Weak and strong coupling in a two-lane asymmetric exclusion process

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.

Axonal transport during injury on a theoretical axon

Neurodevelopment, plasticity, and cognition are integral with functional directional transport in neuronal axons that occurs along a unique network of discontinuous polar microtubule (MT) bundles. Axonopathies are caused by brain trauma and genetic diseases that perturb or disrupt the axon MT infrastructure and, with it, the dynamic interplay of motor proteins and cargo essential for axonal maintenance and neuronal signaling. The inability to visualize and quantify normal and altered nanoscale spatio-temporal dynamic transport events prevents a full mechanistic understanding of injury, disease progression, and recovery. To address this gap, we generated DyNAMO, a Dynamic Nanoscale Axonal MT Organization model, which is a biologically realistic theoretical axon framework. We use DyNAMO to experimentally simulate multi-kinesin traffic response to focused or distributed tractable injury parameters, which are MT network perturbations affecting MT lengths and multi-MT staggering. We track kinesins with different motility and processivity, as well as their influx rates, in-transit dissociation and reassociation from inter-MT reservoirs, progression, and quantify and spatially represent motor output ratios. DyNAMO demonstrates, in detail, the complex interplay of mixed motor types, crowding, kinesin off/on dissociation and reassociation, and injury consequences of forced intermingling. Stalled forward progression with different injury states is seen as persistent dynamicity of kinesins transiting between MTs and inter-MT reservoirs. DyNAMO analysis provides novel insights and quantification of axonal injury scenarios, including local injury-affected ATP levels, as well as relates these to influences on signaling outputs, including patterns of gating, waves, and pattern switching. The DyNAMO model significantly expands the network of heuristic and mathematical analysis of neuronal functions relevant to axonopathies, diagnostics, and treatment strategies.

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.

Analytical and simulation studies of driven diffusive system with asymmetric heterogeneous interactions

Totally asymmetric simple exclusion process (namely, TASEP) is one of the most vital driven diffusive systems, which depicts stochastic dynamics of self-driven particles unidirectional updating along one-dimensional discrete lattices controlled by hard-core exclusions. Different with pre-existing results, driven diffusive system composed by multiple TASEPs with asymmetric heterogeneous interactions under two-dimensional periodic boundaries is investigated. By using detailed balance principle, particle configurations are extensively studied to obtain universal laws of characteristic order parameters of such stochastic dynamic system. By performing analytical analyses and Monte-Carlo simulations, local densities are found to be monotone increase with global density and spatially homogeneous to site locations. Oppositely, local currents are found to be non-monotonically increasing against global density and proportional to forward rate. Additionally, by calculating different cases of topologies, changing transition rates are found to have greater effects on particle configurations in adjacent subsystems. By intuitively comparing with pre-existing results, the improvement of our work also shows that introducing and considering totally heterogeneous interactions can improve the total current in such multiple TASEPs and optimize the overall transport of such driven-diffusive system. Our research will be helpful to understand microscopic dynamics and non-equilibrium dynamical behaviors of interacting particle systems.

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.

Bulk induced phase transition in driven diffusive systems

This paper studies a weakly and asymmetrically coupled three-lane driven diffusive system. A non-monotonically changing density profile in the middle lane has been observed. When the extreme value of the density profile reaches ρ = 0.5, a bulk induced phase transition occurs which exhibits a shock and a continuously and smoothly decreasing density profile which crosses ρ = 0.5 upstream or downstream of the shock. The existence of double shocks has also been observed. A mean-field approach has been used to interpret the numerical results obtained by Monte Carlo simulations. The current minimization principle has excluded the occurrence of two or more bulk induced shocks in the general case of nonzero lane changing rates.

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

We use boundary layer analysis for an open system consisting of two parallel totally asymmetric simple exclusion processes with Langmuir kinetics under a biased lane-changing rule. The two kinds of phase transitions--bulk transitions and surface transitions--have been examined. The dynamics of shock and their dependence on the system parameters have been investigated. We find a reduction in the number of steady-state phases with increase in lane-changing rate.

Phase diagrams of the Katz-Lebowitz-Spohn process on lattices with a junction

This paper studies the Katz-Lebowitz-Spohn (KLS) process on lattices with a junction, where particles move on parallel lattice branches that combine into a single lattice at the junction. It is shown that 11 kinds of phase diagrams could be observed, depending on the two parameters ε and δ in the KLS process. We have investigated the phase diagrams as well as bulk density analytically based on flow rate conservation and the extremal current principle. Extensive Monte Carlo computer simulations are performed, and it is found that they are in excellent agreement with theoretical prediction.

Positive congestion effect on a totally asymmetric simple exclusion process with an adsorption lane

We propose a type of asymmetric simple exclusion process by introducing an adsorption lane. In the system, each particle can be adsorbed by the adsorption lane only once per travel. The adsorption and desorption probabilities control the density of adsorption sites and the number of adsorbed particles. The ratio of the adsorbed particles shows reversal dynamics for congestion of the system, which is called the "positive congestion effect." We analyze this phenomenon by simulations and an approximation and successfully derive its critical condition. The spatial distribution of particles controlled by the adsorption and desorption probabilities is also investigated through balance equations of particles.

Exact solution of a heterogeneous multilane asymmetric simple exclusion process

We have proved an exact solution of a multilane totally asymmetric simple exclusion process (TASEP) with heterogeneous lane-changing rates on a torus. In the expression, the TASEP in each lane and lane-changing transition can be separable. Moreover, the lane-changing transitions satisfy the detailed balance condition, and this is the key to constructing the solution. Using the saddle-point method, the current of particles has been derived in a simple form in a thermodynamic limit. It is interesting that the dynamics depends only on a set of lane-changing parameters, not on the configuration of lanes.

Driven transport on parallel lanes with particle exclusion and obstruction

We investigate a driven two-channel system where particles on different lanes mutually obstruct each other's motion, extending an earlier model by Popkov and Peschel [Phys. Rev. E 64, 026126 (2001)]. This obstruction may occur in biological contexts due to steric hinderance where motor proteins carry cargos by "walking" on microtubules. Similarly, the model serves as a description for classical spin transport where charged particles with internal states move unidirectionally on a lattice. Three regimes of qualitatively different behavior are identified, depending on the strength of coupling between the lanes. For small and large coupling strengths the model can be mapped to a one-channel problem, whereas a rich phase behavior emerges for intermediate ones. We derive an approximate but quantitatively accurate theoretical description in terms of a one-site cluster approximation, and obtain insight into the phase behavior through the current-density relations combined with an extremal-current principle. Our results are confirmed by stochastic simulations.