Confined run-and-tumble particles with non-Markovian tumbling statistics.

Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution g(t) of waiting times between tumbling events whose mean value is equal to τ. Unless g(t) is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviation and/or small-τ regime, where the SSD can be related to the the large-deviation function, s(x), via the scaling relation P_{st}(x)∼e^{-s(x)/τ}.

Characterizing the heterogeneity of membrane liquid-ordered domains.

We use a lattice model of a ternary mixture containing saturated and unsaturated lipids with cholesterol (Chol), to study the structural properties characterizing the coexistence between the liquid-disordered and liquid-ordered phases. Depending on the affinity of the saturated and unsaturated lipids, the system may exhibit macroscopic (thermodynamic) liquid-liquid phase separation or be divided into small-size liquid-ordered domains surrounded by a liquid-disordered matrix. In both cases, it is found that the nanoscale structure of the liquid-ordered regions is heterogeneous, and that they are partitioned into Chol-rich sub-domains and Chol-free, gel-like, nano-clusters. This emerges as a characteristic feature of the liquid-ordered state, which helps distinguishing between liquid-ordered domains in a two-phase mixture, and similar-looking domains in a one-phase mixture that are rich in saturated lipids and Chol, but are merely thermal density fluctuations. The nano-structure heterogeneity of the liquid-ordered phase can be detected by suitable experimental spectroscopic methods and is observed also in atomistic computer simulations.

A lattice model of ternary mixtures of lipids and cholesterol with tunable domain sizes.

Much of our understanding of the physical properties of raft domains in biological membranes, and some insight into the mechanisms underlying their formation stem from atomistic simulations of simple model systems, especially ternary mixtures consisting of saturated and unsaturated lipids, and cholesterol (Chol). To explore the properties of such systems at large spatial scales, we here present a simple ternary mixture lattice model, involving a small number of nearest neighbor interaction terms. Monte Carlo simulations of mixtures with different compositions show excellent agreement with experimental and atomistic simulation observations across multiple scales, ranging from the local distributions of lipids to the phase diagram of the system. The simplicity of the model allows us to identify the roles played by the different interactions between components, and the interplay between them. Importantly, by changing the value of one of the model parameters, we can tune the size of the liquid-ordered domains, thereby simulating both Type II mixtures exhibiting macroscopic phase separation and Type I mixtures with nanoscopic domains. The Type II mixture simulation results fit well to the experimentally determined phase diagram of mixtures containing saturated DPPC/unsaturated DOPC/Chol. When the tunable parameter is changed, we obtain the Type I version of DPPC/DOPC/Chol, i.e., a mixture not showing thermodynamic phase transitions but one that may be fitted to the same phase diagram if local measures are used to distinguish between the different states. Our model results suggest that short range packing is likely to be a key regulator of the stability and size distribution of biological rafts.

300-Times-Increased Diffusive Skyrmion Dynamics and Effective Pinning Reduction by Periodic Field Excitation.

Thermally induced skyrmion dynamics, as well as skyrmion pinning effects, in thin films have attracted significant interest. While pinning poses challenges in deterministic skyrmion devices and slows down skyrmion diffusion, for applications in non-conventional computing, both pinning of an appropriate strength and skyrmion diffusion speed are key. Here, periodic field excitations are employed to realize an increase of the skyrmion diffusion by more than two orders of magnitude. Amplifying the excitation, a drastic reduction of the effective skyrmion pinning, is reported, and a transition from pinning-dominated diffusive hopping to dynamics approaching free diffusion is observed. By tailoring the field oscillation frequency and amplitude, a continuous tuning of the effective pinning and skyrmion dynamics is demonstrated, which is a key asset and enabler for non-conventional computing applications. It is found that the periodic excitations additionally allow stabilization of skyrmions at different sizes for field values that are inaccessible in static systems, opening up new approaches to ultrafast skyrmion motion by transiently exciting moving skyrmions.

Nonequilibrium steady state for harmonically confined active particles.

We study the full nonequilibrium steady-state distribution P_{st}(X) of the position X of a damped particle confined in a harmonic trapping potential and experiencing active noise whose correlation time τ_{c} is assumed to be very short. Typical fluctuations of X are governed by a Boltzmann distribution with an effective temperature that is found by approximating the noise as white Gaussian thermal noise. However, large deviations of X are described by a non-Boltzmann steady-state distribution. We find that, in the limit τ_{c}→0, they display the scaling behavior P_{st}(X)∼e^{-s(X)/τ_{c}}, where s(X) is the large-deviation function. We obtain an expression for s(X) for a general active noise and calculate it exactly for the particular case of telegraphic (dichotomous) noise.

Thermodynamics of a Brownian particle in a nonconfining potential.

We consider the overdamped Brownian dynamics of a particle starting inside a square potential well which, upon exiting the well, experiences a flat potential where it is free to diffuse. We calculate the particle's probability distribution function (PDF) at coordinate x and time t, P(x,t), by solving the corresponding Smoluchowski equation. The solution is expressed by a multipole expansion, with each term decaying t^{1/2} faster than the previous one. At asymptotically large times, the PDF outside the well converges to the Gaussian PDF of a free Brownian particle. The average energy, which is proportional to the probability of finding the particle inside the well, diminishes as E∼1/t^{1/2}. Interestingly, we find that the free energy of the particle, F, approaches the free energy of a freely diffusing particle, F_{0}, as δF=F-F_{0}∼1/t, i.e., at a rate faster than E. We provide analytical and computational evidence that this scaling behavior of δF is a general feature of Brownian dynamics in nonconfining potential fields. Furthermore, we argue that δF represents a diminishing entropic component which is localized in the region of the potential, and which diffuses away with the spreading particle without being transferred to the heat bath.

A Langevin dynamics approach for multi-layer mass transfer problems.

We use Langevin dynamics simulations to study the mass diffusion problem across two adjacent porous layers of different transport properties. At the interface between the layers, we impose the Kedem-Katchalsky (KK) interfacial boundary condition that is well suited in a general situation. A detailed algorithm for the implementation of the KK interfacial condition in the Langevin dynamics framework is presented. As a case study, we consider a two-layer diffusion model of a drug-eluting stent. The simulation results are compared with those obtained from the solution of the corresponding continuum diffusion equation, and an excellent agreement is shown.

Reactive Momentum Transfer Contributes to the Self-Propulsion of Janus Particles.

We report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system's short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.

Defining velocities for accurate kinetic statistics in the Grønbech-Jensen Farago thermostat.

We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Grønbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite-difference approximations to the velocity, we arrive at two main conclusions: (1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and (2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.

A simple statistical-mechanical interpretation of Onsager reciprocal relations and Derjaguin theory of thermo-osmosis.

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing "thermo-osmotic" flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: i) an incopressible continuum solvent containing non-interacting solute particles, and ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly charged surface in the strong screening (Debye-Hückel) regime.

Different measures for characterizing the motion of molecules along a temperature gradient.

We study the motion of a Brownian particle in a medium with inhomogeneous temperature. In the overdamped regime of low Reynolds numbers, the probability distribution function (PDF) of the particle is obtained from the van Kampen diffusion equation [J. Phys. Chem. Solids 49, 673 (1988)JPCSAW0022-369710.1016/0022-3697(88)90199-0]. The thermophoretic behavior is commonly described by the Soret coefficient, a parameter that can be calculated from the steady-state PDF. Motivated by recent advances in experimental methods for observing and analyzing single nanoparticle trajectories, we here consider the time-dependent van Kampen equation from which the temporal evolution of the PDF of individual particles can be derived. We analytically calculate the PDF describing dynamics driven by a generalized thermophoretic force. Single-particle statistics are characterized by measures such as the mean displacement (drift) and the probability difference between moving along and against the temperature gradient (bias). We demonstrate that these quantities do not necessarily have the same sign as the Soret coefficient, which causes ambiguity in the distinction between thermophilic and thermophobic response (i.e., migration in and against the direction of the temperature gradient). The different factors determining the thermophoretic response and their influence on each measure are discussed.

Non-steady-state diffusion in two-dimensional periodic channels.

The dynamics of a freely diffusing particle in a two-dimensional channel with cross-sectional area A(x) can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force U(x)=-k_{B}Tln[A(x)] (where k_{B}T is the thermal energy) in a system with a spatially dependent diffusion coefficient D(x). Several attempts to derive expressions relating D(x) to A(x) and its derivatives have been made, which were based on considering stationary flows in periodic channels. Here we take an alternative approach and consider non-steady-state single-particle diffusion in an open periodic channel. The approach allows us to express D(x) as a series of terms of increasing powers of ε-a parameter associated with the aspect ratio of the channel. When the expansion is truncated at the leading term, we recover the expression suggested by Zwanzig [J. Phys. Chem. 96, 3926 (1992)10.1021/j100189a004] for D(x). Furthermore, comparison of the first few terms in our expansion for D(x) with the one proposed by Kalinay and Percus [Phys. Rev. E 74, 041203 (2006)10.1103/PhysRevE.74.041203] shows that they are consistent with each other. In the limit of long-wavelength channels (ε≪1), the expansion converges rapidly and the leading approximation provides a very accurate description of the two-dimensional dynamics. For short-wavelength channels, the expansion does not converge and the validity of the effective one-dimensional description is questionable.

Interplay between membrane elasticity and active cytoskeleton forces regulates the aggregation dynamics of the immunological synapse.

Adhesion between a T cell and an antigen presenting cell is achieved by TCR-pMHC and LFA1-ICAM1 protein complexes. These segregate to form a special pattern, known as the immunological synapse (IS), consisting of a central quasi-circular domain of TCR-pMHC bonds surrounded by a peripheral domain of LFA1-ICAM1 complexes. Insights gained from imaging studies had led to the conclusion that the formation of the central adhesion domain in the IS is driven by active (ATP-driven) mechanisms. Recent studies, however, suggested that passive (thermodynamic) mechanisms may also play an important role in this process. Here, we present a simple physical model, taking into account the membrane-mediated thermodynamic attraction between the TCR-pMHC bonds and the effective forces that they experience due to ATP-driven actin retrograde flow and transport by dynein motor proteins. Monte Carlo simulations of the model exhibit a good spatio-temporal agreement with the experimentally observed pattern evolution of the TCR-pMHC microclusters. The agreement is lost when one of the aggregation mechanisms is "muted", which helps to identify their respective roles in the process. We conclude that actin retrograde flow drives the centripetal motion of TCR-pMHC bonds, while the membrane-mediated interactions facilitate microcluster formation and growth. In the absence of dynein motors, the system evolves into a ring-shaped pattern, which highlights the role of dynein motors in the formation of the final concentric pattern. The interplay between the passive and active mechanisms regulates the rate of the accumulation process, which in the absence of one them proceeds either too quickly or slowly.

Noise-induced drift in two-dimensional anisotropic systems.

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Isothermal Langevin dynamics in systems with power-law spatially dependent friction.

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

Formation of semi-dilute adhesion domains driven by weak elasticity-mediated interactions.

Cell-cell adhesion is established by specific binding of receptor and ligand proteins anchored in the cell membranes. The adhesion bonds attract each other and often aggregate into large clusters that are central to many biological processes. One possible origin of attractive interactions between adhesion bonds is the elastic response of the membranes to their deformation by the bonds. Here, we analyze these elasticity-mediated interactions using a novel mean-field approach. Our analysis of systems at different densities of bonds, ϕ, reveals that the phase diagram, i.e., the binodal and spinodal lines, exhibit a nearly universal behavior when the temperature T is plotted against the scaled density x = ϕξ(2), where ξ is the linear size of the membrane's region affected by the presence of a single isolated bond. The critical point (ϕc , Tc) is located at very low densities, and slightly below Tc we identify phase coexistence between two low-density phases. Dense adhesion domains are observed only when the height by which the bonds deform the membranes, h0, is much larger than their thermal roughness, Δ, which occurs at very low temperatures T≪Tc. We, thus, conclude that the elasticity-mediated interactions are weak and cannot be regarded as responsible for the formation of dense adhesion domains. The weakness of the elasticity-mediated effect and its relevance to dilute systems only can be attributed to the fact that the membrane's elastic energy saturates in the semi-dilute regime, when the typical spacing between the bonds r≳ξ, i.e., for x≲ 1. Therefore, at higher densities, only the mixing entropy of the bonds (which always favors uniform distributions) is thermodynamically relevant. We discuss the implications of our results for the question of immunological synapse formation, and demonstrate that the elasticity-mediated interactions may be involved in the aggregation of these semi-dilute membrane domains.

On the connection between dissipative particle dynamics and the Itô-Stratonovich dilemma.

Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system particles, thus allowing them to overlap. This supposedly permits relatively large integration time steps, which is an important feature for simulations on large temporal scales. In practice, however, an increase in the integration time step leads to increasingly larger systematic errors in the sampling statistics. Here, we demonstrate that the prime origin of these systematic errors is the multiplicative nature of the thermal noise term in Langevin's equation, i.e., the fact that it depends on the instantaneous coordinates of the particles. This lead to an ambiguity in the interpretation of the stochastic differential Langevin equation, known as the Itô-Stratonovich dilemma. Based on insights from previous studies of the dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an order of magnitude improvement in accuracy, and nearly twice the efficiency of commonly used DPD Langevin thermostats.

Correction: The thermodynamics of endosomal escape and DNA release from lipoplexes.

Correction for 'The thermodynamics of endosomal escape and DNA release from lipoplexes' by Yotam Y. Avital et al., Phys. Chem. Chem. Phys., 2016, 18, 2591-2596.

The thermodynamics of endosomal escape and DNA release from lipoplexes.

Complexes of cationic and neutral lipids and DNA (lipoplexes) are emerging as promising vectors for gene therapy applications. Their appeal stems from their non pathogenic nature and the fact that they self-assemble under conditions of thermal equilibrium. Lipoplex adhesion to the cell plasma membrane initiates a three-stage process termed transfection, consisting of (i) endocytosis, (ii) lipoplex breakdown, and (iii) DNA release followed by gene expression. As successful transfection requires lipoplex degradation, it tends to be hindered by the lipoplex thermodynamic stability; nevertheless, it is known that the transfection process may proceed spontaneously. Here, we use a simple model to study the thermodynamic driving forces governing transfection. We demonstrate that after endocytosis [stage (i)], the lipoplex becomes inherently unstable. This instability, which is triggered by interactions between the cationic lipids of the lipoplex and the anionic lipids of the enveloping plasma membrane, is entropically controlled involving both remixing of the lipids and counterions release. Our detailed calculation shows that the free energy gain during stage (ii) is approximately linear in Φ+, the mole fraction of cationic lipids in the lipoplex. This free energy gain, ΔF, reduces the barrier for fusion between the enveloping and the lipoplex bilayers, which produces a hole allowing for DNA release [stage (iii)]. The linear relationship between ΔF and the fraction of cationic lipids explains the experimentally observed exponential increase of transfection efficiency with Φ+ in lamellar lipoplexes.

Formation of adhesion domains in stressed and confined membranes.

The adhesion bonds connecting a lipid bilayer to an underlying surface may undergo a condensation transition resulting from an interplay between a short range attractive potential between them, and a long range fluctuation-induced potential of mean force. Here, we use computer simulations of a coarse-grained molecular model of supported lipid bilayers to study this transition in confined membranes, and in membranes subjected to a non-vanishing surface tension. Our results show that confinement may alter significantly the condensation transition of the adhesion bonds, whereas the application of surface tension has a very minor effect on it. We also investigate domain formation in membranes under negative tension which, in free membranes, causes the enhancement of the amplitude of membrane thermal undulations. Our results indicate that in supported membranes, this effect of a negative surface tension on the fluctuation spectrum is largely eliminated by the pressure resulting from the mixing entropy of the adhesion bonds.