arXiv subjects

Oded Farago

Publications and source records attributed to Oded Farago.

At least 37 records · Page 2Linked to original sources

arXiv2019

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 {\bf 49}, 673 (1988)]. The thermophoretic behavior is commonly described by the Soret coefficient - a parameter which can be calculated from the steady-state PDF. Motivated by recent advances in experimental methods for observing and analyzing single nano-particle 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 particles statistics is characterized by measures like 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.

cond-mat.stat-mech↗

arXiv2019

Langevin thermostat for robust configurational and kinetic sampling

We reformulate the algorithm of Grønbech-Jensen and Farago (GJF) for Langevin dynamics simulations at constant temperature. The GJF algorithm has become increasingly popular in molecular dynamics simulations because it provides robust (i.e., insensitive to variations in the time step) and accurate configurational sampling of the phase space with larger time steps than other Langevin thermostats. In the original derivation [Mol. Phys. {\bf 111}, 983 (2013)], the algorithm was formulated as a velocity-Verlet type integrator with an in-site velocity variable. Here, we reformulate it as a leap frog scheme with a half-step velocity variable. In contrast to the original form, the reforumlated one also provides robust and accurate estimations of kinetic measures such as the average kinetic energy. We analytically prove that the newly presented algorithm gives the exact configurational and kinetic temperatures of a harmonic oscillator for any time step smaller than the Verlet stability limit, and use computer simulations to demonstrate the configurational and kinetic robustness of the algorithm in strongly non-linear systems. This property of the new formulation of the GJF thermostat makes it very attractive for implementation in computer simulations.

cond-mat.stat-mech↗

arXiv2019

Nonsteady-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 $U(x)=-k_BT\ln [A(x)]$ (where $k_BT$ 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. {\bf 96}, 3926 (1992)] 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 {\bf 74}, 041203 (2006)] shows that they are consistent with each other. In the limit of long wavelength channels ($ε\ll 1$), 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.

cond-mat.stat-mech↗

arXiv2018

The probability distribution of Brownian motion in periodic potentials

We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the solution for any periodic even function $U(x)$, and demonstrate that it is asymptotically (at large time $t$) correct up to terms decaying faster than $\sim t^{-3/2}$. As part of the derivation, we also recover the Lifson-Jackson formula for the effective diffusion coefficient of the dynamics. The derived solution exhibits agreement with Langevin dynamics simulations when (i) the periodic length is much larger than the ballistic length of the dynamics, and (ii) when the potential barrier $ΔU=\max(U(x))-\min(U(x))$ is not much larger than the thermal energy $k_BT$.

cond-mat.stat-mech↗

arXiv2018

Application of underdamped Langevin dynamics simulations for the study of diffusion from a drug-eluting stent

We use a one-dimensional two layer model with a semi-permeable membrane to study the diffusion of a therapeutic drug delivered from a drug-eluting stent (DES). The rate of drug transfer from the stent coating to the arterial wall is calculated by using underdamped Langevin dynamics simulations. Our results reveal that the membrane has virtually no delay effect on the rate of delivery from the DES. The work demonstrates the great potential of underdamped Langevin dynamics simulations as an easy to implement, efficient, method for solving complicated diffusion problems in systems with a spatially-dependent diffusion coefficient.

cond-mat.stat-mech↗

arXiv2017

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 diffusvity 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 system, 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.

cond-mat.stat-mech↗

arXiv2017

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 the 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.

cond-mat.soft↗

arXiv2016

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

Cell-cell adhesion is established by specific binding of receptor and ligand proteins. 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. Analysis of systems at different densities of bonds, $ϕ$, reveals that the phase diagram exhibits a nearly-universal behavior when the temperature $T$ is plotted vs. the scaled density $x=ϕξ^2$, where $ξ$ is the linear size of the membrane's region affected by a single bond. The critical point $(ϕ_c,T_c)$ is located at very low densities and slightly below $T_c$ we identify phase coexistence between two low-density phases. Dense domains are observed only when the height by which the bonds deform the membranes, $h_0$, is much larger than their thermal roughness, $Δ$, which occurs at very low temperatures $T\ll T_c$. We 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 $r\gtrsim ξ$, i.e., for $x\lesssim 1$. Therefore, at higher densities, only the mixing entropy of the bonds (which favors uniform distributions) is thermodynamically relevant. We discuss the implications of our results to the question of immunological synapse formation, and demonstrate the elasticity-mediated interactions may be involved in the aggregation of these semi-dilute membrane domains.

cond-mat.soft↗

arXiv2016

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 $D(x)\sim |x|^c$, 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 large times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for $c<0$, and superdiffusion for $0 1$, 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 ($\left\langle x^2\right\rangle \sim t^2$). 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.

cond-mat.stat-mech↗

arXiv2016

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.

cond-mat.soft↗

arXiv2016

The G-JF Thermostat for Accurate Configurational Sampling in Soft-Matter Simulations

We implement the statistically sound G-JF thermostat for Langevin Dynamics simulations into the ESPREesSo molecular package for large-scale simulations of soft matter systems. The implemented integration method is tested against the integrator currently used by the molecular package in simulations of a fluid bilayer membrane. While the latter exhibits deviations in the sampling statistics that increase with the integration time step dt, the former reproduces near-correct configurational statistics for all dt within the stability range of the simulations. We conclude that, with very modest revisions to existing codes, one can significantly improve the performance of statistical sampling using Langevin thermostats.

physics.comp-ph↗

arXiv2016

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.

cond-mat.stat-mech↗

arXiv2015

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 enhancement of the amplitude of the 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.

cond-mat.soft↗

arXiv2015

Small membranes under negative surface tension

We use computer simulations and a simple free energy model to study the response of a bilayer membrane to the application of a negative (compressive) mechanical tension. Such a tension destabilizes the long wavelength undulation modes of giant vesicles, but it can be sustained when small membranes and vesicles are considered. Our negative tension simulation results reveal two regimes - (i) a weak negative tension regime characterized by stretching-dominated elasticity, and (ii) a strong negative tension regime featuring bending-dominated elastic behavior. This resembles the findings of the classic Evans and Rawicz micropipette aspiration experiment in giant unilamellar vesicles (GUVs) [Phys, Rev. Lett. {\bf 64}, 2094 (1990)]. However, while in GUVs the crossover between the two elasticity regimes occurs at a small positive surface tension, in smaller membranes it takes place at a moderate negative tension. Another interesting observation concerning the response of a small membrane to negative surface tension is related to the relationship between the mechanical and fluctuation tensions, which are equal to each other for non-negative values. When the tension decreases to negative values, the fluctuation tension $γ$ drops somewhat faster than $τ$ in the small negative tension regime, before it saturates (and becomes larger than $τ$) for large negative tensions. The bending modulus exhibit an "opposite" trend. It remains almost unchanged in the stretching-dominated elastic regime, and decreases in the bending-dominated regime. Both the amplitudes of the thermal height undulations and the projected area variations diverge at the onset of mechanical instability.

cond-mat.soft↗

arXiv2014

Constant pressure and temperature discrete-time Langevin molecular dynamics

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are build on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems - a one dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb & Dunweg, show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

cond-mat.stat-mech↗

arXiv2014

Elasticity and mechanical instability of charged lipid bilayers in ionic solutions

We use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the multivalent counterions condense on the membrane and, through spatial charge correlations, make the effective interactions due the charged lipids attractive. The differences in the elastic properties of the charged membranes in monovalent and multivalent counterion solutions are reflected in the mechanisms leading to their mechanical instability at high charge densities. In the former case, the membranes develop pores to relieve the electrostatic tensile stresses, while in the latter case, the membrane exhibit large wavelength bending instability.

cond-mat.soft↗

arXiv2014

Coarse grained molecular simulations of membrane adhesion domains

We use a coarse grained molecular model of supported lipid bilayers to study the formation of adhesion domains. We find that this process is a first order phase transition, triggered by a combination of pairwise short range attractive interactions between the adhesion bonds and many-body Casimir-like interactions, mediated by the membrane thermal undulations. The simulation results display an excellent agreement with the recently proposed Weil-Farago 2D lattice model, in which the occupied and empty sites represent, respectively, the adhesion bonds and unbound segments of the membrane. A second phase transition, into a hexatic phase, is observed when the attraction between the adhesion bonds is further strengthened.

cond-mat.soft↗

arXiv2014

Fluctuation-dissipation relation for systems with spatially varying friction

When a particle diffuses in a medium with spatially dependent friction coefficient $α(r)$ at constant temperature $T$, it drifts toward the low friction end of the system even in the absence of any real physical force $f$. This phenomenon, which has been previously studied in the context of non-inertial Brownian dynamics, is termed "spurious drift", although the drift is real and stems from an inertial effect taking place at the short temporal scales. Here, we study the diffusion of particles in inhomogeneous media within the framework of the inertial Langevin equation. We demonstrate that the quantity which characterizes the dynamics with non-uniform $α(r)$ is not the displacement of the particle $Δr=r-r^0$ (where $r^0$ is the initial position), but rather $ΔA(r)=A(r)-A(r^0)$, where $A(r)$ is the primitive function of $α(r)$. We derive expressions relating the mean and variance of $ΔA$ to $f$, $T$, and the duration of the dynamics $Δt$. For a constant friction coefficient $α(r)=α$, these expressions reduce to the well known forms of the force-drift and fluctuation-dissipation relations. We introduce a very accurate method for Langevin dynamics simulations in systems with spatially varying $α(r)$, and use the method to validate the newly derived expressions.

cond-mat.stat-mech↗