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Permeability of drugs and hormones through a lipid bilayer: insights fromdual-resolution molecular dynamics†

Mario Orsi and Jonathan W. Essex*

Received 20th March 2010, Accepted 21st May 2010

DOI: 10.1039/c0sm00136h

The unassisted permeation process of b-blocker drugs (alprenolol, atenolol, pindolol) and steroid

hormones (progesterone, testosterone) through a lipid membrane is simulated by a novel dual-

resolution molecular dynamics approach. The lipid and water molecules are described by simple and

efficient coarse-grain models, whereas the drug and hormone permeants are represented by traditional

atomistic models. Our hybrid method is about two orders of magnitude faster than standard atomic-

level counterparts. For each permeant, we calculate the transfer free energy as a function of depth inside

the bilayer; these data indicate the location across the membrane where the solutes preferentially

partition. Using the free energy profiles, we develop a simple expression that proves remarkably

accurate in predicting experimental permeability rankings; the proposed permeation model highlights

and addresses potentially problematic aspects of the standard solubility-diffusion theory. We also

calculate the diffusion coefficients of the permeants, and track their lateral motion to study their

diffusive patterns. Furthermore, we show the drugs’ perturbing effect on the bilayer structure and

quantify the steroids’ preferred orientations. The results obtained compare favourably with

experimental measurements and traditional atomic-level simulation data reported in the literature.

Promising potential applications of our methodology to areas such as drug design and membrane-

protein modelling are discussed.

Introduction

Passive permeation is a fundamental mechanism for the trans-

port of molecules across biological membranes. Biosystems

absorb, distribute and eliminate the majority of chemicals by

unassisted, spontaneous diffusion through phospholipid

bilayers.1 The biological importance of studying and under-

standing passive permeation is therefore evident. Moreover, such

knowledge is extremely beneficial for industrial applications in

medicinal chemistry, nanotechnology, environmental toxicology

and many other fields. Unfortunately, the mechanism of solute

permeation through membranes is difficult to study experi-

mentally, because of the small scale and complexity of lipid

bilayer systems.

Particle-based computer models represent particularly attr-

active tools to study permeation; simulations have the potential

to unveil the molecular basis of the permeability mechanism and

provide estimates of the permeability coefficient. In principle,

simulations can directly reproduce the spontaneous permeability

phenomenon. For example, using a simplified model, we have

recently been able to calculate the transmembrane permeability

coefficient of water from the direct observation of membrane

School of Chemistry, University of Southampton, Highfield, Southampton,SO17 1BJ, United Kingdom. E-mail: [email protected]; Fax:+ 44 (0)23 8059 3781; Tel: + 44 (0)23 8059 2794

† Electronic supplementary information (ESI) available: Inertial featuresof permeant molecules, examples of time evolution of constraint forces,numerical results of permeability predictor, comparison betweenpermeant free energy profiles and lateral pressure profile. See DOI:10.1039/c0sm00136h

This journal is ª The Royal Society of Chemistry 2010

crossing events over microsecond-long simulations.2,3 However,

standard atomic-level (AL) membrane simulations cannot

currently reach such a timescale, and indeed passive water

transport has never been quantified with these traditional

models. For example, in a recent state-of-the-art molecular

dynamics study,4 four phosphatidylcholine bilayers, each

comprising 128 lipids, have been simulated for 50 ns. In the four

simulations, only 2, 4, 6 and 7 crossing events of water molecules

were respectively observed; from such limited statistics, an

estimation of the permeability coefficient would not be reliable.

Moreover, for many other important solute molecules, such as

large hydrophilic drugs, the timescales required to directly

observe a statistically significant number of translocation events

are expected to be in the range of (at least) milliseconds, beyond

the capabilities of any particle-based simulation model.

Fortunately, permeation processes can still be simulated through

indirect techniques, typically involving the imposition of

constraints on the permeant; with such methods, AL molecular

dynamics simulations have indeed been successfully employed to

predict permeability coefficients and to investigate the general

permeation mechanism for several solutes.5–7 However, there is

a huge computational cost inevitably associated with the simu-

lation of traditional AL membrane models, and this negatively

affects permeability simulation studies. For example, obtaining

well-converged data is difficult. Computational issues also limit

the size of the bilayer; this can induce artefacts, especially when

large drugs are inserted into the membrane. Also, the number of

different permeants that can be investigated in a reasonable

amount of time is limited to a handful of molecules; this prevents

applications in a drug design context, where the concurrent study

Soft Matter, 2010, 6, 3797–3808 | 3797

Fig. 2 Steroid hormone structures.

of large sets of candidate compounds is normally required. For

these reasons, permeability studies would benefit enormously

from improvements in simulation efficiency.

A popular approach to cut computational cost involves

adopting coarse-grain (CG) descriptions, where entire clusters of

atoms are reduced to single ‘‘supersites’’; this simplification

process dramatically lowers the number of interactions to be

calculated. CG methods can increase simulation speed by several

orders of magnitude with respect to corresponding AL methods,

while still retaining the fundamental physics.8–12 However,

transmembrane permeability is extremely sensitive to the atomic

details of the permeating species; marginal alterations in the

solute structures can lead to differences of several orders of

magnitude in the permeability coefficients.13 Standard CG

models lack atomic detail, and hence are arguably unsuited to

study membrane permeability phenomena. A promising

compromise involves combining the accuracy of AL force fields

to the efficiency of CG models through multiresolution methods,

also called concurrent schemes, where the ‘‘chemically sensitive’’

parts of the system (for example, the solutes in membrane

permeation studies) are modelled atomistically, while the

surrounding environment (the membrane) is simplified with CG

representations. Recent work in this field is described thoroughly

in several reviews.8–11,14 Here we note that none of the reviewed

multiresolution methods has yet been used to simulate trans-

membrane permeation processes; in fact, applications have so far

been limited to rather simple systems, such as basic structural

and dynamical properties of proteins,15 an idealised liquid of

nonpolar particles,14 methane,16,17 water14 and a generic solvated

macromolecule.14 The main difficulty that has so far hindered

these approaches concerns the interfacing between the different

resolution levels; in particular, problems arise whenever mole-

cules diffuse across regions of different representations, as the

models for the AL and CG particles are not compatible.

In this study, we describe multiresolution simulations based on

a simple and direct interfacing, where AL and CG particles

interact through compatible potentials. Permeant molecules,

represented with standard AL models, interact ‘‘naturally’’

with lipids and water represented at the CG level, as mixed

AL-CG interactions are treated using standard mixing rules,

without the need for interface regions. Such a straightforward

dual-resolution approach relies on the characteristics of our

Fig. 1 b-blocke

3798 | Soft Matter, 2010, 6, 3797–3808

recently-developed CG membrane model;2,3 this model, uniquely

in the current CG landscape, retains compatibility with AL force

fields, particularly with respect to the electrostatics. We recently

validated our multiscale methodology by calculating water-

octane partition coefficients for a set of AL amino acid side

chains embedded in CG solvent representations18 and by simu-

lating the permeation of a set of small (molecular weight < 100)

AL organic molecules across a CG membrane.19 In the study

presented here, we apply this dual-resolution approach to

investigate the permeability properties of larger (molecular

weight z 300) solutes: three drugs (alprenolol, atenolol and

pindolol) and two hormones (progesterone and testosterone).

Alprenolol, atenolol and pindolol belong to the b-blocker drug

class, recommended as first-line treatments of numerous

cardiovascular conditions.20 The chemical structures of these

molecules are shown in Fig. 1. Steroid hormones form a category

of substances that regulate a great variety of physiological

functions, including growth, sexual development and carbo-

hydrate metabolism.21 The chemical structures of progesterone

and testosterone, two steroid hormones which also have

anaesthetic properties,22 are shown in Fig. 2.

In the following sections, we first describe the models

employed, the dual-resolution strategy, the z-constraint method

(through which most permeability properties are obtained) and

the simulation details. A first set of results, including transfer free

energies and diffusion properties of the permeants, is sub-

sequently reported. From the free energy data, we then propose

and validate a simple expression aimed at ranking permeants

according to their permeability coefficients. Additional obser-

vations in terms of the orientation of the permeants and their

effect on the membrane structure are subsequently described. In

r structures.


general, the results obtained are compared to available experi-

mental and AL simulation data from the literature. We then

further discuss our findings, along with the advantages and

limitations of the methodology. Ongoing work and future

extensions are also considered, especially in the context of drug

design and membrane protein simulations.

Coarse-grain models of the lipid bilayer and hydratingwater

Dimyristoylphosphatidylcholine (DMPC) lipid bilayers are

modelled using our recently developed CG method.2,3 Each

lipid molecule is represented by only ten CG sites (as opposed

to the over one hundred atoms that constitute the corres-

ponding real molecule). Using the Lennard-Jones potential,

the lipid headgroup is modelled as two spherical CG sites; in

each lipid, these two macrounits account for the choline and

phosphate moieties. The phosphocholine headgroup is char-

acterised by a large electrical dipole, arising from a positive

net charge on the choline group and a corresponding negative

one on the phosphate group. We represent these electrostatic

features by a positive point-charge embedded in the choline

CG particle and a negative one in the phosphate CG particle.

The glycerol and hydrocarbon regions are represented as soft

uniaxial ellipsoids through the Gay-Berne potential.23 The

Gay-Berne potential can be regarded as a generalisation of the

Lennard-Jones potential to non-spherical shapes. In our CG

representation, the glycerol-ester groups are described by two

Gay-Berne ellipsoidal units, each embedded with a point-

dipole to model the dipolar charge distribution in this region.

The two hydrocarbon tails (attached to the glycerol-ester

segments) are represented by chains of three uncharged

Gay-Berne ellipsoids.24 Each tail ellipsoid can be seen as

representing a segment of four consecutive CH2 groups. The

bonds between the lipid CG sites are described by the Hooke

(harmonic) potential, as is standard practice. A thorough

description of our lipid CG model can be found elsewhere.2,3

Some of the force field parameters have been recently refined;

the complete updated parameter set, which has been adopted

for the simulations reported in this article, can be found

elsewhere.3,19

Water is described by the soft sticky dipole (SSD) model,25

with parameters optimised for electrostatic cutoff simulations.26

The SSD water particle is represented by a single interaction

centre, which comprises a Lennard-Jones spherical core, a point-

dipole to capture electrostatics, and a tetrahedral ‘‘sticky’’ term

to represent hydrogen bonding. Detailed formulae of the SSD

potential, and corresponding forces and torques, can be found

elsewhere.27

The Lennard-Jones term of the SSD potential interacts with

the Gay-Berne lipid terms (tail and glycerol sites) through the

generalised Gay-Berne potential.28

Regarding the electrostatics, all charges and dipoles in our

model interact with each other, through either charge-charge,

charge–dipole or dipole–dipole potentials.29 An important and

distinguishing feature of our model is that all electrostatic

interactions are realistically treated assuming a relative dielectric

constant 3r ¼ 1.


Atomic-level permeant models

The permeant molecules considered in this study comprise three

b-blocker drugs (alprenolol, atenolol and pindolol) and two

steroid hormones (progesterone and testosterone); the chemical

structures are reported in Fig. 1 and 2. The coordinates of the

models were obtained from AL molecular dynamics permeability

simulations;30,31 for each solute, a single representative structure

was employed. The AMBER program32 was used to optimise the

geometry, assign the Lennard-Jones parameters from the GAFF

force field33 and assign partial charges with the AM1/BCC

model.34 For simplicity, no intramolecular degrees of freedom

are taken into account, that is, solute molecules are simulated as

rigid bodies; the permeants’ inertial features are reported in the

Supplementary Information. Solutes are assigned no net charge,

on the assumption that only the neutral species diffuse across the

bilayer.

Mixed atomic-level/coarse-grain interactions

All the interacting sites in our dual-resolution membrane-water-

solute systems are directly compatible with each other, and

therefore mixed interactions between CG sites and AL atoms can

be treated straightforwardly by the formulae available for the

corresponding potentials. In particular, standard mixing rules

are adopted for the Lennard-Jones,35 Gay-Berne28 and electro-

static29 potentials. The only exception to this general approach

involves the introduction of two scaling factors to calibrate some

of the AL-CG interactions, as described in the following. Such

minor adjustments should be expected, given that we are mixing

two rather different empirical models, that is, our coarse-grain

force field2,3 and the GAFF atomic-level force field.33 The cali-

bration of the electrostatic potential between CG and AL sites

involved calculating hydration free energies for a range of solutes

by Monte Carlo simulations;18 water was represented with the

SSD potential,25,26 (as in the simulations reported in this article)

and the solutes with the GAFF all-atom force field33 (also used to

model the b-blocker drugs and steroid hormones). The solutes

used were 15 analogues of neutral amino acid side chains. In that

work,18 results could be brought into excellent agreement with

experimental data by introducing one parameter to scale the

electrostatic potential energy between water and solutes. In

particular, the scaling factor a calibrates the electrostatic energy

UEij between an AL atom i, bearing the partial charge Qi, and an

SSD water site j, characterised by the dipole mj:

UEij ¼ a

Qimjrij

4p30

��rij

��3 (1)

with 30 the permittivity of vacuum and rij the distance between

the interacting pair. The value for a obtained from the hydration

free energy calculations18 is transferred unaltered to the simula-

tions reported in this article; we therefore set a¼ 1.1. The second

scaling factor, b, controls the Lennard-Jones/Gay-Berne mixed

energy term 3ij between an AL atom i and an ellipsoidal CG site j:

3ij ¼ bffiffiffiffiffiffiffi3i3j

p(2)

with 3i the Lennard-Jones energy term for atom i and 3j the Gay-

Berne energy term for the CG site j. The constant b was para-

metrised by fitting the permeability coefficients of a set of small

Soft Matter, 2010, 6, 3797–3808 | 3799

organic molecules obtained using our dual-resolution approach19

to corresponding results obtained by standard AL simulations.36

The best fit was obtained for b ¼ 0.5;19 this value has been

transferred to the simulations reported in this article.

Calculation of permeability properties

An important advantage of studying transmembrane permeation

properties by simulation methods is the possibility of obtaining

local data from the various regions across the membrane.

However, standard molecular dynamics calculations are limited

in this respect, as the accessible simulation timescales are orders

of magnitude too short to allow most permeants to spontane-

ously diffuse across the bilayer (let alone to visit the various

intramembrane regions to a statistically significant level).

Fortunately, a number of special techniques are available to

‘‘push’’ molecules through the membrane and rigorously recon-

struct properties of interest.5 In this work, we employ one such

technique, the z-constraint method,37 which involves fixing the

permeant centre of mass at different positions along the direction

perpendicular to the bilayer plane (which is conventionally

parallel to the z axis of the simulation coordinate system) while

keeping track of the corresponding constraining force. In fact,

recently, we19 and Meineke et al.38 identified a potential flaw in

traditional implementations of the z-constraint technique, which

may result in violations of conservation laws and related simu-

lation artefacts. Here we employ a refined, rigorous algorithm

that we recently developed.19

A fundamental property governing membrane-solute interac-

tions is the transfer free energy profile DG(z), which characterises

the difference between the solute free energy at depth z inside the

bilayer and its reference value in the outer water phase. Using the

z-constraint method, DG(z) is calculated as:37

DGðzÞ ¼ðz

water

�f c

z

�z0��

dz0

(3)

hfzc(z0)i being the z component of the constraint force on the

solute at position z0 averaged over the total simulation time. The

local diffusion coefficient Dz(z) along the z-dimension can also be

obtained with:37

DzðzÞ ¼ðkBTÞ2ÐN

0

�Df c

z ðz; tÞ Df cz ðz; 0Þ

�dt

(4)

with kB the Boltzmann constant, T the temperature and

Dfzc(z, t) the ‘‘random’’ force, defined as the deviation of the

instantaneous force from the average constraining force acting

on the solute: Dfzc(z, t) ¼ fz

c(z, t) – hfzc(z)i.

Computational details

Molecular dynamics simulations were conducted using our

software BRAHMS,39 which implements the advanced rigid-

body integrator of Dullweber et al.;40 the integration time step

was 20 fs. Pressure and temperature were maintained at 1 atm

and 30 �C using the weak-coupling scheme.41 Lipid, water and

solute temperatures were coupled separately with time constants

sT ¼ 0.1 ps for lipid and water, and sT ¼ 0.02 ps for the solute.

The pressure was controlled by semi-isotropic volume scaling,

meaning that the normal and tangential components of the

3800 | Soft Matter, 2010, 6, 3797–3808

pressure tensor were regulated separately. In particular, the

pressure along the z-axis, that is, along the direction normal to

the interface, was controlled by rescaling the z-dimension of the

simulation region, whereas the tangential pressure was controlled

by rescaling the xy area, with the constraint that the interface

remains a square. The pressure-coupling time constant was sP ¼0.2 ps, and the isothermal compressibility is b ¼ 4.6 �10�5 atm�1. The cutoff radius for both Lennard-Jones and elec-

trostatic water-water interactions was 0.9 nm, as prescribed for

the SSD parametrisation adopted.26 Nonbonded interactions

involving permeant molecules were treated as group-based with

a cutoff distance of 1.5 nm; the interactions between all solute

atoms and the interacting site (either a lipid or a water site) were

evaluated if the distance between the solute mass centre and the

interacting site was less than the cutoff. All other nonbonded

cutoff radii were set to 1.2 nm. Electrostatic interactions were

treated using cutoff schemes. In particular, all charge-charge and

charge–dipole interactions (including those between AL and CG

sites) were implemented using the shifted-force cutoff method.35

We employed the SSD parameters optimised to evaluate dipole–

dipole interactions with a cubic switching cutoff scheme;26 for

consistency, all dipole–dipole interactions were treated in this

manner. The CG bilayer model comprised 128 DMPC lipids and

3400 hydrating SSD water molecules. For each of the AL per-

meants, the z-constraint method was applied to sample 16

equally-spaced z-positions across one monolayer; results are

considered valid also for the other monolayer by symmetry. In

particular, we sampled distances from 3.1 nm to 0.1 nm from the

bilayer centre in 0.2 nm increments along the z-axis (normal to

the membrane plane). In each simulation, a single solute mole-

cule was present in the bilayer. For each solute, 16 systems were

prepared (to cover the selected z-depths). Molecules were initially

inserted at 0.0002% of their actual size, and with charges and

Lennard-Jones parameters set to 0.0002% of their actual values.

The solutes were then incrementally grown back, and the inter-

action parameters incrementally increased toward their real

values, over 500000 molecular dynamics steps, corresponding to

10 ns of simulation time. This insertion procedure proved robust,

as it allowed a gradual relaxation of the bilayer around the

permeant. For each solute, the 16 systems were subsequently

equilibrated for a further 100 ns. For each of these systems,

production runs were then conducted for 200 ns, divided into

eight consecutive 25 ns batches. Accordingly, results will be

presented as average values and standard errors computed from

the averages over the eight 25 ns consecutive blocks of each of the

200 ns runs. The simulation length was set to facilitate conver-

gence of the data of interest, and especially the average constraint

force, from which free energy and diffusion coefficients are

derived (eqn (3) and (4)). We showed previously19 that the

constraint force fluctuates significantly over time scales of up to

few tens of ns; a choice for the sampling time of 200 ns seems

therefore appropriate. Examples of the time evolution of the

constraint force on a solute during the permeability simulations

conducted in this study are reported in the Supplementary

Information; there are evident substantial fluctuations, but

thanks to the extent of the sampling time we believe that overall

the data are statistically reliable. In fact, it will be seen in the

following sections that the estimated errors in the average values

of the permeability properties studied are relatively small.


Incidentally, the sampling time attainable by standard atomistic

permeability simulations5,30,36,42 is typically 1–2 orders of magni-

tude shorter than that achieved here by our dual-resolution

technique. All simulations could be run almost concurrently on

a supercomputer43 in a coarsely parallel fashion, meaning that

each (independent) constraint simulation ran on a different

processor. The entire set of calculations, totalling z 25 ms of

simulation time, could be completed in about one month.

Transfer free energies

The free energies of transfer from the water phase into the

bilayer, calculated with eqn (3), are reported in Fig. 3. All per-

meants display profiles of similar shape, characterised in parti-

cular by deep and broad free energy minima (indicating

preferential location) inside the membrane.

The b-blockers’ free energy minima correspond to distances of

1.7–1.9 nm between the drug’s mass centre and the bilayer centre;

these permeants are thus predicted to preferentially partition in

the lipid headgroup region. Unfortunately, no experimental

measurements of the intramembrane location of these drugs

are available. However, there are data for propanolol, also

a b-blocker, characterised by a structure similar to those of the

drugs considered in this study. When interacting with phospho-

lipid bilayers, propanolol was found to preferentially localise at

the interface between the headgroups and the hydrophobic

core;1,44,45 this is broadly consistent with the results from our

calculations.

The free energy curves of progesterone and testosterone are

rather similar to each other, as intuitively expected considering

the structural similarity of these two molecules. The steroids

generally display lower free energy values with respect to the

b-blockers, indicating a more pronounced lipophilic character.

The profiles are characterised by global minima at 1.1 nm from

the bilayer centre; the hormones’ mass centres are therefore

predicted to preferentially localise in the lipid glycerol region.

Fig. 3 Free energies of transfer from water to selected z-distances along

the bilayer normal. To facilitate interpretation, different regions across

the system are marked in italics, namely, the bulk water region, the lipid

headgroup region, the lipid glycerol region and the hydrocarbon tail core.

Approximate boundaries between these regions are defined by the vertical

dotted lines.


Fig. 3 also shows that the transfer free energy of progesterone is

consistently lower than that of testosterone; hence, the bilayer/

water partition coefficient of progesterone is predicted to be

larger than that of testosterone (see eqn (8) below). This agrees

with experimental measurements; partition coefficients in stratum

corneum lipid bilayers46 and in hydrocarbon (octanol)47–49 are

reported to be larger for progesterone than for testosterone. Early

experimental data seemed to suggest that steroids do not incor-

porate within the membrane, but rather remain in the water phase

outside the bilayer.50–52 However, more recent measurements22,53

clearly indicate that steroid hormones preferentially partition

inside the bilayer; this is now the accepted view,21 and is consistent

with our simulation findings. Moreover, recent AL simulations of

cortisone, another steroid hormone, also show a preferential

partitioning inside the membrane, particularly corresponding to

the headgroup-tail interface;42 this is in agreement with our

results.

Diffusion properties

Using eqn (4), we calculated the permeants’ ‘‘normal’’ diffusion

coefficient Dz along the direction perpendicular to the membrane

plane (z-axis). Also, we quantified net displacements tangential

to the bilayer plane through the ‘‘lateral’’ diffusion coefficient

Dxy:

Dxy ¼ [r(tm) � r(0)]2/4tm (5)

where tm is the measurement time, here corresponding to the

simulation time length (200 ns), and r(tm) and r(0) are the per-

meant positions at time tm and at the beginning of the simulation,

respectively. Fig. 4 collects the normal and lateral diffusion

coefficients of each permeant, calculated for each selected

z-depth across the bilayer. For all solutes studied, the normal

Fig. 4 Diffusion coefficients. The normal diffusion coefficients Dz

(continuous lines) were obtained using eqn (4). The lateral diffusion

coefficients Dxy (dashed lines) were obtained using eqn (5); they do not

feature error bars as they were obtained from single estimates over the

entire duration (200 ns) of each run. To facilitate interpretation, different

regions across the system are marked in italics, namely, the bulk water

region, the lipid headgroup region, the lipid glycerol region and the

hydrocarbon tail core. Approximate boundaries between these regions

are defined by the vertical dotted lines.

Soft Matter, 2010, 6, 3797–3808 | 3801

diffusion coefficients display relatively constant values across the

bilayer; in particular, Dz coefficients are z 50–100 nm2/ms,

irrespective of the location across the bilayer. The diffusion

coefficients obtained in this study are generally lower than those

calculated in previous simulations of small (molecular weight <

100) molecules.19,36,37,54,55 This is expected, considering the larger

size (molecular weight z 300) of the permeants simulated in this

study. Also, small molecules can display enhanced diffusion in

the bilayer centre;19,37,54,55 this effect is typically ascribed to their

increased ability to jump between enlarged free volume pockets

present in the middle of the bilayer (the lowest-density region of

the system). Such a phenomenon is not observed for the (larger)

permeants studied here; it can be argued that these molecules are

not small enough to experience enhanced diffusion in the lipid

core. A similar conclusion was reached by Alper and Stouch56 on

the basis of their simulation data for benzene (a small molecule)

and a large nifedipine drug analogue (molecular weight z 300);

benzene displayed enhanced diffusion in the bilayer centre,

a phenomenon ascribed to a ‘‘hole-jumping’’ mechanism,

whereas the nifedipine drug was characterised by position-

independent diffusion rates.56

Regarding the lateral diffusion coefficients Dxy, it can be seen

that they tend to be lower than the normal diffusion coefficients

Dz, especially when permeants are constrained inside the

membrane. This effect can be rationalised considering that lipid

molecules, despite their high degree of conformational disorder,

are on average oriented and stretched along the normal axis.

Pockets of free-volume through which permeants diffuse are then

also likely to be elongated and preferentially oriented along the z

normal axis, thus favouring faster rates of diffusion along z.

Moreover, we should stress that the calculated Dxy do not

correspond to the lateral component of ‘‘free’’ diffusing particles,

but instead to that of molecules forced to remain in a particular

plane. ‘‘Real’’ lateral diffusion coefficients might well be higher

(hence more consistent with the normal coefficients), because

lateral displacements of free particles should be facilitated

compared to particles constrained to a particular depth. The

lateral diffusion mechanism was also investigated qualitatively by

tracking the mass centre motion of the permeants and projecting

it onto the (xy) plane of the bilayer; representative trajectories are

reported in Fig. 5. In general, diffusive patterns seem to be

characterised by localised, fast random rattlings that slowly build

Fig. 5 Lateral mass centre traces of atenolol, for representative z-distance

positions are marked with ‘‘B’’ symbols, final positions with ‘‘ � ’’ symbols. T

dashed lines.

3802 | Soft Matter, 2010, 6, 3797–3808

up to net displacements. Unsurprisingly, we observed a similar

behaviour for the lateral motion of individual lipid molecules.2,3

To our knowledge, there are no experiments directly showing the

diffusive mechanism at this level of resolution.

Solubility-diffusion theory and related issues

In this section, we summarise the solubility-diffusion theory of

permeation and discuss why it might be unsuited to predict the

transmembrane permeability of hydrophobic molecules.

According to the popular solubility-diffusion model (also known

as the Meyer-Overton rule), the transmembrane permeability P

of a molecule is directly proportional to its hydrocarbon/water

partition coefficient K via the simple relation:

P ¼ KD/h (6)

with D the solute’s diffusion coefficient inside the membrane and

h the membrane thickness. This expression, first proposed 110

years ago,57 is still widely applied to predict transbilayer

permeability coefficients.58 To account for the heterogeneity of

lipid bilayers, the following refined expression has also been

proposed:59,37

P ¼ 1=

ðz2

z1

dz

KðzÞDzðzÞ(7)

with K(z) and Dz(z) the solute’s partition coefficient and the z

component of the diffusion coefficients, respectively, at position

z along the direction normal to the membrane interfacial plane.

The integration extremes z1 and z2 are taken in the water phases

at the two sides of the membrane, so that the integration is

performed over the entire bilayer thickness (equal to h in eqn (6)).

Both the standard (eqn (6)) and inhomogeneous (eqn (7)) solu-

bility-diffusion expressions therefore predict that the larger the

partition coefficient of a molecule, the larger its permeability

coefficient. The partition coefficient K(z) is related to the transfer

free energy DG(z) via:

K(z) ¼ exp(� DG(z)/kBT) (8)

with kB the Boltzmann constant and T the temperature. It then

follows that the lower the transfer free energy, the higher the

s across the membrane, from 200 ns-long simulations. Initial permeant

he x and y lateral edges of the (central) simulation cell are represented by


permeability coefficient will be (and vice versa). This is evidently

correct for permeants whose transfer free energy profiles are

characterised by ‘‘barrier’’ regions (normally, the hydrocarbon

core) of large positive values; for example, this is a typical case

for hydrophilic compounds. However, the transfer free energy

profiles of hydrophobic solutes can be mostly negative, and

particularly it can be characterised by deep negative minima

inside the bilayer (as exemplified in Fig. 3 for the permeants

studied here). For such solutes, the solubility-diffusion theory

would then predict large permeability values. However, it is

physically intuitive that deep negative free energy minima (like

those observed in this study) act as ‘‘traps’’ where permeants are

likely to accumulate; in such cases, the overall transmembrane

permeability rate is expected to decrease substantially. Therefore,

for hydrophobic molecules the solubility-diffusion model is

arguably unsuited to predict transmembrane permeability

coefficients. Interestingly, the general validity of the solubility-

diffusion model has recently been questioned also by Grime

et al.,60 who found experimentally that the permeability coeffi-

cient of a series of aliphatic (hydrophobic) weak acids decreased

with increasing hydrocarbon/water partition coefficient, in

striking contradiction with the Meyer-Overton rule (eqn (6)). It is

possible that these molecules fit into the scenario we depicted

above for hydrophobic permeants; the larger the partition

coefficient, the deeper the free energy ‘‘traps’’ inside the bilayer,

and ultimately the smaller the permeability.

These issues stimulated us to develop a new expression,

presented in the next section, aimed at estimating permeability

rankings within series of compounds. As will be seen, this new

simple model builds on the solubility-diffusion theory in that

positive free energy maxima retain their permeability barrier

effect; however, the model addresses the controversy involving

hydrophobic permeants by treating transfer free energy minima

as obstacles to permeation.

Table 1 Comparison of permeability rankings

Method Permeability ranking

PDGdata from this work PDG

atenolol < PDGpindolol < (PDG

progesterone z PDGalprenolol)

< PDGtestosterone

Experiment62 P atenolol < P pindolol < P alprenolol < P testosterone

Experiment61 P atenolol < P pindolol < P alprenolol

A simple permeability-ranking expression

The transfer free energy and diffusion profiles characterise,

respectively, the thermodynamic and kinetic aspects of the

transmembrane permeation process of a solute. The transfer free

energy (related to the partition coefficient as reported in eqn (8))

is typically considered the dominating component. More

specifically, we propose here that the most crucial factor deter-

mining the propensity of a molecule to permeate across

membranes is the difference between the maximum and the

minimum values of the transfer free energy profile across the

membrane, i.e., DGmax – DGmin; this quantity indeed represents

the main barrier to permeation. For example, typical polar,

hydrophilic compounds are characterised by positive free energy

maxima in the bilayer hydrophobic core; intuitively, the higher

these maxima, the greater will be the difference DGmax – DGmin,

and the lower will ultimately be the permeability coefficients. If

we now consider a nonpolar, hydrophobic compound, we expect

instead the transfer free energy to display a negative minimum

inside the hydrocarbon region; this would attract the compound

towards the bilayer core, but it would then also act as a ‘‘trap’’. In

fact, to fully permeate across the membrane, such a compound

would encounter a permeability barrier on trying to escape from

the bilayer core towards the outer water phase. Such a barrier


would again be related to the difference DGmax – DGmin (where in

this case DGmax is likely to be the value corresponding to

a position in the water or lipid headgroup region while DGmin will

be a negative value corresponding to a location in the lipid tail

region); again, the larger this difference, the higher the perme-

ability barrier, and the lower the permeability coefficient should

intuitively be. Incidentally, since the relation DGmax > DGmin is

obviously always satisfied, the permeation barrier defined above

is consistently positive, i.e., DGmax – DGmin > 0.

On the basis of these considerations, we have developed

a simple permeation model aimed at predicting the permeability

ranking within a set of molecules given their transfer free energy

profiles. In particular, we propose to quantify the propensity of

a compound to cross the membrane with the following ‘‘perme-

ability predictor’’ PDG:

PDG ¼kBT

DGmax � DGmin

(9)

with DGmax and DGmin the maximum and minimum values,

respectively, of the permeant transfer free energy profile, and kBT

the standard energy factor given by the product of the Boltzmann

constant kB with the temperature T. The PDG values obtained

from the free energy data of the set of permeants considered in

this work (Fig. 3) yield the following ranking: PDGatenolol < PDG

pindolol < (PDGprogesterone z PDG

alprenolol) < PDGtestosterone. Atenolol is

therefore predicted to be the slowest permeant, followed by

pindolol, then progesterone and alprenolol, and finally testos-

terone (fastest permeant). The permeability ranking obtained by

applying our simple free energy based predictor can be compared

to corresponding sets of experimental measurements reported in

the literature. Drug permeabilities are typically measured using

colorectal carcinoma cell monolayers (Caco-2) and parallel

artificial membrane permeability assays (Pampa). For a mean-

ingful comparison, we only consider literature studies reporting

‘‘intrinsic’’ permeability coefficients,61 that is, permeability

coefficients characterising unassisted transport of the uncharged

species through the lipid components of the experimental assay

(in fact, the majority of literature data are ‘‘apparent’’ perme-

abilities, which typically include contributions from water layers,

paracellular routes and assay porosity61). Also, we compare our

results only with permeability measurements from sets obtained

from the same experiment; permeability coefficients are so

sensitive to the specific experimental setups and conditions that

rankings obtained by mixing data from different experiments

would not be reliable. The comparison is reported in Table 1; our

permeability ranking prediction is on the first row, and the

subsequent rows report the available literature results for

intrinsic permeabilities obtained from Caco-262,61 and Pampa61

experiments (note that Avdeef et al.61 performed both Caco-2

and Pampa measurements, obtaining the same ranking for the

Soft Matter, 2010, 6, 3797–3808 | 3803

three drugs considered in our study). It can be seen that our

simple permeability predictor perfectly reproduces the available

experimental rankings.

The proposed expression (eqn (9)) has also been further tested

on free energy profiles, for different sets of solutes, available in

the literature. Again, for these tests to be reliable, we only

considered sets of data obtained from the same series of simu-

lations and experiments; as already mentioned, this is necessary

for meaningful comparisons, given the sensitivity of permeability

properties to the particular simulation/experimental methods

and conditions. First, we tested our simple expression on two

collections of free energy data36,19 obtained in our research group

for the same set of small molecules simulated respectively in an

atomistic dipalmitoylphosphatidylcholine (DPPC)36 bilayer and

in a coarse-grain DMPC19 bilayer. The results obtained are

presented in Table 2, along with a corresponding set of experi-

mental data63 obtained with real phosphatidylcholine bilayers. It

can be seen that the two rankings predicted by our simple

permeability model are in remarkable agreement with the

experimental data. The only discrepancy involves the relative

ranking of water and acetamide obtained when using one of the

two sets of free energy data (first row of Table 2). We then tested

our expression on literature data reported by other simulation

groups. First, we applied our permeability predictor on a set of

free energy data64 comprising urea, glycerol and water, simulated

in a palmitoyloleoylphosphatidylcholine (POPC) bilayer; the

ranking obtained is reported in Table 3, together with a corres-

ponding experimental ranking from measurements on phos-

phatidylcholine bilayers.65 Our PDG prediction is in good

agreement with the experimental data. We then tested the model

on simulation free energy data66 for sugars in a POPC bilayer.

The ranking obtained is reported in Table 4, along with the

corresponding data from experimental measurements on POPC

membranes.67 The agreement is again satisfactory; in particular,

it can be seen that our permeability model correctly reproduces



PDGdata from ref.19 PDG

water < (PDGacetamide z PDG

aceticacid) < PDGmethylamine

PDGdata from ref.36 (PDG

acetamide z PDGwater) < PDG

aceticacid < PDGmethylamine

Experiment63 P acetamide < P water < P aceticacid < P methylamine



PDGdata from ref.64 PDG

urea < (PDGglycerol z PDG

water)Experiment 65 P urea < P glycerol < P water



PDGdata from ref.66 (PDG

arabinose z PDGxylose) < PDG

ribose

Experiment67 (P arabinose z P xylose) < P ribose

3804 | Soft Matter, 2010, 6, 3797–3808

the (important67) experimental finding that ribose is the fastest

permeant in the set.

The actual numerical results obtained by applying eqn (9),

which underlie the rankings of Tables 1, 2, 3 and 4, are reported

in the Supplementary Information.

Additional observations - membrane perturbation,water intrusion and permeant orientation

By visually inspecting the simulation trajectories, we can obtain

qualitative insights into the permeation mechanism. When con-

strained in the water region outside the membrane, all permeants

show random orientations and do not perturb the bilayer

structure; this behaviour, intuitively expected, is consistent with

AL simulations of the same b-blockers30 and dual-resolution

simulations of small molecules.19 However, when constrained

inside the membrane, the solutes display a tendency for tilted

orientations with respect to the direction normal to the

membrane plane.

Inside the bilayer region, the b-blockers tend to point their

central oxygens towards the outside; such behaviour is probably

determined by the favourable electrostatic interactions between

the most polar atoms of the permeant and the (outer) polar

moieties of the membrane system (lipid headgroups and

glycerols, and hydrating water). Previous AL simulations30 of the

same drugs could not identify any conclusive equilibrium

distribution of orientations inside the membrane due to the short

simulation times achieved (3 ns). However, it was noticed that the

b-blocker orientations were mainly tilted with respect to the

bilayer normal;30 this is broadly consistent with our observations

from the dual-resolution simulations. A representative snapshot

from a b-blocker simulation is shown in Fig. 6. It is interesting to

note the perturbing effect caused by the permeant to the bilayer

Fig. 6 Simulation snapshot from a dual-resolution z-constraint simu-

lation. The permeant alprenolol is located at a distance of 0.1 nm from

the bilayer centre towards the left monolayer. CG colour code: water

molecules are blue, lipid headgroups are grey, lipid tails are transparent

green. AL permeant colour code: carbon atoms are cyan, hydrogen atoms

are white, oxygen atoms are red, nitrogen atoms are blue.



lation. The permeant testosterone is located at a distance of 1.1 nm from

the bilayer centre towards the left monolayer. Colour codes are the same

as those reported in Fig. 6, although here all CG components are made

transparent for clarity.

structure, with lipid headgroups and water locally penetrating

into the hydrocarbon region to interact with the drug; such

membrane defects are similar to those previously reported from

simulations of smaller permeants.30,5,19 More generally, these

data are consistent with a view of the phospholipid bilayer as

a dynamic structure which can readily deform to locally adapt to

the presence of inclusions.

The steroid hormones also show preferential orientations

when constrained inside the membrane; they favour a tilted

orientation with respect to the direction normal to the membrane

plane, and their carbonyl group (C]O) attached to the five-

membered ring tends to point towards the more polar regions of

the system (lipid headgroups and glycerols, and outer water

phase). To quantify the steroid orientations, we calculated the

order parameter P2:

P2 ¼ h3 cos2 g � 1i/2 (10)

with g the instantaneous angle between the steroid ‘‘main’’ axis

(corresponding to the principal axis of inertia which is roughly

parallel to the direction connecting the terminal oxygens) and the

membrane normal (z-axis); the angular brackets indicate aver-

aging over the simulation time. By definition, – 0.5 # P2 # 1; in

particular, P2 ¼ � 0.5 indicates alignment parallel to the bilayer

plane, P2 ¼ 0 indicates random orientation and P2 ¼ 1 indicates

alignment parallel to the normal to the bilayer plane.

Results are shown in Fig. 7. For z ¼ � 3.1 nm, corresponding

to the centre of the water phase, the steroid order parameters are

z 0, indicating random orientation (as intuitively expected). On

entering the bilayer through to the tail region, the order

parameters are negative (reaching minimum values of z � 0.4),

indicating a tendency to align perpendicular to the membrane

normal (hence parallel to the membrane plane). Such preferential

orientations are consistent with recent AL simulations42 of

cortisone, another steroid hormone with a similar structure to

that of the molecules considered here. As an example, Fig. 8

Fig. 7 Order parameter P2, defined in eqn (10), plotted as a function of

the distance between the steroid centre of mass and the bilayer centre,

along the direction normal to the bilayer plane (z-axis). To facilitate

interpretation, different regions across the system are marked in italics,

namely, the bulk water region, the lipid headgroup region, the lipid

glycerol region and the hydrocarbon tail core. Approximate boundaries

between these regions are defined by the vertical dotted lines.


shows a typical orientation of a steroid constrained at a depth

corresponding to the lipid glycerol region. Interestingly, when

approaching the bilayer centre the steroid order parameters

steeply increase, reaching positive values (Fig. 7). In particular,

the maximum P2 values for progesterone and testosterone are,

respectively, z 0.3 and z 0.1. These data indicate a slight

tendency to order parallel to the bilayer normal. A typical

snapshot from a simulation with a steroid constrained near the


lation. The permeant progesterone is located at a distance of 0.3 nm from

the bilayer centre towards the left monolayer. Colour codes are the same

as those reported in Fig. 6.

Soft Matter, 2010, 6, 3797–3808 | 3805

membrane centre is reported in Fig. 9. Finally, we note that the

steroids do not cause pronounced membrane defects as in the

case of the b-blockers; they display a more lipophilic character,

consistent with their lower transfer free energies inside the

membrane (Fig. 3).

Discussion

We applied a novel multiscale molecular dynamics method to

investigate the unassisted permeation process of large drugs and

steroid hormones through a phospholipid bilayer. In particular,

dual-resolution systems have been simulated by incorporating

AL models of the drug and hormone permeants into our recently

developed CG membrane model.2,3 Our multiscale approach

benefits from a particularly advantageous feature with respect to

alternative methods:8–11,14 particles described with different levels

of resolution can interact directly, without the need for interface

regions. This is possible because our CG force field,2,3 uniquely

amongst the existing CG membrane models, includes the

fundamental electrostatics of lipid and water molecules, and

hence it is compatible with standard AL molecular models. In

our dual-resolution method, the interactions between AL and

CG particles retain all the basic components that contribute to

the total intermolecular interaction energy of standard molecular

mechanics force fields; in particular, the repulsion-dispersion

component is captured through the Lennard-Jones and Gay-

Berne potentials, whereas the electrostatic component is

represented through classical charge-charge and charge–dipole

potentials. Another important characteristic of our approach is

its improved efficiency compared to standard AL methods,

corresponding to approximately two orders of magnitude. For

each permeant considered, we calculated transfer free energies

and diffusion constants across the bilayer. Free energy profiles

allow the identification of the depth across the membrane where

permeants preferentially localise; for all solutes considered in this

study the transfer free energy data indicate a preferential incor-

poration inside the bilayer, at a depth roughly corresponding to

the interface between the polar region (comprising hydrating

water and headgroups) and the apolar region (central hydro-

carbon core) of the membrane. In particular, the mass centres of

the b-blockers were predicted to localise in the headgroup region;

the mass centres of the steroid hormones were instead localised

somewhat deeper inside the membrane, roughly corresponding

to the glycerol region. Overall, these predictions from our

multiscale simulations are in good agreement with corresponding

experimental1,22,44–49,53 and AL simulation42 data.

In general, the (extended) polar/apolar interface seems to be

the preferential location for most molecules interacting with lipid

bilayers.5–7 We believe that this phenomenon can be rationalised

considering the intramembrane pressure distribution, also known

as the lateral pressure profile. The lateral pressure profile

quantifies the variation of the intramembrane forces as a function

of depth across the bilayer.2–4 In particular, the pressure distri-

bution features large and wide regions of negative, attractive

pressure precisely corresponding to the polar/apolar interface

region; these forces originate from the interfacial tension trying to

contract the bilayer hydrophobic core to minimise its exposure to

the outer polar environment. The attractive (membrane-con-

tracting) forces acting at the polar/apolar interface regions are

3806 | Soft Matter, 2010, 6, 3797–3808

counterbalanced by repulsive (membrane-expanding) forces at

the headgroup/water interface and in the hydrocarbon tail region.

The peak pressures involved are of the order of several hundreds

of atmospheres, with the largest pressures in absolute terms at the

polar/apolar interfaces. The lateral pressure profile plays signifi-

cant roles in an impressively large number of membrane processes

(as discussed extensively elsewhere2–4); here we focus on the

possible influence of this property on the partitioning of mole-

cules inside membranes. Xiang and Anderson already proposed

over 15 years ago that the lateral pressure profile is the only

physical parameter required for a quantitative prediction of the

distribution of solutes inside an interphase (such as, in particular,

a lipid bilayer);68 however, due to computational limitations,

their calculations had to be based on a rather crude bilayer model

lacking lipid headgroups and hydrating water, and hence the

lateral pressure in the polar/apolar interface could not be

studied.68 Since it is now possible to characterise the pressure

distribution over realistic hydrated lipid bilayer models,2–4 we can

directly investigate the relation between the lateral pressure

profile and the transfer free energy of permeants (and hence their

preferential location inside the membrane). In particular, we

propose that most solutes tend to accumulate at the polar/apolar

interface of lipid bilayers because they are guided and stabilised

there by the large attractive lateral pressure troughs. A diagram

highlighting the correlation between the membrane lateral

pressure and the transfer free energy profiles of two of the

permeants studied here is reported in the Supplementary Infor-

mation. Xiang and Anderson68 also focused on the phenomenon

of size selectivity, whereby the transbilayer permeability of

solutes seems to exhibit an unusually high dependency on

permeant size; they put forward the hypothesis that the larger the

permeant, the more work against the lateral pressure profile is

required to create an intramembrane cavity which is large enough

to accommodate the solute while it permeates through the regions

of repulsive membrane pressure. This is consistent with the

discussed hypothesis of a preferential solute partitioning at the

polar/apolar interface, because there the formation of a cavity is

actually favoured by the attractive pressure, whereas elsewhere

(hydrocarbon core and headgroup/water interface) it is opposed

by the presence of repulsive forces. Small permeants (such as

water and ions), are expected to be less sensitive to the lateral

pressure profile, because the cost of cavity formation is obviously

smaller, and other contributions (such as electrostatic forces)

might prevail in determining the preferred partitioning location.

In this work, we also presented a new permeability expression

(eqn (9)) aimed at predicting transbilayer permeability rankings;

the model is very simple, only requiring as input the permeants’

transfer free energy profiles across the membrane (typically

obtained by simulation). The model was tested on this work’s

free energy data for drugs and hormones, and on several different

sets of data reported in the literature for a range of molecules

including water, acetamide, acetic acid, methylamine, urea,

glycerol and three sugars. Remarkably, our permeability

predictor accurately reproduced the experimentally-obtained

permeability rankings within the various sets of permeants

(Tables 1, 2, 3 and 4).

In general, the ability of our overall methodology to reliably

predict permeability rankings could be effectively applied in the

context of rational drug design. To reach their biological target,


drugs must typically cross cell membranes by unassisted perme-

ation, and hence valid tools for predicting permeability coeffi-

cients before synthesis are highly desirable to minimise the

investment in pharmaceutical design and development.5 Stand-

ard permeability assays, such as Caco-269 and Pampa70 systems,

are not without drawbacks, as they can be expensive and time-

consuming. Also, given their complexity and variability, data

reproducibility and interpretation can be problematic.71 Our

computational method represents a promising alternative; given

the current (growing) availability of supercomputers, it would be

possible to apply our methodology to conduct screening studies

on large sets of compounds. This would allow the cheap and fast

estimation of the permeability ranking within a set of drug

candidates, thus offering a simple way to identify possible lead

compounds. Moreover, since results would be obtained using

a consistent protocol, interpretation and comparison amongst

different sets of data would be straightforward.

In terms of limitations and drawbacks, we should point out

that it is difficult to assess a priori the general validity of our

simple dual-resolution method. While the results presented here

and elsewhere19 encouragingly agree with experimental

measurements and atomistic simulation data, more work is

needed to establish the extent to which the inevitable loss of

accuracy (compared with full atomistic models) due to the

simplified membrane representation still allows the relevant

lipid-solute interactions to be correctly modelled. A related

specific issue is the lack of an explicit hydrogen bonding

representation, due to the absence of hydrogens in the coarse-

grain description of lipids and water.2,3 Although our explicit

treatment of electrostatics probably allows the fundamental

features of hydrogen bonding to be captured, the exact effect of

this approximation remains to be established. The hydrogen

bonding ability of drug molecules is recognised as an important

factor for drug permeation and absorption,72 and indeed

previous AL data indicated a correlation between the number of

drug-water hydrogen bonds and the ranking of the permeability

coefficients, with the permeability coefficient decreasing with the

formation of an increasing number of hydrogen bonds.30

Although the absence of explicit hydrogen bonds does not seem

to have compromised our results for the drug and hormone

permeants studied here, and for the small molecule solutes

investigated elsewhere,19 more tests are desirable to clarify the

issue. Another limitation of the method presented lies in the

assumption of intramolecular rigidity. While such a simplifying

treatment is arguably acceptable for intrinsically rigid molecules

such as the steroid hormones (given their stiff four-ringed

structure), it is more problematic to justify its use for the

b-blocker models. In fact, atomistic simulations of the same

b-blockers highlighted depth-dependent conformational

changes.30 Even though the rigid-body assumption does not seem

to compromise the reliability of the method in predicting the

relative permeability coefficients for the permeants investigated

here, we are working on the implementation of intramolecular

flexibility for atomistic solutes. This extension will require the

implementation of additional force-field terms to account for the

atomistic bonded interactions (such as bond stretching and angle

bending); while the technical aspect is straightforward, there will

be related efficiency issues. In particular, the integration of

the fastest atomistic intramolecular motions would require


a reduction of the timestep, thus potentially compromising the

overall efficiency of our methodology. However, this problem

could be tackled by implementing a multiple-timestep method,

allowing different degrees of freedom to be integrated at different

frequencies; the faster atomistic components of the system will be

integrated with a small timestep, whereas the coarse-grain sites

will be treated with the usual larger timestep. The implement-

ation of atomistic flexibility, besides allowing a more realistic

representation of large drug permeants, could also be exploited

to model membrane proteins; it will be possible to run dual-

resolution simulations where AL protein models are embedded

in a CG description of lipids and water. Further attractive and

relatively straightforward extensions to such systems might

involve the modelling of protein active sites by quantum

mechanics/molecular mechanics methods,10,9 thus constructing

truly multiresolution simulation models.

Conclusion

A novel dual-resolution molecular dynamics method was applied

to investigate the permeation process of atomistically-modelled

drugs and hormones through a coarse-grain membrane. Our

simulation approach is simple, since all particles interact with

each other directly through compatible potentials, that is,

without the need to implement interface regions. The proposed

methodology is also general, as any permeant can be quickly set

up using a standard force field. Computationally, our hybrid

simulations are two orders of magnitude faster than standard

atomic-level methods. We calculated several important perme-

ability properties, such as preferential partitioning locations,

diffusion coefficients and orientations of the permeants inside the

membrane; our results proved consistent with available literature

data from experiments and standard atomistic simulations.

Notably, we also proposed and successfully tested a simple

expression to predict the permeability rankings from transfer free

energy data.

Acknowledgements

This work has been funded by the UK Biotechnology and Bio-

logical Sciences Research Council (BBSRC). We thank Jochen

Hub, Bert de Groot, Chenyu Wei and Andrew Pohorille for

sharing their free energy data.

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