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Computer Simulations of
Protein-Peptide Complexes Using the
Myosin Light Chain Protein as a Model
Thesis submitted for the degree
"Doctor of Philosophy"
by
Assaf Ganoth
Submitted to the Senate of Tel-Aviv University
July 2006
II
This work was carried out under the supervision of
Prof. Menachem Gutman
III
ACKNOWLEDGMENTS
It has been a long journey. During the journey, I was fortunate to come in touch
with a variety of people who helped me to pursuit my dreams.
It is my pleasure to thank them.
Prof. Hemi Gutman,
For guidance, unconditional support, brainstorm sessions and, most important,
believing in me. His special personality and profound knowledge accompanied me
throughout the research. I doubt I will ever be able to convey my appreciation fully,
but I owe him my scientific career.
Dr. Eti Nachliel,
For continuous help, professional advices, inspirational ideas, and endless assistance.
Ran Friedman,
For teaching me Molecular Dynamics, expert knowledge, being for me whenever I
encountered scientific problems or difficulties, and for bicycle trips.
Elad Project,
For assistance with Molecular Dynamics simulations, programming skills, and
unlimited help with solving computer problems.
Dr. Dani Canaani, Dr. Yossi Tsfadia and Prof. Rimona Margalit,
For professional and moral support during the last years. Each provided unique
insights and challenged my thinking, substantially contributing to a successful
completion of this thesis.
Finally, I would like to express my deepest gratitude to my friends in the lab, past and
present, for close collaboration: Anna Seltzer, Assaf Amitay, Cintia Sbarsky, Dana
Baron, Eran Bosis, Tom Mark, Aviv Mezer, Limor Radozkowicz, and Yael Rabin.
IV
"Two roads diverged in a wood, and I-
- I took the one less traveled by,
And that has made all the difference"
Robert Lee Frost (1874-1963)
V
TABLE OF CONTENTS
ABSTRACT IX
LIST OF ABBREVIATIONS XII
I. INTRODUCTION
1. Biological and Biochemical Background................................................................ 1
1.1 The Myosin Family......................................................................................... 1
1.2 The Myosin V Protein..................................................................................... 2
1.3 The Mlc1p Protein.......................................................................................... 5
1.4 IQ Motif Peptides............................................................................................ 6
1.5 The Calmodulin Protein.................................................................................. 7
1.6 Calmodulin-Peptide Complexes..................................................................... 8
1.7 Mlc1p-IQ Complexes...................................................................................... 9
2. Computer Simulations............................................................................................. 9
2.1 Molecular Dynamics....................................................................................... 10
2.1.1 General Overview.................................................................................. 10
2.1.2 Methodology.......................................................................................... 11
2.1.3 Molecular Dynamics of Calmodulin...................................................... 13
2.1.4 Molecular Dynamics of Calmodulin's Complexes................................. 14
2.2 Free Energy..................................................................................................... 14
2.2.1 Free Energy of Interaction..................................................................... 15
2.2.2 The MM-PBSA Approach..................................................................... 15
3. Significance of Study.............................................................................................. 16
VI
II. METHODS
1. MD Simulations...................................................................................................... 18
1.1 Simulations of Protein-Peptide Complexes.................................................... 18
1.1.1 Mlc1p-IQ2 Complex.............................................................................. 18
1.1.2 Mlc1p-IQ4 Complex.............................................................................. 19
1.2 Simulations of Peptides................................................................................... 19
1.2.1 IQ2 Peptide............................................................................................ 19
1.2.2 IQ4 Peptide............................................................................................ 20
2. Visual Presentations................................................................................................ 20
3. Inter-Helical Angles................................................................................................ 21
4. Dihedral Angle Calculations................................................................................... 21
5. The Electrostatic Potential Around the Peptides..................................................... 21
6. The Protein-Peptide Interaction Free Energies....................................................... 22
6.1 Molecular Mechanics Calculations................................................................. 23
6.2 Polar Solvation Calculations........................................................................... 23
6.3 Nonpolar Solvation Calculation...................................................................... 24
6.4 Entropy Calculations....................................................................................... 25
III. RESULTS & DISCUSSION
1. Simulations of Protein-Peptide Complexes............................................................ 26
1.1 Mlc1p-IQ2 Complex....................................................................................... 26
1.1.1 The Crystallographic and Simulated Structures..................................... 26
1.1.2 The Dynamics of the Protein-Peptide Complexes................................. 27
1.1.3 Summary................................................................................................ 29
VII
1.2 Mlc1p-IQ4 Complex....................................................................................... 30
1.2.1 Overall Conformational Changes During the Simulation...................... 30
1.2.2 Relative Rotation of the Helices During the Simulation........................ 34
1.2.3 The Structural Characteristics of the Compaction Event....................... 37
1.2.4 The Forces that Stabilize the Refolded Model Structure of the
Complex.................................................................................................
39
1.2.5 The Interactions Between Residues During the Structural Change of
the Complex...........................................................................................
44
1.2.6 MD Simulation of the Mlc1p-IQ4 Complex at 400 K........................... 47
1.2.7 Summary................................................................................................ 49
2. Comparison Between the Mlc1p-IQ2 and the Mlc1p-IQ4 Complexes................... 52
2.1 Crystallographic and Simulated Structures Comparison................................ 52
2.2 Structural Evolution of the Simulated Mlc1p Protein at the Protein-Peptide
Complexes.......................................................................................................
54
2.3 The Root Mean Square Fluctuation (RMSF) of the Mlc1p Protein at the
Protein-Peptide Complexes.............................................................................
57
2.4 The Electrostatic Field Around the IQ Peptides............................................. 60
2.5 The Protein-Peptide Interaction Free Energies............................................... 62
2.6 The Contacts Between the Protein and the Peptides....................................... 67
2.7 Summary......................................................................................................... 70
3. Simulations of Free IQ Peptides............................................................................. 72
3.1 Synopsis of the Presented Simulations........................................................... 72
3.2 Overall Conformational Changes During the Simulations............................. 73
3.3 Structural Characteristics of the Refolding Process of the IQ Peptides.......... 78
3.4 Secondary Structures of the IQ Peptides......................................................... 81
VIII
3.5 Salt Bridges Analysis of the IQ4 Peptide Simulation..................................... 84
3.6 Dynamics of the IQ4 Peptide at Different Salt Concentrations...................... 86
3.7 Summary......................................................................................................... 88
4. The Structure of the Light Chain-Binding Domain (LCBD) of Myosin V............ 89
4.1 The Current Structural Model......................................................................... 89
4.2 Structure and Dynamics of an Extended IQ4 Peptide..................................... 92
4.3 The Suggested Solution Model....................................................................... 94
4.4 Summary......................................................................................................... 96
IV. OVERALL GENERAL DISCUSSION................................................ 98
V. SUPPLEMENT............................................................................................... 102
1.1 Articles............................................................................................................ 102
(I) Ganoth, A., E. Nachliel, R. Friedman, and M. Gutman. 2006.
Molecular dynamics study of a calmodulin-like protein with an IQ peptide:
Spontaneous refolding of the protein around the peptide. Proteins 64: 133-146
(II) Ganoth, A., R. Friedman, E. Nachliel, and M. Gutman. 2006. A
molecular dynamics study and free energy analysis of complexes between the
Mlc1p protein and two IQ motif peptides. Biophys J 91:2436-2450
REFERENCES..................................................................................................... 103
IX
ABSTRACT
The Mlc1p protein, which is a member of the Calmodulin family, is an
essential component of the mechano-chemical myosin system. At the budding yeast
Saccharomyces cerevisiae, six Mlc1p proteins bind the neck domain of myosin V,
composed of six IQ motif peptides. The structures of a few Mlc1p complexes with IQ
peptides had been resolved by X-ray crystallography. The present thesis expands our
knowledge, by investigating, through molecular dynamics simulations and subsequent
calculations, of the structures, dynamics and energetics of Mlc1p-IQ complexes.
Besides grossly extending the structural data embedded in the crystalline structures,
our study provides atomistic understanding about the movement mode of myosin V
over the actin filament. We found out how bending of a specific site, located on the
neck of the myosin, can serve as the flexible joint along the myosin, securing a proper
function of its stroke lever arm.
The thesis includes four main chapters: (I) Molecular dynamics simulations of
the IQ2 and the IQ4 peptides in a complex with the Mlc1p protein; (II) A detailed
comparison between the simulations of both Mlc1p-IQ complexes; (III) Molecular
dynamics simulations of free IQ peptides; (IV) Reevaluation of the structure of the
light chain-binding domain of myosin V.
In the first chapter of the thesis, we present molecular dynamics simulations of
the Mlc1p-IQ2 and the Mlc1p-IQ4 complexes, following their relaxation in a
physiological salt solution. The Mlc1p-IQ2 complex relaxed without loosing its main
packing features, exhibiting a limited conformational change throughout the
simulation. The other complex, with the IQ4 peptide, experienced a major refolding
process, where the protein transformed its conformation from an extended to a
compact one, and the peptide was snapped into two sections. In the second chapter of
X
the thesis, we offer a detailed comparative study between the molecular dynamics
simulations of both complexes. We performed a comprehensive comparison between
the structure and the dynamics of the Mlc1p-IQ complexes and an extensive
interaction free energy analysis. The latter includes an analysis of the various forces
operating on the protein-peptide complexes by indicating their specific contributions.
In the third chapter of the thesis, molecular dynamics simulations of free IQ peptides
at different conditions for various durations are given. Variations between the
conformations of the bound and the free peptides, and differences between the
configurations that the two IQ peptides make take in solution, are discussed. The
results of the molecular dynamics simulations of the protein-peptide complexes and
the free peptides enable to assess the structural model of the light chain-binding
domain of myosin V, being composed of six complexes between light chain proteins
(such as the Mlc1p) and IQ peptides, presented in the fourth chapter of the thesis. At
the core of our suggested model stands the notion that the light chain-binding domain
is a dynamic cellular entity, and hence the proposed model incorporates the ability of
the Mlc1p protein and the IQ peptides to flex and curve in a mutual manner.
The results of the thesis were summed up in three articles. The first article,
which describes the molecular dynamics simulation of the Mlc1p-IQ4 complex, was
recently published (Ganoth, A., E. Nachliel, R. Friedman, and M. Gutman. 2006.
Molecular dynamics study of a calmodulin-like protein with an IQ peptide:
Spontaneous refolding of the protein around the peptide. Proteins 64:133-146). The
second paper presents a comprehensive comparison between the simulations of the
Mlc1p-IQ4 and the Mlc1p-IQ2 complexes, including an energetic analysis and a
reevaluation of the structure of the light chain-binding domain of myosin V (Ganoth,
A., R. Friedman, E. Nachliel, and M. Gutman. 2006. A molecular dynamics study and
XI
free energy analysis of complexes between the Mlc1p protein and two IQ motif
peptides. Biophys J 91:2436-2450 (Cover article)); A third paper, dealing with
simulations of the free IQ peptides, is in preparation.
The current research is a novel MD study of IQ peptides in a complex with a
CaM-like protein and at its absence. In view of the major role taken by the IQ
peptides in mechano-chemical processes, the thesis provides a comprehensive
description at atomic resolution for their interaction with CaM and CaM-like proteins.
The study, which portrays a computerized journey, starting from molecular dynamics
simulations and ending at physiological insights concerning myosin V, exemplifies
that cooperation between crystallographers and biophysicists may contribute to a
better understanding of structure-function relationship.
XII
LIST OF ABBREVIATIONS
APBS Adaptive Poisson-Boltzmann Solver
Apo-CaM Ca+2
-deprived CaM
ATP Adenosine Triphosphate
CaM Calmodulin
CL C-lobe
FIONA Fluorescence Imaging with One-Nanometer Accuracy
GTP Guanosine Triphosphate
Holo-CaM Ca+2
-bound CaM
ID Inter-domain
LCBD Light Chain-Binding Domain
LJ Lennard-Jones
MD Molecular Dynamics
MM-PBSA Molecular Mechanics - Poisson-Boltzmann Surface Area
mRNA messenger RNA
NL N-lobe
NMR Nuclear Magnetic Resonance
PB Poisson-Boltzmann
PDB Protein Data Bank
PME Particle Mesh Ewald
RMSD Root Mean Square Deviation
RMSF Root Mean Square Fluctuation
SASA Solvent Accessible Surface Area
SMFP Single Molecule Fluorescence Polarization
SPC Single Point Charge
XIII
TFP Trifluoperazine
VdW Van der Waals
VMD Visual Molecular Dynamics
1
I. INTRODUCTION
1. Biological and Biochemical Background
1.1 The Myosin Family
Within all eukaryotic cells, the generation of mechanical force is provided by
specific motor proteins necessary for performing vast array of sub-cellular tasks required
to sustain life. The motors that move along actin filaments make up a diverse protein
family, collectively referred to as myosins (1). The myosin family of molecular motors
consists of at least 20 structurally and functionally distinct classes. Myosins have been
implicated in a variety of intra-cellular functions, including cell migration and adhesion,
intra-cellular transport and localization of organelles and macromolecules, signal
transduction, and tumor suppression. The myosins constitute a large family of actin-
dependent motors found in many organisms from yeast to humans. Upon interaction with
actin filaments, they convert energy from ATP hydrolysis into mechanical force
(reviewed in (2)).
The first identified motor protein was skeletal muscle myosin, which is
responsible for generating the force for muscle contraction (3). This protein, called
myosin II (for two-headed), was also found in non-muscle cells, including protozoan
cells. Myosin II is composed of two heavy chains; each bears a globular motor domain
that includes a binding site for ATP and a domain that interacts with actin. Two light
chains wrap around the elongated neck region of each heavy chain. In the late 1970's (4),
one-headed myosin (called myosin I), was found in the fresh water amoeba
Acanthamoeba castellanii. Myosin I is considered an unconventional myosin since it
functions as a monomer and consists of very short neck domain. Since then, many other
2
myosin types were discovered. The new types of myosins include a number of one-
headed and two-headed varieties that are related to myosin I and myosin II, and the
nomenclature now reflects their approximate order of discovery (myosin III through at
least myosin XX).
The myosin tails (and the tails of motor proteins generally) have apparently
diversified during evolution to permit the proteins to dimerize with other subunits and to
interact with different cargoes. Some myosins (such as VIII and XI) have been found
only in plants, and some are exclusive to vertebrates (IX). However, most of them are
common to all eukaryotes, suggesting that myosins arose early in eukaryotic evolution
(reviewed in (5, 6)).
1.2 The Myosin V Protein
The family of myosin V is a class that differs structurally from other myosins by
having an extended neck domain and a tail domain that allows dimerization, but not the
formation of filaments due to the presence of a globular carboxy-terminus. Members of
the myosin V family have been identified in humans, mice, chickens, flies, fungi, worms,
yeast and plants. The myosin V proteins are molecular motors involved in a range of
organelle-transporting functions, including the transport of melanosomes and synaptic
vesicles in mammals and vacuoles and mRNA in yeast (reviewed in (7, 8)). Myosin V is
essential for transport of vesicles in actin-rich cortical regions of neurons, i.e. dendritic
spines and axon termini. Moreover, vesicle-associated myosins, like myosin V, may do
more than serve as mechanical feet, transporting vesicles from one location to another
along actin tracks. They may interact with membrane-associated F-actin to "stitch"
3
membranes together during membrane fusion (9), and to sort proteins from the fluid
phase into lipid rafts during the assembly of membrane protein complexes (10). Based on
phylogenetic analysis of the myosin family, myosin V evolved after myosins II and I, the
two most ancient members of the myosin super-family (1, 11).
Myosin V is composed of two identical heavy chains, each one is capable of
binding six light chains (reviewed in (12, 13)). The two heavy chains dimerize to produce
a two-headed protein consisting of three distinct domains (Fig. 1).
The first domain is the head domain (green), the second domain constitutes the
neck (red), and third domain is the tail domain (colored yellow for its proximal and
medial modules, and blue for its distal module). When bound to the actin filaments, it has
the ability to convert the energy released by ATP hydrolysis into mechanical work, i.e.
Figure 1: A cartoon diagram of myosin V. The three domains are color coded: the head
domain is green, the neck domain is red, and the tail domain is yellow/blue. The light
chains, which engulf the neck domain, are colored in gray.
4
movement (14). Successive cycles of ATP hydrolysis allow the two heads to "step" on
the actin filament towards its barbed or plus end (15).
The head domain of myosin V contains ATP and actin binding sites (16). Since
the force required for transport of cargoes is generated in the head domain, it is often
referred also as motor domain. The neck domain contains six repeating amino acid
sequences called IQ motifs (designated IQ1-IQ6), each of which binds a light chain. The
light chains have been shown to be CaM or CaM-like proteins, and their primary function
is to regulate the ATPase activity of the globular heads (17, 18). According to the lever
arm hypothesis (19, 20), the step size of myosin V motors is proportional to the length of
the neck domain, which functions as a lever. The long neck domain of myosin V gives
rise to a step size of ~ 36 nm, the largest step size thus far measured for a myosin motor.
Not surprisingly, the step size of myosin V shortens when one or more of the IQ motifs
from the neck domain is truncated (21).
It has been clearly established that myosin V motors from vertebrates are
processive, i.e. have a long duty cycle, enabling it to undergo multiple steps before
dissociating from the actin filament. This allows a single motor to transport cargo, in ~ 36
nm steps, for several micrometers along the actin filament (20). Yet, not all class V
myosins are processive. A recent kinetic analysis of myosin V from drosophila concluded
that it is not a processive motor (22). The two classes of myosin V from the yeast
Saccharomyces cerevisiae, Myo2p and Myo4p (the former is the myosin V discussed in
this research), have been reported to be low duty non-processive motors, based upon
motility and landing rate assays (23).
The tail domain can be divided into two modules: proximal/medial and distal. The
5
proximal/medial module is the site of dimerization of the two heavy chains. In this
module of the tail, alpha-helical regions of the heavy chains are predicted to interact to
form a coiled coil segment that is interrupted by small globular regions (16). A PEST site,
which has been shown to be a cleavage site for the calcium-dependent protease calpain
(14), is located in the N-terminus of the proximal/medial tail module. The proximal/distal
module of the tail domain, in addition to its primary role in dimerization, also serves as
the link between the neck domain and the cargo-binding module of the tail. The distal
module of the tail domain is the cargo-binding domain (24). When bound to vesicles by
the distal tail module, myosin V becomes part of a large proteinous complex that includes
the membrane receptor.
1.3 The Mlc1p Protein
The Mlc1p protein is a CaM-like protein from the budding yeast Saccharomyces
cerevisiae, associated with the yeast's mechano-chemical myosin system. It was
originally identified as a light chain protein of the Myo2p protein, which is a myosin type
V (25). The Mlc1p protein is essential for viability and secretory vesicle delivery at the
mother bud neck domain during cytokinesis due to its ability to bind to the IQ motifs of
the Myo2p protein (26). While calcium binding to CaM promotes its binding/release
to/from the IQ motifs, the Mlc1p protein is unable to bind calcium since its EF-hand
motifs are abortive (27, 28). The signal that stimulates its interaction with target IQ
motifs is still unknown, but recently it was found that its interaction with the Myo2p
protein is mediated by GTP (29). Though also the exact function of the Mlc1p protein has
not been clarified yet, it is assumed that its binding to the neck domain of the Myo2p
6
protein has a stabilizing effect on the latter (25). The three-dimensional structure of the
Mlc1p was determined when it was co-crystallized with the IQ2, IQ2/3 and IQ4 peptides
of the Myo2p protein (28). The Mlc1p protein shares a structural similarity with CaM;
both possess a dumbbell-shaped conformation, consisting N- and C- globular lobes
(referred, at the thesis, as NL for the N-lobe and CL for the C-lobe) that are connected by
a flexible inter-domain (referred, at the thesis, as ID).
1.4 IQ Motif Peptides
The IQ motifs constitute common target peptides for CaM and CaM-like proteins.
These motifs are widely distributed among different kinds of proteins, contributing >3700
Pfam entries in the database (30). The motifs are ~ 25 amino acids long, alpha-helical,
and carry a net positive charge. They conform to the general consensus sequence
IQXXXRGXXXXR, but in many cases, the sequence is rather loosely adhered to this
consensus. For example, the isoleucine in the first position is frequently replaced by other
branched-chain amino acids (leucine or valine) or, rarely, by a methionine. The arginines
in both the sixth and the terminal positions are sometimes replaced by lysine or histidine,
and the seventh position glycine is poorly conserved. Despite the lack of strict
conservation, there is no doubt that this sequence is a recognizable protein motif that
binds CaM and CaM-related proteins, such as Troponin C and myosin light chains.
IQ motifs are present in a number of neuronal growth proteins, sodium and
calcium voltage-dependent channels, EF-hand-containing protein phosphatases, spindle
pole and centrosomal proteins, transient receptor potential proteins, plant cyclic
nucleotide-regulated channels, certain signaling molecules, and at the neck region of the
7
myosins. In most cases, the IQ motifs appear in tandem repeats, and therefore enable to
bind multiple copies of CaM and CaM-like proteins. IQ motifs were first identified as
Apo-CaM (Ca+2
-deprived CaM) binding sites; however, it is now clear that IQ motifs can
show different levels of Ca+2
dependency (31-33).
1.5 The Calmodulin Protein
The Calmodulin (CaM) protein is recognized as a prototypical calcium sensor and
regulation orchestrator of cellular events through its interaction with a diverse group of
proteins. The CaM protein is a small (16.7 kDa), highly acidic, ubiquitous, evolutionary
conserved protein. It is considered as the major calcium sensor and is expressed in all
eukaryotic cells, where it participates in signaling pathways that regulate crucial
processes such as growth, proliferation, and movement. The concentration and location of
CaM appear to play an important role in regulating its biological activity. CaM
constitutes at least 0.1% of the total protein present in cells (10-6
M – 10-5
M) and is
expressed at even higher levels in rapidly growing cells, especially those undergoing cell
division and differentiation. The local intra-cellular availability of CaM is likely to be
biologically significant because various CaM-dependent proteins are regulated over a
wide range of CaM concentrations. The dynamics of CaM and its interactions with target
proteins had been extensively studied (reviewed in (34, 35)).
CaM and CaM-like proteins belong to a family of soluble proteins that share a
common structure. These proteins are built of three structural domains: the NL, the CL,
and an elongated, mostly helical, ID that connects the two lobes to form a dumbbell-like
shape. Each lobe possesses two Ca+2
-binding domains, each of which is made of two
8
helix-loop-helix EF-hand motifs. These proteins are present at two configurations: a
dumbbell extended state, where the ID is stretched; and a folded configuration, where the
ID bends, bringing the lobes into close contact. The CaM and CaM-like proteins can form
protein-protein complexes with specific target peptides, a reaction that is a key event in
many intra-cellular regulatory processes. On the binding of Ca+2
and in the presence of
target peptides, the CaM undergoes a conformational change that enables it to bind its
target. This basic mechanism activates well over 100 distinct target proteins. However, in
some cases (as at the Mlc1p protein), the reaction with target peptides can be mediated by
the Apo-CaM. The promiscuity of CaM on one hand, and binding specificity on the other
hand, made it one of the most studied proteins (reviewed in (36-38)).
1.6 Calmodulin-Peptide Complexes
Investigations of the CaM protein in a complex with different bound peptides
have been carried out by genetic methods, such as site-directed mutagenesis of the
protein (39-41), or the target peptide (42-44), and their thermodynamical properties were
explored (45, 46). In addition to these studies, the structure of the protein-peptide
complexes was investigated by NMR (47), and crystallographic studies (48-54). These
studies revealed that, upon binding of the peptides, the ID of Holo-CaM (Ca+2
-bound
CaM) adopts a bent conformation accompanied by its partial unwinding. The bending of
the ID brings together the two lobes of the protein. Thus, the flexibility of the ID region is
critical for the ability of CaM to interact with target peptides. The various aspects of these
interactions, such as recognition and activation, are reviewed by Vetter et al. (55).
9
1.7 Mlc1p-IQ Complexes
The structure of the Mlc1p protein was solved by X-ray crystallography in
complexes with the IQ2, IQ2/3, and IQ4 peptides (28, 56). These Mlc1p-IQ protein-
peptide complexes were formed and crystallized in the absence of Ca+2
ions. According
to these structures, when bound to the IQ2 peptide, the Mlc1p protein adopts a compact
conformation in which both the NL and CL interact with the IQ motif. However, in the
complex with the IQ4 peptide, the NL of the protein does not interact with the IQ motif,
resulting in an extended conformation of the protein. Based on these crystal structures,
combined with comparative sequence analysis, a model for the entire poly-IQ (IQ1-IQ6)
sequence of the neck domain of myosin V, together with six light chain proteins, was
built (57). The model of the Light Chain-Binding Domain (LCBD) of myosin V has
important implications for the understanding of the structure-function relationship of the
lever arm of myosin V. In the present study, the crystal structures of the Mlc1p-IQ4,
Mlc1p-IQ2 and the model of the LCBD are discussed, analyzed, and reevaluated.
2. Computer Simulations
Dynamic simulation methods are widely used to obtain information on the time
evolution of conformations of proteins and other biological macromolecules (58-61), as
well as kinetic and thermodynamic information. Simulations can provide fine details
concerning the motions of individual particles as a function of time. They can be utilized
to quantify the properties of a system at a precision and on a time scale that is otherwise
inaccessible, providing a valuable tool in extending our understanding of model systems.
Theoretical computational consideration of a system additionally allows one to
10
investigate specific contributions of property through “computational alchemy” (62), that
is, modifying the system in a way that is nonphysical but nonetheless allows a model’s
characteristics to be probed.
2.1 Molecular Dynamics
MD simulations have become valuable tools for investigating the basis of protein
structure and function. Given the structure of a biomolecular system, that is, the relative
coordinates of the constituent atoms, MD is used to investigate and study the dynamics of
that system. A brief outline of its history and methodology is offered below.
2.1.1 General Overview
The conformational dynamics of proteins, which is encoded in their structures, is a
critical element of their function. A fundamental appreciation for how proteins work
requires an understanding of the connection between three-dimensional
structures,
obtained by X-ray crystallography and NMR, and dynamics, which is much more difficult
to probe experimentally. Molecular Dynamics (MD) simulations provide links
between
structure and dynamics by enabling the exploration of
the conformational energy
landscape accessible to protein molecules (59, 63, 64). The first MD simulation of a
protein was reported in the year 1977 and consisted of a 9.2-ps trajectory for
a small
protein in vacuum (65). Eleven years later, a 210-ps simulation of the same protein in
water was reported (66), and the phenomenal increase in computing power since then
makes it routine to run simulations of much larger proteins for 1000-10000 times longer
than the original simulation (tenths of nanoseconds), in which the protein is surrounded
11
by water and salt. Significant improvements in the potential
functions have also been
achieved, making the simulations much more stable and accurate (67).
Biomolecular dynamics simulations find two major areas of application today.
Firstly, MD simulations are used to bring biomolecular structures alive, giving insights
into the natural dynamics on different timescales of biomolecules in solution. Secondly,
MD simulations can explore which conformations of a molecule or a complex are
energetically accessible, by searching the conformational space. Driven by improvements
in simulation methodology, increasing accuracy of biomolecular force fields and the
ever-increasing power of computers, MD simulations is a rapidly progressing scientific
discipline. Nowadays, it is well established that MD is not a mere historical phenomenon,
but an important fundamental developing field of science (68-71).
2.1.2 Methodology
We briefly sum up the methodology of MD, but for a comprehensive inclusive
literature the reader is referred to (72, 73). MD simulations calculate the "real" dynamics
of the system, from which time averages of properties can be calculated. Sets of atomic
positions are derived in sequence by applying Newton's equations of motion. MD is a
deterministic method, i.e. the state of the system at any future time can be predicted from
its current state. The first MD simulations were performed using very simple potentials
such as the hard-sphere potential. The behavior of the particles in this potential is similar
to that of billiard balls: the particles move in straight lines at a constant velocity between
collisions. The collisions are perfectly elastic and occur when the separation between a
pair of spheres equals the sum of their radii. After a collision, the new velocities of the
12
colliding spheres are calculated using the principle of conservation of linear momentum.
The hard-sphere model has provided many useful results but is obviously not ideal for
simulating atomic or molecular systems. In potentials such as the Lennard-Jones (LJ)
potential, the force between two atoms or molecules changes continuously with their
separation. The continues nature of more realistic potentials requires the equations of
motion to be integrated by breaking the calculation into a series of very short time steps
(in our simulations the time step was usually 2-fs). At each step, the forces operating on
the atoms are computed and combined with the current positions and velocities to
generate new positions and velocities. The force acting on each atom is assumed to be
constant during the time interval. The atoms are then moved to the new positions; an
updated set of forces is computed, and so on. In this way, an MD simulation generates a
trajectory that specifies how the positions and velocities of the particles in a system
change with time.
In biomolecular simulations, such as presented in this study, successive
configurations of the system are produced by iterative numerical calculations of
instantaneous forces present in a molecular mechanical system and the consequential
movements in that system. The molecular mechanical system consists of a set of particles
that move in response to their interactions according to the equations of motion defined in
classical Newtonian laws of motion. Newton's laws of motion can be stated as follows:
(I) A body continues to move in a straight line at a constant velocity unless a force acts
upon it.
(II) Force equals the rate of change of momentum.
(III) To every action there is an equal and opposite reaction.
13
The trajectory is obtained by solving the differential equation embodied in
Newton's second law (F = m·a):
(1)
Equation 1 describes the motion of a particle of mass (mi) along one coordinate
(xi) with (Fxi) being the force on the particle in that direction.
2.1.3 Molecular Dynamics of Calmodulin
The unique structure of CaM and its fundamental role in Ca+2
-signaling processes
has also drawn the attention of computational scientists besides the experimental
biologists and biochemists. Early MD simulations of Holo-CaM confirmed the flexibility
of its ID (74-76). However, due to limited computational power available at that time,
these simulations were carried out over sub nanosecond time scales and included
relatively few, if any, water molecules. In the recent decade, MD simulations of CaM
were extensively performed under more realistic conditions, addressing issues concerning
the relative positions of its NL and CL and the nature of its flexible ID. In the year 1996,
Van Der Spoel et al. (77) performed an MD simulation of the ID of Holo-CaM, and
observed its bending. Since this pioneering MD simulation of CaM in an aqueous
solution, simulations of Apo- (78, 79) and Holo- CaM (79-87) have been performed for
durations ranging from hundreds of picoseconds to 20-ns. These MD studies
demonstrated the unwinding and curvature of the ID of the protein. Moreover, it was
found out that, although bound Ca+2
ions harden the structure of the protein, it collapses
i
Xi
m
F
dt
xdi=
2
2
14
to a form resembling a dumbbell with a hinged bar connecting its lobes.
2.1.4 Molecular Dynamics of Calmodulin's Complexes
Only a few MD simulations of CaM together with target molecules or peptides
had been performed. An MD simulation of CaM-TFP complex was carried out,
comparing the binding affinities of the NL and CL of Holo-CaM to TFP (88). The
binding dynamics of melatonin to Holo-CaM were examined by means of MD after
molecular docking (89). The dynamics and entropy of a Holo-CaM complexed with a
peptide were studied by NMR and MD. A good agreement was found between amide
order parameters measured by NMR, and those obtained from the simulation (90).
Finally, an MD simulation of a complex between Holo-CaM and a peptide examined the
structure, dynamics and the interaction mode between the protein and the peptide. In a 4-
ns MD simulation, the CaM-peptide complex was quite rigid and did not exhibit any
large amplitude domain motions (91, 92).
2.2 Free Energy
The calculation of free energy from molecular simulations is an area of intense
research activity (reviewed in (93)). This is because free energy is at once one of the most
central and one of the most difficult thermodynamic quantities to compute from atomic
level simulations. It is of paramount importance in efforts to relate microscopic details
stemming from atomic interactions to measurable macroscopic quantities, and to
understand the physical and structural basis of biological phenomena. In particular, free
energy of interaction is a measure of the stability of a complex, a measure that is
15
fundamental to all studies of biomolecular binding processes.
2.2.1 Free Energy of Interaction
The interactions between proteins and other molecules are critical to all biological
systems and processes. Signal transduction, metabolic regulation, enzyme cooperativity,
physiological response, and other processes are all dependent upon noncovalent binding.
These processes may be investigated through modeling and computer simulations. At this
study, we estimate interaction free energy for the protein-peptide complexes through MD
simulations and complementary computation techniques. Approaches available for
estimating interaction free energies cover a broad range of accuracies and computational
requirements. Given that the purpose of this research is not to carry a comparative study
of interaction free energy calculations' techniques, but rather use the interaction free
energy to characterize the protein-peptide complexes, we chose to calculate the
interaction free energy in a nonrigorous technique, called the MM-PBSA approach.
2.2.2 The MM-PBSA Approach
Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) is basically
a post-processing method to evaluate the standard free energies of molecules or the
interaction free energies of molecular complexes in a relatively computationally efficient
manner. The MM-PBSA approach was developed by Srinivasan and co-workers in 1998
(94). Since then, it has been widely used for estimation of free energies of different RNA
(94), DNA (95, 96) and protein conformations (97), binding affinities of protein
complexes and mutational analysis on them (98-102), binding affinities of small
16
compound-protein complexes (103, 104), interaction free energies of RNA-protein (105),
RNA and metal ions (106), and RNA-ligand (107) complexes. The strategy of
calculations is based on applying of a continuum model to solute configurations derived
from an MD simulation in explicit solvent. For each selected solute configuration,
molecular mechanics energy is determined. Free energies of solvation are estimated by
using Poisson-Boltzmann (PB) calculations for the electrostatic contribution and a
surface-area-dependent term for the nonelectrostatic contribution to solvation. Solute
entropic contributions are estimated from a normal mode analysis. To get a statistically
meaningful value of the interaction free energy of a complex, calculations are commonly
carried out on several snapshots extracted from an MD trajectory with explicit solvent.
3. Significance of Study
The general significance of this research lies in the fact that it demonstrates that
careful application of MD can be used for evaluation of proteinous structures, offering
close analysis as well as deeper insights of crystalline configurations. We have employed
a multi-stage approach in order to investigate the Mlc1p-IQ complexes. For this purpose
we performed MD simulations of the Mlc1p-IQ2 complex, the Mlc1p-IQ4 complex, and
the free IQ2 and IQ4 peptides at various conditions. Our MD simulations enable to
propose solution conformations of protein complexes, which were not offered by X-ray
crystallography studies. Besides grossly expanding the structural data embedded in the
crystalline configurations of these protein complexes, our study provides detailed analysis
of the protein-peptide interaction energy, and atomistic understanding about the
movement mode of myosin V over the actin filament. Thus, this research, which starts
17
from MD simulations and ends at an enlightment of the dynamic aspects of a
physiological phenomenon, illustrates the biophyiological relevance of the MD
methodology.
18
II. METHODS
1. MD Simulations
1.1 Simulations of Protein-Peptide Complexes
1.1.1 Mlc1p-IQ2 Complex
The MD simulations were performed using the GROMACS 3.2.1 package of
programs (108-110), with the GROMOS96 43a1 force field (111). The crystal structure
of the Mlc1p protein bound to an IQ2 peptide of the Myo2p protein (PDB file 1M45),
determined by X-ray crystallography at 1.65 Å (56), was downloaded from the Protein
Data Bank (112). Four missing residues (D-50, S-51, R-54, D-55) were added to the
structure using the PROFIX program, which is incorporated in the JACKAL molecular
modeling package (113). The protein-peptide complex was embedded in a box containing
the SPC water model (114), that extended to at least 12 Å between the protein-peptide
structure and the edge of the box. Assuming normal charge states of ionizable groups
corresponding to pH 7, the net charge of the Mlc1p-IQ2 structure is -7e. Hence, 35
sodium and 28 chloride ions were added to the simulation box at random positions, to
neutralize the system at a physiological salt concentration of ~ 100 mM. Prior to the
dynamics simulation, internal constraints were relaxed by energy minimization.
Following the minimization, an MD equilibration run was performed under position
restraints for 40-ps. Then, an unrestrained MD run was initiated. The first 100-ps of the
run were treated as a further equilibration simulation, and the remainder 12-ns were saved
and used for the analysis. During the MD run, the LINCS algorithm (115) was used in
order to constrain the lengths of all bonds; the waters were restrained using the SETTLE
algorithm (116). The time step for the simulation was 2-fs. The simulation was run under
19
NPT conditions, using Berendsen's coupling algorithm for keeping the temperature and
the pressure constant (117) (P = 1 bar; τP = 0.5 ps; τT = 0.1 ps; T = 300 K). Van der
Waals (VdW) forces were treated using a cutoff of 12 Å. Long-range electrostatic forces
were treated using the PME method (118). The coordinates were saved every 1-ps.
1.1.2 Mlc1p-IQ4 Complex
The simulations' conditions for the Mlc1p-IQ4 protein-peptide complex were the
same as those for the Mlc1p-IQ2 protein-peptide complex. The calculations were carried
out using the crystal structure of the Mlc1p protein bound to an IQ4 peptide of the Myo2p
protein (PDB code 1M46) determined by X-ray crystallography at 2.1 Å (56), that was
downloaded from the Protein Data Bank (112). The net charge of the complex is -3e, and
hence 43 sodium and 40 chloride ions were added in random positions to neutralize the
system at a physiological salt concentration of ~ 100 mM. The simulations were
performed at two temperatures, 300 K and 400 K. The simulations' conditions were
similar at both temperatures, except for the time step and τP that, at the 400 K, were 1.5-fs
and 2-ps, respectively.
1.2 Simulations of Peptides
1.2.1 IQ2 Peptide
The coordinates for the IQ2 peptide were derived from the crystal structure of the
Mlc1p-IQ2 protein-peptide complex. The net charge of the IQ2 peptide is +2e, and hence
13 sodium and 15 chloride ions were added in random positions to neutralize the system
at a physiological salt concentration of ~ 100 mM. The conditions of the simulation were
20
similar to those described for the Mlc1p-IQ2 complex.
1.2.2 IQ4 Peptide
The coordinates for the IQ4 peptide were derived from the crystal structure of the
Mlc1p-IQ4 protein-peptide complex. MD simulations were performed at various
conditions as elaborated on Table 1. The net charge of the IQ4 peptide is +6e, whereas
the number of ions that were added at the simulations varied according to the specific
conditions of each simulation. The conditions of the simulations were similar to those
described for the Mlc1p-IQ4 complex.
Table 1
Summary of the MD Simulations of the IQ Peptides
* High temperature (400 K). †
Low salt concentration. ‡
High salt concentration. ¶ Very high salt concentration.
§ An IQ4 peptide containing 10 additional amino acids flanking each of its terminals was
built using Swiss PDB Viewer (119). These added 20 residues belong to the IQ3 and IQ5
peptides. Thus, the 45 amino acids elongated IQ4 peptide constitutes a portion of the
poly-IQ sequence as present at the neck of the myosin.
2. Visual Presentations
All protein and peptides figures were created using the VMD computer program
(120).
Duration (ns)
Concentration
of Salt
Number of
added Na+
ions
Number of
added Cl-
ions
IQ4 peptide 100 ~ 100 mM 12 18
IQ4 peptide * 30 ~ 100 mM 12 18
IQ4 peptide † 20 ~ 30 mM 4 10
IQ4 peptide ‡ 20 ~ 300 mM 36 42
IQ4 peptide ¶ 20 ~ 2.4 M 288 294
Extended IQ4 peptide § 20 ~ 100 mM 10 17
21
3. Inter-Helical Angles
For the protein-peptide complexes, inter-helical angles were calculated according
to the following procedure: The secondary structure of the protein and the peptide were
determined using the STRIDE algorithm (121). Three residues were selected at the N-
and C- terminals of each alpha helix. The C-alpha atoms' center of mass of each triplet of
residues was determined. A vector-defining-helix was drawn between these centers of
mass along each helix. The inter-helical angle was calculated between each two
successive vectors. For the IQ peptides, intra-helical angle was calculated according to
the same procedure.
4. Dihedral Angle Calculations
The position of the protein’s lobes towards each other can be expressed by
measuring the dihedral angle between the planes defined by the two lobes and the ID.
Each plane was defined by the straight section of the ID and a selected representative
residue located at each lobe. The C-alpha atoms of residues N-47, L-58, and V-69 defined
one plane; whereas the C-alpha atoms of residues L-58, V-69, and E-129 defined the
other. The calculation of the dihedral angles was performed for the last snapshot of the
simulations at t = 12-ns using a standard GROMACS utility.
5. The Electrostatic Potential Around the Peptides
The electrostatic potential around the IQ peptides was calculated for the model
structures of the peptides as derived from the Mlc1p-IQ protein-peptide simulations. The
coordinates of 21 snapshot structures, extracted every 100-ps from t = 10 until t = 12-ns,
22
were used for the electrostatic potentials calculations. The electrostatic potential surface
around each peptide was calculated by solving the nonlinear Poisson-Boltzmann (PB)
equation through the use of the APBS (Adaptive Poisson-Boltzmann Solver) software
package (122) with a grid spacing of 0.5 Å. The volumes of the averaged positive and
negative electrostatic fields of both peptides (for the time frame t = 10 until t = 12-ns) and
the Coulomb cages at the last snapshot (t = 12-ns) of the simulations are presented.
6. The Protein-Peptide Interaction Free Energies
The general strategy used for calculating the protein-peptide interaction free
energy is based on the MM-PBSA method. This method was successfully employed by
numerous studies (94-107), and involves calculating energies for snapshot configurations
taken from the MD trajectories of the Mlc1p-IQ complexes. The configurations of the
protein-peptide complexes, the protein and the peptides were obtained from the MD
simulations of the Mlc1p-IQ2 and the Mlc1p-IQ4 structures. The coordinates of 21
snapshot model structures, extracted at 100-ps intervals during the last 2-ns of the
simulations, where both complexes appeared to gain a stable configuration, were used for
the calculations. The calculations, which were performed for each of these snapshots and
their average values are presented, were intended for estimation of the protein-peptide
free energy interaction.
The changes in the Gibbs free energy of interaction were calculated from the
atomic model structures of the protein and the peptide undergoing the binding to form the
protein-peptide complex. Thus, the free energy of interaction was defined as presented in
equation 2:
23
(2) ∆Ginteraction = (Gcomplex) − (Gprotein) − (Gpeptide)
The calculations of the free energy of each molecule were carried out according to
equation 3:
(3) TSGGE)(G solvation nonpolar,solvation polar,MMmolecule −⟩⟨+⟩⟨+⟩⟨=
where the free energy was decomposed into molecular mechanics (⟨EMM⟩), polar
solvation (⟨Gpolar,solvation⟩), nonpolar solvation (⟨Gnonpolar,solvation⟩) and entropy (TS)
contributions. ⟨ ⟩ denotes an average over a set a snapshots along an MD trajectory. Each
term on the right side of the equation was calculated as detailed below.
6.1 Molecular Mechanics Calculations
The molecular mechanics contribution to the free energy of interaction energy
was calculated according to equation 4:
(4) ⟩⟨+⟩⟨+⟩⟨=⟩⟨ VdWticelectrostaintMM EEEE
(⟨Eint⟩) includes bond, angle, and torsional angle energies, while (⟨Eelectrostatic⟩) and
(⟨EVdW⟩) denote the intra-molecular electrostatic and VdW energies. (⟨Eelectrostatic⟩) was
calculated using the APBS software package (122). (⟨EVdW⟩) was calculated using a
standard GROMACS utility.
6.2 Polar Solvation Calculations
The electrostatic contribution to the solvation energy, (⟨Gpolar,solvation⟩), was
determined by using a continuum electrostatic with the Poisson-Boltzmann (PB)
approach (123). We used the APBS software package (122), with a grid spacing of 0.5 Å
and solution of 100 mM NaCl, for the numerical solution of the nonlinear PB equation.
24
The term (⟨Gpolar,solvation⟩) refers to the energy associated with the transfer of the solute
from a continuum medium with a low dielectric constant (ε = 4) to a continuum medium
with the dielectric constant of water (ε = 78.4).
Crucial to the application of PB models, and a source of many scientific disputes,
is the so-called macromolecule dielectric constant, ε. It is generally accepted that, in a
continuum electrostatics approach, the dielectric constant of the solute is a scaling factor
that represents all the contributions that are not treated explicitly, rather than a true
dielectric constant (124, 125). Different protein-associated dielectric constants are
frequently used in the literature, and we chose to perform the calculation with a dielectric
constant of 4 as commonly employed (123, 126-128). To make sure that the conclusions
derived from our calculations are not dependent upon the choice of the value used, we
repeated the calculation for representative snapshots with a lower (ε = 2) and a higher (ε
= 8) dielectric constants. Comparison between the results indicated that, although the
value of the calculated (⟨Gpolar,solvation⟩) varies with ε, its trend is independent from the
dielectric constant used.
6.3 Nonpolar Solvation Calculations
The nonpolar contribution to the solvation free energy, (⟨Gnonpolar,solvation⟩), was
determined by using the Solvent Accessible Surface Area (SASA). The SASA was
calculated by a standard GROMACS utility, which implements the double cube lattice
method (129) with a probe radius of 1.4 Å. The nonpolar solvation energy was described
as Gnonpolar,solvation= γ·(SASA) + β. The constants γ and β are 2.2 kJ mol-1
nm-2
and 3.84 kJ
mol-1
, respectively. These values of γ and β are in accord with the MM-PBSA approach
25
(101, 103-105, 107).
6.4 Entropy Calculations
Entropy changes upon binding of the peptide were calculated by use
of normal mode analysis. The conformations of the protein, the peptide and
the protein-peptide complex were extracted from the last frame of each of the trajectories
as performed in (101). The model structures were subjected to rigorous energy
minimization, until the maximal force operating on an atom was less than 10-6
kJ mol-1
nm-1
. Normal mode analysis (130-132) was performed by calculating and diagonalizing
the mass-weighted Hessian matrix. The frequency of the normal mode was then used to
calculate the vibration entropy (133) as given by equation 5:
(5)
where Svib is the vibrational entropy, h is Planck's constant, ν0 is the frequency of the
normal mode, k is the Boltzmann constant, T is the absolute temperature and NA is
Avogadro's number. All calculations were performed with the GROMACS program,
compiled with double precision.
)T(
hvN)(R
vibee
eS /kThv
/kThv
A/kThv
0
0
0
11ln
0
−
−
−
−+−−=
26
III. RESULTS & DISCUSSION
1. Simulations of Protein-Peptide Complexes
In this chapter of the thesis, we describe an investigation, through MD
simulations, of the dynamics of two Mlc1p-IQ complexes: the Mlc1p-IQ2 and the Mlc1p-
IQ4 complexes.
1.1 Mlc1p-IQ2 Complex
The Mlc1p-IQ2 complex, which had been resolved by crystallography to 1.65 Å,
confers to a Ca+2
-independent stable structure. Its 12-ns MD simulation is presented.
1.1.1 Crystallographic and Simulated Structures
The crystallographic structures and those obtained by the simulations of the
Mlc1p protein with the IQ2 peptides are presented in Fig. 1.1. The NL, the ID, the CL
and the IQ peptides are colored in blue, red, green and yellow, respectively.
At the crystalline structure of the Mlc1p-IQ2 complex (Fig. 1.1A), the Mlc1p
protein is found at a compact state as evident by its curved ID. In this configuration, the
CL of the protein engulfs the IQ2 peptide, which interacts also with the NL and the ID of
the protein. Overall, the configurations of the Mlc1p protein and the IQ2 peptide only
slightly change throughout the 12-ns long simulation, and hence their final simulated
state structures (Fig. 1.1B) resemble the crystalline ones. Thus, the simulated structure of
the Mlc1p-IQ2 complex exhibits just a few minor conformational deformations compared
to its crystalline structure. These deformations consist of appearance of a new kink
located at helix D of the protein's ID (Fig. 1.1B, see arrow), a consequent rotation of the
27
NL, and minor changes of the inter-helical angles observed mainly at its CL, as
elaborated below.
1.1.2 The Dynamics of the Protein-Peptide Complexes
A quantitative expression of the conformational change is given by the RMSD
(Root Mean Square Deviation) of the backbone atoms of the protein-peptide complexes.
Fig. 1.2A depicts the RMSD values as calculated for the whole Mlc1p-IQ2 complex
(black), and its components: the Mlc1p protein (red), and the IQ2 peptide (green). The
RMSD of the protein-peptide complex exhibits some structural fluctuations that can be
fully attributed to the Mlc1p protein. It increases until ~ 0.35 nm, stays around this value
for ~ 4-ns, decreases for a short while and then stabilizes at ~ 0.28 nm. The RMSD track
Figure 1.1: Cartoon diagrams of the crystal and the simulated structures of the Mlc1p
protein when it binds the IQ2 peptide (PDB 1M45). The NL (residues 1−59), the ID
(residues 60−92), the CL (residues (93−148), and the IQ peptide are shown in blue, red,
green and yellow, respectively. Both crystal structures, and both simulated solution
structures, are presented with the same orientation, where the NLs are structurally
aligned. (A) The crystal structure of the Mlc1p-IQ2 complex; (B) The simulated
structure of the Mlc1p-IQ2 complex after 12-ns simulation. The arrow points towards a
kink discussed at the text.
B A
C-lobe
N-lobe Inter-domain
28
of the IQ2 peptide, which contributes little to the RMSD of the complex, exhibits a
different pattern. It appears to explore the configurational space until ~ 3.2-ns, and then
increases to a value of ~ 0.23 nm. From this time point until the end of the simulation, the
RMSD of the IQ2 peptide is relatively stable.
The fluctuations of the Mlc1p protein can be resolved into a contribution of its
structural domains. Accordingly, the RMSD of its NL (black), ID (red), and CL (green)
are presented in Fig. 1.2B.
The RMSD of the NL exhibits a sharp increase at ~ 5-ns, and then stabilizes at a
value of ~ 0.24 nm. The RMSD of the ID, which is the flexible domain of the Mlc1p
protein, hardly changes. The stability of the ID throughout the simulation time is not
surprising since its structure is already bent and curved at the Mlc1p-IQ2 protein-peptide
A B
Figure 1.2: (A) The RMSD of the backbone atoms of the Mlc1p-IQ2 complex (black), the
Mlc1p protein (red), and the IQ2 peptide (green) as a function of the simulation time; (B)
The RMSD of the backbone atoms of the different domains of the Mlc1p protein as a
function of the simulation time. The domains of the protein are defined as follows: residues
1−59 for the NL (black), 60−92 for the ID (red), and 93−148 for the CL (green).
29
crystalline structure. Apparently, the CL is much more flexible than the other structural
domains, exhibiting the largest variations in its RMSD value. Inspection of the Mlc1p-
IQ2 model structure reveals that most of its eight alpha helices retain their structures and
the angles between them, except the angles found at the CL. The angle between its G and
H helices increases from ~ 100° at the beginning of the simulation to ~ 115° at the end of
it. The angle between its E and F helices changes from ~ 110° to ~ 123° during the time
frame of 2.7 until 5.5-ns, but settles back at its original value. The fluctuations of the
RMSD of the CL are due to these inter-helical motions.
1.1.3 Summary
Overall, the configurations of the Mlc1p protein and the IQ2 peptide barely
change throughout the 12-ns long simulation. This relative stability of the complex
inspired us to perform MD simulation for another complex, the Mlc1p-IQ4 complex,
which is composed of the same protein and a slightly different peptide.
30
1.2 Mlc1p-IQ4 Complex
The Mlc1p-IQ4 complex, which had been resolved by crystallography to 2.1 Å,
confers to a Ca+2
-independent stable structure. During its MD simulations, the complex
undergoes a complicated modulation process, which involves bending of the angles
between the alpha-helices of the protein, breaking of the alpha-helical structure of the
IQ4 peptide into two sections, and formation of new contact points between the protein
and the peptide. The dynamics of the process consist of fast sub picosecond events and
much slower ones that take a few nanoseconds to completion. Our study expands the
information embedded in the crystal structure of the Mlc1p-IQ4 complex by describing
its dynamic behavior as it evolves from the crystal structure to a form stable in solution.
1.2.1 Overall Conformational Changes During the Simulation
Fig. 1.3 depicts the structure of the Mlc1p-IQ4 complex as present in the crystal
structure (Fig. 1.3A), and after 12-ns of simulation at 300 K (Fig. 1.3B). The structures
were aligned over their NLs, to present them from the same orientation. In its crystalline
configuration, the Mlc1p-IQ4 complex, (PDB file 1M46), has an extended structure,
where the IQ4 peptide is mainly bound to the CL of the Mlc1p protein (for details see
Fig. 1.3 below). The ID (residues 60−92, colored red) that connects the NL (1−59,
colored blue) with the CL (residues 93−148, colored green) is a straight alpha helix. The
IQ4 peptide (colored in yellow) also keeps a straight alpha helix configuration,
perpendicular to the long axis of the ID. It forms few contacts with the CL and the ID of
the Mlc1p protein. At the end of the 12- ns simulation, the complex reached a new
conformation. The most stable part of the Mlc1p-IQ4 complex is the NL, which even
31
after 12-ns retained most of its original conformation and its contact points with the N-
terminal section of the ID. The ID had refolded, so that its two helices (helices D and E),
became perpendicular each to the other and are in contact with the NL and CL. The CL
itself rotated and refolded into a shape that engulfs the IQ4 peptide, snapping its straight
helix into two, almost perpendicular sections. In the final configuration, the number of
contact points between the peptide and protein increased and the three sections of the
protein are in contact with the peptide.
The modulation of the protein and peptide with time can be followed by
examination of the backbone RMSD relative to the crystal structure. Fig. 1.4A depicts the
RMSD values as calculated for the whole complex (black), and its components: the
A
C-lobe
N-lobe
Inter-domain
B
Figure 1.3: Cartoon diagram of the crystal and the simulated structures of the Mlc1p
protein bound to the IQ4 peptide (PDB 1M46). The N-lobe, the inter-domain, the C-lobe,
and the IQ4 peptide are shown in blue, red, green, and yellow, respectively. The domains
of the protein are defined as residues 1–59, NL; 60–92, ID; and 93–148, CL. (A): The
crystal structure; (B): The simulated structure at 300 K after the 12-ns simulation in the
presence of water and ions. Both structures are presented with the same orientation.
32
Mlc1p protein (red) and the IQ4 peptide (green).
Some 3.2-ns after the initiation of the simulation, the RMSD trace reveals a major
structural modulation. The RMSD value of the entire Mlc1p-IQ4 complex and that of the
Mlc1p protein almost double (from ~ 0.4 to ~ 0.7 nm). The rise continues in a moderate
fashion till the end of the simulation. In contrast to the complex and the protein, the
RMSD calculated for the IQ4 peptide (green line) exhibits different dynamics. The trace
A B
C D
Figure 1.4: (A) The RMSD of the backbone atoms of the Mlc1p-IQ4 complex (black), the
Mlc1p protein (red), and the IQ4 peptide (green) as a function of the simulation time; (B)
The RMSD of the backbone atoms of the different domains of the Mlc1p protein as a
function of the simulation time. The domains of the protein are defined as residues 1−59
for the NL (black), 60−92 for the ID (red), and 93−148 for the CL (green); (C) Expansion
of frame B between 2- and 3.5- ns; (D) The RMSD of the backbone atoms of the last two
ns of the simulation (10−12 ns) relative to the position of the same set of atoms at t = 10-
ns.
33
reveals a reversible increment at ~ 1.75-ns, followed by a minor response to the structural
change of the Mlc1p protein at 3.2-ns. A short time later, the peptide undergoes some
structural modification, which increases its RMSD to ~ 0.4 nm. From this time point on,
the RMSD of the peptide is practically constant. The fact that the RMSD values of the
peptide hardly reflect the transition detected in the RMSD of the Mlc1p protein, implies
that the structural changes are driven by the Mlc1p protein itself, as evident in Fig. 1.4B.
Fig. 1.4B presents the RMSD values of the structural elements of the protein: the
NL, the CL and the ID as shown (marked in black, green and red, respectively). The NL
and the CL exhibit only moderate deviations from their initial structures, reaching, at the
end of the simulation, RMSD values of ~ 0.27 nm and ~ 0.36 nm, respectively. The ID
section of the protein is much more flexible than the lobes, as its RMSD exhibits large
variations before and after the conformational change of the complex. These events are
depicted with higher temporal resolution in Fig. 1.4C. During the 2.1−2.8-ns time
interval, the ID flexes for a very short time. Its RMSD increases to > 0.3 nm, but
eventually the ID relaxes to its original structure. Within this time frame, the CL slowly
regains a new conformation, roughly doubling its RMSD from 0.1 to 0.2 nm. Once the
new conformation of the CL was attained, the next structural modulation of the ID
appears to lead to the main conformational change at t ~ 3.2-ns. The RMSD of the CL
further increases and, after a short delay, the NL undergoes its conformation change.
Thus, the structural transition process experiencing the protein-peptide complex is
composed of a set of sequential steps, not a concerted motion.
Once the complex had reached its new stable conformation, the protein and the
peptide do not exhibit further major conformational changes. The calculation of the
34
backbone RMSD value for the last 2-ns of the simulation, relative to the backbone heavy
atoms’ position at t = 10-ns, reveals only moderate deviations around 0.25 nm (Fig.
1.4D). This is an indication that, in the refolded state, the complex does not sample many
other conformations but rather settles down to a stable configuration with no further
evolution.
1.2.2 Relative Rotation of the Helices During the Simulation
The Mlc1p protein, like CaM, consists of 8 well-defined helices (A−H).
Inspection of the Mlc1p-IQ4 complex's structure (Fig. 1.3) reveals that most of the alpha
helices retained their structure. The variations of the RMSD reflect mostly the rotation of
the helices one with respect to the other. This motion can be expressed in changes of the
angle between the helices. Thus, in order to examine the relative rotation of the helices
during the simulation, we have calculated the inter-helical angles between each
successive pair of them, and present the results in Fig. 1.5A−C. A snapshot from the time
point t = 12-ns is shown on the right of each panel in order to highlight the discussed
helices. It should be noted that the cartoon diagram of the Mlc1p-IQ4 complex is
presented solely clarification purposes, and we can not deduce the angle itself from it.
The first three helices (A−C) are located at the NL, which hardly experienced
conformational changes (see Fig. 1.3). The angles between the helices of this lobe barely
changed throughout the simulation course (data not shown). The angle between the NL
and the first helix of the ID was also stable with time, and not affected by the structural
transition of the complex. The rest of the protein was more flexible, and the dynamics of
the relative motions of its helices is presented in Fig. 1.5. The first global motion of the
35
Mlc1p protein is a slow (~ 1-ns), ~ 35° modulation in the F-G angle (Fig. 1.5A),
representing a deformation of the CL (~ 1−2 ns). Immediately later, this angle exhibits a
reversible bending, a process that may be considered as a preparation for the major
structural deformation event. This event is characterized by rotations of two pairs of
helices (D vs. E and G vs. H).
A
F G
B
D
E
C
H
G
D
N-section
C-section
Figure 1.5: The dynamics of the relative rotation of the alpha helices of the Mlc1p
protein and the IQ4 peptide during the 12-ns simulation time. In order to clarify which
angle is presented on each panel, a cartoon diagram of the complex after 12-ns of
simulation is shown on the right of each panel in black, whereas the discussed helices
are shown in the domain's characteristic color. (A) The inter-helical angle between
helix F (residues 102−111) and helix G (residues 119−126) of the CL; (B) The inter-
helical angle between helix D (residues 60−70) and helix E (residues 81−92) of the
ID; (C) The inter-helical angle between helix G (residues 119−126) and helix H
(residues 138−147) of the CL; (D) The inter-helical angle between the N- (residues
3−8) and C- (residues 18−23) sections of the IQ peptide.
36
The D and E helices are the components of the ID, with a hinge located between
them at residues 71−80. This hinge exhibits a considerable flexibility, demonstrated by
NMR studies of Apo-CaM (134, 135), crystal structures of Holo-CaM by itself (136) and
in a complex with peptides (49, 50), and MD simulations of Apo- and Holo-CaM (78,
81). Hence, it is well established that the ID is a flexible bar rather than a stiff stick. Also
in the present simulation the hinge flexes, initiating the collapse of the extended structure.
The angle between the helices of the ID increases by almost 80° within 400-ps starting at
~ 3.2-ns (Fig. 1.5B). This bending leads to the refolding of the dumbbell-like shape of the
Mlc1p protein to its final model solution structure.
Another pair of rotating helices (G and H) is located at the CL (Fig. 1.5C). The
angle between them decreases gradually by ~ 50° during a time frame that precedes the
major structural change event (~ 2−3 ns). This change is followed by a sharp increase in
the angle, corresponding with the snapping of the straight helix of the peptide into two,
almost perpendicular, sections.
In order to demonstrate the modulation of the IQ4 peptide during the simulation,
two alpha helices, in its N- and C- sections, were defined. The angle between them is
presented in Fig. 1.5D. The IQ4 peptide, which at the initial state consists of a single
alpha helix, shows a significant flexibility. Its straight alpha helical structure is snapped
in its middle during the complex's structural transition, in a process that is slightly
delayed with respect to the major conformational change, when the two shorter helices
attain an almost perpendicular relation. The process, in which the angle between the
helices increases from ~ 20° to ~ 70°, is sharp and quick.
The major conformational change of the Mlc1p protein is preceded by reversible
37
changes at the RMSD values of the ID (Fig. 1.4C), and the inter-helical angle between
helices of the CL (Figs. 1.5A and 1.5C). Analysis of these events shows that the protein
undergoes several minor conformational changes that precede the major conformational
modulation. These changes may be needed to allow the modulation of the protein
structure, and to enable the structural change (i.e. the accumulation of many minor
changes drives the major refolding of the complex). It is of interest to point out that the
rotation of the CL protein’s helices (Figs. 1.4A and 1.4C) precedes the sharp rise at the
RMSD values (Figs. 1.3A−C), and then proceeds, although after that the RMSD function
seemed to reach constant values. This may indicate that the structural modulation of the
structure is not an instantaneous event, but rather a complex “Plate Tectonics”, whereas
the forces are operating well before and after the deformation event.
1.2.3 The Structural Characteristics of the Compaction Event
The variations of three major structural characteristics of the Mlc1p protein with
simulation time (namely, the length of its ID, the distance between its N- and C- lobes'
centers of mass, and its gyration radius) are presented in Fig. 1.6A.
A B
Figure 1.6: (A) The modulation of the structure of the Mlc1p protein as a function of the
simulation time. ID's length (green); Distance between the NL center of mass and the CL
center of mass (red); Radius of gyration (black); (B) Solvent Accessible Surface Area
(SASA) of the structure of the Mlc1p-IQ4 complex as a function of the simulation time.
38
As the ID of the Mlc1p protein experiences the most dramatic changes of
structure, we quantified its contraction during the simulation. The distance between the
first and the last alpha carbons of the ID of the protein was followed throughout the
course of the 12-ns simulation (Fig. 1.6A, green). The ID gradually shortens from 4.77 to
2.78 nm, demonstrating a significant conformational flexibility. The flexible ID
extensively curves, bringing the two lobes of the Mlc1p protein closer. The approach of
the lobes towards each other is also expressed by a decline of the distance between the
mass centers of the NL and the CL of the protein (Fig. 1.6A, red), from 4.11 to 2.99 nm.
This modulation reflects the transition from the extended complex structure at the crystal
to a more compact structure at the end of the simulation. The decrease of the distance
between the lobes occurs due to a twist of the ID. This can be manifested by calculation
of the gyration radius of the Mlc1p protein (Fig. 1.6A, black), which drops from 2.22 to
1.78 nm. The decrease in the radius of gyration demonstrates the decline in the overall
dimension of the Mlc1p protein. Overall, the conformational change at t ~ 3.2 ns leads to
a compaction of the protein. This can be observed by variations of the ID's length, the
distance between the N- and C- lobes' centers of mass, and the gyration radius.
The effect of the compaction of the protein on the Solvent Accessible Surface
Area (SASA) of the complex was calculated for both the hydrophobic and the hydrophilic
residues, and the combined SASA is presented in Fig. 1.6B. Both parameters exhibited a
significant reduction. The total SASA decreased with time, exhibiting a sharp drop (at t ~
3.2-ns) of the surface area within less than 100-ps from ~ 112 nm2 to ~ 102 nm
2. The time
point of this drop is associated with the major structural change of the complex. This
suggests that when one inspects the SASA criteria, taken as a whole, the structural
39
change is quick rather than gradual.
The dynamics of the various parameters reflecting the contraction, as presented in
Fig. 1.6A, demonstrate that the structural changes are not an instantaneous event, but
rather a prolonged event stretching over ~ 1500-ps (~ 2.5-4 ns). Thus, the transition that
appears to be rapid when the RMSD (as displayed in Figs. 1.4A−C), the inter-helical
angles of the protein and the peptide (Figs. 1.5B and 1.5D), or the SASA (as displayed in
Fig. 1.6B) are examined, is actually a sum of individual steps as presented in Fig. 1.6A.
Some aspects of the overall compaction are abrupt, while other aspects are gradual. What
is more, after the major contraction takes place, the protein-peptide complex continues to
reshape for a long period. This shows that the post compaction relaxation is also a
complex, multi-component process.
1.2.4 The Forces that Stabilize the Refolded Model Structure of the Complex
To gain a comprehensive evaluation of the energetic aspects of the structural
modulation process, one needs to examine not only the protein-peptide complex but also
its interaction with the solvent, and the solvent-solvent interactions. However,
determination of parameters such as the solvent's cavitation energy, solvent's entropy,
solvation energy and the Long-Range electrostatic energies in a periodic system pose
both practical and conceptual difficulties when dealing with MD simulations. Therefore,
we shall limit our discussion only to certain specific aspects of the protein's energy, being
aware that only part of the overall system is analyzed. Accordingly, the variations of the
contraction of the protein in terms of VdW interactions (the Lennard-Jones component of
the potential energy), electrostatic interactions (Short-Range Coulomb potential), and
40
entropy changes are presented below.
The Lennard-Jones (LJ) component of the potential energy interaction among the
residues of the Mlc1p protein, and the LJ component of the potential energy of the
protein-peptide interaction, are presented in Figs. 1.7A and 1.7B, respectively. The LJ
contribution to the potential energy, calculated for the interaction between the residues of
the Mlc1p protein, is changing rapidly, covering the time frame associated with the major
contraction event (Fig. 1.7A). The gain in stability, due to the better interaction between
hydrophobic residues of the Mlc1p protein, is ~ 200 kJ/mol. The contraction also
increases the contact between the protein and the IQ4 peptide, a process that contributes a
similar amount of stabilization but follows a different time course (Fig. 1.7B). Instead of
a rapid formation of LJ stabilization energy, the process is stretched over ~ 4-ns, slowly
gaining its final level. Thus, the slow evolution of the LJ stabilization, in a time frame
where there is hardly a change at the RMSD value, is attributed to minor rearrangements
of the side chains; these small motions make a large contribution to the stabilizing
energy. The LJ potential of the peptide with itself was constant in time (data not shown).
Figure 1.7: The contribution of the Lennard-Jones interactions to the stabilization of the
refolded model state of the Mlc1p-IQ4 complex. (A) The LJ component of potential
energy of the interactions among the residues of the Mlc1p protein; (B) The LJ
component of potential energy of the interactions between the Mlc1p protein and the
IQ4 peptide.
B A
41
The contribution of the Short-Range (SR) electrostatic interactions to the stability
of the contracted complex is rather small (Fig. 1.8). However, it should be mentioned that
the mode of calculation is more qualitative than quantitative as described below.
The Coulomb SR intra-complex electrostatic interactions between the charges on
the protein and the peptide exhibit a transient nature. As the structural elements of the
system shift their relative position (2.5–4 ns time frame), there is a gradual decrease of
the overall electrostatic potential. Yet, when the side chains readjust (4–6 ns time frame),
the Coulomb SR potential increases and becomes less favorable. This leads to initial and
final levels of the overall electrostatic interactions being about the same.
Though the calculation of the Coulomb SR interactions was performed using a
cut-off of 12 Å, inspection of the variation of the Coulomb SR interactions, calculated for
longer cut-off distances (14, 16, 18, and 20 Å), revealed pattern similar in shape with that
presented in Fig. 1.8. As the amplitude of the electrostatic potential varies with the cut-off
distance, the values presented in Fig. 1.8 should not be taken as a quantitative
Figure 1.8: The electrostatic potential of the Mlc1p-IQ4 complex as a function of the
simulation time. The data is a summation of all Short-Range Coulomb potentials
between charges on the complex.
42
representation of the electrostatic interactions. Apparently, the qualitative description of
the process is independent of the cut-off used. Thus, we conclude that the overall
electrostatic potential responses transiently to the structural modification process,
relaxing after few nano-seconds to its original value. According to our simulation results,
the stabilization of the Mlc1p-IQ4 complex is the sum of VdW interactions and a
transient variation of the electrostatic potential of the system. However, the VdW
interactions seem to be the dominant stabilizing force operating on the complex, while
the electrostatic interactions exhibit reversible changes. Apparently, the stability gained
by the rearrangements of the side chains, located both on the Mlc1p protein and on the
IQ4 peptide, follows the major changes of the main structural elements of the protein.
While the compaction event is brief, the LJ forces leading to the refolding operating for a
relatively long time.
In addition to the potential energy and electrostatic terms, one should also
consider the entropic changes associated with the compaction of the complex's structure.
The refolding of the protein and the tighter packing of its side chains reduced the freedom
of motion of the interacting residues, thus affecting the entropy of the system. To
estimate the contribution of this term, we calculated the entropy of the protein-peptide
complex (prior to and following the compaction event). These calculations indicated that
the entropy of the complex decreased, upon compaction, from an average value of 26.02
± 0.16 kJ mol-1
K-1
(calculated in time frames of 1000-ps between 1000 and 3000 ps) to
25.31 ± 0.29 kJ mol-1
K-1
(calculated in time frames of 1000-ps between 4000 and 12000
ps). This is equivalent to an entropic destabilization of the refolded conformation by ~
210 kJ/mol (300 K). The decrease of the complex’s entropy is due to formation of a
43
tighter, more compact conformation of the refolded protein. However, the entropy of the
solvent, which cannot be directly obtained from the MD simulation, is likely to increase
upon the compaction event due to release of water molecules from the protein's surface to
the bulk.
To account for the release of water molecules from the solvation layer of the
Mlc1p protein, its first solvation layer was defined as a 2.8-Å-thick shell around it. The
number of water molecules found within the solvation layer, as it varies with time, is
presented in Fig. 1.9.
It can be seen that the compaction process is accompanied with a sharp decrease
in the number of water molecules that are in the VdW contact with the protein. Some 20
water molecules are released from the interface of the protein to the bulk at a time point
associated with the major structural modification event. Besides the abrupt fast reduction,
a slow trend of a decrease in the number of water molecules in the solvation layer
throughout the time is also observed. The detachment of the water molecules from the
Water Molecules at the First Hydration Shell
Figure 1.9: The number of water molecules at the first solvation layer (2.8Å) of the
Mlc1p protein as a function of the simulation time.
44
hydration shell of the solute and their rejoining to the solvent, produce an entropic
advantage for the new, refolded model structure of the protein-peptide complex.
Apparently, the release of water molecules from the solvation layer compensates for the
reduction at the protein's entropy, thus assisting in the overall free energy balance.
1.2.5 The Interactions Between Residues During the Structural Change of the
Complex
The detailed interactions between individual residues of the Mlc1p protein and the
IQ4 peptide were followed at three stages: at the crystal structure, during the simulation
but before the compaction event (from the beginning of the simulation till 2-ns), and at
the last half of the simulation when the new compact configuration was already formed
(6−12-ns). For each state we listed the residues on the peptide which are in contact (less
than 4 Å) with the protein. In the case of the crystal structure, we searched for present
contacts between residues at the static presentation. For the simulated solution structures,
either before or after the compaction, we chose to present only contacts between residues
that were present in at least 80 % of the snapshots. This restriction eliminated transient
interactions that make a negligible contribution to the stabilization of the compacted
complex. The results are summarized in Fig. 1.10.
At the crystal structure, 31 contacts between the IQ4 peptide and the Mlc1p
protein are found (Fig. 1.10A). 24 of these contacts involve the CL of the protein (green),
and the rest are with residues of ID (red). During the MD simulation, the complex
underwent an initial relaxation and assumed the initial solution model structure, in which
the number of contacts between the IQ4 peptide and the CL was reduced to 18 (Fig.
45
1.10B), 3 of them not being present at the crystal structure. In this intermediate state, the
number of contacts with the ID was reduced to 5.
Figure 1.10: Contacts between residues of the IQ4 peptide with side chains of the
Mlc1p protein. The residues of the protein are marked by their location for identification
of their presence. The color code: NL (blue), ID (red), CL (green). (A) Contacts (less
than 4 Å) between residues of the Mlc1p protein and the bound IQ4 peptide obtained
from the crystal structure PDB 1M46; (B) Contacts (less than 4 Å) between residues of
the Mlc1p protein and the bound IQ4 peptide obtained from the simulation at t <= 2 ns.
Only contacts persist at least 80 % of the examined period are presented; (C) Contacts
(less than 4 Å) between residues of the Mlc1p protein and the bound IQ4 peptide
obtained from the simulation at t >= 6 ns. Only contacts persist at least 80 % of the
examined period are presented. In Figs. 1.10B and 1.10C, contacts that are common for
the solution states and the crystal structure, are marked by bold letters.
46
After the structural transition of the complex's structure, the number of contacts
between the peptide and the protein increased to 42 (Fig. 1.10C). 25 of these contacts are
with the CL, 4 new contacts are with the NL (colored in blue), and 13 with the ID (8 of
which were not present at the crystal structure). It is of interest to point out that the
residues 21−23 of the IQ4 peptide, which at the crystallized complex made no contacts
with the Mlc1p protein, interacted with its CL during the simulation.
Each of the interactions summarized in Fig. 1.10 had its own time evolution. Most
of the contacts appear in conjunction with the major structural transition event, yet in
some cases the interaction appears to be composed from more than two states. Hence, in
order to examine more closely the interaction between the amino acids formed the
contacts presented in Fig. 1.10, the minimal distances between all of the pairs were
followed as a function of time. Two representative examples are shown in Fig. 1.11.
As presented in Fig. 1.11A, the interaction of R4 (of the IQ4 peptide) with N36
(located at the NL of the Mlc1p protein) has at least two states. Before the compaction
event, the distance between the residues was larger than 1 nm; after that, it fluctuated
wildly since there was no interaction between the residues. At t ~ 3.2-ns, the structural
deformation of the complex' model structure imposed a stable separation of ~ 0.7 nm
between the residues. Yet, at t ~ 5-ns, a new structural organization took place and atoms
of the two residues almost reached a contact of their VdW radii (d = 2.5 Å). A different
scenario was observed concerning the interaction of Q10 of the IQ4 peptide (a conserved
residue of the IQ family), with residue F92 (located at the ID of the Mlc1p protein),
presented in Fig. 1.11B. In this case, the approach of the two residues towards each other
is a slow, gradual process, which resembles the slow evolution of the LJ stabilization of
47
the complex (Fig. 1.7B). Apparently, the initiation of the approach precedes the structural
deformation event, yet proceeds for several ns.
1.2.6 MD Simulation of the Mlc1p-IQ4 Complex at 400 K
CaM and CaM-like proteins are rather stable and, in some cases, their purification
employs a brief boiling of the proteins’ mixture (137-139). Most of the proteins, unlike
the CaM and CaM-like proteins, cannot stand this treatment and precipitate. To check
whether the elevated temperature may cause further structural changes of the protein, and
detect changes not observed at 300 K, we repeated the simulation at 400 K.
According to our simulation results, the elevated temperature does not affect the
refolding mechanism of the protein-peptide complex, but rather its rate. Fig. 1.12A
depicts the structure of the Mlc1p-IQ4 complex after 12-ns of simulation at 400 K., while
superposition between the structures of the complex at both temperatures is presented on
Fig. 1.12B. Inspection of the model structure of the complex at the end of the simulation
A B
Figure 1.11: Representative examples of contacts between the IQ4 peptide and the
Mlc1p protein as a function of the simulation time. (A) Minimal distance between
residue R4 of the peptide and residue N36 of the protein; (B) Minimal distance between
residue Q10 of the peptide and residue F92 of the protein.
48
Figure 1.12: (A) Cartoon diagram of the Mlc1p protein bound to the IQ4 peptide (PDB
file 1M46). Simulated model structure, after 12-ns of MD simulation at 400 K in the
presence of water and ions. The NL, the ID, the CL and the IQ4 peptide are shown in
blue, red, green and yellow, respectively. The domains of the protein are defined as
residues 1−59, NL; 60−92, ID; and 93−148, CL. Structure is presented with the same
orientation as in Fig. 1; (B) Superposition of the cartoon diagrams of the simulated model
structures of the Mlc1p-IQ4 complexes at 300 K and 400K. The Mlc1p protein and the
IQ4 peptide at 300 K are shown in black and gray, respectively; whereas the Mlc1p
protein and the IQ4 peptide at 400 K are shown in red and orange, respectively. (C) The
backbone atom RMSD of the different domains of the Mlc1p protein as a function of the
simulation time, for the MD simulation at 400 K. The NL, ID and CL of the Mlc1p
protein are shown in black, red and green, respectively.
A
C B
at 400 K reveals similarity with the 300 K simulation: 1. The Mlc1p protein lost its
extended configuration, exhibiting a compact configuration; 2. The NL retained two of its
helices and a good contact with the N-terminal section of the peptide; 3. The ID folded in
a mode similar to that gained at 300 K; 4. The CL retained its three helices while
engulfing the IQ4 peptide; 4. At the elevated temperature the IQ4 peptide lost a fair
fraction of its alpha helix structure. Yet, as can be seen from the superimposed structures,
it is located between the lobes of the protein at both temperatures.
49
The mechanism of the conformational transition is basically comparable at the
two temperatures with a clear acceleration at the higher temperature. The RMSD values,
calculated for the structural elements of the protein: the NL, the CL and the ID (marked
in black, green and red, respectively), are presented in Fig. 1.12C. The quick rise of the
RMSDs of the structural elements of the protein within the first nano-second of the
simulation, especially that of the ID, illustrates the fast alternation of the protein's initial
structure when the temperature is elevated. Evidently, the RMSDs of the MD simulation
at 400 K increased at the beginning of the simulation to levels achieved only after ~ 3.2-
ns by the MD simulation at 300 K. A careful analysis of the trajectories at both
simulations reveals high similarity. Moreover, since also the final level of RMSDs is akin
at both simulations, we suggest that the modulation's speed of the complex' structure is
temperature-dependent.
1.2.7 Summary
In the present study we investigated, through MD simulations, the dynamics of a
complex between a CaM-like protein and its target peptide, the IQ4 peptide. This
complex, which is a Ca+2
-independent stable structure, underwent a complicated
structural transition process. The process appeared to be initiated by fluctuations of the
model structure in the multi-dimensional parameter space, with no clear triggering event.
Once the proper situation was attained, the reaction became unidirectional and the system
gained stability in few steps. Only 15 out of 31 contact points detected at the crystal
structure were retained in the solution model structure, while 27 new interactions were
established. The structural modification of the complex involved bending of the angles
50
between the alpha helices of the Mlc1p protein, and breaking of the alpha helical
structure of the IQ4 peptide into two, almost perpendicular sections. Some of the
structural changes coincide with the main conformational transition event. This event was
preceded by preparatory events that proceed in time, and followed by some “after-
shocks” that helped to seal and stabilize the refolded model structure.
It is likely that the progression of the simulation, even before the major structural
transition event, included stepwise preparatory steps. Since the MD simulation at 400 K
yielded a final conformation similar to the one at 300 K, we suggest that the pattern of the
structural transition is embedded as an inherent instability of the crystal structure of the
Mlc1p-IQ4 complex. Once the restraints imposed by the crystallization conditions were
released, the system progressed into a stable model solution structure at a temperature-
dependant rate.
The refolding of the protein-peptide complex is composed of both fast, sub pico-
seconds events, and also slow events that take up a few ns. The stabilization of the
compact state is mostly hydrophobic in nature, although electrostatic interactions also
take part in this process. The main deformation is probably directed by introductory
events, followed by the rapid process of compaction. The continuing stabilization of the
protein-peptide complex can be considered as optimization of the packing of the refolded
model structure, minimizing the LJ potential energy by local shuffling of atoms at the
Mlc1p-IQ4 complex contact surface. These proceeding events help to “close the deal”,
thus completing the process till a new configuration is formed.
The number of residues involved in the interaction between the IQ4 peptide and
the Mlc1p protein is much larger than the number of conserved residues that define the
51
IQ motif. What is more, the 4 conserved motif residues L9, Q10, R14 and R20 contribute
only 15 out of the 42 contact points that stabilize the refolded complex. Apparently, the
plethora of residues that participate in the interaction between the Mlc1p protein and the
IQ4 peptide allows some tolerance to a single point mutation of a given site.
We wish to note that the proposed simulated model solution structure of the
Mlc1p-IQ4 complex presented in this study differs from its crystalline structure. Our
suggested solution model structure resembles structures of Holo-CaM and Apo-CaM in a
complex with peptides, obtained by NMR (47) and crystallography studies (48-54).
Moreover, the crystal structure of the Mlc1p protein in a complex with the IQ2 peptide
(28, 56) is similar to the simulated model structure of the Mlc1p-IQ4 complex. However,
experimental methods, like Dynamic Light Scattering or NMR, may be carried out to
verify the proposed simulated model solution structure of the Mlc1p-IQ4 complex.
Nevertheless, this kind of experiments is beyond the scope of the present study.
52
2. Comparison Between the Mlc1p-IQ2 and the Mlc1p-IQ4 Complexes
In this chapter of the thesis, the MD simulations of the Mlc1p-IQ2 and the Mlc1p-
IQ4 are compared. The crystal and the simulated structures are judged against each other,
the dynamic properties of both complexes are described, and a comprehensive energetic
detailed analysis using the MM-PBSA approach is presented.
2.1 Crystallographic and Simulated Structures Comparison
The crystallographic structures and those obtained by the simulations of the
Mlc1p protein with the IQ2 and IQ4 peptides are presented at the previous chapter of the
thesis. At the crystal state of the Mlc1p-IQ2 complex, the protein assumes a compact
state; while at the crystal state of the Mlc1p-IQ4 complex, the Mlc1p confers to an
extended configuration. These distinctive states can be attributed either to complex-
specific interactions, to the different crystallization conditions of each complex (28, 56),
or to a combination of both. A close examination of the crystal and simulated structures
of both protein-peptide complexes (Fig. 2.1) reveals that, following the simulations, the
protein’s model structures are more similar than in their crystalline states.
The calculated backbone atoms RMSD between the Mlc1p proteins found at the
Mlc1p-IQ2 and the Mlc1p-IQ4 crystal structures (Figs. 2.1A and 2.1C), is as large as
1.296 nm. However, this value drops to 0.959 nm when calculated between the solution
model of the protein after 12-ns simulations (Figs. 2.1B and 2.1D). A value of 0.959 nm
may still seem to be quite high, but it should be noted that, due to the shape of the
protein, any attempt to align two of its structures is expected to result in a relatively high
RMSD. Therefore, the decline of the RMSD from 1.296 nm to 0.959 nm is structurally
53
notable, as seen in Fig. 2.1. On the top of the RMSD calculation, other structural
indicators (such as length of the ID, distance between the lobes center-of-mass and
gyration radius) were calculated for the crystal and the simulated structures of the protein
(data not shown). All these point out that the solution configurations of the Mlc1p protein
are more similar than its crystalline ones. Additionally, it should be mentioned that the
simulated model structures of the protein acquire special conformational features not
present in either of the crystals. Besides exhibiting a common compact form of the
simulated protein, during the simulations a new kink appears at both of its model
structures (Figs. 2.1B and 2.1D, see arrow). This kink is missing from the crystal
structures of neither of the Mlc1p-IQ complexes.
A CB D
Figure 2.1: Cartoon diagrams of the crystal and the simulated structures of the Mlc1p
protein when it binds the IQ2 peptide (PDB 1M45), and the IQ4 peptide (PDB 1M46).
The NL (residues 1−59), the ID (residues 60−92), the CL (residues (93−148), and the IQ
peptides are shown in blue, red, green and yellow, respectively. Both crystal structures,
and both simulated solution structures, are presented with the same orientation, where
the N-lobes are structurally aligned. (A) The crystal structure of the Mlc1p-IQ2
complex; (B) The simulated model structure of the Mlc1p-IQ2 complex after 12-ns
simulation; (C) The crystal structure of the Mlc1p-IQ4 complex; (D) The simulated
model structure of the Mlc1p-IQ4 complex after 12-ns simulation. The black arrows in
frames B and D mark the kink of helix D.
54
Though both simulated model structures are characterized by an overall similarity,
there is still a difference between them, as the CL of the protein points towards opposite
directions. The position of the CL of the Mlc1p protein in respect to its NL may be
expressed by calculation of the dihedral angle between the planes defined by the two
lobes and the ID. We found that, at the end of the simulations, the dihedral angle at the
Mlc1p-IQ2 simulated model structure is 128.54°, while the dihedral angle at the Mlc1p-
IQ4 simulated model structure is significantly smaller, 72.1°. The difference represents
two binding modes and orientations of the IQ peptides in respect to the protein, and two
different conformations of the latter. Apparently, various Mlc1p-binding partners may
affect and dictate its structure. The Mlc1p protein is very flexible, enabling it to wrap
around the IQ peptides in different ways. Its tolerance and adaptivity towards different IQ
peptides make it an appropriate candidate to bind a variety of target helical peptides.
Evidently, this unique property enables it to bind six IQ peptides of the LCBD of myosin
V, each distinguished by a unique sequence.
2.2 Structural Evolution of the Simulated Mlc1p Protein at the Protein-Peptide
Complexes
A dynamic comparison of the trajectories of the Mlc1p protein in both simulations
is shown in Fig. 2.2. The RMSD of the C-alpha atoms of the Mlc1p protein obtained
from the Mlc1p-IQ4 simulation's trajectory is presented in relation to the C-alpha atoms
of the Mlc1p protein obtained from the Mlc1p-IQ2 simulation's trajectory. The two-
dimensional matrix representation exemplifies the time evolution of the protein's
configurations as a function of the simulations time. A color code is used for visualizing
55
Figure 2.2: Matrix representation of mutual C-alpha atoms' RMSD of the Mlc1p protein
obtained upon comparison of the two simulations. The RMSD values of the Mlc1p protein
for the Mlc1p-IQ4 simulation's trajectory were calculated in relation to those of the Mlc1p
protein obtained from the Mlc1p-IQ2 simulation's trajectory and vice versa. The values
are given by color codes; where blue and red represent high and low similarity,
respectively.
how the two model structures of the Mlc1p protein, in the Mlc1p-IQ protein-peptide
complexes, approach a common compact shape during the simulations. The pattern of the
colors exhibits progressive yet reversible changes, indicating that both model structures
are fluctuating, and the similarity between them varies. The mutual evolution of the
conformational changes, as shown in Fig. 2.2, suggests that the convergence and settling
of the Mlc1p protein's model structures towards relatively similar compact configurations
can be divided into three phases: a relaxation phase (from the beginning of the simulation
till ~ 3.2-ns), a progression phase (from ~ 3.2 till ~ 10-ns), and a quiescent phase (from ~
10-ns till the end of the simulations).
56
The relaxation phase is represented by the yellow-reddish color laying at the
bottom of the figure, stretching over its full width and extending up to ~ 3.2-ns mark of
the ordinate. At this phase, the Mlc1p protein at the Mlc1p-IQ4 complex responds to the
absence of the packing forces present at the crystal lattice. Hence, the model structures
sampled by the protein from both simulations are still remarkably different, each
remaining close to its crystal form. At the progression phase, the Mlc1p protein at the
Mlc1p-IQ4 simulation undergoes a major conformational change (140), rendering it more
similar to that of the Mlc1p-IQ2 simulation. This newly gained configuration is stabilized
by hydrophobic interactions, where minor rearrangements of the side chains contribute to
a relatively slow progression stabilizing process. The refolded conformation of the Mlc1p
protein obtained from the Mlc1p-IQ4 simulation becomes more similar to the model
structure of the Mlc1p protein obtained from the Mlc1p-IQ2 simulation. This tendency
increases along the ordinate as seen by the shift from the yellow-greenish to the green-
bluish colors. Finally, at the quiescent phase, the new model structure of the Mlc1p
protein obtained from the Mlc1p-IQ4 simulation is already stabilized. The higher degree
of similarity between the protein’s model structures, as reflected by the smaller RMSD
values one with respect to the other, is observed at this phase (represented by the bluish
hue). Evidently, as the simulations progress, the model structures of the proteins become
more similar in a time-dependent manner. Thus, the final MD-derived solution model
structures of the protein are more similar than its crystal structures states. Furthermore,
these final MD-derived solution model structures of the protein resemble also compact
configurations of the CaM protein presented at crystal structures of Holo-CaM with target
peptides (48-54, 141).
57
It is of interest to point out that the model structures of the protein at both
simulations do not co-evolve in parallel. The model derived from the Mlc1p-IQ2
simulation experiences limited changes, whereas that derived from the Mlc1p-IQ4
simulation assumes a significant modification. Thus, the Mlc1p' model structures evolve
at different rates towards a more similar configuration.
Carrying out the same analysis only for the ID of the Mlc1p protein (data not
shown) reveals a pattern resembling that of the whole protein. The structure of the ID of
the Mlc1p protein, obtained from the Mlc1p-IQ2 simulation, is almost invariable, while
that obtained from the Mlc1p-IQ4 simulation evolves with time. A high degree of
similarity is obtained after ~ 10-ns, as observed for the whole protein.
2.3 The Root Mean Square Fluctuation (RMSF) of the Mlc1p Protein at the Protein-
Peptide Complexes
In order to further analyze the trajectories of the Mlc1p protein at both
simulations, we computed the standard deviation from the RMSD for each of its residues,
i.e. their Root Mean Square Fluctuations (RMSF). Fig. 2.3A presents the RMSF of the
Mlc1p protein at the Mlc1p-IQ2 structure simulation (solid line), and at the Mlc1p-IQ4
structure simulation (dashed line). Residues of the Mlc1p protein, that comprise alpha
helices at the crystalline configurations of the Mlc1p-IQ protein-peptide complexes, are
shown as bold horizontal bars parallel to the abscissa. The RMSF curves reveal the
different behavior of the protein at both simulations, characterizing the mobility of each
of its residues during the MD runs.
In general, the structural sections of the protein, namely its eight alpha helices, are
58
more rigid and confined and tend to be less flexible than its other sections (e.g. residues
39−50).
Correspondingly, the protein's unstructured sections show an increased motility.
Thus, at both simulations, the RMSF data indicate large fluctuations of segments
belonging to loops that connect secondary structure elements (e.g. residues 14−20 and
128−137), as well as of residues located at the edges of the alpha helical sections (e.g.
residues 90−92, and 123−125). While these features are common to both complexes, the
Mlc1p protein exhibits a different mobility when it binds the IQ2 or the IQ4 peptides as
the absolute values of the RMSF differ. The RMSF curve of the Mlc1p protein at the
Mlc1p-IQ4 simulation consistently reveals a higher extent of motion than that of the
protein at the Mlc1p-IQ2 simulation. Despite these different degrees of motion, the
A B
Figure 2.3: The Root Mean Square Fluctuation (RMSF) as a function of the residue
number of the Mlc1p protein. The RMSF was calculated for the backbone atoms of the
Mlc1p protein for each residue at both simulations. The solid line represents the RMSF of
the Mlc1p protein at the simulation of the Mlc1p-IQ2 structure, while the dashed line
represents the RMSF of the Mlc1p protein at the simulation of the Mlc1p-IQ4 structure.
The bold horizontal bars, drawn in parallel to the abscissa, represent the alpha helices that
the Mlc1p protein comprises. The RMSF of both MD trajectories is presented for the
entire simulations time (A), and for the time frame t = 10-ns till t = 12-ns (B).
59
RMSF of some sections of the protein is correlated (for example, the RMSF of the NL of
the protein, between both simulations, is correlated, with R2 = 0.69). However, other
sections of the protein do not exhibit such correlation. The variation in the correlations
between the structural domains of the protein implies that the main differences regarding
the dynamics of the protein at both simulations are located at its ID and CL.
It can be argued that the relatively high RMSF of the protein at the Mlc1p-IQ4
simulation is due to its structural modification process, by which it refolds, and that
process is still going-on. However, detailed structural and energy analysis presented in
our previous publication (140) suggests that its major conformational change had been
completed in the course of the simulation. In order to observe the behavior of the Mlc1p
protein at the stable period at both simulations, we repeated the RMSF analysis during the
time frame 10-ns till 12-ns (Fig. 2.3B). The RMSF curves reveal a pattern similar to that
calculated for the entire simulations time, although the extent of the fluctuations is
smaller. Nevertheless, the RMSF curves resemble each other more than those obtained
for the entire simulations' time. This indicates as well that the Mlc1p protein at the
Mlc1p-IQ4 simulation had already experienced its structural modification and may not
significantly evolve at the discussed time frame. We wish to note that, even at this time
frame, we found that the RMSF of the protein derived from the Mlc1p-IQ4 simulation is
still higher than that obtained by the protein from the Mlc1p-IQ2 simulation. This is in
accord with the observation that more contacts are involved in the Mlc1p-IQ2 interaction
than in the Mlc1p-IQ4 interaction (See Fig. 2.5, below). Thus, the protein at the latter
simulation is not strongly retained to its position and may be more mobile.
60
2.4 The Electrostatic Field Around the IQ Peptides
The Mlc1p-IQ protein-peptide complexes are composed of the same protein, and
similar, although not identical, peptides. Yet, the protein-peptide complexes differ one
from the other by their crystalline structures (Figs. 2.1A and 2.1C), and to some extent by
the simulated model structures obtained by means of MD simulations (Figs. 2.2B and
2.2D). Evidently, the differences between the structures of the protein-peptide complexes
reflect the variation sequence of the bound IQ peptides. To account for the difference
between the peptides, we calculated the electrostatic field surrounding the IQ2 and IQ4
peptides. The volumes of the averaged (for the time frame t = 10 until t = 12-ns) positive
and negative electrostatic fields of both peptides are presented in Table 2, while in Fig.
2.4 we show the Coulomb cages of the IQ peptides at the last snapshot (t = 12-ns) of the
simulations.
Table 2
The Electrostatic Field Around the IQ Peptides
* Calculated by summation of the volumes of the positive and the negative Coulomb
cages.
The positive (transparent blue) and negative (transparent red) domains are drawn
where the electrostatic potential equals 1 kBT/e. The C-alpha traces of both peptides are
IQ2 Peptide IQ4 Peptide
Charge +2 +6
Positively-charged residues K-7, K-14, R-19, R-21 R-4, K-11, K-12, R-14,
K-15, K-18, R-20, K-23
Negatively-charged residues D-24, E-25 E-16, E-25
Volume of the positive
Coulomb cage (Å3)
4257.12 ± 264.48 10180.42 ± 426.12
Volume of the negative
Coulomb cage (Å3)
2080.56 ± 147.25 796.02 ± 144.94
Total volume of the
Coulomb cage* (Å
3)
6337.69 ± 395.11 10976.76 ± 498.02
61
Figure 2.4: The electrostatic potential surface around the IQ2 peptide (A) and the IQ4
peptide (B) at the last snapshot (t = 12-ns) of both simulations. Both peptides are
presented in yellow with the same orientation, while their positive and negative residues
are drawn in blue and red, respectively. The Coulomb cages for the positive (transparent
blue) and negative (transparent red) domains are drawn at the distance where the
electrostatic potential equals 1 kBT/e.
A B
colored in yellow, while their positive and negative residues are shown in blue and red,
respectively. The potential field of the IQ peptides consists of two main lobes, one
positive and the other negative. However, although the IQ2 and IQ4 peptides are both
basic, alpha-helical, 25 amino acids long, they produce different electrostatic fields
around them. The volume of the positive Coulomb cage around the IQ2 peptide is
4257.12 ± 264.48 Å3, while the volume of its negative Coulomb cage is 2080.56 ± 147.25
Å3. The volume of the positive Coulomb cage around the IQ4 peptide is 10180.42 ±
426.12 Å3, while the volume of its negative Coulomb cage is 796.02 ± 144.94 Å
3.
62
The differences between the electrostatic fields surrounding the peptides are
caused by variations in their local charge and charge distribution. The total charge of the
IQ2 peptide is Z = +2, while that of the IQ4 peptide is Z = +6. The peptides differ not
only in their total net charge, but in the distribution of the charges along them as well.
Four positive residues (K-7, K-14, R-19, R-21) are scattered along the IQ2 peptide, while
its negative residues (D-24, E-25) are concentrated at its C-terminal edge. The IQ4
peptide consists a series of four positive residues (K-11, K-12, R-14, K-15) located in its
middle section, whereas its other positive residues (R-4, K-18, R-20, K-23) are
distributed along it. The mid-cluster of positive charge contributes to the high volume
positive Coulomb cage bulb at the center of the peptide. The differences between the
electrostatic fields of the two peptides may suggest that electrostatic forces play a major
key role in the protein-peptide interactions.
2.5 The Protein-Peptide Interaction Free Energies
In order to analyze the energetics of peptide binding to the Mlc1p protein, the
various components of the interaction free energy of the two protein-peptide complexes
were evaluated during the last 2-ns for each simulation. This time frame corresponds with
the stable MD-derived model solution structures of the protein-peptide complexes at both
simulations, from which we can calculate the energy associated with protein-peptide
interaction. The detailed results of the energetic analysis are presented in Table 3.
The analysis was based on the MM-PBSA approach (94), in which the interaction
free energy, (∆Ginteraction), for each of the complexes is composed of three energetic terms:
The molecular mechanics energy term (⟨∆EMM⟩), the solvation energy term (⟨∆Gsolvation⟩),
63
and the solute entropic contribution (T∆S). The first term includes internal (⟨∆Eint⟩), VdW
(⟨∆EVdW⟩) and electrostatic (⟨∆Eelectrostatic⟩) components. The second term consists of
electrostatic (⟨∆Gpolar,solvation⟩) and nonpolar (⟨∆Gnonpolar,solvation⟩) contributions. Solute
entropies were determined at the last snapshots of the MD trajectories. Note that the
internal component of the molecular mechanics energy, (⟨∆Eint⟩), is set per definition as
zero and thus cancels out, making no contribution at all (101, 103, 104).
Table 3
Components of the Mlc1p-IQ Interaction Free Energy
Energies are presented in kJ/mol. The calculations present the average values
obtained from t = 10 till t = 12-ns for both Mlc1p-IQ simulations. ⟨ ⟩ denotes an average
over a set a snapshots along an MD trajectory. Atomic charge and radii values were taken
from the PARSE parameter set (142).
Definitions of the energetic components are as follows: (⟨∆Eelectrostatic⟩),
electrostatic molecular mechanics energy; (⟨∆EVdW⟩), VdW molecular mechanics energy;
(⟨∆EMM⟩), total molecular mechanics energy defined as ⟨∆EMM⟩ = (⟨∆Eint⟩ + ⟨Eelectrostatic⟩ +
⟨∆EVdW⟩); ⟨∆Gpolar,solvation⟩, electrostatic contribution to the solvation energy calculated by
the PB approach; ⟨∆Gnonpolar,solvation⟩, nonpolar contribution to the solvation energy;
⟨∆Gsolvation⟩, total solvation energy defined as (⟨∆Gpolar,solvation⟩ + ⟨∆Gnonpolar,solvation⟩); T∆S,
solute entropic contribution; and (∆Ginteraction), total free energy of interaction defined as
(⟨∆EMM⟩ + ⟨∆Gsolvation⟩ – (T∆S)).
On combining the (⟨∆EMM⟩) with the (⟨∆Gsolvation⟩) and the (T∆S) terms, we end
up with interaction free energy, (∆Ginteraction), for the complexes' formation. The estimated
interaction free energy of the Mlc1p-IQ2 and the Mlc1p-IQ4 complexes is ~ -560 kJ/mol
Mlc1p-IQ2 Complex Mlc1p-IQ4 Complex
⟨∆Eelectrostatic⟩ -590.77 ± 49.96 -1534.02 ± 84.28
⟨∆EVdW⟩ -664.18 ± 25.2 -547.7 ± 25.88
⟨∆EMM⟩ -1254.95 -2081.72
⟨∆Gpolar,solvation⟩ 678.25 ± 41.85 1594.88 ± 78.84
⟨∆Gnonpolar,solvation⟩ -58.69 ± 5.59 -53.98 ± 5.48
⟨∆Gsolvation⟩ 619.56 1540.9
-T∆S 75 372
∆Ginteraction -560 -169
64
and ~ -169 kJ/mol respectively, consistent with their observed stability. These data
represent a balance between enthalpy and entropy in which, according to our calculations,
the complexes' formation is an enthalpically driven process and is entropically
unfavorable. The favorable formation of both Mlc1p-IQ complexes is driven by the
electrostatic (⟨∆Eelectrostatic⟩) and the VdW (⟨∆EVdW⟩) terms of the molecular mechanics
energy and the nonpolar component of the solvation energy (⟨∆Gnonpolar,solvation⟩).
Of particular interest is the total solvation energy, (⟨∆Gsolvation⟩), composed of
polar (⟨∆Gpolar,solvation⟩) and nonpolar (⟨∆Gnonpolar,solvation⟩) terms. The total solvation energy
is unfavorable at both complexes (619.56 kJ/mol for the Mlc1p-IQ2 complex, and 1540.9
kJ/mol for the Mlc1p-IQ4 complex). Thus, considering the solvation energy, it appears
that the protein-peptide complexes would rather not be formed at all. Yet, the molecular
mechanics energy component of the interaction energy strongly favors the complexes
over the unbound molecules.
Electrostatic interactions were assumed to play a dominant major role in the
interaction between CaM and target peptides (49, 143-145). This view was emerged from
X-ray structures of complexes showing close proximity between the negatively charged
CaM and positively charged peptides (47-54, 141). Accordingly, electrostatic interactions
have been anticipated to be significant in the Mlc1p-IQ systems, as the Mlc1p-IQ
complexes also present a close distance between a negatively charged protein and highly
positively charged peptides. It is of high importance to consider the electrostatic
component of the molecular mechanics energy, (⟨∆Eelectrostatic⟩), together with the
electrostatic contribution to solvation, (⟨∆Gpolar,solvation⟩), when examining the role of
electrostatics in the protein-peptide complexes formation. At both protein-peptide
65
complexes, the nature of the electrostatic interactions is similar: The molecular
mechanics electrostatic term per se favors the bound state of the complexes (⟨∆Eelectrostatic⟩
< 0), while the electrostatic PB solvation energy favors the unbound state of the protein-
peptide complexes (⟨∆Gpolar, solvation⟩ > 0). As the latter is dominant (|⟨∆Gpolar,solvation⟩| >
|⟨∆Eelectrostatic⟩|), their sum, representing the total electrostatic energy, opposes the
formation of the protein-peptide complexes. Thus, the positive solvation energy
electrostatic term penalty paid by the electrostatics of solvation is not completely covered
by favorable electrostatic interactions within the resulting protein-peptide complexes.
Evidently, the same phenomenon was also demonstrated by numerous studies (101, 103,
104, 128, 146-148), in which the total electrostatics between two interacting molecules
unfavors their bound state over the unbound due to intense solvation forces. Interestingly,
the electrostatic energy terms (⟨∆Eelectrostatic⟩) and (⟨∆Gpolar,solvation⟩) are more prominent in
the Mlc1p-IQ4 complex compared to the Mlc1p-IQ2 complex by approximately a factor
of three, which is proportional to the charge of the peptides (The charges of the IQ2 and
IQ4 peptides are +2 and +6, respectively). Hence, the differences in charges between the
protein and the peptide are more substantial in the Mlc1p-IQ4 complex, and consequently
its electrostatic terms are more profound.
It is not surprising that, at both complexes, the entropic term does not support the
interaction between the protein and the peptide. The Mlc1p protein, as well as the IQ
peptides, are characterized by higher entropy in their unbound states. In its free state, the
lobes of the Mlc1p protein can tumble more or less independently of one another,
constrained only by the ID. However, in the bound state, its lobes interact with the
peptide and hence are relatively at fixed positions. Similarly, the free IQ peptides may
66
also acquire more structural freedom when they are not constrained by the protein.
The energy calculations agree fairly well with isothermal titration calorimetry
(45, 149) and NMR relaxation (150) experiments, in which it was found that the binding
of a peptide to Holo-CaM is favored by enthalpy and opposed by entropy. Our results are
also in accord with an MD study of Holo-CaM complexed with a target peptide
suggesting that the protein-peptide free energy is enthalpy-dependent and not entropy-
dependent (92). As pointed out by these authors, identification of changes in entropy (45,
150) or enthalpy (92) upon complex formation is fraught with difficulty. Therefore, the
qualitative agreement between our calculations regarding the Mlc1p-IQ complexes
obtained by computer simulations, and experimental and theoretical calculations
regarding Holo-CaM peptide complexes, is encouraging and promising.
Finally, it must be stressed that the values given in Table 3 are model-dependent
and reflect all of the approximations implemented in the MM-PBSA formalism. Thus, the
numerical values should be taken as indicative, representing qualitative trends rather than
actual quantitative ones. The consistency of the results with the observed stability of the
complexes supports the acceptance of this mode of calculation as a proper representation
of the operating forces.
Owing to the opposite charges of the protein and the peptide, the electrostatic
interactions may serve as the initial driving force for long-range molecular recognition
between the Mlc1p protein and the IQ peptides. On the other hand, the highly charged
protein and peptides strongly interact with the solvent, leading to intensive solvation
forces. Upon formation of the protein-peptide complexes, the Mlc1p protein approaches
into a close vicinity to the IQ peptides. This desolvation process, which is unfavorable, is
67
accompanied by a release of water molecules from their interfaces, replacing solute-
solvent interactions by intra-complex interactions. The unfavorable change in the
electrostatics of solvation is mostly, but not fully, compensated by the favorable
electrostatic charge-charge interactions within the resulting Mlc1p-IQ complexes. The
close interaction of the Mlc1p protein with the IQ peptides is grossly mediated by the LJ
interactions, whereas their opposite highly charged surfaces contribute to their initial
attraction. The major role played by the molecular mechanics VdW interactions
demonstrates how inter-residues contacts, where the tight fitting of the surface atoms
occurs, contribute to the LJ stabilization energy term and consequently to the stability of
the complexes. In conclusion, electrostatic interactions seem to operate mostly during the
long-range attraction between the protein and the peptides before the complexes are
formed. Once protein-peptide contact occurs, VdW and non-specific hydrophobic
interactions stabilize the Mlc1p-IQ structures, whereas the contribution of salt bridges is
relatively negligible.
2.6 The Contacts Between the Protein and the Peptides
The detailed interactions between individual residues of the Mlc1p protein and the
IQ peptides were followed during the last half of the simulations (6−12-ns). Residues of
the peptides, which were in a contact (less than 4 Å) with the Mlc1p protein, were listed.
The rapid motion of the residues during the simulations led to numerous encounters, but
most of them were temporary and made a marginal contribution to the protein-peptide
interaction. To account for that, we selected only those contacts, between residues of the
IQ2 or the IQ4 peptides with the Mlc1p protein, which were present in at least 80 % of
68
the snapshots. These lasting interactions are presented in Fig. 2.5.
Altogether, 51 contacts between the peptide and the protein were found at the
Mlc1p-IQ2 simulation. 15 of these contacts involve the NL of the protein (blue), 14 the
ID (red), and 22 the CL (green). Similarly, at the Mlc1p-IQ4 simulation, 42 contacts were
found between the peptide and the protein (140). Only 4 of these contacts involve the NL
of the protein (blue), 13 the ID (red) and 25 the CL (green). It is of interest to point out
that 20 residues of the Mlc1p protein interact with both IQ peptides (underlined in Fig.
2.5), 12 of its residues interact only the IQ2 peptide, whereas 7 of its residues exclusively
interact the IQ4 peptide. Residues 24−25 of both IQ peptides made no contact with the
Mlc1p protein in neither of the simulations.
Figure 2.5: Contacts (less than 4 Å) between residues of the Mlc1p protein and the
bound IQ peptides obtained from the MD simulations at t >= 6-ns. Data regarding the
Mlc1p-IQ4 model structure simulation (140) are presented at the upper half of the
illustration, whereas data regarding the Mlc1p-IQ2 model structure simulation are
presented at its lower half. The IQ peptides, the NL of the protein, the ID of the protein,
and the CL of the protein are colored in black, blue, red, and green, respectively.
Residues of the Mlc1p protein that interact with both peptides are underlined. Only
contacts persist at least 80 % of the examined period are presented.
The IQ2 peptide has 4 positive residues (K-7, K-14, R-19, R-21), and 2 negative
69
residues (D-24, E-25) located in its C-terminal edge. These negative residues repel the
negatively charged Mlc1p protein, and hence only one residue of the protein (I-9)
interacts with the last 5 residues of the IQ2 peptide. In comparison, the IQ4 peptide is
more positive. It has a substantial cluster of positive residues (K-11, K-12, R-14, K-15,
K-18, R-20, K-23) located at its mid- and C-terminal parts. These positive residues are
bound to the CL of the Mlc1p protein mainly through hydrophobic interactions (i.e. R-14
− L-116, R-20 − V-128), but two salt bridges are also present (K-11 − E-114, R-14 − E-
120).
The different binding modes of the two peptides are reflected by their different
regions of contact with the Mlc1p protein at each simulation. At the Mlc1p-IQ2
simulation, the mid- and C-terminal regions of the peptide (residues 13−25) interact with
8 residues of the NL and 12 residues of the CL of the protein. On the other hand, at the
Mlc1p-IQ4 simulation, the mid- and C-terminal regions of the peptide (residues 13−25)
do not interact with the NL of the protein as they are bound to 17 residues of its CL. The
fact that the mid- and C-terminal sections of the IQ2 peptide interact with the NL of the
protein, while those regions of the IQ4 peptide do not interact with it, is manifested by
the various orientations of the peptides when bound to the protein (Figs. 2.2B and 2.2D).
Although the protein and the peptides are highly charged in opposite charges, out
of the 51 contacts between the IQ2 peptide and the Mlc1p protein, only 2 involve
electrostatic interactions (K-7 − E-114, K-14 − D-28). Similarly, out of the 42 contacts
between the IQ4 peptide and the Mlc1p protein, only 2 involve electrostatic interactions
(K-11 − E-114, R-14 − E-120). Besides these few electrostatic interactions, all the other
protein-peptide interactions are hydrophobic in nature. Matter of fact, even the positive
70
residues of the peptides interact with the positive residues of protein (K-14 − R-31, R-19
− R-147 for the Mlc1p-IQ2 protein-peptide complex; R-4 − R-31, R-14 − K-115, R-19 −
R-147, K-23 − R-147 for the Mlc1p-IQ4 protein-peptide complex). Considering the
repulsive force between positive charges, the interactions between the basic residues are
clearly hydrophobic. These data are consistent with the findings regarding the dominant
role played by the LJ component of the molecular mechanics energy and the nonpolar
component of the solvation energy in the stabilization of the protein-peptide complexes
(Table 3).
2.7 Summary
The present study provides a fundamental understanding of the Mlc1p protein’s
solution behavior in a complex with IQ peptides by sampling the conformational space of
two Mlc1p-IQ complexes. Our findings suggest that, although the IQ2 and the IQ4
peptides share similar sequence and structure, the fine details of each individual IQ
sequence determine its binding mode to the Mlc1p protein. The ability of the Mlc1p
protein to assume different conformations, which is driven by the specific IQ peptides, is
crucial. The flexibility of the protein and the dominance of its nonspecific hydrophobic
interactions with the IQ peptides are probably correlated with its ability to bind a wide
range of targets. Besides describing the structure and dynamics of the protein in the
presence of the peptides, we analyze the interaction free energy that governs the protein-
peptide formation. Using a combination of energies derived from MD simulations in an
explicit solvent, a continuum solvent model, and solute entropies contributions derived
from normal mode analysis, we have obtained approximate values for the protein-peptide
71
interaction free energy of both complexes. We found that favorable molecular mechanics
energy contribution profoundly supports this protein-peptide interaction, while the polar
solvation energy and the entropy oppose it.
72
3. Simulations of Free IQ Peptides
In the first two chapters of the thesis we found out that the solution model
structures of the Mlc1p-IQ complexes are both compact, while the IQ peptide is located
between the lobes of the protein. These observations may imply that the Mlc1p protein
contributes to the relative stability of the IQ peptides, while the peptides affect the
specific folding form of the protein. Since the only difference between the Mlc1p-IQ2
and the Mlc1p-IQ4 simulations is the IQ peptide, and in order to check how the IQ
peptides refold at the absence of the Mlc1p protein, we have performed MD simulations
of the peptides in solution. Accordingly, this chapter deals with MD simulations of free
IQ peptides. These simulations complement our research of the Mlc1p-IQ complexes, and
aim for elucidation the dynamic behavior of isolated IQ peptides without the presence of
the Mlc1p protein. Since none of the IQ peptides were crystallized at the absence of the
protein, their structures, which are basically alpha-helical, were derived from the
published crystal structures of the Mlc1p-IQ protein-peptide complexes (28, 56).
Considering the long duration of our simulations and the repetitive pattern of the models
obtained at different simulations' conditions, we argue that the predicted model structures
of both IQ peptides represent their solution conformations. Comparisons between the
dynamics of the free and the bound IQ peptides, between the free IQ2 and IQ4 peptides,
and between the simulations of the free IQ4 peptide at different conditions, were
performed.
3.1 Synopsis of the Presented Simulations
A series of MD simulations, presented in Table 4, was performed for various
73
durations and conditions. These simulations include one MD run of the IQ2 peptide, and
five MD runs of the IQ4 peptide. Additionally, an extended IQ4 was constructed and
subjected to an MD run as further elaborated.
Table 4
Summary of the MD Simulations of the IQ Peptides
* 400 K. †
~ 30 mM NaCl. ‡
~ 300 mM NaCl. ¶ ~ 2.4 M NaCl (mimicking the salt concentration in which the Mlc1p-IQ4 complex was
crystallized (56)). § An IQ4 peptide containing 10 additional amino acids flanking each of its terminals.
These added 20 residues belong to the IQ3 and IQ5 peptides. Thus, the 45 amino acids
elongated IQ4 peptide constitutes a portion of the poly-IQ sequence as present at the neck
of the myosin. This simulation is described in chapter 4 of the thesis.
3.2 Overall Conformational Changes During the Simulations
The crystallographic and simulated structures of the free IQ2 peptide are
presented in Fig. 3.1 (Snapshots from the simulation are shown every 20-ns). At its initial
configuration (Fig. 3.1A), the peptide is almost linear alpha-helix. After 20-ns, the
peptide stretches (Fig. 3.1B), keeping its linearity. At the next snapshots (Figs. 3.1C-F),
its N- and C- edges loose, while its mid-section retains its straight conformation. From
40-ns till 100-ns, the model structure of the peptide hardly changes.
In contrast to the IQ2 peptide, snapshots of the IQ4 peptide reveal a different
Duration
(ns) Conditions of simulation
IQ2 peptide 100 As written in section 1.2 of the Methods
IQ4 peptide 100 As written in section 1.2 of the Methods
IQ4 peptide 30 High temperature *
IQ4 peptide 20 Low salt concentration †
IQ4 peptide 20 High salt concentration ‡
IQ4 peptide 20 Very high salt concentration ¶
Extended IQ4 peptide 20 An elongated IQ4 peptide §
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scenario (Fig. 3.2). The initial configuration of the IQ4 peptide is a linear alpha-helix
(Fig. 3.2A). After 20-ns of simulation it bends (Fig. 3.2B), whereas most of its secondary
structure is no longer alpha-helix. The conformation of the peptide continues to explore
the configurational space reaching a new configuration, observed at the next snapshots
(Figs. 3.2C-F). At this newly gained conformation, the IQ4 peptide is refolded in a
manner that its N- and C- edges are relatively close to each other. At the final
configuration, the IQ4 peptide is composed of two helices, separated by a coiled hinge.
The refolding process of the peptide, in which it loses most of its alpha-helical structure,
occurs in less than 20-ns. It can be seen that its conformation after only 20-ns of
simulation (Fig. 3.2B) grossly deviates from its initial one (Fig 3.2A). The secondary
structure analysis, presented in section 3.4 of this research, emphasizes the abrupt
transition of the peptide from an elongated alpha-helix into a conformation of two helices
separated by a coiled section.
A B C D E F
Figure 3.1: Snapshots of the crystal and the simulated structures of the free IQ2 peptide.
The structure of the IQ2 peptide as derived from the crystal structure of the Mlc1p-IQ2
complex (A). The simulated model structure of the IQ2 peptide after 20-ns (B); 40-ns (C);
60-ns (D); 80-ns (E) and 100-ns (F) of MD run.
75
From the comparison of the snapshots between the two free IQ peptides, it is
evident that the IQ2 peptide is more rigid and stiff than the IQ4 peptide. Whereas the IQ2
peptide keeps most of its structural features, the IQ4 peptide modifies into a helix-loop-
helix conformation through an intermediate state. This argument will be further
strengthened and elaborated
We repeated the simulation of the IQ4 peptide at a high temperature (400 K). Our
aim was to check whether the elevated temperature may cause further structural changes
Figure 3.2: Snapshots of the crystal and the simulated structures of the free IQ4 peptide.
The structure of the IQ4 peptide as derived from the crystal structure of the Mlc1p-IQ4
complex (A). The simulated model structure of the IQ4 peptide after 20-ns (B); 40-ns (C);
60-ns (D); 80-ns (E) and 100-ns (F) of MD run. The simulated model structure of the IQ4
peptide after 30-ns (G) of MD run at 400 K.
A B C D
GE F
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to the peptide and detect changes not observed at 300 K. Fig. 3.2G depicts the model
structure of the IQ4 peptide after 30-ns of simulation at 400 K. Inspection of the peptide's
model at the end of the simulation at 400 K reveals a high similarity to the model
structure of the peptide after 100-ns simulation at 300 K. According to our simulations,
the elevated temperature does not affect the refolding mechanism of the peptide but,
rather, its rate (as also observed for the Mlc1p-IQ4 simulation at 400 K presented in
chapter 1 of the thesis). Thus, the progression of the conformational transition is basically
comparable at the two temperatures with a clear acceleration at the higher temperature.
Hence, we suggest that the modulation's speed of the peptide's model structure is
temperature-dependent.
The modulation of the IQ peptides' model structures with time can be followed by
examination of their backbone RMSD relative to their crystal structures in the protein-
peptide, as given in Fig. 3.3 (black for the IQ2 peptide, red for the IQ4 peptide). The
RMSD of the free IQ2 peptide (Fig. 3.3A, black) increases in a moderate fashion for the
first 13-ns of the simulation. Then, it rises abruptly to a value of ~ 0.76 nm, drops and
stabilizes at ~ 0.48 nm till the end of the simulation. The RMSD of the free IQ4 peptide
(Fig. 3.3A, red) increases at the very first nanoseconds of the simulation till a value of ~
0.5 nm, then gradually rises till it stabilizes on t ~ 50-ns at ~ 0.9 nm. Once the peptides
had reached their new stable conformations, they do not exhibit further configurational
changes. The calculation of the backbone RMSD value for the last 20-ns of the
simulations, relative to the backbone heavy atoms’ position at t = 80-ns (Fig. 3.3B),
reveals that both free IQ peptides hold steady solution model structures. These model
structures do not further evolve and thus represent settled down configurations.
77
Figure 3.3: (A) The RMSD of the
backbone atoms of the free IQ2 (black)
and IQ4 (red) peptides as a function of
the simulation time; (B) The RMSD of
the backbone atoms of the last 20-ns of
the simulations (80−100 ns) relative to
the position of the same set of atoms at t
= 80-ns; (C) The RMSD of the backbone
atoms of the bound IQ2 (black) and IQ4
(red) peptides as a function of the
simulation time. Note the differences in
the abscissa between the simulations of
the free and the bound peptides.
B
C
A
The evaluation of the structural stability of the free peptides calls for comparison
with their stability in a complex with the Mlc1p protein. The RMSDs of the bound IQ
peptides were reported in Figs. 1.2A and 1.4A, and presented also in Fig. 3.3C. That for
the bound IQ2 peptide increases after ~ 3-ns to a value of ~ 0.23 nm and stabilizes,
whereas that for the bound IQ4 peptide doubles after ~ 3.3-ns from ~ 0.2 nm to ~ 0.4 nm,
and stays at this value till the end of the simulation. When one compares the simulations
of the free and the bound peptides, it can be clearly seen that free peptides tend to loose
their structure in a more profound manner than the bound ones.
78
The Mlc1p protein is likely to shield or protect the bound peptides from a gross
deviation from their initial structure observed for the free peptides. It causes a steric
hindrance that prevents the peptide to assume conformations observed when simulated at
its absence. It should be mentioned that at both the free and at the bound peptide's
simulations, the IQ4 peptide is more flexible and tends more to deviate from its original
structure than the IQ2 peptide.
3.3 Structural Characteristics of the Refolding Process of the IQ Peptides
To demonstrate the modulation of the IQ peptides during the simulations, two
alpha-helices in their N- and C- sections, as present in their crystalline structures, were
defined. The angle between them is presented in Fig. 3.4.
Figure 3.4: The dynamics of the relative rotation of the free and the bound IQ peptides
during the simulations time. (A) The intra-helical angle between the N- and C- sections
of the free IQ2 (black). The arrow points towards a conformation of the free IQ2 peptide
at 15-ns; (B) The intra-helical angle between the N- and C- sections of the bound IQ2
(black) and IQ4 (red) peptides.
A B
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For the free IQ2 peptide, the angle is relatively constant at a value of ~27°,
besides a transient increase to a value of ~125° at the time range ~13-ns till ~20-ns. This
temporary rise, corresponds to the short-lived configuration of the peptide marked with
an arrow, coincides with the increment of the RMSD observed at Fig. 3.3. Thus, even
though the IQ2 peptide explores the parametrical space and tries to refold, it relatively
returns to its initial conformation and does not grossly deviate from it. For the free IQ4
peptide, the intra-helical calculation is not given since the peptide does not hold two
defined sections throughout the entire simulation. However, its structural modulation is
clearly detected on Fig. 3.2.
A different scenario is observed when dealing with the bound IQ peptides (Fig.
3.4B). The angle of the bound IQ2 peptide remains constant throughout the entire
simulation time. The bound IQ4 peptide, which at the initial state consists of a single
alpha-helix, shows a significant flexibility. Its straight alpha-helical structure is snapped
in its middle during the complex's structural transition, when the two shorter helices
attain an almost perpendicular relation. The process, in which the angle between the
helices increases from ~ 20° to ~ 70°, is sharp and quick.
As demonstrated, the IQ4 peptide is characterized by a greater flexibility than the
IQ2 peptide, both in its free and its bound configurations. While the former experienced a
refolding process, the latter keeps its linearity. Upon comparison of the extent of the
curvature of the free and the bound IQ4 peptides in solution, it is evident that the free
peptide bends much more than the bound one. The considerable modification of the free
IQ4 peptide enables it to form intra-peptide bonds (between its N- and C- terminals),
whereas the bound IQ4 peptide exhibits two defined, almost vertical, sections.
80
Figure 3.5: The end-to-end distance (from C-alpha of the first residue till C-alpha of the
last residue) of the free IQ2 (black) and IQ4 (red) peptides.
The refolding of the IQ peptides can be also expressed when calculating the
distance between their first and last alpha-carbons (Fig. 3.5). For the free IQ2 peptide
(black), the end-to-end distance hardly changes during the simulation. After decreasing
from ~ 3.7 nm to ~ 2.5 nm, it keeps a relatively constant distance. However, this end-to-
end distance decreases for a short while (~ 13-ns till ~ 20-ns) to a distance that is even
shorter than 1 nm. The short end-to-end distance reflects its transient curved
conformation, which is not stable and alternates back to the initial straight configuration.
The refolding of the free IQ4 peptide (red) is clearly seen as its length shortens from ~
3.7 nm to ~ 2 nm. Afterwards, at t ~ 22-ns it drops to ~ 0.75 nm, rises to ~ 1.5 nm and
finally stabilizes at ~ 0.7 nm. The free IQ4 peptide shows a significant conformational
flexibility, shown when its bending brings its ends into a closer contact than seen at their
initial state. Overall, the structural characteristics of the extensive conformational change
of the peptide are presented by variation of its length as well as by the increase of the
angle between its N- and C- sections.
81
3.4 Secondary Structures of the IQ Peptides
We followed the secondary structure of the free IQ peptides as a function of the
simulation time and the analyses of the free IQ2 (Fig. 3.6) and the free IQ4 (Fig. 3.7) are
presented.
The initial alpha helical conformation of the free IQ2 (Fig. 3.6) peptide remains
stable for more than 20-ns, and then transforms into a 5-helix conformation while
keeping its linearity. A 5-helix conformation, also known as a Π-helix, is a helical
structure in which the backbone C=O group of the i residue forms a hydrogen bond with
Figure 3.6: Secondary structure analysis of the free IQ2 peptide as a function of the
simulation time. The residue number runs along the ordinate and time along the abscissa.
Color codes are used to represent secondary structure elements.
82
Figure 3.7: Secondary structure analysis of the free IQ4 peptide as a function of the
simulation time. The residue number runs along the ordinate and time along the abscissa.
Color codes are used to represent secondary structure elements.
the backbone N-H group of the residue five amino acids ahead (i → i + 5 hydrogen
bonding). The 5-helix conformation becomes the dominant secondary structure element
and holds till the end of the simulation of the free IQ2 peptide.
The secondary structure analysis of the free IQ4 peptide (Fig. 3.7) reveals a
different pattern than that for the IQ2 peptide.
After a short relaxation period, the peptide is no longer composed of only alpha
helical elements. While its first ~ 15 residues still keep their alpha helical configuration,
the remaining 10 residues become composed of bends and turns. At ~ 16-ns, a 5-helix
83
appears and gradually controls over the model structure till ~ 38-ns (besides a middle
coil/turn section). Apparently, the 5-helix conformation is not stable enough to persist for
the entire helix, and the first ~ 15 residues reverse back to the alpha-helical conformation.
From this time point on, the model structure of the peptide exhibits three secondary
structure elements, reflecting an energetically stable configuration of the peptide: the N-
section, composed of an alpha-helix; the C-section, composed of a 5-helix; and a hinge,
composed of turn and coil, separating between these N- and C- sections.
The secondary structure analyses of both peptides add an additional value to the
data presented by the snapshots and the RMSD of the peptides. Subtle changes in the
secondary structure composition of the peptides, that are not necessarily observed in Figs.
3.1−3.3, are clearly seen in this type of analysis. For the IQ2 peptide, although one can
allegedly think that the peptide barely changes during its simulation; this analysis
demonstrates that it loses most of its alpha-helical structure at the expense of gaining a 5-
helix structure. For the IQ4 peptide, it can be assumed that its alpha-helix had practically
lost. However, we demonstrated that it attains about 50 % from its initial alpha-helix
content, while the newly appearing 5-helix and coil/turn configurations form the other
half. Interestingly, the alpha- to 5- helix transition (full-length and partial for the IQ2 and
the IQ4 peptides, respectively), which was detected in both simulations, was observed, as
well, in previous MD simulations of peptides. 5-helix propagation at the expense of an
alpha-helix was noticed in simulations of the transmembrane domain of ErbB-2 (151,
152), the central domain of caldesmon (153) and synthetic peptides (154). Besides
theoretical MD simulations reporting a formation of the 5-helix structure, there are also
experimental evidences to the existence of this secondary structure element in proteins
84
and peptides. For example, 5-helix was identified by x-ray crystallography and NMR in
fumarase C (155), glycogen phosphorylase b (156), lipoxygenase (157), catechol O-
methyltransferase (158), serine carboxypeptidase (159), and the protein NMA1147 (160).
5-helix was also identified at the vasoactive intestinal protein, using an empirical
approach involving peptide design, construction, and distribution frequency techniques
(161).
Both peptides explore the conformational space till they find a stable
configuration. At more (for the IQ2 peptide) or less (for the IQ4 peptide) 20-ns, both
loose they initial structures, and then, following more exploration, new stable model
structures emerge.
3.5 Salt Bridges Analysis of the IQ4 Peptide Simulation
An analysis for the presence of salt bridges was performed for the 100-ns long
simulation of the IQ4 peptide.
The IQ4 peptide is a highly-charged peptide, containing 8 positive residues and 2
negative ones. The oppositively-charged residues can form salt bridges between them,
and thus we followed the minimal distance between each pair of oppositively-charged
residues, and present the main results in Fig. 3.8. A ribbon diagram of the IQ4 peptide,
presenting its positive and negative residues (blue and red, respectively) is shown on the
right.
Only one salt bridge (R20-E16) persisted over the whole simulation time (Fig.
3.8A), keeping the minimal distance between the residues as ~ 0.25 nm. Two salt bridges
(K12-E16, K11-E16) were broken during the simulation at a time point corresponding
85
Figure 3.8: Salt bridges analysis of the free IQ4 peptide simulation. (A) Minimal
distance between R20 and E16; (B) Minimal distance between K12 and E16; (C)
Minimal distance between K11 and E16; (D) Minimal distance between R20 and E25;
(E) Minimal distance between K11 and E25; (F) Minimal distance between R4 and
E25. The crystalline conformation of the IQ4 peptide, as derived from the crystal
structure of the Mlc1p-IQ4 complex, is presented on the right side. The positive and
negative residues of the IQ4 peptide are shown in blue and red, respectively.
A B C
D E F
R20
E25
R4
E16
K11
K12
K23
K18
R14
K15
with the major conformational change of the peptide (Figs. 3.8B-C). Two salt bridges
(R20-E25, K11-E25) were detached at ~ 62-ns (Figs. 3.8D-E). One salt bridge (R4-E25)
was formed (Fig. 3.8F) at the end of the simulation when the two edges of the peptide got
close enough to be linked through a salt bridge. This latter is of particular interest since it
represents the structural modification of the peptide and reflects its curvature. The
residues R4 and E25 are located at the edges of the IQ4 peptide. At the beginning of the
simulation, they are at a distance that exceeds 3 nm. As the simulation progresses, these
residues become closer to each other, keeping a distance of ~ 1.1 nm. Finally, the
structural deformation of the peptide imposed a stable contact of the residues, in which
their VdW radii almost reached (d = 0.25 nm).
86
From the salt bridge analysis it becomes clear that only two salt bridges maintain
the refolded model structure of the peptide, while four pre-existing salt bridges detached.
However, these bonding salt bridges contribute to the enhanced stability of the refolded
model structure of the IQ4 peptide.
3.6 Dynamics of the IQ4 Peptide at Different Salt Concentrations
We repeated the MD simulations of the free IQ4 peptide, for a duration of 20-ns
each, in three different salt concentrations: ~ 30 mM (low), ~ 300 mM (high) and ~ 2.4 M
(very high). Snapshots of the structures after 20-ns simulations (Fig. 3.9) are presented.
At the low salt concentration, the IQ4 peptide refolded into two distinctive
sections separated by a hinge (Fig. 3.9A). However, at the high salt concentration, it did
not refold, although its N- and C- terminals were loosen (Fig. 3.9B). The high salt
concentration prevented the peptide to assume a different conformation from its initial
Figure 3.9: Snapshots of the crystal and the simulated structures of the IQ4 peptide at
different salt concentrations. The simulated model structures of the IQ4 peptide after 20-
ns simulation at low (A), high (B), and very high salt (C) concentrations.
A B C
87
one, keeping it as an elongated helix.
Given that the Mlc1p-IQ4 complex was crystallized at a very high salt
concentration (56) (~ 2.4 M), we suggest that its crystal structure was imposed by its
crystallization conditions. According to this argument, which is compatible with the
results we present in chapter 1 of the thesis, the crystal structure of the Mlc1p-IQ4
complex does not represent its physiological solution structure. Thus, we repeated the
simulation of the free IQ4 peptide at salt conditions mimicking its crystallographic ones,
and a snapshot of the simulated model structure after 20-ns simulation (Fig. 3.9C) is
shown. The snapshot resembles the one obtained by the simulation at the high salt
because that already at ~ 300 mM of NaCl the screening effect caused by the ions is
extensive. The 8-fold increase at the NaCl concentration did not significantly change the
screening effect and thus the results of the high and the very high salt concentrations'
simulations are close.
Since the peptide hardly bends at the high salt concentrations (as opposed to the
bending at ~ 30 mM and ~ 100 mM salt concentrations), it is obvious that its refolding
pattern is influenced by the concentration of ions in its surrounding. High salt
concentrations probably prevent the peptide to assume a conformation that reflects its
solution structure, and thus yield a configuration that differs from a physiological one.
We can generalize the argument and suggest that the conditions of the crystallization,
such as the salt concentration of the crystallization buffer, may influence the
configuration of the protein inside the crystal lattice. A clear influence of the crystal
environment on protein structures was also found by others (162, 163). Therefore, the
simulations' results at the high salt concentrations strengthen our conclusion that the
88
crystallization conditions of the Mlc1p-IQ4 affected its crystal packing forces, while the
latter determined the crystalline structure. Hence, the simulations of the peptide at the
high and the very high salt concentrations exemplify how crystallographic conditions
may determine the outcome structure of the crystal.
3.7 Summary
MD simulations of IQ peptides indicate that the free (and also the bound) IQ2
peptides almost do not refold in a solution and maintain a stable helical structure. In
comparison, both the free and the bound IQ4 peptides are less stiff and tend to curve and
flex in a profound manner. This is attributed to the higher net charge (Z = +6) of the IQ4
peptide than this of the IQ2 peptide (Z = +2), and reflected by the electrostatic attraction
between positive and negative residues located on its N- and C- terminals (for example,
R4-E25). The IQ4 peptide presents an intrinsic instability and an increased tendency to
flexibility at a more or less defined location (further discussed in the next chapter).
Though the IQ4 peptide exhibits a structural modification when simulated at the presence
of the protein, its extent of refolding is considerably higher when it is simulated at its
absence. Secondary structure analysis of both free IQ peptides followed their secondary
structure change throughout the simulations, revealing their stable solution
conformations. The curved shape of the free IQ4 peptide was observed when it was
simulated under sub-physiological and physiological salt concentrations (~ 30 mM and ~
100 mM), and was not detected when the simulations were performed under over-
physiological salt concentrations (~ 300 mM and ~ 2.4 M).
89
4. The Structure of the Light Chain-Binding Domain (LCBD) of Myosin
V
Given our results presented in chapters 1−3 of the thesis, and an MD simulation
of extended IQ4 peptide presented below, we propose a dynamic solution model of the
LCBD of myosin V (section 4.3). The model, which involves mutual modulations of the
structures of the light chain proteins in respect to the IQ peptides of the myosin's neck
towards each other, may have important implications regarding the structure-function
relationship of the lever arm of myosin V.
4.1 The Current Structural Model
Myosin V is a versatile motor involved in the short-range transport of vesicles in
the actin-rich cortex of the cell. Its long neck domain, serving as a lever arm (19, 20),
gives rise to a step size of ~ 36 nm, the largest step size thus far measured for a myosin
motor. The LCBD neck of myosin V consists of six tandem IQ motifs, to which light
chain proteins, such as the CaM and the Mlc1p, are bound. The primary function of the
light chains is to regulate the ATPase activity of the globular head of myosin V (13, 17,
164). The crystal structures of the Mlc1p-IQ2, Mlc1p-IQ4 and Mlc1p-IQ2/3 complexes
had been determined by Terrak and co-workers (28, 56). On the basis of these structures,
and sequence similarity among the six IQ motifs, Terrak and co-workers suggested a
model for the LCBD (Fig. 4.1) (57). According to this model, the six IQ motifs, that
constitute the neck domain of the myosin V, adopt a straight long alpha helical
configuration (green). Moreover, two of the light chain proteins retain an extended
configuration (see the arrows pointing towards the light chains that bind the IQ4 and the
90
IQ6 peptides), in which their NL does not interact with the IQ motif, as determined by the
crystalline form of the Mlc1p-IQ4 complex.
Figure 4.1: Model of the LCBD of myosin V. The light chains, which can be either CaM
or CaM-related molecules such as the Mlc1p, are colored cyan (NLs) and magenta (CLs),
and the six-IQ fragment of the heavy chain is colored green. The black arrows point
towards the light chains that bind the IQ4 and the IQ6 peptides. An enlargement
illustrates the interaction between adjacent light chains. Adapted from (57).
This proposed model of the LCBD does not take into account the conformations
that the proteins may reveal in solution; rather, it is constrained by the packing forces of
the Mlc1p-IQ crystal structures. These packing forces may vary between the Mlc1p-IQ2
and the Mlc1p-IQ4 structures because each complex was crystallized solely under unique
crystallographic conditions. Attempts to grow crystals of both complexes under identical
or similar conditions failed (Terrak-M, personal communication). The elucidation, by
MD simulations, of the solution structures of two Mlc1p-IQ complexes (presented in
chapters 1-2), and with a combination of MD simulation of free IQ2 and IQ4 peptides
(presented in chapters 3-4), calls for reevaluation of the Mlc1p-LCBD model structure.
Our reevaluation of the current structural model and suggestion for a solution
model, which are discussed in section 4.3, are based on a wide range of experimental data
91
as well. Fluorescence imaging with one-nanometer accuracy (FIONA) (165-167) and
time-resolved single-molecule fluorescence polarization studies (SMFP) (168) suggest a
fundamental role to the elasticity of the LCBD during the movement of the myosin V.
Myosin V "walks" following an asymmetric hand-over-hand mechanism, where its heads
alternate leading and trailing positions along the actin filament, analogous to the hands of
a rope climber. In the course of its stride, a conformational change was demonstrated
during the transition of the lever-arm from a pre-stroke to post-stroke state. This change
is manifested by a tilting of the LCBD between two distinct conformations, a straight one
and a bent one. The curvature of the LCBD deduced from these experiments is in a very
good accord with the one predicted in our MD studies as further discussed. In addition,
when actin-bound myosin V was imaged by electron microscopy (Fig. 4.2) (169, 170), a
bent lever-arm was observed.
Figure 4.2: Two electron microscopy images showing filaments of actin with two-
headed myosin V "walking". The red arrows point towards the myosin's lead arm, seen in
a bent conformation. These electron microscopy images, by presenting myosins with
curved lever arms, strengthen our suggested model. The scale bar is 50 nm (note that the
myosin was found with fringes and thus spans ~ 50 nm). Images adapted from (169).
The leading head was curved backwards, whereas the rear head was straighter,
92
resembling a skier in a telemark stance. Thus, the electron microscopy data confirms the
curved shape of the LCBD of the lead head pre-stroke state. Furthermore, when the
crystal structure of scallop’s myosin S1 was determined (171), a ~ 90° curvature of the
myosin's IQ4 motif neck domain was observed. It was found that the lever arm of the
scallop's myosin S1 does not move as a rigid body, but rather flexes when the myosin is
in motion.
4.2 Structure and Dynamics of an Extended IQ4 Peptide
In order to verify that the kink presented by the bound (Fig. 3.4B and chapter 1)
and the free IQ4 peptides (Figs. 3.2 and 3.4A) has a physiological relevance, we build an
extended IQ4 peptide and performed an MD simulation for it. The sequence of this
peptide consists of the IQ4 peptide, as present at the crystal structure of the Mlc1p-IQ4
complex, and an additional twenty residues. Ten of these residues flank its N-terminus
and are part of the IQ3 peptide sequence, while the other ten of these residues flank its C-
terminus and belong to the IQ5 peptide sequence. Hence, this 45 long amino acids
sequence represents a section from the poly-IQ (IQ1-IQ6) of the neck of myosin V.
Comparison between the model solution structures of the free IQ4 peptide after
100-ns of simulation, the bound IQ4 peptide after 12-ns with the Mlc1p protein, and the
extended IQ4 peptide after 20-ns of simulation are, presented in Fig. 4.3 (A-C,
respectively). All model structures exhibit a major kink (see the black arrows), that is
roughly located at the same location along the peptides. The common position of the
angular shift of the peptide (from a linear peptide with a ~ 180° angle to a curved one
with a hinge) can be referred as a "hot spot", which tends to curve rather than assume a
93
Figure 4.3: Snapshots of the simulated model structures of the IQ4 peptides. (A) After
100-ns simulation of free IQ4 peptide; (B) After 12-ns simulation of bound IQ4 peptide;
(C) After 20-ns simulation of extended IQ4 peptide (the IQ4 peptide is drawn in blue,
while its extended residues are colored in red). The black arrows indicate the "hot spot"
position.
C B A
straight conformation. This "hot spot" is also seen at the simulation of the free IQ4
peptide at the low salt concentration (Fig. 3.9A).
We use the term "hot spot" not only as a phrase to describe the location of the
peptide's twist but literally as an idiom to characterize a sequence encompassing a high
B-factor. B-factor or temperature factor is an indicator of thermal motion of an atom, and
is commonly used as a measure of how much an atom oscillates or vibrates around a
specified position. Thus, the high B-factor that is observed at the location of the kink in
the simulations of the IQ4 peptide reflects its local inherent instability. Moreover, when
the RMSF was calculated for the IQ4 peptide's simulations, it turned out that residues that
present high RMSF values correspond to those that curve. Therefore, intrinsic flexibility
of the IQ4 peptide was already embedded in its X-ray structure, and, as such, our finding
is not surprising.
The RMSD analysis of the extended IQ4 peptide is presented in Fig. 4.4. It
increases from ~ 0.1 nm to ~ 0.5 nm, and stabilizes on this value. Since the RMSD
94
Figure 4.4: The RMSD of the backbone atoms of the MD run of the extended IQ4
peptide as a function of the simulation time.
reached to a relatively constant value for the last 10-ns of the simulation, further major
conformational changes are not expected. Thus, the curved extended IQ4 peptide seems
to be structurally steady and hence may represent a physiological entity. This finding
strengthens and supports our reevaluation regarding the structural model of the LCBD
presented in section 4.3.
4.3 The Suggested Solution Model
The following suggested solution model of the LCBD is a consequence of our
overall findings presented throughout this study. We propose that the light chains of the
myosin, namely the CaM and the Mlc1p proteins, may maintain a compact conformation
and not an extended one as their ID is bent (as in Figs. 1.1B and 1.3B). Their NL is
probably not free to engage in protein-protein interactions as claimed by Terrak and co-
workers, but rather interacts with the IQ peptides, coming into a close contact with their
CL. In addition, and not less important, we propose that the poly-IQ sequence of the
95
myosin's neck may curve when bound to the light chain proteins. This structural
flexibility of the poly-IQ is associated with the myosin's walking over the actin filament,
generating the bended knee conformation of the lead arm of the LCBD, which is a crucial
element in its mechano-chemical mechanism. Therefore, the banana-shaped arm of the
myosin, which was not included in the structural model of Terrak and co-workers, is
revealed by our simulations. Besides supplying a dynamic model of the poly-IQ
sequence, we point out the exact location of its knee. According to our simulations, it
appears that the curvature of the neck may be located within the IQ4 peptide sequence.
The hinge presented by the IQ4 peptide, observed in all our simulations under
physiological salt conditions (and also for the extended IQ4 peptide), may correspond to
a physiologically relevant bent solution structure of the lever arm of myosin. This unique
observation regarding the location of the curve, which was not specified by electron
fluorescence or electron microscopy studies, exemplifies the ability of MD simulations to
provide additional information to the one obtained by experimental biologists.
The tight refolding of the protein around the peptides and the bending of the IQ4
peptide point out the difficulty of predicting the solution structure of a large protein-
peptide complex based on crystal structures of some of its isolated components. The
schematic description of the IQ motifs as constitutes of a rigid straight alpha helix (as
shown on Fig. 4.1), which is not consistent with the dynamics of the peptides and
complexes, represents an unlikely physiological conformation.
Our view about myosin V is corroborated by an illustration, in which the
movement of myosin V over an actin filament is shown (Fig. 4.5). Though this is only an
illustration, we feel that it faithfully delivers our proposed solution model. The lead arm
96
of the neck is curved at a position that corresponds to the IQ4 peptide (see the white
arrow), exemplifying that the flexibility of the neck is embedded in the myosin's motion.
Thus, the flexibility of the neck, as opposed to the model proposed by Terrak and co-
workers, is necessary for the proper function of the mechano-chemical function of the
myosin molecules.
Figure 4.5: Myosin V (green), a biomolecular motor that moves in nanometer size steps
on actin (red), transports cargo within cells. By placing a fluorophore near one foot
(rainbow colored oval), and following the motion a single myosin V, it was determined
that myosin V "walks", placing one foot over the other, and does not "crawl". The
illustration demonstrates that the neck domain of myosin V, as predicted by our
simulations, curves when it strides over the actin filament. The white arrow points
towards the IQ4 peptide of the lead arm of the myosin. The light chains were omitted
from the illustration for simplicity. Adapted from Yildiz et al. (166).
4.4 Summary
On this chapter we addressed the structure of the LCBD of myosin V from the
yeast Saccharomyces cerevisiae. We presented the current structural model and proposed
a modified model, based upon the various MD simulations discussed on the thesis. The
97
crystal structure of the Mlc1p-IQ4 protein-peptide complex was obtained under high salt
conditions. As such, the IQ4 peptide exhibits a straight alpha-helical configuration and
the protein, restricted by the linear conformation of the peptide, warps itself around it.
According to our suggestion, which was elaborated throughout the thesis, the crystal
structure of the Mlc1p-IQ4 protein-peptide complex may not represent its physiological
one, and thus the model proposed by Terrak and co-workers may be misleading. We wish
to stress out that although a wide plethora of evidences point out to this conclusion, it
would be interesting to perform a simulation of that complex under high salt conditions.
Such an MD simulation will provide a further verification for the influence of the
crystallization conditions, i.e. high salt and ionic strength of the crystallization buffer, on
the configuration of the protein inside the crystal lattice.
Apparently, the solution structure of the LCBD of myosin V is more complicated
than the one based on crystal structures of a few individual Mlc1p-IQ complexes, as
predicted by Terrak and co-workers. When our simulations are taken into account
together with the experimental data presented above, it is reasonable to conclude that the
LCBD is not a passive structural device but dynamic proteinous machinery. We argue
that mutual structural flexibility of the light chain proteins and the IQ peptides represents
a more realistic model of the neck region of myosin V. Our proposed solution model of
the flexed neck of myosin V IQ4 peptide is in accord with all our MD simulations and
also in agreement with other research groups reporting the flexible nature of the neck.
However, a word of caution should be stated. We cannot preclude the possibility that the
neck may curve and break its linearity along other IQ peptides, besides the primary kink
at the IQ4 sequence.
98
IV. OVERALL GENERAL DISCUSSION
The current research is the first MD study of IQ peptides in a complex with a
CaM-like protein and at its absence. Since IQ motifs are widely spread in nature, serving
as binding sites for CaM and CaM-like proteins, and as the structure of CaM resembles
that of Mlc1p, it was of great importance to conduct this research in order to elucidate the
structural mechanism underlying the interaction of CaM and CaM-like proteins with IQ
peptides. Analysis of the structure, dynamics and energetic aspects of the Mlc1p-IQ
complexes was of high significance also due to their important role in the regulation of
the mechano-chemical myosin system of the yeast Saccharomyces cerevisiae. Given that
the Mlc1p protein functions and binds myosin V at the absence of Ca+2
, fulfilling roles
taken by Holo-CaM in other classes of myosins, our conclusions presented in this study
may, as well, hold for the entire family of myosins.
In this study, we described a usage of the MD methodology as a tool to analyze
the crystal structures of Mlc1p-IQ complexes. The reported simulations addressed the
manifold structures of the Mlc1p-IQ complexes as found in crystal structures and in
solution. We have clearly demonstrated that the crystal structure of the Mlc1p-IQ4
complex, obtained under high salt conditions, does not represent its solution structure. At
this high ionic strength, the IQ4 peptide assumes a straight alpha helix and does not bend.
It supplies a scaffold on which the protein binds but the latter keeps an extended
conformation. At a physiological ion strength, the IQ4 peptide curves and consequently
the protein may hold a compact structure. We speculate that at low-medium ionic
strength the Mlc1p-IQ4 could not well diffract, representing an inhomogeneous crystals
population.
99
We can generalize the above mentioned argument and claim that crystal structures
of proteins do not necessarily represent their solution structures. Though this claim may
not seem to be too adventurous or innovative, our research clarifies that a crystal structure
can be influenced by the crystallographic conditions, while the latter determine the
packing forces operating at the crystal lattice. Furthermore, crystalline forms of proteins
can be imposed by specific crystallographic conditions, consequently leading to a
fundamental deviation of the obtained X-ray structure from the native configuration.
We have noticed that the Mlc1p protein had a structural versatility, allowing it to
bind the IQ peptides in a mode reflecting their precise sequence, hardly using the "IQ
motif residues" as key anchoring sites. Apparently, the Mlc1p protein can be flexed in
many configurations, each suitable for a certain IQ structure. Thus, the sequence variation
among the IQ motif peptides is sufficiently large to induce non-identical interactions with
the same protein. Taking a broader view, we suggest that when two similar (but not
identical) peptides, which belong to the same family, bind the same protein, each protein-
peptide structure may assume a unique conformation.
Following a comprehensive energy analysis, we found that the protein-peptide
complexes formation is mediated by enthalpy, while entropy opposes it. The close
interaction between the Mlc1p protein and the IQ peptides is grossly mediated by LJ
interactions, whereas their opposite highly charged surfaces contribute to their initial
encounter. Electrostatic interactions may serve as the driving force for long-range
molecular recognition, but once protein-peptide contact occurs, highly specific VdW
interactions and non-specific hydrophobic interactions stabilize the Mlc1p-IQ complexes.
This finding may also be valid for pairs of highly opposite charged proteins that form
100
protein-protein or protein-ligand complexes.
The simulations of the protein-peptide complexes, combined with the simulations
of the free IQ peptides, allow us to offer a comprehensive solution model of the LCBD.
According to our simulations, and in contrast to a structural model for the LCBD
suggested by Terrak and co-workers, the solution structures of the Mlc1p-IQ protein-
peptide complexes may impose refolding of the light chain proteins around the IQ
peptides. Thus, the light chain proteins may reveal a compact configuration and not an
extended one. Considering a poly-sequence of IQ motifs, as present in the LCBD, it
appears that its final structure, saturated by the CaM-like proteins, is under intensive
internal stress. The internal stress may be associated with the mechano-chemical function
of the myosin molecules. When the myosin "walks" over the actin filament, its lead arm
of the neck domain must flex in every stride. Our simulations, by adding a dynamic
nature to the structural model, demonstrate the curvature of the LCBD. As suggested by
our simulations, the LCBD assumes a banana-like conformation, while the location of its
knee corresponds to the IQ4 peptide. The knee-shape structure that the LCBD may hold
is essential to its functionality. We wish to note that our model emphasizes that the
LCBD is a dynamic proteinous machinery, and not a passive structural device as
previously suggested.
In a broader perspective, our research shows that careful application of MD
simulations can be used for extending the structural information presented by crystal
structures, thereby revealing the dynamic configurations of proteins in their physiological
environment. It is to be hoped that experimental structural biologists will make increasing
use of MD simulations for obtaining a deeper understanding of particular biological
101
systems. When MD simulations for long durations will become routine procedures, a
constructive interplay between the simulations and experiments will be useful and
informative regarding both sides. Given the availability of several MD programs, large
amounts of computer time, and examples for which MD has really played a role in
furthering our understanding of protein structure and functions (as presented in this
research), we look forward to a wide field of biological and biophysical applications for
MD in the future.
102
V. SUPPLEMENT
1.1 Articles
The outcome of the thesis is three articles:
(I) Ganoth, A., E. Nachliel, R. Friedman, and M. Gutman. 2006. Molecular dynamics
study of a calmodulin-like protein with an IQ peptide: Spontaneous refolding of the
protein around the peptide. Proteins 64:133-146. (The article is attached at the following
pages).
(II) Ganoth, A., R. Friedman, E. Nachliel, and M. Gutman. 2006. A molecular
dynamics study and free energy analysis of complexes between the Mlc1p protein and
two IQ motif peptides. Biophys J 91:2436-2450. (Cover article. Both article and cover are
attached at the following pages).
(III) Ganoth, A., R. Friedman, E. Nachliel, and M. Gutman. The structural basis for
myosin V movement: A molecular dynamics study (temporary title). In Preparation.
103
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סימולציות מחשב של קומפלקסים
בין חלבון לפפטיד תוך שימוש
מודלמערכתבשרשרת הקלה של מיוזין כ
לשם קבלת התוארחיבור
"דוקטור לפילוסופיה"
מאת
אסף גנות
אביב-הוגש לסנאט אוניברסיטת תל
2006 יולי
עבודה זו נעשתה בהדרכת
מנחם גוטמן' פרופ
תקציר
. מית של מיוזיןיכ-הוא רכיב חיוני במערכת המכנו, חבר במשפחת הקלמודולין, Mlc1pהחלבון
ואר של ו קושרים את מתחם הצMlc1pשישה חלבוני , Saccharomyces cerevisiaeבשמר ההנצה
לבין Mlc1p מבנים של מספר קומפלקסים בין החלבון .IQ פפטידים מסוג המורכב משישה, Vמיוזין
, המחקר הנוכחי מרחיב את ההבנה שלנו.X של קרני קריסטלוגרפיהבאמצעות נפתרו IQפפטידי
דינמיקה ואנרגטיקה של , על מבנים,י דינמיקה מולקולרית וחישובים נוספים"באמצעות מחקר ע
המחקר , הרחבה ניכרת של המידע המבני האצור במבנים הגבישייםל בנוסף. Mlc1p-IQהקומפלקסים
כיצד קיפול באתר מסוים ו מצאנ. על סיב האקטיןVמספק הבנה אטומית אודות דגם התנועה של מיוזין
מנוף תקינה שלה תופעולאת ובכך להבטיח , כואר המיוזין יכול לשמש כמפרק גמיש לאורוהממוקם על צו
.זרוע המיוזין
4IQ ו 2IQסימולציות של דינמיקה מולקולרית של הפפטידים ) I: (כוללת ארבעה פרקיםהתיזה
-Mlc1p השוואה מפורטת בין הסימולציות של שני הקומפלקסים ) Mlc1p;) IIבקומפלקס עם החלבון
IQ;) III ( סימולציות של דינמיקה מולקולרית של פפטידיIQחופשיים ;) IV (של הערכה מחודשת
.Vתחם הקושר שרשראות קלות של מיוזין המבנה של המ
פלקסיםמבפרק הראשון של התיזה אנחנו מציגים סימולציות של דינמיקה מולקולרית של הקו
Mlc1p-IQ4 ו Mlc1p-IQ2 ,הקומפלקס.לאחר רלקסציה שלהם בתמיסת מלח פיזיולוגית Mlc1p-
IQ2 בות הסימולציה אופיין בשינוי עיקריים שלו ובעקהעבר רלקסציה ללא איבוד של כוחות האריזה
עבר תהליך של קיפול מחדש במהלכו החלבון שינה את , 4IQעם הפפטיד , פלקס הנוסףמ הקו.מבני מוגבל
אנו מציגים השוואה , בפרק השני של התיזה. מבנהו ממתוח לקומפקטי והפפטיד התקפל לשני חלקים
, בצענו השוואה מקיפה בין המבנים. קסיםפלממפורטת בין סימולציות הדינמיקה המולקולרית של שני הקו
אנליזת האנרגיה כוללת ניתוח של . פפטיד- חלבוןנמיקה והאנרגיה החופשית של האינטראקציהיהד
. פטיד וציון תרומתם של רכיבים אנרגטיים שונים והפחלבון בין הפלקסיםמהכוחות הפועלים על הקו
ך פרקי זמן משתנים ובתנאים מש חופשיים לIQהפרק השלישי של התיזה עוסק בסימולציות של פפטידי
שלושינויים בין מבני התמיסה, שינויים בין הקונפורמציות של פפטידים בנוכחות ובהעדר חלבון. שונים
פלקסים מקוה התוצאות של סימולציות הדינמיקה המולקולרית של . נידונים, החופשייםIQשני פפטידי ה
ושל פפטידים חופשיים מאפשרות לבצע הערכה של המבנה של המתחם הקושר שרשראות פפטיד -חלבון
. IQלבין פפטידי ) Mlc1pכמו (לקסים בין שרשראות קלות פה קומשהמורכב משי, Vקלות של מיוזין
במרכז המודל המוצע עומדת התפיסה שהמתחם הקושר . הערכה זו מוצגת בפרק הרביעי של התיזה
ולכן המודל לוקח בחשבון את יכולתם של החלבון ,נמיתי הוא ישות תאית דVוזין שרשראות קלות של מי
Mlc1p ושל פפטידי IQלהתגמש ולהתכופף באופן הדדי .
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4IQ-p1Mlc) . and M, Friedman.R, Nachliel. E, .A, Ganothמולקולרית של הקומפלקס
Gutman. 2006. Molecular dynamics study of a calmodulin-like protein with an IQ
peptide: Spontaneous refolding of the protein around the peptide. Proteins 64:133-
ללת הכו, Mlc1p-IQ2 ו Mlc1p-IQ4 מציג השוואה נרחבת בין הקומפלקסים המאמר השני;)146
V ). R, .A, anothGאנליזה אנרגטית והערכה מחודשת של המתחם הקושר שרשראות קלות של מיוזין
Friedman, E. Nachliel, and M. Gutman. 2006. A molecular dynamics study and free
energy analysis of complexes between the Mlc1p protein and two IQ motif peptides.
Biophys J 91:2436-2450(; העוסק בסימולציות של פפטידי , המאמר השלישיIQבהכנה, חופשיים.
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- בתהליכים מכנוIQפפטידי תפקידם העיקרי של לאור . קלמודולין ובהעדרו בקומפלקס עם חלבון דמוי
ה מספקת תיאור ברזולוציה אטומית של האינטראקציות שלהם עם קלמודולין וחלבונים התיז, כימיים
ולציות דינמיקה מולקולרית ונגמר מחיל בסיתמשרטט טיול ממוחשב המ המחקר. דמויי קלמודולין
מדענים ששיתוף פעולה בין ומדגים ,Vבתובנות אודות המתחם הקושר שרשראות קלות של מיוזין
.מבנה-נה טובה יותר של יחסי תפקודהבפיזיקאים יכול לתרום ל-ביובין להגרפילוטקריסהעוסקים ב
