Totally asymmetric simple exclusion process simulations of molecular motor transport on random networks with asymmetric exit rates

Correlated particle transport enables biological free energy transduction

Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. We show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).

Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder

We consider the totally asymmetric simple exclusion processes on quenched random energy landscapes. We show that the current and the diffusion coefficient differ from those for homogeneous environments. Using the mean-field approximation, we analytically obtain the site density when the particle density is low or high. As a result, the current and the diffusion coefficient are described by the dilute limit of particles or holes, respectively. However, in the intermediate regime, due to the many-body effect, the current and the diffusion coefficient differ from those for single-particle dynamics. The current is almost constant and becomes the maximal value in the intermediate regime. Moreover, the diffusion coefficient decreases with the particle density in the intermediate regime. We obtain analytical expressions for the maximal current and the diffusion coefficient based on the renewal theory. The deepest energy depth plays a central role in determining the maximal current and the diffusion coefficient. As a result, the maximal current and the diffusion coefficient depend crucially on the disorder, i.e., non-self-averaging. Based on the extreme value theory, we find that sample-to-sample fluctuations of the maximal current and diffusion coefficient are characterized by the Weibull distribution. We show that the disorder averages of the maximal current and the diffusion coefficient converge to zero as the system size is increased and quantify the degree of the non-self-averaging effect for the maximal current and the diffusion coefficient.

Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder

We investigate the current properties in the totally asymmetric simple exclusion process (TASEP) on a quenched random energy landscape. In low- and high-density regimes, the properties are characterized by single-particle dynamics. In the intermediate one, the current becomes constant and is maximized. Based on the renewal theory, we derive accurate results for the maximum current. The maximum current significantly depends on a disorder realization, i.e., non-self-averaging (SA). We demonstrate that the disorder average of the maximum current decreases with the system size, and the sample-to-sample fluctuations of the maximum current exceed those of current in the low- and high-density regimes. We find a significant difference between single-particle dynamics and the TASEP. In particular, the non-SA behavior of the maximum current is always observed, whereas the transition from non-SA to SA for current in single-particle dynamics exists.

First passage of molecular motors on networks of cytoskeletal filaments

Molecular motors facilitate intracellular transport through a combination of passive motion in the cytoplasm and active transport along cytoskeletal filaments. Although the motion of motors on individual filaments is often well characterized, it remains a challenge to understand their transport on networks of filaments. Here we use computer simulations of a stochastic jump process to determine first-passage times (FPTs) of a molecular motor traversing an interval containing randomly distributed filaments of fixed length. We characterize the mean first-passage time (MFPT) as a function of the number and length of filaments. Intervals containing moderate numbers of long filaments lead to the largest MFPTs with the largest relative standard deviation; in this regime, some filament configurations lead to anomalously large FPTs due to spatial regions where motors become trapped for long times. For specific filament configurations, we systematically reverse the directionality of single filaments and determine the MFPT of the perturbed configuration. Surprisingly, altering a single filament can dramatically impact the MFPT, and filaments leading to the largest changes are commonly found in different regions than the traps. We conclude by analyzing the mean square displacement of motors in unconfined systems with a large density of filaments and show that they behave diffusively at times substantially less than the MFPT to traverse the interval. However, the effective diffusion coefficient underestimates the MFPT across the bounded interval, emphasizing the importance of local configurations of filaments on first-passage properties.

Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site assignments

This study proposes a model of a totally asymmetric simple exclusion process on a single-channel lane with functions of site assignments along the pit lane. The system model attempts to insert a new particle to the leftmost site at a certain probability by randomly selecting one of the empty sites in the pit lane, and reserving it for the particle. Thereafter, the particle is directed to stop at the site only once during its travel. Recently, the system was determined to show a self-deflection effect, in which the site usage distribution biases spontaneously toward the leftmost site, and the throughput becomes maximum when the site usage distribution is slightly biased to the rightmost site. Our exact analysis describes this deflection effect and show a good agreement with simulations.

Lattice model of reduced jamming by a barrier

We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.