Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: phase diagrams and boundary layers

Competition for resources in an exclusion model with biased lane-changing mechanism

The motivation for the proposed work is drawn from the attachment-detachment observed in biological and physical transport processes that entail finite resources. We investigate the influence of limited particle availability on particle dynamics within two parallel totally asymmetric simple exclusion lanes, with one lane incorporating only particle detachment and the other considering particle attachment. We establish a theoretical framework by employing vertical mean-field theory in conjunction with singular perturbation technique. The analytical findings are supported by numerical and stochastic validation using a finite-difference scheme and the Gillespie algorithm. By utilizing these approaches, we scrutinize various stationary properties, including particle densities, phase boundaries, and particle currents for both lanes. Our analysis reveals that the complexity of the phase diagram exhibits a nonmonotonic trend in the number of stationary phases as the particle count increases. Each phase diagram is constructed with respect to the intrinsic boundary parameters, illustrating both bulk and surface transitions occurring within the lanes. The interplay between finite resources and coupling mechanisms gives rise to two phases involving upward shock in one of the lanes, while two phases exhibit synchronized downward shock in both lanes. Finally, we delve into shock dynamics to comprehend critical phase transitions occurring in the system.

Multiple reentrance transitions in exclusion process with finite reservoir

The proposed study is motivated by the scenario of two-way vehicular traffic. We consider a totally asymmetric simple exclusion process in the presence of a finite reservoir along with the particle attachment, detachment, and lane-switching phenomena. The various system properties in terms of phase diagrams, density profiles, phase transitions, finite size effect, and shock position are analyzed, considering the available number of particles in the system and different values of coupling rate, by employing the generalized mean-field theory and the obtained results are detected to be a good match with the Monte Carlo simulation outcomes. It is discovered that the finite resources significantly affect the phase diagram for different coupling rate values, which leads to nonmonotonic changes in the number of phases in the phase plane for comparatively minor lane-changing rates and produces various exciting features. We calculate the critical value of the total number of particles in the system at which the multiple phases in the phase diagram appear or disappear. The competition between the limited particles, bidirectional motion, Langmuir kinetics, and particle lane-shifting behavior yields unanticipated and unique mixed phases, including the double shock phase, multiple reentrance and bulk-induced phase transitions, and phase segregation of the single shock phase.

Asymmetric coupling induces two-directional reentrance transition in three-lane exclusion process

Inspired by vehicular traffic phenomena, we study a three-lane open totally asymmetric simple exclusion process with both-sided lane switching in the companionship of Langmuir kinetics. We calculate the phase diagrams, density profiles, and phase transitions through mean-field theory and successfully validate these findings with Monte Carlo simulation results. It has been found that both the qualitative and quantitative topology of phase diagrams crucially rely on the ratio of lane-switching rates called coupling strength. The proposed model has various unique mixed phases, including a double shock resulting in bulk-induced phase transitions. The interplay between both-sided coupling, third lane, and Langmuir kinetics produces unusual features, including a back-and-forth phase transition, also called a reentrance transition, in two directions for relatively nominal values of coupling strength. The presence of reentrance transition and peculiar phase boundaries leads to a rare type of phase division in which one phase lies entirely within another region. Moreover, we scrutinize the shock dynamics by analyzing four different types of shock and finite-size effects.

Reservoir crowding in a resource-constrained exclusion process with a dynamic defect

To understand the complicated transport processes that occur in biological and physical systems, we investigate a constrained totally asymmetric simple exclusion process with a stochastic defect particle. The defect particle might randomly emerge or vanish, resulting in a dynamic defect, and slows down the flow of moving particles when attached to the lattice. Using a mean-field technique, we examine the steady-state characteristics and boundary-layer analysis is provided to comprehend the properties of finite system. In a simplification, our theoretical method unifies three different parameter used to define the defect dynamics into one parameter termed the obstruction factor. It is found that the defect kinetics lead to emergence of phases where the current is defect restricted. The system shows nine phases overall, including bulk-induced and boundary-induced shock phases, with the phase schema showing no more than eight phases depending on the dynamics. We found that variation of obstruction does not lead to qualitative transition in the system, whereas the change in constraint on total particles affect the system qualitatively. All the theoretical outcomes have been validated using extensive Monte Carlo simulations.

Role of extended coupling in bidirectional transport system

Motivated by vehicular traffic phenomena, we study a bidirectional two-lane open totally asymmetric simple exclusion process with extended symmetric coupling conditions in the presence of Langmuir kinetics. The phase diagrams and density profiles are calculated utilizing mean-field theory for different lane-changing rates and are found to be in a good match with Monte Carlo simulation results. It has been observed that the qualitative topology of phase diagrams depends on the lane-switching rate significantly, resulting in nonmonotonic variations in the number of steady-state phases. The proposed model provides various mixed phases leading to bulk induced phase transitions. The interplay between bidirectional movement, extended coupling conditions, and Langmuir kinetics produces unusual phenomena, including a back-and-forth phase transition and partial phase division of the shock region for comparatively smaller values of the lane-changing rate. Moreover, we analyze the shock dynamics and calculate critical values for the lane-changing rate at which the phases appear or disappear.

Particle creation and annihilation in a dynamically disordered totally asymmetric simple exclusion process

We study a single-channel dynamically disordered totally asymmetric simple exclusion process with bulk particle attachment and detachment. The continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The effects of various parameters, namely particle attachment rate, defect binding and unbinding rates, and binding constant, have been investigated. An increase in the attachment rate of particles reduces the number of steady-state phases, whereas a variation in defect binding and unbinding rates shifts the phase boundaries. One of the important consequences of introducing particle nonconserving dynamics is the appearance of shock in the steady state. The shock dynamics have been thoroughly examined and the defect strength is found to have a significant effect on the shock position. The mean-field solutions are validated using extensive Monte Carlo simulations.

Cooperative motor action to regulate microtubule length dynamics

Motivated by the recent experimental observations on motor induced cooperative mechanism controlling the length dynamics of microtubules (MTs), we examine how plus-end-targeted proteins of the kinesin family regulate MT polymerization and depolymerization routines. Here, we study a stochastic mathematical model capturing the unusual form of collective motor interaction on MT dynamics originating due to the molecular traffic near the MT tip. We provide an extensive analysis of the joint effect of motor impelled MT polymerization and complete depolymerization. The effect of the cooperative action is included by modifying the intrinsic depolymerization rate. We analyze the model within the framework of continuum mean-field theory and the resultant steady-state analytic solution is expressed in terms of Lambert W functions. Four distinct steady-state phases including a shock phase have been reported. The significant features of the shock including its position and height have been analyzed. Theoretical outcomes are supported by extensive Monte Carlo simulations. To explore the system alterations between the regime of growth and shrinkage phase, we consider kymographs of the microtubule along with the length distributions. Finally, we investigated the dependence of MT length kinetics both on modifying factor of depolymerization rate and motor concentration. The overall extensive study reveals that the flux of molecular traffic at the microtubule plus end initiates a cooperative mechanism, resulting in significant change in MT growth and shrinkage regime as also observed experimentally.

Far-from-equilibrium bidirectional transport system with constrained entrances competing for pool of limited resources

Motivated by the wide occurrence of limited resources in many real-life systems, we investigate two-lane totally asymmetric simple exclusion process with constrained entrances under finite supply of particles. We analyze the system within the framework of mean-field theory and examine various complex phenomena, including phase separation, phase transition, and symmetry breaking. Based on the theoretical analysis, we analytically derive the phase boundaries for various symmetric as well as asymmetric phases. It has been observed that the symmetry-breaking phenomenon initiates even for very small number of particles in the system. The phases with broken symmetry originates as shock-low density phase under limited resources, which is in contrast to the scenario with infinite number of particles. As expected, the symmetry breaking continues to persist even for higher values of system particles. Seven stationary phases are observed, with three of them exhibiting symmetry-breaking phenomena. The critical values of a total number of system particles, beyond which various symmetrical and asymmetrical phases appear and disappear are identified. Theoretical outcomes are supported by extensive Monte Carlo simulations. Finally, the size-scaling effect and symmetry-breaking phenomenon on the simulation results have also been examined based on particle density histograms.

Generic Transport Mechanisms for Molecular Traffic in Cellular Protrusions

Transport of molecular motors along protein filaments in a half-closed geometry is a common feature of biologically relevant processes in cellular protrusions. Using a lattice-gas model we study how the interplay between active and diffusive transport and mass conservation leads to localized domain walls and tip localization of the motors. We identify a mechanism for task sharing between the active motors (maintaining a gradient) and the diffusive motion (transport to the tip), which ensures that energy consumption is low and motor exchange mostly happens at the tip. These features are attributed to strong nearest-neighbor correlations that lead to a strong reduction of active currents, which we calculate analytically using an exact moment identity, and might prove useful for the understanding of correlations and active transport also in more elaborate systems.

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state-the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model's fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions.

Phase coexistence and particle nonconservation in a closed asymmetric exclusion process with inhomogeneities

We construct a one-dimensional totally asymmetric simple exclusion process (TASEP) on a ring with two segments having unequal hopping rates, coupled to particle nonconserving Langmuir kinetics (LK) characterized by equal attachment and detachment rates. In the steady state, in the limit of competing LK and TASEP, the model is always found in states of phase coexistence. We uncover a nonequilibrium phase transition between a three-phase and a two-phase coexistence in the faster segment, controlled by the underlying inhomogeneity configurations and LK. The model is always found to be half-filled on average in the steady state, regardless of the hopping rates and the attachment-detachment rate.

Effect of coupling strength on a two-lane partially asymmetric coupled totally asymmetric simple exclusion process with Langmuir kinetics

We analyze an open system comprised of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk under partially asymmetric coupling conditions. The phase diagrams are obtained using boundary layer analysis of continuum mean-field equations and characterized for different values of lane-changing rates. The structure of the phase diagram remains qualitatively the same as the one in fully asymmetric coupling conditions up to a certain critical order of lane-changing rates, after which significant changes are found in the phase diagram. The effect of system size on the steady-state dynamics has also been examined. To validate theoretical findings, extensive Monte Carlo simulations are carried out.