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International audience; Here, we review recent advances towards the modelling of protein-protein interactions (PPI) at the coarse-grained (CG) level, a technique that is now widely used to understand protein affinity, aggregation and self-assembly behaviour. PPI models of soluble proteins and membrane proteins are separately described, but we note the parallel development that is present in both research fields with three important themes: firstly, combining CG modelling with knowledge-based approaches to predict and refine protein-protein complexes; secondly, using physics-based CG models for de novo prediction of protein-protein complexes; and thirdly modelling of large scale protein aggregates.

Using an atom based force field, molecular dynamics (MD) simulations of 54 dodecylphosphocholine (DPC) surfactant molecules in water at two different concentrations above the critical micelle concentration have been performed. Starting from a random distribution of surfactants, we observed the spontaneous aggregation of the surfactants into a single micelle. At the higher DPC concentration (0.46 M) the surfactants aggregated into a worm-like micelle within 1 ns, whereas at lower concentration (0.12 M) they aggregated on a slower time scale (~12 ns) into a spherical micelle. The difference in the final aggregate is a direct consequence of the system achieving the lowest free energy configuration for a given quantity of surfactant within the periodic boundary conditions. The simulation at low surfactant concentration was repeated three times in order to obtain statistics on the rate of aggregation. It was found that the aggregation occurs at a (virtually) constant rate with a rate constant of k = 1 × 10-4 ps-1. This is an unexpected result. On the basis of Monte Carlo simulations of a stochastic description of the system, using diffusion rates and cluster radii as determined by separate MD simulations of single DPC clusters, a lower rate constant which diminishes in the course of the aggregation process had been predicted. Neglect of hydrodynamic interactions, of long-range hydrophobic interactions, or of spatial correlations in the stochastic approach might account for the descrepancies with the more accurate MD simulations.

We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of L d 1 nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically. Important contributions to understanding two-phase flow observations in porous media and rock have been made using percolation theory (1-3). Random percolation (RP) is relevant to two-phase displacement if the flow is very slow and the invading fluid is completely wetting. Invasion percolation (IP) is relevant when the invading fluid is completely nonwetting. Both variants of percolation have been used to explain the structure and the amounts of fluids in a two-phase displacement at breakthrough. The fractal structure of the invading fluid paths have been analysed and the properties of IP are believed to be consistent with RP. In spite of this the spanning clusters are not precisely the same, and no relationship between the cluster density at spanning in RP and the breakthrough threshold in IP is known. Estimates of IP thresholds are neglected, particularly in three dimensions, due to the large computational effort required when compared with RP. In most studies of percolation theory a simple square or cubic geometry is considered. In many applications one must consider systems with nonquadratic and noncubic geometries. For example, in the petroleum industry, laboratory measurements (e.g., residual saturations, capillary pressure) are performed on rock cores of high aspect ratio. These measurements are then used as input to reservoir simulation models. The crucial parameter measured is the value of the critical thresholds. Using scaling arguments and small-scale numerical simulations, Monetti and Albano (4) presented scaling laws for the percolation probability in an elongated geometry that depend on the aspect ratio n of the lattice. In this paper we derive new scaling laws for percolation properties of elongated lattices (ELs) in both two and three dimensions, and present simulation data to confirm the theoretical results. We also derive relationships between thresholds observed in RP and IP for ELs and verify the relationships numerically. Using finite-size scaling arguments, Monetti and Albano assumed the expectation value of the percolation thresholdhpc .n/ .L/i/ L 1= n 1= where is the critical exponent for the correlation length. We define a lattice in d dimensions of size L d as a simple lattice (SL).

The effect of viscosity on the encounter rate of two interacting membranes was investigated by combining a non-equilibrium Fokker-Planck model together with extensive Molecular Dynamics (MD) calculations. The encounter probability and stabilization of transient contact points represent the preliminary steps toward short-range adhesion and fusion of lipid leaflets. To strengthen our analytical model, we used a Coarse Grained MD method to follow the behavior of two charged palmitoyl oleoyl phosphatidylglycerol membranes embedded in a electrolyte-containing box at different viscosity regimes. Solvent friction was modulated by varying the concentration of a neutral, water-soluble polymer, polyethylene glycol, while contact points were stabilized by divalent ions that form bridges among juxtaposed membranes. While a naive picture foresees a monotonous decrease of the membranes encounter rate with solvent viscosity, both the analytical model and MD simulations show a complex behavior. Under particular conditions, the encounter rate could exhibit a maximum at a critical viscosity value or for a critical concentration of bridging ions. These results seem to be confirmed by experimental observations taken from the literature. (C) 2013 AIP Publishing LLC.

We calculate the Gaussian curvature modulus (k) over bar of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value (k) over bar /k = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce (k) over bar (m)/k(m) approximate to -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z(0) of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K-0m. By also analyzing the lateral stress profile sigma(0)(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K-0m and (k) over bar through the first and second moment of sigma(0)(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

Beta-cyclodextrins (beta-CDs) can form inclusion complexes with cholesterol, and are commonly used to manipulate cholesterol levels of biomembranes. In this work, we have used multiscale molecular dynamics simulations to provide a detailed view on the interaction between beta-CDs and lipid model membranes. We show that cholesterol can be extracted efficiently upon adsorption of beta-CD dimers at the membrane/water interface. However, extraction is only observed to occur spontaneously in membranes with high cholesterol levels. Free energy calculations reveal the presence of a kinetic barrier for cholesterol extraction in the case of low cholesterol content. Cholesterol uptake is facilitated in case of (poly) unsaturated lipid membranes, which increases the free energy of the membrane bound state of cholesterol. Comparing lipid/cholesterol compositions typical of liquid-disordered (L-d) and liquid-order (L-o) domains, we furthermore show that cholesterol is preferentially extracted from the disordered regions, in line with recent experimental data.

Hybrid molecular dynamics simulations of atomistic (AA) solutes embedded in coarse-grained (CG) environment can substantially reduce the computational cost with respect to fully atomistic simulations. However, interfacing both levels of resolution is a major challenge that includes a balanced description of the relevant interactions. This is especially the case for polar solvents such as water, which screen the electrostatic interactions and thus require explicit electrostatic coupling between AA and CG subsystems. Here, we present and critically test computationally efficient hybrid AA/CG models. We combined the Gromos atomistic force field with the MARTINI coarse-grained force field. To enact electrostatic coupling, two recently developed CG water models with explicit electrostatic interactions were used: the polarizable MARTINI water model and the BMW model. The hybrid model was found to be sensitive to the strength of the AA-CG electrostatic coupling, which was adjusted through the relative dielectric permittivity epsilon(r)(AA-CG). Potentials of mean force (PMFs) between pairs of amino acid side chain analogues in water and partitioning free enthalpies of uncharged amino acid side chain analogues between apolar solvent and water show significant differences between the hybrid simulations and the fully AA or CG simulations, in particular for charged and polar molecules. For apolar molecules, the results obtained with the hybrid AA/CG models are in better agreement with the fully atomistic results. The structures of atomistic ubiquitin solvated in CG water and of a single atomistic transmembrane a-helix and the transmembrane portion of an atomistic mechanosensitive channel in CG lipid bilayers were largely maintained during 50-100 ns of AA/CG simulations, partly due to an overstabilization of intramolecular interactions. This work highlights some key challenges on the way toward hybrid AA/CG models that are both computationally efficient and sufficiently accurate for biomolecular simulations.

The respiratory chain or oxidative phosphorylation system (OxPhos) generates most of the chemical energy (ATP) used by our cells. The cytochrome c oxidase (CcO) is one of three protein complexes of OxPhos building up a proton gradient across the inner mitochondrial membrane, which is ultimately used by the ATP synthase to produce ATP. We present molecular dynamic simulations of CcO in a mimic of the mitochondrial membrane, and identify precise binding sites of cardiolipin (CL, signature phospholipid of mitochondria) on the protein surface. Two of these CL binding sites reveal pathways linking CLs to the entrance of the D and H proton channels across CcO. CLs being able to carry protons our results strongly support an involvement of CLs in the proton delivery machinery to CcO. The ubiquitous nature of CL interactions with the components of the OxPhos suggests that this delivery mechanism might extend to the other respiratory complexes.

We report the simulated vibrational spectra of a mechanosensitive membrane channel in different gating states. Our results show that while linear absorption is insensitive to structural differences, linear dichroism and sum-frequency generation spectroscopies are sensitive to the orientation of the transmembrane helices, which is changing during the opening process. Linear dichroism cannot distinguish an intermediate structure from the closed structure, but sum-frequency generation can. In addition, we find that two-dimensional infrared spectroscopy can be used to distinguish all three investigated gating states of the mechanosensitive membrane channel.

The captions of supporting information files Figures S1-S4 were erroneously omitted. The supporting information captions read

In this paper, an extensive analysis of free volume related properties of a lipid membrane is given. Using percolation theory, and comparing the free volume properties to those of a soft polymer, additional insights are obtained. The analyses are discussed within the framework of the four region model. It is concluded that the four regions have very different free volume properties. The region containing the dense part of the lipid tails resembles a soft polymer membrane to a large extent. The middle part of the membrane is more similar to a low density alkane. The consequences of the computed free volume properties on the permeation process of small penetrants are discussed. (C) 1996 American Institute of physics.

The molecular dynamics simulation technique was used to study the folding and complexation process of a short amylose fragment in the presence of lipids. In aqueous solution, the amylose chain remains as an extended left-handed helix. After the addition of lipids in the system, however, we observe spontaneous folding of the amylose chain into a helical structure, with helical pitch and hydrogen bond network compatible with the V-amylose structure observed in X-ray experiments. Our results suggest that under the influence of external non polar ligands, the conformation of amylose undergoes a transition from an extended to a V-amylose structure in line with experimental evidence. (C) 2012 Elsevier Ltd. All rights reserved.

Amphotericin B is the most potent antimycotic known to date. However due to its large col- lateral toxicity, its use, although long standing, had been limited. Many attempts have been made to produce derivatives with reduced collateral damage. The molecular mechanism of polyene has also been closely studied for this purpose and understanding it would contrib- ute to the development of safe derivatives. Our study examined polyene action, including chemical synthesis, electrophysiology, pharmacology, toxicology and molecular dynamics. The results were used to support a novel Amphotericin B derivative with increased selectiv- ity: L-histidine methyl ester of Amphotericin B. We found that this derivative has the same form of action as Amphotericin B, i.e. pore formation in the cell membrane. Its reduced dimerization in solution, when compared to Amphotericin B, is at least partially responsible for its increased selectivity. Here we also present the results of preclinical tests, which show that the derivative is just as potent as Amphotericin B and has increased safety.

The detailed lipid organization of cellular membranes remains elusive. A typical plasma membrane contains hundreds of different lipid species that are actively regulated by the cell. Currently over 40,000 biologically relevant lipids have been identified and specific organisms often synthesize thousands of different lipid types. This is far greater diversity than is needed to maintain bilayer barrier properties and to solvate membrane proteins. Why do organisms go through the costly process of creating and maintaining such a large diversity of lipids? What is the individual role of these lipids, and how do they interact and organize in the membrane plane?To start to address these questions we model biologically realistic membranes using coarse-grained Martini molecular dynamics simulations. We optimized and developed the Martini lipidome and systematically explored physiochemical properties of >100 different Martini lipid types. Bulk properties of each type (e.g. bilayer thickness, area per lipid, diffusion, order parameter and area compressibility) were analyzed and overall trends compared to experimental values. Biologically realistic idealized membrane compositions were constructed and simulated, such as in (Ingolfsson, et al. Lipid organization of the plasma membrane. JACS, 136:14554-14559, 2014). These large-scale simulations (∼70 by 70 nm and multi microsecond long) are in terms of lipid composition by an order of magnitude the most complex simulations to date. They provide a high-resolution view of the lipid organization of biologically relevant membranes; revealing a complex global non-ideal lipid mixing of different species at different spatiotemporal scales. We analyze a variety of membrane physicochemical properties, including: lipid-lipid interactions, bilayer bulk material properties, domain formation and coupling between the bilayer leaflets, for a number of lipid mixtures and conditions.

In this article, we present several algorithms for stochastic dynamics, including Langevin dynamics and different variants of Dissipative Particle Dynamics (DPD), applicable to systems with or without constraints. The algorithms are based on the impulsive application of friction and noise, thus avoiding the computational complexity of algorithms that apply continuous friction and noise. Simulation results on thermostat strength and diffusion properties for ideal gas, coarse-grained (MARTINI) water, and constrained atomic (SPC/E) water systems are discussed. We show that the measured thermal relaxation rates agree well with theoretical predictions. The influence of various parameters on the diffusion coefficient is discussed.

The mechanosensitive channel of large conductance (MscL) has become a model system in which to understand mechanosensation, a process involved in osmoregulation and many other physiological functions. While a high resolution closed state structure is available, details of the open structure and the gating mechanism remain unknown. In this study we combine coarse grained simulations with restraints from EPR and FRET experiments to study the structural changes involved in gating with much greater level of conformational sampling than has previously been possible. We generated a set of plausible open pore structures that agree well with existing open pore structures and gating models. Most interestingly, we found that membrane thinning induces a kink in the upper part of TM1 that causes an outward motion of the periplasmic loop away from the pore centre. This previously unobserved structural change might present a new mechanism of tension sensing and might be related to a functional role in osmoregulation., Author Summary Cells in biological organisms have to be able to respond to mechanical forces during processes such as touch, hearing, pain sensation and tissue growth. One way this is achieved is through mechanosensitive ion channels, membrane embedded proteins that initiate electrical signalling upon tension within the cell or cell membrane. The malfunction of such channels is also associated with a range of diseases including muscular dystrophy and cardiac arrhythmia. In this manuscript, we study in detail the mechanosensitive channel of large conductance (MscL) from bacteria, a model system in which to understand the principles of mechanosensation. Despite many years of investigative work the details of how the protein senses tension in the surrounding membrane remain unknown. By combining structural data from experiments with computer simulation we are able to model the open channel structure of the protein and report previously unobserved structural changes that might present a new mechanism of sensing tension. The methods developed in this paper are not limited to the study of mechanosensitive ion channels and may be useful in understanding the structure and function of other membrane proteins.

We studied compositionally heterogeneous multi-component model membranes comprised of saturated lipids, unsaturated lipids, cholesterol, and a-helical TM protein models using coarse-grained molecular dynamics simulations. Reducing the mismatch between the length of the saturated and unsaturated lipid tails reduced the driving force for segregation into liquid-ordered (l(o)) and liquid-disordered (l(d)) lipid domains. Cholesterol depletion had a similar effect, and binary lipid mixtures without cholesterol did not undergo large-scale phase separation under the simulation conditions. The phase-separating ternary dipalmitoyl-phosphatidylcholine (DPPC)/dilinoleoyl-PC (DLiPC)/cholesterol bilayer was found to segregate into l(o) and l(d) domains also in the presence of a high concentration of TM helices. The l(d) domain was highly crowded with TM helices (protein-to-lipid ratio -1:5), slowing down lateral diffusion by a factor of 5-10 as compared to the dilute case, with anomalous (sub)-diffusion on the mu s time scale. The membrane with the less strongly unsaturated palmitoyl-linoleoyl-PC instead of DLiPC, which in the absence of TM alpha-helices less strongly deviated from ideal mixing, could be brought closer to a miscibility critical point by introducing a high concentration of TM helices. Finally, the 7-TM protein bacteriorhodopsin was found to partition into the l(d) domains irrespective of hydrophobic matching. These results show that it is possible to directly study the lateral reorganization of lipids and proteins in compositionally heterogeneous and crowded model biomembranes with coarse-grained molecular dynamics simulations, a step toward simulations of realistic, compositionally complex cellular membranes. This article is part of a Special Issue entitled: Protein Folding in Membranes. (C) 2011 Elsevier B.V. All rights reserved.

The interactions between amino acid side chains govern protein secondary, tertiary; and quaternary structure formation. For molecular modeling approaches to be able to realistically describe these phenomena, the underlying force fields have to represent these interactions as accurately as possible. Here, we compare the side chain side chain interactions for a number of commonly used force fields, namely the all-atom OPLS, the united-atom GROMOS, and the coarse-grain MARTINI force field. We do so by calculating the dimerization free energies between selected pairs of side chains and structural characterization of their binding modes. To mimic both polar and nonpolar environments, the simulations are performed in water, n-octanol, and decane. In general, reasonable correlations are found between all three force fields, with deviations on the order of 1 kT in aqueous solvent. In apolar solvent, however, significantly larger differences are found, especially for charged amino acid pairs between the OPLS and GROMOS force fields, and for polar interactions in the MARTINI force field in comparison to the higher resolution models. Interestingly, even in cases where the dimerization free energies are similar, the binding mode may differ substantially between the force fields. This was found to be especially the case for aromatic residues. In addition to the inter-force-field comparison, we compared the various force fields to a knowledge-based potential. The two independent approaches show good correlation in aqueous solvent with an exception of aromatic residues for which the interaction strength is lower in the knowledge-based potentials.

Cholesterol concentration balance in biological membranes is of vital importance for the regulation of several critical processes (e.g. domain formation, membrane protein activity, signaling etc.) and tightly regulated during cell development. Abnormal cholesterol levels may eventually lead to clinical disorders like Niemann-Pick type C disease, with minimal chances of survival for the patient.It is well known that cyclodextrins (CDs), and especially beta-cyclodextrin, are able to modify the cholesterol concentration in membranes; either in situ (e.g. model membranes) or in vivo (cells). However, the molecular mechanism of this process is still unknown. Using molecular dynamics simulations, we have been able to study the CD-mediated cholesterol extraction from lipid membrane models.View Large Image | View Hi-Res Image | Download PowerPoint SlideCD dimers strongly bind to membranes (free energy of adsorption ∼ −35 kJ mol−1); however, only the extraction of cholesterol by a dimer from the cholesterol-poor Liquid disordered (ld) region is a favorable process (−40 kJ mol−1). We suggest that the continued extraction of cholesterol from the ld region eventually destabilizes the domain separation.With a clearer understanding of the basic molecular mechanism, we can begin to rationalize the design of more efficient CDs in numerous applications.

This article presents the GPU parallelization of new algorithms SD and DPD types for molecular dynamics systems developed by the Molecular Dynamics Group, University of Groningen, the Netherlands. One should note that molecular dynamics simulations are time-consuming simulations of systems, running time ranging from days to weeks and months. Therefore parallelization is a key issue for the well-running and use of MD software. The paper presents the main ingredients of GPU parallelization of the new algorithms and simulation results. It can be concluded that the parallelization through the use of graphical cards improves the performances of the runs as compared to the serial version of the code.

The mechanism of action of antimicrobial peptides is, to our knowledge, still poorly understood. To probe the biophysical characteristics that confer activity, we present here a molecular-dynamics and biophysical study of a cyclic antimicrobial peptide and its inactive linear analog. In the simulations, the cyclic peptide caused large perturbations in the bilayer and cooperatively opened a disordered toroidal pore, 1–2 nm in diameter. Electrophysiology measurements confirm discrete poration events of comparable size. We also show that lysine residues aligning parallel to each other in the cyclic but not linear peptide are crucial for function. By employing dual-color fluorescence burst analysis, we show that both peptides are able to fuse/aggregate liposomes but only the cyclic peptide is able to porate them. The results provide detailed insight on the molecular basis of activity of cyclic antimicrobial peptides.

Increasing experimental evidence has shown that membrane protein functionality depends on molecular composition of cell membranes. However, the origin of this dependence is not fully understood. It is reasonable to assume that specific lipid-protein interactions are important, yet more generic effects due to mechanical properties of lipid bilayers likely play a significant role too. Previously it has been demonstrated using models for elastic properties of membranes and lateral pressure profiles of lipid bilayers that the mechanical properties of a lipid bilayer can contribute as much as similar to 10 k(B) T to the free energy difference associated with a change in protein conformational state. Here, we extend those previous approaches to a more realistic model for a large mechanosensitive channel (MscL). We use molecular dynamics together with the MARTINI model to simulate the open and closed states of MscL embedded in a DOPC bilayer. We introduce a procedure to calculate the mechanical energy change in the channel gating using a three-dimensional pressure distribution inside a membrane, computed from the molecular dynamics simulations. We decompose the mechanical energy to terms associated with area dilation and shape contribution. Our results highlight that the lateral pressure profile of a lipid bilayer together with the shape change in gating can induce a contribution of similar to 30 k(B) T on the gating energy of MscL. This contribution arises largely from the interfacial tension between hydrophobic and hydrophilic regions in a lipid bilayer.

How the components of the G protein-coupled receptor (GPCR) “signalosome” assemble and function in the membrane bilayer is not known. Nevertheless the highly symmetrical organization of visual receptors (rhodopsin, rho) in rows-of-dimers suggested by AFM images of the rod cell disk membrane has a simple and direct consequence: the exposure of one unique surface of the receptor to the lipid phase of the membrane. This organization defines the encounter complex between rho and the G protein (transducin, Gt), and the orientation of rho in the dimer is therefore determinant. We have previously identified both computationally[1] and experimentally[2] a stable rho dimer involving TM1/TM2 and H8. Here we describe the investigation of alternative receptor binding modes leading to the identification of a new interface involving TM5/TM6. PMF analysis of this interface using the MARTINI coarse grain model indicates a similar order of stability as the TM1/TM2/H8 interface. However it involves a significant conformational change of a loop as compared to the ground state structure we originally used (PDB:1U19). This finding underlines the importance of loop flexibility in membrane protein interactions. Interestingly, when dimers of rho based on this new interface are arranged in rows-of-dimers, Gt placed on rho following the arrangement recently described for Gs on the β2AR correctly embed the lipid anchors of Gtα and Gtγ in the lipid phase. We also discuss the pros and cons of the different models of rho dimers for the visual phototransduction machinery, in the context of the rows-of-dimers arrangement, the functional implications of such supramolecular organization, the binding of Gt to rho and the structural, biochemical and physiological data available and the potential relevance for other GPCRs.[1] Periole, et al.(2012)JAmChemSoc134,10959-10965.[2] Knepp, et al.(2012)Biochemistry51,1819-1821.

Small-angle neutron scattering and coarse-grained molecular dynamics simulations have been used to determine the structural parameters (bilayer thickness D, polar region thickness D(H), interfacial lateral area of the unit cell A(UC) and alcohol partial interfacial area A(CnOH)) of fluid dioleoylphosphatidylcholine:dioleoylphosphatidylserine (PCPS, DOPC:DOPS=24.7mol:mol) bilayers in extruded unilamellar vesicles with incorporated aliphatic alcohols (CnOH, n=8-18 is the even number of carbons in alkyl chain). External ((2))H(2)O/H(2)O contrast variation experiments revealed that D(H) decreases as a function of alkyl chain length and CnOH:PCPS molar ratio. Using measurements at single 100% ((2))H(2)O contrast we found that (i) D decreases with CnOH:PCPS molar ratio and increases with CnOH chain length (at 0.4 molar ratio); (ii) A(UC) significantly increases already in the presence of shortest CnOH studied (at 0.4 molar ratio), further increase is observed with longer CnOHs and at higher molar ratios; (iii) A(CnOH) of alcohol molecules in PCPS bilayer increases linearly with the alkyl chain length, A(CnOH) obtained for CnOHs with n≤10 corresponds to A(CnOH)≤20Å(2) - a value specific for the crystalline or solid rotator phase of alkanes. All these structural modifications induced by studied CnOHs were reproduced in MD simulations. The computational results give an accurate description of the alcohol effects at the molecular level, explaining the experimental data. The anomaly in A(CnOH) is discussed via the "umbrella" effect described for cholesterol.

With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form Delta G alpha ln(P(1)/P(0)). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics. (C) 2011 Wiley Periodicals, Inc. J Comput Chem 32: 1919-1928, 2011

Using neutron diffraction Harroun et al. [(2006) Biochemistry 45, 1227-1233; (2008) Biochemistry 47, 7090-7096] carried out studies that unequivocally demonstrated cholesterol preferentially sequestering in the middle of bilayers (i.e., flat orientation) made of lipids with polyunsaturated fatty acids (PUFA), in contrast to its "usual" position where its hydroxyl group locates near the lipid/water interface (i.e., upright orientation). Here we clearly show, using neutron diffraction, cholesterol's orientational preference in different lipid bilayers. For example, although it requires 50 mol % POPC (16:0-18:1 PC) in DAPC (di20:4 PC) bilayers to cause cholesterol to revert to its upright orientation, only 5 mol % DMPC (di14:0 PC) is needed to achieve the same effect. This result demonstrates not only cholesterol's affinity for saturated hydrocarbon chains, but also its aversion for PUFAs. Molecular dynamics (MD) simulations performed on similar systems show that in high PUFA content bilayers cholesterol is simultaneously capable of assuming different orientations within a bilayer. Although this result is known from previous MD studies by Marrink et al. [(2008) J. Am. Chem. Soc. 130, 10-11], it has yet to be confirmed experimentally. Importantly, MD simulations predict the formation of DMPC-rich domains, data corroborated by experiment (i.e., 10 mol % DMPC-doped DAPC bilayers), where cholesterol preferentially locates in its upright orientation, while in DMPC-depleted domains cholesterol is found mostly in the bilayer center (i.e., flat orientation). These results lend credence to DMPC's aversion for PUFAs, supporting the notion that domain formation is primarily driven by lipids. © 2010 American Chemical Society.

Coarse-grained (CG) simulations have become an essential tool to study a large variety of biomolecular processes, exploring temporal and spatial scales inaccessible to traditional models of atomistic resolution. One of the major simplifications of CG models is the representation of the solvent, which is either implicit or modeled explicitly as a van der Waals particle. The effect of polarization, and thus a proper screening of interactions depending on the local environment, is absent. Given the important role of water as a ubiquitous solvent in biological systems, its treatment is crucial to the properties derived from simulation studies. Here, we parameterize a polarizable coarse-grained water model to be used in combination with the CG MARTINI force field. Using a three-bead model to represent four water molecules, we show that the orientational polarizability of real water can be effectively accounted for. This has the consequence that the dielectric screening of bulk water is reproduced. At the same time, we parameterized our new water model such that bulk water density and oil/water partitioning data remain at the same level of accuracy as for the standard MARTINI force field. We apply the new model to two cases for which current CG force fields are inadequate. First, we address the transport of ions across a lipid membrane. The computed potential of mean force shows that the ions now naturally feel the change in dielectric medium when moving from the high dielectric aqueous phase toward the low dielectric membrane interior. In the second application we consider the electroporation process of both an oil slab and a lipid bilayer. The electrostatic field drives the formation of water filled pores in both cases, following a similar mechanism as seen with atomistically detailed models., Author Summary Many biomolecular processes involve charged species moving between regions of high polarity, such as the water phase, and regions of lower polarity, such as the lipid membrane. Due to the change in electrostatic screening between these two environments, the strength of the interactions between the moving charge and the surrounding molecules also changes. This has important consequences for the way biological activity is controlled. To help understand the forces driving the movement of biomolecules, we developed a computational model which is capable of describing these processes at near-atomic detail. To do so efficiently, we use a coarse-grained description of the molecules, in which some of the atomistic detail is averaged out. To capture the inhomogeneous nature of the dielectric response, we re-introduce some detail in the water model; the new model effectively mimics the orientational polarizability of real water molecules, and screens electrostatic interactions realistically. This enables the study of a number of important biological processes that were hitherto considered challenging for coarse-grained models, such as the permeation of ions across a lipid membrane and the rupture of membranes due to an electrostatic field, at relatively low computational cost.

We present an algorithm to reconstruct atomistic structures from their corresponding coarse-grained (CG) representations and its implementation into the freely available molecular dynamics (MD) program package GROMACS. The central part of the algorithm is a simulated annealing MD simulation in which the CG and atomistic structures are coupled via restraints. A number of examples demonstrate the application of the reconstruction procedure to obtain low-energy atomistic structural ensembles from their CO counterparts. We reconstructed individual molecules in vacuo (NCQ tripeptide, dipalmitoylphosphatidylcholine, and cholesterol), bulk water, and a WALP transmembrane peptide embedded in a solvated lipid bilayer. The first examples serve to optimize the parameters for the reconstruction procedure, whereas the latter examples illustrate the applicability to condensed-phase biomolecular systems. (C) 2010 Wiley Periodicals, Inc. J Comput Chem 31 : 1333-1343, 2010

Antimicrobial peptides are a large family of peptides that include small cationic peptides that can permeabilize lipid membranes by disrupting the bilayer structure. Previous atomistic simulations of two specific antimicrobial peptides, magainin and melittin, show that they act by forming toroidal transmembrane pores in model bilayers. However, only systems of limited size and length scales have been studied and direct comparisons to experimental observations could not be made. Here, we study the poration propensity of these peptides with lipid vesicles using a coarse-grain description. A new version of the MARTINI force-field has been used which accounts for the polarizability of water. The explicit screening of the new MARTINI force-field provides for a more realistic description of membrane poration by antimicrobial peptides.Figure: A snapshot of the starting structure of simulations of magainin-H2, an antimicrobial peptide, “attacking” a DPPC lipid vesicle. The vesicle is cut through to reveal its cross section. The head group beads are shown in purple and pink and the tails in gray. The antimicrobial peptides are shown in green (backbone beads) and yellow (side-chain beads). The water beads are not shown for clarity.View Large Image | View Hi-Res Image | Download PowerPoint Slide

The relative stability of cholesterol in cellular membranes and the thermodynamics of fluctuations from equilibrium have important consequences for sterol trafficking and lateral domain formation. We used molecular dynamics computer simulations to investigate the partitioning of cholesterol in a systematic set of lipid bilayers. In addition to atomistic simulations, we undertook a large set of coarse grained simulations, which allowed longer time and length scales to be sampled. Our results agree with recent experiments (Steck, T. L.; et al. Biophys. J. 2002, 83, 2118-2125) that the rate of cholesterol flip-flop can be fast on physiological time scales, while extending our understanding of this process to a range of lipids. We predicted that the rate of flip-flop is strongly dependent on the composition of the bilayer. In polyunsaturated bilayers, cholesterol undergoes flip-flop on a submicrosecond time scale, while flip-flop occurs in the second range in saturated bilayers with high cholesterol content. We also calculated the free energy of cholesterol desorption, which can be equated to the excess chemical potential of cholesterol in the bilayer compared to water. The free energy of cholesterol desorption from a DPPC bilayer is 80 kJ/mol, compared to 67 kJ/mol for a DAPC bilayer. In general, cholesterol prefers more ordered and rigid bilayers and has the lowest affinity for bilayers with two polyunsaturated chains. Overall, the simulations provide a detailed molecular level thermodynamic description of cholesterol interactions with lipid bilayers, of fundamental importance to eukaryotic life.

Amyloid oligomers are considered to play causal roles in the pathogenesis of amyloid-related degenerative diseases including Alzheimer's disease. Using MD simulation techniques, we explored the contributions of the different structural elements of trimeric and pentameric full-length Aβ 1-42 aggregates in solution to their stability and conformational dynamics. We found that our models are stable at a temperature of 310 K, and converge toward an interdigitated side-chain packing for intermolecular contacts within the two β-sheet regions of the aggregates: β1 (residues 18-26) and β2 (residues 31-42). MD simulations reveal that the /3-strand twist is a characteristic element of Aβ-aggregates, permitting a compact, interdigitated packing of side chains from neighboring β-sheets. The β2 portion formed a tightly organized β-helix, whereas the β1 portion did not show such a firm structural organization, although it maintained its β-sheet conformation. Our simulations indicate that the hydrophobic core comprising the β2 portion of the aggregate is a crucial stabilizing element in the Aβ aggregation process. On the basis of these structure-stability findings, the β2 portion emerges as an optimal target for further antiamyloid drug design. Fil: Masman, Marcelo Fabricio. University of Groningen; Países Bajos. Universidad Nacional de San Luis; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis; Argentina Fil: Eisel, Ulrich L. M.. University of Groningen; Países Bajos Fil: Csizmadia, Imre G.. University of Toronto; Canadá. University of Szeged; Hungría Fil: Penke, Botond. University of Szeged; Hungría Fil: Enriz, Ricardo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto Multidisciplinario de Investigaciones Biológicas de San Luis. Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto Multidisciplinario de Investigaciones Biológicas de San Luis; Argentina Fil: Marrink, Siewert Jan. University of Groningen; Países Bajos Fil: Luiten, Paul G. M.. University of Groningen; Países Bajos

Molecular dynamics (MD) simulations can yield the structural dynamics of biomolecules at a femtoseconds time resolution and, simultaneously, at atomic spatial resolution. However, due to the large computational effort involved, MD was hitherto limited to rather small systems, such as a single molecule in water, and to timescales of a few hundred nanoseconds. Furthermore, the current molecular mechanical (MM) force fields cannot describe the making and breaking of chemical bonds or light-activated processes, which requires a quantum mechanical description.

Resorcinolic lipids, or resorcinols, are commonly found in plant membranes. They consist of a substituted benzene ring forming the hydrophilic lipid head, attached to an alkyl chain forming the hydrophobic tail. Experimental results show alternative effects of resorcinols on lipid membranes. Depending on whether they are added to lipid solutions before or after the formation of the liposomes, they either stabilize or destabilize these liposomes. Here we use atomistic molecular dynamics simulations to elucidate the molecular nature of this dual effect. Systems composed of either one of three resorcinol homologs, differing in the alkyl tail length, interacting with dimyristoylphosphatidylcholine lipid bilayers were studied. It is shown that resorcinols preincorporated into bilayers induce order within the lipid acyl chains, decrease the hydration of the lipid headgroups, and make the bilayers less permeable to water. In contrast, simulations in which the resorcinols are incorporated from the aqueous solution into a preformed phospholipid bilayer induce local disruption, leading to either transient pore formation or even complete rupture of the membrane. In line with the experimental data, our simulations thus demonstrate that resorcinols can either disturb or stabilize the membrane structure, and offer a detailed view of the underlying molecular mechanism.

This article presents the parallel implementation of a new multiscale model that is currently developed in the Molecular Dynamics Group from the University of Groningen. Multiscale methods combine the advantages of two levels of simulation, an atomistic and a coarse-grain one, with a small loss of performance. We designed a parallel implementation of this multiscale approach based on the improved parallel algorithms from the GROMACS MD simulator. The properties of the simulated systems were undisturbed and the errors were kept to a minimum. By having a parallel multiscale simulation, one can take advantage of a reduced simulation time by running it on multiple processors, and in the same time, access to both atomistic and macroscopic details is offered for a better understanding of the desired phenomenon.

Udgivelsesdato: 2009-Feb-20 We calculate full 3D pressure fields for inhomogeneous nanoscale systems using molecular dynamics simulation data. The fields represent systems with increasing level of complexity, ranging from semivesicles and vesicles to membranes characterized by coexistence of two phases, including also a protein-membrane complex. We show that the 3D pressure field is distinctly different for curved and planar bilayers, the pressure field depends strongly on the phase of the membrane, and that an integral protein modulates the tension and elastic properties of the membrane.

Bolalipids are bi-polar lipids, consisting of two mono-polar lipids chemically linked together at either one or both of the lipid tails. Membranes formed by these lipids or by their mixtures with mono-polar lipids are known to have additional mechanical stability while retaining membrane fluidity. This is traditionally attributed to the fact that bolalipids can span the bilayer with their two polar heads positioned at opposite membrane-water interfaces. Our primary interest is to confirm this hypothesis by studying the relation between bolalipid configurations inside the membrane and the structural and mechanical properties of the membrane.To this end, we performed molecular dynamics simulations using the coarse grained MARTINI force field [1]. We start with self-assembly simulations of bolalipids in mixtures with mono-polar lipids, to elucidate the preferred orientation of the bolalipids, i.e. spanning versus a looping configuration in which both head groups reside in the same monolayer. To assure proper equilibration between the spanning and looping conformations, we introduce artificial pores in the membrane to allow lipid flip-flops. We consider different types of linkage, including also bi-polar lipids attached at head group level for which spanning configurations are inaccessible.After equilibration, the membrane properties are characterized in terms of a variety of structural properties and the lateral pressure profile. The resistance of the membrane to mechanical rupture is also investigated. We find that both the spanning/looping ratio and the stability of the membrane depend strongly on the type of crosslink, as well as on the concentration of bolalipids and length of the lipid tails. Our study can help designing new artificial membranes, with higher stability under a variety of extreme conditions.[1] S.J. Marrink, H.J. Risselada, S. Yefimov, D.P. Tieleman, A.H. de Vries, J. Phys. Chem. B 111 (2007) 7812-7824.

We have used molecular dynamics simulations to study the lateral stress profiles in lipid monolayers at the air/water interface. From the calculations, we determined the “surface of tension” in the complex interfacial layer. We identified the factors for monolayer stability, which allows explaining the maximum surface pressure sustained by a selected lipid mixture (collapse pressure). This is relevant for understanding the function of biological interfaces, such as the surfactant-covered gas exchange interface in the lungs, and designing artificial/replacement surfactant mixtures.We calculated the stress distributions for lipid monolayers of different composition under varying surface pressure, including both liquid-expanded and liquid-condensed phases. The stress distribution in the hydrocarbon chain region is most affected by the surface pressure. In the liquid-expanded phase, the stress becomes negative at the chain/air interface. In the liquid-condensed phase, the negative stress in the chains is partially compensated by positive pressure due to increased density, and the profile is characterized by multiple peaks originating from chain and head group ordering. The simulations were performed with both atomistic and coarse-grained molecular models, which led to qualitatively similar results. To test the estimated collapse pressures, the coarse-grained model was used to simulate monolayer collapse upon lateral compression. To induce 2D-3D transformations that require long time scales, small defects were introduced, which provided nucleation sites for monolayer folding.

Lipid monolayers at an air–water interface can be compressed laterally and reach high surface density. Beyond a certain threshold, they become unstable and collapse. Lipid monolayer collapse plays an important role in the regulation of surface tension at the air–liquid interface in the lungs. Although the structures of lipid aggregates formed upon collapse can be characterized experimentally, the mechanism leading to these structures is not fully understood. We investigate the molecular mechanism of monolayer collapse using molecular dynamics simulations. Upon lateral compression, the collapse begins with buckling of the monolayer, followed by folding of the buckle into a bilayer in the water phase. Folding leads to an increase in the monolayer surface tension, which reaches the equilibrium spreading value. Immediately after their formation, the bilayer folds have a flat semielliptical shape, in agreement with theoretical predictions. The folds undergo further transformation and form either flat circular bilayers or vesicles. The transformation pathway depends on macroscopic parameters of the system: the bending modulus, the line tension at the monolayer–bilayer connection, and the line tension at the bilayer perimeter. These parameters are determined by the system composition and temperature. Coexistence of the monolayer with lipid aggregates is favorable at lower tensions of the monolayer–bilayer connection. Transformation into a vesicle reduces the energy of the fold perimeter and is facilitated for softer bilayers, e.g., those with a higher content of unsaturated lipids, or at higher temperatures.

Voltage-gated potassium (Kv) channels are ubiquitous transmembrane proteins involved in electric signaling of excitable tissues. A fundamental property of these channels is the ability to open or close in response to changes in the membrane potential. To date, their structure-based activation mechanism remains unclear, and there is a large controversy on how these gates function at the molecular level, in particular, how movements of the voltage sensor domain are coupled to channel gating. So far, all mechanisms proposed for this coupling are based on the crystal structure of the open voltage-gated Kv1.2 channel and structural models of the closed form based on electrophysiology experiments. Here, we use coarse-grain (CG) molecular dynamics simulations that allow conformational changes from the open to the closed form of the channel (embedded in its membrane environment) to be followed. Despite the low specificity of the CG force field, the obtained closed structure satisfies several experimental constraints. The overall results suggest a gating mechanism in which a lateral displacement the S4-S5 linker leads to a closing of the gate. Only a small up-down movement of the S4 helices is noticed. Additionally, the study suggests a peculiar upward motion of the intracellular tetramerization domain of the channel, hence providing a molecular view on how this domain may further regulate conduction in Kv channels.

Recent neutron scattering experiments showed a striking manifestation of the aversion between polyunsaturated fatty acid (PUFA)-containing lipids and cholesterol. Selectively deuterated cholesterol/ 1,2-diarachidonylphosphatidylcholine (DAPC) samples revealed that the hydroxyl of the sterol resides at the center of the bilayer. Here we use a recently parametrized coarse grain simulation model to shed light on these puzzling experimental observations. Using a simulation setup in close correspondence to the experimental conditions, we reproduce the experimental neutron scattering profiles to a large extent. The simulations allow us to analyze the behavior of cholesterol in detail; we show that the interaction of cholesterol with the PUFA chains of DAPC leads to a fast flip-flop rate for the sterol and an increased preference of the sterol for the unusual location embedded between the monolayer leaflets.

We describe molecular dynamics simulations elucidating the molecular details of the process of fusion for small lipid vesicles. The simulations are based on a coarse grained (CG) lipid model that accurately represents the lamellar state of a variety of phospholipids and enables us to observe intermediate stages during fusion at near atomic detail. Simulations were conducted on a variety of systems containing common phospholipids such as phosphatidylcholine (PC), phosphatidylethanolamine (PE), lysoPC, and mixtures of the above. The fusion intermediates found are in general agreement with the stalk-pore mechanism. Transient pores sometimes form adjacent to the stalk, however, resulting in the mixing of lipids from the outer and inner monolayers. The speed of stalk formation and the opening of the fusion pore can be modulated by altering the lipid composition in qualitative agreement with experimental observations.

Molecular dynamics simulations have been used to study the spontaneous aggregation of a concentrated solution of dipalmitoylphosphatidylcholine (DPPC) molecules in water into a small vesicle. The molecules were represented in atomistic detail. Starting from a DPPC solution in water, an oblong vesicle with a long axis of 15 nm and short axes of 10 nm was formed spontaneously. After 90 ns of simulation, the vesicle contained a number of water pores. Water pores were shown to facilitate exchange of lipids between inner and outer leaflets. Lipid tails were shown to be less ordered in the inner leaflet of the vesicle, as compared to those in the outer leaflet of the vesicle and an equilibrated lamellar bilayer.

Hydrophilic pores are formed in peptide free lipid bilayers under mechanical stress. It has been proposed that the transport of ionic species across such membranes is largely determined by the existence of such meta-stable hydrophilic pores. To study the properties of these structures and understand the mechanism by which pore expansion leads to membrane rupture, a series of molecular dynamics simulations of a dipalmitoylphosphatidylcholine (DPPC) bilayer have been conducted. The system was simulated in two different states; first, as a bilayer containing a meta-stable pore and second, as an equilibrated bilayer without a pore. Surface tension in both cases was applied to study the formation and stability of hydrophilic pores inside the bilayers. It is observed that below a critical threshold tension of approximately 38 mN/m the pores are stabilized. The minimum radius at which a pore can be stabilized is 0.7 nm. Based on the critical threshold tension the line tension of the bilayer was estimated to be approximately 3 x 10(-11) N, in good agreement with experimental measurements. The flux of water molecules through these stabilized pores was analyzed, and the structure and size of the pores characterized. When the lateral pressure exceeds the threshold tension, the pores become unstable and start to expand causing the rupture of the membrane. In the simulations the mechanical threshold tension necessary to cause rupture of the membrane on a nanosecond timescale is much higher in the case of the equilibrated bilayers, as compared with membranes containing preexisting pores.

Methodological issues in molecular dynamics (MD) simulations, such as the treatment of long-range electrostatic interactions or the type of pressure coupling, have important consequences for the equilibrium properties observed. We report a series of long (up to 150 ns) MD simulations of dipalmitoylphosphatidylcholine (DPPC) bilayers in which the methodology of simulation is systematically varied. Comparisons of simulations with truncation schemes, Ewald summations, and modified Coulomb interactions, either by shift functions or reaction field models, to describe long-range electrostatics point out the artifacts inherent in each of these methods and above all those of straight cutoff methods. We further show that bilayer properties are less sensitive to the details of the pressure-coupling algorithm and that an increased integration time step of 5 fs can be safely used in simulations of phosphatidylcholine lipid bilayers.

Molecular dynamics simulations of pore formation and mem-brane rupture in phospholipid bilayers under mechanical andelectrical stress at an atomic level are presented. Pore formationcan be induced on a nanosecond time scale in simulations wherethe lateral pressure exceeds -200 bar or where an electric field of0.5 V/nm is applied across the membrane.Lipid bilayer membranes are remarkable structures consistingof two leaflets of phospholipids. Their mechanical properties arecentral to understanding the behavior of cell membranes. Forexample, the formation of transient water pores is believed tounderlie the passive transport of protons and hydrophilic compoundsthrough the bilayer. Pore formation is also relevant during processessuch as cell fusion and is important for drug release from liposomes.Experimentally, pores can be induced in membranes by applyingmechanical stress (i.e., pipet aspiration experiments) or an electricfield (electroporation). The precise mechanism by which pores formand their size, structure, and stability are, however, poorlyunderstood.

The association behaviour of a number of glucitol amine gemini surfactants has been investigated by means of molecular dynamics and self-consistent-field calculations. We have shown that the titratable head group of the surfactant is responsible for a micelle-to-membrane transition when changing the pH. Furthermore, the association structure of this group of surfactants is shown to be very sensitive to ionic strength. The combination of a charged head group, a spacer, and the hydrophilic glucitol side chains is responsible for the possible structural transitions in the associates as a function of ionic strength and pH.