepwise construction diminish the possibility of producing metastable states in the system, i.e., the structural characteristics of the simulated system should not be unfavourably affected by the initial conformations. Lately, the combination of Monte Carlo and MD simulation has been used in the equilibration of DOPC and POPC bilayers [98]. The challenge of the equilibration is especially enhanced in simulations of mixed lipid membranes, such as PC-cholesterol mixtures, as the time-scale of mixing exceeds

30

1 ns. The combination of Monte Carlo and MD simulations provides a possibility to handle these systems efficiently [45].

The energy of the system is usually carefully minimised during and after the construction so that there would not be any unfavourably close contacts between atoms. Thereafter, the system is heated to the simulation temperature by assigning the atoms the initial velocities. Usually the starting period of the simulation is considered as equilibration. During the equilibration, the energy in constant energy simulations and the box dimensions of constant pressure simulations should have stabilised. Also the average amount of gauche bonds, for instance, can be used to monitor the structural equilibrium of the system.

3.3 Analysis of trajectories

MD simulations produce trajectories for the atomic positions and velocities. These quantities are saved at regular intervals, usually every 25th or 50th time step. The energy components are also saved. Usually the positional information is mainly used in the analysis of MD simulations, because the MD simulations carried out so far have been able to provide information only on very short time scale dynamics of the lipid molecules. The focus of the analysis has mostly been on the structural characteristics of the lipid membrane and the water layer. Since the diffusion of water molecules is fast compared to lipids, dynamic properties have been calculated for water molecules. Recently, long enough simulations have been performed to study the dynamic properties of lipid molecules as well [80,81].

Options for the analysis are numerous and the final analysis is naturally determined by the aims of the particular study. However, structural properties that can easily be compared with the results from the experimental studies are firstly used to validate the simulation. Thereafter, new results can be considered and molecular level interpretation of experimental observations can be performed. As discussed, for example, by Tobias et al. [42] and Tieleman et al. [35], many structural parameters are provided by X-ray and neutron diffraction, and by deuterium NMR as well as IR spectroscopies. These techniques are able to provide information on the positions of the atoms along the bilayer normal (X-ray and neutron diffraction), the order parameters of the methylene and methyl groups (NMR), and the amount of gauche defects at different parts of the hydrocarbon chains (IR) [99-102]. This information can be readily calculated also from the simulation trajectories. However, the convergence of the calculated values should be checked from the simulations as, for instance, the order parameters may converge slowly depending on the position of the chain segment. Also, a proper way of calculating the order parameter should be chosen for the comparison with experimental data, especially in the case of the chain beginnings and the region of double bonds (for details, see paper II).

Other frequently determined characteristics of the lipid membrane are (i) the gauche isomerisation rate (ii) the headgroup and glycerol backbone conformations (iii) electron density distribution in the direction of the membrane normal and (iv) orientations of various vectors such as the headgroup P-N vector. The properties of the water layer at the

31

membrane surface are analysed in detail, especially when investigating the origins of the hydration force. The often-determined aspects of water include the radial distribution functions around the headgroup phosphorus and nitrogen atoms, the orientational distribution of water along the membrane normal, the diffusion of water molecules, as well as the hydrogen bonding behavior. Over the whole system, for example, the charge distribution can be calculated and doubly integrated to obtain the electrostatic potential profile across the membrane. Because the determination of this variety of properties mentioned above is often dependent on the particular system under consideration, the details of the calculations carried on for this thesis are given in chapter 5.2.

In computer simulation studies it is particularly important to obtain estimates of the statistical significance of the results. One way of estimating the statistical error of the calculated structural parameters is to calculate the standard error of mean (SEM). However, due to the correlation between the successive time steps as well as between the lipid molecules, the SEM taken from the whole data set underestimates the statistical error in membrane simulations. In these simulations, the correlation between the successive time steps dominates. Thus, a relatively realistic error estimate can be obtained by defining the time averages for each molecule as group averages, which are then used as the data for calculating the SEM.

3.3.1 Self-organising maps in analysis of lipid conformations

Simulations of lipid membranes produce a large amount of individual lipid conformations that should be efficiently analysed to gain insight into the structural and dynamic features of the system. Besides the visualisation and standard analysis discussed above, conformations in the trajectory have been analysed using clustering algorithms that firstly, assume the existence of clusters and secondly, may require advance selection of cut-offs for the cluster size or the number of clusters [103-106]. In this thesis, the analysis of lipid conformations has been approached with the aid of artificial neural networks (paper IV) that does not require such a priori knowledge.

Neural network -based analyses have been extensively used to handle complex multidimensional data in many fields of science and technology [107-110]. This methodology has been proven efficient when traditional analysis would be time-consuming or even incapable of extracting a comprehensive view [111-119]. Although no a priori knowledge of main lipid conformations is readily available from biomembrane MD simulation trajectories, self-organising map (SOM) based analysis [120,121] may be expected to provide an efficient means to handle the data.

The idea of SOM is to transform n-dimensional input vectors to the neurons in a two-dimensional array, where the input vectors sharing common features end up to the same or neighbouring neurons [120,121]. This requires no assumption of the existence of clusters nor information on the amount or size of the clusters. Also, the map is able to reflect the variations in the statistics of the data and to select good features to approximate the distribution of the data. Each neuron is associated with an n-dimensional reference vector, which provides a link between the output and input spaces. The size of

32

the map as defined by the number of neurons can be freely varied depending on the application; the more neurons are used the more details appear.

The SOM analysis includes an unsupervised learning process. Firstly, random values for the initial reference vectors are sampled from an even distribution, the limits of which are determined by the input data. During learning, the input data vector is mapped onto a particular neuron based on minimal n-dimensional distance between the input vector and the reference vectors of the neurons. The neighbours of the central activated neuron are also activated according to a network-topology-dependent neighbourhood function. For instance, the bubble neighbourhood function, which is a step function around the central activated neuron, has been considered especially suitable for SOM [122]. A common procedure is to initially use a large bubble function, which is reduced to the level of individual neurons during the learning process. The reference vectors of the activated neurons are then updated. This procedure features a local smoothing effect on the reference vectors of the neurons in the neighbourhood, leading eventually to a global ordering.

Potential application for the information obtained from SOM-based analysis of lipid conformations include selection of relevant structures for electronic structure calculations of, for example, specific interactions taking place at active sites, as well as the use of molecular assemblies of main conformations as good “pre-equilibrated” starting structures for further simulations. Moreover, the main conformations and their relative probabilities can offer a basis for the construction of minimalistic, non-atomistic models [123] that rely on the prevailing conformational states of the constituent molecules. The SOM-based conformation analysis is also directly applicable to molecular simulations of various molecular species.

4 Review of literature

4.1 Simulation studies on model membranes

The pioneering MD simulation study on lipid bilayer with explicit solvent was done by Egberts in 1988 [5,6]. Since then there has been increasing interest in performing simulations on lipid systems and a variety of lipid membranes has been studied. With the exception of a study of lysophospholipid micelle with an explicit water model reported already in 1989 [124], only lamellar structures of phospholipids have been investigated. After establishing neat lipid bilayer models, a lot of work has concentrated on combined systems of lipids and proteins, such as ion channels [125]. In this field interesting applications include, for instance, the modeling of the disk-shaped HDL lipoproteins [126,127]. Membrane simulations have been reviewed several times during the 90’s [7,35,42-45,128]. Since the number of pure lipid simulation studies is already large, only lipid membrane simulations concentrating on structural and dynamic properties of the saturated phospholipid membranes in the liquid crystalline state as well as the water layer at the membrane surface are considered here, together with the effects of different headgroups and cholesterol. In addition, other interesting applications on membrane simulations exist, including those on gel state membranes [62,75,87,94], diffusion of small molecules and ions across the membranes [129-135], the origin of the adhesion force of lipids [136], hybrid bilayers of phospholipids and alkanethiol on a gold surface [137], the distribution of anesthetic halothane in a membrane [138], and the effects of fluorination on a phospholipid bilayer [139].

4.1.1 General characteristics of saturated phospholipid membranes

The distribution of atoms along the membrane normal is often used to illustrate the overall structure of the simulated system. Such atomic distributions indicate roughness at the membrane-water interface [6,56,86,89,140-142]. Water has been observed to

34

penetrate to the height of the carbonyl groups [6,56,57,86,89,140,141] and the distributions of the phosphorus and nitrogen atoms indicate an almost parallel orientation of the headgroup with respect to the membrane plane [89,141]. These properties are consistent among different PC and PE species and are also valid at the 10-ns time scale [80]. Intercalation of acyl chains of opposite bilayer leaflets in the center of the bilayer is commonly reported [57,86,89,141].

The general structure of the DPPC bilayer has been presented in terms of the "four- region" model [142], to take into account the inhomogeneous structure in the membrane normal direction. This model is illustrated in Fig. 5.

Fig. 5. Illustration of the “four-region” model of the lipid bilayer. Adapted from [142]. The low density of the headgroups characterises the first region (1). It begins where the presence of headgroups starts to perturb the water structure and continues until the headgroup and water densities are comparable. The second region (2) has high headgroup density and lasts until the water density drops under 1% of the bulk density. The high hydrocarbon chain density characterizes the third region (3) that continues to the depth where the density of hydrocarbons equals that of liquid hexadecane. Furthermore, the middle part of the membrane represents the fourth region (4) and is characterized by the low chain density.

In relation to the “four-region” model, the free volume properties of lipid membranes

have been investigated [143]. They are of major importance for the permeation process of small penetrants. Surprisingly, although the first and second regions have very different atomic composition, the free volume properties are very similar. These regions are concluded to resemble a fluid consisting of small molecules, and are characterized by a low free volume fraction. The fraction of free volume is lowest in the second region. Such a decrease of the free volume is claimed to be a common property of hydrophobic interfaces. Furthermore, since the density is quite high, the free volume is distributed in many small spherical voids at these regions. The third region resembles a soft polymer,

35

more than a bulk alkane, due to the presence of strong interchain correlation. This results in aspherical voids preferentially oriented along the bilayer normal. In the fourth region, a large amount of free volume is observed in resemblance to a low-density fluid alkane. The free volume is distributed more isotropically than in the third region and appears in relatively large voids. Thus, even penetrants with diameters of 0.5 nm could fit locally into this region without causing an effect on the hydrocarbon chain conformations [143].

4.1.2 Hydrophilic parts of PC lipids

The average PC headgroup orientation, i.e., the orientation of the phosphorus-nitrogen vector with respect to the plane of the membrane is usually calculated from simulation trajectories, because the orientational behavior of this dipole affects the electrostatic properties of the membrane. For the PC headgroup in bilayers, inclination angles of 5° [96], 8° [144], and about 30° [6,145] towards the water region have been reported. In monolayer studies with varying parameter sets, the values of 15° and 30° were obtained [51]. These are in reasonable agreement with the experimental estimate of 18° based on NMR and laser Raman studies of DPPC [146]. However, the variability of the value may reflect the short simulation times: the movements of the headgroups are rather slow and thus, the simulation based values may not have fully converged. Despite these variations it seems safe to conclude that: the headgroups lie on the average almost parallel to the membrane surface pointing only slightly to the water phase. They also have a relatively large orientational freedom. This orientation of the headgroup dipoles has a net negative contribution to the dipole potential of the membrane.

Early experiments have demonstrated strong interactions between the phosphate group and the choline moiety of different lipid molecules [147]. In a recent 5 ns simulation of the DMPC bilayer, the PC headgroup properties were thoroughly studied to determine the type and stability of their interactions [79]. It was shown that, together with the very stable direct pairing between the PC groups, there exists also an important amount of more labile water bridges. In all, 98% of DMPC molecules are linked via the water bridges and/or choline-phosphate and/or choline-carbonyl charge pairs to form long-lived clusters. Direct PC-PC associations show high stability with the life-times ranging to several nanoseconds. They were thus not adequately sampled in earlier simulations of a few hundreds of picoseconds.

In some simulation studies, also the conformation and the properties of the glycerol backbone are commented on. Egberts et al. [6] conclude that the glycerol backbone is more rigid than the headgroup. Also, they propose the sequence tg- for θ3-θ4 to be the major stabilizing factor of the glycerol backbone. This is consistent with the finding from 1H NMR studies indicating that this sequence is the dominating conformation of the glycerol backbone [148]. It leads to a conformation where the beginning of the sn-1 chain is in the direction of the glycerol backbone, whereas the sn-2 chain starts merely parallel to the membrane surface. In simulations of DMPC membranes [149] the average inclination angle of 60° from the membrane plane has been determined for the glycerol backbone.

36

The last hydrophilic groups towards the membrane interior are the ester groups, for which a preferable orientation of the CO vector towards the water layer has been reported [145].

4.1.3 Hydrophobic parts of saturated PC lipids

In some simulation studies, the hydrocarbon chain tilt with respect to the bilayer normal has been reported to have a non-zero most probable tilt angle [96,149]. However, in liquid-crystalline state this tilt is not collective.

One of the features commonly calculated from the simulation trajectories is the orientational order parameter profile, which can also be readily obtained experimentally by measuring the quadrupolar splittings of the deuterium NMR signals. Thus, for many lipid species, a direct comparison between the simulations and experiments is possible. The characteristic properties of the profile include the dip for the beginning of the chain, the subsequent plateau and the decrease in the parameters towards the ends of the chains. The absolute values vary approximately from the 0.2 in the beginnings to 0.1 at the ends of the chains. Although both for DMPC and DPPC relatively good accordance with experiments has been reported in general [6,53-56,72,86,89,96,149-151], there have been inconsistencies in the values of the order parameters. The possible reasons for this may lie in the force field parameters, short simulation lengths, macroscopic boundary conditions, or in the application of the united atom model for the chain carbon segments [53,57,150].

Unfortunately, the order parameter profiles from the experiments of saturated PCs are determined for both chains simultaneously. Therefore many simulation studies report only the average profile to allow comparison with the experimental data. However, the difference in the behavior of the sn-1 and sn-2 chains has been reported to be evident when the orientational order of the chains has been considered separately. For instance, the order parameters are higher for the beginning of the sn-1 chain as compared to the sn-2 chain, reflecting most likely different positioning of the ester groups relative to the surface of the membrane [151].

The fraction of the gauche states is usually determined both as a function of the simulation time to ensure convergence, and as a function of the position along the chain to investigate the properties of the hydrocarbon chains. The fraction of the trans state varies between 70 and 80% [6,72,86,89,151]. The average number of gauche states per chain of 3.4 for sn-1 and 3.6 for sn-2 have been reported from a DPPC simulation [151]. This is slightly less than 3.9 and 3.8 estimated using IR or NMR spectroscopy [152,153]. However, the number of gauche states is not uniform along the chains: a larger fraction is observed at the beginning of the sn-2 chains and at the ends [51,88,149]. The isomerisation rate is also sometimes reported and, usually slower isomerisation is observed for the beginning of the chains compared to the ends of the chains [6,149,150]. Egberts et al. [6] report the average time of about 20 ps between two transitions, whereas Stouch [149] found the average time of 45 ps.

37

Since a gauche state causes bending of the chain, it has been observed that the +/- gauche state at position i is often compensated by the -/+ gauche at position i+2. The occurrence of these so called "kinks", which retain the overall cylindrical conformation of the chain, has been investigated and 0.5 to 1 kinks per chain have been reported [6,88,149]. For the random distribution of gauche states the number of kinks should be 0.26 [6]. This clearly indicates the favorable nature of this conformation, which can be understood to reduce the amount of serious defects in the chain packing due to the occurrence of bond isomerisation.

4.1.4 Lipid and membrane dynamics

Although several studies have included determination of the dynamic properties of the lipid molecules, such as the lateral and rotational diffusion, the common conclusion has been that the simulation length is insufficient to adequately sample the dynamics of these phenomena [51,86,150]. At the nanosecond time scale, the internal dynamics of the lipid molecules can be observed together with the "rattling in the cage movement" of the lipid molecules [42]. The diffusion coefficient of this localized motion for the DPPC molecules has been determined to be 2 × 10-6 cm2s-1 [86,150] while twice as large a value was found for the acyl chains and headgroups [86], in agreement with the quasi-elastic neutron scattering based estimation of 4 × 10-6 cm2s-1 [154]. However, the overall lateral diffusion of lipids is not adequately sampled, which has been shown by Tu et al. in a 1.6 ns simulation, for example. It was found that only a few of the lipid molecules were about to start to escape from their “cages” [72]. A recent 10-ns simulation trajectory has provided the possibility to investigate the dynamic properties of DPPC phospholipids [80]. The lipid dynamics was characterized by the center-of-mass movement and the displacement of individual atom groups. The calculated rotational (describing the spinning motion around the molecular long axis) and lateral diffusion coefficients, D|| = 1.6 × 108 s-1 and Dlat = 3 × 10-7 cm2/s, respectively, were found to be in good agreement with experiments. It should be noted, however, that large variations in the experimental diffusion constant exist [155].

The longest simulation of 60 ns for the large DPPC membrane patch offers information on motions at the membrane level [81]. The collective dynamics of lipids is concluded to be a combination of several processes with different length and time scales. Within the scale from individual lipids to a few of them the predominant motions are single or collective protrusions of lipid molecules. From this on undulatory and peristaltic motions dominate the dynamics. At a scale larger than the membrane thickness there appears to be correlated undulatory motions between the monolayers of the membrane. Membrane thickness fluctuations are strongest at wavelengths of 3-4 times the membrane thickness. After that their relative importance diminishes and the bilayer behaves more like a single surface.

38

4.1.5 Water structure and dynamics

Concerning the functionality of a biological membrane the water molecules hydrating the phospholipids are essential, and thus, the hydrating water has been of particular interest in simulations. In general, it has been observed that the lipids significantly influence the water out to several hydration shells, and that the water hydrating the lipids behaves differently from the bulk water [35,42]. As already mentioned, the water layer ranges to the depth of the carbonyl groups of the lipid molecules and although water molecules are known to spontaneously penetrate across the phospholipid bilayer [156], this is unlikely to happen in the present time scales of the simulations.

Usually the structure of the hydrating water around the PC headgroup dipole has been characterized by the radial distribution of the water molecules around the phosphorus and nitrogen atoms. These studies have indicated that a clear preference is observed for the water hydrogens to orient towards the phosphorus due to hydrogen bonding to the phosphoryl oxygens. In contrast, around choline, the water molecules form a clathrate-like structure due to the hydrophobic nature of the choline methyl groups [63,75,145,157,158]. The polarization profile of the water molecules in the membrane normal direction has revealed that the water dipoles at the membrane surface preferably orient towards the membrane interior [57,61,63,89,141,145].

Some lipid membrane simulations have been specifically designed to investigate the origin of the hydration force between PC bilayers [75,140]. The hydration force acts repulsively between the opposing membrane surfaces and becomes dominant at small separation (under about 10 solvent molecular diameters). The force has been named after the suggestion that it rises from the ordering of the water layer between the surfaces. The simulation studies, however, emphasize the possible role of the surface roughness i.e. the protrusion of individual lipid molecules towards the opposing surface. The roughness results in a smoothly decaying polarization profile of water [140]. Marrink et al. point out that due to this smooth decay the hydration force will also exhibit similar decay, and therefore it originates from the ordering of the water molecules at the rough membrane interface [140]. Other findings are, firstly, the layer of water molecules with strong hydrogen bonds around the headgroups and secondly, the possibility of occasional direct contacts between the headgroups of opposing surfaces [75]. In all, Essmann et al. conclude the hydration force to be most likely due to the spatially very thin water layer between the rough membrane surfaces: the repulsion may arise both from the direct close contact between the headgroups of the protruding lipids and from the contact of ordered water shells bound to the headgroups [75]. Also a novel proposal exists for the origin of hydration force, namely the finite size of absorbed hydrated counterions [159]. So far, the possible role of ions has not been probed by MD simulations.

Since the water diffusion is fast compared to the movement of lipid molecules, it can be well sampled already within a few hundreds of picoseconds. Diffusion constants of 2.6, 2.7, 4.4, and 8.8 × 10-5 cm2/s have been reported for bulk water using the SPC/E water model [53,89,141,145]. For comparison, the self-diffusion coefficient of water is 2.5 × 10-5 cm2/s [89]. Simulations have revealed the more restricted motion of water molecules towards the membrane interior [53,63,89,141,145,157], which has been suggested to be due to several factors, including density and mobility of the surrounding

39

lipid material as well as the more ordered structure of the water molecules at the surface region [89].

4.1.6 Electrostatics

The electrostatic properties of the membrane are often characterized by the electrostatic potential, i.e., the dipole potential across the membrane, which is obtained by the double integration of the charge density in the direction of the membrane normal [53,56,75,80,89,140,144,145]. Except for the early simulation of the DPPC/water interface [140], all studies produce negative electrostatic potential for the water region with respect to the membrane interior [53,56,61,75,80,89,144,145], which is in accordance with measurements. In simulation studies, the contributions from the lipids and the water can be considered separately; a positive potential of about 1-5 V arises due to the lipids and a negative potential with a slightly larger absolute value due to the water. In all, the water overcompensates the potential caused by the lipids and a total potential from -100 to -2300 mV is obtained in simulations. The experimental values for the potential range from -200 mV to -575 mV for different PC/water interfaces [160-162]. The wide range of the experimental values most likely reflects the difficulty of the measurements [163]. The electrostatic potential seems also to be very sensitive to simulation parameters and conditions [42,53,56]. This is reflected also in the fact that in some simulations a positive barrier in the potential profile is observed at the headgroup region [53,56,89], while others do not show this behavior [53,56,75,80]. As the headgroups have been found to fluctuate strongly, this has been suspected to lead to the fluctuations of the dipole potential. However, as a response to the headgroup fluctuations, the water molecules reorient themselves and actually compensate for the fluctuating field. Overall, the dipole potential is stable; it does not vary remarkably at a 10-ns time scale [80].

In addition to the potential across the PC water interface, the electrostatics in the plane of the surface may be of importance, as the variation in this respect may considerably affect the interaction of the surface with the enzymes [149], for example.

4.1.7 Effects of different headgroups

In addition to choline, the other phospholipids used in MD simulations of biological membranes are ethanolamine [57,141,157,164] and serine [68,69]. The former has been extensively studied using experimental techniques.

Radial distribution functions calculated from the simulations of DLPE systems reveal that the solvent order around the ethanolamine group differs remarkably from that formed with choline; clathrate is not observed in the former case, as the water oxygens orient towards nitrogen due to hydrogen bonding [57,141]. The average tilt of the PE headgroup is reported to be 20° with respect to the membrane plane [57], i.e., approximately similar

40

to that of PC. Comparison of the velocity autocorrelation functions indicates frequent collisions due to formation and rupturing of the hydrogen bonds in the case of PE, whereas in the case of PC, these motions are not observed. Also, the headgroup-headgroup and headgroup-solvent interactions have been found to be stronger for PE, leading to a more restricted motion than in the case of PC [141]. The orientational order parameters were reported to be higher than the experimentally observed ones for the DPPC [57,141]. The water molecules penetrate until the depth of the carbonyl oxygens [57,141], as was also concluded for PC. Due to the smaller area per lipid, the penetration is less extensive in the case of DLPE than in DMPC [141]. Similarly to the case of PC, the bound waters are moving more slowly than the bulk waters. The only difference seen in the orientational polarization profile of water is a reduction of the polarization at the DLPE/water interface in comparison to the PC system [57,141]. The membrane dipole potential profile of DLPE bilayer shows a negative potential for the water region with respect to the lipid interior, the value for the potential being -600 mV [57]. This value falls into the range observed for PC systems.

Due to the net negative charge of the PS group, important differences are observed in the simulated DPPS system in comparison to the PC systems, especially at the interfacial region [68,69]. Under the constant pressure simulation conditions, a 10% smaller area per lipid was found as compared to DPPC. The radial distribution functions show the tendency of the serine ammonium group to be hydrogen bonded to the serine carbonyl oxygens of the neighboring lipids, which is suggested to be the possible origin for the reduced surface area [69]. The atomic distribution of the serine atoms are narrower than in the case of choline, indicating a more constrained structure of the PS region than for PC that can explain the observation that the phosphate groups appear to be less hydrated in PS than in PC [69] and that the coordination number of water about lipids is notably reduced in DPPS system [68]. Due to the constrained nature of the PS headgroup region, the DPPS bilayer more closely resembles the model of a charged condenser with a diffuse double layer [69]. The order parameters of the first carbons in the hydrocarbon chains are reported to be significantly lower than in DPPC due to the hydrogen bonding between the carbonyl oxygen of the chain beginning and the serine ammonium. This interaction may pull the chain beginnings to a more parallel orientation with the membrane plane and thus cause the decreased order parameters. However, the hydrocarbon interior seems to remain unaffected [69]. As in the cases of PC and PE, diffusion of the bound water molecules is slower compared to the bulk water. In all, only minor changes in the water properties are observed due to charged headgroups, as the presence of the counterions and charge interactions between adjacent phospholipids reduces the strength of the lipid-water interactions. However, contrary to the PC bilayers, the total electrostatic potential across the membrane was determined to be positive (about 2.5 V): the lipids and the Na+ counterions produce a potential of 6 V, which is only partially compensated by the water dipole orientation [68].

41

4.1.8 Effects of cholesterol

Cholesterol is a constituent of all biological membranes. Consequently, its effects on the membrane are of major importance, and they have been extensively studied using varying experimental techniques [20,21]. Cholesterol has therefore also been increasingly incorporated in MD simulations of model membranes [144,158,165-167]. Additionally, the effects of cholesterol sulfate [168] have been studied.

The headgroup behavior is reported to be affected by the incorporation of the cholesterol molecules, but contradictory effects of the increased tendency of the headgroups to point either towards the membrane interior [144,166] or water region [167] have been reported. The magnitude of the electrostatic potential between the water and the bilayer interior has been concluded to increase due to the incorporation of cholesterol [166,167], which is in accordance with the experimental findings [169]. However, the opposite was observed in an earlier simulation study [144].

Cholesterol has been concluded to cause an increase in the fraction of trans dihedrals and order parameters of the lipid chains [165,167], in accordance with the experimental data [21]. Also in the simulations of Gabdoulline et al., decrease in gauche states was observed in the presence of cholesterol at high concentrations [144], whereas the simulations of Tu et al. do not show a notable difference in this respect [166]. However, Tu et al. report a significant decrease in the “rattling in the cage” motion in the DPPC neighbouring a cholesterol molecule. As the occurrence of gauche states has been related to the enhanced diffusion of small molecules through a membrane, the increased prevalence of trans states especially in the upper half of the chain (where the solute molecule would enter the membrane) would act as a barrier for diffusion through the membrane [165]. Indeed, decreased diffusion rate has been experimentally observed in model membranes due to the presence of cholesterol [156]. The cholesterol molecules tend to tilt with respect to the membrane normal to match the hydrophobic thickness with the hydrocarbon chains. This tilt was observed to be dependent on the concentration of the cholesterol: with high concentration the amount of cholesterol is enough to order the hydrocarbon chains and requires a smaller tilt angle for the cholesterol molecules, whereas with the lower concentration, the disorder of chains is high and effective thickness smaller, which enhances the tilt of cholesterol molecules [167].

Cholesterol is seen to hydrogen bond to the oxygens of the phosphate and carbonyl groups together with the water molecules [165,166]. Pasenkiewicz-Gierula et al. have performed a detailed analysis of the linking of the cholesterol with DMPC molecules [158]. They conclude that 70% of the cholesterol molecules is linked via short-distance interactions, where either the hydroxyl oxygen atom of the cholesterol molecule is charge paired to the choline moiety, or the hydroxyl group is hydrogen bonded or water bridged to the carbonyl and nonester-phosphate oxygen atoms of the DMPC molecule.

If cholesterol is replaced with cholesterol sulfate [168], a lipid that naturally occurs in some biological membranes, a weaker ordering or the hydrocarbon chains is observed than with cholesterol. Particularly, the sulfate significantly alters the properties of the interfacial region, as the membrane potential reverses its sign and the hydrogen bonding to the DPPC molecules occurs to lesser extent.

42

4.2 Unsaturated membranes

The existence of double bonds in the specific positions of the acyl chains of phospholipids is known to be essential for the properties and the functionality of biological membranes. The degree of unsaturation has been reported to be an important factor for (i) the activity of the protein kinase C enzyme [170], (ii) the conformational equilibrium of a membrane receptor [171], (iii) the properties of tumor cells [172,173], and (iv) the shape of the human erythrocyte [12], to mention but a few. Cells carefully control chain unsaturation to maintain optimal conditions for the cell functions [174]. Many experimental techniques, such as fluorescence, Raman, electron spin resonance and NMR spectroscopies together with X-ray and neutron diffraction can be used to probe the effects of unsaturation at the molecular level [3]. Computational studies are able to give precise molecular level information, and thus they also have been used, although relatively rarely. Here, the MD simulation studies related to the effects of unsaturation are reviewed together with experimental investigations. Although also the trans configuration of the double bond is of some interest, only the effects of the cis double bonds will be considered.

The effects of acyl chain unsaturation are strongly dependent on whether PC or PE systems are considered [175,176]. As the ethanolamine headgroup has a small area requirement relative to the unsaturated chains, the unsaturated PE bilayers are under a curvature-associated lateral press and are therefore predisposed to adopt an inverted hexagonal phase. The importance of this phenomenon has been widely recognized. However, as in this thesis the PC unsaturation has been considered, the review here focuses on PC lipids.

In the early study of Demel et al. [23], the force-area characteristics of unsaturated PC monolayers were determined. The area per molecule was observed to increase stepwise with the number of the double bonds, the most significant increase occuring upon the introduction of the first double bond. This first double bond induces bending of the chain that is difficult to compensate by the isomerisation of single bonds. Thus, the packing of the chains is heavily affected. In the case of 1-palmitoyl-2-acyl PC, the incorporation of the first and third cis double bonds to the 18-carbon sn-2 chain induced the largest increase in the molecular area, whereas for the 22-carbon chains the largest increase is found upon addition of the first and second double bonds [177]. The area requirements due to unsaturation increase the tendency to form inverted hexagonal structures.

The membranes constructed from unsaturated phospholipids have generally a lower gel-to-liquid-crystalline phase transition temperature than their saturated counterparts [178-180]. However, the transition temperature does not decrease monotonically with increasing unsaturation. In the sn-1-stearoyl-2-acyl PC species with the 18:1∆9, 18:2∆9,12 and 18:3∆9,12,15 chains in the sn-2 position the transition temperature is about -1, -15 and -12°C, respectively. Also the chain length has an effect, e.g., the incorporation of 20:2∆11,14 chain into the sn-2 position of sn-1-stearoyl-2-acyl PC results in the transition temperature of -5°C [179]. Stubbs and Smith [178] have concluded that the transition temperature is affected maximally upon the incorporation of the double bonds near the middle of the fatty acid chain. The double bonds have progressively less effect when they are towards the carbonyl or methyl end of the chains. In accordance with this suggestion,

43

the NMR 13C spin-lattice relaxation rate is enhanced in unsaturated chains, particularly when the double bond is located in the middle of the chain [181].

2H NMR has been widely used to investigate the orientational order of both saturated and unsaturated hydrocarbon chains. The early studies were performed using specifically deuterated lipids, which offer the possibility to obtain the order parameters separately for each carbon segment [182]. Later, it has been more common to use perdeuterated lipids, i.e., all carbon segments of the chain have been deuterated simultaneously leading to the determination of the whole order parameter profile at once [183]. While this reduces the amount of measurements significantly, it raises a question of whether the order parameter profile fully shows the details of the order behavior. The order parameter profiles of perdeuterated lipids show the general trend of the decreasing order of the saturated sn-1 chain due to unsaturation in the sn-2 chain, if the comparison is performed at the same absolute temperature [180,184]. This was already concluded in the early study where saturated DPPC and monounsaturated POPC lipids were compared [185]. In conclusion, the transition temperature and the order parameters are generally smaller in unsaturated membranes than in their saturated counterparts, but there is necessarily no simple correlation between these quantities and the content of the double bonds [178].

Both in natural and artificial membranes, increasing unsaturation is linked to increased permeability [186]. Upon stepwise unsaturation, the permeability of the monolayer to small molecules increases, as does the area per molecule [23]. Furthermore, permeability of water in varying phospholipid black films increases with unsaturation [156].

4.2.1 Monounsaturated PC membranes

Recently, an area per lipid of 72.2 ± 1.1 Å2 for the DOPC bilayer with full hydration has been reported [38]. The earlier study with low hydration reports an area of 59.4 Å2, which points out the importance of hydration for the structural quantities [187].

In MD simulation studies focusing on monounsaturation, the oleic acid (18:1∆9) has been used either in the sn-2 position of POPC [62,98], or in both sn-1 and sn-2 positions of DOPC and DOPE [98,188]. The order parameter profiles for the oleoyl chains in each case show very different behavior as compared to the saturated chains. The most striking feature is the dip of the order parameter profile at the position C10, previously observed by deuterium NMR [185]. This dip has been suggested to derive from the distinct geometry of the cis double bond.

As mentioned above, at equal temperature, the order parameters of the sn-1 chains in the POPC bilayer are smaller than in the DPPC bilayer. However, if the comparison is performed at the same relative temperatures with respect to transition temperature, the opposite is found, i.e., the unsaturated system has more ordered saturated chains, especially around the carbon C6 [185]. An increase of deuterium order parameters at equal reduced temperatures has also been observed for perdeuterated palmitoyl chains, when the sn-2 chain of DPPC is replaced with its monounsaturated counterpart (16:1) [189]. This effect can also be seen from the order profiles at the absolute temperature as only a slight decrease takes place until the carbon C8. Thereafter, the decrease is more

44

apparent [180]. This has been interpreted as a local stiffening effect caused by the incorporation of the cis double bond. The double bond is a rigid unit having restricted rotational freedom, which reduces the number of the rotational isomeric states for the adjacent saturated chains [185]. The local effect of the double bonds on adjacent lipids has also been observed in the conformation and dynamics of conjugated pyrenes residing at the depth of the DOPC double bonds, as measured using steady-state and time-resolved fluorescence spectroscopy [190]. Although the double bond region in the sn-2 chains of POPC is well reproduced by simulation studies, the correspondence between experiments and the simulations is not as good for the saturated sn-1 chains of the POPC bilayers.

Both the X-ray and neutron diffraction data for the DOPC system and the simulation of POPC bilayers show that the double bond distribution in the direction of the bilayer normal overlaps both at the center of the bilayer and with the water distribution [62,191,192]. This overlap has been suggested to be hydration-dependent in the sense that the volume explored by the double bonds increases with hydration [192]. Such distribution of double bonds has been suggested to enhance the permeability of water by providing a “ferry” mechanism for water molecules [191].

Experiments and the simulation agree in the case of the average tilt of the P-N vector, as the values of 22° and 21° are presented, respectively [62,191]. The comparison of these values with the ones reported for saturated systems (see chapter 4.1.2) suggests no difference in the headgroup characteristics due to unsaturation. The conformations of the beginnings of the sn-1 and sn-2 chains are observed to be inequivalent also in unsaturated chains. The observed smaller order parameters of the sn-2 chain beginnings have been suggested to result from the bent conformation [185,191].

4.2.2 Polyunsaturated PC membranes

Although numerous experimental studies on polyunsaturated lipids have been published, the detailed structural and dynamic characteristics of the simplest polyunsaturated lipid having two cis double bonds in the fatty acyl chain have rarely been considered. The most detailed information is provided by 2H NMR measurements of the 1-palmitoyl-2-isolinoleoyl-sn-glycero-3-phosphocholine (PiLPC, 16:0/18:2∆6,9) containing specifically deuterated sn-2 chain [17,193-195]. Unfortunately, the deuteration of the sn-1 chain was not performed in these studies and thus, information on the saturated palmitoyl chain of the PiLPC molecules is not available. It was observed that both the motional freedom and the average structure are affected by the double bonds. As in the case of the monounsaturated chain, a strong decrease in the order parameter values was observed in the middle of the chain. In this case, however, a double-dip was seen at positions C8 and C10. The order parameters for most of the carbons of the isolinoleoyl chain decreased with increasing temperature. The parameters of the deuterons at the positions C8 and C9 increased, however, suggesting a change in the average orientation due to thermalisation [17]. Interestingly, separate order parameters could be determined for the deuterons attached to the carbon segment between the double bonds. This indicates a magnetic inequivalence of the deuterons [194]. During the synthesis of PiLPC, also some PLPC

45

(16:0/18:2∆9,12) specifically deuterated at C6 had been formed and thus also its SCD value could be measured.

Based on quadrupolar splitting and relaxation time measurements, Baenziger et al. proposed a motional model for the double bond region of PiLPC. In this model, the double bond region adapts to main conformations, between which jump movement occurs due to the isomerisation of the C7-C8 and C8-C9 bonds. The conformations are characterized by almost parallel orientation of the double bonds that tilt away from the bilayer normal. However, the model does not achieve an exact fit with the experimental data. The correlation time for the jump movement at 30°C is estimated to be 1.1×10-10 s, i.e., it is significantly slower than the normal trans-gauche isomerisation of the single bonds having correlation times to the order of 10-11 - 10-12. Baenziger et al. hypothesise further that in the case of highly unsaturated lipids this kind of motion with relatively large amplitude is most likely not possible. Instead, polyunsaturation could lead to highly ordered structures [17,195], like the “angle iron” or helical conformations proposed by the packing studies of Applegate and Glomset [196,197].

The effects of the polyunsaturation on adjacent saturated chains have usually been probed by perdeuterated saturated chains. The incorporation of three or more double bonds to the sn-2 chain decreases the order of the saturated sn-1 chains as compared with the incorporation of mono and diunsaturation at equal temperatures. However, only a small decrease is seen. Among polyunsaturated sn-2 chains, the decrease of the order in saturated sn-1 chains is no longer uniform, but depends on the position of the double bonds [180]. Comparison of the mono and diunsaturated systems at the same reduced temperatures shows increased order in the saturated sn-1 chains due to increased unsaturation in the adjacent sn-2 chains (see above), but the increase is not always uniform upon increasing unsaturation. The 22:6 chains induce slightly less order than 16:1 chains on the adjacent 16:0 chains [189]. The ordering effect at reduced temperatures has also been observed in the case of 16:0/22:6 PC, whereas the opposite was found at the same temperatures [198]. The effect of the double bond position is well demonstrated in the study of McCabe et al. [199], indicating that the ordering effect at the reduced temperature is less pronounced when the three double bonds are shifted from positions 6,9,12 to positions 9,12,15. In other words, the double bonds located in the middle of the sn-2 chain have the strongest ordering effect on the adjacent saturated sn-1 chains.

The order of the polyunsaturated chains themselves has not been addressed for some reason, and only some data are available for 22:4 arachidonic acid in the sn-2 position of 1-palmitoyl-2-acyl PC. Rajamoorthi and Brown measured smaller quadrupole splittings for the 22:4 chain in comparison to its saturated and monounsaturated counterparts. This was suggested to reflect geometrical factors or statistical fluctuations. They also found, in accordance with the suggestion of Baenziger et al. [17,195], larger relaxation rates in the chain segments, which may indicate hindered rotations of the chain due to double bonded segments [200]. Increased relaxation rates were also found for chains with three double bonds supporting the idea of hindered rotations [181].

The packing characteristics of polyunsaturated lipids has been studied by Litman et al. [201] and a packing model has been proposed [202]. The combination of saturated and polyenoic chains in the same phospholipid molecule would induce a specific type of

46

arrangement, in which the interaction of the saturated chains is maximized by the packing of the polyenoic chains together.

Although cholesterol has a pronounced effect on many lipid membranes, these effects are diminished in the case of dipolyunsaturated PCs, i.e., lipids with polyunsaturation in both chains [203]. Such lipids are suggested to potentially promote lateral domains in the presence of cholesterol, i.e. to induce cholesterol-rich and cholesterol-poor environments. An acyl chain unsaturation dependent effect of cholesterol has been observed also by Smaby et al. They found, using Langmuir films at membrane-mimicking surface pressures, that the in-plane elasticity moduli of PC species with higher sn-2 unsaturation levels was affected to a lesser extent by cholesterol than in more saturated PCs [204].

4.3 The relationship between membrane structure and PLA2 function

Mammalian PLA2 enzymes can be classified into three large groups, namely, secretory, cytosolic, and Ca2+-independent enzymes [8]. The function of PLA2 is to liberate a free fatty acid and a lysophospholipid (Fig. 3). PLA2 is known to preferably hydrolyze lipids at the lipid-water interface [34]. Because of the central role of PLA2 enzymes in mammalian physiology, a number of studies have focused on the mechanisms of their action. Particularly, the secretory type II PLA2 has been studied extensively. The results have revealed that in addition to the properties of the interfacial binding surface of the enzyme [205], the characteristics of the membrane itself regulate the activity of the enzyme (reviewed by Burack et al. [10,206]). The positively charged type II PLA2 is known to interact preferentially with negatively charged membrane surfaces [207-210]. In addition, various surface defects or perturbations caused by, for example, lipid peroxidation [211], a phase transition of the substrate [212-214], osmotic stress [215], incorporation of diacylglycerol [213] or lysophospholipids [216], or even by pressure from the tip of an atomic force microscope [217] are known to activate PLA2. In addition to its physiological impact, the PLA2-membrane complex is of interest as a biophysical model system for studies on protein-membrane interactions [206,214] .

Control of the action of water-soluble phospholipases on membranes is an important regulatory mechanism for preventing the degradation of intact biomembranes [218]. Zwitterionic PC molecules, the main lipid constituents of biomembranes, are poor substrates to PLA2 in an intact membrane, which typically results in a lag period of low PLA2 activity. After this initial lag period, a sudden increase can occur in the enzyme activity [206]. Much evidence suggests that this abrupt increase in PLA2 activity is due to the accumulation of hydrolysis products, i.e., fatty acid and lysoPC molecules [213,219-224]. This can lead to the formation of microenvironments enriched in lysoPC and fatty acid molecules. This may cause a new temporary decrease in activity but can also result in increased interaction between the PLA2 enzyme molecules and the negatively charged surfaces of the resultant microenvironments. As this enhanced interaction has been achieved, in time, the lipid and/or protein diffusion leads to the contact of the enzyme with unhydrolyzed lipids and may thus result to a new rapid action of PLA2.

47

The possible effects of the accumulation of hydrolysis products are now discussed together with MD simulation studies concerning the PLA2 action. Recent work [10] has indicated that the lateral segregation of the reaction products of PLA2 activity in large unilamellar vesicles is associated with global structural rearrangements (e.g., formation of disk-shaped edges). The authors concluded that the structures formed during hydrolysis are likely to be heterogeneous and include morphological intermediates that may be important determinants of PLA2 activity. The mechanism by which compositional phase separation affects PLA2 activity may be nonspecific: separation may be only one of the many ways in which structural perturbations are induced in the membrane. It has also been shown that the effects of membrane structure on the catalytic rate of PLA2 are exerted not merely by enhanced association of the enzyme with the membrane surface, but a membrane-bound inactive enzyme has been identified spectroscopically [206].

The changes in the membrane properties upon PLA2 action have been explored using the fluorescent probe Prodan [222], which is sensitive to the polarity of its immediate environment in the headgroup region. This study suggested an increased ingress of water molecules to the vicinity of Prodan, or the movement of Prodan molecules to a more polar environment. Either possibility suggests some disruption of the membrane structure, affecting the properties of the membrane at the headgroup region. On the other hand, the use of the bis-pyrene fluorescence that senses the motional freedom in the hydrophobic core region of the bilayer, indicates no change during or after the lag period of PLA2 activity. Thus, the increase in the enzyme activity seems not to require changes in the order of phospholipid acyl chains deep in the membrane.

The effects of hydrolysis products have been probed in several studies. Interestingly, the unionized fatty acids have been found to descend toward the hydrophobic region as indicated by fluorecent fatty acids [225]. This has been suggested to enhance the separation of the headgroups, which would allow easier access for the PLA2 active site to the sn-2 bond of the phospholipids [224]. Interestingly, also the addition of the lysoPC has been observed to enhance the availability of the substrate to the active site of the enzyme [222,224].

The three-dimensional structure has been determined by X-ray crystallography for porcine and bovine pancreatic PLA2 [226], as well as for human synovial PLA2 [209], for example. Although these structural data are readily usable in the MD simulation studies, the PLA2 function has rarely been studied using the MD methodology. The first PLA2-related work utilizing MD simulation was the preliminary study of the PLA2-membrane complex [227]. The PLA2 molecule was simulated for 155 ps at the surface of didecanoylPC monolayer, but apparently the equilibration was too short to draw any conclusions. The MD methodology was also used in the study aiming at the prediction of the structure of the enzyme-substrate complex [228]. The substrate molecule (didecanoylPC) was found to be in very similar conformation to that seen in the crystal in the end of the short simulation of 48 ps. The MD simulation study of Zhou and Schulten [229] approached the PLA2-membrane complex by investigating the enzyme molecule at the surface of DLPE monolayer. They simulated both loose and tighter contact between the enzyme and the surface, and found out that the desolvation of lipids in the tighter complex promoted an enhanced interaction. They also suggested that the changes in the membrane properties would be more important in the regulation of PLA2-membrane interactions than the conformational changes in the enzyme itself.

5 Applications

5.1 Modelling and simulations

The molecules used in the four membrane simulations (referred as A, B, C, and D) are shown in Fig. 6 together with the membranes constructed. Information on the simulations has been summarized in Table 1. The PLPC molecule was used in the first two simulations. In the bilayer system for simulation C, as the PLA2 enzyme is known to catalyze the hydrolysis of the sn-2 fatty acid bond, the bilayer consisted of lysophosphatidylcholine (1-palmitoyl PC, PPC) molecules and free negatively charged linoleate chains (L

-). In simulation D, the free sn-2 chains were protonated and appeared

thus as uncharged linoleic acid (LH) molecules. At the physiological pH of 7.4, both charged L

- and uncharged LH molecules are expected to appear in nearly equivalent

amounts [230]. Table 1. Summary of simulations showing the number of lipid and water molecules, ions, and atoms together with the dimensions of the primary simulation box, the type of bilayer modelling, the length and temperature of simulations, as well as the number of the original paper, in which the analysis is presented.

Simulation A B C D

Lipids 36 PLPC 72 PLPC 72 PPC + 72 L- 72 PPC + 72 LH

Water + ions 1368 H2O 2572 H2O 2500 H2O + 72 Na+ 2572 H2O

Atoms 8856 17229 17220 17436

Dimensions: x×y×z (Å) 50.4×36.75×50.4 50.4×71.0×50.4 50.4×71.0×50.4 50.4×71.0×50.4

Bilayer modelling rotary-reflection explicit explicit explicit

Length: eq + final (ns) 0.2 + 1.0 1.25 + 1.0 1.259 + 1.0 0.195 + 1.0

Temperature (K) 321 310 310 314

Analysis I, II, III, IV V V V

49

50

Fig. 6. Lipid molecules used in simulations A, B, C, and D. A single PLPC molecule (simulations A & B), together with the hydrolysis products PPC (simulations C and D), charged L- (simulation C), and uncharged LH (simulation D). The numbering of the bonds in PLPC is shown for the SOM analysis. In addition, snapshots from the ends of simulations A, B, and C are presented with the colour coding as presented in the pictures of the single molecules. The spheres in light grey are Na+ ions. No snapshot from simulation D is shown as its appearance closely resembles the snapshot of simulation B. The hydrogen atoms are omitted for clarity, except for the hydrogens of the water molecules of simulation A.

The PLPC was built up for simulation A with the two double bonds in cis and the other chain bonds in trans configuration after which the energy was minimized. The layer construction was started by placing four identical PLPC molecules into a square-like configuration with the headgroups pointing up along the y axis that was chosen as the membrane normal. Each PLPC was given a different orientation in the x-z plane to avoid a collective tilt and to ensure the formation of a liquid crystalline phase. A surface area of 8.4×8.4 Å2 per a PLPC molecule was used based on X-ray scattering experiments for membranes with various PC species [231]. The block of four PLPC molecules was stabilized by an energy minimization and a dynamic heating-annealing cycle using PBC in the x-z plane. Such blocks were added together to form a 4×4 grid, which was stabilized in the above manner. Finally, five more blocks were added and the energy was minimized. This resulted in a monolayer of 36 PLPC molecules in a grid with an area of 50.4×50.4 Å2. The monolayer was solvated by placing an equilibrated water box of 50.4×22.0×50.4 Å3 (density ≈ 1 kg/dm3) so that it overlapped the headgroup region. This ensured that the void volume between the headgroups was filled with water. The water molecules overlapping the PLPC molecules were then removed.

The 36-molecule piece of monolayer was used to model an infinite bilayer in simulation A by applying suitable symmetry operations and PBC. First, the bilayer was modeled with a 180° rotation about an axis parallel to the x axis and a further 90° rotation about the y axis, resulting in a rotary-reflection operation. The position of the first rotation axis was chosen to result in a phosphorus-to-phosphorus distance of 37 Å, which was estimated from experiments [231]. Second, conventional PBC were used in the x-z plane to model an infinite bilayer. The final energy minimization was done by first stabilizing the water molecules and then the whole system. Thereafter, to reach the temperature of 310 K, a 10 ps dynamic heating period was performed, followed by an equilibration period of 200 ps. Velocities were scaled once at t = 33 ps from the start of the equilibration, because of a drift in the temperature. It should be noted that in the early stage of this study, only the first 150 ps were considered as the equilibration period and the following 180 ps were treated as the simulation period to report some preliminary results (paper I). However, in papers II, III, IV, the full analysis was performed for the 1 ns simulation period (refered as simulation A in Table 1), which followed the total equilibration period of 200 ps.

The explicit PLPC bilayer model of simulation B was based on the final structure of simulation A. To model the bilayer explicitly, the monolayer system was copied and placed similarly to the way the image of the monolayer had been in the implicit bilayer model. Additionally, a 1.25 Å slice from both water layers was removed. Conventional PBC were employed in all directions to model an infinite bilayer. The system was

51

stabilized by energy minimization. Dynamic heating was then applied for a 10-ps period, resulting in a temperature of 310 K, followed by a 150-ps equilibration period and a simulation of 1 ns. This simulation was, however, affected by a typing mistake in the parameter file that restricted the rotation of the single bonds between the double bonds. Thus, this simulation was not used for the analysis; instead, its final structure was taken as the starting point for the actual simulation with corrected parameters. Again, an energy minimization, a 10-ps heating period, and a 100-ps equilibration period were employed. Finally, simulation B was run for 1 ns to collect the data for the analysis. The temperature and the energies were monitored during the simulation to ensure their stability and an adequate equilibration time.

For simulation C, the construction of the modified bilayer with PPC and charged L-

molecules was based on the well-equilibrated structure from simulation B. First, the bond between the glycerol backbone carbon Cg2 and the corresponding oxygen was broken and an OH group was added to Cg2, to form L

- and PPC molecules. To remove extensive

overlap of atoms in the modified region near the Cg2 carbon, the energy was minimized at this stage. In order to end up with an uncharged system, 72 water molecules evenly distributed at the headgroup regions were replaced by Na+ ions. The energy was again minimized for the whole system. As in the case of the PLPC system, the first simulation was rejected from the analysis because of the erroneous parameter mentioned above, and the final structure was accepted for the new energy minimization with correct parameters. Also, at this point the distribution of Na+ ions was calculated from the trajectory in order to compare them with the final distributions and thus, to ensure the convergence of the ion distribution. Finally, this was followed by a 10-ps period of dynamic heating to a temperature of 310 K as well as equilibration and simulation periods of 109 ps and 1 ns, respectively.

The initial structure of the bilayer for simulation D was based on the well-equilibrated structure from the PLPC bilayer simulation. The structural modifications were performed similarly to those for the simulation C to form PPC and free fatty acids, except that instead of COO

- the uncharged COOH group was formed to construct LH molecules. As

no Na+ ions were added, this model did not contain charged species. After the construction, the energy of the system was minimized, followed by the heating period of 10 ps and the equilibration period of 195 ps. Finally, the simulation was run for 1 ns.

The simulations were performed in a microcanonical (NVE) ensemble. The use of a constant volume ensemble corresponds to the assumption that the release of the sn-2 fatty acid from the phospholipid does not significantly change the surface area per lipid molecule. Surface tensions were calculated frame by frame according to the method of Venable et al. [94] from the last 30 ps of simulations B, C, and D. Essentially zero average surface tension can be concluded with the large fluctuations of similar size in all three systems (-3 ± 60 mN/m, -12 ± 0.60 mN/m and 0 ± 57 mN/m for the simulations B, C, and D, respectively). Thus, at least in this particular case, the approximation of a constant volume seems justified for the purposes of the study. Although presently the constant-pressure ensemble is favored, the methodological aspects are currently not clear, as discussed above (chapter 3.2.5).

The commercial CHARMm software (Ver. 22.2, Molecular Simulations Inc.) was applied in simulation A and its academic version CHARMM (Ver. 25b2) in simulations B, C and D [67]. Lipid force field parameters were used [48] (personal communication),

52

except for the double bond region that was not parameterised. The partial charges of this region were estimated by employing local density functional electronic structure calculations (DMol, Version 2.3) (charges partitioned using the method of Hirshfeld [232]) and adapted to the charge distribution of the rest of the molecule. Other parameters for the double bond region were obtained from the CHARMm parameter set for amino acids. Because the COO

- and COOH groups were not present in the lipid force field, the

parameters for them were adapted from the CHARMM parameter set for amino acids. For the water molecules, the TIP3P parameters [60] were used. Every atom was taken into account independently in the MD simulations. The lengths of the bonds involving hydrogen atoms were fixed, using the SHAKE algorithm with 10-9 tolerance allowing the use of a 1 fs time step [233]. The long-range interactions were truncated using an atom-based cut-off radius of 13 Å with a shifting function for the electrostatic and a switching function for the van der Waals interactions [67].

Especially in the case of charged species the truncation of electrostatic interactions involves risks. However, in the simulations of charged membrane species, the truncation has been applied without noted artifacts [68-70]. To test the effect of cutoff distance, an additional 0.5 ns simulation for the system of PPC and charged L

- molecules was

performed using a cutoff distance of 18 Å for electrostatic interactions. This system should be most sensitive for changes in the treatment of the electrostatic interactions. However, the results were essentially similar with cutoff distances of 13 Å and 18 Å, as will be shown in chapter 5.4. Simulation D was performed with the uncharged fatty acids. Thus, it serves us with an additional opportunity to explore which results from simulation C are related to the presence of charged species and thus might be affected by the truncation of electrostatic interactions.

In simulation A, the Verlet algorithm was used to integrate the Newtonian equations of motion, whereas in simulations B, C, and D, the leap-frog Verlet was applied [39,40]. The nonbonded interactions were updated every 25th step (0.025 ps) during the heating and the first 80 ps of equilibration of simulation A, after which update was performed every 10th step in all simulations, which was enough to maintain constant energy. Energies, coordinates, and velocities were saved at every 25th step in simulation A and every 50th step in subsequent simulations. Simulation A was carried out using SGI Power Challenge (5 hours CPU / 1 ps) and Cray C94 (9 minutes CPU / 1 ps) computers and simulations B, C, and D using 64 processors of a Cray T3E computer at the Center for Scientific Computing, Espoo, Finland.

53

5.2 Data analysis

5.2.1 Traditional analysis tools

Here, the description of the applied analysis tools is given. Not all of the tools described were applied for all simulations. Details of such information can be found in the individual papers. In the analysis, the averages have been calculated over all saved time steps and over all individual molecular species, if not indicated otherwise.

Atomic single particle distribution functions in the direction of the bilayer normal were evaluated by calculating the total amount of each atom in 0.25 Å thick slices. The distributions were averaged over time. Further, they were used to calculate the mass density profiles for the main components of the bilayer and the total mass and electron density across the bilayer. Radial distributions of the oxygen and hydrogen atoms of the water molecules around the phosphorus and nitrogen atoms of the PC headgroups were averaged from the last 400 frames of the simulation using the SCARECROW software [234]. In addition, similar calculations were performed for the water molecules around the carbon atoms of the COO

- groups of L

- and for the Na+ ions around the PC and COO

-

headgroups. The mean cosine of the angle between the dipole moment vector of the water molecules and the bilayer normal was also calculated in 0.25 Å horizontal slices along the bilayer normal. A zero value is obtained for a random orientation and a negative value corresponds to the orientation of the dipole toward the bilayer center at positive values of y, while the opposite corresponds to the negative values of y. The orientation angle of the headgroup and glycerol backbone vectors with respect to the bilayer normal as well as the angle distributions were determined using one degree slices. In the case of explicit bilayer models, the positive direction of the bilayer normal in both the upper and the lower layer was toward the water region. In addition, the orientational angle distributions of varying bonds and vectors in the chains were calculated with respect to the bilayer normal. Note that here the bilayer normal was considered as a vector pointing towards the bilayer center. This was done in order to keep the numerical values mainly below 90°. For the two single bonds between the double bonds the values of the dihedral angles were monitored during the simulation and the angular distributions were determined. The percentage fraction of conformations with different combinations of these angles was also determined.

The fractions of gauche+ (g+), gauche- (g-) and trans (t ) states were determined for the dihedral angles. The division into g+ and g- states was performed in the preliminary study (paper I) using the ranges of -100° ... -20° and 20° ... 100°. However, later the division was performed using the ranges of -120° ... 0° and 0° ... 120° for the g+ and g- states, respectively, and the rest for the t states. Similar allocation was used for evaluating the rate of isomerisation between g+, g- and t states for each bond. The isomerisation rate was averaged over molecules. The root mean square (RMS) fluctuations of the atomic positions were calculated for carbon segments of the chains.

The orientational order of a carbon segment j is described by the order parameter Sj, which is defined as

54

1cos321 2 −= jjS θ (9)

where θj is the angle between the orientation vector and the reference direction. The brackets denote both the ensemble and time average. A 2H NMR observable order parameter, S

j

CD, is obtained by defining the orientation vector along the CHj bond, and the

bilayer normal as the reference direction. According to this definition we calculated from the 1-ns PLPC simulation the order parameters for the two CH bonds, CHaj and CHbj, at each saturated carbon atom in the chains. In order to estimate a statistical error (see chapter 3.3), the time averages for each molecule were defined as group averages, which were then used to calculate SEM. It is conventional in MD simulations to define the orientation vector either along the normal of the HC

jH plane or from C j-1 to Cj+1. In our

preliminary study (paper I), the former definition was used for the saturated and the latter for the unsaturated carbon segments. These definitions lead to the molecular order parameter S

j

mol. When isotropic rotations around the HCjH plane normal are assumed, the

CH bonds and corresponding Sj

CD values become equivalent, and Sj

CD can be compared with the S

j

mol values according to the relation -2Sj

CD = Sj

mol [235]. The Sj

mol may vary between -1/2 and 1 corresponding to the variation between perpendicular (90°) and parallel (0°) orientation with respect to the bilayer normal. The zero value of S

j indicates

isotropic orientational distribution but also a single orientation angle of 54.7° in the sample results in the zero value. In addition, to assess the origin of the order parameters (paper II), the angular distributions between the individual CHaj and CHbj bonds and the bilayer normal were calculated.

The reduced temperature θ, i.e., the temperature of a system with respect to the gel to liquid crystalline phase transition temperature Tm, is defined as

mm TTT )( −=θ , (10)

where T is the absolute temperature of the system. Electrostatic potential profile along the bilayer normal y was calculated based upon

Poisson’s equation

,''')''(1)0()(0

'

00∫ ∫−=−y y

dydyyy ρε

ψψ (11)

where ψ(y) is the electrostatic potential, ρ(y) is the charge density and ε0 is the vacuum permittivity. The charge density was determined for 0.25 Å horizontal slices and averaged from the monolayers. The position y = 0 resides in the middle of the bilayer.

Due to the symmetry operations used to model the bilayer implicitly, the tails of the PLPC molecules may occasionally be close to their images in the opposite leaflet at the center of the simulation box. In order to check that there was no significant bias between the inner and outer regions, equal volumes were determined by dividing the area in the x-z plane equally into an inner square and an outer part. The average atomic distributions of representative atoms in the headgroup (N, P), glycerol backbone (Cg2), sn-1 (C8, C15) and sn-2 chain (C8, C17) were calculated separately in these volumes. The orientational

55

order parameters for C8 and C15 of the sn-1 chain and for C8 and C17 of the sn-2 chain were also compared in these inner and outer volumes. No significant differences were noticed between the corresponding averages.

5.2.2 SOM based conformational analysis

Conformational data of the PLPC lipids in simulation A was subjected to SOM analysis. The data consisted of 40000 × 36 PLPC, i.e., 1440000 conformations in total. The conformation of the PLPC molecule was described by the sequence of its 41 dihedral angle values (see numbering of the bonds in Fig. 6). The values of the angles were within –90° to 270° over the bonds 9, 11, 34, and 37, and within 0° to 360° over the other bonds. These two ranges were needed to eliminate the possibility that jumps of nearly 360° would appear in an angle. For instance, in the case of single bonds the scale could not be set from –180° to 180° as the fluctuations around the trans state (±180°) would cause the artificial appearance of two clusters with negative and positive values. Beside performing the analysis for the whole molecule, molecular parts were also treated separately. The SOM analysis is reported for the whole molecule (angles 1-41) and its unsaturated sn-2 chain (angles 26-41). Visualization of molecular structures was carried out using the QUANTA software (Molecular Simulations Inc.).

The sequence of dihedral angles pertaining to a PLPC molecule in a simulation snapshot is used as a 41-dimensional input vector for the SOM. By varying the size of the map, the level of features affecting the organisation can be varied. Upon increasing the map size, small-scale features start to have an increasing effect. However, analysis of smaller scale features can also be performed using a small map by covering only certain parts of the molecule. Maps of 100 neurons in a 10×10 hexagonal arrangement were chosen for the final analysis since they provided a clear picture of the main conformational features while still allowing the visualization of some minor structural characteristics. The bubble neighborhood function was used. Every tenth conformation of each molecule was taken for the learning process after which all molecular conformations were assigned to the neurons of the trained map. To visualize the results, the reference vectors of each neuron were used to construct the corresponding molecular structures, which are called reference conformations. To aid in the visual comparison of the molecular conformations, the glycerol backbone bond Cg2-Cg3 (bond number 6) was aligned identically in all the reference conformations. In the case of the sn-2 chain, the dihedral angles constituted a 16-dimensional input vector. The analysis of the conformations of the sn-2 chains was performed identically to that for the whole molecule. However, in the construction of the reference conformations, the first double bond C9-C10 (bond number 34) was aligned to aid the comparison. It should be kept in mind that the reference conformations do not necessarily occur in the actual simulation, but should be considered as an abstraction of the common features of the real conformations that share this reference vector.

To introduce this novel methodology, the SOM analysis was performed with the basic procedures according to the instructions of the software. However, the procedure can be

56

optimized for certain molecular systems, for instance, by adding extra conformational parameters (such as intramolecular distances) to the input vector, and by coupling certain dihedral angle sequences presenting a similar shape together to end up in the same neuron. Also, if the minimum image convention were incorporated into the software, the present adjustment for the dihedral angle scales would not be necessary.

5.3 Structural characteristics of PLPC bilayer

The data produced by simulation A was used to investigate the structural characteristics of the PLPC membrane. The atomic single particle distribution functions and average positions along the bilayer normal (y) were calculated and are shown in Fig. 7. They provide general information on the structure of the system. The glycerol backbone and the beginning of the sn-2 chain have the narrowest distributions, implying them to be the most rigid parts when motion in the y direction is considered. In general, the width of the distributions for the chain carbons increases towards the center of the bilayer. The distribution of the nitrogen atoms is also slightly wider than the one for the phosphorus atoms. These observations are consistent with the X-ray and neutron diffraction results of DOPC [191]. Generally, the distributions are wider in the simulation than the ones based on the X-ray and neutron diffraction results of DOPC. This is probably due to the relatively low hydration of the DOPC bilayer in the experiments. Upon increasing hydration the effective size of the polar headgroup increases, the lateral packing of the chains loosens and the thermal motion increases [191,236].

The distributions reveal nonparallel average orientation of the glycerol backbone as well as the P-N vector of the headgroup with respect to the bilayer surface. The vertical displacement of the average positions of the Cg1 and Cg2 carbons of the glycerol backbone is 0.8 Å. Interestingly, a similar average value for the vertical displacement of acyl chain methylene units between the sn-1 and sn-2 chains has been concluded by Eklund et al. [237] from fluorescence spectroscopic measurements. However, in our simulation the vertical displacement increases towards the interior of the bilayer (see Fig. 7), probably due to the larger amount of gauche states in the sn-2 chain beginning compared to the sn-1 chain. For carbons C6 the displacement between sn-1 and sn-2 chains is about 2 Å. This results in the overlap of the atomic distributions of the double bond region (C9-C13) with the distributions of the sn-1 carbons C6-C9. Therefore, these fragments in the sn-1 chains are most directly affected by the double bonds. Furthermore, toward the end of the sn-2 chains the spacing decreases after the double bonds, which is an indication of the existence of bent conformations at the end of the sn-2 chains.

57

Fig. 7. Atomic distributions along the bilayer normal (y) in simulation A. The sn-1 chain carbons, water (- - -) and glycerol backbone carbons (Cg1-Cg3) (left panel) and the sn-2 chain carbons, phosphorus and nitrogen (right panel). The distributions of the sn-2 double bond region carbons (C9-C13) are drawn in bold together with the carbons C6-C9 of the sn-1 chain, which lie approximately at the same height in the layer with the double bonds. Also average positions for each atom are shown (!!!!). The center of the bilayer is at zero and the scales are identical in both panels.

The total mass density and electron density profiles can be approximated with high accuracy as the atomic positions are known. The shape of the profiles for the PLPC from simulation A (paper III) was remarkably similar to the X-ray density profiles of DPPC and POPC [191,238].

The hydrating water molecules appear to be strongly oriented around the PLPC headgroup phosphorus atoms due to hydrogen bonding, but only weak orientation is observed around the nitrogen atoms. Very similar behaviour has also been observed in other MD simulations [63,75,141]. The dominating orientation of the water dipole moments at the bilayer surface is towards the bilayer interior. This is related firstly to the strong tendency of the hydrogen atoms of the water molecules to orient towards the phosphorus atoms, and secondly to the larger number of hydrogen-bonded water molecules around the phosphatidyl group on the side of the water region.

The headgroups have plenty of orientational freedom, as indicated by the simulated angular distribution of the phosphorus-nitrogen vector in Fig. 8. The most prevailing orientation of the phosphorus-nitrogen vector is 17° from the bilayer surface towards the water. This is in agreement with the general conclusions from the experimental studies that, on average, the PC headgroup is oriented almost parallel to the surface [100,146,239-241]. The most prevailing orientation angle of the Cg1-Cg3 vector is 25° from the bilayer normal. However, the distributions reveal that the glycerol backbones have a variety of possible orientations. The most probable states for each dihedral angle, θ1-θ4 / α1-α5, were t g+ t g- / t g+ g+ t g-. It is interesting to note that if these dihedral angles occur in a single molecular conformation, one of the structures reported for DMPC molecule in a crystal [242] results. However, in the simulation only 5.8% of all the conformations had this sequence. Another crystal structure, g- t t g- / t g- g- t g+, was even less prevalent (1.0%). This implies that in a liquid crystalline phase the glycerol

0 10 2 0 3 0

sn-2, C18 C1 NP

0 10 2 0 3 0 (Å)

Cg1-Cg3water

C16sn-1, C1

(Å)

dist

ribut

ion

(arb

itrar

y un

its)

3 3 2 2

58

backbones and the PC headgroups are apparently dynamic, but not completely free, i.e., a relationship with the crystal structures still exists. Generally, the overall structure of the simulated PLPC bilayer is consistent with both experiments and bilayer simulations for other systems.

Fig. 8. The distribution of the orientation angle between the phosphorus-nitrogen vector and the bilayer normal from simulation A (left) together with the time series of the orientation angle for one of the PLPC molecules (right).

Comparison of the simulated orientational order parameter (SCD) profile of the PLPC

sn-1 chains with the experimental ones for DPPC and POPC systems at approximately the same reduced temperature (Fig. 9), suggests that the double bonds in an acyl chain increase the orientational order of the neighboring saturated chains. This has also been observed by 2H NMR [185,189,199,243]. Differences in the profiles are seen especially at the region C4-C10, and are interpreted to indicate a stiffening effect due to the rigid cis double bonds at approximately the same height in the bilayer. The stiffening is also indicated by the inequivalence in the SCD values of the methylene hydrogens at C6-C7 as well as by the low fraction of gauche bonds around C6 compared to a DPPC system, and by the relatively low bond isomerisation rate. It is notable that the SCD values for the sn-2 chain of PLPC from the simulation are remarkably similar to the experimental ones for PiLPC (16:0/18:2∆6,9) provided that the three carbon shift of the double bond region is taken into account. Comparison with the experimental SCD value for C6 of PLPC is also possible and a good accordance is found. Moreover, in the beginning of the sn-2 chain, as well as at the vicinity of the double bonds, the inequivalence of the SCD values of methylene hydrogens is remarkable, the fraction of gauche states is large and the isomerisation rate is low. The RMS fluctuations were increasingly enhanced towards the bilayer center for both chains and cannot thus explain the low SCD values at the beginning and at the double bond region of the sn-2 chain. Therefore, the low SCD values are probably caused mainly by the local effects of the rigid cis double bonds and the tilted chain beginnings on the bond isomerisation.

180

150

120

90

60

30

0

distribution

angl

e (d

egre

es)

0.0 0.2 0.4 0.6 0.8 1.0

bilayer interior

water

surface

time (ns)

59

Fig. 9. The simulated -Sj

CD orientational order parameters along the sn-1 (����) and sn-2 ("""") chains of PLPC. For comparison at approximately the same reduced temperature, also the 2H NMR based values are shown for the sn-1 chains of a DPPC system (####) [243] (for details of approximation, see paper III) and of a POPC system ($$$$)[185] together with the values for the sn-2 chains of a PLPC (◊◊◊◊) and PiLPC system (∆∆∆∆) [17]. Error bars indicate the SEMs of the molecular averages.

The prevailing orientation angle of the double bond region with respect to the bilayer normal was 37°. The internal structure of the double bond region was investigated in detail in order to find out whether the conformations proposed by Baenziger et al. [195] in the case of the PiLPC bilayer would be observed in the simulation. It was found that the conformations of the two-state model of Baenziger et al. represent the populations of 32 and 39% of all the conformations in simulation A. These two conformations, PP and MM, are characterized by the two torsion angles between the double bonds, +120° and +120°, and -120° and -120°, respectively. In the simulation also two other conformations, PM and MP, exist but with lower populations of 9 and 19%, respectively. These four main structures of the double bond region are illustrated in Fig. 10. In the two dominating conformations, the orientation of the two double bonds with respect to the bilayer normal is approximately the same. In the other two, the orientation of the second double bond is nearly perpendicular to the first one, thus affecting the packing of the chains quite dramatically. The existence of such conformations might be necessary to explain the role of the double bonds in the increased permeability of small molecules. Based on these findings, it is also tempting to speculate that the main conformations are enough to result in a stable membrane structure whereas some bent conformations are allowed. These less common structures can locally perturb the packing without destabilizing the bilayer structure and may have a role in the proper (local) functioning of the membrane.

2 4 6 8 10 1 2 14 1 6 1 8

simexp

sn-2PLPC

PiLPC PLPC

carbon atom2 4 6 8 10 1 2 14 1 6 1 8

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

carbon atom

-CD

exp

appr

exp

sim

sn-1

DPPC

POPC

PLPC

1 1 1 1 1 1

60

Fig. 10. The four model conformations of the double bond region together with the percentage of each conformation as found in simulation A.

5.3.1 Main conformations and conformational dynamics

The self-organising map for the whole molecule presenting the total amount of hits (number of assigned input vectors) for each reference vector is shown in Fig. 11, together with the reference conformations of the most representative neurons. Generally, the headgroups and sn-1 chains are straight continuations of the glycerol backbone, whereas the sn-2 chain begins perpendicularly to the glycerol backbone. However, the reference conformations of, for instance, neurons 61 and 81 show structures where also the sn-1 chain is initially perpendicularly oriented. The reference conformations of the molecule are visually very distinct if major torsional differences occur near the glycerol backbone. A general feature of the headgroup structures is that mostly the phosphorus atom is approximately in-line with the glycerol backbone. This is followed by a tilt of the phosphorus-nitrogen vector with respect to the membrane surface. However, neuron 96 shows an example of the choline group pointing upwards as an almost straight continuation of a glycerol backbone. Bending of the choline groups towards the chains is also possible, as shown by neurons 20 and 61.

The sn-1 chains (the chains on the right-hand side) in the depicted lipids present rather straight conformations. The sn-2 chain appears in bent conformations, where the bending occurs most frequently in the region of the first carbons due to the perpendicular orientation of the chain beginning, and in the middle due to the unsaturation. In all, the map demonstrates the conformational flexibility of the phospholipids and indicates that no well-defined structural clusters exist.

PP: 32.1% MM: 39.0%

PM: 9.3% MP: 19.0%

9 9

9 9

10 10

10 10

12

12

1212

13

13

13

13

61

Fig. 11. SOM of the PLPC molecule. The size of the depicted neuron indicates the number of hits. The reference conformations related to the most popular neurons (>25000 hits) are shown.

The map for the sn-2 chain of the PLPC molecule indicating the number of hits per

neuron is shown in Fig. 12, together with the most popular reference conformations. The unsaturation of the sn-2 chain is often thought to cause the appearance of heavily bent conformations due to the cis state of the double bonds. However, in the case of two or more cis double bonds, the conformation of the double bond region is dominated by the dihedral angles over the single bonds located between the double bonds, i.e. single bonds 35 and 36 in the case of PLPC (bond numbering in Fig. 6). These bonds determine either straight or bent conformations in the double bond region (see the main conformations of the double bond region in Fig. 10). From the reference conformations shown here, neuron 1 shows an example of a straight conformation of the double bond region and the whole chain. An utterly bent conformation is displayed by neuron 33 where the double bond region together with some gauche states of the single bonds causes the chain to bend

62

heavily. Overall, this conformation is U-shaped and suggests a possibility of the methyl end of the chain occasionally residing at the level of the glycerol backbone in the membrane. This kind of conformation is also visible in the reference conformation of neuron 94 in the map of the whole molecule (Fig. 11). These bent conformations can be speculated to have a role in the experimentally observed increased permeability induced by double bonds or might also serve as a preceding stage for the suggested appearance of extended conformations where the sn-2 chain penetrates to the water phase. Extended conformations have been suggested as having a role in the interaction with peripheral proteins and in the early stage of membrane fusion [2,244].

Fig. 12. SOM of the sn-2 chain of the PLPC molecule. The size of the depicted neuron indicates the number of hits. The reference conformations related to the most popular neurons (>20000 hits) are shown.

63

Conformational dynamics of individual molecules can be studied by determining the trajectories of lipids in the map, as illustrated for a single arbitrarily chosen molecule in Fig. 13. These transition paths also aid in distinguishing between large conformational changes and small-scale oscillations. The average number of neurones visited by one lipid molecule during the 1 ns trajectory was 23.5 in the map of the whole molecule and 64.8 in the map of the sn-2 chain. Thus, if the map in both cases presents the whole conformational space, the trajectory is clearly not long enough for one molecule to visit all possible conformations. A large number of rapid transitions between closely related neurons dominates the average lengths for one visit in each neuron. The transition between the popular conformations is not likely to occur directly. Instead such transitions can occur via several intermediate conformations, which is probably due to the several differing bonds in these popular conformations.

Fig. 13. SOM for a selected PLPC molecule (left) and its sn-2 chain (right). Gray hexagonals indicate the average time for one visit in each neuron with the size of the neuron. The transitions between the neurons are represented with lines.

5.4 Structural differences between PLPC bilayer and its PLA2

modified counterpart

The atomic single-particle distributions from simulation B (PLPC bilayer), simulation C (bilayer of PPC, L

- and Na+ species), and simulation D (bilayer of PPC and LH

molecules) are shown for several atoms in Fig. 14. The distributions are wider for the modified systems than for the PLPC bilayer. However, the effect is significantly enhanced in simulation C of the PPC and charged L

- molecules. The distributions are also

essentially similar in the test simulation with a larger cut-off distance for electrostatic interactions (see section 5.1). The wider distributions imply an increased mobility of the molecules in the direction normal to the bilayer. A change in the orientation of the headgroup as well as in the average membrane thickness is observed in simulation C

64

containing charged L- molecules, whereas in the case of simulation D only a slight

change in the thickness is observed.

Fig. 14. Distributions of water molecules, Na+ ions, nitrogen, phosphorus, sn-1 chain carbons C1 and C16, and sn-2 chain carbons C1 and C18 along the bilayer normal in simulations B (thick line), C (thin line) and D (dashed line). The distributions from the test simulation (corresponding to simulation C) with a larger cut-off distance for electrostatic interactions are also shown (dotted line).

The average distances of the chain carbons from the bilayer center in simulation C

show a shift of the PPC and charged L- molecules toward the water region as compared

with the intact PLPC bilayer (data not shown). However, in simulation D only a slight shift toward the water region was observed for the PPC and, contrary to the L

-, the LH

molecules move slightly (by less than 1 Å) toward the center of the bilayer. The descent of the neutral fatty acid toward the hydrophobic region has been observed using fluorescent probes [225] and has been suggested for enhancing the separation of the headgroups. This would allow the PLA2 active site easier access to the sn-2 bond of the phospholipids [224].

The distribution of water is different in the three systems. In the modified systems, the water molecules penetrate deeper into the bilayer interior than in the intact PLPC bilayer. The penetration is especially enhanced in the bilayer with L

- molecules. In fact, there are

studies of the membrane structure during the PLA2 action (and accumulation of reaction products) with the fluorescent probe Prodan [222], which is sensitive to the polarity of the headgroup region. The results indicated that disruption of the membrane structure was sufficient to allow increased ingress of water molecules to this region. The changes in the water penetration might also lead to changes in the diffusion of small molecules through the modified membrane systems.

In all, the observed decreased integrity of the bilayers consisting of the hydrolysis products implies structural perturbations in the hydrolyzed bilayer area. Loss of integrity

dist

ribut

ion

(arb

itrar

y un

its)

Na+

Na+ H2O

C1C18

C16

P

C1

N

-30 -20 -10 0 10 20 30 (Å)

sn-2,L-,LH

sn-1

-30 -20 -10 0 10 20 30 (Å)

65

would also most likely appear in a partly hydrolyzed membrane. This is in accord with the observations that, in addition to the presence of the hydrolysis products, varying perturbations may also activate PLA2 by allowing the substrate molecules to move more freely in the membrane-normal direction and, accordingly, better access to the active site of the enzyme [9,10,212-217,219,221,222,224]. In addition, surface defects have been suggested to help the enzyme residues to penetrate the membrane and facilitate better contact between the membrane and the enzyme [229].

There are remarkable changes in the headgroup and in the water orientational behavior of the bilayer consisting of PPCs, charged L

- molecules and Na+ ions. As shown in Fig.

15, simulations B and D produce very similar angle distribution for the P–N vector. The average orientation angles are 17° and 18° in simulations B and D, respectively, which accords with the value of 18° estimated from NMR and Raman studies of dipalmitoylphosphatidylcholine (DPPC) [146]. Figure 15 illustrates, however, that all angles are possible in simulation C with PPC and charged L

- molecules, which reflects an

increased orientational freedom for the PC headgroups of the PPC molecules. The average orientational angle of the P–N dipole was -2° in this modified bilayer. The presence of charged L

- molecules and Na+ ions therefore seem to cause a drastic change

in the orientational behavior of the PC headgroups, resulting in a structure in which the choline groups are more often buried in the bilayer. This may be due to an enhanced interaction of the choline group with the COO

- group of L

-.

Fig. 15. Averaged distribution of the orientation angle between the phosphorus-nitrogen vector and the bilayer normal in simulation B (thick line), C (thin line) and D (dashed line). The distribution from the test simulation (corresponding to simulation C) with a larger cut-off is also shown (dotted line). The positive direction of the bilayer normal is toward the water region.

The distributions indicate that in the presence of the negatively charged L-s, the change

in the orientational behavior of the PC headgroups occurs so that the negatively charged phosphatidyl groups are now more accessible at the outermost surface of the membrane. They would thus be able to promote the negative surface charge originally caused by the L

- molecules, a property that is thought to facilitate the tight association between PLA2

and the membrane interface [207,208,210].

-90 -60 -30 0 30 60 90

interiorbilayer watersurface

dist

ribut

ion

(arb

itrar

y un

its)

angle (degrees)

66

As shown in Fig. 16, in both simulations B and D the water dipoles at the surface of the bilayer tend to orient toward the bilayer interior, as discussed already in connection with simulation A (section 5.3, paper III). Thus, the liberation of the sn-2 chain in the uncharged state does not seem to remarkably alter the orientational behavior of the water molecules at the membrane surface. In simulation C for the PPCs and charged L

-

molecules, the orientation of the water dipoles is seemingly different. Oriented water extends over a much wider region than in the PLPC system. Over this wider range, the orientation is also generally stronger than in the PLPC system. This can be assumed partly from the widened atomic distributions in the direction normal to the bilayer in simulation C and partly from the fact that this modified system also includes water molecules oriented in a similar way around the COO

- headgroups of L

- molecules as

around the phosphatidyl groups. The increased number of water dipoles orienting toward the interior of this L

- containing system means that, in effect, there is a larger number of

negatively charged oxygen atoms of the water molecules pointing away from the membrane surface. It is tempting to speculate that this oriented water could affect the ability of PLA2 to recognize the surface. However, the water orientation is not changed in simulation D, which suggests that in real PLA2-hydrolyzed membranes the possible effects to the water orientation would not be as prominent as observed in simulation C.

Fig. 16. The mean cosine of the angle between the dipole moment vector of water molecules and the bilayer normal (y) in simulations B (thick line), C (thin line) and D (dashed line). The distribution from the test simulation (corresponding to simulation C) with a larger cut-off is also shown (dotted line). y = 0 corresponds to the center of the bilayer.

Increase in the orientational order parameters of the chain beginnings is also observed in the simulations, because in the free sn-2 chains the chain beginnings orient more freely along the bilayer normal. Along the chains, the differences gradually disappear. Towards the ends of the chains the order parameters for the intact and modified bilayers become identical, except in the sn-2 chains in simulation D where some change is observed at the double bond region and at the chain ends of LH molecules. These changes occur near the zero value of the order parameter and could possibly be reflected by the above mentioned slight shift of the LH molecules towards the bilayer center. A 4-5% decrease in the number of the straight conformations of the double bond region in simulation D could also be related (i) to the minor changes noticed in the orientational order parameters at

-30 -20 -10 0 10 20 30-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

<cos

>

(Å)

67

the double bond and chain end region and (ii) to the shift of the LH chains. In summary, accumulation of the PLA2 hydrolysis products in the membrane seems to affect the orientational order of the fatty acid chains near the surface regions, but less so in the interior of the membrane. This proposion is supported by the data of Sheffield et al. [222] indicating that the increase in the enzyme activity does not require significant changes in the order of the phospholipid acyl chains.

In all simulated systems, the electrostatic potential was negative in the water region compared with the membrane interior (Fig. 17). Other simulation studies have suggested that this is due to the positive potential from the lipid molecules, which then would be overcompensated by the ordering of the water molecules [35,42]. This behavior was qualitatively reproduced also here. As truncation has been reported to enhance the ordering of the water molecules in simulations, the potential values obtained here cannot be considered to be quantitative. However, the values of the total potential vary significantly between the compositionally different bilayer systems studied here, implying changes in the membrane potential due to the presence of the hydrolysis products.

Fig. 17. Electrostatic potential along the bilayer normal. The contributions (left) from the lipids (three upper curves) and water (three lower curves) together with the total potential profile (right) in simulations B (thick line), C (thin line) and D (dashed line). The distribution from the test simulation (corresponding to simulation C) with a larger cut-off for electrostatic interaction is also shown (dotted line). The profiles are averaged over the monolayers and y = 0 corresponds the center of the bilayer.

0 1 0 20 30

-8

-6

-4

-2

0

2

4

6

8

lipid

water

(V)

(Å)0 1 0 20 30

contributions total

(Å)1 1

6 Conclusions

Generally, the overall structure of the simulated PLPC bilayer is consistent with both experiments as well as membrane simulations carried out with other lipid systems. For instance, the dominating orientation (i) of the water dipole moments at the bilayer surface is toward the bilayer interior and (ii) of the phosphorus-nitrogen vector is slightly from the bilayer surface toward the water. Features connected to unsaturation, e.g., the dip in the orientational order parameter profile of the sn-2 chain, are in accordance with experimental data. Simulation reveals inequivalence in the SCD values of the methylene hydrogens of a single carbon segment, which is most apparent in the regions of restricted motion. Furthermore, conformations of the double bond regions show both dominating straight structures that fit well the overall packing of the chains, and less frequent bent structures. The latter might explain the role of double bonds in the experimentally observed increased permeability of the membranes for small molecules.

Efficient methods of analyzing conformations from MD simulations of large lipid assemblies have been lacking. The data from the PLPC simulation was used to apply self-organising neural networks (self-organising map, SOM) in the analysis of the conformations of lipids. All main structural features could be distinguished. Conformational dynamics of an individual lipid on a map enables us to distinguish the main transitions from the minor conformational changes. The merit of SOM is in giving quick insight into the key molecular features without demands for a priori knowledge.

The last study focuses on the structural effects induced by phospholipase A2 (PLA2) hydrolysis on the membrane. An intact PLPC bilayer and PLA2-treated bilayers consisting totally of hydrolysis products were simulated. The bilayers consisting of hydrolysis products have a loosened structure in the direction normal to the bilayer compared with the intact PLPC system, accompanied by increased ingress of the water to the bilayer. These effects are enhanced in the system with the charged species, but are also clearly seen in the uncharged bilayer. The observed changes imply structural perturbations also in a partially hydrolyzed bilayer. Experimental observations suggest that varying perturbations in the membrane structure may activate PLA2. In simulation, also a slight shift of the uncharged linoleic acid molecules toward the bilayer center is observed. This is in accordance with experimental observations and it has been suggested that it enhances the availability of the substrate to the active site of PLA2.

7 Future perspectives

The studies of this thesis open up further possibilities in the field of membrane simulations. Firstly, one could endeavor to achieve a more complete view on polyunsaturated membranes by performing MD simulations on bilayers consisting of various polyunsaturated lipids. Secondly, neural network analysis of simulation trajectories could be further developed. Thirdly, it will be of interest to apply MD simulations for assessing the structural effects of the compositional changes in membranes due to the action of various lipases.

As long as, for instance, the lipid-lipid interactions and membrane characteristics in the case of lipid mixtures are as poorly understood as they currently are, the simulation studies on lipid membranes themselves will be valuable. Already now many groups have concentrated on membrane proteins. Thus, there should also appear studies that probe the effects of various lipid environments on the membrane proteins. Membrane proteins will continue to have a high impact, as there are plenty of membrane proteins and important related phenomena for which simulation studies can shed light at the molecular level. Since lipoproteins and other curved membrane structures are significant in the human metabolism, there will most likely appear simulations dealing with these aspects. Also research of drug transport, nanostructures, new materials and biosensors, to mention but a few, can use knowledge on biological membranes and may find simulations useful.

MD simulations on biomembranes are still restricted by severe limitations both in the membrane models and in the methodological side of the work. A lot of effort is needed to be able to build up model systems that resemble more their real counterparts, by incorporating various structurally and functionally important lipid molecules as well as increasing the size of the system and the length of the simulation. Since the simulation of biomolecular systems is a new field of research, the techniques and algorithms are continuously assessed and developed. Especially the application of constant pressure algorithms, together with an improved treatment of the electrostatics, is important. In addition, methods taking into account the polarizability of the molecules are waiting to be introduced. MD simulations on biomembranes are increasingly important as a producer of information on biologically relevant systems. This progress will continue, as with increasing computational power, biochemically more realistic and methodologically more advanced simulations on biomembranes are expected in the near future.

8 References

1. Singer SJ & Nicolson GL (1972) The fluid mosaic model of the structure of cell membranes. Science 175: 720-731.

2. Mouritsen OG & Kinnunen P (1996) Role of lipid organization and dynamics for membrane functionality. In: Merz Jr KM & Roux B (eds) Biological membranes: A molecular perspective from computation and experiment. Birkhäuser, Boston p 463-502.

3. Merz Jr KM & Roux B (1996) Biological membranes: a molecular perspective from computation and experiment. Birkhäuser, Boston.

4. Marcelja S (1974) Chain ordering in liquid crystals II. Structure of bilayer membranes. Biochim Biophys Acta 367: 165-176.

5. Egberts, E. (1988) Molecular dynamics simulations of multibilayer membranes. PhD thesis. University of Groningen, The Netherlands.

6. Egberts E, Marrink S-J & Berendsen HJC (1994) Molecular dynamics simulation of a phospholipid membrane. Eur Biophys J 22: 423-436.

7. Pastor RW (1994) Molecular dynamics and Monte Carlo simulations of lipid bilayers. Curr Opin Struct Biol 4: 486-492.

8. Murakami M, Nakatani Y, Atsumi G, Inoue K & Kudo I (1997) Regulatory functions of phospholipase A2. Crit Rev Immunol 17: 225-283.

9. Burack WR, Gadd ME & Biltonen RL (1995) Modulation of phospholipase A2: identification of an inactive membrane-bound state. Biochemistry 34: 14819-14828.

10. Burack WR, Dibble ARG, Allietta MM & Biltonen RL (1997) Changes in vesicle morphology induced by lateral phase separation modulate phospholipase A2 activity. Biochemistry 36: 10551-10557.

11. Voet D & Voet JG (1995) Biochemistry. John Wiley & Sons, Inc.. 12. Op den Kamp JAF, Roelofsen B & van Deenen LLM (1985) Structural and

dynamic aspects of phosphatidylcholine in the human erythrocyte membrane. Trends Biochem Sci 8: 320-323.

13. Cullis PR, Fenske DB & Hope MJ (1996) Physical properties and functional roles of lipids in membranes. In: Vance DE & Vance J (eds) Biochemistry of lipids, lipoproteins and membranes. Elsevier, New York p 1-33.

71

14. Blume A (1983) Apparent molar heat capacities of phospholipids in aqueous dispersion. Effects of chain length and head group structure. Biochemistry 22: 5436-5442.

15. Huang C & Shusen L (1999) Calorimetric and molecular mechanics studies of the thermotropic phase behavior of membrane phospholipids. Biochim Biophys Acta 1422: 273-307.

16. Lafleur M, Cullis PR & Bloom M (1990) Modulation of the orientational order profile of the lipid acyl chain in the Lα phase. Eur Biophys J 19: 55-62.

17. Baenziger JE, Jarrel HC, Hill RJ & Smith ICP (1991) Average structural and motional properties of a diunsaturated acyl chain in a lipid bilayer: effects of two cis-unsaturated double bonds. Biochemistry 30: 894-903.

18. Kinnunen P (1996) On the molecular-level mechanisms of peripheral protein-membrane interactions induced by lipids forming inverted non-lamellar phases. Chem Phys Lipids 81: 151-166.

19. Siegel DP & Epand RM (1997) The mechanism of lamellar-to-hexagonal phase transitions in phosphatidylethanolamine: implications for membrane fusion mechanisms. Biophys J 73: 3089-3111.

20. Yeagle PL (1985) Cholesterol and the cell membrane. Biochim Biophys Acta 822: 267-287.

21. McMullen TPW & McElhaney RN (1996) Physical studies on cholesterol-phospholipid interaction. Curr Opin Coll Int Sci 1: 83-90.

22. Mouritsen OG (1991) Theoretical models of phospholipid phase transitions. Chem Phys Lipids 57: 179-194.

23. Demel RA, Geurts van Kessel WSM & van Deenen LLM (1972) The properties of polyunsaturated lecithins in monolayers and liposomes and the interactions of these lecithins with cholesterol. Biochim Biophys Acta 266: 26-40.

24. Virtanen JA, Ruonala M, Vauhkonen M & Somerharju P (1995) Lateral organization of liquid-crystalline cholestrol-dimyristoylphosphatidylcholine bilayers. Evidence for domains with hexagonal and centered rectangular cholestrol superlattices. Biochemistry 34: 11568-11581.

25. Ramstedt B & Slotte JP (1999) Interaction of cholesterol with sphingomyelin and phosphatidylcholine in mixed monolayers containing both phospholipids. Biophys J 76: 908-915.

26. Mattjus P & Slotte JP (1996) Does cholesterol discriminate between sphingomyelin and phosphatidylcholine in mixed monolayers containing both lipids. Chem Phys Lipids 81: 69-80.

27. Somerharju P, Virtanen JA & Cheng KH (1999) Lateral organisation of membrane lipids. The superlattice view. Biochim Biophys Acta 1440: 32-48.

28. Jorgensen K, Sperotto MM, Mouritsen OG, Ipsen JH & Zuckermann MJ (1993) Phase equilibria and local structure in binary lipid bilayers. Biochim Biophys Acta 1152: 135-145.

29. Pasenkiewicz-Gierula M, Subczynski WK & Kusumi A (1991) Influence of phospholipid unsaturation on the cholesterol distribution in membranes. Biochimie 73: 1311-1316.

30. Simons K & Ikonen E (2000) How cells handle cholesterol. Science 290: 1721-1726.

72

31. Frank PG & Marcel YL (2000) Apolipoprotein A-I: structure-function relationships. J Lipid Res 41: 853-872.

32. Hevonoja T, Pentikäinen MO, Hyvönen MT, Kovanen PT & Ala-Korpela M (2000) Structure of low density lipoprotein (LDL) particles. Basis for understanding molecular changes in modified LDL. Biochim Biophys Acta 1488: 189-210.

33. Öörni K, Pentikäinen MO, Ala-Korpela M & Kovanen PT (2000) Aggregation, fusion, and vesicle formation of modified low density lipoprotein particles: molecular mechanisms and effects on matrix interactions. J Lipid Res 41: 1703-1714.

34. Seaton BA & Roberts MF (1996) Peripheral membrane proteins. In: Merz Jr KM & Roux B (eds) Biological membranes: a molecular perspective from computation and experiment. Birkhäuser, Boston p 355-403.

35. Tieleman DP, Marrink S-J & Berendsen HJC (1997) A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems. Biochim Biophys Acta 1331: 235-270.

36. Nagle JF, Zhang R, Tristam-Nagle S, Petrache HI & Suter RM (1996) X-ray structure determination of fully hydrated Lα phase dipalmitoylphosphatidylcholine bilayers. Biophys J 70: 1419-1431.

37. Petrache HI, Tristam-Nagle S & Nagle JF (1998) Fluid phase structure of EPC and DMPC bilayers. Chem Phys Lipids 95: 83-94.

38. Tristam-Nagle S, Petrache HI & Nagle JF (1998) Structure and Interactions of fully hydrated dioleoylphosphatidylcholine bilayers. Biophys J 75: 917-925.

39. Allen MP & Tildesley DJ (1987) Computer simulation of liquids. Clarendon Press, Oxford.

40. Leach AR (1996) Molecular modelling. Principles and applications. Addison Wesley Longman Limited, Singapore.

41. Brooks III CL, Karplus M & Pettitt BM (1988) Proteins: a theoretical perspective of dynamics, structure and thermodynamics. John Wiley & Sons, New York.

42. Tobias DJ, Tu K & Klein ML (1997) Atomic-scale molecular dynamics simulations of lipid membranes. Curr Opin Coll Int Sci 2 : 15-26.

43. Merz Jr KM (1997) Molecular dynamics simulations of lipid bilayers. Curr Opin Struct Biol 7: 511-517.

44. Berendsen HJC & Tieleman DP (1998) Molecular dynamics: studies of lipid bilayers.Encyclopedia of Computational Chemistry. John Wiley & Sons, p 1639-1650.

45. Forrest LR & Sansom MSP (2000) Membrane simulations: bigger and better? Curr Opin Struct Biol 10: 174-181.

46. Stouch TR, Ward KB, Altieri A & Hagler AT (1991) Simulations of lipid crystals: characterization of potential energy functions and parameters for lecithin molecules. J Comput Chem 12: 1033-1046.

47. Williams DE & Stouch TR (1993) Characterization of force fields for lipid molecules: applications to crystal structures. J Comput Chem 14: 1066-1076.

48. Schlenkrich M, Brickmann J, MacKerell Jr AD & Karplus M (1996) An empirical potential energy function for phospholipids: criteria for parameter optimization and applications. In: Merz Jr KM & Roux B (eds) Biological membranes: a

73

molecular perspective from computation and experiment. Birkhäuser, Boston p 31-81.

49. Chiu S-W, Clark M, Jakobsson E, Subramaniam S & Scott HL (1999) Optimization of hydrocarbon chain interaction parameters: application to the simulation of fluid phase lipid bilayers. J Phys Chem B 103: 6323-6327.

50. Feller SE & MacKerell Jr AD (2000) An improved empirical potential energy function for molecular simulations of phospholipids. J Phys Chem B 104: 7510-7515.

51. Ahlström P & Berendsen HJC (1993) A molecular dynamics study of lecithin monolayers. J Phys Chem 97: 13691-13702.

52. Tu K, Tobias DJ & Klein ML (1995) Constant pressure and temperature molecular dynamics simulations of crystals of the lecithin fragments: glycerylphosphoryl-choline and dilauroylglycerol. J Phys Chem 99: 10035-10042.

53. Tieleman DP & Berendsen HJC (1996) Molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine bilayer with different macroscopic boundary conditions and parameters. J Chem Phys 105: 4871-4880.

54. Takaoka Y, Miyagawa H & Kitamura K (1998) Molecular dynamics simulation of phospholipid bilayer membrane. Fluid Phase Equilibr 144: 387-393.

55. Feller SE, Zhang Y & Pastor RW (1995) Computer simulation of liquid/liquid interfaces. II. Surface tension area dependence of a bilayer and monolayer. J Chem Phys 103: 10267-10276.

56. Berger O, Edholm O & Jähnig F (1997) Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys J 72: 2002-2013.

57. Zhou F & Schulten K (1995) Molecular dynamics study of a membrane-water interface. J Phys Chem 99: 2194-2207.

58. Orozco M & Luque FJ (2000) Theoretical methods for the description of the solvent effect in biomolecular systems. Chem Rev 100: 4187-4226.

59. Berendsen HJC, Postma JPM, van Gunsteren W & Hermans J (1981) Interaction models for water in relation to protein hydration. In: Pullman A, Jortner J & Pullman B (eds) Intermolecular forces. Reidel, Dordrecht p 331-342.

60. Jorgensen WL, Chandrasekhar L, Madura JD, Impey RW & Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79: 926-935.

61. Feller SE, Pastor M, Rojnuckarin A, Bogusz S & Brooks BR (1996) Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100: 17011-17020.

62. Heller H, Schaefer M & Schulten K (1993) Molecular dynamics simulation of a bilayer of 200 lipids in a gel and in the liquid-crystal phase. J Phys Chem 97: 8343-8360.

63. Alper HE, Bassolino-Klimas D & Stouch TR (1993) The limiting behaviour of water hydrating a phospholipid monolayer: A computer simulation study. J Chem Phys 99: 5547-5559.

64. Alper HE, Bassolino-Klimas D & Stouch TR (1993) Computer simulation of a phospholipid monolayer-water system: the influence of long range forces on water structure and dynamics. J Chem Phys 98: 9798-9807.

74

65. Chen B, Xing J & Siepmann JI (2000) Development of polarizable water force fields for phase equilibrium calculations. J Phys Chem 104: 2391-2401.

66. Greengard & Rohklin (1987) J Comput Phys 73: 325. 67. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S & Karplus M

(1983) CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4: 187-217.

68. Lopez-Cascales JJ, Berendsen HJC & Garcia de la Torre J (1996) Molecular dynamics simulation of water between two charged layers of dipalmitoyl-phosphatidylserine. J Phys Chem 100: 8621-8627.

69. Lopez-Cascales JJ, Garcia de la Torre J, Marrink S-J & Berendsen HJC (1996) Molecular dynamics simulation of a charged biological membrane. J Chem Phys 104: 2713-2720.

70. Wymore T & Wong TC (1999) Molecular dynamics study of substance P peptides partitioned in a sodium dodecylsulfate micelle. Biophys J 76: 1213-1227.

71. Watanabe M, Ferrario M & Klein ML (1988) Molecular dynamics study of a sodium octanoate micelle in aqueous solution. J Phys Chem 92: 819-821.

72. Tu K, Tobias DJ & Klein ML (1995) Constant pressure and temperature molecular dynamics simulation of a fully hydrated liquid crystal phase dipalmitoyl-phosphatidylcholine bilayer. Biophys J 69: 2558-2562.

73. Darden T, York D & Pedersen LG (1993) Particle mesh Ewald: An N log(N) method for Ewald sums in large systems. J Chem Phys 98: 10089-10092.

74. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H & Pedersen LG (1995) A smooth particle mesh Ewald method. J Chem Phys 103: 8577-8593.

75. Essmann U, Perera L & Berkowitz ML (1995) The origin of the hydration interaction of lipid bilayers from MD simulation of dipalmitoylphosphatidyl-choline membranes in gel and liquid crystalline phases. Langmuir 11: 4519-4531.

76. Board Jr JA, Causey JW, Leathrum Jr JF, Windemuth A & Schulten K (1992) Accelerated molecular dynamics simulation with the parallel fast multipole algorithm. Chem Phys Lett 198: 89-94.

77. Jakobsson E (1997) Computer simulation studies of biological membranes: progress, promise and pitfalls. Trends Biochem Sci 9: 339-344.

78. Martyna GJ (1996) Explicit reversible integrators for extended systems dynamics. Mol Phys 87: 1117-1157.

79. Pasenkiewicz-Gierula M, Takaoka Y, Miyagawa H, Kitamura K & Kusumi A (1999) Charge pairing of headgroupd in phosphatidylcholine membranes: a molecular dynamics simulation study. Biophys J 76: 1228-1240.

80. Essmann U & Berkowitz ML (1999) Dynamical properties of phospholipid bilayers from computer simulation. Biophys J 76: 2081-2089.

81. Lindahl E & Edholm O (2000) Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys J 79: 426-433.

82. Chiu S-W, Clark M, Subramaniam S & Jakobsson E (2000) Collective motion artifacts arising in long-duration molecular dynamics simulations. J Comp Chem 21: 121-131.

83. Berendsen HJC, Postma JPM, van Gunsteren W, DiNola A & Haak JR (1984) Molecular dynamics with coupling to an external bath. J Chem Phys 81: 3684-3690.

75

84. Nose S & Klein ML (1983) Constant pressure dynamics for molecular systems. Mol Phys 52: 1055-1076.

85. Hoover WG (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A 31: 1695-1697.

86. Shinoda W, Fukada T, Okazaki S & Okada I (1995) Molecular dynamics simulation of the dipalmitoylphosphatidylcholine (DPPC) lipid bilayer in the fluid phase using the Nosé-Parrinello-Rahman NPT enseble. Chem Phys Lett 232: 308-322.

87. Tu K, Tobias DJ, Blasie JK & Klein ML (1996) Molecular dynamics investigation of the structure of a fully hydrated gel-phase dipalmitoylphoshphatidylcholine bilayers. Biophys J 70: 595-608.

88. Shinoda W, Namiki N & Okazaki S (1997) Molecular dynamics study of a lipid bilayer:convergence, structure and long-time dynamics. J Chem Phys 106: 5731-5743.

89. Chiu S-W, Clark M, Balaji S, Subramaniam S, Scott HL & Jakobsson E (1995) Incorporation of surface tension into molecular dynamics simulation of an interface: A fluid phase lipid bilayer membrane. Biophys J 69: 1230-1245.

90. Roux B (1996) Commentary: surface tension of biomembranes. Biophys J 71: 1346-1347.

91. Jähnig F (1996) What is the surface tension of a lipid bilayer membrane? Biophys J 71: 1348-1349.

92. Feller SE & Pastor RW (1996) On simulating lipid bilayers with an applied surface tension: periodic boundary conditions and undulations. Biophys J 71: 1350-1355.

93. Feller SE & Pastor RW (1999) Constant surface tension simulations of lipid bilayers: the sensitivity of surface areas and compressibilities. J Chem Phys 111: 1281-1287.

94. Venable RM, Brooks B & Pastor RW (2000) Molecular dynamics simulations of gel (LβI) phase lipid bilayers in constant pressure and constant surface area ensembles. J Chem Phys 112: 4822-4832.

95. Zubrzycki IZ, Xu Y, Madrid M & Tang P (2000) Molecular dynamics simulations of a fully hydrated dimyristoylphosphatidylcholine membrane in liquid-crystalline phase. J Chem Phys 112: 3437-3441.

96. Robinson AJ, Richards WG, Thomas PJ & Hann MM (1995) Head group and chain behavior in biological membranes: a molecular dynamics computer simulation. Biophys J 67: 2345-2354.

97. Hardy BJ & Pastor RW (1994) Conformational sampling of hydrocarbon and lipid chains in an orienting potential. J Comput Chem 15: 208-226.

98. Chiu SW, Jakobsson E, Subramaniam S & Scott HL (1999) Combined Monte Carlo and molecular dynamics simulation of fully hydrated dioleoyl and palmitoyl-oleoyl phosphatidylcholine lipid bilayers. Biophys J 77: 2462-2469.

99. White SH & Wiener MC (1996) The liquid-crystallographic structure of fluid lipid bilayer membranes. In: Merz Jr KM & Roux B (eds) Biological membranes: a molecular perspective from computation and experiment. Birkhäuser, Boston p 127-144.

100. Seelig J & Seelig A (1980) Lipid conformation in model membranes and biological membranes. Q Rev Biophys 13: 19-61.

76

101. Brown MF (1996) Membrane structure and dynamics studied with NMR spectroscopy. In: Merz Jr KM & Roux B (eds) Biological membranes: a molecular perspective from computation and experiment. Birkhäuser, Boston p 175-252.

102. Mendelsohn R & Snyder RG (1996) Infrared spectroscopic determination of conformational disorder and microphase separation in phospholipid acyl chains. In: Merz Jr KM & Roux B (eds) Biological membranes: a molecular perspective from computation and experiment. Birkhäuser, Boston p 145-174.

103. Shenkin PS & McDonald DQ (1994) Cluster analysis of molecular conformations. J Comput Chem 15: 899-916.

104. Torda AE & van Gunsteren W (1994) Algorithms for clustering molecular dynamics configurations. J Comput Chem 15: 1331-1340.

105. Troyer JM & Cohen FE (1995) Protein conformation landscapes: energy minimization and clustering of a long molecular dynamics trajectory. Proteins: Structure, Function and Genetics 23: 97-110.

106. Bravi G, Gancia E, Zaliani A & Pegna M (1997) SONHICA (simple optimized non-hierarchial cluster analysis): a new tool for analysis of molecular conformations. J Comput Chem 18: 1296-1311.

107. Kangas J & Kohonen T (1996) Developments and applications of the self-organizing map and related algorithms. Math Comput Simulat 41: 3-12.

108. Kohonen T, Oja E, Simula O, Visa A & Kangas J (1996) Engineering applications of the self-organizing map. Proc IEEE 84: 1358-1384.

109. Kohonen T, Kaski S, Lagus KK, Salojärvi J, Paatero V & Saarela A (2000) Self-organization of a massive document collection. IEEE T Neural Networks 11: 574-585.

110. Zhu B, Ramsey M & Chen H (2000) Creating a large-scale content-based airphoto image digital library. IEEE T Image Processing 9: 163-167.

111. Rose VS, Croall IF & MacFie HJH (1991) An application of unsupervised neural network methodology Kohonen (topology-preserving mapping) to QSAR analysis. Quant Struct -Act Relat 10: 6-15.

112. Karpen ME, Tobias DJ & Brooks III CL (1993) Statistical clustering techniques for the analysis of long molecular dynamics trajectories: analysis of 2.2-ns trajectories of YPGDV. Biochemistry 32: 412-420.

113. Marabini R & Carazo JM (1994) Pattern recognition and classification of images of biological macromolecules using artificial neural networks. Biophys J 66: 1804-1814.

114. Schuchhardt J, Schneider G, Reichelt J, Schomburg D & Wrede P (1996) Local structural motifs of protein backbones are classified by self-organizing neural networks. Protein Engng 9: 833-842.

115. Chastrette M, Cretin D & l Aidi C (1996) Structure-odor relationships: using neural networks in the estimation of camphoraceous or fruity odors and olfactory thresholds of aliphatic alcohols. J Chem Inf Comput Sci 36: 108-113.

116. Usenius J-P, Tuohimetsä S, Vainio P, Ala-Korpela M, Hiltunen Y & Kauppinen RA (1996) Automated classification of human brain tumours by neural network analysis using in vivo 1H magnetic resonance spectroscopic metabolite phenotypes. NeuroReport 7: 1597-1600.

77

117. Haydon GH, Jalan R, Ala-Korpela M, Hiltunen Y, Hanley J, Jarvis LM, Ludlum CA & Hayes PC (1998) Prediction of cirrhosis in patients with chronic hepatitis C infection by artificial neural network analysis of virus and clinical factors. J Viral Hepatitis 5: 255-264.

118. Kaartinen J, Hiltunen Y, Kovanen PT & Ala-Korpela M (1998) Application of self-organising maps for the detection and classification of human blood plasma lipoprotein lipid profiles on the basis of 1H NMR spectroscopy data. NMR Biomed 11: 168-176.

119. Tafeit E & Reibnegger G (1999) Artificial neural networks in laboratory medicine and medical outcome prediction. Clin Chem Lab Med 37: 845-853.

120. Kohonen T (1995) Self-organizing Maps. Springer-Verlag, Heidelberg. 121. Haykin S (1999) Neural Networks, A Comprehensive Foundation. Prentice Hall,

New Jersey. 122. Erwin E, Obermayer K & Schulten K (1992) Self-organizing maps: ordering,

convergence properties and energy functions. Biol Cybern 67: 47-55. 123. Mouritsen OG (1993) Structural properties of lamellar assemblies of biological

surfactants. Tenside Surf Det 30: 275-280. 124. Wendoloski JJ, Kimatian SJ, Schutt CE & Salemme RF (1989) Molecular

dynamics simulation of a phospholipid micelle. Science 243: 636-638. 125. Sansom MSP, Shrivastava IH, Ranatunga KM & Smith GR (2000) Simulations of

ion channels - watching ions and water move. Trends Biochem Sci 25: 368-374. 126. Phillips JC, Wriggers W, Li Z, Jonas A & Schulten K (1997) Predicting the

structure of apolipoprotein A-I in reconstituted high-density lipoprotein disks. Biophys J 73: 2337-2346.

127. Sheldahl C & Harvey SC (1999) Molecular dynamics on a model for nascent high-density lipoprotein: role of salt bridges. Biophys J 76: 1198.

128. Bandyopadhyay S, Tarek M & Klein ML (1998) Computer simulation studies of amphiphilic interfaces. Curr Opin Coll Int Sci 3: 242-246.

129. Bassolino-Klimas D, Alper HE & Stouch TR (1993) Solute diffusion in lipid bilayer membranes: an atomic level study by molecular dynamics simulation. Biochemistry 32: 12624-12637.

130. Berendsen HJC & Marrink S-J (1993) Molecular dynamics of water transport through membranes: Water from solvent to solute. Pure and Appl Chem 65: 2513-2520.

131. Paci E & Marchi M (1994) Membrane crossing by a polar molecule: a molecular dynamics simulation. Mol Simulat 14: 1-10.

132. Bassolino-Klimas D, Alper HE & Stouch TR (1995) Mechanism of solute diffusion through lipid bilayer membranes by molecular dynamics simulation. J Am Chem Soc 117: 4118-4129.

133. Jin B & Hopfinger AJ (1996) Characterization of lipid membrane dynamics by simulation: 3. Probing molecular transport across the phospholipid bilayer. Pharmaceut Res 13: 1786-1794.

134. Marrink S-J, Jähnig F & Berendsen HJC (1996) Proton transfer across transient single-file water pores in a lipid membrane studied by molecular dynamics simulations. Biophys J 71: 632-647.

78

135. Wilson MA & Pohorille A (1996) Mechanism of unassisted ion transport across membrane bilayers. J Am Chem Soc 118: 6580-6587.

136. Marrink S-J, Berger O, Tieleman DP & Jähnig F (1998) Adhesion forces of lipids in a phospholipid membrane studied by molecular dynamics simulations. Biophys J 74: 931-943.

137. Tarek M, Tu K, Klein ML & Tobias DJ (1999) Molecular dynamics simulations of supported phospholipid/alkanethiol bilayers on a gold surface. Biophys J 77: 964-972.

138. Koubi L, Tarek M, Klein ML & Scharf D (2000) Distribution of halothane in a dipalmitoylphosphatidylcholine bilayer from molecular dynamics calculations. Biophys J 78: 800-811.

139. Smondyrev AM & Berkowitz ML (1999) Molecular dynamics simulation of fluorination effects on a phospholipid bilayer. J Chem Phys 111: 9864-9870.

140. Marrink S-J, Berkowitz ML & Berendsen HJC (1993) Molecular dynamics simulation of a membrane / water interface: the ordering of water and its relation to the hydration force. Langmuir 9: 3122-3131.

141. Damodaran KV & Merz Jr KM (1994) A comparison of DMPC- and DLPE-based lipid bilayers. Biophys J 66: 1076-1087.

142. Marrink S-J & Berendsen HJC (1994) Simulation of water transport through lipid membrane. J Phys Chem 98: 4155-4168.

143. Marrink SJ, Sok RM & Berendsen HJC (1996) Free volume properties of a simulated lipid membrane. J Chem Phys 104: 9090-9099.

144. Gabdoulline RR, Vanderkooi G & Zheng C (1996) Comparison of the structures of dimyristoylphosphatidylcholine in the presence and absence of cholesterol by molecular dynamics simulations. J Phys Chem 100: 15942-15946.

145. Shinoda W, Shimizu M & Okazaki S (1998) Molecular dynamics study on electrostatic properties of a lipid bilayer: polarization, electrostatic potential, and the effects on structure and dynamics of water near the interface. J Phys Chem B 102: 6647-6654.

146. Akutsu H & Nagamori T (1991) Conformational analysis of the polar head group in phosphatidylcholine bilayers. A structural change induced by cations. Biochemistry 30: 4510-4516.

147. Yeagle PL, Hutton WC, Huang C & Martin RB (1977) Phospholipid head-group conformations; Intermolecular interactions and cholesterol effects. Biochemistry 16: 4344-4349.

148. Hauser H, Pascher I & Sundell S (1988) Preferred conformation and dynamics of the glycerol backbone in phospholipids. An NMR and x-ray single-crystal analysis. Biochemistry 27: 9166-9174.

149. Stouch TR (1993) Lipid membrane structure and dynamics studied by all-atom molecular dynamics simulations of hydrated phospholipid bilayers. Mol Simulat 10: 335-362.

150. Venable RM, Zhang Y, Hardy RJ & Pastor RW (1993) Molecular dynamics simulations of a lipid bilayer and of hexadecane: an investigation of membrane fluidity. Science 262: 223-226.

79

151. Smondyrev AM & Berkowitz ML (1999) Molecular dynamics study of sn-1 and sn-2 chain conformations in dipalmitoylphosphatidylcholine membranes. J Chem Phys 110: 3981-3985.

152. Mendelsohn R, Davies MA, Schuster HF, Zu ZG & Bittman R (1991) CD2 rocking modes as quantitative infrared probes of one-, two-, and three-bond conformational disorder in dipalmitoylphosphatidylcholine and dipalmitoyl-phosphatidylcholine/cholesterol mixtures. Biochemistry 30: 8558-8563.

153. Douliez J-P, Leonard A & Dufourc EJ (1995) Restatement of order parameters in biomembranes: Calculation of C-C bond order parameters from C-D quadrupolar splittings. Biophys J 68: 1727-1739.

154. Tabony J & Perly B (1990) Quasielastic neutron scattering measurements of fast local translational diffusion of lipid molecules in phospholipid bilayers. Biochim Biophys Acta 1063: 67-72.

155. Vaz WL & Almeida PF (1991) Microscopic versus macroscopic diffusion in one-component fluid phase lipid bilayer membranes. Biophys J 60: 1553-1554.

156. Fettiplace R & Haydon DA (1980) Water permeability of lipid membranes. Physiol Rev 60: 510-550.

157. Damodaran KV & Merz Jr KM (1993) Head group-water interactions in lipid bilayers: A comparison between DMPC- and DLPE-based lipid bilayers. Langmuir 9: 1179-1183.

158. Pasenkiewicz-Gierula M, Takaoka Y, Miyagawa H, Kitamura K & Kusumi A (1997) Hydrogen bonding of water to phosphatidylcholine in the membrane as studied by a molecular dynamics simulation: location, geometry, and lipid-lipid bridging via hydrogen-bonded water. J Phys Chem A 101: 3677-3691.

159. Israelachvili JN & Wennerström H (1996) Role of hydration and water structure in biological and colloidal interactions. Nature 379: 219-225.

160. Flewelling R & Hubbell W (1986) The membrane dipole potential in a total membrane potential model. Applications to hydrophobic ion interactions with membranes. Biophys J 49: 541-552.

161. Simon SA & McIntosh TJ (1989) Magnitude of the solvation pressure depends on dipole potential. Proc Natl Acad Sci USA 86: 9263-9267.

162. Gawrisch K, Ruston D, Zimmerberg J, Parsegian VA, Rand RP & Fuller N (1992) Membrane dipole potentials, hydration forces, and the ordering of water at membrane surfaces. Biophys J 61: 1213-1223.

163. Brockman HL (1994) Dipole potential of lipid membranes. Chem Phys Lipids 73: 57-79.

164. Damodaran KV, Merz Jr KM & Gaber BP (1992) Structure and dynamics of the dilauroylphosphatidylethanolamine lipid bilayer. Biochemistry 31: 7656-7664.

165. Robinson AJ, Richards WG, Thomas PJ & Hann MM (1995) Behavior of cholesterol and its effect on head group and chain conformations in lipid bilayers: A molecular dynamics study. Biophys J 68: 164-170.

166. Tu K, Klein ML & Tobias DJ (1998) Constant-pressure molecular dynamics investigation of cholesterol effects in a dipalmitoylphosphatidylcholine bilayer. Biophys J 75: 2147-2156.

80

167. Smondyrev AM & Berkowitz ML (1999) Structure of dipalmitoylphosphatidyl-choline/cholesterol bilayer at low and high cholesterol concentrations: molecular dynamics study. Biophys J 77: 2075-2089.

168. Smondyrev AM & Berkowitz ML (2000) Molecular dynamics simulation of dipalmitoylphosphatidylcholine membrane with cholesterol sulfate. Biophys J 78: 1672-1680.

169. McIntosh TJ, Magid AD & Simon SA (1989) Cholesterol modifies the short-range repulsive interactions between phosphatidylcholine bilayers. Biochemistry 28: 17-25.

170. Slater SJ, Kelly MB, Yeager MD, Larkin J, Ho C & Stubbs CD (1996) Polyunsaturation in cell membranes and lipid bilayers and its effects on membrane proteins. Lipids 31: 189-192.

171. Mitchell DC, Straume M & Litman BJ (1992) Role of sn-1-saturated, sn-2 polyunsaturated phospholipids in control of membrane receptor conformational equilibrium: effects of cholesterol and acyl chain unsaturation on the metarhodopsin I - metarhodopsin II equilibrium. Biochemistry 31: 662-670.

172. Jenski LJ, Sturdevant LK, Ehringer WD & Stillwell W (1993) Omega-3 fatty acid modification of membrane structure and function. I. Dietary manipulation of tumor cell susceptibility to cell- and complement-mediated lysis. Nutr Cancer 19: 135-146.

173. Stillwell W, Ehringer WD & Jenski LJ (1993) Docosahexaenoic acid increases permeability of lipid vesicles and tumor cells. Lipids 28: 103-108.

174. Salem NJr & Niebylski CD (1995) The nervous system has an absolute requirement for proper function. Mol Membr Biol 12: 131-134.

175. Thurmond RL, Lindblom G & Brown MF (1993) Curvature, order, and dynamics of lipid hexagonal phases studied by deuterium NMR spectroscopy. Biochemistry 32: 5394-5410.

176. Separovic F & Gawrisch K (1996) Effect of unsaturation on the chain order of phosphatidylcholines in a dioleoylphosphatidylethanolamine matrix. Biophys J 71: 274-282.

177. Evans RW, Williams MA & Tinoco J (1987) Surface areas of 1-palmitoyl phosphatidylcholines and their interactions with cholesterol. Biochem J 245: 455-462.

178. Stubbs CD & Smith AD (1984) The modification of mammalian membrane polyunsaturated fatty acid composition in relation to membrane fluidity and function. Biochim Biophys Acta 779: 89-137.

179. Niebylski CD & Salem NJr (1994) A calorimetric investigation of a series of mixed-chain polyunsaturated phosphatidylcholines: effect of sn-2 chain length and degree of unsaturation. Biophys J 67: 2387-2393.

180. Holte LL, Senaka AP, Sinnwell T & Gawrisch K (1995) 2H nuclear magnetic resonance order parameter profiles suggest a change of molecular shape for phosphatidylcholines containing a polyunsaturated acyl chain. Biophys J 68: 2396-2403.

181. Zajicek J, Ellena JF, Williams GD, Khadim MA & Brown MF (1995) Molecular dynamics of vesicles of unsaturated phosphatidylcholines studied by 13C NMR spin-lattice relaxation. Cikkect Czech Chem Commun 60: 719-735.

81

182. Seelig A & Seelig J (1974) The dynamic structure of fatty acyl chains in a phospholipid bilayer measured by deuterium magnetic resonance. Biochemistry 13: 4839-4845.

183. Lafleur M, Fine B, Sternin E, Cullis PR & Bloom M (1989) Smoothed orientational order profile of lipid bilayers by 2H-nuclear magnetic resonance. Biophys J 56: 1037-1041.

184. Holte LL, Separovic F & Gawrisch K (1996) Nuclear magnetic resonance investigation of hydrocarbon chain packing in bilayers of polyunsaturated phospholipids. Lipids 31: 199-203.

185. Seelig A & Seelig J (1977) Effect of single cis double bond on the structure of a phospholipid bilayer. Biochemistry 16: 45-50.

186. van Deenen LLM, de Gier J & Demel RA (1972) Relations between lipid compositon and permeability of membranes. Biochem Soc Symp 35: 377-382.

187. Wiener MC & White SH (1992) Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. II. Distribution and packing of terminal methyl groups. Biophys J 61: 428-433.

188. Huang P, Perez JJ & Loew GH (1994) Molecular dynamics simulations of phospholipid bilayers. J Biomol Struct Dyn 11: 927-956.

189. Paddy MR, Dahlquist FW, Dratz EA & Deese AJ (1985) Simultaneous observation of order and dynamics at several defined positions in a single chain using 2H NMR of single acyl chain perdeuterated phosphatidylcholines. Biochemistry 24: 5988-5995.

190. Cheng KH & Somerharju P (1996) Effects of unsaturation and curvature on the transverse distribution of intramolecular dynamics of dipyrenyl lipids. Biophys J 70: 2287-2298.

191. Wiener MC & White SH (1992) Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. III. Complete structure. Biophys J 61: 434-447.

192. Hristova K & White SH (1998) Determination of the hydrocarbon core structure of fluid dioleoylphosphocholine (DOPC) bilayers by x-ray diffraction using specific bromination of the double bonds: effect of hydration. Biophys J 74: 2419-2433.

193. Baenziger JE, Smith ICP & Hill RJ (1987) Biosynthesis of a specifically deuteriated diunsaturated fatty acid for 2H NMR membrane studies. Biochemistry 26: 8405-8410.

194. Baenziger JE, Smith ICP, Hill RJ & Jarrel HC (1988) Direct measurement of deuterium-deuterium dipolar coupling and analysis of the ordering of a specifically deuterated diunsaturated lipid. J Am Chem Soc 110: 8229-8231.

195. Baenziger JE, Jarrel HC & Smith ICP (1992) Molecular motions and dynamics of a diunsaturated acyl chain in a lipid bilayer: Implications for the role of polyunsaturation in biological membranes. Biochemistry 31: 3377-3385.

196. Applegate KR & Glomset JA (1991) Computer-based modeling of the conformation and packing properties of docosahexaenoic acid. J Lipid Res 27: 658-680.

197. Applegate KR & Glomset JA (1991) Effect of acyl chain unsaturation on the packing of model diacylglycerols in simulated monolayers. J Lipid Res 32: 1645-1655.

82

198. Salmon A, Dodd SW, Williams GD, Beach JM & Brown MF (1987) Configurational statistics of acyl chains in polyunsaturated lipid bilayers from 2H NMR. J Am Chem Soc 109: 2600-2609.

199. McCabe MA, Griffin GL, Ehringer WD, Stillwell W & Wassal SR (1994) 2H NMR studies of isomeric ω3 and ω6 polyunsaturated phospholipid membranes. Biochemistry 33: 7203-7210.

200. Rajamoorthi K & Brown MF (1991) Bilayers of arachidonic acid containing phospholipids studied by 2H and 31P NMR spectroscopy. Biochemistry 30 : 4204-4212.

201. Litman BJ, Lewis EN & Levin IW (1991) Packing characteristics of highly unsaturated bilayer lipids: raman spectroscopic studies of multilamellar phosphatidylcholine dispersions. Biochemistry 30: 313-319.

202. Litman BJ & Mitchell DC (1996) A role for phospholipid polyunsaturation in modulating membrane protein function. Lipids 31: 193-197.

203. Mitchell DC & Litman BJ (1998) Effect of cholesterol on molecular order and dynamics in highly polyunsaturated phospholipid bilayers. Biophys J 75: 896-908.

204. Smaby JM, Momsen M, Brockman HL & Brown RE (1997) Phosphatidylcholine acyl unsaturation modulates the decrease in interfacial elasticity induced by cholesterol. Biophys J 73: 1492-1505.

205. Gelb MH, Cho W & Wilton DC (1999) Interfacial binding of secreted phospholipases A2: more than electrostatics and a major role for tryptophan. Curr Opin Struct Biol 9: 428-432.

206. Burack WR & Biltonen RL (1994) Lipid bilayer heterogeneities and modulation of phospholipase A2 activity. Chem Phys Lipids 73: 209-222.

207. Volwerk JJ, Jost PC, de Haas GH & Griffith OH (1986) Activation of porcine pancreatic phospholipase A2 by the presence of negative charges at the lipid-water interface. Biochemistry 25: 1726-1733.

208. Ghomashchi F, Yu B-Z, Berg O, Jain MK & Gelb MH (1991) Interfacial catalysis by phospholipase A2: substrate specificity in vesicles. Biochemistry 30: 7318-7329.

209. Scott DL & Sigler PB (1994) Structure and catalytic mechanism of secretory phospholipases A2. Adv Protein Chem 45: 53-88.

210. Han SK, Yoon ET, Scott DL, Sigler PB & Cho W (1997) Structural aspects of interfacial adsorption. A crystallographic and site-directed mutagenesis study of the phospholipase A2 from the venom of Agkistrodon piscivorus piscivorus. J Biol Chem 272: 3573-3582.

211. McLean LR, Hagaman KA & Davidson WS (1993) Role of lipid structure in the activation of phospholipase A2 by peroxidized phospholipids. Lipids 28: 505-509.

212. Jain MK & Jahagirdar DV (1985) Action of phospholipase A2 on bilayers. Effect of fatty acid and lysophospholipid additives on the kinetic parameters. Biochim Biophys Acta 814: 313-318.

213. Bell JD, Burnside M, Owen JA, Rovall MI & Baker ML (1996) Relationships between bilayer structure and phospholipase A2 activity: interactions among temperature, diacylglycerol, lysolecithin, palmitic acid, and dipalmitoyl-phosphatidylcholine. Biochemistry 35: 4945-4955.

83

214. Hønger T, Jørgensen K, Biltonen RL & Mouritsen OG (1996) Systematic relationship between phospholipase A2 activity and dynamic lipid bilayer microheterogeneity. Biochemistry 35: 9003-9006.

215. Lehtonen JYA & Kinnunen P (1995) Phospholipase A2 as a Mechanosensor. Biophys J 68: 1888-1894.

216. Jain MK & de Haas GH (1983) Activation of phospholipase A2 by freshly added lysophospholipids. Biochim Biophys Acta 736: 157-162.

217. Grandbois M, Clausen-Schaumann H & Gaub H (1998) Atomic force microscope imaging of phospholipid bilayer degradation by phospholipase A2. Biophys J 74: 2398-2404.

218. Waite M (1996) Phospholipases. In Biochemistry of lipids, lipoproteins and membranes. In: Vance DE & Vance J (eds) Biochemistry of lipids, lipoproteins and membranes. Elsevier, New York p 211-236.

219. Apitz-Castro R, Jain MK & de Haas GH (1982) Origin of the latency phase during the action of phospholipase A2 on unmodified phosphatidylcholine vesicles. Biochim Biophys Acta 688: 349-356.

220. Bell JD & Biltonen RL (1992) Molecular details of the activation of soluble phospholipase A2 on lipid bilayers. J Biol Chem 267: 11046-11056.

221. Burack WR, Yuan Q & Biltonen RL (1993) Role of lateral phase separation in the modulation of phospholipase A2 activity. Biochemistry 32: 583-589.

222. Sheffield MJ, Baker BL, Owen NL, Baker ML & Bell JD (1995) Enhancement of Agkistrodon piscivorus piscivorus venom phospholipase A2 activity toward phosphatidylcholine vesicles by lysolecithin and palmitic acid: studies with fluorecent probes of membrane structure. Biochemistry 34: 7796-7806.

223. Bent ED & Bell JD (1995) Quantification of the interactions among fatty acid, lysophosphatidylcholine, calcium, dimyristoylphosphatidylcholine vesicles, and phospholipase A2. Biochim Biophys Acta 1254: 349-360.

224. Henshaw JB, Olsen CA, Farnbach AR, Nielson KH & Bell JD (1998) Definition of specific roles of lysolecithin and palmitic acid in altering the susceptibility of dipalmitoylphosphatidylcholine bilayers to phospholipase A2. Biochemistry 37: 10709-10721.

225. Abrams FS, Chattopadhyay A & London E (1992) Determination of the location of fluorecent probes attached to fatty acids using parallax analysis of fluorescence quenching: effect of carbonyl ionization state and environment on depth. Biochemistry 31: 5322-5327.

226. Dijkstra BW, Renetseder R, Kalk KH, Hol WG & Drenth J (1983) Structure of porcine pancreatic phospholipase A2 at 2.6 A resolution and comparison with bovine phospholipase A2. J Mol Biol 168: 163-179.

227. Berendsen HJC, Egberts B, Marrink S-J & Ahlström P (1992) Molecular dynamics simulations of phospholipid membranes and their interaction with phospholipase A2. In: Pullman A & et.al (eds) Membrane proteins: structures, interactions and models. Kluwer Academic Publishers, p 457-470.

228. Jones ST, Ahlström P, Berendsen HJC & Pickersgill RW (1993) Molecular dynamics simulation of a phospholipase A2-substrate complex. Biochim Biophys Acta 1162: 135-142.

84

229. Zhou F & Schulten K (1996) Molecular dynamics study of phospholipase A2 on a membrane surface. Proteins 25: 12-27.

230. Hamilton JA (1995) 13C NMR studies of the interactions of fatty acids with phospholipid bilayers, plasma lipoproteins and proteins. In: Beckmann N (ed) Carbon-13 NMR spectroscopy of biological systems. Academic Press Inc., London p 117-159.

231. Lewis BA & Engelman DM (1983) Lipid bilayer thickness varies linearly with acyl chain length in fluid phosphatidylcholine vesicles. J Mol Biol 166: 211-217.

232. Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theoret Chim Acta 44: 129-138.

233. van Gunsteren W & Berendsen HJC (1977) Algorithms for macromolecular dynamics and constraint dynamics. Mol Phys 34: 1311-1327.

234. Laaksonen L (1992) A graphics program for the analysis and display of molecular dynamics trajectories. J Mol Graphics 10: 33-34.

235. Seelig J & Niederberger W (1974) Deuterium-labeled lipids as structural probes in liquid crystalline bilayers. A deuterium magnetic resonance study. J Am Chem Soc 96: 2069-2072.

236. Lehtonen JYA & Kinnunen P (1994) Changes in the lipid dynamics of liposomal membranes induced by poly(ethylene glycol): free volyme alterations revealed by inter- and intramolecular excimer-forming phospholipid analogs. Biophys J 66: 1981-1990.

237. Eklund KK, Virtanen JA, Kinnunen PKJ, Kasurinen J & Somerharju PJ (1992) Conformation of phosphatidylcholine in neat and cholesterol-containing liquid-crystalline bilayers. Application of a novel method. Biochemistry 31: 8560-8565.

238. McIntosh TJ & Simon SA (1986) Hydration force and bilayer deformation: A reevaluation. Biochemistry 25: 4058-4066.

239. Seelig J, Gally H-U & Wohlgemuth R (1977) Orientation and flexibility of the choline head group in phosphatidylcholine bilayers. Biochim Biophys Acta 467: 109-119.

240. Buldt G & Wohlgemuth R (1981) The headgroup conformation of phospholipids in membranes. J Membrane Biol 58: 81-100.

241. Hauser H, Pascher I, Pearson RH & Sundell S (1981) Preferred conformation and molecular packing of phosphatidylethanolamine and phosphatidylcholine. Biochim Biophys Acta 650: 21-51.

242. Pascher I, Lundmark M, Nyholm P-G & Sundell S (1992) Crystal structures of membrane lipids. Biochim Biophys Acta 1113: 339-373.

243. Seelig J & Browning JL (1978) General features of phospholipid conformation in membranes. FEBS Lett 98: 41-44.

244. Holopainen JM, Lehtonen JYA & Kinnunen PKJ (1999) Evidence for the extended phospholipid conformation in membrane fusion and hemifusion. Biophys J 76: 2111-2120.