Mechanical properties of surfactant bilayer membranes from atomistic and coarse-grained molecular dynamics simulations

We use simulations to predict the stability and mechanical properties of two amphiphilic bilayer membranes. We carry out atomistic MD simulations and investigate whether it is possible to use an existing coarse-grained (CG) surfactant model to map the membrane properties. We find that certain membranes can be represented well by the CG model, whereas others cannot. Atomistic MD simulations of the erucate membrane yield a headgroup area per surfactant a(0) of 0.26 nm(2), an elastic modulus K(A) of 1.7 N/m, and a bending rigidity kappa of 5 k(B)T. We find that the CG model, with the right choice for the size and potential well depth of the head, correctly reproduces a(0), kappa, as well as the fluctuation spectrum over the whole range of q values. Atomistic MD simulations of EHAC, on the other hand, suggest that this membrane is unstable. This is indicated by the fact that kappa is of the order of k(B)T, which means that the interface is extremely flexible and diffuse, and K(A) is close to zero, which means that the surface tension is zero. We argue that the CG model can be used if the headgroups are uncharged, dipolar, or effectively dipolar due to headgroup charge screening induced by counterion condensation.     

A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations

The development of coarse-grained (CG) models that correctly represent the important features of compounds is essential to overcome the limitations in time scale and system size currently encountered in atomistic molecular dynamics simulations. Most approaches reported in the literature model one or several molecules into a single uncharged CG bead. For water, this implicit treatment of the electrostatic interactions, however, fails to mimic important properties, e.g., the dielectric screening. Therefore, a coarse-grained model for water is proposed which treats the electrostatic interactions between clusters of water molecules explicitly. Five water molecules are embedded in a spherical CG bead consisting of two oppositely charged particles which represent a dipole. The bond connecting the two particles in a bead is unconstrained, which makes the model polarizable. Experimental and all-atom simulated data of liquid water at room temperature are used for parametrization of the model. The experimental density and the relative static dielectric permittivity were chosen as primary target properties. The model properties are compared with those obtained from experiment, from clusters of simple-point-charge water molecules of appropriate size in the liquid phase, and for other CG water models if available. The comparison shows that not all atomistic properties can be reproduced by a CG model, so properties of key importance have to be selected when coarse graining is applied. Yet, the CG model reproduces the key characteristics of liquid water while being computationally 1-2 orders of magnitude more efficient than standard fine-grained atomistic water models.     

Nucleation free energy of pore formation in an amphiphilic bilayer studied by molecular dynamics simulations

The formation of a pore in a membrane requires a considerable rearrangement of the amphiphilic molecules about to form the bilayer edge surrounding the pore, and hence is accompanied by a steep increase of the free energy. Recent rupture and conductance experiments suggest that this reshuffling process is also responsible for a small energy barrier that stabilizes "prepores" with diameters of less than 1 nm, rendering both the opening and closing of pores an activated process. We use the potential of mean constraint force method to study this free energy profile, as a function of pore radius, in a coarse grained bilayer model. The calculations show that the free energy rises by (15-20) kT during pore opening, making it an extremely rare nucleation event. Although we do not observe a barrier to pore closure, the results do make the existence of such a barrier plausible. For larger pores we find a smooth transition to Litster's model, from which a line tension coefficient of about 3.7 x 10(-11) J m(-1) is deduced.     

Spin-labeled alkylphospholipids in a dipalmitoylphosphatidylcholine bilayer: molecular dynamics simulations

Molecular dynamics simulation has been performed to investigate the structural properties of perifosine and its synthetic spin-labeled alkylphospholipid analogues. The conformations adopted by these compounds in water and in a dipalmitoylphosphatidylcholine bilayer as a function of the presence and position of the N-oxyl-4',4'-dimethyloxazolidine ring (doxyl group) have been investigated by all-atom molecular dynamics. No predominant conformation was observed in water, but the molecules adopt specific orientations and conformations in the lipid bilayer. As is expected, alkyl chains tend to insert into the hydrophobic core, while charged groups stay at the lipid-water interface. A doxyl group in the middle of the alkyl chain moves up to the interface region, thus preventing adoption of the extended conformation. Compounds with a doxyl group close to the polar head group adopt conformations similar to that of unlabeled perifosine within the first nanoseconds of simulation. When the doxyl group is at the end of alkyl chain, the spin-labeled molecule needs more time to reach equilibrium. These results indicate a considerable effect of the doxyl position within the alkyl chain on its localization in the lipid bilayer and can be extended further to other similar spin probes used in the electron paramagnetic resonance spectroscopy of biological membranes.     

Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.     

Reconstructing protein remodeled membranes in molecular detail from mesoscopic models

We present a method for "inverse coarse graining," rebuilding a higher resolution model from a lower resolution one, in order to rebuild protein coats for remodeled membranes of complex topology. The specific case of membrane remodeling by N-BAR domain containing proteins is considered here, although the overall method is general and thus applicable to other membrane remodeling phenomena. Our approach begins with a previously developed, discretized mesoscopic continuum membrane model (EM2) which has been shown to capture the reticulated membrane topologies often observed for N-BAR/liposome systems by electron microscopy (EM). The information in the EM2 model-directions of the local curvatures and a low resolution sample of the membrane surface-is then used to construct a coarse-grained (CG) system with one site per lipid and 26 sites per protein. We demonstrate the approach on pieces of EM2 structures with three different topologies that have been observed by EM: A tubule, a "Y" junction, and a torus. We show that the approach leads to structures that are stable under subsequent constant temperature CG simulation, and end by considering the future application of the methodology as a hybrid approach that combines experimental information with computer modeling.     

Steered molecular dynamics simulations of cobra cytotoxin interaction with zwitterionic lipid bilayer: no penetration of loop tips into membranes

Cobra cytotoxins, small proteins of three-fingered toxin family, unspecifically damage membranes in different cells and artificial vesicles. However, the molecular mechanism of this damage is not yet completely understood. We used steered molecular dynamics simulations to study the interaction of cardiotoxin A3 from Naja atra cobra venom with hydrated 1-palmitoyl-2-oleoyl-1-sn-3-phosphatidylcholine (POPC) bilayer. The studied system included one cytotoxin molecule, 64 lipid molecules (32 molecules in each monolayer) and 2500 water molecules. It was found that the toxin interacted with zwitterionic bilayer formed by POPC. During first nanosecond of simulation the toxin molecule was oriented toward membrane surface by loops' basement including cytotoxin regions Cys14-Asn19 and Cys38-Ser46. This orientation was stable enough and was not changed during next 6 ns of simulation. The obtained data suggest that cytotoxin molecule cannot penetrate into membrane composed of zwitterionic lipids without some auxiliary interaction.     

Statistical temperature molecular dynamics: application to coarse-grained beta-barrel-forming protein models

Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.     

Area compressibility and buckling of amphiphilic bilayers in molecular dynamics simulations

The elastic modulus or area compressibility of a membrane is routinely calculated in molecular dynamics simulations as the proportionality constant relating surface tension and projected surface area. Recent studies, however, have revealed a marked system size dependence of these moduli, which we attribute to the neglect of thermal undulations in the area calculation. We discuss several methods, based on the Helfrich model and on numerical triangulation, to remedy this situation, and find a satisfying agreement between them. The Helfrich model also quantitatively describes a buckling transition observed for compressed bilayers.     

Gating motions in voltage-gated potassium channels revealed by coarse-grained molecular dynamics simulations

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.     

Mixing coarse-grained and fine-grained water in molecular dynamics simulations of a single system

The use of a supra-molecular coarse-grained (CG) model for liquid water as solvent in molecular dynamics simulations of biomolecules represented at the fine-grained (FG) atomic level of modelling may reduce the computational effort by one or two orders of magnitude. However, even if the pure FG model and the pure CG model represent the properties of the particular substance of interest rather well, their application in a hybrid FG/CG system containing varying ratios of FG versus CG particles is highly non-trivial, because it requires an appropriate balance between FG-FG, FG-CG, and CG-CG energies, and FG and CG entropies. Here, the properties of liquid water are used to calibrate the FG-CG interactions for the simple-point-charge water model at the FG level and a recently proposed supra-molecular water model at the CG level that represents five water molecules by one CG bead containing two interaction sites. Only two parameters are needed to reproduce different thermodynamic and dielectric properties of liquid water at physiological temperature and pressure for various mole fractions of CG water in FG water. The parametrisation strategy for the FG-CG interactions is simple and can be easily transferred to interactions between atomistic biomolecules and CG water.     

Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

Molecular dynamics simulations of amphiphilic graft copolymer molecules at a water/air interface

Fully atomistic molecular dynamics simulations of amphiphilic graft copolymer molecules have been performed at a range of surface concentrations at a water/air interface. These simulations are compared to experimental results from a corresponding system over a similar range of surface concentrations. Neutron reflectivity data calculated from the simulation trajectories agrees well with experimentally acquired profiles. In particular, excellent agreement in neutron reflectivity is found for lower surface concentration simulations. A simulation of a poly(ethylene oxide) (PEO) chain in aqueous solution has also been performed. This simulation allows the conformational behavior of the free PEO chain and those tethered to the interface in the previous simulations to be compared.     

Dynamic models of G-protein coupled receptor dimers: indications of asymmetry in the rhodopsin dimer from molecular dynamics simulations in a POPC bilayer

Based on the growing evidence that G-protein coupled receptors (GPCRs) form homo- and hetero-oligomers, models of GPCR signaling are now considering macromolecular assemblies rather than monomers, with the homo-dimer regarded as the minimal oligomeric arrangement required for functional coupling to the G-protein. The dynamic mechanisms of such signaling assemblies are unknown. To gain some insight into properties of GPCR dimers that may be relevant to functional mechanisms, we study their current structural prototype, rhodopsin. We have carried out nanosecond time-scale molecular dynamics (MD) simulations of a rhodopsin dimer and compared the results to the monomer simulated in the same type of bilayer membrane model composed of an equilibrated unit cell of hydrated palmitoyl-oleoyl-phosphatidyl choline (POPC). The dynamic representation of the homo-dimer reveals the location of structural changes in several regions of the monomeric subunits. These changes appear to be more pronounced at the dimerization interface that had been shown to be involved in the activation process [Proc Natl Acad Sci USA 102:17495, 2005]. The results are consistent with a model of GPCR activation that involves allosteric modulation through a single GPCR subunit per dimer.     

An implemented potential of non-rigid water molecules for molecular dynamics simulations

The central force model for a water molecule is corrected by adding a three-body term. The present potential fits both an accurate ab initio potential energy surface and the fundamental vibrational frequencies of gas-phase water. The three-body terms allow us to reproduce the gas-phase IR spectrum by molecular dynamics simulations. Some problems connected with MD simulations of IR spectra are discussed.     

Configurational entropies of lipids in pure and mixed bilayers from atomic-level and coarse-grained molecular dynamics simulations

Single-chain and single-fragment configurational entropies of lipid tails in hydrated lipid bilayers are evaluated from molecular dynamics simulations using the quasi-harmonic approximation. The entropy distribution along individual acyl tails is obtained and compared to that of corresponding hydrocarbon chains in the liquid phase. We consider pure dipalmitoylphosphatidylcholine and mixed dioleoylphosphatidylcholine/dioleoylphosphatidylethanolamine bilayers. The systems are modeled at different levels of spatial resolution: In an atomic-level (AL) model all (heavy) atoms are explicitly simulated; in a coarse-grained (CG) model particles (beads) representing groups of covalently bound atoms are used, which map approximately four non-hydrogen atoms to one interaction site. Single-chain and single-fragment entropies and correlations between the motions of (single) acyl chains are compared. A good correspondence is found between the flexibility of the AL and CG models. The loss in configurational entropy due to the reduction in the number of degrees of freedom upon coarse-graining of the model is estimated. The CG model shows about 4 times faster convergence of the chain entropies than the more detailed AL model. Corrections to the quasi-harmonic entropy estimates were found to be small for the CG model. For the AL model, the correction due to mode anharmonicities is small, but the correction due to pairwise (supralinear) mode correlations is sizable.     

On achieving experimental accuracy from molecular dynamics simulations of flexible molecules: aqueous glycerol

The rotational isomeric states (RIS) of glycerol at infinite dilution have been characterized in the aqueous phase via a 1 micros conventional molecular dynamics (MD) simulation, a 40 ns enhanced sampling replica exchange molecular dynamics (REMD) simulation, and a reevaluation of the experimental NMR data. The MD and REMD simulations employed the GLYCAM06/AMBER force field with explicit treatment of solvation. The shorter time scale of the REMD sampling method gave rise to RIS and theoretical scalar 3J(HH) coupling constants that were comparable to those from the much longer traditional MD simulation. The 3J(HH) coupling constants computed from the MD methods were in excellent agreement with those observed experimentally. Despite the agreement between the computed and the experimental J-values, there were variations between the rotamer populations computed directly from the MD data and those derived from the experimental NMR data. The experimentally derived populations were determined utilizing limiting J-values from an analysis of NMR data from substituted ethane molecules and may not be completely appropriate for application in more complex molecules, such as glycerol. Here, new limiting J-values have been derived via a combined MD and quantum mechanical approach and were used to decompose the experimental 3J(HH) coupling constants into population distributions for the glycerol RIS.     

Mechanical properties of hard–soft block copolymers calculated from coarse-grained molecular dynamics models

To relate the mechanical responses of hard–soft copolymer systems with their microstructures, a coarse-grained molecular dynamics approach is employed, and mechanical properties of both hard and soft domains are calculated. We first investigate the enhancement mechanism of hard domains under tensile and shear loading conditions with pressure. The energy factor that denotes the interaction between hard beads dominates the microphase separation and morphology. Our numerical experiments show that pressure is the most crucial factor in shear-under-pressure tests, with larger pressure leading to higher shearing resistance of the copolymers. The viscoelastic behaviors of hard–soft copolymers are computed from the stress autocorrelation function. The stress relaxation indicates that the soft matrix is in a rubbery state at room temperature while hard domains are “glass-like” and can be viewed as elastic solids in a macroscale model. In addition, local elastic constants of hard domains are computed using the stress–strain fluctuation method with purely local stress and local strain. Those results can be used as inputs for macroscale models for copolymers and can provide guidelines for designing polymeric materials. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1552–1566