Mesoscopic models of biological membranes

TL;DR: In this article, the authors compare various strategies to coarse-grained simulation of a biological membrane and conclude that the results obtained by the various mesoscopic models are surprisingly consistent. But they do not discuss the effect of transmembrane peptides on the local structure of a membrane and the mechanism of vesicle fusion and fission.

About: This article is published in Physics Reports.The article was published on 2006-12-01 and is currently open access. It has received 307 citations till now. The article focuses on the topics: Membrane biophysics & Lipid bilayer.

Summary

1. Introduction to biomembranes

• Biological membranes are soft condensed matter structures which surround the cell and its inner organelles.
• Lipids are a special form of amphiphilic molecules and the structures shown in Fig. 3 can also be observed in surfactant solutions or special types of block co-polymers.
• Atomistic MD simulations are, however, computationally very expensive to investigate membrane phenomena which occur on the mesoscopic time and length scales.
• The interesting aspect is that these models have been developed with very different applications in mind.

2. Mesoscopic models

• The formation and stability in water of lipid self-assembled structures is mainly due to the hydrophobic effect.
• In mesoscopic models of lipid-water systems, water is either modeled implicitly by the use of effective forces which act on the lipids to form aggregates and to guaranty their stability in the solvent, or water is explicitly modeled.
• Because implicit solvent models have recently been reviewed [28], here the authors will just give a short description of these models and their applications in relation to biomembranes.

2.1. Implicit solvent models

• Implicit solvent models may be grouped into two main types [28]: continuum elastic-models and particle-based coarse-grained models.
• Models that consider the lipids as rigid molecules may show limitations in reproducing the elastic properties of real lipid membranes, resulting in bilayers with a much higher bending rigidity.
• Upon increasing the projected area (which is analogous to increasing the temperature) it was found that the model membrane undergoes a solid–fluid phase transition.
• Therefore, to recognize structures of CL-DNA complexes may strongly advance the understanding of their function.
• In general, an iterative procedure is used by comparing the RDFs of the atomistic and coarse-grained simulations, using tabulated potentials for the coarse-grained model, until convergence is reached.

2.2. Explicit solvent models

• In this section the authors review the coarse-grain models for phospholipid molecules where the solvent is explicitly treated.
• Among these models one can distinguish between two main types.
• The beads interact with one another via effective potentials, which do not aim to represent the true nature of the underlying atomistic interactions.
• These lipid models have many points in common with the earlier models developed to study the self-assembly of micelles and surfactant monolayers [69–73].

2.2.1. Empirical coarse-grained models

• Goetz and Lipowsky [74] introduced a simple coarse-grained model for lipid membranes based on a binary Lennard– Jones fluid of solvent beads and amphiphilic molecules.
• These models are based on a simple ‘bead-and-spring’ representation of the lipid molecules, where the nonbonded interactions are represented by soft-repulsive potential .
• Each lipid is modeled by a three-bead headgroup, and two tails of five hydrophobic beads each.
• Kranenburg et al. [94] showed that the experimental trend can be reproduced (see Fig. 7) if chain stiffness, via a bond-bending potential, is considered in the coarse-grained model.
• Also, the density profile of a bilayer made of coarse-grained lipids with bond-bending rigidity is in good agreement with the one obtained from atomistic simulations [94] .

2.2.2. From atomistic to a coarse-grained description

• In the following, the authors review some mesoscopic modeling approaches which aim at establishing a link between the coarse-grain representation and the underlying atomistic nature of the molecules.
• One of the advantages of this model is that the parameterization of the interaction potentials is not tailored to a specific lipid type, and different phospholipids can therefore be constructed from a small set of building blocks.
• Alkanes and lipid molecules are built by connecting coarse-grained beads via an harmonic potential, as shown in Fig.
• Using MD simulations on this coarse-grained model, Marrink and co-workers were able to obtain self-assembly of phospholipids into a bilayer [111].
• Results from the mesoscopic model were qualitatively different than those of a MD atomistic study [121], although better agreement was found by adjusting the nonbonded interaction parameters, showing that careful parameterization of the model is essential.

3. Membrane processes studied with mesoscopic models

• The development of mesoscopic models has made it possible to investigate a number of biomembrane phenomena that are outside the range of time- and length-scale which one can reach with the use of atomistic models.
• Nevertheless, the model should be able reproduce some of the features of the systems one wants to study.
• Once that a coarsegrained model is validated, the fact that it is based on a simplified molecular structure can be exploited to gain insight into the type of interactions and lipid architecture that are responsible for a particular phase behavior.
• Studies of mixed systems will be discussed in Sections 3.2 and 3.3.
• Coarse-grained lipid models have also been used to investigate bilayer systems which are not in planar geometry.

3.1. Thermotropic phase behavior of lipid bilayers

• Phospholipid bilayers, even the simplest ones composed of only one lipid type, display a rich temperature phase behavior [132,133].
• The stable phase at low temperature is the sub-gel phase, commonly labeled Lc. Upon heating, the transition to the gel, or L ′ , phase occurs.
• The values of the transition temperatures depend on the lipid type [132].
• In the case of a bilayer formed by lipids with a small head group, a gel-like phase, L , may appear at temperatures below the main transition, in which the tails do not tilt with respect to the bilayer normal (see Fig. 12(a)).

3.1.1. Single-tail lipid bilayers

• Both single- and double-tail phospholipids can form bilayers [134].
• The phase behavior of single-tail lipids with varying chain length was investigated [97.
• Interestingly, two gel-phases were found below the main transition temperature, depending on the repulsion parameter between the headgroups.
• This can be understood considering that in the interdigitated phase the average distance between the lipid heads is already much larger compared to the noninterdigitated phase, and a further increase of this distance does not have a dramatic effect on the stability of the gel phase.
• These authors used MC simulations to study bilayer phase changes as a function of temperature and pressure.

3.1.2. Double-tail lipid bilayers

• The phase behavior of double-tail coarse-grained lipid bilayers was also studied using coarse-grained models, both minimal [79,98,101] and semi-quantitative [112].
• It is interesting to note that, despite the fact that the model of Smit and co-workers and the model of Stevens differ in the lipid architecture (see Fig. 17), in the functional form of interaction potentials and in the simulation technique with which they are studied, they both display remarkably similar behaviors.
• Also, the kink disrupts the bilayer ordering, thus increasing the area per lipid and decreasing the main transition temperature, in agreement with experimental results.
• In contrast to the case of single-tail lipid bilayers, no interdigitated gel phase was found by Smit and co-workers, even for large values of the repulsion parameter between the lipid headgroups [98,101].
• For models such as the DPD systems presented above, in which reduced units are used, a mapping is required to convert those into physical units.

3.1.3. The rippled gel-phase

• As the authors have already mentioned, for some lipids the transition from the ordered gel phase to the disordered liquid crystalline phase occurs via the so-called rippled phase (P ′ ).
• For chains containing more than 20 carbon atoms the pretransition disappears or merges with the main transition [142].
• Simulations of coarse-grained lipid bilayers do give evidence of a phase separation into micro domains, which might indicate the onset of a rippled phase [79,100,101].
• Once the period of the ripple is optimized, a linear relation between the system size and the number of ripples was observed.

3.2. Effect of small molecules on lipid bilayers

• Coarse grained models were also used to study the effect of small molecules (for example alcohols, anesthetics, or cholesterol) on the structural, mechanical and thermodynamic properties of the membrane.
• In the following, the authors review some of these applications, which range from the formation of the bilayer interdigitated phase, to the formation of bilayer pores, and the occurrence of the liquid-ordered phase.

3.2.1. Alcohols

• As the authors have discussed in the previous section, an interdigitated bilayer phase, L I , may appear in some coarse-grained bilayers systems below the main transition temperature.
• Simon and McIntosh [135] observed the formation of the interdigitated phase at high alcohol concentrations, which explains the biphasic effect.
• At low concentrations of alcohol the disorder of the lipid tails increases, leading to a lower transition temperature.
• The mechanism of alcohol-induced interdigitation was studied with DPD simulations on coarsegrained lipid–alcohol bilayers.
• In addition, these simulations show that surfactants reduce both the extensibility and the maximum stress that the bilayer can withstand.

3.2.2. Anesthetics

• The mechanism through which anesthetics work on cells via the cell membrane is still a matter of debate.
• In fact there are two schools, one that believes that the action of anesthetics is mediated by proteins; and the other that thinks that the lipid matrix plays an active role [174,175].
• Using the coarse-grained model of Klein and co-workers described in Section 2, Pickholz et al. [122] performed MD simulations to gain insight into the mechanism of drug action on membranes at the molecular level and into the role played by the lipid bilayer.
• It was found a monotonic increase of the area per lipid with anesthetic concentration and a decrease in the interlamellar spacing; both results are in good agreement with previous atomistic simulations [121,176].

3.2.3. Cholesterol

• Because, and in contrast to a phospholipid molecule, cholesterol is essentially rigid and has a relatively smooth hydrophobic section, its interaction with the lipids is of dual nature, which is thought to result in a new bilayer phase called the liquid-ordered phase [177].
• Recently, the importance of this liquid-ordered phase has been recognized.
• The model was parameterized using the inverse Monte Carlo method, where the effective interactions between the beads are derived from MD simulations on the corresponding all-atom system.
• Also, it is not clear in which concentration range the effective potentials are valid.
• More recently, Izvekov and Voth [179] also studied the effect of cholesterol on DPPC lipid bilayers using an explicitsolvent coarse-grained model.

3.3.1. Hydrophobic mismatch

• To minimize exposure of nonpolar moieties to the water environment, hydrophobic matching between the lipid bilayer hydrophobic thickness and the hydrophobic length of transmembrane proteins has to occur.
• Indeed, MD simulations on atomistic models have confirmed too that, within the short time scale of these types of simulations, a protein can induce a deformation of the bilayer under mismatch conditions [219–222]; that the deformation is of the exponential type; and that its extent is protein-size dependent [223].
• It was found that the larger protein tilts systematically less than the smaller one.
• For a positive hydrophobic mismatch, (Fig. 30(a)), the protein prefers to segregate in the striated region formed by lipids in the gel-like state.

3.3.2. Protein–protein interaction

• The nonspecific lipid-mediated attraction between two cylindrical proteins embedded in a bilayer membrane was studied by Sintes and Baumgärtner [32,33] using Monte Carlo simulations on a mesoscopic model.
• It was found that the lipid-induced protein–protein attraction mechanism has two regimes: there appears 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.
• It was found that in both cases (parallel and antiparallel) the interaction is attractive, independent of the interaction-range considered, and of the shape of the proteins—in contrast to what was previously found by elastic theories.
• Sintes and Baumgärtner attribute the difference between their results and the elastic theories to their somehow ‘unrealistic’ lipid model.

3.3.3. Protein insertion into membranes

• The macromolecule is modeled by a hydrophobic tube with hydrophilic end caps.
• The size of these pores may depend, among others, on the hydrophobic mismatch interaction [239,240].
• They found that the antimicrobial molecules spontaneously insert into the lipid bilayer, however, at high concentration, the insertion process becomes cooperative, with molecular rearrangements and interactions between antimicrobial molecules that assist the insertion.
• The details at the molecular level of the hydraphile–membrane interactions still remain to be understood.
• These authors extended the mesoscopic model of Marrink et al. [111] to study the insertion and self-assembly into DPPC lipid bilayers of a -helical protein, Glycophorin A (GpA), and a bacterial -barrel protein OmpA.

3.4. Vesicles fusion, budding and fission

• Living cells host a number of biological processes where fusion, budding and fission are involved: for example endoand exo-cytosis and molecular trafficking within or through the cell all involve shape changes of the outer or inner membrane of the cell [244].
• Already in 1984 [246], it was suggested that fusion involves the ‘stalk’ mechanism, according to which fusion can start with the appearance of a stalk between approaching membranes.
• Then the inner monolayer in the tube-shaped region is deformed, and a cylindrical structure is formed between two vesicles.
• Cook and Deserno [49] used an implicit solvent model to investigate the kinetics of domain formation and the budding process in vesicles made of two lipid types, A and B.
• By choosing the interaction parameter between lipids of the same type smaller than the one between different lipid types, the formation of a domain was observed, with a symmetric transversal distribution of the lipids, i.e. there was approximately the same number of lipids (for each type) in the inner and outer monolayer (see also Fig. 36(b)).

4. Concluding remarks

• The material properties of biological membranes, and their relation to the biological functioning, have been a subject of experimental and theoretical investigations for decades.
• The development of mesoscopic models may help to bridge the macroscopic-microscopic gap.
• The power of the coarse-grain modeling approach is two-fold.
• The fact that many different coarse-grained models give such a coherent picture on the structure of a membrane is very encouraging.
• Most of the models have been tested against structural data, but little dynamics has been included in the validation step.

Acknowledgments

• This work is partially supported by the EC through the Marie Curie EXT project MEXT-CT-2005-023311 .
• M.M.S. thanks the Center for Biological Sequence Analysis at DTU, Kgs. Lyngby , and CECAM, Lyon and the Marie Curie EST project MEST-CT-2005-020491, for hospitality.

Figures

Fig. 7.Area per lipid in the fluid phase as a function of tail length obtained using the coarse-grained model of Kranenburg et al. [94] (black symbols). The squares are the values obtained using the fully flexible lipid model and the diamonds the values calculated from the model with additional bond-bending potentials. The shaded area indicates the range of the experimentally obtained values [102–107].

Fig. 22. Snapshots of a bilayer at increasing alcohol concentration (number of alcohol molecules in the bilayer, Nht2 ), at a constant temperature below the main transition. The red bonds represent the lipid tails and the gray ones the lipid headgroup. The terminal beads of both the lipids and the alcohols are depicted as larger spheres (red for the lipids and yellow for the alcohols). Color online only.

Fig. 37. Snapshots of the fusion pathway of two mixed DPPC/DPPE vesicles. Reprinted with permission from [250]. Copyright 2003 American Chemical Society.

Fig. 36. Schematic drawing illustrating the two possible paths of the budding and fission process. (a) Asymmetric distribution of lipids between the inner and outer monolayer, (b) symmetric distribution. Reused with permission from SatoruYamamoto and Shi-aki Hyodo [110]. Copyright 2001, American Institute of Physics.

Table 1 Bilayer hydrophobic thickness, Dc , and area per lipid, AL, at different temperatures. DPD simulations on a coarse-grained model of DMPC [109] and experimental values

Fig. 26. Snapshots of the L -to-inverted phase transition from the simulations of Nielsen et al. [208]: (a) peptide-induced meniscus; (b) water penetration and membrane contact; (c) pore solvation by lipid headgroups; (d) inverted phase. Reprinted with permission from [208]. Copyright 2004 Biophysical Society.

Fig. 4. Membrane with a hydrophobic (left) and a hydrophilic (right) pore. Hydrophilic particles are depicted in red and hydrophobic ones in yellow (color online only). Reused with permission from Zun-Jing Wang and Daan Frenkel [51]. Copyright 2005, American Institute of Physics.

Fig. 19. Structure of the rippled phase. From the simulations of Kranenburg et al. [100,101]. The contourplot (a) shows the thickness of the bilayer as a function of the position in the bilayer plane, where the colors indicate the hydrophobic thickness. Fig. (b) represents a side view of the bilayer, in which the head groups are colored black and the tails gray. The darker color gray is used to indicate the end segments of the tails. The water particles are depicted as smaller spheres.

Fig. 32. Self-assembly of a GpA helix dimer in a lipid bilayer. Reprinted with permission from [243]. Copyright 2006 American Chemical Society.

Fig. 10. Coarse-grained DMPCmolecule according to the model of Shelley et al. [116]. Different bead types are used for the choline (CH), phosphate (PH), glycerol (GL), ester (E1), carbons in the tails (SM) and terminal carbon (ST) groups. Reprinted with permission from [116]. Copyright 2001 American Chemical Society.

Fig. 1. A schematic drawing illustrating the complexity of a biological membrane.

Fig. 2. Schematic drawing of a typical phospholipid (left), and the chemical structure of a specific phospholipid molecule, dimyristoylphosphatidylcholine (DMPC) (right). ‘Gly’ denotes the glycerol group.

Fig. 31. Snapshots of the spontaneous adsorption of a model ‘nanosyringe’ into a membrane. From Lopez et al. [234].

Fig. 33. Snapshots of the fusion pathway of two vesicles at low (a) and high temperature (b). Schematic representation of the different fusion mechanisms (c). Reused with permission from Hiroshi Noguchi and Masako Takasu [44]. Copyright 2001, American Institute of Physics.

Fig. 15. Phase diagrams as a function of the repulsion parameter between the lipid headgroups ahh and of reduced temperature T ∗ for lipids of different chain length: (a) 6, (b) 7, (c) 8, and (d) 9 beads in the tail. From the work of Kranenburg et al. [98].

Fig. 20. Phase diagram for a bilayer consisting of the model lipid shown in the inset, which has an additional hydrophobic bead in the headgroup. Hydrophilic beads are depicted in black and hydrophobic ones in white.

Fig. 24. Schematic illustration which shows the quantities calculated from the simulations of Venturoli et al. [109] described in the text. Pure lipid bilayer hydrophobic thickness (doL); perturbed lipid bilayer hydrophobic thickness (dL(r)) as a function of the distance r from the protein hydrophobic surface; protein hydrophobic length (dP); tilted-protein hydrophobic length (d eff P ); and protein tilt-angle, ( tilt ), with deffP = dP cos( tilt).

Fig. 25. Bilayer thickness profiles as a function of the distance r from the protein surface for different protein sizes, NP. The cases for negative (left column) and positive (right column) mismatch, d, are shown. dfitL is the thickness profile fitted using equation (1). From the simulations of Venturoli et al. [109].

Fig. 8. Site types used to build the coarse-grained model of Marrink et al. [111]: polar (P), nonpolar (N), apolar (C), and charged (Q). To build alkanes and phospholipids the sites are linked together via harmonic springs; next nearest neighbors interact through a harmonic angle potential. Charged groups also interact through a short-range electrostatic potential. Reprinted with permission from [111]. Copyright 2004American Chemical Society.

Fig. 9. Thermotropic transition from multilamellar to inverted hexagonal phase for the coarse-grained model of DOPE (shown in the top left figure) simulated by Marrink and Mark [114]. Reprinted with permission from [114]. Copyright 2004 Biophysical Society.

Fig. 5. Phase diagrams of model lipid bilayers obtained using the implicit solvent model of Cooke and Deserno [40]. Gel (crosses) and fluid (full circles) phases are obtained as a function of temperature and of the width (wc) of the range of attraction for two types of pair potential (inset in the figures). Reused with permission from Cooke and Deserno [40]. Copyright 2005, American Institute of Physics.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Mesoscopic models of biological membranes" ?

The properties of lipid bilayers can be studied at different time and length scales. In this review, the authors focus on an intermediate level, where groups of atoms are lumped into pseudo-particles to arrive at a coarse-grained, or mesoscopic, description of a bilayer, which is subsequently studied using molecular simulation. The aim of this review is to compare various strategies to coarse grain a biological membrane. A second objective of this review is to illustrate how mesoscopic models can be used to obtain a better understanding of experimental systems. The advantage of coarse-grained models is that these can be simulated very efficiently, so that phenomena involving large systems, or requiring a large number of simulations, can be studied in detail. This is illustrated with the study of the relation between the phase behavior of a membrane and the structure of the phospholipids, and the membrane structural changes due to molecules ( such as alcohols, cholesterol and anesthetics ) adsorbed to the membrane. The authors then discuss the effect of transmembrane peptides on the local structure of a membrane and the mechanism of vesicle fusion and fission. 

Q2. What is the mechanism of insertion of the antimicrobial molecules into the lipid bilayer?

They found that the antimicrobial molecules spontaneously insert into the lipid bilayer, however, at high concentration, the insertion process becomes cooperative, with molecular rearrangements and interactions between antimicrobial molecules that assist the insertion. 

Q3. How can the authors solve the system of linear equations of the fitting approach?

By choosing a sufficiently large number of distinct atomic configurations selected along the atomistic trajectories, the system of linear equations of the fitting approach becomes overdetermined and can be efficiently solved by standard least square methods. 

Q4. What pressure range can be observed in the case where the solvent was explicitly modeled?

In the case where the solvent was explicitly modeled, it was found that the gel–fluid phase transition can be observed over a wide pressure range. 

Q5. What mechanism was considered for interdigitation in lipid bilayers?

Two mechanisms were considered: interdigitation induced by changes in the molecular structure of the lipids forming the bilayer, and interdigitation induced by short-chain alcohols (from methanol to heptanol). 

Q6. What are the common physiological phenomena and diseases related to the formation of rafts?

A number of physiological phenomena and diseases [178] are thought to be related to the formation of ‘rafts’, namely lipid domains whichhave a high cholesterol content. 

Q7. What is the approach to derive the effective interactions between coarse-grained molecules?

A promising approach to derive the effective interactions between coarse-grained molecules is based on the inverse MC method [65]. 

Q8. How can the attractive potential be tuned?

Cooke et al. [49] have also shown that the value of the bending rigidity (at zero tension) can be tuned via the range of the attractive potential, to which it is related by a monotonous linear dependence. 

Q9. How did Kranenburg et al. study the mechanism of interdigitation in more?

Using DPD simulations on coarse-grained models of lipids, Kranenburg et al. studied the mechanism of induced interdigitation in more realistic, double-tail lipid bilayers. 

Q10. What is the reason for the tilting effect of skinny synthetic peptides?

MD simulations on atomistic models [221,225,224] predicted that, when subjected to positive mismatch, skinny synthetic peptides may tilt (or even bend)—although, at similar mismatch conditions, the degree of tilting varies from system to system. 

Q11. What is the reason for the nonmonotonic behavior of dL(r)?

It is worth stressing that, although the results from phenomenological elastic model studies predicted a nonmonotonic behavior of dL(r), showing an overshooting effect similar to what can be seen in Fig. 25(e), the nonmonotonic behavior observed by Nielsen et al. [24] is most likely due to the boundary conditions (for example, the angle of incidence between the bilayer and the protein) imposed a priori on the system, rather than to the competition between the stretching and bending modes of the bilayer, or to the constraint of uniform bilayer density. 

Q12. What are the main methods of studying reconstituted membranes?

reconstituted membranes are extensively investigated by a number of experimental methods, based on spectroscopy, microscopy, fluorescence, scattering, and calorimetry, as well as by theoretical methods. 

Q13. What is the effect of increasing the distance between the lipid heads on the stability of the gel?

This can be understood considering that in the interdigitated phase the average distance between the lipid heads is already much larger compared to the noninterdigitated phase, and a further increase of this distance does not have a dramatic effect on the stability of the gel phase. 

Q14. What is the effect of increasing the distance between the lipid heads on the stability of the gel?

This can be understood considering that in the interdigitated phase the average distance between the lipid heads is already much larger compared to the noninterdigitated phase, and a further increase of this distance does not have a dramatic effect on the stability of the gel phase.