495
Modeling the lipid component of membranes
H Larry Scott
During the past several years, there have been a number of
advances in the computational and theoretical modeling of lipid
bilayer structural and dynamical properties. Molecular
dynamics (MD) simulations have increased in length and time
scales by about an order of magnitude. MD simulations
continue to be applied to more complex systems, including
mixed bilayers and bilayer self-assembly. A critical problem is
bridging the gap between the still very small MD simulations
and the time and length scales of experimental observations.
Several new and promising techniques, which use atomic-level
correlation and response functions from simulations as input to
coarse-grained modeling, are being pursued.
Addresses
Department of Biological, Chemical and Physical Sciences,
Illinois Institute of Technology, Chicago, IL 60616, USA;
e-mail: [email protected]
Current Opinion in Structural Biology 2002, 12:495–502
0959-440X/02/$ — see front matter
© 2002 Elsevier Science Ltd. All rights reserved.
Abbreviations
CBMC
configurational bias MC
CS
cholesterol sulfate
DMPC
dimyristoyl phosphatidylcholine
DOPC
dioleoyl phosphatidylcholine
DOPE
dioleoyl phosphatidylethanolamine
DPPC
dipalmitoyl phosphatidylcholine
DPPG
dipalmitoyl phosphatidylglycerol
DPPS
dipalmitoyl phosphatidylserine
GMO
glycerolmonoolein
HNC
hypernetted chain
MC
Monte Carlo
MD
molecular dynamics
NOESY nuclear Overhauser enhancement spectroscopy
POPC
palmitoyl-oleoyl phosphatidylcholine
SDPC
1-stearoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine
Introduction
Biological membranes are enormously complex in terms of
both structure and their dynamical properties. In order to
begin to understand membrane properties, model systems
consisting of simple lipid bilayers with well-known composition are generally studied. However, even these
systems pose formidable modeling challenges due to the
flexible nature of lipid molecules and the occurrence of
complex hydrophilic and hydrophobic interactions. For
this reason, computer simulation has emerged as a critical
tool for modeling the lipid component of membranes. As
earlier reviews of lipid bilayer modeling have pointed out
[1–6], the increasing availability of fast desktop workstations
or linux clusters, and of fast modeling software has led to
rapid progress in atomic-level simulations. Figure 1 shows
a bilayer of 1600 DPPC molecules, which is indicative
of the size scales accessible to current simulations. In
addition, simulations are now beginning to provide data of
sufficiently high quality that workers can begin to use
these data as input for more coarse-grained macroscopic
modeling work. Concurrently, new experimental data are
available (e.g. [7]) and communication between membrane
structure experimentalists and simulators has increased.
The purpose of this review is to summarize the most
recent advances in lipid bilayer modeling work and to
describe promising new uses of atomistic simulations as
input to efforts to model lipid bilayers over macroscopic
time and length scales.
Methodological advances
Figure 2 shows atomic structures for three representative
lipid molecules used in simulations. Atomic-level simulations require as input expressions for the potential energies
between all atoms in the system, including those between
bonded pairs of atoms and between nonbonded pairs of
atoms. Harmonic expressions are generally used to model
chemical bonds between atoms. For atom pairs that are not
chemically bonded, potential energy expressions include
coulombic plus ‘6-12’ interactions. The 6-12 expression
consists of a repulsive part, which falls off as 1/r12, and an
attractive part, which falls off as 1/r6, and is designed to
model interactions due to polarization effects between
atomic electron clouds. Torsional potentials model the
interactions between next-nearest neighbor atoms on the
same molecule. The set of functions, and the parameters
characterizing the strengths of the various interactions, is
commonly referred to as the ‘force field’. Force fields are
generally independently developed and tested against
experimental data before being applied to lipid bilayers.
The improvement of simulation force fields is a continuous
process. Feller and MacKerrell have reported improvements to the CHARMM all-atom force field for lipid
simulations for torsion and 6-12 parameters [8], and for
polyunsaturated lipids [9••]. The latter parameterization
effort extends simulation force fields to the important class
of multiply unsaturated lipid bilayers. The force field
reveals the extremely high flexibility of these systems. An
interesting new methodological advance is the development of periodic boundary conditions, which allow lipids
to switch leaflets [10]. This is an important advance for the
simulation of unsymmetrical bilayer systems, as it will
allow the redistribution of lipids to ease stresses induced
by asymmetries.
Ongoing issues in simulation methodology include the
treatment of electrostatic interactions and the use of
constant surface tension ensembles. For the electrostatics
issue, recent simulations of the lipid gel phase by Venable
et al. [11] show clearly the necessity of including Ewald
summation corrections in the simulation of this phase,
which consists of tightly packed, ordered hydrocarbon
chains with greatly restricted lateral and conformational
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Membranes
Figure 1
Figure 2
(a)
(b)
(c)
Current Opinion in Structural Biology
Snapshot of a large bilayer of 1600 DPPC molecules, constructed by
replication from a 100 DPPC bilayer, after 1.5 ns of MD at constant
isotropic pressure and zero surface tension. The area per DPPC
molecule is about 63 Å2, which agrees with the experimental value [7].
Waters are removed for clarity. Gray: carbon atoms; red: oxygen atoms;
blue: nitrogen atoms; and yellow: phosphorus atoms. The nitrogen and
phosphorus atoms are not readily visible at this resolution.
molecular mobility. For the simulation of lipid fluid
phases, in which lipid molecules are more disordered and
liquid-like than in the gel phase, the situation, in the
opinion of this writer, is less clear. The use of Ewald
summations in zwitterionic systems in disordered phases
can potentially induce unwanted periodicities, leading to
errors no less significant than those which result when the
interaction is simply ‘switched off’ for interatomic
distances beyond some cutoff (spherical cutoffs). For
smaller simulation boxes, the effect will be more severe.
For the surface tension issue, discussions are ongoing
concerning the nature of the lipid/water interface and the
appropriateness of a constant surface tension ensemble
[12,13]. The difficulty associated with dissecting the
surface stresses in a bilayer is addressed in simulations by
Lindahl and Edholm [14]. They use local virial calculations to show that the tension in a bilayer is the sum of two
large opposing tensions: an attractive energy in the polar
region and a repulsive energy in the hydrocarbon region.
These two contributions must exactly balance for the overall surface tension to vanish. In simulations of 256 DPPC
in excess water, Lindahl and Edholm found that the two
tensions do, in fact, nearly sum to zero, albeit with a fairly
large uncertainty.
There is general agreement among simulation practitioners
that the surface tension in a simulation cell decreases to a
small value with increasing size of the system [13], so that,
for sufficiently large systems, an applied surface tension
ensemble is not needed. As a test of this hypothesis, in
Ball-and-stick models of three phospholipid molecular structures
commonly used in simulations. (a) DPPC. (b) DOPC. Yellow atoms
are C=C double bonded and are the 9 and 10 carbon atoms on each
chain. (c) Cholesterol. In all cases, color code is as in Figure 1, but
also includes hydrogen atoms (white). Hydrogen atoms are not shown
except for those bonded to cholesterol ring carbon atoms. DMPC is
identical to DPPC, except each hydrocarbon chain is two carbons
shorter. POPC is identical to DOPC, except only the second (oleyl)
hydrocarbon chain has a double bond between the 9 and 10 carbon
atoms. DOPE is identical to DOPC, except the three methyls
connected to the nitrogen at the polar terminus of the molecule are
replaced by hydrogen atoms. All of the molecules are extracted from
simulated bilayer coordinate files.
unpublished work, a member of my laboratory has
constructed a bilayer of 1600 DPPC molecules plus 51 280
waters by replication of a small bilayer of 100 DPPC
molecules plus 3205 waters (S Vasudevan, personal
communication). The smaller bilayer was equilibrated at
constant surface tension (80 dynes/cm or 40 dynes/cm per
leaflet, a value we used for our earlier simulations of this
small bilayer in order to reproduce the experimental value
of the area per molecule for DPPC, 63 Å2 [7]). The large
bilayer, shown in Figure 1, was then simulated for 1.5 ns of
molecular dynamics (MD) at a constant isotropic pressure
of 1 atm, that is, zero surface tension. The area per molecule of this large system remained stable, supporting the
finite size argument of Feller and Pastor [13]. A different
conclusion is reached by Marrink and Mark [15], who
simulated bilayers of glycerolmonoolein (GMO) over a range
of system sizes from 200 GMO to 1800 GMO. Marrink and
Mark found only a weak dependence of the area per
molecule on the system size when the simulations were
performed at zero surface tension, in apparent contradiction
to the results of Feller and Pastor [13]. In addition to using
a single-chain lipid (GMO) in their simulations, the range
of system sizes used by Mark and Marrink is substantially
larger than that used by Feller and Pastor, who simulated
bilayers of 18, 32 and 72 double-chain DPPC molecules.
Another important difference is the use of Ewald sums for
electrostatic interactions by Pastor and Feller [13] versus
Modeling the lipid component of membranes Scott
the use of small spherical cutoffs of 1.2 nm for electrostatics
by Marrink and Mark [15]. To this reviewer, it seems likely
that the threshold system size above which simulations
may be performed at zero surface tension depends on the
type of lipid and the force fields used.
The equilibration of a membrane simulation and the efficiency
of the sampling of equilibrium thermodynamic states can
both be improved by augmenting MD trajectory calculations
with carefully chosen Monte Carlo (MC) steps. Chiu et al.
[16] showed that the computational time required to
equilibrate a fluid phase membrane simulation was reduced
several fold by interspersing MD intervals with intervals of
configurational bias MC (CBMC) trial moves. This has the
effect of occasionally hopping part of the system over an
energy barrier and thereby into a different region of phase
space from which a new MD trajectory can be launched.
Simulations of pure lipid bilayers
Perhaps the most important progress in MD simulations
over the past two years has been the increase in length and
time scales of simulations. This is dramatically evident
from the MD simulations of Lindahl and Edholm [17••], in
which a small hydrated (64 DPPC lipids plus 23 waters per
lipid) bilayer was simulated over 60 ns and a large bilayer
of 1024 DPPC lipids plus 23 waters per lipid was simulated
over 10 ns. Also studied was a DPPC bilayer of 256 lipids
plus 23 waters per lipid. [A bilayer of 1024 lipids is ‘large’
in comparison to a bilayer of less than 100 lipids because,
for the 100 lipid system (50 per leaflet), half of the lipids
are at an edge of the simulation cell. For the 1024 lipid
system (512 per leaflet), less than 10% of the lipids are
located at an edge. This reduces the artifacts associated
with periodic boundary conditions. Also, the conformation
space of a single lipid molecule, with two flexible acyl
chains, is very large. By using over 1000 lipids in a simulation, the molecular conformation space will be sampled to
a far greater extent.] The large length and time scales
enable the analysis of dynamical fluctuations, the decomposition of these modes into undulation and thickness
fluctuations, and the calculation of a bending modulus for
DPPC in good agreement with experiment. A finite size
scaling analysis of the three simulations led the authors to
conclude that thickness fluctuations are primarily responsible
for the dependence of the simulation area per molecule on
the size of the simulation box. A striking example of the
propagation of MD simulations to longer time scales is the
observation of the self-assembly of a lipid bilayer from
initially random dispersions of 64 lipids in a box with 3000
water molecules [18•]. For separate systems of 64 DPPC,
POPC, DOPC and DOPE molecules plus 3000 waters,
symmetric bilayers formed by about 25 ns of MD. For larger
systems of 128 and 256 DPPC molecules, the assembly
process was slower and, in the 256 DPPC system, a micelle
formed in addition to a bilayer. The fact that self-assembly
occurred in just 25 ns is probably a consequence of the
small system size, which reduces the number of molecules
that need to cooperatively align in order to form a bilayer.
497
Nonetheless, the simulation provides a unique glimpse of
a critical biological and physical process, and the observed
intermediate assembly states may also be present in larger-scale
events, including membrane fusion, exocytosis and endocytosis.
Venable et al. [11] have successfully carried out MD simulations of the gel phase of DPPC. This is tricky because of the
tight molecular packing and the parallel, tilted hydrocarbon
chains, with chain axes extending straight across both
leaflets [19]. Simulations of seven systems were carried out
to examine the effect of constant surface tension versus constant lateral area, and the effect of Ewald summation versus
spherical cutoffs. The simulations demonstrate convincingly
that all-atom models are necessary for the simulation of the
gel phase, as is the use of constant pressure, rather than constant volume simulation constraints. Interestingly, although
the use of Ewald summation is arguably the correct method
for including long-range electrostatic effects in the simulation
of the gel phase, simulations using Ewald sums predicted a
consistently lower area per molecule than experiment by
1–2 Å2 per molecule [19] and than simulations for which a
spherical cutoff was used. Simulations using Ewald sums
gave better agreement with experiment for D-spacing,
measured by X-ray scattering experiments, and chain tilt
angle, however.
Simulations of DPPC and DMPC bilayers with an emphasis
on calculating dynamical properties were carried out by
Moore et al. [20]. Trajectories for fluid phase DMPC bilayers
were analyzed to examine rotational diffusion for entire
lipid molecules, and for head groups and acyl chains separately. It was found that whole-chain rotational diffusion is
slower than head group rotational diffusion, which in turn
is slower than whole-molecule diffusion. The results are
significant for their insights into the details of rotational
diffusion for lipids over the 3 ns time scales of these
simulations. Due to the size and flexible nature of lipids,
rotational diffusion may be defined in a number of ways.
Moore et al. [20] use three definitions: the rotational diffusion of the P-N vector in the polar group, the rotational
diffusion of vectors from the top carbon to the bottom
carbon for each of the two acyl chains, and a vector between
the selected atoms on each of the acyl chains on each
molecule. The values Moore et al. calculate range from
0.04 rad2/ns for the vector between the eighth carbons on
the two chains to 25 rad2/ns for the rotational diffusion of
vectors from the top carbon to the bottom carbon for each
of the acyl chains. The experimental value measured from
POPC labeled with a fluorophore is 0.7 rad2/ns [21], smaller
than the calculated P-N rotational diffusion constant,
2.2 rad2/ns, which is the most directly comparable value in
the simulations. The discrepancy may be due to the necessity
of going beyond 3 ns in the simulations to fully sample the
rotational mechanisms that contribute to diffusion.
Two excellent examples of the increasing level of interaction
between experimental work and simulations in the lipid
bilayer field are provided by the work of Feller et al. [9••,22].
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Membranes
In [22], MD simulation trajectory data for a bilayer
consisting of 72 POPC molecules, 72 ethanol molecules
and 720 waters were used to calculate nuclear Overhauser
enhancement spectroscopy (NOESY) cross-relaxation
rates. The simulation predictions were used in the interpretation of experimental NOESY data. Results reveal
details of the binding of ethanol to the bilayer surface,
including hydrogen bonding and hydrophobic interactions.
The second study, which extends the application of MD to
more biologically interesting systems and is also a collaboration between experimental and simulation groups,
examines polyunsaturated SDPC bilayers [9••]. This is the
first systematic combined experiment and simulation
study of a lipid system consisting of one saturated chain
and one polyunsaturated chain with a sequence of six
double-bonded carbons, each preceded and followed by a
single-bonded carbon. The simulation system consists of
72 SDPC lipids plus 15.1 waters per lipid using a fixed lateral
area plus 1 atm normal pressure ensemble. The area was
set from experimental data [23]. The experiments and
simulations reveal the effects of the very high degree of
flexibility of the polyunsaturated chain. The order parameters for this chain, as calculated in the simulation and
measured experimentally, have uniformly low values
(between 0 and about 0.09) along the entire chain and are
in excellent agreement with experimental values measured
by the same authors [23].
Motivated by the experimental studies of Hristova and
White [24], an atomic-level simulation study of the effect
of hydration on lipid bilayer structure was carried out by
Mashl et al. [25]. This study consisted of simulations of
bilayers containing 128 DOPC molecules and 5.4, 11.4, 16,
23 and 30 waters per lipid. They found that DOPC head
groups became more parallel to the membrane surface
with increasing hydration and that the dipole potential
reversed sign at low hydration. The simulations support
the hypothesis that 12 waters per lipid make up the first
hydration shell, consistent with an observed break point in
a plot of Bragg spacing versus hydration level [24].
Simulations of new systems include the study of a DPPS
bilayer with Na+ counterions by Pandit and Berkowitz
[26•], and simulations of DPPC and DPPG monolayers by
Kaznessis et al. [27••]. Pandit and Berkowitz [26•] found
that hydrogen bonding between the NH3+ and phosphate
groups on neighboring lipids causes DPPS bilayers to have
a smaller area per molecule than DPPC. The Na+ counterions
tend to coordinate with serine and phosphate oxygens on a
single DPPS molecule. Kaznessis et al. [27••] have run simulations of DPPC and DPPG monolayers at an air/water
interface using NaCl/water and CaCl2/water subphases.
Curiously, they found that the well-known ‘plateau’ region
in acyl chain order parameter profiles extends to carbon 14.
In bilayers, the plateau extends only to about carbon 10
before the order parameters decrease with carbon number.
If this result is verified by further studies, it indicates a
significant structural difference between monolayers and
bilayers, which addresses the old issue of the relevance of
monolayers for understanding bilayer membranes.
Simulation of nonbilayer lipid phases can add insights into
lipid packing that are relevant to bilayers and to important
biological processes such as cell fusion. The first such
simulation of a cubic phase of GMO was recently reported
by Marrink and Tieleman [28]. In all, four simulations
were run using varying GMO:water ratios. Of special
interest was a system with a 504:3503 GMO:water ratio,
which became unstable and spontaneously transformed
into a hexagonal phase.
Simulations of lipid bilayers containing
cholesterol
Cholesterol is present in all mammalian cell membranes, at
concentrations varying from less than 20% to around 50%.
That cholesterol modifies the mechanical, thermophysical
and lateral organizational properties of membranes has
been known for some time [29]. However, only very
recently have simulations begun to contribute to unraveling
the atomic nature of the interactions between cholesterol
and lipids in bilayers. Early simulations focused on
reduced models of lipid bilayers (because of limited
computer power) [30–32]. During the period of this review,
a number of atomic-level lipid/cholesterol simulations of
hydrated bilayers, using simulation methods tested fully
on pure lipid bilayers, have been reported. PasenkiewiczGierula et al. [33], and Rog and Pasenkiewicz-Gierula [34]
have simulated a DMPC bilayer containing 56 DMPC
molecules, 16 cholesterol molecules and 1622 water
molecules, generating a 15 ns MD trajectory. They found
that the area per DMPC molecule was decreased by about
2 Å2 from the value for pure DMPC and that order
parameters increased by an amount in agreement with
experimental values for DMPC [35]. Of interest is their
detailed breakdown of order parameters for lipid/cholesterol
neighbor pairs, an example of the ability of simulations to
examine properties beyond the reach of current experimental methods. As the cholesterol molecule has a smooth
(alpha) face with no protruding methyl groups and a rough
(beta) face with protruding methyls, it is natural to
compare the order of lipid chains adjacent to each face. They
found that the alpha face of cholesterol has a stronger
ordering effect on the lipid chains compared to the beta
face, and that the sn-1 chains appear to be most strongly
ordered by cholesterol. In the polar region, they found that
cholesterol can form hydrogen bonds preferentially with
DMPC carbonyl oxygens and also with water molecules.
Smondryev and Berkowitz have extended their earlier
DPPC/cholesterol simulations [36] to consider the effect of
cholesterol sulfate (CS) [37] and cholesterol structural
analogs [38]. For the CS simulations, performed at 1:1
DPPC:CS, the sulfate group clearly reduces the condensing
effect that cholesterol has on DPPC. Chain order parameters
are larger for the 1:1 DPPC/CS system compared to pure
DPPC bilayers, but are not as large as those calculated for
Modeling the lipid component of membranes Scott
499
a 1:1 DPPC/cholesterol simulation [36]. Interestingly, the
1:1 DPPC/CS system has a dipole potential that is opposite
in sign (–200 mV) to that of 1:1 DPPC/cholesterol
(+1000 mV, from [36]). The simulations of 1:8 ergosterol/
DMPC and 1:8 lanosterol/DMPC bilayers (with the same
numbers of lipids and waters as their earlier simulations)
are of interest because of the presence of ergosterol in the
membranes of some primitive organisms and because
lanosterol is an evolutionary precursor to both cholesterol
and ergosterol. In these simulations, the areas per molecule appear to fluctuate around 58 Å2/mol for all systems
and may be drifting downward, even after 4 ns of MD.
Unfortunately, there are no experimental values for areas
per molecule for lipid/cholesterol bilayers with which to
test the simulation predictions. Order parameter profiles
for the three sterols with DMPC are basically identical;
thus, each seems to condense the bilayer by the same
amount. The lanosterol polar group appears to be located
deeper in the bilayer than those of cholesterol and ergosterol,
resulting in fewer hydrogen bonds between the lanosterol
hydroxyl and DMPC phosphate oxygens. Again, there are
no experimental data to test the order parameter predictions
more quantitatively for lipids with ergosterol or lanosterol.
Figure 3
Chiu et al. have presented analyses of new simulation data
for DPPC/cholesterol bilayers with nine different cholesterol concentrations, ranging from 4% to 50%. These data
build on earlier simulations, using MD and CBMC [39,40],
with 5 ns trajectories for each system, providing a full range
of atomic-level simulation data for lipid/cholesterol bilayers
[41••]. In all cases, the systems contained in excess of 100
lipid molecules and 32 waters per lipid. Simulations were
performed in a constant surface tension ensemble, using a
value for the surface tension (80 dynes/cm) that reproduced the experimental area per molecule for pure DPPC
bilayers [42]. For sterol:lipid ratios above 1:8, the area per
molecule of the membrane varied linearly with cholesterol
concentration. From the slope and intercept of this line,
the cross-sectional area of cholesterol in these mixtures is
found to be surprisingly small, about 22.3 Å2, and the area
of a DPPC molecule is nearly gel-like, about 50.7 Å2 (the
experimental value for the gel phase area per molecule for
pure DPPC is 47.9 Å2 [7]. The low cross-sectional area per
cholesterol is consistent with minimal cross-sectional measurements of a space-filling molecular cholesterol model
by Rothman and Engleman [43]. For lower concentrations
of cholesterol, the cross-sectional area approaches the area
per molecule for pure fluid phase DPPC, indicating the
melting of most of the DPPC into a fluid state. This result
suggests that cholesterol induces a liquid-ordered phase in
DPPC at concentrations above about 12%, and that the
average area per DPPC and the average area per cholesterol
are about the same throughout this range of concentrations.
Experimental phase diagrams put this transition at a higher
cholesterol concentration, around 20% [44–46], but this
difference may be due to small size effects in the simulations,
which reduce the required cooperativity. Figure 3 shows a
snapshot from the 1:1 DPPC/cholesterol simulation that
Snapshot from a 1:1 DPPC/cholesterol simulation. Waters are
removed for clarity. Cholesterols are shown in green, otherwise the
color code is as in Figures 1 and 2.
illustrates the high degree of ordering of the lipid chains in
this system. Chiu et al. [41••] find differences in lipid chain
ordering between 10% and 50% cholesterol, with the
simulation order parameter profiles gradually increasing with
cholesterol concentration, as observed experimentally [44].
But the data clearly demonstrate that the bilayer is able to
maintain an average area per DPPC that is consistently low
and constant between 12% and 50% cholesterol concentration.
Using simulations as input to macroscopic
modeling
Although simulations have become larger and longer,
reaching scales of nanometers and nanoseconds, they are
still several orders of magnitude from the time and/or
length scales of the most complex biological events. For
example, the process by which lipid vesicles bud from the
plasma membrane of cells involves length scales of about
100 nm and time scales of milliseconds or more. Because
such a large gap will not be bridged any time soon by
brute-force MD or MC simulations, it is natural to attempt
to find ways to use the microscopic detail provided by
atomistic simulations as input to coarse-grained theoretical
and computational modeling efforts, which can reach larger
scales of length and time.
Hakansson et al. [47] have used data from an MD simulation
of DPPC in excess water as input for the calculation of
slow-motion electron paramagnetic resonance (EPR) line
shapes via the stochastic Liouville equation. This work
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Membranes
involved the generation of a 100 ns MD trajectory (the
longest known to this writer so far) of a system of 64 lipids
with 23 waters per lipid. The long trajectory was used to
calculate the lipid reorientational correlation function,
which was then extrapolated to ~600 ns in a stochastic
simulation. This work represents the first calculation of
the slow dynamics of a probe (the nitroxide spin label) in a
lipid bilayer using MD simulation. As simulation times are
extended, this type of extrapolative calculation will
become more useful and reliable.
Although MD simulations of 100 ns can form the basis for
studying slightly longer time scale motions, the problem of
phase separation and lateral organization in membranes
requires millisecond or longer time scales. Models that
describe this kind of phase transition behavior work at
the statistical mechanics level, requiring as input a
Hamiltonian function far simpler than atomistic MD energy
functions. This type of modeling has, to date, been done
using simplified lattice models for the lipid bilayer in
which lipid chains, cholesterol and other membrane molecules
occupy points on a two-dimensional lattice and interact via
simple spin variables [48,49]. These models, although
interesting and capable of fitting a wide range of experimental data, suffer from a lack of connection to atomistic
interactions, which must ultimately be responsible for
phase separation and domain formation.
In an innovative attempt to form a connection between
atomic detail and coarse-grained interactions suitable for
lattice modeling, Lague et al. [50,51] have used MD simulations of DPPC as input to integral equation studies from
liquid state physics. Density–density response functions
calculated from an MD trajectory are input into the kernel
of a hypernetted chain (HNC) integral equation [52]. The
HNC equations were written for a two-dimensional plane
in which a fixed number of fixed cylindrical inclusions are
added in order to model membrane proteins. From the
self-consistent solution of the HNC equation, one obtains
a distance-dependent potential of mean force between
pairs of inclusions, as a function of their separation in the
plane. This is a promising new technique that may allow
the development of simulation-based lattice MC models
for lateral organization. However, more refinements may
be needed, as the use of purely repulsive cylinders for
model proteins probably is too simplistic.
Ayton et al. [53,54] have used nonequilibrium MD simulations to calculate input density functional properties that
are then input into a flexible sheet calculation that serves
as a continuum model for the membrane. Within this
model, material properties such as the bulk modulus can
be calculated. The nonequilibrium MD is carried out by
applying a periodic compressive force to the simulation
box. The bulk modulus of the system is then calculated
from the resulting strain (averaged over several MD trajectories). The mapping of an MD simulation box onto an
elastic ‘particle’ in a network of identical particles connected
by elastic interactions appears to limit the usefulness of
this method to the calculation of elastic properties of the
model network.
Conclusions
Atomic-level simulations of lipid membranes continue to
provide useful and reliable atomic-level insights into a
growing variety of systems of increasing size and complexity.
New simulations are being applied to mixed lipid systems
and lipid–protein systems, simulation boxes containing
over 1000 lipids and for times approaching 0.1 µs. Equally
important, ingenious new methods and algorithms for
extending the quantitative data from atomistic simulations
to the microscopic scale and above are now beginning to
have an impact on the lipid modeling field.
Update
A recent example of a close collaboration between experimental and simulation groups is provided by Snyder et al.
[55]. This work consists of a detailed analysis of the population of bond conformational sequences (i.e. strings of trans,
t, or gauche, g, bonds in a specified order such as tt or gt or gg),
as determined by IR spectroscopy and by MD simulations.
The interesting conclusion is that the predicted values from
the simulation are larger than those measured experimentally.
The overall concentration of gauche bonds is experimentally
determined to be 0.14, whereas the MD simulation predicts
this concentration to be 0.28. Until other simulation groups
determine the conformer concentrations in their simulations,
it is unclear whether the disagreement is unique to the
reported simulation or is a general problem with all simulations.
Acknowledgements
I thank S Feller, O Edholm, M Pasenkiewicz-Gierula, B Roux and G Voth
for providing preprints and reprints of their work, JF Nagle for comments
on the manuscript and E Jakobsson for many insightful discussions.
Research is supported by National Institutes of Health grant GM 54561.
References and recommended reading
Papers of particular interest, published within the annual period of review,
have been highlighted as:
• of special interest
•• of outstanding interest
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