We study the non-equilibrium steady states in a closed system consisting of interacting particles obeying exclusion principle with quenched hopping rate. Cluster mean field approach is utilized to theoretically analyze the system dynamics in terms of phase diagram, density profiles, current, etc, with respect to interaction energy E. It turns out that on increasing the interaction energy beyond a critical value, E c, shock region shows non-monotonic behavior and contracts until another critical value E c 1 is attained; a further increase leads to its expansion. Moreover, the phase diagram of an interacting system with specific set of parameters has a good agreement with its non-interacting analogue. For interaction energy below E c, a new shock phase displaying features different from non-interacting version is observed leading to two distinct shock phases. We have also performed Monte Carlo simulations extensively to validate our theoretical findings.

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and potentially also the internal ribosome entry rates along each RFMLK. Ribosomes that detach from an RFMLK owing to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules that must be accounted for in any analysis of translation.

The present study proposes a generalized mean-field approach to examine the significant effect of the finite supply of particles on multi-lane coupled system with non-conserving dynamics. The steadystate behavior is analyzed by exploring vital characteristics such as phase diagrams, density profiles, residence time and power spectra. Despite the fully asymmetrical coupling environment, symmetrical phases are identified along with asymmetrical phases. The emergence of shock results in the breaking of symmetry prevailing among the lanes for a critical value of the total number of particles in the system. Additionally, bulk induced phase transition results in the shifting from low density to high density regime. As expected, jamming length increases with increase in the total number of particles in the system. Particles follow the pseudo-Gaussian distribution with decreasing variance exhibiting the significant effect of limited resources on the system properties. For the lower values of the total number of particles, the current initially increases and then saturate beyond its critical value. Through power spectra damped oscillations are observed in the particles occupancy in one of the lanes while other lane and reservoir show undamped profile with non-conserving dynamics in the bulk.Experimental studies on the transport of motor proteins across microtubules suggest that along with the translational motion, individual motors interact with the surrounding environment by permitting particle absorption (desorption) to (from) the filament [27,28]. The competing dynamics of the non-conserved particles can also be significantly visualized in vehicular as well as pedestrian flow. These findings have been quantitatively characterized by integrating the constrained availability of resources with Langmuir kinetics (LK) resulting in more general single lane TASEP with LK [11].Further, to understand physical and biological complex processes more realistically, some studies on twolane TASEP with coupling between lanes have been conducted under infinite reservoir. In this direction, Pronina et al [20] studied a two-lane TASEP with fully asymmetrical coupling conditions and concluded that even one sided coupling affects the system dynamics significantly. Recently, few studies have been conducted on both fully and partially asymmetric coupling in a two-lane standard TASEP with [21,22,24,29] and without LK [30]. Nevertheless, the existing works on coupling between lanes focus only on the two-lane TASEP with infinite particles.Motivated by the crucial effect of the lane changing process along with absorption-desorption scenario on the systems with infinite resources, we wish to explore two-lane coupled non-conserved TASEP with a finite pool of reservoir. As a first step towards the understanding of the two-lane constrained TASEP, we consider fully asymmetrical coupling among the lanes in the proposed system. Since, the existing studies on constrained TASEP mainly focus on domain wall theory [12,13] and modified mean field theory [14...

Biological molecular motors are special enzymes that support biological processes such as intracellular transport, vesicle locomotion, RNA translation and many more. Experimental works suggest that the motor proteins interact among each other and moreover they experience a push by other motors during the intracellular transport. To incorporate these dynamics, we consider a variant of open one-dimensional totally asymmetric simple exclusion process with sitedependent hopping rates and interactions. The qualitative properties of our system do not depend on the hopping rate function. We utilize the simple meaneld, the cluster mean-eld, the correlated cluster mean-eld to theoretically calculate the stationary phase diagrams, density and the maximal particle current. The limitations of all the three theories are extensively discussed. It has been found that although the interactions do not change the number of phases in a phase diagram, it signi cantly changes the density pro les, the phase transition lines and the maximal particle current. The theoretical results obtained are supported by Monte Carlo simulations.

We study a deterministic framework for important cellular transport phenomena involving a large number of interacting molecules called the excluded flow of extended interacting objects with drop-off effect (EFEIOD). This model incorporates many realistic features of biological transport process including the length of biological “particles” and the fact that they can detach along the biological ‘tracks’. The flow between the consecutive sites is unidirectional and is described by a “soft” simple exclusion principle and by repelling or attracting forces between neighboring particles. We show that the model admits a unique steady-state. Furthermore, if the parameters are periodic with common period T, then the steady-state profile converge to a unique periodic solution of period T. Simulations of the EFEIOD demonstrate several non-trivial effects of the interactions on the system steady-state profile. For example, detachment rates may help in increasing the steady-state flow by alleviating traffic jams that can exist due to several reasons like bottleneck rate or interactive forces between the particles. We also analyze the special case of our model, when there are no forces exerted by neighboring particles, and called it as the ribosome flow model of extended objects with drop-off effect (RFMEOD), and study the sensitivity of its steady-state to variations in the parameters.