Simulations of Phospholipids Using a Coarse Grain Model

Learning Force Field Parameters from Differentiable Particle-Field Molecular Dynamics

We develop ∂-HylleraasMD (∂-HyMD), a fully end-to-end differentiable molecular dynamics software based on the Hamiltonian hybrid particle-field formalism, and use it to establish a protocol for automated optimization of force field parameters. ∂-HyMD is templated on the recently released HylleraaasMD software, while using the JAX autodiff framework as the main engine for the differentiable dynamics. ∂-HyMD exploits an embarrassingly parallel optimization algorithm by spawning independent simulations, whose trajectories are simultaneously processed by reverse mode automatic differentiation to calculate the gradient of the loss function, which is in turn used for iterative optimization of the force-field parameters. We show that parallel organization facilitates the convergence of the minimization procedure, avoiding the known memory and numerical stability issues of differentiable molecular dynamics approaches. We showcase the effectiveness of our implementation by producing a library of force field parameters for standard phospholipids, with either zwitterionic or anionic heads and with saturated or unsaturated tails. Compared to the all-atom reference, the force field obtained by ∂-HyMD yields better density profiles than the parameters derived from previously utilized gradient-free optimization procedures. Moreover, ∂-HyMD models can predict with good accuracy properties not included in the learning objective, such as lateral pressure profiles, and are transferable to other systems, including triglycerides.

Data-Driven Approach to Coarse-Graining Simple Liquids in Confinement

We propose a data-driven framework for identifying coarse-grained (CG) Lennard-Jones (LJ) potential parameters in confined systems for simple liquids. Our approach involves the use of a Deep Neural Network (DNN) that is trained to approximate the solution of the Inverse Liquid State (ILST) problem for confined systems. The DNN model inherently incorporates essential physical characteristics specific to confined fluids, enabling an accurate prediction of inhomogeneity effects. By utilizing transfer learning, we predict single-site LJ potentials of simple multiatomic liquids confined in a slit-like channel, which effectively replicate both the fluid structure and molecular force of the target All-Atom (AA) system when the electrostatic interactions are not dominant. In addition, we showcase the synergy between the data-driven approach and the well-known Bottom-Up coarse-graining method utilizing Relative-Entropy (RE) Minimization. Through the sequential utilization of these two methods, the robustness of the iterative RE method is significantly augmented, leading to a remarkable enhancement in convergence.

A brief history of visualizing membrane systems in molecular dynamics simulations

Understanding lipid dynamics and function, from the level of single, isolated molecules to large assemblies, is more than ever an intensive area of research. The interactions of lipids with other molecules, particularly membrane proteins, are now extensively studied. With advances in the development of force fields for molecular dynamics simulations (MD) and increases in computational resources, the creation of realistic and complex membrane systems is now common. In this perspective, we will review four decades of the history of molecular dynamics simulations applied to membranes and lipids through the prism of molecular graphics.

Frame-guided assembly from a theoretical perspective

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress towards fabrics of predefined shape and size, following an initially provided frame of guiding elements. Here we study frame-guided assembly into a two-dimensional membrane via computer simulations, based on a single-bead coarse grained surfactant model in continuous space. In agreement with the experiment the assembly process already starts for surfactant concentrations below the critical micelle concentration. Furthermore, upon increasing temperature the formation process gets more delocalized. Additionally, the assembly process of the resulting membrane plane is modelled by a lattice gas model. It displays a similar phenomenology but additionally allows the derivation of analytical mean-field predictions. In this way a fundamental understanding of frame-guided assembly can be gained.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

Coarse-grained implicit solvent lipid force field with a compatible resolution to the Cα protein representation

Biological membranes have been prominent targets for coarse-grained (CG) molecular dynamics simulations. While minimal CG lipid models with three beads per lipid and quantitative CG lipid models with >10 beads per lipid have been well studied, in between them, CG lipid models with a compatible resolution to residue-level CG protein models are much less developed. Here, we extended a previously developed three-bead lipid model into a five-bead model and parameterized it for two phospholipids, POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine). The developed model, iSoLF, reproduced the area per lipid, hydrophobic thickness, and phase behaviors of the target phospholipid bilayer membranes at the physiological temperature. The model POPC and DPPC membranes were in liquid and gel phases, respectively, in accordance with experiments. We further examined the spontaneous formation of a membrane bilayer, the temperature dependence of physical properties, the vesicle dynamics, and the POPC/DPPC two-component membrane dynamics of the CG lipid model, showing some promise. Once combined with standard Cα protein models, the iSoLF model will be a powerful tool to simulate large biological membrane systems made of lipids and proteins.

Formation and Properties of a Self-Assembled Nanoparticle-Supported Lipid Bilayer Probed through Molecular Dynamics Simulations

We have carried out coarse-grained molecular dynamics (MD) simulations to study the self-assembly procedure of a system of randomly placed lipid molecules, water beads, and a nanoparticle (NP). The self-assembly results in the formation of the nanoparticle-supported lipid bilayer (NPSLBL), with the self-assembly mechanism being driven by events such as the formation of small lipid clusters, merging of the lipid clusters in the vicinity of the NP to form NP-embedded vesicle with a pore, and collapsing of that pore to eventually form the equilibrated NPSLBL system overcoming a large free-energy barrier. Subsequently, we quantify the properties and the configurations of this NPSLBL system. We reveal that unlike our proposition of an equal number of lipid molecules occupying the inner and outer leaflets in a recent report studying the properties of a preassembled lipid bilayer, the equilibrated self-assembled NPSLBL system demonstrates a much larger number of lipid molecules occupying the outer leaflet as compared to the inner leaflet. Second, the thickness of the water layer entrapped between the NP and the inner leaflet shows similar values as predicted by experiments and our previous study. Finally, we reveal that, similar to our previous study, the diffusivity of the lipid molecules in the outer leaflet is larger than that in the inner leaflet but, due to higher temperature employed during our simulations, are even larger than that predicted by our previous study.

Structure and dynamics of liposomes designed for drug delivery: coarse-grained molecular dynamics simulations to reveal the role of lipopolymer incorporation

In this work, coarse-grained molecular dynamics simulations are carried out in NPTH and NVTE statistical ensembles in order to study the structure and dynamics properties of liposomes coated with polyethylene glycol (PEG).

The conical shape of DIM lipids promotes Mycobacterium tuberculosis infection of macrophages

Phthiocerol dimycocerosate (DIM) is a major virulence factor of the pathogen Mycobacterium tuberculosis (Mtb). While this lipid promotes the entry of Mtb into macrophages, which occurs via phagocytosis, its molecular mechanism of action is unknown. Here, we combined biophysical, cell biology, and modeling approaches to reveal the molecular mechanism of DIM action on macrophage membranes leading to the first step of Mtb infection. Matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) mass spectrometry showed that DIM molecules are transferred from the Mtb envelope to macrophage membranes during infection. Multiscale molecular modeling and ³¹P-NMR experiments revealed that DIM adopts a conical shape in membranes and aggregates in the stalks formed between 2 opposing lipid bilayers. Infection of macrophages pretreated with lipids of various shapes uncovered a general role for conical lipids in promoting phagocytosis. Taken together, these results reveal how the molecular shape of a mycobacterial lipid can modulate the biological response of macrophages.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Interaction between nanoparticles and charged phospholipid membranes

Charged lipids in cell membranes and subcellular organelles are arranged in the form of a bilayer with the hydrocarbon tails sequestered away from the water and the polar head groups exposed to the aqueous environment. Most of them bear net negative charges leading to the negatively charged cell membranes. Charged lipid-lipid and lipid-protein interactions are generally dynamic and heavily depend on their local molecular concentrations. To examine the electrostatic properties of charged lipid layers in contact with an electrolyte solution, we incorporate the single chain mean field theory with Poisson-Boltzmann theory to explore the equilibrium structure of charged phospholipid membranes. Using the three bead coarse-grained model we reproduced the essential equilibrium properties of the charged phospholipid bilayer. We also investigate the influence of the mobile ions on the thickness of the layer, the area per lipid (APL), and the electrostatic potential of the membrane. Then we investigate the attraction-repulsion property of two charged nanoparticles which are stuck on the charged lipid molecules surrounded with mobile ions. After that we simulated the interaction between the Pleckstrin homology domain (PH domain) of Akt and the cytoplasmic membrane. Taking into account the electrostatic interaction, we observe the structure changes of the membrane at different concentrations of mobile ions in its equilibrium state. Also we discuss the influence of mobile ions on the size of the pore opened in the membrane by the charged protein. Such an observation may shed light on the activation of oncogenic Akt (or protein kinase B) around the membrane at the molecular level.

Muscle membrane integrity in Duchenne muscular dystrophy: recent advances in copolymer-based muscle membrane stabilizers

The scientific premise, design, and structure-function analysis of chemical-based muscle membrane stabilizing block copolymers are reviewed here for applications in striated muscle membrane injury. Synthetic block copolymers have a rich history and wide array of applications from industry to biology. Potential for discovery is enabled by a large chemical space for block copolymers, including modifications in block copolymer mass, composition, and molecular architecture. Collectively, this presents an impressive chemical landscape to leverage distinct structure-function outcomes. Of particular relevance to biology and medicine, stabilization of damaged phospholipid membranes using amphiphilic block copolymers, classified as poloxamers or pluronics, has been the subject of increasing scientific inquiry. This review focuses on implementing block copolymers to protect fragile muscle membranes against mechanical stress. The review highlights interventions in Duchenne muscular dystrophy, a fatal disease of progressive muscle deterioration owing to marked instability of the striated muscle membrane. Biophysical and chemical engineering advances are presented that delineate and expand upon current understanding of copolymer-lipid membrane interactions and the mechanism of stabilization. The studies presented here serve to underscore the utility of copolymer discovery leading toward the therapeutic application of block copolymers in Duchenne muscular dystrophy and potentially other biomedical applications in which membrane integrity is compromised.

Rate of hemifusion diaphragm dissipation and ability to form three-junction bound HD determined by lipid composition

Though the hemifusion diaphragm (HD) is widely accepted as an intermediate in bilayer membrane fusion, lipid contributions toward HD stability and dynamics are still not fully understood. In this paper, we study large, binary, protein-free HD systems at varying compositions of negative intrinsic curvature (NIC) lipids using molecular dynamics (MD) simulations of a solvent-free coarse-grained lipid model. Under MD, initially created HDs are found to relax to three major end states depending on the composition and lipid intrinsic curvature. Low compositions of NIC lipids or weak intrinsic curvature result in double-bilayer end states, and moderate compositions of moderate to strong NIC lipids result in metastable fusion pores. Importantly, high compositions of moderate NIC lipids result in a metastable HD that persists beyond μs time scales. NIC lipids stabilize the HD by filling the junction core around the HD. Sorting of NIC lipids toward the three-junction region occurs in fused-endpoint systems, but no significant sorting was seen in systems that end in a double bilayer indicating that high line tension at the triple junction drives HD dissipation faster than sorting can enrich that junction enough to lower that line tension. The appearance of three end states dependent on the NIC lipid composition highlights the necessity of NIC lipids for non-leaky fusion.

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.

Predicting ligand binding poses for low-resolution membrane protein models: Perspectives from multiscale simulations

Membrane receptors constitute major targets for pharmaceutical intervention. Drug design efforts rely on the identification of ligand binding poses. However, the limited experimental structural information available may make this extremely challenging, especially when only low-resolution homology models are accessible. In these cases, the predictions may be improved by molecular dynamics simulation approaches. Here we review recent developments of multiscale, hybrid molecular mechanics/coarse-grained (MM/CG) methods applied to membrane proteins. In particular, we focus on our in-house MM/CG approach. It is especially tailored for G-protein coupled receptors, the largest membrane receptor family in humans. We show that our MM/CG approach is able to capture the atomistic details of the receptor/ligand binding interactions, while keeping the computational cost low by representing the protein frame and the membrane environment in a highly simplified manner. We close this review by discussing ongoing improvements and challenges of the current implementation of our MM/CG code.

All-Atom Molecular Dynamics-Based Analysis of Membrane-Stabilizing Copolymer Interactions with Lipid Bilayers Probed under Constant Surface Tensions

An all-atom phospholipid bilayer and triblock copolymer model was developed for molecular dynamics (MD) studies. These were performed to investigate the mechanism of interaction between membrane-stabilizing triblock copolymer P188 and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) lipid bilayers under applied lateral surface tension (γ) to model membrane mechanical stress. Results showed that P188 insertion is driven by the hydrophobic poly(propylene oxide) (PPO) core and dependent on bilayer area per lipid. Moreover, insertion of P188 increased the bilayer's resistance to mechanical rupture, as observed by a significant increase in the absolute lateral pressure required to disrupt the bilayer. To further investigate the specific chemical features of P188 underlying membrane stabilizer function, a series of MD simulations with triblock copolymers of the same class as P188 but of varying chemical composition and sizes were performed. Results showed that triblock copolymer insertion into the lipid bilayer is dependent on overall copolymer hydrophobicity, with higher copolymer hydrophobicity requiring a reduced bilayer area per lipid ratio for insertion. Further analysis revealed that the effect of copolymer insertion on membrane mechanical integrity was also dependent on hydrophobicity. Here, P188 insertion significantly increased the absolute apparent lateral pressure required to rupture the POPC bilayer, thereby protecting the membrane against mechanical stress. In marked contrast, highly hydrophobic copolymers decreased the lateral pressure necessary for membrane rupture and thus rendering the membrane significantly more susceptible to mechanical stress. These new in silico findings align with recent experimental findings using synthetic lipid bilayers and in muscle cells in vitro and mouse models in vivo. Collectively, these data underscore the importance of PEO-PPO-PEO copolymer chemical composition in copolymer-based muscle membrane stabilization in vitro and in vivo. All-atom modeling with MD simulations holds promise for investigating novel copolymers with enhanced membrane interacting properties.

On the Calculation of Acyl Chain Order Parameters from Lipid Simulations

For molecular dynamics simulations of biological membrane systems to live up to the potential of providing accurate atomic level detail into membrane properties and functions, it is essential that the force fields used to model such systems are as accurate as possible. One membrane property that is often used to assess force field accuracy is the carbon-hydrogen (or carbon-deuterium) order parameters of the lipid tails, which can be accurately measured using experimental NMR techniques. There are a variety of analysis tools available to calculate these order parameters from simulations and it is essential that these computational tools work correctly to ensure the accurate assessment of the simulation force fields. In this work we compare many of these computational tools for calculating the order parameters of POPC membranes. While tools that work on all-atom systems and tools that work on saturated lipid tails in general work extremely well, we demonstrate that the majority of the tested tools that calculate the order parameters for unsaturated united-atom lipid tails do so incorrectly. We identify tools that do perform accurate calculations and include one such program with this work, enabling rapid and accurate calculation of united-atom lipid order parameters. Furthermore, we discuss cases in which it is nontrivial to appropriately predict the unsaturated carbon order parameters in united-atom systems. Finally, we examine order parameter splitting for carbon 2 in sn-2 lipid chains, demonstrating substantial deviations from experimental values in several all-atom and united-atom lipid force fields.

A New Mixed All-Atom/Coarse-Grained Model: Application to Melittin Aggregation in Aqueous Solution

We introduce a new mixed resolution, all-atom/coarse-grained approach (AACG), for modeling peptides in aqueous solution and apply it to characterizing the aggregation of melittin. All of the atoms in peptidic components are represented, while a single site is used for each water molecule. With the full flexibility of the peptide retained, our AACG method achieves speedups by a factor of 3-4 for CPU time reduction and another factor of roughly 7 for diffusion. An Ewald treatment permits the inclusion of long-range electrostatic interactions. These characteristics fit well with the requirements for studying peptide association and aggregation, where the system sizes and time scales require considerable computational resources with all-atom models. In particular, AACG is well suited for biologics since changes in peptide shape and long-range electrostatics may play an important role. The application of AACG to melittin, a 26-residue peptide with a well-known propensity to aggregate in solution, serves as an initial demonstration of this technology for studying peptide aggregation. We observed the formation of melittin aggregates during our simulations and characterized the time-evolution of aggregate size distribution, buried surface areas, and residue contacts. Key interactions including π-cation and π-stacking involving TRP19 were also examined. Our AACG simulations demonstrated a clear salt effect and a moderate temperature effect on aggregation and support the molten globule model of melittin aggregates. As a showcase, this work illustrates the useful role for AACG in investigations of peptide aggregation and its potential to guide formulation and design of biologics.

Evaluation of the hybrid resolution PACE model for the study of folding, insertion, and pore formation of membrane associated peptides

The PACE force field presents an attractive model for conducting molecular dynamics simulations of membrane-protein systems. PACE is a hybrid model, in which lipids and solvents are coarse-grained consistent with the MARTINI mapping, while proteins are described by a united atom model. However, given PACE is linked to MARTINI, which is widely used to study membranes, the behavior of proteins interacting with membranes has only been limitedly examined in PACE. In this study, PACE is used to examine the behavior of several peptides in membrane environments, namely WALP peptides, melittin and influenza hemagglutinin fusion peptide (HAfp). Overall, we find PACE provides an improvement over MARTINI for modeling helical peptides, based on the membrane insertion energetics for WALP16 and more realistic melittin pore dynamics. Our studies on HAfp, which forms a helical hairpin structure, do not show the hairpin structure to be stable, which may point toward a deficiency in the model. © 2017 Wiley Periodicals, Inc.

Mechanism of NTP Binding to the Active Site of T7 RNA Polymerase Revealed by Free-Energy Simulation

In genetic transcription, molecular dynamic details and energetics of NTP binding to the active site of RNA polymerase (RNAP) are poorly understood. In this article, we investigated the NTP binding process in T7 RNAP using all-atom MD simulation combined with the umbrella sampling technique. Based on our simulations, a two-step mechanism was proposed to explain NTP binding: first, substrate NTP in aqueous solution, which carries a magnesium ion, diffuses through a secondary channel of RNAP to attain a pore region, where it undergoes conformational changes to give a correct orientation; next, the NTP establishes initial basepairing contacts with the template nucleoside (TN). Our free-energy calculations suggest that both steps are spontaneous. This mechanism can easily explain the problem of NTP binding with different orientations. Moreover, it is found that the nascent NTP:TN basepair is fragile and easily broken by thermal disturbance. Therefore, we speculate that the fingers domain will be triggered to close, so as to create a steady environment for the next chemical step. The observations from the work provide valuable information for comprehensively understanding the mechanism of the basic step in genetic transcription.

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.

Atomic-level description of protein-lipid interactions using an accelerated membrane model

Peripheral membrane proteins are structurally diverse proteins that are involved in fundamental cellular processes. Their activity of these proteins is frequently modulated through their interaction with cellular membranes, and as a result techniques to study the interfacial interaction between peripheral proteins and the membrane are in high demand. Due to the fluid nature of the membrane and the reversibility of protein-membrane interactions, the experimental study of these systems remains a challenging task. Molecular dynamics simulations offer a suitable approach to study protein-lipid interactions; however, the slow dynamics of the lipids often prevents sufficient sampling of specific membrane-protein interactions in atomistic simulations. To increase lipid dynamics while preserving the atomistic detail of protein-lipid interactions, in the highly mobile membrane-mimetic (HMMM) model the membrane core is replaced by an organic solvent, while short-tailed lipids provide a nearly complete representation of natural lipids at the organic solvent/water interface. Here, we present a brief introduction and a summary of recent applications of the HMMM to study different membrane proteins, complementing the experimental characterization of the presented systems, and we offer a perspective of future applications of the HMMM to study other classes of membrane proteins. This article is part of a Special Issue entitled: Membrane proteins edited by J.C. Gumbart and Sergei Noskov.

On the dynamics of molecular self-assembly and the structural analysis of bilayer membranes using coarse-grained molecular dynamics simulations

We present a molecular dynamics simulation study of the self-assembly of coarse-grained lipid molecules from unbiased random initial configurations. Our lipid model is based on a well-tried CG polymer model with an additional potential that mimics the hydrophobic properties of lipid tails. We find that several stages of self-organization of lipid clusters are involved in the dynamics of bilayer formation and that the resulting equilibrium structures sensitively depend on the strength of hydrophobic interactions hc of the lipid tails and on temperature T. The obtained stable lipid membranes are quantitatively analyzed with respect to their local structure and their degree of order. At equilibrium, we obtain self-stabilizing bilayer membrane structures that exhibit a bending stiffness κB and compression modulus KC comparable to experimental measurements under physiological conditions. We present a phase diagram of our lipid model which covers a sol-gel transition, a liquid (or gel-like) phase including stable bilayer structures and vesicle formation, as well as a quasi-crystalline phase. We also determine the exact conditions for temperature T and degree of hydrophobicity hc for stable bilayer formation including closed vesicles.

Transferability of a coarse-grained atactic polystyrene model: the non-bonded potential effect

In this paper, we construct an efficient and simple coarse grained (CG) model for atactic polystyrene (PS) by using a 1 : 1 mapping scheme at 463 K and 1 atm pressure and derive the corresponding bonded and non-bonded potentials in the CG force field (FF) via a direct Boltzmann inversion approach and a combined structure-based and thermodynamic quantities-based CG method, respectively.

A Nonradial Coarse-Grained Potential for Proteins Produces Naturally Stable Secondary Structure Elements

We introduce a nonradial potential term for coarse-grained (CG) molecular simulations of proteins. This term mimics the backbone dipole-dipole interactions and accounts for the needed directionality to form stable folded secondary structure elements. We show that α-helical and β-sheet peptide chains are correctly described in dynamics without the need of introducing any a priori bias potentials or ad hoc parametrizations, which limit broader applicability of CG simulations for proteins. Moreover, our model is able to catch the formation of supersecondary structural motifs, like transitions from long single α-helices to helix-coil-helix or β-hairpin assemblies. This novel scheme requires the structural information of Cα beads only; it does not introduce any additional degrees of freedom to the system and has a general formulation, which allows it to be used in synergy with various CG protocols, leading to an improved description of the structural and dynamic properties of protein assemblies and networks.

Biomembranes in atomistic and coarse-grained simulations

The architecture of biological membranes is tightly coupled to the localization, organization, and function of membrane proteins. The organelle-specific distribution of lipids allows for the formation of functional microdomains (also called rafts) that facilitate the segregation and aggregation of membrane proteins and thus shape their function. Molecular dynamics simulations enable to directly access the formation, structure, and dynamics of membrane microdomains at the molecular scale and the specific interactions among lipids and proteins on timescales from picoseconds to microseconds. This review focuses on the latest developments of biomembrane force fields for both atomistic and coarse-grained molecular dynamics (MD) simulations, and the different levels of coarsening of biomolecular structures. It also briefly introduces scale-bridging methods applicable to biomembrane studies, and highlights selected recent applications.

Efficient Exploration of Membrane-Associated Phenomena at Atomic Resolution

Biological membranes constitute a critical component in all living cells. In addition to providing a conducive environment to a wide range of cellular processes, including transport and signaling, mounting evidence has established active participation of specific lipids in modulating membrane protein function through various mechanisms. Understanding lipid-protein interactions underlying these mechanisms at a sufficiently high resolution has proven extremely challenging, partly due to the semi-fluid nature of the membrane. In order to address this challenge computationally, multiple methods have been developed, including an alternative membrane representation termed highly mobile membrane mimetic (HMMM) in which lateral lipid diffusion has been significantly enhanced without compromising atomic details. The model allows for efficient sampling of lipid-protein interactions at atomic resolution, thereby significantly enhancing the effectiveness of molecular dynamics simulations in capturing membrane-associated phenomena. In this review, after providing an overview of HMMM model development, we will describe briefly successful application of the model to study a variety of membrane processes, including lipid-dependent binding and insertion of peripheral proteins, the mechanism of phospholipid insertion into lipid bilayers, and characterization of optimal tilt angle of transmembrane helices. We conclude with practical recommendations for proper usage of the model in simulation studies of membrane processes.

Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.

Molecular dynamics simulations of membrane proteins

Membrane protein structures are underrepresented in the Protein Data Bank (PDB) due to difficulties associated with expression and crystallization. As such, it is one area where computational studies, particularly Molecular Dynamics (MD) simulations, can provide useful additional information. Recently, there has been substantial progress in the simulation of lipid bilayers and membrane proteins embedded within them. Initial efforts at simulating membrane proteins embedded within a lipid bilayer were relatively slow and interactive processes, but recent advances now mean that the setup and running of membrane protein simulations is somewhat more straightforward, though not without its problems. In this chapter, we outline practical methods for setting up and running MD simulations of a membrane protein embedded within a lipid bilayer and discuss methodologies that are likely to contribute future improvements.

Instability of carbon nanoparticles interacting with lipid bilayers

For nanoparticles penetrating biological tissue, modelling indicates that without external forces, carbon nanoparticles will remain trapped in lipid bilayers.

Structure-based prediction of drug distribution across the headgroup and core strata of a phospholipid bilayer using surrogate phases

Solvation of drugs in the core (C) and headgroup (H) strata of phospholipid bilayers affects their physiological transport rates and accumulation. These characteristics, especially a complete drug distribution profile across the bilayer strata, are tedious to obtain experimentally, to the point that even simplified preferred locations are only available for a few dozen compounds. Recently, we showed that the partition coefficient (P) values in the system of hydrated diacetyl phosphatidylcholine (DAcPC) and n-hexadecane (C16), as surrogates of the H- and C-strata of the bilayer composed of the most abundant mammalian phospholipid, PC, agree well with the preferred bilayer location of compounds. High P values are typical for lipophiles accumulating in the core, and low P values are characteristic of cephalophiles preferring the headgroups. This simple pattern does not hold for most compounds, which usually have more even distribution and may also accumulate at the H/C interface. To model complete distribution, the correlates of solvation energies are needed for each drug state in the bilayer: (1) for the H-stratum it is the DAcPC/W P value, calculated as the ratio of the C16/W and C16/DAcPC (W for water) P values; (2) for the C-stratum, the C16/W P value; (3) for the H/C interface, the P values for all plausible molecular poses are characterized using the fragment DAcPC/W and C16/W solvation parameters for the parts of the molecule embedded in the H- and C-strata, respectively. The correlates, each scaled by two Collander coefficients, were used in a nonlinear, mass-balance based model of intrabilayer distribution, which was applied to the easily measurable overall P values of compounds in the DMPC (M = myristoyl) bilayers and monolayers as the dependent variables. The calibrated model for 107 neutral compounds explains 94% of experimental variance, achieves similar cross-validation levels, and agrees well with the nontrivial, experimentally determined bilayer locations for 27 compounds. The resulting structure-based prediction system for intrabilayer distribution will facilitate more realistic modeling of passive transport and drug interactions with those integral membrane proteins, which have the binding sites located in the bilayer, such as some enzymes, influx and efflux transporters, and receptors. If only overall bilayer accumulation is of interest, the 1-octanol/W P values suffice to model the studied set.

Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

Parameterizing the Morse Potential for Coarse-Grained Modeling of Blood Plasma

Multiscale simulations of fluids such as blood represent a major computational challenge of coupling the disparate spatiotemporal scales between molecular and macroscopic transport phenomena characterizing such complex fluids. In this paper, a coarse-grained (CG) particle model is developed for simulating blood flow by modifying the Morse potential, traditionally used in Molecular Dynamics for modeling vibrating structures. The modified Morse potential is parameterized with effective mass scales for reproducing blood viscous flow properties, including density, pressure, viscosity, compressibility and characteristic flow dynamics of human blood plasma fluid. The parameterization follows a standard inverse-problem approach in which the optimal micro parameters are systematically searched, by gradually decoupling loosely correlated parameter spaces, to match the macro physical quantities of viscous blood flow. The predictions of this particle based multiscale model compare favorably to classic viscous flow solutions such as Counter-Poiseuille and Couette flows. It demonstrates that such coarse grained particle model can be applied to replicate the dynamics of viscous blood flow, with the advantage of bridging the gap between macroscopic flow scales and the cellular scales characterizing blood flow that continuum based models fail to handle adequately.

Polymer micelle assisted transport and delivery of model hydrophilic components inside a biological lipid vesicle: a coarse-grain simulation study

Understanding drug transportation and delivery mechanism from a molecular viewpoint is essential to find better treatment pathways. Despite the fact that many significant drugs such as anticancer doxorubicin and mitoxantrone are predominantly hydrophilic, an efficient methodology to deliver hydrophilic drug components is not well established. Here we explore this problem by studying "patchy" polymeric micelle assisted hydrophilic component transportation across a lipid membrane and delivery inside a biological lipid vesicle. Using the MARTINI force field as the basis, we study the interaction of polymeric micelle with DPPC lipid vesicles in detail. In order to facilitate hydrophilic drug transportation study, a primitive CG model for hydrophilic drug component is used. Extensive simulations carried out over hundreds of nanoseconds demonstrate successful encapsulation, transportation of hydrophilic components by patchy polymeric micelles. Results show the polymeric micelle releases a significant portion of hydrophilic contents inside the lipid vesicle. The present simulation study also reveals a possible mechanism for efficient hydrophilic component transportation and delivery. Insights from this study could potentially help the experimental community to design better delivery vehicles, especially for hydrophilic drug molecules.

Coarse-grained molecular dynamics simulations of photoswitchable assembly and disassembly

The supramolecular self-assembly and disassembly that are responsive to external stimuli are of critical importance to the design and synthesis of functional supramolecular materials. In this work, we performed a coarse-grained molecular dynamics study of photo-controlled assembly and disassembly on a timescale of ten microseconds. The spontaneous assembly of cis-AzoC10, trans-AzoC10, and cis-AzoC10/α-CD into micelle-like aggregates, and the disassembly of trans-AzoC10/α-CD starting from a pre-assembled micelle were directly simulated. Our results of simulations have revealed a significant size and shape dependence of aggregates on the molecular structure and concentrations of monomers. As demonstrated, with careful design, coarse-grained molecular dynamics simulations are useful in the study of controlled assembly and disassembly to bridge the gap between atomistic simulations and experiments.