arXiv subjects

Oded Farago

Publications and source records attributed to Oded Farago.

At least 55 records · Page 3Linked to original sources

arXiv2013

Langevin dynamics in inhomogeneous media: Re-examining the Itô-Stratonovich Dilemma

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly developed method for Langevin simulations to measure the probability distribution of a particle diffusing in a flat potential. Our results reveal that both the Itô and Stratonovich interpretations converge very slowly to the uniform equilibrium distribution for vanishing time step sizes. Three other conventions exhibit significantly improved accuracy: (i) the "isothermal" (Hänggi) convention, (ii) the Stratonovich convention corrected by a drift term, and (iii) a new convention employing two different effective friction coefficients representing two different averages of the friction function during the time step. We argue that the most physically accurate dynamical description is provided by the third convention, in which the particle experiences a drift originating from the dissipation instead of the fluctuation term. This feature is directly related to the fact that the drift is a result of an inertial effect that cannot be well understood in the Brownian, overdamped limit of the Langevin equation.

cond-mat.stat-mech↗

arXiv2013

Application of the G-JF Discrete-Time Thermostat for Fast and Accurate Molecular Simulations

A new Langevin-Verlet thermostat that preserves the fluctuation-dissipation relationship for discrete time steps, is applied to molecular modeling and tested against several popular suites (AMBER, GROMACS, LAMMPS) using a small molecule as an example that can be easily simulated by all three packages. Contrary to existing methods, the new thermostat exhibits no detectable changes in the sampling statistics as the time step is varied in the entire numerical stability range. The simple form of the method, which we express in the three common forms (Velocity-Explicit, Stormer-Verlet, and Leap-Frog), allows for easy implementation within existing molecular simulation packages to achieve faster and more accurate results with no cost in either computing time or programming complexity.

cond-mat.mtrl-sci↗

arXiv2013

Muscle contraction and the elasticity-mediated crosstalk effect

Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively generate in actin filaments. Here, we use a statistical mechanical analysis to investigate the influence of the EMC effect on the sarcomere - the basic contractile unit of skeletal muscles. We demonstrate that the EMC effect leads to an increase in the attachment probability of motors located near the end of the sarcomere while, simultaneously, decreasing the attachment probability of the motors in the central part. Such a polarized attachment probability would impair the motors ability to cooperate efficiently. Interestingly, this undesired phenomenon becomes significant only when the system size exceeds that of the sarcomere in skeletal muscles, which provides an explanation for the remarkable lack of sarcomere variability in vertebrates. Another phenomenon that we investigate is the recently observed increase in the duty ratio of the motors with the tension in muscle. We reveal that the celebrated Hill's equation for muscle contraction is very closely related to this observation.

physics.bio-ph↗

arXiv2013

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behavior of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency, and time step for both underdamped and over damped behavior within the usual the stability limit of the Verlet algorithm. Given the structure and simplicity of the method we conclude this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.

cond-mat.stat-mech↗

arXiv2012

Hierarchical self-organization of cytoskeletal active networks

The structural reorganization of the actin cytoskeleton is facilitated through the action of motor proteins that crosslink the actin filaments and transport them relative to each other. Here, we present a combined experimental-computational study that probes the dynamic evolution of mixtures of actin filaments and clusters of myosin motors. While on small spatial and temporal scales the system behaves in a very noisy manner, on larger scales it evolves into several well distinct patterns such as bundles, asters, and networks. These patterns are characterized by junctions with high connectivity, whose formation is possible due to the organization of the motors in "oligoclusters" (intermediate-size aggregates). The simulations reveal that the self-organization process proceeds through a series of hierarchical steps, starting from local microscopic moves and ranging up to the macroscopic large scales where the steady-state structures are formed. Our results shed light into the mechanisms involved in processes like cytokinesis and cellular contractility, where myosin motors organized in clusters operate cooperatively to induce structural organization of cytoskeletal networks.

physics.bio-ph↗

arXiv2012

Duty-ratio of cooperative molecular motors

Molecular motors are found throughout the cells of the human body, and have many different and important roles. These micro-machines move along filament tracks, and have the ability to convert chemical energy into mechanical work that powers cellular motility. Different types of motors are characterized by different duty-ratios, which is the fraction of time that a motor is attached to its filament. In the case of myosin II - a non-processive molecular machine with a low duty ratio - cooperativity between several motors is essential to induce motion along its actin filament track. In this work we use statistical mechanical tools to calculate the duty ratio of cooperative molecular motors. The model suggests that the effective duty ratio of non-processive motors that work in cooperation is lower than the duty ratio of the individual motors. The origin of this effect is the elastic tension that develops in the filament which is relieved when motors detach from the track.

physics.bio-ph↗

arXiv2011

Entropic attraction of adhesion bonds toward cell boundaries

Adhesion bonds between membranes and surfaces are attracted to each other via effective interactions whose origin the entropy loss due to the reduction in the amplitude of the membrane thermal fluctuations in the vicinity of the adhesion bonds. These fluctuation-induced interactions are also expected to drive the adhesion bonds toward the rim of the cell, as well as toward the surfaces of membrane inclusions. In this paper, we analyze the attraction of adhesion bonds to the cell inner and outer boundaries. Our analysis shows that the probability distribution function of a single (diffusing) adhesion bond decay algebraically with the distance from the boundaries. Upon increasing the concentration of the adhesion bonds, the attraction to the boundaries becomes strongly self-screened.

cond-mat.soft↗

arXiv2011

Mechanical surface tension governs membrane thermal fluctuations

Motivated by the still ongoing debate about the various possible meanings of the term surface tension of bilayer membranes, we present here a detailed discussion that explains the differences between the "intrinsic", "renormalized", and "mechanical" tensions. We use analytical considerations and computer simulations to show that the membrane spectrum of thermal fluctuations is governed by the mechanical and not the intrinsic tension. Our study highlights the fact that the commonly used quadratic approximation of Helfrich effective Hamiltonian is not rotationally invariant. We demonstrate that this non-physical feature leads to a calculated mechanical tension that differs dramatically from the correct mechanical tension. Specifically, our results suggest that the mechanical and intrinsic tensions vanish simultaneously, which contradicts recent theoretical predictions derived for the approximated Hamiltonian.

cond-mat.soft↗

arXiv2011

Statistical thermodynamics of adhesion points in supported membranes

Supported lipid membranes are useful and important model systems for studying cell membrane properties and membrane mediated processes. One attractive application of supported membranes is the design of phantom cells exhibiting well defined adhesive properties and receptor densities. Adhesion of membranes may be achieved by specific and non-specific interactions, and typically requires the clustering of many adhesion bonds into "adhesion domains". One potential mediator of the early stages of the aggregation process is the Casimir-type forces between adhesion sites induced by the membrane thermal fluctuations. In this review, I will present a theoretical analysis of fluctuation induced aggregation of adhesion sites in supported membranes. I will first discuss the influence of a single attachment point on the spectrum of membrane thermal fluctuations, from which the free energy cost of the attachment point will be deduced. I will then analyze the problem of a supported membrane with two adhesion points. Using scaling arguments and Monte Carlo simulations, I will demonstrate that two adhesion points attract each other via an infinitely long range effective potential that grows logarithmically with the pair distance. Finally, I will discuss the many-body nature of the fluctuation induced interactions. I will show that while these interactions alone are not sufficient to allow the formation of aggregation clusters, they greatly reduce the strength of the residual interactions required to facilitate cluster formation. Specifically, for adhesion molecules interacting via a short range attractive potential, the strength of the direct interactions required for aggregation is reduced by about a factor of two to below the thermal energy $k_BT$.

cond-mat.soft↗

arXiv2011

Molecular simulation analysis of structural variations in lipoplexes

We use a coarse-grained molecular model to study the self-assembly process of complexes of cationic and neutral lipids with DNA molecules ("lipoplexes") - a promising nonviral carrier of DNA for gene therapy. We identify the resulting structures through direct visualization of the molecular arrangements and through calculations of the corresponding scattering plots. The latter approach provides a means for comparison with published data from X-ray scattering experiments. Consistent with experimental results, we find that upon increasing the stiffness of the lipid material, the system tends to form lamellar structures. Two characteristic distances can be extracted from the scattering plots of lamellar complexes - the lamellar (interlayer) spacing and the DNA-spacing within each layer. We find a remarkable agreement between the computed values of these two quantities and the experimental data [J. O. Rädler, I. Koltover, T. Salditt and C. R. Safinya, Science Vol. 275, 810 (1997)] over the entire range of mole fractions of charged lipids (CLs) studied experimentally. A visual inspection of the simulated systems reveals that, for very high fractions of CLs, disordered structures consisting of DNA molecules bound to small membrane fragments are spontaneously formed. The diffraction plots of these non-lamellar disordered complexes appear very similar to that of the lamellar structure, which makes the interpretation of the X-ray data ambiguous. The loss of lamellar order may be the origin of the observed increase in the efficiency of lipoplexes as gene delivery vectors at high charge densities.

cond-mat.soft↗

arXiv2011

Crosstalk between non-processive myosin motors mediated by the actin filament elasticity

Many biological processes involve the action of molecular motors that interact with the cell cytoskeleton. Some processes, such as the transport of cargoes is achieved mainly by the action of individual motors. Other, such as cell motility and division, require the cooperative work of many motors. Collective motor dynamics can be quite complex and unexpected. One beautiful example is the bidirectional ("back and forth") motion of filaments which is induced when the motors within a group exert forces in opposite directions. This review tackles the puzzle emerging from a recent experimental work in which it has been shown that the characteristic reversal times of the bidirectional motion are practically independent of the number of motors. This result is in a striking contradiction with existing theoretical models that predict an exponential growth of the reversal times with the size of the system. We argue that the solution to this puzzle may be the crosstalk between the motors which is mediated by the elastic tensile stress that develops in the cytoskeleton track. The crosstalk does not directly correlate the attachment and detachment of the motors, which work independently of each other. However, it highly accelerates their detachments by making the detachment rates system size dependent.

physics.bio-ph↗

arXiv2010

Entropy driven aggregation of adhesion sites of supported membranes

We study, by means of mean field calculations and Monte Carlo simulations of a lattice-gas model, the distribution of adhesion sites of a bilayer membrane and a supporting flat surface. Our model accounts for the many-body character of the attractive interactions between adhesion points induced by the membrane thermal fluctuations. We show that while the fluctuation-mediated interactions alone are not sufficient to allow the formation of aggregation domains, they greatly reduce the strength of the direct interactions required to facilitate cluster formation. Specifically, for adhesion molecules interacting via a short range attractive potential, the strength of the direct interactions required for aggregation is reduced by about a factor of two to below the thermal energy $k_BT$.

cond-mat.soft↗

arXiv2010

Biased transport of elastic cytoskeletal filaments with alternating polarities by molecular motors

We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with non-processive myosin motors. In the model, the bundle is represented as an elastic chain consisting of monomers with positive and negative polarities. The motion of the bundle is induced by the pulling forces of the underlying motors which stochastically attach to the monomers and, depending on the polarity of the monomers, pull them in the right or left direction. We demonstrate that perfectly a-polar chains consisting of equal numbers of monomers with positive and negative polarities may exhibit biased bidirectional motion with non-zero drift. This effect is attributed to the elastic tension developed in the chain due to the action of the myosin motors. We also show that as a result of this tension, the attachment probability of the motors is greatly reduced and becomes strongly dependent on the length of the chain. These surprising effects point to the necessity of considering the elasticity of the cytoskeleton in theoretical studies of cooperative dynamics of molecular motors.

cond-mat.soft↗

arXiv2010

Fluctuation induced attraction between adhesion sites of supported membranes

We use scaling arguments and coarse grained Monte Carlo simulations to study the fluctuation mediated interactions between a pair of adhesion sites of a bilayer membrane and a supporting surface. We find that the potential of mean force is an infinitely long range attractive potential that grows logarithmically with the pair distance $r$: $ϕ(\vec{r})/k_BT=c\ln r$, where the constant $c=2$ and $c=1$ for non-stressed and stressed membranes, respectively. When, in addition to excluded volume repulsion, the membrane also interacts with the underlying surface through a height-dependent attractive potential, the potential $ϕ(\vec{r})$ is screened at large pair distances.

cond-mat.soft↗

arXiv2009

Cooperative molecular motors moving back and forth

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc. Natl. Acad. Sci. USA} {\bf 99}, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) a-polar tracks, while on even slightly polar tracks the motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion.

cond-mat.soft↗

arXiv2009

Bidirectional cooperative motion of myosin-II motors on actin tracks with randomly alternating polarities

The cooperative action of many molecular motors is essential for dynamic processes such as cell motility and mitosis. This action can be studied by using motility assays in which the motion of cytoskeletal filaments over a surface coated with motor proteins is tracked. In previous studies of actin-myosin II systems, fast directional motion was observed, reflecting the tendency of myosin II motors to propagate unidirectionally along actin filaments. Here, we present a motility assay with actin bundles consisting of short filamentous segments with randomly alternating polarities. These actin tracks exhibit bidirectional motion with macroscopically large time intervals (of the order of several seconds) between direction reversals. Analysis of this bidirectional motion reveals that the characteristic reversal time, $τ_{rev}$, does not depend on the size of the moving bundle or on the number of motors, $N$. This observation contradicts previous theoretical calculations based on a two-state ratchet model [Badoual et al., Proc. Natl. Acad. Sci. USA, vol. 99, p. 6696 (2002)], predicting an exponential increase of $τ_{rev}$ with $N$. We present a modified version of this model that takes into account the elastic energy due to the stretching of the actin track by the myosin II motors. The new model yields a very good quantitative agreement with the experimental results.

cond-mat.soft↗

arXiv2008

Membrane fluctuations near a plane rigid surface

We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface. Our analysis shows that the surface influence on the bilayer fluctuations can be effectively described in terms of a uniform confining potential that grows quadratically with the height of the membrane $h$ relative to the surface: $V=(1/2)γh^2$. The strength $γ$ of the harmonic confining potential vanishes when the corners of the membrane patch are placed directly on the surface ($d=0$), and achieves its maximum value when $d$ is of the order of a few nanometers. However, even at maximum strength the confinement effect is quite small and has noticeable impact only on the amplitude of the largest bending mode.

cond-mat.soft↗

arXiv2008

Mode excitation Monte Carlo simulations of mesoscopically large membranes

Solvent-free coarse grained models represent one of the most promising approaches for molecular simulations of mesoscopically large membranes. In these models, the size of the simulated membrane is limited by the slow relaxation time of longest bending mode. Here, we present a Monte Carlo algorithm with update moves in which all the lipids are displaced simultaneously. These collective moves result in fast excitation and relaxation of the long wavelength thermal fluctuations. We apply the method to simulations of a bilayer membrane of linear size $\sim 50 {\rm nm}$ and show reduction of the relaxation time by two orders of magnitudes when compared to conventional Monte Carlo.

cond-mat.soft↗