Chemistry and Physics of Lipids 141 (2006) 2–29
Review
Modelling of proteins in membranes
Maria Maddalena Sperotto a , Sylvio May b , Artur Baumgaertner c,∗
a
Biocentrum, The Technical University of Denmark, Lyngby, Denmark
Department of Physics, North Dakota State University, Fargo, USA
Department of Solid State Research, Research Centre Jülich, Germany
b
c
Received 20 December 2005; accepted 20 February 2006
Available online 27 March 2006
Abstract
This review describes some recent theories and simulations of mesoscopic and microscopic models of lipid membranes with
embedded or attached proteins. We summarize results supporting our understanding of phenomena for which the activities of
proteins in membranes are expected to be significantly affected by the lipid environment. Theoretical predictions are pointed
out, and compared to experimental findings, if available. Among others, the following phenomena are discussed: interactions of
interfacially adsorbed peptides, pore-forming amphipathic peptides, adsorption of charged proteins onto oppositely charged lipid
membranes, lipid-induced tilting of proteins embedded in lipid bilayers, protein-induced bilayer deformations, protein insertion and
assembly, and lipid-controlled functioning of membrane proteins.
© 2006 Elsevier Ireland Ltd. All rights reserved.
Keywords: Dissipative particle dynamics; Coarse-grain model; Mesoscopic model; Molecular dynamics; Monte Carlo; Hydrophobic mismatch;
Tilting; Phase transition; Cooperative behavior; Protein insertion; Ion channel; Poisson–Boltzmann; Lipid–protein interaction
Contents
1.
2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistical mean-field theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. Chain-packing theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Membrane elasticity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Poisson–Boltzmann theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mesoscopic modelling and DPD simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1. Mesoscopic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Dissipative particle dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. Protein-induced bilayer perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Lipid-induced protein tilting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
6
6
7
8
10
10
12
12
15
Abbreviations: DPD, dissipative particle dynamics; MC, Monte Carlo; MD, molecular dynamics; CG, coarse grain (or mesoscopic); DMPC,
dimyristoylphosphatidylcholine; DPPC, dipalmitoylphosphatidylcholine; POPC, palmitoyloleoylphosphatidylcholine; POPE, palmitoyloleoylphosphatidylethanolamine; PB, Poisson–Boltzmann; TM, transmembrane
∗ Corresponding author. Tel.: +49 2461 614074; fax: +49 2461 612893.
E-mail address: [email protected] (A. Baumgaertner).
0009-3084/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved.
doi:10.1016/j.chemphyslip.2006.02.024
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
4.
5.
Simulations of membrane processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1. Protein translocation into membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Protein assemblies in membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1. Protein assemblies in membranes: single peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2. Protein assemblies in membranes: interacting peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Lipid-controlled function of membrane proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concluding remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Biological membranes are heterogeneous, highly
cooperative and very complex systems. Because of the
intricate interplay between biomembrane functioning,
membrane chemistry, and physical properties of the
lipid bilayer (Sackmann, 1995), to relate the physical
properties of biomembranes to their biological function
(Sackmann, 1995) – the ultimate goal of biomembrane
science – it is not only common but usually necessary to study model (or reconstituted) membranes: lipid
bilayers composed of few lipid species with embedded proteins, or natural or artificial peptides, or other
biologically relevant molecules. Therefore reconstituted
membranes have become the subject of an enormous
number of interdisciplinary experimental, as well as
theoretical, investigations, which have and are helping
to understand membrane organization and biofunctioning. Interestingly, experimental findings have initially
motivated the development of lipid–protein interaction
models, which have then, in turn, started to help designing useful experiments.
This review focuses on some selected lipid–protein
modelling approaches that have been used to investigate
phenomena occurring in biomembrane mimetic system,
such as the formation of domains, lipid-induced structural changes (and activities) of membrane proteins,
protein-induced changes in lateral membrane organization, the role of charges for the binding of proteins
to membranes, or the insertion of proteins into membranes. Theoretical studies have also been used to proof
conceptual hypothesis which in the recent years have
constituted a matter of debate among scientists. One
example is the role played for some biomembrane phenomena by the hydrophobia matching (between the lipidbilayer hydrophobic thickness and the protein hydrophobic length). There are roughly three different classes
of modelling approaches, each with their own advantages and limitations: statistical theories, mesoscopic
models, and all-atom models. The three main sections
of this review focus each on one of these classes. This
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19
19
21
22
24
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25
review focus on the results obtained by theoretical studies (and their possible interplay with experimental investigations), rather than with the theoretical or computational methods used to study the models. Details of the
methodologies can be found in the references cited in
the various sections of the review.
During the last decades, it has become evident that
the behavior of biomembranes is governed by some
basic physical principles, which manifest themselves
in some detectable properties. Among them, membrane
elasticity seems to play a role in the budding, fusion,
fission, and pore formation processes. Also, the shape
of the lipid molecules is important for determining the
stability of the three-dimensional structure of the lipid
aggregates. A hypothesis that has early been proposed
is that of hydrophobic matching (Mouritsen and Blom,
1984; Sackmann, 1984; Mouritsen and Sperotto, 1993;
Gil et al., 1998; Killian, 1998; Dumas et al., 1999) and
related theories (see references in Abney and Owicki,
1985). According to this hypothesis, hydrophobic mismatch may affect membrane organization and biological
functions: it is now known that hydrophobic matching is involved, among others, in the secretory pathway in the Golgi (Munro, 1995, 1998; Bretscher and
Munro, 1993; Pelham and Munro, 1993). Hydrophobic matching also seems to play a role in sequestering
proteins with long transmembrane regions (McIntosh et
al., 2003) into sphingolipids–cholesterol biomembrane
domains denoted as ‘rafts’ (Simons and Ikonen, 1997;
Binder et al., 2003; Mukherijee and Maxfield, 2004),
which are known to be involved in numerous diseases
(Fantini et al., 2002). The ways that biological membranes may use to compensate for hydrophobic mismatch (de Planque and Killian, 2003) imply changes
of the membrane structure and dynamics on a microscopic as well as on a macroscopic scale (Killian, 1992;
Epand, 1998; Mouritsen, 1998; Gil et al., 1998; Dumas
et al., 1997; Morein et al., 2002; Fahsel et al., 2002;
Mall et al., 2001; Fernandes et al., 2003; Harroun et
al., 1999a,b)—and may therefore affect biological functions (Montecucco et al., 1982; Johansson et al., 1981;
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M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
In’t Veld et al., 1991; Lee, 1998, 2003). Regarding the
mismatch-induced membrane changes happening on the
microscopic scale, there are a number of experimental evidences indicating that, on the one end, proteininduced bilayer deformations may arise in the vicinity
of the protein–lipid interface (Jost et al., 1973; Hesketh
et al., 1976; Jost and Hayes Griffith, 1980; Rehorek et
al., 1985; Piknová et al., 1993; Harroun et al., 1999a,b;
Bryl and Yoshihara, 2001). Also, the protein may prefer,
on a statistical basis, to be associated with the type of
lipids that best matches its hydrophobic surface (Dumas
et al., 1997; Lehtonen and Kinnunen, 1997; Fahsel et al.,
2002; Fernandes et al., 2003). Phenomena like the one
described above may induce the formation of bilayer
domains (Binder et al., 2003), the possible precursors of
the rafts, whose functional properties differ from those
of the bulk, i.e. the unperturbed bilayer (Tocanne, 1992;
Tocanne et al., 1994; Thomson et al., 1995). On the
other end, there may be mismatch effects which are lipidmediated, such as the tilting (or even bending) of a whole
protein/peptide to adapt to a too-thin bilayer (Glaubitz
et al., 2000; Harzer and Bechinger, 2000; Killian, 1998;
Sharpe et al., 2002; van der Wei et al., 2002; Koehorst
et al., 2004; Strandberg et al., 2004; Özdirekcan et al.,
2005; Ramakrishnan et al., 2005), or even tilting of the
individual helices which form a protein; there is indeed
some experimental evidence that the latter phenomenon
may occur in channel proteins (Lee, 2003), and that a
change of the tilt angle of the individual helices could be
the cause of a change in protein activity. The issues about
the protein-induced bilayers deformations and the lipidinduced proteins tilting are discussed below in Sections
2.2, 3.3 and 3.4.
Because of the many degrees of freedom involved,
biomembrane processes occur over a wide range of time
and length scales (König and Sackmann, 1996). There
are fast processes such as the trans-gauche isomerization
time of the lipid chains (10−10 s), or the time of a lipid to
diffuse within the membrane a distance that corresponds
to its own size (10−8 s). Among the slow processes are
the flip-flop motion of a single lipid from one leaflet of
a bilayer to the other (103 s), or cooperative phenomena such as a lateral phase separation of two immiscible
lipid species. Similarly for length scales, a process might
depend only on the local membrane environment, as is
the case when a lipid chain changes its conformation. On
the other hand, cooperative phenomena typically involve
correlated fluctuations over large length scales, such as in
the fluid–gel phase transition. To model membranes it is
necessary to decide, a priori, on the level of description
of the system (i.e. to deliberately neglect those details
unimportant to the process one wants to investigate).
Often, this necessity follows the fact that some theoretical methods are limited in their applicability by the
long computational times needed to calculate statistical
quantities. Generally, the level of description needs to
match the time and length scale of the process under
consideration. That is, processes occurring on short time
scales can be integrated out whereas all slow processes
can be assumed to be infinitely slow. In fact, these general considerations provide the basis for the application
of equilibrium-thermodynamics methods.
In the past, mean-field theories, thermodynamical
models, phenomenological and statistical microscopic
models have been developed, often in conjunction with
experimental investigations to study macroscopic, as
well as mesoscopic, behavior of lipid–protein model systems (Gil et al., 1998).
For example, lattice models have been useful to investigate the cooperative behavior of lipid–protein mixtures,
and how the presence of protein-like impurities affects
the phase behavior of the lipid-bilayer system (Sperotto
and Mouritsen, 1991; Sperotto, 1997; Dumas et al., 1997;
Morein et al., 2002). However, lattice models have limitations as the discrete lattice structure, its connectivity
and topology does not adequately reflect the fluid-like
and self-assembled nature of a lipid membrane. Still,
these models turn out to be useful in connection with their
ability to predict mechanisms for membrane domain formation (Hinderliter et al., 2001).
One advantage of lattice models is, that they can be
analyzed on a mean-field level (May, 2000), allowing to
obtain simple expressions for the system’s free energies
that can be combined with other theoretical approaches.
With regard to modelling lipid–protein interaction there
are a number of other phenomenological approaches
ranging from elasticity to Poisson–Boltzmann theory,
some of which will be discussed in Section 2. All these
methods involve parameters that reflect the energetics
of the system on a microscopic scale. They appear, for
example, as elastic moduli or as interaction strength in
a MC simulation. Clearly, the determination of these
parameters is outside the scope of phenomenological
approaches but requires alternatives such as experimental determination, microscopic-level methods, or atomistic simulations.
Despite the development of powerful experimental techniques such as X-ray crystallography, electron microscopy, variants of nuclear magnetic resonance (NMR), fluorescence spectroscopy, electron-spinresonance (ESR), and others, the characterization of
lipid–protein systems on the molecular level remains
difficult because of their complexity. At the present
time, even qualitative information gained by perform-
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
ing detailed computer simulations of protein–membrane
complexes can be valuable, because only scarce information is available from experiments about the structure
and dynamics of these systems. Therefore, the investigation of proteins solvated in water and in lipids employing
molecular dynamics (MD) methods is becoming increasingly important. The length and time scales covered
by MD simulations have reached considerably beyond
the nanosecond and nanometer ranges where important
structural and dynamical phenomena are expected. In
particular, in Section 4.1 we discuss MD studies which
reveal molecular details of the insertion mechanism of
peptides into membranes. The individual and collective
behavior of membrane peptides solvated in an explicit
environment of fully hydrated membrane models are discussed in Section 4.2. Among others, the characteristics
of single melittin, alamethicin, dynorphin, and SP-C are
presented, as well as some results on the oligomerization of transmembrane ␣-helices. Very recently a few
MD studies have addressed the significance of lipids
for the control and active regulation of the function of
large membrane proteins: the lipid-mediated gating of
mechanosensitive ion channels. This is summarized in
Section 4.3.
Beside pure atomistic models used for simulations,
there are notable also hybrid- and multi-scale approaches
(Chang et al., 2005). For example, Biggin and Sansom
(2003) used atomistic MD simulations to model the
behavior of a protein channel in the membrane whereas
the lipid bilayer was described by a mean-field potential.
Because of the extremely long time required for the simulations, the information that can be obtained by all-atom
simulations are limited to phenomena that occur at the
nanoscopic level and on a nanosecond time-scale (up to
100 nm). Therefore, hybrid- and multi-scale approaches
which use implicit models of lipids and/or water are
in some cases unavoidable to study biologically relevant membrane processes which occur much beyond the
nanosecond time range (König and Sackmann, 1996), for
example in-plane phase transitions, phase separations,
membrane fusion, or the self-assembly of peptides in a
membrane.
To bridge the gap between the informations that can
be obtained by using phenomenological modelling and
those from all-atom modelling, a number of solvent free
membrane models (Goetz and Lipowsky, 1998; Cooke
et al., 2005; Brannigan et al., 2005) and coarse-grain
(or mesoscopic) models have been developed, which
have been studied by MD simulations (Shelley et al.,
2001a,b; van der Eerden et al., 2002; Nielsen et al.,
2004; Nielsen et al., 2005a,b), and off-lattice MC simulations (Sintes and Baumgärtner, 1997; Gompper and
5
Kroll, 1997). The mesoscopic approach is based on the
idea of modelling the system by an ensemble of effective
particles, or ‘beads’. Each particle represents a lump of
atoms (or even lipids) whose atomistic details are not
relevant to the process under consideration. The internal degrees of freedom of each ‘bead’ are integrated out,
contributing merely to a set of interaction parameters
that defines bead–bead interactions. The main advantage
of this approach is that it allows to access longer time
and length scales compared to what is permitted by MD
simulations all-atom models. The obvious limitation is
the loss of atomistic information. There are biomembrane processes that ultimately have to be studied using
both approaches, the mesoscopic and the atomistic. For
example, the fusion event between two apposed membranes involves a high activation energy and thus is a
rare event (happening at times longer that milliseconds)
that becomes only accessible using CG methods. However, once it happens, its progression depends on molecular details (specified by the fusion protein machinery). To capture both levels is one of the major future
challenges.
Despite the advantages that arise by minimal modelling in connection with simulation methods like MD
and MC, the possibility to study processes that involve
the cooperative nature of biomembranes is still limited. To try to overcome this limitation, the use of a
faster simulation technique, dissipative particle dynamics (DPD), on CG models has thus been considered. In
fact, the DPD simulations allow for a timestep that is
at least three orders of magnitude longer than what is
used in atomistic MD simulations, which is typically of
the order of a few femtoseconds (Groot, 2000; Groot
and Rabone, 2001). The DPD method was first used
to study mesoscopic models for pure lipid-bilayer systems (Venturoli and Smit, 1999; Shillcock and Lipowsky,
2002), and then lipid bilayers containing impurities such
as alcohols (Kranenburg and Smit, 2004; Kranenburg
et al., 2004b). The results from the simulation studies demonstrated that with the DPD–CG approach one
was able to reproduce structural and thermodynamic
properties resulting from the cooperative behavior of
the investigated system (Kranenburg et al., 2003a,b).
Based on the mesoscopic model for pure phospholipid bilayer (Venturoli and Smit, 1999), Venturoli et al.
(2005) have developed a coarse-grain model for proteins of different sizes and have then used the DPD
simulation method to study the behavior of a mesoscopic model for lipid bilayers with embedded proteins. These authors have correlated in a systematic
way the extent of the protein-induced bilayer perturbation and the lipid-induced protein tilting with the
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M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
lipid–protein hydrophobic mismatch. Comparison with
experimental data indicates that some details of the
protein structures are not relevant in relation to how
much proteins tilt in a mismatched lipid bilayer. Brief
descriptions of the lipid–protein systems studied with
CG models by the MD or MC simulation methods, of
the CG + DPD modelling approach, and of the membrane issues investigated by this approach are found in
Section 3.
2. Statistical mean-field theories
2.1. Chain-packing theory
Membrane-inserted proteins perturb the host membrane. One reason for this perturbation is the rigidity of the protein facing the fluid-like lipid environment. The lipid chains close to the protein surface
are no longer able to explore their full conformational
space as they cannot penetrate into the protein’s interior. This implies a penalty in conformational entropy
which rises the lipid–protein interaction energy. A fairly
simple molecular-level approach, able to predict the corresponding energies, is the chain-packing theory developed by Ben-Shaul and coworkers (Ben-Shaul, 1995).
This theory was originally applied to homogeneous
lipid aggregates and has later been generalized to nonhomogeneous membranes, including membranes that
contain rigid inclusions. The basis of the chain-packing
theory forms the constraint of uniform segment density
within the entire membrane’s hydrocarbon core. This
constraint is approximatively fulfilled in any lipid aggregate. As discussed recently (Siegel, 1999), there are no
regions within the membrane that are void of chain segments. On the other hand, X-ray scattering experiments
and MD simulations both show that the assumption of
a constant and homogeneous segment density is not
strictly valid (Wiener and White, 1992; Tieleman et al.,
1997). The generalized version of the chain-packing
approach is concerned with two functional degrees of
freedom. One is the density σ(r) of lipid headgroups on
the aggregate interface A. The other one is the conditional probability P(α|r) to find a lipid chain in a given
conformation α if the corresponding headgroup of this
chain is located at position r ∈ A. The overall free energy
of the inclusion-containing membrane F[σ(r), P(α|r)] is
then written on a mean-field level and minimized with
respect to σ(r) and P(α|r) under the constraint of uniform chain segment density everywhere (May and BenShaul, 2000). Fattal and Ben-Shaul (1993) have used the
chain-packing approach to investigate the perturbation
of a lipid bilayer induced by the presence of a single
transmembrane protein. The protein was modelled as a
straight wall, impenetrable to the hydrocarbon chains of
the lipids and imposing a certain degree of hydrophobic
mismatch between protein and membrane. While their
study was mainly aimed to get insight into the energetics
of hydrophobic mismatch (discussed below) there was
another notable result: protein insertion into the host
bilayer involves an energetic penalty that results from
conformational restrictions of the perturbed lipid chains.
It may be speculated that this penalty contributes to driving protein aggregation in membranes. To further pursue
the mechanism, the interaction between two parallel,
membrane-inserted rigid walls was calculated using the
chain-packing approach (May and Ben-Shaul, 2000).
The result indicated that the energy gain upon aggregation between the two walls is preceded by an energetic
barrier. Such a barrier was also predicted by other theoretical approaches, including membrane elasticity theory (Dan et al., 1993) and MC simulations (Sintes and
Baumgaertner, 1998). The barrier generally locates at
distances between the inclusions that correspond to the
size of at most a few lipid molecules. It is notable that a
simple “toy” model (May and Ben-Shaul, 2000) recovers
some of the predictions made by chain-packing theory, including the non-monotonic membrane-mediated
interaction potential between two walls. This so-called
director model approximates the conformational space
of a lipid hydrocarbon chain by the different orientations of a single (unit) vector. Thereby it is assumed that
all accessible orientations of this vector occur with the
same probability. Not accessible are those orientations
for which the vector leaves the hydrocarbon core of the
membrane. The presence of rigid membrane inclusions,
such as one or more rigid walls, further restricts the
orientational space, rendering all inclusion-penetrating
vector orientations inaccessible. Calculating the loss of
orientational entropy imposed by a rigid wall (and similarly for any given inclusion shape) involves summation
over the individual contributions of all affected chains.
It turns out that the corresponding free energy measured
per unit length of a membrane-inserted wall is predicted to be 0.24 kB T/Å, in reasonable agreement with
the more detailed chain-packing calculations for which
0.37 kB T/Å were obtained for (CH2 )13 CH3 chains.
More important, qualitative agreement is also observed
for several other observables: for the wall-induced tilt of
the lipid chains, for the non-monotonic interaction potential between two walls (May and Ben-Shaul, 2000), and
for the calculation of the so-called tilt modulus (May et
al., 2004), discussed further below. It is this agreement
which makes the simple director model a candidate to
use for more complex geometries (Kessel et al., 2001)
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
(those that are numerically difficult to access using the
chain-packing theory) or to interpret the results of chainpacking calculations.
Another recent application of the chain-packing
approach concerns the interaction of interfacially
adsorbed and pore-forming amphipathic peptides with
a lipid membrane. Amphipathic peptides, such as mellitin, magainin or alamethicin, are typically alpha-helical
with a hydrophobic and a polar (typically cationic) face.
They often possess antimicrobial activity which makes
them naturally occurring antibiotics (Tossi et al., 2000).
That is, upon interaction with a lipid membrane they are
able to exert lytic activity. Among the suggested mechanisms is the formation of pores (Epand et al., 1995).
In this case, the peptides are initially adsorbed – driven
mostly by electrostatic and hydrophobic interaction – to
the membrane in interfacial orientation, inserting their
hydrophobic face into the host bilayer. Peptide aggregation and self-assembly then can lead to an orientational change upon which the peptides rearrange into
a membrane-inserted, pore-forming structure (Huang,
2000). Yet, in order for the peptides to self-assemble
there must be an energetic driving force that compensates
for the loss of their in-plane translational and orientational entropy. A recent model study (Zemel et al., 2005)
offers an interesting and new explanation for the origin
of this driving force. In this study, the mean-field chainpacking approach was applied to a membrane-adsorbed
cylinder-like particle and a membrane-spanning wall
as models for amphipathic peptides in their isolated
and pore-forming states, respectively. The calculations
showed that the perturbation of the hydrocarbon chain
region induced by an isolated cylinder-like particle is
quite substantial and results from the need of the lipids to
fill out and pack with uniform segment density the region
just underneath the cylinder. This need is predicted to
result in local membrane thinning and in a decrease of the
average segmental order parameter of the lipid hydrocarbon chains (Zemel et al., 2004), both being in agreement
with experimental data (Ludtke et al., 1995; Koenig et al.,
1999). Further analysis shows that the lipid chains in the
two apposed lipid monolayers are perturbed differently:
those in the cylinder-containing monolayer curl on average toward the region underneath the adsorbed cylinder
whereas those in the opposite monolayer stretch toward
the cylinder. The behavior for the membrane-adsorbed
cylinder is in notable contrast to a simple membranespanning wall for which the conformational confinement
of the lipid chains (discussed above in terms of the director model) provides the main contribution to the membrane perturbation free energy. As a consequence, the
membrane-spanning wall is energetically preferred over
7
the adsorbed cylinder; the chain-packing calculations
predict about 4–5 kB T per peptide which would provide the energy to account for experimentally observed
peptide self-assembly (and pore formation). It should be
mentioned that various interactions not accounted for by
the chain-packing approach are likely to modify the peptide’s propensity to self-assemble. Most notable among
these are interactions between acidic lipid headgroups
and basic peptide residues (Zemel et al., 2003). Still, the
perturbation of the membrane chain region would provide a plausible non-specific driving force that complements with alternative mechanisms (Huang et al., 2004)
and could underlie the biological function of amphipathic pore-forming peptides.
2.2. Membrane elasticity theory
Transmembrane proteins or peptides are rigid bodies when compared to the fluid-like host membrane.
It is therefore common to model these molecules as
rigid inclusions that reside in the membrane. An important class of transmembrane proteins/peptides can be
represented as inclusions with up-down symmetry. In
this case, the mid-surface of the inclusion-containing
membrane (that is the surface that divides between the
two membrane leaflets) remains planar. At the same
time, the thickness of the membrane-inserted hydrophobic part of an inclusion need generally not match that
of the host membrane, a case which is referred to as
hydrophobic mismatch (Mouritsen and Blom, 1984). In
fact, hydrophobic mismatch can be positive or negative
depending on whether the thickness of the inclusion’s
hydrophobic part is larger or smaller than that of the
host membrane. It is notable that the thickness mismatch
between transmembrane proteins (or peptides) and lipid
membranes can be altered experimentally (say, by using
lipids of different chain length) and can thus be studied
systematically. Among the implications of hydrophobic
mismatch are protein aggregation and conformational
changes, lipid sorting, peptide tilt, and structural phase
transitions of membranes (Killian, 1998). All these are
the consequence of an unfavorably high energy penalty
associated with a too large hydrophobic mismatch. From
a theoretical perspective it is desirable to estimate the
corresponding free energy cost: one convenient and frequently used method is the application of membrane
elasticity theory. Here, a number of different deformation modes such as splay, saddle splay, compression,
and tilt contribute to the free energy of an inclusioncontaining membrane. The former two modes are well
known as they are energetically equivalent to a curvature
deformation of a lipid layer, described by the bending
8
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
rigidity κ and the Gaussian modulus κ̄ (Helfrich, 1973).
The compression mode is related (through the volume
conservation constraint of the membrane) to a lateral
extension. Here too, the corresponding elastic modulus
– the lateral area compressibility modulus K – is well
known from experiments. The remaining deformation
mode is associated with tilt of the lipid chains. We note
that for a fluid-like lipid layer tilt represents the average over the (conveniently defined) tilt of many different
chain conformations. Unlike for the other deformation
modes, the corresponding modulus of a tilt deformation – the tilt modulus κt – is not known from experiment but has been estimated based on several different
theoretical approaches including the above-mentioned
mean-field chain-packing approach (May et al., 2004).
To apply membrane elasticity theory, the energies associated with the different deformation modes are expressed
in terms of conveniently defined functional order parameters such as the relative change in membrane thickness
and/or the (average) orientation of the lipid chains. Minimization of the overall free energy with respect to the
order parameters results in differential equations whose
boundary conditions are determined by the inclusion
geometry.
The membrane perturbation induced by a single symmetric inclusion exhibits a typical damped oscillating
behavior. The wave-length ξ C of the oscillating part and
the characteristic length ξ P of the exponential decay are
given by
−1/2
dL0
1
0 −1/2
ξC/P = dL K
∓
(1)
κt
(κK)1/2
where dL0 is the equilibrium thickness of the membrane
(May, 2002). Typically, lipid membranes are characterized by both a large stretching and tilt modulus and
a comparatively small bending stiffness. This leads to
both ξ P and ξ C being small, on the order of 1 nm, indicating that the elastic perturbation of the membrane
decays fast – within a few lipids – to its equilibrium
value dL0 . Even though this raises concerns about the
appropriateness of elasticity theory in the first place,
this approach has frequently been applied to interpret
experimental results (Harroun et al., 1999a,b; Lundbæk
and Andersen, 1999). Moreover, as will be discussed in
Section 3.3, the typical overshooting effect (Dan et al.,
1993) is also observed in computer simulations such as
DPD (Venturoli et al., 2005) or self-consistent field theory (Kik et al., 2005) that take into account the discrete
nature of the lipids. (In Fig. 8, we shall compare the
predictions of membrane elasticity theory with results
from a DPD simulation.) The general reason for the non-
monotonic membrane relaxation lies in the competition
between the stretching and bending modes of deformation. This has an interesting implication concerning the
membrane-mediated elastic interaction between two (or
more) inclusions which, too, is non-monotonic. That is,
there is an energy barrier that separates an attractive from
a repulsive region, a prediction similar to that derived
within the chain-packing approach and within the director model as discussed above.
Under the assumption that the elastic energy of
the membrane and the inclusion-induced conformational restrictions are the main energetic contributions
to lipid–protein interaction (that is, neglecting all specific and particularly all lipid headgroup–protein interactions), an approach has recently been made (May, 2002;
Bohinc et al., 2003) to combine elasticity theory with
the director model. Among the predictions is that even a
matching transmembrane inclusion induces a small but
notable membrane thickening and that the optimal “mismatch” is a negative one. Similar predictions are made
by self-consistent field theory (Kik et al., 2005) but still
await a systematic experimental inspection.
2.3. Poisson–Boltzmann theory
Charged water soluble proteins (and other macroions
such as DNA) interact with oppositely charged lipid
membranes predominantly through electrostatic interactions. The corresponding energetics can be described on
the mean-field level by Poisson–Boltzmann (PB) theory. The crucial quantities in this theory are the local
concentrations n+ and n− of the positively and negatively charged mobile ions, respectively, near the protein
and membrane. On the mean-field level, they are given
by the Boltzmann distributions n± = n0 exp(∓Ψ ) where
n0 is the corresponding bulk concentration and Ψ is
the (reduced) electrostatic potential. Combination with
Poisson’s law of electrostatics leads to the PB equation
2 Ψ = sinh Ψ where denotes the Laplacian and l
lD
D
the Debye screening length. We note that in the presence
of di- and higher valent mobile ions, the PB approach
becomes increasingly inappropriate as ionic correlations
start affecting (and eventually dominate) the free energy
(Grosberg et al., 2002). Hence, most applications of PB
theory are restricted to deal with monovalent ions. Yet,
within this restriction the PB approach is powerful as
it can be used to derive membrane–protein interaction
energies on an atomistic level (Wang et al., 2004).
When well separated, both the membrane and the protein individually immobilize corresponding counterions
by forming a diffuse double layer. This layer reflects a
compromise between the loss in translational entropy of
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
9
Fig. 1. Schematic illustration of a spherical protein adsorbed onto a two-component membrane. In the fluid-like state, the lipids are mobile in lateral
direction, implying the possibility of local compositional changes. The diagram shows predictions of PB theory for the adsorption of a single sphere
(of radius R = 10 Å with uniform charge density corresponding to seven positive charges) onto a mixed membrane that contains 20% negatively
charged lipids as a function of the scaled protein–membrane distance h/lD where lD = 10 Å is the Debye length (reproduced from May et al. (2000),
with permission). The three adsorption free energies (in units of kB T) correspond to fixed surface charge density (Fφ ), mobile lipids (F), and constant
membrane surface potential (FΨ ). The inset shows the local membrane composition, η, for the three cases at h/lD = 0.3.
the counterions and electrostatic energy. Upon adsorption of the protein onto the membrane, some of the
previously immobile counterions can be released into
the aqueous solution. As is well known, the release of
counterions generally constitutes the driving force for
the association of oppositely charged macroions. Yet,
for the adsorption of proteins onto lipid membranes a
peculiarity arises in the case of a mixed lipid membrane: mixed lipid membranes, consisting of a charged
and an uncharged lipid species, are two-dimensional fluids, able to adjust their local composition (and thus,
charge density). Hence, upon adsorption, proteins should
in principle be able to sequester oppositely charged
lipids as is schematically illustrated in Fig. 1. This is
a physically interesting situation because the release of
counterions is driven by an energetically similar process, namely the immobilization of charged lipids in the
vicinity of the protein. In other words, the diffuse ionic
layer is replaced by a diffuse in-plane layer of charged
lipids.
The additional demixing degree of freedom can be
taken into account within Poisson–Boltzmann theory by
a special boundary condition that was first derived in a
study to model cationic DNA–lipid complexes (Harries
et al., 1998). The boundary condition accounts for the
possibility of lipid migration within the membrane but
assigns an (ideal) demixing free energy penalty to variations in the local composition. As a result, the boundary condition describes a case intermediate between the
two thermodynamic limits: fixed surface charge density (that is, suppressed demixing) and constant electrostatic potential at the membrane surface. Indeed, it was
shown that also the adsorption free energy of a spherical
model protein is intermediate between that of the two
thermodynamic limits (May et al., 2000). Lipid sequestration could be a biologically important phenomenon
as is suggested for the enrichment of phosphatidylinositol 4,5-bisphosphate (PIP2 ) induced by myristoylated
alanine-rich C kinase substrate (Gambhir et al., 2004).
Yet, we also note that – in contrast to the prediction of
PB theory – there is currently no experimental indication
that charged peptides are also able to sequester monovalently charged lipids (Golebiewska et al., 2005).
Generally, two-component lipid membranes exhibit
non-ideal mixing behavior, often characterized by an
effective attraction between lipids of the same species
(Garidel and Blume, 2000). If this attraction is sufficiently large it will drive lateral phase separation
between the two membrane components. The electrostatic repulsion between the like-charged lipid headgroups is expected (at least on the mean-field level) to
stabilize the mixed membrane. That is even, if a hypothetically uncharged membrane would phase separate,
the charged one need not. Within a combination of a
mean-field lattice gas description and PB theory, the
influence of the electrostatic interactions on the stability of the membrane can be calculated (Gelbart and
Bruinsma, 1997; May et al., 2002). It is then interesting
to speculate that the adsorption of oppositely charged
proteins tends to effectively neutralize the membrane
and could thus re-introduce an instability of the membrane. However, a recently proposed two-state model
suggests a different scenario: protein-adsorption generates compositional gradients within the membrane plane
that are associated with an unfavorable energy due to
the non-ideal demixing properties. This energy acts as a
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M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
line tension around the circumference of each proteinadsorption region, giving rise to an effective membranemediated protein–protein attraction that can render the
membrane unstable (May et al., 2002).
The emergence of a line tension induced by the
adsorption of proteins and the subsequent membrane
destabilization is also corroborated by calculations on
the PB level beyond the two-state model. Mbamala
et al. (2005) have recently calculated the stability of
mixed membranes decorated by (cylindrically symmetric) model proteins of various disk-like and sphere-like
shapes. Notably, due to the non-ideal lipid demixing,
the boundary condition for the PB equation at the membrane surface becomes itself a differential equation. It
was found that the protein’s ability to induce phase separation depends sensitively on its charge distribution and
shape. The most potent candidate for inducing phase separation would be a large protein with a cluster of negative
charges on a flat face in immediate vicinity to the lipid
headgroups. No additional charges should be located at
the side face of that protein as these would give rise to
direct electrostatic protein–protein repulsion.
Experimental evidence corroborates the notable influence of non-ideal lipid demixing on membrane domain
formation. Hinderliter et al. (2001, 2004) have observed
that small changes in the chemical structure of the lipids
– for example by changing the chain length of the
uncharged lipid component – affect the ability of certain
proteins (such as the C2A and C2B domains of synaptotagmin) to induce membrane domain formation. A
discussion of this ability in connection with cholesterolcontaining membranes was recently provided by Epand
(2004).
3. Mesoscopic modelling and DPD simulations
3.1. Mesoscopic models
Thanks to the development of mesoscopic models –
also referred to as coarse-grain (CG) models – it has been
possible to investigate a number of processes related
to biomembrane physics, which would have been difficult to study by MD simulation methods on all-atom
models: the self-assembly of phospholipids into various phases, both in the absence and in the presence
of biologically relevant molecules such as anaesthetics,
and alkanes (Shelley et al., 2001a,b); the lipid-mediated
range of attraction between proteins embedded in a lipid
bilayer (Sintes and Baumgärtner, 1997); the formation
of the striped (or striated) phases which were detected
in supported phospholipid bilayers with embedded synthetic ␣-helical peptides (van der Eerden et al., 2002).
Very recently, Nielsen et al. (2005a,b) have carried out
MD simulations on a mesoscopic model to analyze
the lipid-bilayer perturbation around a transmembrane
hydrophobic nanotube. The simulation results are in
qualitative agreement with those obtained previously
by MC simulations on a lattice model (Sperotto and
Mouritsen, 1991), and all-atom MD simulations (Jensen
et al., 2001; Jensen and Mouritsen, 2004). The same
CG + MD approach has been used to study the process
of insertion of a nanotube (simulating a protein channel or a pore) into a membrane, and how the insertion
may depend on the presence of hydrophilic sites at the
heads of a hydrophobic nanotube (Lopez et al., 2005).
Nielsen et al. (2004) studied, by MD on a CG model,
the lipid-sorting mechanism which occurs when a protein is embedded in a bilayer formed by a mixture of
phospholipids having very different chain lengths. The
simulation results confirms what was observed in the
past by an investigation which combined fluorescence
spectroscopy experiments with MC simulations on a
lattice model (Dumas et al., 1997): the protein selects
in its vicinity the lipid type which better matches its
hydrophobic surface. Nielsen et al. (2004) suggest that
the lipid-sorting mechanism can explain the onset of
the fusion process; this occurs via the formation of a
meniscus in the vicinity of the protein, which is then the
triggering factor for the transition from the bilayer to a
non-bilayer phase.
The use of a relatively new simulation method on
CG models, the dissipative particle dynamics (DPD)
method, opens the possibility to investigate thermodynamic processes, such as phase transitions, that
involve the cooperative nature of biomembrane systems
(Venturoli and Smit, 1999), and that are outside the timeand length-scale range of all-atom simulations methods.
The DPD method has been adopted to study mesoscopic
models for pure lipid-bilayer systems (Venturoli and
Smit, 1999; Shillcock and Lipowsky, 2002), for bilayers
containing co-surfactants (Kranenburg and Smit, 2004;
Kranenburg et al., 2004b). Very recently, Venturoli et al.
(2005) have developed a CG model (and studied by the
DPD method) for a DMPC lipid bilayer with embedded
proteins of different sizes and hydrophobic lengths. The
aim of the model study was to understand whether, due
to hydrophobic mismatch and via the cooperative nature
of the system, proteins may prefer to tilt (with respect
to the normal direction of the bilayer plane) or even
to bend, rather than to induce a bilayer deformation
without a tilting. To illustrate the application of the DPD
method to lipid membranes, some details of the mesoscopic model of Venturoli et al. (2005) are discussed
below.
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
11
Fig. 2. Atomistic and mesoscopic representation of DMPC. Hydrophilic head-beads are indicated in shading and hydrophobic tail-beads in open
representation.
To build a mesoscopic model of membrane, one
starts by coarse-graining each molecule of the system
(or groups of molecules) by a set of beads, which –
depending on whether they refer to water molecules,
hydrophobic or hydrophilic part of the lipids or the proteins – interact differently with the surrounding beads.
An atomistic representation of a DMPC lipid and its corresponding coarse-grain model is shown in Fig. 2, where
the hydrophilic beads are indicated in shading and the
acyl-chain beads in open representation. In Venturoli et
al. (2005), the phospholipid is modelled by three headgroup beads and five beads in each chain (Kranenburg
et al., 2004a). The model of for a transmembrane protein is built by first connecting a varying number of
hydrophobic-like beads into a chain, to the ends of which
are attached three headgroup-like beads; these are then
linked together into a bundle of NP amphipathic beadchains. Three typical model-protein sizes were considered, consisting of NP = 4, 7 and 43 chains, respectively.
These sizes represent typical protein/peptide sizes: the
hydrophobic section of single-spanning membrane proteins like glycophorin (MacKenzie et al., 1997), and
the M13 major coat protein from phage (Stopar et al.,
2003; Bechinger, 1997) or ␣-helical synthetic peptides
(Morein et al., 2002) may be modelled by a skinny NP = 4
type. ␤-Helix proteins like gramicidin A (Killian, 1992)
may be modelled by a NP = 7 type. Larger proteins consisting of transmembrane ␣-helical peptides that associate in bundles, or ␤-barrel proteins (von Heijne and
Manoil, 1990) may be modelled by a NP = 43 type: bacteriorhodopsin (Henderson and Unwin, 1975), lactose
permease (Foster et al., 1983), the photosynthetic reaction center (Deisenhofer et al., 1985), cytochrome c oxidase (Iwata et al., 1995), or aquaglyceroporin (Fu et al.,
2000). By varying the protein hydrophobic sections, i.e.,
the number of hydrophobic chain-beads, one can sample different hydrophobic mismatch conditions. Fig. 3a
and b shows a cartoon of a model lipid and a protein
of size NP = 43, respectively. Fig. 3c shows the snapshots of typical configurations of the assembled bilayer
Fig. 3. Schematic representation of a model-lipid (a), and a model protein (NP = 43) (b). In the snapshots in (c) are shown typical configurations (as
results from the simulations) of the assembled bilayer with embedded model proteins with NP = 43, 7 and 4, respectively.
12
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
with embedded proteins with three different sizes, corresponding to NP = 43, 7 and 4, respectively.
3.2. Dissipative particle dynamics
The (DPD) simulation method (Hoogerbrugge and
Koelman, 1992; Warren, 1998; Jury et al., 1999) was
originally based on the idea of simulating the fluid hydrodynamics of systems composed of beads (where in the
case of a fluid the ‘bead’ is a small droplet of the fluid),
in analogy with the way the Navier–Stokes equations
reproduce the motion of a real fluid. Each bead moves
according to Newton’s equation of motion, and interacts
according to simplified force laws. The beads interact
with each other via conservative, random, and dissipative
forces of the pairwise-additive type. The combined effect
of the dissipative and the random forces, acts as a thermostat, which conserves the (angular) momentum, and
thus provides the correct hydrodynamics to the system.
The total force acting on each bead i, is thus expressed as
a sum over all other beads, j, which are within a certain
cutoff radius Rc from bead i. The force of conservative
type is related to the interactions between beads which
may be bound or not bound together. In the case of
beads not bound together (i.e., not belonging to the same
mesoscopic molecule) the interaction potential is softrepulsive, having an extension range defined by a cutoff
radius. The conservative force may also have an elastic contribution, which derives from the harmonic force
used to tie two consecutive beads in the chains of either
the lipid or the protein. A detailed description of the
DPD-simulation potentials, and other physical parameters, can be found in Venturoli et al. (2005).
A physical quantity which still constitute a matter of
debate is the value of the surface tension to use in the
simulations of a model bilayer. It has been suggested
(Jähnig, 1996) that unconstrained, self-assembled bilayers are at their free energy minimum, characterized by
having a zero value of the surface tension. Nevertheless,
it is still a matter of debate which value of the surface
tension should be used in molecular simulations (Feller
and Pastor, 1996, 1999; Marrink and Mark, 2001; Goetz
et al., 1998). Venturoli et al. (2005) have adopted an
approach in which they mimic the experimental condition by simulating a system in which they impose a value
of the surface tension. This is done by using a hybrid
scheme based on both the DPD and the Monte Carlo
(MC) simulation method. The DPD method was used to
evolve the positions of the beads, and the MC method
was used to impose a given surface tension on the bilayer.
This hybrid method ensures the total volume of the system to remain constant (Venturoli and Smit, 1999).
The next two sections focus on the issues concerning
the range of perturbation induced by a protein on the
nearby mismatched lipid bilayer, and its dependence on
protein size, and on the simultaneous occurrence of protein tilting (or even bending) to adjust for hydrophobic
mismatch.
3.3. Protein-induced bilayer perturbations
The spatial fluctuations which may occur in biomembranes give rise to inhomogeneities in the lateral distribution of membrane components. Lateral inhomogeneities
can be induced, as well as harvested, by the presence of
proteins. In the past, the following quantities have been
determined by computer simulations on lattice models:
the extent of the lipid-bilayer perturbation induced by
proteins (Sperotto and Mouritsen, 1991), and its dependence on factors such as the degree of hydrophobic
mismatch and the size of the protein (i.e. the curvature of
the protein hydrophobic surface in contact with the lipid
hydrocarbon chains). It was found that, away from the
protein, the perturbation decays in a exponential manner,
and can therefore by characterized by a decay length, ξ P .
ξ P is a measure of the size of small-scale inhomogeneities
(i.e. domains) experienced by proteins when embedded
in the lipid bilayer. In a sense, ξ P is also a measure of
the extension of the range over which the lipid-mediated
interaction between proteins may operate. Data from
MD simulations on all-atom models have confirmed
too that, within the time scale of the simulations, under
mismatch conditions, a protein can induce a deformation
of the lipid-bilayer structure (Chiu et al., 1999; Petrache
et al., 2000, 2002; Jensen et al., 2001), and that the
deformation is of the exponential type (Jensen and
Mouritsen, 2004). The same type of studies have also
shown that tilting may also occur for membrane peptides
(Belohorcová et al., 1997; Shen et al., 1997); however,
to reduce a possible hydrophobic mismatch synthetic
peptides might instead prefer to deform the lipid bilayer,
or even bend, rather than undergo tilting (Petrache et al.,
2002).
To determine the structural changes of the bilayer
due to the presence of the protein, Venturoli et al.
(2005) calculated first the hydrophobic thickness, dL0 ,
of the pure lipid bilayer, i.e., far a way from the protein
surface (see Fig. 4). The effect of the protein, on the
surrounding bilayer structure, was then determined by
calculating the lipid-bilayer hydrophobic thickness,
dL (r), as function of the radial distance r from the protein
hydrophobic surface, namely at the interface with the
lipid hydrocarbon chains, as schematically illustrated in
Fig. 4; while the bilayer-induced effects on the protein
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
Fig. 4. Schematic illustration which shows the statistical quantities
calculated from the simulations: the pure lipid-bilayer hydrophobic
thickness, dL0 , the perturbed lipid-bilayer hydrophobic thickness, dL (r),
the protein hydrophobic length, dP , the tilted-protein hydrophobic
length, dPeff , and the tilt angle, φtilt .
were quantify in terms of the protein tilt angle φtilt with
respect to the bilayer normal, as shown in Fig. 4, where
dP is the protein hydrophobic length, and dPeff is defined
as the projection onto the normal of the bilayer plane of
the protein hydrophobic length, dPeff = dP cos(φtilt ). The
protein tilt issue is discussed in the following section.
The method of calculation of dL (r), dPeff , dP , and φtilt
are discussed in details in Venturoli et al. (2005). The
behavior of dL (r) allows to access the extension of the
protein-mediated perturbation on the bilayer. Based on
previous theoretical findings (Sperotto and Mouritsen,
1991; Fattal and Ben-Shaul, 1993), one can first assume
that the perturbation induced by the protein on the surrounding lipids is of an exponential type. One can then
verify this assumption later by analyzing the deviation
of the functional form of the calculated dL (r) from the
assumed one. If the behavior of dL (r) is exponential, the
protein-induced perturbation can be expressed in terms
of a typical coherence length, i.e. the decay length ξ P :
dL (r) = dL0 + (dP − dL0 ) e−r/ξP
(2)
where dL0 is the mean hydrophobic thickness of the unperturbed pure lipid bilayer. The above equation expresses
the fact that away from the protein surface, and at distances at least of the order of ξ P , the perturbed dL (r)
decays to the bulk value dL0 , namely the value corresponding to that of the pure lipid system at a chosen temperature. By knowing dL (r), dP , and dL0 , and by using Eq.
(2), one can estimate ξ P . Since the proteins may be subjected to tilt, the input parameter for dP that one uses to fit
Eq. (2) is not the actual hydrophobic length of the model
protein, but instead the effective length, dPeff (see Fig. 4).
Venturoli et al. (2005) have calculated the lipidbilayer hydrophobic thickness profile, dL (r), as a function of the distance r from the protein surface, and for
a number of systems, containing proteins having one of
the three different sizes, NP = 4, 7, and 43, and with different hydrophobic lengths dP , i.e., hence subjected to
different hydrophobic mismatch, d. It was found that,
13
when subjected to hydrophobic mismatch, the protein
induces a perturbation of the lipid bilayer in its vicinity,
and that the perturbation decays in a manner that depends
on the mismatch, and on protein size. For a given protein
size, NP , if d < 0 the correlation length of the perturbation, ξ P , increases with decreasing mismatch (absolute
value), while for positive mismatch the opposite happens, and the correlation length increases with increasing
mismatch. Also, in the case of d < 0 the decay length
increases by increasing the protein size. Instead there
is no detectable ξ P dependence on d in the case of
d > 0, at least at the considered temperature, around
60 ◦ C, well above the melting temperature of the pure
system. Fig. 5 shows the thickness profiles for two values of mismatch, d < 0 (left column), and d < 0 (right
column), and for the three considered protein sizes. In
the case of d < 0, the lipids around the protein shrink
to match the protein hydrophobic surface, while in the
case of d > 0 the lipids in the vicinity of the protein
stretch and become more gel-like than the bulk lipids far
away from the protein. Also, at negative mismatch, the
orientation of the protein is perpendicular to the bilayer
plane (see Fig. 5a, c and e, where dP = dPeff ), while at
positive mismatch, the protein tilts to decrease its effective hydrophobic length, the more skinny the protein is
the more pronounced the effect becomes (see Fig. 5b,
d and f, where dP = dPeff ). The tilt issue is discussed in
details in the following section.
MD simulations (Jensen and Mouritsen, 2004) on allatom model of bilayers of fluid POPE and POPC with
embedded the membrane channel aquaglycerolporin –
which would correspond to the mesoscopic-protein size
NP = 43, and to a negative mismatch d ∼ −4 Å – predict
an exponential protein-induced bilayer deformation with
a decay length ξ P ∼ 10 Å, in good agreement with the
results from the DPD simulations. Also, MD simulations
on POPC bilayers with embedded the membrane channel gramicidin A – corresponding to the mesoscopicprotein size NP = 7 – show an exponential deformation
with a coherence length smaller than that obtained for
aquaglycerolporin (M.Ø. Jensen, private communication). The few experimental attempts to estimate the
extent of the protein-induced bilayer perturbation confirm a mismatch dependence of the extent of the perturbation, too. These experiments refers to pure lipid
bilayers with embedded Bacteriorhodopsin (Rehorek et
al., 1985; Bryl and Yoshihara, 2001), lactose permease
(Lehtonen and Kinnunen, 1997), and the synthetic ␣helical peptides (Ridder et al., 2004; Weiss et al., 2003).
Experimental studies on protein-induced lipid flip-flop
(Kol et al., 2003) indicate that the larger the protein size
the more reduced is its ability to induce flip-flop. This
14
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
Fig. 5. Calculated values of dL (r) (open circles) and fitted ones using Eq. (2) (solid line) as function of the distance r from the protein surface. For
convenience, in each plot is also shown the level value of the pure lipid-bilayer thickness (dashed line), the measured protein hydrophobic length dP
(shaded area), and the effective protein hydrophobic length dPeff (open area) which is defined as the projection of dP onto the normal to the bilayer
plane. The data refer to the three protein sizes: NP = 4 (a and b), NP = 7 (c and d), and NP = 43 (e and f), and to a negative (see plots in 1st column of
page), and to a positive mismatch (see plots in 2nd column of page). The systems are studied at a temperature around 60 ◦ C.
fact is an indirect confirmation of the protein-size dependence of the extent of the perturbation induced by the
protein (Ridder et al., 2004), as suggested by the MD, as
well as, the DPD simulation data.
An interesting prediction which arises from the DPD
simulations is that the larger the protein, the more the
behavior of dL (r) deviate from an exponential one (see
Fig. 5e and f). The DPD simulation data show an ‘over-
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
Fig. 6. Re-plot of the DPD simulation data (open circles) from Fig. 5e
and f (). The solid lines are obtained from membrane elasticity theory
(May, 2002) through fitting of the data points to Eq. (3). The fitting
parameters are dP , dL0 , ξ P , and ξ C .
shooting’ (at d < 0) or ‘undershooting’ (d > 0) effect.
The ‘undershooting’ (‘overshooting’) phenomenon is a
consequence of the constraint of uniform density in the
bilayer core, and occurs if the protein is large enough that
tilting is unfavorable, and if the mismatch is high (low)
enough that even the ordered, gel-like (disordered, fluidlike) lipids closest to the protein are not able to match
the protein hydrophobic surface. One can imagine the
undershooting region as forming a sector of an inverted
micelle, and the overshooting region as forming a sector of a micelle. The occurrence of ‘undershooting’ and
‘overshooting’ is also a signature for the damped oscillatory behavior predicted by membrane elasticity theory
(Dan et al., 1993; Nielsen et al., 1998; May, 2002)—that
is discussed in details in Section 2.2. It is particularly pronounced for large proteins and adds to the characteristic
decay length, ξ P , of the membrane thickness relaxation a
second characteristic length, ξ C , corresponding the wave
length of the oscillatory part. The two lengths ξ P and
ξ C depend on the elastic membrane properties; see Eq.
(1). According to the elasticity theory the reason for the
overshooting and undershooting effect is the competition
between stretching and bending modes of the membrane.
Fig. 6 shows again the DPD data sets corresponding to
the large proteins displayed in Fig. 5e and f. The solid
lines are fits to the data sets from membrane elasticity
theory (May, 2002) according to
dL (r) = dL0 + (dP + dL0 ) e−r/ξP
ξC2 − 3ξP
r
r
+ 2
× cos
sin
ξC
ξP
ξP − 3ξC
(3)
In both cases it was found a value of ξ P ≈ ξ C ≈ 1 nm
in agreement with the expectation from membrane elasticity theory: see Eq. (1). This is remarkable because
15
the DPD simulation operates with discrete lipid models whereas elasticity theory is based on a continuum approach. It suggests that the membrane elasticity
approach is reasonable even though only a few lipid
shells around the protein are perturbed. However, while
it is easy to include the finite radius of the protein into
Eq. (3), no statistical model is yet available that accounts
for the ability of the protein to tilt. The advantage of
the mesoscopic approach is that it can account for protein tilting, as discussed in the next section. Incidentally,
Nielsen et al. (1998), using a phenomenological elastic
lipid–protein model predicted an overshooting behavior
of dL (r) similar to what is shown in Fig. 6. However,
despite this similarity, the non-monotonic behavior of
dL (r) observed by Nielsen et al. (1998) is probably due
to the some specific boundary conditions imposed a priori on the system (like, for example, the contact slope
of the lipids nearest to the protein), rather than to the
competition between the stretching and bending modes
of the bilayer, or – said in mesoscopic terms – to constant density requirements. The perturbations of the lipid
structure around a protein may have biological implications. In particular, they could promote lipid sorting
and, hence, favor bilayer fusion and affect lipid-mediated
protein–protein interactions, as recently suggested by
Nielsen et al. (2004). Such curved structures might also
affect passive permeability in the vicinity of the protein.
Also, if the amount of lipids involved in the ‘overshooting’ (‘undershooting’) phenomenon is sufficiently high
to be detected experimentally, the value of the lipid order
parameters measured by spectroscopic techniques could
be affected in such a way that the derived values of the
lipid-bilayer hydrophobic thickness may be underestimated (overestimate).
3.4. Lipid-induced protein tilting
To adapt to a too-thin bilayer, and to minimize the
exposure of their hydrophobic moieties to the water
environment, proteins may tilt in a manner that is
mismatch- and protein-size dependent (i.e. the larger the
protein, the less pronounced the tilting). Very recently,
Ramakrishnan et al. (2005) have confirmed the tilt
dependence on protein size. By infrared spectroscopy
they measured the tilt angle of ␤-barrel proteins, OmpA
and PhuA, characterized by the same hydrophobic
length, but having two very different sizes; they found
that the larger protein tilt systematically less than the
smaller, at equal mismatch. Despite the limited timescale sampled by MD simulations, the possibility that
different type of skinny synthetic peptides may tilt (or
even bend) when subjected to positive mismatch condi-
16
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
Fig. 7. The protein tilt angle, φtilt , dependence on mismatch, d = d̃P − dL0 (i.e. different protein hydrophobic lengths). The results refer to a
temperature around 60 ◦ C – hence a fixed value of mismatch – and to the three protein sizes NP = 4, 7 and 43. The dashed lines are only a guideline
for the eye. On the right are shown the snapshots of typical configurations of the systems with embedded proteins of different sizes.
tions has also been confirmed by MD simulations on allatom models (Shen et al., 1997; Belohorcová et al., 1997;
Petrache et al., 2002)—although the degree of tilting
varies from system to system. This might suggest that the
degree of tilting depend on local features of the peptides,
for example their amino acid sequence. Recent experimental investigations, which were performed to systematically correlate peptide-tilting with mismatch might
confirm this suggestion. In fact the data from solid state
NMR spectroscopy (Strandberg et al., 2004; Özdirekcan
et al., 2005) referring to hydrophobic synthetic ␣-helical
peptides, WALP23 and KALP23, flanked by either
tryptophan or lysines residues (Strandberg et al.,
2004; Özdirekcan et al., 2005), and from fluorescence
spectroscopy referring to the M13 major coat protein
peptides (Koehorst et al., 2004), indicates that –
although in all three cases it was found that the tilt angle
systematically increases by increasing hydrophobic
mismatch – the actual values of the tilt angles is different
even if the different types of peptides are subjected to
approximately the same hydrophobic positive mismatch.
Turning now to the simulation data shown in Fig. 5a,
c and e, the difference between the values of dP and
dPeff suggest too that proteins may tilt when subjected to
positive mismatch. Fig. 7 shows the calculated protein
tilt angle, φtilt (see schematic representation in Fig. 4,
where dPeff is defined as the projection onto the normal
of the bilayer plane of the protein hydrophobic length,
dPeff = dP cos(φtilt )), with respect to the bilayer normal as
function of d, and for the three protein sizes, NP = 4, 7,
and 43. As the dP increases (and d becomes positive),
the protein may undergo a significant tilting: depending
on NP , the more skinny the protein is, the more pronounced the tilt becomes, consistently with the experimental data of Ramakrishnan et al. (2005)—as illustrated
by the snapshots on the right of Fig. 7, which refers to the
three chosen protein sizes, and to the highest (positive)
value of mismatch. Also, when the skinny model protein
(NP = 4) experiences a high positive mismatch, bending
of the protein may take place (in addition to tilting), as
shown in the snap-shot in Fig. 7(top, right), and as predicted by MD simulations on all-atom models (Shen et
al., 1997; Belohorcová et al., 1997). In an attempt to see
if the functional dependence of the tilt angle on mismatch
is similar for the three types of ␣-helical peptides, mentioned above, WALP23, KALP23, and M13, and if the
dependence bears some resemblance to the one predicted
by the DPD simulations, in Fig. 8 is plotted φtilt as a function of mismatch, for the three different type of peptides,
and for the model peptide with NP = 4. The coloured
areas are defined by the error bars. The plotted φtilt values show a remarkable resemblance of the functional
dependence on d between the considered experimental
systems and the simulated one. The predicted functional
dependence of the tilt on mismatch for the case of the
smaller model proteins, NP (see Fig. 8) might suggest
that, while the actual values of the protein tilt angle might
depend on the specific peptide sequence, the functional
dependence on mismatch might have a somehow general character—although more experiments are needed
to confirm this idea.
Model studies on tilt angle like the one presented in
this section may help to understand whether the tilting
of helices belonging to bundles is due to an intrinsic
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
Fig. 8. The protein tilt angle, φtilt , dependence on mismatch, d =
d̃P − dL0 , at temperatures above the melting temperature of the pure
lipid bilayer. The simulation data refer to a model protein corresponding to NP = 4 (in black), and the experimental data refer to three
different types of ␣-helical peptides: M13 coat protein peptide (in
red), KALP23 synthetic peptide (in blue), and the WALP23 synthetic
peptide (in green). The dashed lines are a guideline for the eye. (For
interpretation of the references to colour in this figure legend, the reader
is referred to the web version of the article.)
property of the helices or is due, instead, to hydrophobic
matching. The results shown in Fig. 8 and the proteinsize dependence shown in Fig. 7 might help to predict
how the tilt angle can change by changing the number of synthetic ␣-helical peptides of which a proteinbundle may be made. In fact, knowing the tilt angle
of individual peptides, and the relative change of tilt
angle (as shown in Fig. 7) upon protein-size changes,
one could suggest what would be the tilt angle of the
bundle.
4. Simulations of membrane processes
4.1. Protein translocation into membranes
For membrane proteins to perform certain biological
functions as channels, transporters, signal transducers
and other devices (Baumgaertner, 2006) they need to be
inserted into compartmental walls made of lipid bilayers.
The majority of membrane proteins, so-called constitutive membrane proteins (White and Wimley, 1994), are
inserted into a lipid bilayer at the same time as they are
synthesized. This class of peptides and proteins usually accomplish insertion into or translocation across
membranes assisted by a complex proteinacious machinery, “translocon” (Schnell and Hebert, 2003; White and
17
von Heijne, 2004), or through fusion of membranes.
The translocon, binds to the ribosome synthesizing the
membrane protein and threads the protein into a lipid
bilayer through an internal channel. In contrast, the
non-constitutive membrane proteins, such as toxins and
antimicrobial peptides, insert themselves into a lipid
bilayer without assistance. Since the membrane itself
keeps the function of a permeability barrier between the
compartments involved, and since proteins are macromolecules, their passage through or insertion into the
membrane creates a non-trivial problem. The insertion mechanism of such proteins is poorly understood.
The spontaneous insertion is based on physicochemical processes, for which two-stage or four-stage models
have been proposed (Engelman and Steitz, 1981; Popot
and Engelman, 2000; White and Wimley, 1994, 1999).
According to the models, the peptides first get adsorbed
to the membrane surface where they change their conformation into an ␣-helix, and then they start insertion,
whose molecular mechanism is not well understood, followed by aggregation into an organized structure. Wellaccepted driving force of insertion is the hydrophobic
nature of the peptide segments, and in fact peptide insertions are usually discussed by use of the hydrophobicity
scale of the component amino acids.
The field-driven insertion process of the antimicrobial peptide alamethicin in lipid–water and octane–water
environments have been studied by MD simulations
(Tieleman et al., 2001). An external electric field was
used to mimic the membrane potential. They found during MD simulation of 10 ns that alamethicin did not
insert into a phospholipid bilayer which was attributed
to the slow dynamics of the peptide and lipids. However, in octane N-terminal insertion occurs at sufficiently
high field strengths. Insertion of alamethicin occurred in
two steps, corresponding to desolvation of the Gln7 side
chain, and the backbone of Aib10 and Gly11.
Surface binding and subsequent penetration of the
bilayer was observed during MD simulations (Shepherd
et al., 2003) for the hydrophobic ally oriented peptides, while the charge-oriented peptides demonstrated at
most partial surface binding. The peptides were initially
placed in an ␣-helical conformation on either side of a
zwitterionic lipid bilayer about 10 Å from the interface.
Insertion of the peptides into the bilayer caused a dramatic increase in the lateral area per lipid and decrease in
the bilayer thickness, resulting in substantial disordering
of the lipid chains.
The work of Lopez et al. (2004) demonstrates how a
direct insertion of a typical non-constitutive protein into a
lipid membrane could take place. Modelling a membrane
protein as a hydrophobic tube with hydrophilic sites at
18
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
the tube’s ends, they observed a spontaneous insertion
of a generic nanosyringe into a lipid bilayer. One of the
main findings was that lipids assist one of the ends of the
nanosyringe to cross the hydrophobic core of the membrane. In the simulated model, small groups of atoms
were represented by sites interacting with each other by
bounded and non-bounded forces, like atoms in conventional MD simulations. In a subsequent work (Lopez et
al., 2005) the authors considered the insertion of a model
pore into a membrane using a mesoscopic approach. The
papers of Lopez et al. (2004, 2005) as well as the mesoscopic modelling approach are discussed in more detail
in Section 3.
Im and Brooks (2005) have explored membrane insertion and interfacial folding for the WALP and TMX
series of peptides by using an implicit membrane generalized Born model and replica exchange molecular
dynamics. All WALP and TMX peptides showed spontaneous N-terminal-led insertion through the formation of
a continuous ␣-helix arising from thermal fluctuations of
␣-helical hairpin conformations formed at the interface
or in the membrane. A straight ␣-helix was not observed
as a stable interface-bound conformation but existed as
a transient conformation before membrane insertion as a
TM helix. The authors suggest that the formation of such
a straight ␣-helix is a rate-determining step in insertion.
The conformation associated during the MD simulations
suggest that a revision in traditional membrane insertion/association free energy calculations is necessary to
include the influence the conformational changes that
occur between peptide–membrane association and inser-
tion, i.e., the presence of helical hairpins at the interface.
However, it must be noted that the implicit membrane
generalized Born model may not include correctly the
proper interfacial characteristics of the lipid–water interface, which may have a significant effect on the transient
protein structure while crossing the interface.
The interactions of a model peptide (WALP-16) with
an explicitly represented DPPC membrane bilayer was
simulated (Nymeyer et al., 2005) using the replica
exchange molecular dynamics algorithm (Swendsen and
Wang, 1986; Sugita and Okamoto, 1999; Nymeyer et al.,
2004). A spontaneous, unbiased insertion of WALP-16
into the DPPC bilayer and its folding into an ␣-helix with
a transbilayer orientation was observed. From calculations of the free energy surface it is concluded that insertion of the peptide into the DPPC bilayer precedes secondary structure formation. This latter observation disagrees with the dominant conceptual model (Popot and
Engelman, 2000; White and Wimley, 1999) which is that
a surface-bound helix is an obligatory intermediate for
the insertion of ␣-helical peptides into lipid bilayers. The
observed translocation mechanism is favored because of
a large (>100 kcal/mol) increase in system entropy that
occurs when the unstructured WALP-16 peptide enters
the lipid-bilayer interior. The insertion/folding pathway
that is lowest in free energy depends sensitively on the
near cancellation of large enthalpic and entropic terms.
This suggests the possibility that intrinsic membrane
peptides may have a diversity of insertion/folding behaviors depending on the exact system of peptide and lipid
under consideration.
Fig. 9. (a) Snapshot of the extracting melittin pore at time t = 100 ps. (b) Stretching z(t) of the C␣ atoms of the charged residues Lys21-Arg22
(red), Arg22-Lys23 (green), Lys23-Arg24 (blue), Arg24-N27 (black) as function of time t. The vertical broken lines approximately indicates the
transition zone. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
The importance of the lipid–water interface for the
kinetics of the insertion process was concluded from MD
simulation of the “inverse” insertion process, that is, the
extraction of membrane peptides from a lipid-bilayer
membrane (Lin and Baumgaertner, 2005). During the
extraction of a tetrameric ␣-helical melittin pore from a
POPC bilayer (Fig. 9a), it was observed that the force
F(t) increases almost linearly with time until a certain
maximum at time tc1 ≈ 100 ps. Accordingly, the intermolecular distances between the successive residues,
as shown in Fig. 9b, exhibit a characteristic transition regime. Since the pulling force was exerted on
the N-terminus, N27, the distance to its nearest neighbor residue R24, z(t) = z[R24](t) − z[N27](t), exhibits
a significant stretching until R24 undergoes a rupture at
tc2 out of the lipid–water interface. The first (tc1 ) and
the second (tc2 ≈ 200 ps) vertical broken lines in Fig. 9b
indicate approximately the transition regimes where the
first (R24) and the last (K21) charged residue of the
melittin signature KRKR have followed the extraction
process and have left the lipid-head–water interface. A
more detailed analysis of the results from this computer
experiment indicates that Coulomb interactions between
the charged residues and the lipid–water interface plays
a significant role and may represent a barrier against
spontaneous insertion. This suggestion is corroborated
by the experimental observations that in many cases, in
particular for melittin, an aggregate of peptides is necessary in order to induce a significant perturbation of the
lipid–water interface to promote a subsequent insertion
event.
4.2. Protein assemblies in membranes
Membrane protein domains are often organized as
assemblies of polypeptide segments interacting with
the lipid bilayer and constituting a functionally active
and finely regulated biological machine involved in
ion and molecular transport across the membrane, cell
communication, signaling, etc. Studies of membranebound segments are thus essential for understanding
structure–function relationships of membrane proteins.
Studies of proteins in simplified membrane models were described by Roux and Karplus (1994),
Baumgaertner (1996), and others. Often, the hydrophobic core of a membrane is modelled by Lennard–Jones
hydrocarbon-like particles, a polarizable cubic lattice
with low dielectric permeability (reviewed in Roux and
Karplus, 1994), or by a monolayer of hard parallel
cylinders representing the lipid chains (Baumgaertner,
1996). Many other mesoscopic models have been proposed which are discussed in Section 3. Among other
19
properties, these models permit investigation of orientational order and lateral density fluctuation of the lipid
matrix, which are important for partitioning and ␣-helix
formation of TM peptides. In a number of studies the
membrane was approximated by introducing an additional solvation term into the potential energy function
to represent interaction of a protein with its environment. Usually such potentials are taken dependent on
hydrophobic properties of residues and their positions
relative to the bilayer (Edholm and Jähnig, 1988; Milik
and Skolnick, 1993, 1995; Baumgaertner, 1996). The
results obtained provide interesting insights into peptides’ behavior in the membrane environment. However,
such methodology seems to be somewhat oversimplified because amino acid residues are treated as point
“hydrophobic sites” without taking into account the
conformation and hydrophobic nature of atoms and/or
atomic groups.
4.2.1. Protein assemblies in membranes: single
peptides
Specific lipid–protein interactions involved in the
anchoring and stabilization of membrane-bound proteins
are of central importance in a large number of fundamental processes occurring at the surface of the cell. However, despite the development of powerful techniques
such as X-ray crystallography, electron microscopy, and
nuclear magnetic resonance (NMR), the characterization
of lipid–protein interactions remains difficult because of
the complexity of the bilayer environment. At the present
time, even qualitative information gained by performing detailed computer simulations of protein–membrane
complexes can be valuable, because only scarce information is available from experiments about the structure
and dynamics of these systems.
One of the first all-atom simulations of an ␣-helical
peptide in an explicit bilayer membrane with explicit
water molecules was conducted by Tieleman et al.
(1999a). They found that alamethicin underwent hingebending motion about its central Glyf-X-X-Pro sequence
motif, because the polar C-terminal side chains provided
an “anchor” to the bilayer/water interface via formation
of multiple H-bonds. This explains why the preferred
mode of helix insertion of alamethicin into the bilayer is
N-terminal.
The interaction of melittin with a fully hydrated
DMPC bilayer was examined by molecular dynamics
simulations (Bernéche et al., 1998). The initial configuration of the system was constructed with melittin in an ␣-helical conformation bound parallel to
the membrane–solution interface. Melittin perturbs the
bilayer significantly such that the order of the lipid acyl
20
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
chains is smaller in the upper layer, whereas it is larger for
those in the lower layer. The perturbation of the bilayer
results in a local curvature, a reduction of the thickness
of the membrane, and the hydrophobic core of the membrane is reduced by 30%. However, the acyl chains of the
lipids adopt particular conformations to avoid leaving a
large cavity under the amphipathic helix.
Recently, an implicit solvation model for membranebound proteins was proposed (Efremov et al., 1999a).
In this model solvation parameters take into account
the hydrocarbon core of a membrane, water, and weak
polar solvent (octanol). An optimal number of solvation parameters was chosen based on analysis of atomic
hydrophobicities and fitting experimental free energies of gas–cyclohexane, gas–water, and octanol–water
transfer for amino acids. This solvation model was
used to assess membrane-promoting ␣-helix formation. To accomplish this, all-atom models of 20-residue
homopolypeptides – poly-Leu, poly-Val, poly-Ile, and
poly-Gly in initial random coil conformation – were
subjected to non-restrained Monte Carlo conformational
search in vacuo and with the solvation terms mimicking
the water and hydrophobic parts of the bilayer. All the
peptides demonstrated their largest helix-forming tendencies in a non-polar environment. In a subsequent
work Efremov et al. (1999b) have employed Monte Carlo
simulations of the implicit solvation model to explore
conformational space of several membrane-binding peptides in environments of different polarity and in vacuum.
The solvent effects were treated using an atomic solvation parameters (ASP). The simulations were done for
all-atom models of membrane-bound peptides, such as
transmembrane segments A and B of bacteriorhodopsin,
the hydrophobic segment of surfactant lipoprotein, SPC, and magainin2. The results emphasize that the ␣helical conformation is promoted by non-polar solvent
and exists in a wide energy range. Conformational properties of SP-C and magainin2 in the membrane-like environment were also found to be in accord with available
experimental data. The results for SP-C do not confirm
preference of all-helical structure for SP-C in water.
Unlike the membrane-spanning proteins, atomicscale structural information about peripheral membrane
proteins is scarce. Functions of some of these proteins
require them to be folded in an aqueous environment
and also be capable of inserting themselves into membranes. Studies of such “ubiquitous” molecules provide
an opportunity to examine the determinants of an insertion event. Unfortunately, the experimental analysis is
seriously hampered by difficulties in preparation of suitable samples containing these proteins in the membranebound state. Their high-resolution structures obtained so
far reveal the only binding motif: an amphiphilic ␣-helix
either lying on the bilayer surface or partly immersed
into the hydrophobic core (White and Wimley, 1999;
Shai, 1999). Based on these structural data, a number
of successful molecular modelling studies of interactions between ␣-helices and membrane interface have
been reported (Forrest and Samson, 2000; Tieleman et
al., 2001). One question of interest is whether peripheral
membrane proteins possess also other types of binding
motifs. This has been investigated recently (Efremov
et al., 2002) by incorporation of ␤-sheet proteins into
membrane employing Monte Carlo simulations with an
implicit membrane model (Efremov et al., 1999a). Cardiotoxins, are found to retain the overall “three-finger”
fold interacting with membrane core and lipid–water
interface by the tips of the “fingers” (loops). The implementing of the peptide at certain places of the membrane,
critically depends upon the structure, hydrophobicity,
and electrostatics of certain regions. The simulations
reveal apparently distinct binding modes for cardiotoxins
via the first loop or through all three loops, respectively.
This computational study may be used to study “partitioning” of proteins with diverse folds into lipid bilayers.
The structural properties of the endogenous opioid
peptide dynorphin A (1–17) (DynA), a potential analgesic, were studied with MD simulations in DMPC
bilayers (Sankararamakrishnnan and Weinstein, 2000).
Starting with the known NMR structure of the peptide,
the N-terminal helical segment of DynA was initially
inserted in the bilayer in a perpendicular orientation with
respect to the membrane plane. Parallel simulations were
carried out from two starting structures, that differ by
4 Å in the vertical positioning of the peptide helix. The
simulation of the system (dynorphin + 86 lipids + 5300
waters) revealed that the orientation of the helical segment of DynA had undergone a transition from parallel to
tilted with respect to the bilayer normal in both systems.
Analysis shows that the tilted orientation of 50◦ adopted
by the N-terminal helix is due to specific interactions of
residues in the DynA sequence with phospholipid headgroups, water, and the hydrocarbon chains. Key elements
are the “snorkel model”-type interactions of arginine side
chains, the stabilization of the N-terminal hydrophobic
sequence in the lipid environment, and the specific interactions of the first residue, Tyr. Water penetration within
the bilayer is facilitated by the immersed DynA, in particular surrounding the arginine side chains. A mechanism
of receptor interaction is proposed for DynA, involving
the tilted orientation observed from these simulations of
the peptide in the lipid bilayer.
Kandasamy and Larson (2004) have performed
molecular dynamics simulations of the interactions of
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
two ␣-helical antimicrobial peptides, magainin2 and its
synthetic analog of MSI-78 embedded in an explicit
POPC lipid bilayers. They used different initial conditions of the peptide, including a surface-bound state
parallel to the interface, a trans-membrane state, and a
partially inserted state. The simulations showed that both
magainin2 and MSI-78 were most stable in the lipid
environment, with the peptide destabilized to different
extents in both aqueous and lipid–water interfacial environments. From all the simulations, they concluded that
the hydrogen bonding interactions between the lysines
of the peptides and the oxygens of the polar lipid headgroups are the strongest and determine the destabilization of the bilayer environment, as observed by the
increase in lipid tail disorder and the induction of local
curvature on the lipid headgroups by the peptides.
The orientation and motion of a model lysineterminated transmembrane polypeptide, acetyl-KK(LA) 11-KK-amide, implemented in a POPC bilayer
were investigated by MD simulation by Goodyear et
al. (2005). In one simulation, initiated with the peptide
oriented along the bilayer normal, in a second simulation the initial peptide orientation was chosen to match a
set of experimentally observed alanine methyl deuteron
quadrupole splittings. Simulated alanine methyl group
orientations were found to be inequivalent, a result that
is consistent with 2H NMR observations of specifically
labeled polypeptides in POPC bilayers. Helix tilt varied
substantially over the durations of both simulations. In
the first simulation, the peptide tended toward an orientation about the helix axis similar to that suggested
by experiment. In the second simulation, orientation
about the helix axis tended to return to this value after
an excursion. These results showed that interactions at
the bilayer surface can constrain reorientation about the
helix axis while accommodating large changes in helix
tilt. Although large excursions in helix tilt may be accommodated by extension of the terminal lysine side chains,
a situation often referred to as “snorkeling”, the localization of lysine side-chain charges at the bilayer surface
appears to contribute to the adoption of a preferred orientation of the tilted helix about its axis. The results
are relevant to understanding 2H NMR observations
of alanine methyl deuterons on lysine-terminated transmembrane polypeptides.
4.2.2. Protein assemblies in membranes:
interacting peptides
Insertion and formation of membrane proteins
involves the interaction of protein helices with one
another in lipid environments. It has been postulated
(Popot and Engelman, 2000) that individual helices are
21
stable separately as domains in a lipid bilayer. Their stability as domains is a consequence of the hydrophobic
effect and main-chain hydrogen bonding. Other interactions then drive side-to-side helix association, resulting
in a functional protein. Specific folding energy is provided mainly by packing of the preformed helices with
each other, by loop structures, and by interactions with
prosthetic groups. Additionally, ion pairs and hydrogen
bonds between helices are sometimes found, and general contributions are made by interactions with the lipid
environment MD simulations were performed on M13
coat protein (Sanders et al., 1991). The lipid bilayer
was represented by a hydrophobic potential. The ␤-sheet
was more flexible than the ␣-helix. A comparison of
the energies after 100 ps MD simulation showed that of
the monomers, the ␣-helix has the lowest energy. The
energy difference between ␣- and ␤-structures decreases
from 266 to 148 kJ/mol, when going from monomers to
dimers. It was suggested that this difference will decrease
with higher aggregation numbers.
The non-specific lipid-mediated attraction between
two proteins embedded in a bilayer membrane have
been investigated for a model system using Monte Carlo
simulations (Sintes and Baumgärtner, 1997). Two types
of attraction with different regimes were identified: a
depletion-induced attraction at short distances and a
fluctuation-induced long range attraction, which originates from the gradients of density and orientational
fluctuations of the lipids around each protein.
The first MD simulation of an ion channel formed
by a bundle of ␣-helices in a full lipid bilayer was conducted by Tieleman et al. (1999b). They investigated the
effect of bundle stability of the ionization state of the
ring of Glu18 side chains. If all of the Glu18 side chains
were ionized, the bundle was unstable; if none of the
Glu18 side chains were ionized, the bundle was stable.
pKa calculations suggested that either zero or one ionized Glu18 is present at neutral pH, correlating with the
stable form of the helix bundle. The dipole moments of
water molecules within the pore were aligned antiparallel to the helix dipoles which contribute to the stability
of the helix bundle.
Lin and Baumgaertner (2000) have investigated the
configuration and the stability of a single membrane
pore bound by four melittin molecules and embedded
in a fully hydrated POPC bilayer employing MD simulations. It was found that the initial tetrameric configuration decays with increasing time into a stable trimer
and one monomer. This continuous transformation was
accompanied by a lateral expansion of the aqueous pore
exhibiting a final size comparable to experimental findings. The transformation lead to a “hydrophilic pore”
22
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
where some lipid heads had translocated from the rim
to the central part of the interface. It was hypothesized
that pore growth, and hence cell lysis, is induced by a
melittin-mediated line tension of the pore.
MD simulations of glycophorin A (GpA) transmembrane helices embedded in sodium dodecyl sulfate (SDS)
micelles have been performed by Braun et al. (2004) in
order to identify contacts significant for helix dimerization. The simulation shows the formation of a complete
micelle around wild-type GpA from an initially random
placement of SDS molecules in an aqueous environment.
The assembly and oligomerization of transmembrane
␣-helices is known to play a critical role, e.g., in immune
system activity and cancers, genome sequencing studies reveal that 20–30% of open reading frames encode
membrane proteins, indicating their biological significance. However, our understanding of assembly and
oligomerization of membrane proteins is not as advanced
as aggregation processes in soluble proteins. In particular, there have been a series of papers recently on MD
simulations of the aggregation of prion proteins (e.g.,
Sekijima et al., 2003) and the formation of amyloid fibrils (e.g. Urbanc et al., 2004). Amyloid fibril structures
formed by small peptides are amenable to both experimental studies and computer simulations and therefore
they are particularly suitable for the investigation of the
determinants of protein aggregation. Fig. 10 shows a peptide fragment from transthyretin, TTR(105–115). The
native form of transthyretin, one of the 20 or so proteins
Fig. 10. X-ray structure (PDB code 1BMZ) (Peterson et al., 1998) of
the amyloid TTR dimer. The segment Y105-S115, whose sequence
is YTIAALLSPYS, of each monomer is shown in magenta and red.
(For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of the article.)
that have been linked to amyloid diseases, is a homotetramer composed of 127 residue, mainly ␤ subunits The
TTR(105–115) peptide adopts a ␤-strand conformation
both in the native structure (in red and purple) and, with
minor structural changes, in the amyloid fibril.
A major challenge for molecular dynamics simulation in the future will be, following the recent progress
for soluble proteins, to study the aggregation and the
formation of membrane proteins.
4.3. Lipid-controlled function of membrane proteins
Integral membrane proteins interact with lipid
molecules in cellular membranes through their
hydrophobic transmembrane regions. The interactions
between membrane proteins and lipids can be categorized as either general or specific (Popot and Engelman,
2000). By general interactions, it is meant those
resulting from the multiphase (membrane-aqueous)
environment created by lipids in water, necessary
for the stability of most integral membrane proteins.
Specific interactions refer to the close association of
certain lipids that may bind to the membrane protein,
akin to a cofactor, to confer structural stability or to
affect the protein’s function. Biochemical studies have
demonstrated specific lipid binding to certain integral
membrane proteins (Lee, 1998, 2003; Marsh and
Horvath, 1998) and high-resolution crystal structures,
now available for a few membrane proteins, reveal
the presence of associated lipid molecules (Fyfe et
al., 2001; McAuley et al., 1999; Iwata et al., 1995).
The precise role of these specific lipid interactions
is yet to be defined, but their importance is revealed
by functional assays demonstrating that a number of
membrane proteins such as electron transfer complexes
I and III, cytochrome c oxidase (Fry and Green, 1981),
ion channels (Valiyaveetil et al., 2002) and a number of
transporter proteins require specific lipids for optimal
activity (Lin et al., 1990; Vemuri and Philipson, 1989).
The influence of lipid-bilayer deformations on the
function of specific ion channels, ‘mechanosensitive
(MS) channels’, has been investigated by means of
computer simulations very recently by three groups
(Gullingsrud et al., 2001; Elmore and Dougherty, 2001;
Gullingsrud and Schulten, 2003; Biggin and Sansom,
2003; Sotomayor and Schulten, 2004).
Mechanical forces act on living organisms from
all directions throughout the environment, making
mechanosensory transduction one of the fundamental
sensory transduction processes in the biological world.
MS channels are a class of ubiquitous membrane proteins
gated by mechanical strain in the cellular membrane. As
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
molecular switches, MS ion channels convert mechanical forces exerted on cellular membranes into electrical
or biochemical signals in physiological processes ranging from cellular turgor control in bacteria to touch and
hearing in mammals. Some toxic peptides are selective
inhibitor of MS channels. The mechanism of inhibition
remains unknown, but it is known (Suchyna et al., 2004)
that they modify the gating, thus violating a trademark
of the traditional lock-and-key model of ligand–protein
interactions. Suspecting a bilayer-dependent mechanism, the effect of toxins on gramicidin A (gA) channel
gating have been examined experimentally (Suchyna et
al., 2004). It was shown that the inhibition increases with
the degree of hydrophobic mismatch between bilayer
thickness and channel length, meaning that the toxic
peptide decreases the energy required to deform the
boundary lipids adjacent to the channel. These results
suggest that modulation of membrane proteins by
amphipathic peptides (mechanopharmacology) involves
not only the protein itself but also the surrounding
lipids. This has important therapeutic implications.
MscL, a bacterial mechanosensitive channel of large
conductance, is the first structurally characterized
mechanosensor protein (Sukharov et al., 2001; Perozo
and Rees, 2003). The protein is a pentamer (Fig. 11),
approximately 50 Å wide in the plane of the membrane
and 85 Å tall. Each 151-residue subunit consists of
two transmembrane helices, labeled TM1 and TM2,
and a cytoplasmic helix that extends some 35 A below
the membrane. The TM1 helices are arranged so as to
block diffusion through the channel at their N-terminal
ends. Excision of the cytoplasmic domains has been
found to have little effect on the gating properties
of the channel. In general, it is believed that the
gating of MS channels is induced by changes in the
intra-bilayer pressure profiles which originate from
bilayer deformation. In order to change the membrane
tension it has been suggested (Perozo et al., 2002) that
different hydrophobic mismatches at the protein–lipid
interface induced by different types of lipids (mixtures)
may cause an asymmetry of tension across the bilayer
membrane and hence lead to a spontaneous curvature
which controls the open and the closed state. Recently,
MD simulations (Gullingsrud et al., 2001; Elmore and
Dougherty, 2001) have indicated that the least mobile
part of the protein could be identified as the gate, on the
same location suggested by experimental findings. This
part comprises the first five residues of the TM1 helices,
which are shown to be pinched together to form a nonleaky occlusion. In particular, steered MD simulation
(Gullingsrud et al., 2001) of the bare protein without
membrane and without water, but under the application
23
Fig. 11. Ribbon representations of the structures of MscL. The top
part (a) depicts the view from the plane of the membrane (gray area),
whereas the transmembrane region viewed down the membrane normal is illustrated at the bottom (b). Individual subunits are represented
in different colours (PDB code 1MSL). (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of the article.)
of a constant surface tension on the protein have shown
that the transmembrane helices tilted considerably as
the pore opened. The protein refolded into an open conformation, where the transmembrane helices flattened
as the pore widened, with a minimal loss of secondary
structure. The results indicate that membrane thinning
and hydrophobic mismatch within the transmembrane
helices my indeed drive gating. More recently steered
24
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
MD simulations (Gullingsrud and Schulten, 2003) have
revealed the mechanism for transducing membrane
forces into channel opening. The channel was most
easily opened when force was applied predominantly on
the cytoplasmic side of MscL. The expanded state agrees
well with proposed models of MscL gating (Perozo and
Rees, 2003), in that it entails an irislike expansion of
the pore accompanied by tilting of the transmembrane
helices.
MD simulations of the Mycobacterium tuberculosis homolog of the bacterial mechanosensitive channel
of large conductance (Tb-MscL) have been performed
recently (Elmore and Dougherty, 2001). Channel mutations led to observable changes in the trajectories, such
as an alteration of intersubunit interactions in one of the
mutants. In addition, interesting patterns of protein–lipid
interactions, such as hydrogen bonding, arose in the
simulations. MscS, the mechanosensitive channel of
small conductance, is found in the inner membrane of
Escherichia coli and its crystallographic structure in an
open form has been recently solved (Bass et al., 2002;
Edwards et al., 2005). Much of what we know about
the molecular mechanisms of gating in MscS channel is
derived from its crystal structure. Only recently have MD
simulations (Sotomayor and Schulten, 2004) and experimental studies (Edwards et al., 2005) shed additional
light on the structural changes that occur upon MscS
gating. The crystal structure of E. coli MscS solved at
a resolution of 3.9 Å reveals that the channel folds as a
homoheptamer and has a large cytoplasmic region. Each
subunit contains three TM domains. The precise conformation of MscS is controversial at present. Edwards et al.
(2005) proposed a new structural model of MscS gating
that involves rotation and tilt of pore-lining transmembrane helices. Rotation of the transmembrane domains
in MscS closely resembles a current model for gating of MscL (Perozo and Rees, 2003). Recent study
using molecular dynamics simulations (Sotomayor and
Schulten, 2004) implied that water and ions cannot pass
through the channel pore, suggesting that the crystal
structure may reflect an inactive or desensitized state
rather than the open state. When surface tension was
applied, this led to channel widening.
5. Concluding remark
Theoretical approaches like those previously
described may be adopted, either to investigate the biophysical behavior of specific biomembrane systems (see
Section 4), or to understand what are the basic physical
principles that govern the behavior of biomembranes
(see Sections 2 and 3). The choice of one approach
instead of another may depend on how detailed one
needs to describe a system. In general, the more details
are needed the smaller are the system sizes that one
can consider, and the shorter the time scale that can be
sampled. For example, the CG model approach is more
advantageous than the all-atom model approach when
one wants to investigate biomembrane processes which
involve the cooperative rearrangements of large number
of molecules, and which are characterized by long time
scales. The drawback of this approach is due to the
use of ‘beads’ to effectively describe the system: by
modelling a system with a set of beads, one can describe
its overall three-dimensional structure, but not its
microscopic details. However, it is worth stressing that,
to model a systems does not mean to try to reproduce all
the possible details (i.e., consider all possible degrees of
freedom involved), but rather to focus one some of them
and approximate others, depending on the phenomena
that one wants to understand. This a priori choice of
approximation will naturally imply that a model study
will, alone, not be able provide a full understanding
of the biophysical behavior of a chosen investigated
system. Nevertheless, this limitation can be overcome,
if one or more theoretical approaches are used together
with experimental investigations. If used in this intermethodological way, results from theoretical studies
can become really useful for providing a framework
of interpretation for the experimental data and for
revealing information not otherwise accessible; also,
they may constitute a source of inspiration for future
experiments.
Acknowledgements
MMS is grateful to Maddalena Venturoli (FR), and
to Berend Smit (NL, FR), Marcus A. Hemminga (NL),
John H. Ipsen (DK) and J. Antoinette Killian (NL), for
numerous stimulating discussions; and wishes to thank
the Biochemistry and Nutrition Group and the Center
for Biological Sequence analysis, both at Biocentrum
(The Technical University of Denmark, Kgs. Lyngby,
Denmark), and CECAM (Lyon, France) for hospitality.
SM is supported by ND EPSCoR through grant #EPS0132289 and acknowledges discussions with Avinoam
Ben-Shaul, Ales Iglic, Anne Hinderliter, including their
research group members.
The authors thank the European Science Foundation
program COST D22 (“Lipid–protein Interactions”) for
support. They would like to express their gratitude to the
chairman of D22, John Findlay, and to the organizer of
the Dubrovnic conference, Greta Pifat.
M.M. Sperotto et al. / Chemistry and Physics of Lipids 141 (2006) 2–29
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