Hydrodynamics of Diffusion in Lipid Membrane Simulations

Simulating Bacterial Membrane Models at the Atomistic Level: A Force Field Comparison

Molecular dynamics (MD) simulations are currently an indispensable tool to understand both the dynamic and nanoscale organization of cell membrane models. A large number of quantitative parameters can be extracted from these simulations, but their reliability is determined by the quality of the employed force field and the simulation parameters. Much of the work on parametrizing and optimizing force fields for biomembrane modeling has been focused on homogeneous bilayers with a single phospholipid type. However, these may not perform effectively or could even be unsuitable for lipid mixtures commonly employed in membrane models. This work aims to fill this gap by comparing MD simulation results of several bacterial membrane models using different force fields and simulation parameters, namely, CHARMM36, Slipids, and GROMOS-CKP. Furthermore, the hydrogen isotope exchange (HIE) method, combined with GROMOS-CKP (GROMOS-H2Q), was also tested to check for the impact of this acceleration strategy on the performance of the force field. A common set of simulation parameters was employed for all of the force fields in addition to those corresponding to the original parametrization of each of them. Furthermore, new experimental order parameter values determined from NMR of several lipid mixtures are also reported to compare them with those determined from MD simulations. Our results reveal that most of the calculated physical properties of bacterial membrane models from MD simulations are substantially force field and lipid composition dependent. Some lipid mixtures exhibit nearly ideal behaviors, while the interaction of different lipid types in other mixtures is highly synergistic. None of the employed force fields seem to be clearly superior to the other three, each having its own strengths and weaknesses. Slipids are notably effective at replicating the order parameters for all acyl chains, including those in lipid mixtures, but they offer the least accurate results for headgroup parameters. Conversely, CHARMM provides almost perfect estimates for the order parameters of the headgroups but tends to overestimate those of the lipid tails. The GROMOS parametrizations deliver reasonable order parameters for entire lipid molecules, including multicomponent bilayers, although they do not reach the accuracy of Slipids for tails or CHARMM for headgroups. Importantly, GROMOS-H2Q stands out for its computational efficiency, being at least 3 times faster than GROMOS, which is already faster than both CHARMM and Slipids. In turn, GROMOS-H2Q yields much higher compressibilities compared to all other parametrizations.

Nanoporous Membranes of Densely Packed Carbon Nanotubes Formed by Lipid-Mediated Self-Assembly

Nanofiltration technology faces the competing challenges of achieving high fluid flux through uniformly narrow pores of a mechanically and chemically stable filter. Supported dense-packed 2D-crystals of single-walled carbon nanotube (CNT) porins with ∼1 nm wide pores could, in principle, meet these challenges. However, such CNT membranes cannot currently be synthesized at high pore density. Here, we use computer simulations to explore lipid-mediated self-assembly as a route toward densely packed CNT membranes, motivated by the analogy to membrane-protein 2D crystallization. In large-scale coarse-grained molecular dynamics (MD) simulations, we find that CNTs in lipid membranes readily self-assemble into large clusters. Lipids trapped between the CNTs lubricate CNT repacking upon collisions of diffusing clusters, thereby facilitating the formation of large ordered structures. Cluster diffusion follows the Saffman-Delbrück law and its generalization by Hughes, Pailthorpe, and White. On longer time scales, we expect the formation of close-packed CNT structures by depletion of the intervening shared annular lipid shell, depending on the relative strength of CNT-CNT and CNT-lipid interactions. Our simulations identify CNT length, diameter, and end functionalization as major factors for the self-assembly of CNT membranes.

Development of nano-delivery systems for loaded bioactive compounds: using molecular dynamics simulations

Over the past decade, a remarkable surge in the development of functional nano-delivery systems loaded with bioactive compounds for healthcare has been witnessed. Notably, the demanding requirements of high solubility, prolonged circulation, high tissue penetration capability, and strong targeting ability of nanocarriers have posed interdisciplinary research challenges to the community. While extensive experimental studies have been conducted to understand the construction of nano-delivery systems and their metabolic behavior in vivo, less is known about these molecular mechanisms and kinetic pathways during their metabolic process in vivo, and lacking effective means for high-throughput screening. Molecular dynamics (MD) simulation techniques provide a reliable tool for investigating the design of nano-delivery carriers encapsulating these functional ingredients, elucidating the synthesis, translocation, and delivery of nanocarriers. This review introduces the basic MD principles, discusses how to apply MD simulation to design nanocarriers, evaluates the ability of nanocarriers to adhere to or cross gastrointestinal mucosa, and regulates plasma proteins in vivo. Moreover, we presented the critical role of MD simulation in developing delivery systems for precise nutrition and prospects for the future. This review aims to provide insights into the implications of MD simulation techniques for designing and optimizing nano-delivery systems in the healthcare food industry.

Neighbor List Artifacts in Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are widely used in biophysical research. To aid nonexpert users, most simulation packages provide default values for key input parameters. In MD simulations using the GROMACS package with default parameters, we found large membranes to deform under the action of a semi-isotropically coupled barostat. As the primary cause, we identified overly short outer cutoffs and infrequent neighbor list updates that resulted in missed nonbonded interactions. Small but systematic imbalances in the apparent pressure tensor then induce unphysical asymmetric box deformations that crumple the membrane. We also observed rapid oscillations in averages of the instantaneous pressure tensor components and traced these to the use of a dual pair list with dynamic pruning. We confirmed that similar effects are present in MD simulations of neat water in atomistic and coarse-grained representations. Whereas the slight pressure imbalances likely have minimal impact in most current atomistic MD simulations, we expect their impact to grow in studies of ever-larger systems with coarse-grained representation, in particular, in combination with anisotropic pressure coupling. We present measures to diagnose problems with missed interactions and guidelines for practitioners to avoid them, including estimates for appropriate values for the outer cutoff rl and the number of time steps nstlist between neighbor list updates.

Quantitative Comparison against Experiments Reveals Imperfections in Force Fields' Descriptions of POPC-Cholesterol Interactions

Cholesterol is a central building block in biomembranes, where it induces orientational order, slows diffusion, renders the membrane stiffer, and drives domain formation. Molecular dynamics (MD) simulations have played a crucial role in resolving these effects at the molecular level; yet, it has recently become evident that different MD force fields predict quantitatively different behavior. Although easily neglected, identifying such limitations is increasingly important as the field rapidly progresses toward simulations of complex membranes mimicking the in vivo conditions: pertinent multicomponent simulations must capture accurately the interactions between their fundamental building blocks, such as phospholipids and cholesterol. Here, we define quantitative quality measures for simulations of binary lipid mixtures in membranes against the C-H bond order parameters and lateral diffusion coefficients from NMR spectroscopy as well as the form factors from X-ray scattering. Based on these measures, we perform a systematic evaluation of the ability of commonly used force fields to describe the structure and dynamics of binary mixtures of palmitoyloleoylphosphatidylcholine (POPC) and cholesterol. None of the tested force fields clearly outperforms the others across the tested properties and conditions. Still, the Slipids parameters provide the best overall performance in our tests, especially when dynamic properties are included in the evaluation. The quality evaluation metrics introduced in this work will, particularly, foster future force field development and refinement for multicomponent membranes using automated approaches.

Efficient calculation of the free energy for protein partitioning using restraining potentials

An approach for the efficient simulation of phase-separated lipid bilayers, for use in the calculation of equilibrium free energies of partitioning between lipid domains, is proposed. The methodology exploits restraint potentials and rectangular aspect ratios that enforce lipid phase separation, allowing for the simulation of smaller systems that approximately reproduce bulk behavior. The utility of this approach is demonstrated through the calculation of potentials of mean force for the translation of a transmembrane protein between lipid domains. The impact of the imposed restraints on lipid tail ordering and lipid packing are explored, providing insight into how restraints can best be employed to compute accurate free-energy surfaces. This approach should be useful in the accurate calculation of equilibrium partition coefficients for transmembrane protein partitioning in heterogeneous membranes, providing insight into the thermodynamic driving forces that control this fundamental biophysical phenomenon.

Coarse-grained molecular simulation of extracellular vesicle squeezing for drug loading

In recent years, extracellular vesicles have become promising carriers as next-generation drug delivery platforms. Effective loading of exogenous cargos without compromising the extracellular vesicle membrane is a major challenge. Rapid squeezing through nanofluidic channels is a widely used approach to load exogenous cargoes into the EV through the nanopores generated temporarily on the membrane. However, the exact mechanism and dynamics of nanopore opening, as well as cargo loading through nanopores during the squeezing process remains unknown and it is impossible to visualize or quantify it experimentally due to the small size of the EV and the fast transient process. This paper developed a systemic algorithm to simulate nanopore formation and predict drug loading during extracellular vesicle (EV) squeezing by leveraging the power of coarse-grain (CG) molecular dynamics simulations with fluid dynamics. The EV CG beads are coupled with implicit the fluctuating lattice Boltzmann solvent. The effects of EV properties and various squeezing test parameters, such as EV size, flow velocity, channel width, and length, on pore formation and drug loading efficiency are analyzed. Based on the simulation results, a phase diagram is provided as a design guide for nanochannel geometry and squeezing velocity to generate pores on the membrane without damaging the EV. This method can be utilized to optimize the nanofluidic device configuration and flow setup to obtain desired drug loading into EVs.

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.

Structure of POPC Lipid Bilayers in OPLS3e Force Field

It is crucial for molecular dynamics simulations of biomembranes that the force field parameters give a realistic model of the membrane behavior. In this study, we examined the OPLS3e force field for the carbon-hydrogen order parameters S_CH of POPC (1-palmitoyl-2-oleoylphosphatidylcholine) lipid bilayers at varying hydration conditions and ion concentrations. The results show that OPLS3e behaves similarly to the CHARMM36 force field and relatively accurately follows the experimentally measured S_CH for the lipid headgroup, the glycerol backbone, and the acyl tails. Thus, OPLS3e is a good choice for POPC bilayer simulations under many biologically relevant conditions. The exception are systems with an abundancy of ions, as similarly to most other force fields OPLS3e strongly overestimates the membrane-binding of cations, especially Ca²⁺. This leads to undesirable positive charge of the membrane surface and drastically lowers the concentration of Ca²⁺ in the surrounding solvent, which might cause issues in systems sensitive to correct charge distribution profiles across the membrane.

Improved Coarse-Grained Model for Nanoparticles Based on the Martini Force Field and Its Application in Molecular Dynamics Simulation on Gel Ink

Research on the dispersion and stability of nanoparticles in liquid media is one of the key subjects for nanomaterial utilization. In consideration of the preponderance of coarse-grained (CG) molecular dynamics (MD) simulation in following and understanding the structure and dynamics on the nanoscale, an improved CG model for nanoparticles based on the Martini force field is established to facilitate the more extensive applications of this simulation method and further studies on complex nanoparticle liquid systems. Gel ink is selected as the liquid system for nanoparticles to validate the improved CG model on the one hand and introduce the CGMD simulation method into the studies of this system on the other. The calculation shows that the improved model can provide relatively precise results and has good computational stability. The effect mechanisms of the thickener and disperser on the carbon black nanoparticle are similar, namely the result of a delicate balance between the interaction of the thickener/disperser with the carbon black nanoparticle and the interaction of the thickener and disperser with each other. Furthermore, the phase assimilating effect of disperser molecules is key for separating the agglomerated carbon black nanoparticles; thereafter, the space steric hindrance effect and the electrostatic hindrance effect play main roles in maintaining the dispersion of carbon black nanoparticles.

Small ionic radii limit time step in Martini 3 molecular dynamics simulations

Among other improvements, the Martini~3 coarse-grained force field provides a more accurate description of the solvation of protein pockets and channels through the consistent use of various bead types and sizes. Here, we show that the representation of Na+ and Cl- ions as ``tiny' (TQ5) beads limits the accessible time step to 25~fs. By contrast, with Martini~2, time steps of 30-40~fs were possible for lipid bilayer systems without proteins. This limitation is relevant for systems that require long equilibration times. We derive a quantitative kinetic model of time-integration instabilities in molecular dynamics as a function of time step, ion concentration and mass, system size, and simulation time. We demonstrate that ion-water interactions are the main source of instability at physiological conditions, followed closely by ion-ion interactions. We show that increasing the ionic masses makes it possible to use time steps up to 40~fs with minimal impact on static equilibrium properties and on dynamical quantities such as lipid and ion diffusion coefficients. Increasing the size of the bead representing the ions (and thus changing their hydration) also permits longer time steps. For a soluble protein, we find that increasing the mass of tiny beads also on the protein permits simulations with 30-fs time step. The use of larger time steps in Martini~3 results in a more efficient exploration of configuration space. The kinetic model of MD simulation crashes can be used to determine the maximum allowed time step upfront for an efficient use of resources and whenever sampling efficiency is critical.

Rotational Dynamics of The Transmembrane Domains Play an Important Role in Peptide Dynamics of Viral Fusion and Ion Channel Forming Proteins—A Molecular Dynamics Simulation Study

Focusing on the transmembrane domains (TMDs) of viral fusion and channel-forming proteins (VCPs), experimentally available and newly generated peptides in an ideal conformation of the S and E proteins of severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) and SARS-CoV, gp41 and Vpu, both of human immunodeficiency virus type 1 (HIV-1), haemagglutinin and M2 of influenza A, as well as gB of herpes simplex virus (HSV), are embedded in a fully hydrated lipid bilayer and used in multi-nanosecond molecular dynamics simulations. It is aimed to identify differences in the dynamics of the individual TMDs of the two types of viral membrane proteins. The assumption is made that the dynamics of the individual TMDs are decoupled from their extra-membrane domains, and that the mechanics of the TMDs are distinct from each other due to the different mechanism of function of the two types of proteins. The diffusivity coefficient (DC) of the translational and rotational diffusion is decreased in the oligomeric state of the TMDs compared to those values when calculated from simulations in their monomeric state. When comparing the calculations for two different lengths of the TMD, a longer full peptide and a shorter purely TMD stretch, (i) the difference of the calculated DCs begins to level out when the difference exceeds approximately 15 amino acids per peptide chain, and (ii) the channel protein rotational DC is the most affected diffusion parameter. The rotational dynamics of the individual amino acids within the middle section of the TMDs of the fusion peptides remain high upon oligomerization, but decrease for the channel peptides, with an increasing number of monomers forming the oligomeric state, suggesting an entropic penalty on oligomerization for the latter.

A vesicle microrheometer for high-throughput viscosity measurements of lipid and polymer membranes

Viscosity is a key property of cell membranes that controls mobility of embedded proteins and membrane remodeling. Measuring it is challenging because existing approaches involve complex experimental designs and/or models, and the applicability of some methods is limited to specific systems and membrane compositions. As a result there is scarcity of systematic data, and the reported values for membrane viscosity vary by orders of magnitude for the same system. Here, we show how viscosity of membranes can be easily obtained from the transient deformation of giant unilamellar vesicles. The approach enables a noninvasive, probe-independent, and high-throughput measurement of the viscosity of membranes made of lipids or polymers with a wide range of compositions and phase state. Using this novel method, we have collected a significant amount of data that provides insights into the relation between membrane viscosity, composition, and structure.

The ugly, bad, and good stories of large-scale biomolecular simulations

Molecular modeling of large biomolecular assemblies exemplifies a disruptive area holding both promises and contentions. Propelled by peta and exascale computing, several simulation methodologies have now matured into user-friendly tools that are successfully employed for modeling viruses, membranous nano-constructs, and key pieces of the genetic machinery. We present three unifying biophysical themes that emanate from some of the most recent multi-million atom simulation endeavors. Despite connecting molecular changes with phenotypic outcomes, the quality measures of these simulations remain questionable. We discuss the existing and upcoming strategies for constructing representative ensembles of large systems, how new computing technologies will boost this area, and make a point that integrative modeling guided by experimental data is the future of biomolecular computations.

Automatic multi-objective optimization of coarse-grained lipid force fields using SwarmCG

The development of coarse-grained (CG) molecular models typically requires a time-consuming iterative tuning of parameters in order to have the approximated CG models behave correctly and consistently with, e.g., available higher-resolution simulation data and/or experimental observables. Automatic data-driven approaches are increasingly used to develop accurate models for molecular dynamics simulations. However, the parameters obtained via such automatic methods often make use of specifically designed interaction potentials and are typically poorly transferable to molecular systems or conditions other than those used for training them. Using a multi-objective approach in combination with an automatic optimization engine (SwarmCG), here, we show that it is possible to optimize CG models that are also transferable, obtaining optimized CG force fields (FFs). As a proof of concept, here, we use lipids for which we can avail reference experimental data (area per lipid and bilayer thickness) and reliable atomistic simulations to guide the optimization. Once the resolution of the CG models (mapping) is set as an input, SwarmCG optimizes the parameters of the CG lipid models iteratively and simultaneously against higher-resolution simulations (bottom-up) and experimental data (top-down references). Including different types of lipid bilayers in the training set in a parallel optimization guarantees the transferability of the optimized lipid FF parameters. We demonstrate that SwarmCG can reach satisfactory agreement with experimental data for different resolution CG FFs. We also obtain stimulating insights into the precision-resolution balance of the FFs. The approach is general and can be effectively used to develop new FFs and to improve the existing ones.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Anisotropic diffusion of membrane proteins at experimental timescales

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D_r)^-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.

pyPolyBuilder: Automated Preparation of Molecular Topologies and Initial Configurations for Molecular Dynamics Simulations of Arbitrary Supramolecules

The construction of a molecular topology file is a prerequisite for any classical molecular dynamics simulation. However, the generation of such a file may be very challenging at times, especially for large supramolecules. While many tools are available to provide topologies for large proteins and other biomolecules, the scientific community researching nonbiological systems is not equally well equipped. Here, we present a practical tool to generate topologies for arbitrary supramolecules: The pyPolyBuilder. In addition to linear polymer chains, it also provides the possibility to generate topologies of arbitrary, large, branched molecules, such as, e.g., dendrimers. Furthermore, it also generates reasonable starting structures for simulations of these molecules. pyPolyBuilder is a standalone command-line tool implemented in python. Therefore, it may be easily incorporated in persisting simulation pipelines on any operating systems and with different simulation engines. pyPolyBuilder is freely available on github: https://github.com/mssm-labmmol/pypolybuilder.

Martini 3: a general purpose force field for coarse-grained molecular dynamics

The coarse-grained Martini force field is widely used in biomolecular simulations. Here we present the refined model, Martini 3 ( http://cgmartini.nl ), with an improved interaction balance, new bead types and expanded ability to include specific interactions representing, for example, hydrogen bonding and electronic polarizability. The updated model allows more accurate predictions of molecular packing and interactions in general, which is exemplified with a vast and diverse set of applications, ranging from oil/water partitioning and miscibility data to complex molecular systems, involving protein-protein and protein-lipid interactions and material science applications as ionic liquids and aedamers.

Using multiscale molecular dynamics simulations to obtain insights into pore forming toxin mechanisms

Pore forming toxins (PFTs) are virulent proteins released by several species, including many strains of bacteria, to attack and kill host cells. In this article, we focus on the utility of molecular dynamics (MD) simulations and the molecular insights gleaned from these techniques on the pore forming pathways of PFTs. In addition to all-atom simulations which are widely used, coarse-grained MARTINI models and structure-based models have also been used to study PFTs. Here, the emphasis is on methods and techniques involved while setting up, monitoring, and evaluating properties from MD simulations of PFTs in a membrane environment. We draw from several case studies to illustrate how MD simulations have provided molecular insights into protein-protein and protein-lipid interactions, lipid dynamics, conformational transitions and structures of both the oligomeric intermediates and assembled pore structures.

Simulation of FUS Protein Condensates with an Adapted Coarse-Grained Model

Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01-0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625-0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Optimal estimates of self-diffusion coefficients from molecular dynamics simulations

Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules. Nonlinearities in MSD curves at short times are handled with a wide variety of ad hoc practices, such as partial and piece-wise fitting of the data. Here, we present a rigorous framework to obtain reliable estimates of the self-diffusion coefficient and its statistical uncertainty. We also assess in a quantitative manner if the observed dynamics is, indeed, diffusive. By accounting for correlations between MSD values at different times, we reduce the statistical uncertainty of the estimator and, thereby, increase its efficiency. With a Kolmogorov-Smirnov test, we check for possible anomalous diffusion. We provide an easy-to-use Python data analysis script for the estimation of self-diffusion coefficients. As an illustration, we apply the formalism to molecular dynamics simulation data of pure TIP4P-D water and a single ubiquitin protein. In another paper [S. von Bülow, J. T. Bullerjahn, and G. Hummer, J. Chem. Phys. 153, 021101 (2020)], we demonstrate its ability to recognize deviations from regular diffusion caused by systematic errors in a common trajectory "unwrapping" scheme that is implemented in popular simulation and visualization software.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Modelling lipid systems in fluid with Lattice Boltzmann Molecular Dynamics simulations and hydrodynamics

In this work we present the coupling between Dry Martini, an efficient implicit solvent coarse-grained model for lipids, and the Lattice Boltzmann Molecular Dynamics (LBMD) simulation technique in order to include naturally hydrodynamic interactions in implicit solvent simulations of lipid systems. After validating the implementation of the model, we explored several systems where the action of a perturbing fluid plays an important role. Namely, we investigated the role of an external shear flow on the dynamics of a vesicle, the dynamics of substrate release under shear, and inquired the dynamics of proteins and substrates confined inside the core of a vesicle. Our methodology enables future exploration of a large variety of biological entities and processes involving lipid systems at the mesoscopic scale where hydrodynamics plays an essential role, e.g. by modulating the migration of proteins in the proximity of membranes, the dynamics of vesicle-based drug delivery systems, or, more generally, the behaviour of proteins in cellular compartments.

Motion of objects embedded in lipid bilayer membranes: Advection and effective viscosity

An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g., proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid-body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two prior analytical predictions from the literature. Effective viscosity predictions for a dilute suspension of rod-shaped objects in the membrane are also presented.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Lipid Head Group Parameterization for GROMOS 54A8: A Consistent Approach with Protein Force Field Description

Membranes are a crucial component of both bacterial and mammalian cells, being involved in signaling, transport, and compartmentalization. This versatility requires a variety of lipid species to tailor the membrane’s behavior as needed, increasing the complexity of the system. Molecular dynamics simulations have been successfully applied to study model membranes and their interactions with proteins, elucidating some crucial mechanisms at the atomistic detail and thus complementing experimental techniques. An accurate description of the functional interplay of the diverse membrane components crucially depends on the selected parameters that define the adopted force field. A coherent parameterization for lipids and proteins is therefore needed. In this work, we propose and validate new lipid head group parameters for the GROMOS 54A8 force field, making use of recently published parametrizations for key chemical moieties present in lipids. We make use additionally of a new canonical set of partial charges for lipids, chosen to be consistent with the parameterization of soluble molecules such as proteins. We test the derived parameters on five phosphocholine model bilayers, composed of lipid patches four times larger than the ones used in previous studies, and run 500 ns long simulations of each system. Reproduction of experimental data like area per lipid and deuterium order parameters is good and comparable with previous parameterizations, as well as the description of liquid crystal to gel-phase transition. On the other hand, the orientational behavior of the head groups is more realistic for this new parameter set, and this can be crucial in the description of interactions with other polar molecules. For that reason, we tested the interaction of the antimicrobial peptide lactoferricin with two model membranes showing that the new parameters lead to a weaker peptide–membrane binding and give a more realistic outcome in comparing binding to antimicrobial versus mammal membranes.

Finite-Size-Corrected Rotational Diffusion Coefficients of Membrane Proteins and Carbon Nanotubes from Molecular Dynamics Simulations

We investigate system-size effects on the rotational diffusion of membrane proteins and other membrane-embedded molecules in molecular dynamics simulations. We find that the rotational diffusion coefficient slows down relative to the infinite-system value by a factor of one minus the ratio of protein and box areas. This correction factor follows from the hydrodynamics of rotational flows under periodic boundary conditions and is rationalized in terms of Taylor–Couette flow. For membrane proteins like transporters, channels, or receptors in typical simulation setups, the protein-covered area tends to be relatively large, requiring a significant finite-size correction. Molecular dynamics simulations of the protein adenine nucleotide translocase (ANT1) and of a carbon nanotube porin in lipid membranes show that the hydrodynamic finite-size correction for rotational diffusion is accurate in standard-use cases. The dependence of the rotational diffusion on box size can be used to determine the membrane viscosity.

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.

Molecular Dynamics Simulations of Membrane Permeability

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

The Devil Is in the Details: What Do We Really Track in Single-Particle Tracking Experiments of Diffusion in Biological Membranes?

Single-particle tracking (SPT) is an experimental technique that allows one to follow the dynamics of individual molecules in biological membranes with unprecedented precision. Given the importance of lipid and membrane protein diffusion in the formation of nanoscale functional complexes, it is critical to understand what exactly is measured in SPT experiments. To clarify this issue, we employed nanoscale computer simulations designed to match SPT experiments that exploit streptavidin-functionalized Au nanoparticles (AuNPs). The results show that lipid labeling interferes critically with the diffusion process; thus, the diffusion measured in SPT is a far more complex process than what has been assumed. It turns out that the influence of AuNP-based labels on the dynamics of probe lipids includes not only the AuNP-induced viscous drag that is the more significant the larger the NP but, more importantly, also the effects related to the interactions of the streptavidin linker with membrane lipids. Due to these effects, the probe lipid moves in a concerted manner as a complex with the linker protein and numerous unlabeled lipids, which can slow down the motion of the probe by almost an order of magnitude. Furthermore, our simulations show that nonlinker streptavidin tetramers on the AuNP surface are able to interact with the membrane lipids, which could potentially lead to multivalent labeling of the NPs by the probe lipids. Our results further demonstrate that in the submicrosecond time domain the motion of the probe lipid is uncorrelated with the motion of the AuNP, showing that there is a 1 μs limit for the temporal resolution of the SPT technique. However, this limit for the temporal resolution depends on the nanoparticle size and increases rapidly with growing AuNPs. Overall, the results provide a molecular-scale framework to accurately interpret SPT data and to design protocols that minimize label-induced artifacts.

Influence of Bilayer Size and Number in Multi-Bilayer DOPC Simulations at Full and Low Hydration

Biophysical studies of model cell membranes at full and low hydration are usually carried out using scattering measurements on multi-bilayer systems. Molecular simulations of lipid bilayers aimed at reproducing those experimental conditions are usually conducted using single bilayers with different amounts of water. These simulation conditions may lead to artifacts arising from size effects and self-interactions because of periodic boundary conditions. We have tested the influence of the size and number of bilayers on membrane properties using the Lipid14 force field for lipids in molecular dynamics simulations of 1,2-dioleoyl- sn-glycero-3-phosphocholine bilayers at full hydration (44 water molecules per lipid), low hydration (18 water molecules per lipid), and dehydration (9 water molecules per lipid). A number of additional simulations were conducted with the Slipids force field for comparison. We have found that the average area per lipid (APL), thickness, mass density profiles, and acyl tail order parameters are insensitive to the size and the number of bilayers for all hydration states. The Lipid14 force field can also successfully reproduce the experimentally observed decrease in APL and corresponding increase in bilayer thickness upon dehydration, reflecting the increase in ordering as the system becomes more gel-like. Additionally, decreasing hydration levels were associated with a trend away from normal lateral diffusion and toward more subdiffusive regimes across both force fields. In summary, at least for the Lipid14 force field, the use of a single bilayer with 128 phospholipid molecules provides an adequate representation of multi-bilayer systems at varying levels of hydration.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Formation of α-helical and β-sheet structures in membrane-bound human IAPP monomer and the resulting membrane deformation

Upon adsorption on membrane, human IAPP monomer takes conformational changes from coils to α-helices and β-sheets. The helices inserted and β on surface cause different types of membrane deformation, implying two distinct aggregation mechanisms.