Computational determination of the equilibrium state of heterogeneous phospholipid mem-branes is a significant challenge. We wish to explore the rich phase diagram of these multi-component systems. However, the diffusion and mixing times in membranes are long com-pared to typical times of computer simulations. To speed up the relaxation times, advanced simulation methods are used. We evaluate the combination of enhanced sampling tech-niques such as MDAS (Molecular Dynamics with Alchemical Steps) and MC-MD (Monte Carlo with Molecular Dynamics) with a coarse-grained model of membranes (Martini) to re-duce the number of steps and force evaluations that are needed to reach equilibrium. We illustrate a significant gain compared to straightforward Molecular Dynamics of the Martini model by factors between three to ten. The combination is a useful tool to enhance the study of phase separation and the formation of domains in biological membranes.
Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.
Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hyp…
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as $1/r^2$ with interparticle distance $r$. For the common case, where the distance to the substrate is of sub-micron scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbi…
Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased Molecular Dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step towards determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a singl…
We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point, and macroscopic domain formation does not occur. Instead, there is only one phase. This phase is highly heterogeneous, with a structure consisting of micro-domains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is t…
Lipid rafts are heterogeneous dynamic lipid domains of the cell membranes that are involved in several biological processes, like protein and lipids specific transport and signaling. Our understanding of lipid raft formation is still limited, due to the transient and elusive nature of these domains {\it in vivo}, in contrast to the stable phase-separated domains observed in artificial membranes. Inspired by experimental findings highlighting the relevance of transmembrane proteins for lipid rafts, we investigate lipid domain nucleation by coarse-grained molecular dynamics and Ising model simul…
It is difficult to observe a spontaneous translocation of cell-penetrating peptides(CPPs) within a short time scale (e.g., a few hundred ns) in all-atom molecular dynamics(MD) simulations because the time required for the translocation of usual CPPs is on the order of minutes or so. In this work, we report a spontaneous translocation of a single Arg$_9$(R9) across a DOPC/DOPG(4:1) model membrane within an order of a few tens ns scale by using the weighted ensemble(WE) method. We identify how water molecules and the orientation of Arg$_9$ play a role in translocation. We also show how lipid mol…
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic…
Recent experiments have shown that trivalent ion, spermidine$^{3+}$, can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of t…
Mixtures of lipids and cholesterol are commonly used as model systems for studying the formation of liquid-ordered ($L_o$) domains in heterogeneous biological membranes. The simplest model system exhibiting coexistence between $L_o$ domains and a liquid-disordered ($L_d$) matrix is that of a binary mixture of saturated lipids like DPPC and cholesterol (Chol). DPPC/Chol mixtures have been investigated for decades both experimentally, theoretically, and recently also by means of atomistic simulations. Here, we present a minimal lattice model that captures the correct behavior of this mixture acr…
Recent developments in enhanced sampling methods showed that it is possible to reconstruct ligand unbinding pathways with spatial and temporal resolution inaccessible to experiments. Ideally, such techniques should provide an atomistic definition of possibly many reaction pathways, because crude estimates may lead either to overestimating energy barriers, or inability to sample hidden energy barriers that are not captured by reaction pathway estimates. Here we provide an implementation of a new method [J. Rydzewski \& O. Valsson, J. Chem. Phys. {\bf 150}, 221101 (2019)] dedicated entirely to s…
The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales . In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampl…
We performed "weighted ensemble" path-sampling simulations of adenylate kinase, using several semi-atomistic protein models. Our study investigated both the biophysics of conformational transitions as well as the possibility of increasing model accuracy without sacrificing good sampling. Biophysically, the path ensembles show significant heterogeneity and the explicit possibility of two principle pathways in the Open-Closed transition. We recently showed, under certain conditions, a "symmetry of hetereogeneity" is expected between the forward and the reverse transitions: the fraction of transi…
According to the lipid raft hypothesis, biological lipid membranes are laterally heterogeneous and filled with nanoscale ordered "raft" domains, which are believed to play an important role for the organization of proteins in membranes. However, the mechanisms stabilizing such small rafts are not clear, and even their existence is sometimes questioned. Here we report the observation of raft-like structures in a coarse-grained molecular model for multicomponent lipid bilayers. On small scales, our membranes demix into a liquid ordered (lo) and a liquid disordered (ld) phase. On large scales, ph…
Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensionalmotions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hem…
