A hybrid particle–field molecular dynamics approach: a route toward efficient coarse-grained models for biomembranes

On the equivalence of the hybrid particle-field and Gaussian core models

Hybrid particle-field molecular dynamics is a molecular simulation strategy, wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle-field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle-field method and particle-particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle-field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form, in particular, we demonstrate the ability of the Hamiltonian hybrid particle-field model to recover all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle-field filtering length scale on the emergent particle-particle correlations.

HylleraasMD: A Domain Decomposition-Based Hybrid Particle-Field Software for Multiscale Simulations of Soft Matter

We present HylleraasMD (HyMD), a comprehensive implementation of the recently proposed Hamiltonian formulation of hybrid particle-field molecular dynamics. The methodology is based on a tunable, grid-independent length-scale of coarse graining, obtained by filtering particle densities in reciprocal space. This enables systematic convergence of energies and forces by grid refinement, also eliminating nonphysical force aliasing. Separating the time integration of fast modes associated with internal molecular motion from slow modes associated with their density fields, we enable the first time-reversible, energy-conserving hybrid particle-field simulations. HyMD comprises the optional use of explicit electrostatics, which, in this formalism, corresponds to the long-range potential in particle-mesh Ewald. We demonstrate the ability of HyMD to perform simulations in the microcanonical and canonical ensembles with a series of test cases, comprising lipid bilayers and vesicles, surfactant micelles, and polypeptide chains, comparing our results to established literature. An on-the-fly increase of the characteristic coarse-grain length significantly speeds up dynamics, accelerating self-diffusion and leading to expedited aggregation. Exploiting this acceleration, we find that the time scales involved in the self-assembly of polymeric structures can lie in the tens to hundreds of picoseconds instead of the multimicrosecond regime observed with comparable coarse-grained models.

Organizations of melittin peptides after spontaneous penetration into cell membranes

The antimicrobial peptide, melittin, is a potential next-generation antibiotic because melittin can spontaneously form pores in bacterial cell membranes and cause cytoplasm leakage. However, the organizations of melittin peptides in cell membranes remain elusive, which impedes the understanding of the poration mechanism. In this work, we use coarse-grained and all-atom molecular dynamics (MD) simulations to investigate the organizations of melittin peptides during and after spontaneous penetration into DPPC/POPG lipid bilayers. We find that the peptides in lipid bilayers adopt either a transmembrane conformation or a U-shaped conformation, which are referred to as T- and U-peptides, respectively. Several U-peptides and/or T-peptides aggregate to form stable pores. We analyze a T-pore consisting of four T-peptides and a U-pore consisting of three U-peptides and one T-peptide. In both pores, peptides are organized in a manner such that polar residues face inward and hydrophobic residues face outward, which stabilizes the pores and produces water channels. Compared with the U-pore, the T-pore has lower energy, larger pore diameter, and higher permeability. However, the T-pore occurs less frequently than the U-pore in our simulations, probably because the formation of the T-pore is kinetically slower than the U-pore. The stability and permeability of both pores are confirmed by 300 ns all-atom MD simulations. The peptide organizations obtained in this work should deepen the understanding of the stability, poration mechanism, and permeability of melittin, and facilitate the optimization of melittin to enhance the antibacterial ability.

Can Polarity-Inverted Surfactants Self-Assemble in Nonpolar Solvents?

We investigate the self-assembly process of a surfactant with inverted polarity in water and cyclohexane using both all-atom and coarse-grained hybrid particle-field molecular dynamics simulations. Unlike conventional surfactants, the molecule under study, proposed in a recent experiment, is formed by a rigid and compact hydrophobic adamantane moiety, and a long and floppy triethylene glycol tail. In water, we report the formation of stable inverted micelles with the adamantane heads grouping together into a hydrophobic core and the tails forming hydrogen bonds with water. By contrast, microsecond simulations do not provide evidence of stable micelle formation in cyclohexane. Validating the computational results by comparison with experimental diffusion constant and small-angle X-ray scattering intensity, we show that at laboratory thermodynamic conditions the mixture resides in the supercritical region of the phase diagram, where aggregated and free surfactant states coexist in solution. Our simulations also provide indications as to how to escape this region to produce thermodynamically stable micellar aggregates.

Hybrid particle-field molecular dynamics under constant pressure

Hybrid particle-field methods are computationally efficient approaches for modeling soft matter systems. So far, applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particle-field interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations and to produce a qualitatively correct lateral pressure profile.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Intramolecular structural parameters are key modulators of the gel-liquid transition in coarse grained simulations of DPPC and DOPC lipid bilayers

The capability of coarse-grained models based on the MARTINI mapping to reproduce the gel-liquid phase transition in saturated and unsaturated model lipids was investigated. We found that the model is able to reproduce a lower critical temperature for 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) with respect to 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Nonetheless, the appearance of a gel phase for DOPC is strictly dependent on the intramolecular parameters chosen to model its molecular structure. In particular, we show that the bending angle at the coarse-grained bead corresponding to the unsaturated carbon-carbon bond acts as an order parameter determining the temperature of the phase transition. Structural analysis of the molecular dynamics simulations runs evidences that in the gel phase, the packing of the lipophilic tails of DOPC assume a different conformation than in the liquid phase. In the latter phase, the DOPC geometry resembles that of the relaxed free molecule. DPPC:DOPC mixtures show a single phase transition temperature, indicating that the observation of a phase separation between the two lipids requires the simulation of systems with sizes much larger than the ones used here.

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations.

Toward Chemically Resolved Computer Simulations of Dynamics and Remodeling of Biological Membranes

Cellular membranes are fundamental constituents of living organisms. Apart from defining the boundaries of the cells, they are involved in a wide range of biological functions, associated with both their structural and the dynamical properties. Biomembranes can undergo large-scale transformations when subject to specific environmental changes, including gel-liquid phase transitions, change of aggregation structure, formation of microtubules, or rupture into vesicles. All of these processes are dependent on a delicate interplay between intermolecular forces, molecular crowding, and entropy, and their understanding requires approaches that are able to capture and rationalize the details of all of the involved interactions. Molecular dynamics-based computational models at atom-level resolution are, in principle, the best way to perform such investigations. Unfortunately, the relevant spatial and time dimensionalities involved in membrane remodeling phenomena would require computational costs that are today unaffordable on a routinely basis. Such hurdles can be removed by coarse-graining the representations of the individual molecular components of the systems. This procedure anyway reduces the possibility of describing the chemical variations in the lipid mixtures composing biological membranes. New hybrid particle field multiscale approaches offer today a promising alternative to the more traditional particle-based simulations methods. By combining chemically distinguishable molecular representations with mesoscale-based computationally affordable potentials, they appear as one of the most promising ways to keep an accurate description of the chemical complexity of biological membranes and, at the same time, cover the required scales to describe remodeling events.

Biomembrane solubilization mechanism by Triton X-100: a computational study of the three stage model

The solubilization mechanism of lipid membranes in the presence of Triton X-100 (TX-100) is investigated at molecular resolution using hybrid particle field–self consistence field simulations.

MARTINI Coarse-Grained Model of Triton TX-100 in Pure DPPC Monolayer and Bilayer Interfaces

The coarse-grained MARTINI model of Triton TX-100 has been validated by direct comparison of the experimental and calculated area increase in pure DPPC lipid bilayers and monolayers at water/air interfaces in the presence of surfactant and by comparison of electron density profiles calculated with more detailed atomistic models based on the CHARMM force field. Bilayer simulations have been performed and compared with monolayers and with atomistic models. The validated CG model has been employed to study the phase separation of TX-100 molecules in lipid bilayers and the effect of the lipid bilayer curvature.

Hybrid particle–field molecular dynamics simulation for polyelectrolyte systems

An effective hybrid computer simulation method combining molecular dynamics and self-consistent field theory is developed by including electrostatic interactions.

Generation of Well-Relaxed All-Atom Models of Large Molecular Weight Polymer Melts: A Hybrid Particle-Continuum Approach Based on Particle-Field Molecular Dynamics Simulations

A procedure based on Molecular Dynamics (MD) simulations employing soft potentials derived from self-consistent field (SCF) theory (named MD-SCF) able to generate well-relaxed all-atom structures of polymer melts is proposed. All-atom structures having structural correlations indistinguishable from ones obtained by long MD relaxations have been obtained for poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) melts. The proposed procedure leads to computational costs mainly related on system size rather than to the chain length. Several advantages of the proposed procedure over current coarse-graining/reverse mapping strategies are apparent. No parametrization is needed to generate relaxed structures of different polymers at different scales or resolutions. There is no need for special algorithms or back-mapping schemes to change the resolution of the models. This characteristic makes the procedure general and its extension to other polymer architectures straightforward. A similar procedure can be easily extended to the generation of all-atom structures of block copolymer melts and polymer nanocomposites.