Totally asymmetric simple exclusion process on networks

Exclusion processes on a roundabout traffic model with constrained resources

Motivated by the vehicular traffic phenomenon at roundabouts, we examine how the limited availability of resources affects the movement of two distinct types of particles on bidirectional lanes connected by two bridges, with each bridge specifically designated for the transportation of one species. To provide a theoretical ground for our findings, we employ a mean-field framework and successfully validate them through dynamic Monte Carlo simulations. Based on the theoretical analysis, we analytically derive various stationary properties, such as the particle densities, phase boundaries, and particle currents, for all the possible symmetric as well as asymmetric phases. The qualitative as well as quantitative behavior of the system is significantly affected by the constraint on the number of resources. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. Analytical arguments enable the identification of several critical values for the total number of particles, leading to a qualitative change in the phase diagrams. The interplay of the finite resources and the bidirectional transport yields unanticipated and unusual features such as back-and-forth transition, the presence of two congested phases where particle movement is halted, as well as shock phases induced by boundaries and the bulk of the system. Also, it is found that spontaneous symmetry-breaking phenomena are induced even for very few particles in the system. Moreover, we thoroughly examine the location of shocks by varying the parameters controlling the system's boundaries, providing insights into possible phase transitions.

Metastability due to a branching-merging structure in a simple network of an exclusion process

We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits metastability. Specifically, for open boundary conditions, we observe two types of metastability: hysteresis and a nonergodic phase. We analytically determine the tipping points, that is, the critical conditions under which a small disturbance can lead to the collapse of metastability. Our findings provide insights into metastability induced by branching-merging structures, which exist in all network systems in various fields.

Persistence and stability of generalized ribosome flow models with time-varying transition rates

In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.

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.

Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional mass-aggregation models in which the phase transition is calculated analytically.

Exclusion process with scaled resources: Delocalized shocks and interplay of reservoirs

In this paper we study a conserved system comprised of two directed lanes having identical dynamics and two reservoirs with scaled resources that are strategically connected to the boundaries of the lanes, forming a ringlike structure. The steady-state properties of the system have been analyzed in the framework of mean-field theory. Our findings display a rich behavior, emphasizing the nontrivial effects of incorporating two reservoirs. As a consequence, two distinct phases that admit delocalized shocks emerge and occupy a significant region in the phase diagram. Moreover in one of theses phases, each lane admits a delocalized shock whose movements are perfectly synchronized. In another phase, the single shock in the system may traverse both lanes or remain restricted to a single lane, depending upon the size of the system. All the findings are validated by Monte Carlo simulations.

Exclusion process on two intersecting lanes with constrained resources: Symmetry breaking and shock dynamics

We present a study of the exclusion process on a peculiar topology of network with two intersecting lanes, competing for the particles in a reservoir with finite capacity. To provide a theoretical ground for our findings, we exploit mean-field approximation along with domain-wall theory. The stationary properties of the system, including phase transitions, density profiles, and position of the domain wall are derived analytically. Under the similar dynamical rules, the particles of both lanes interact only at the intersected site. The symmetry of the system is maintained until the number of particles do not exceed the total number of sites. However, beyond this, the symmetry breaking phenomenon occurs, resulting in the appearance of asymmetric phases and continues to persist even for an infinite number of particles. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. A bulk induced shock appears in a symmetric phase, whereas, a boundary induced shock is observed in the symmetric as well as the asymmetric phase. Monitoring the location of localized shock with increasing entry of particles, we explain the possible phase transitions. The theoretical results are supported by extensive Monte Carlo simulations and explained using simple physical arguments.

Molecular underpinnings of cytoskeletal cross-talk

Cross-talk between the microtubule and actin networks has come under intense scrutiny following the realization that it is crucial for numerous essential processes, ranging from cytokinesis to cell migration. It is becoming increasingly clear that proteins long-considered highly specific for one or the other cytoskeletal system do, in fact, make use of both filament types. How this functional duality of "shared proteins" has evolved and how their coadaptation enables cross-talk at the molecular level remain largely unknown. We previously discovered that the mammalian adaptor protein melanophilin of the actin-associated myosin motor is one such "shared protein," which also interacts with microtubules in vitro. In a hypothesis-driven in vitro and in silico approach, we turn to early and lower vertebrates and ask two fundamental questions. First, is the capability of interacting with microtubules and actin filaments unique to mammalian melanophilin or did it evolve over time? Second, what is the functional consequence of being able to interact with both filament types at the cellular level? We describe the emergence of a protein domain that confers the capability of interacting with both filament types onto melanophilin. Strikingly, our computational modeling demonstrates that the regulatory power of this domain on the microscopic scale alone is sufficient to recapitulate previously observed behavior of pigment organelles in amphibian melanophores. Collectively, our dissection provides a molecular framework for explaining the underpinnings of functional cross-talk and its potential to orchestrate the cell-wide redistribution of organelles on the cytoskeleton.

Totally asymmetric simple exclusion process on multiplex networks

We study the totally asymmetric simple exclusion process on multiplex networks, which consist of a fixed set of vertices (junctions) connected by different types of links (segments). In particular, we assume that there are two types of segments corresponding to two different values of hopping rate of particles (larger hopping rate indicates particles move with higher speed on the segments). By simple mean-field analysis and extensive simulations, we find that, at the intermediate values of particle density, the global current (a quantity that is related to the number of hops per unit time) drops and then rises slightly as the fraction of low-speed segments increases. The rise in the global current is a counterintuitive phenomenon that cannot be observed in high or low particle density regions. The reason lies in the bimodal distribution of segment densities, which is caused by the high-speed segments.

Biologically motivated three-species exclusion model: Effects of leaky scanning and overlapping genes on initiation of protein synthesis

The totally asymmetric simple exclusion process was originally introduced as a model for the trafficlike collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motorlike forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, prefabricated functionally competent ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the predesignated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of "leaky" scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model with three interconvertible species of hard rods to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the mean time for the initiation of protein synthesis as appropriate mean first-passage time that we calculate analytically using the formalism of backward master equations. Despite the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations.

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.

Theoretical analysis of the distribution of isolated particles in totally asymmetric exclusion processes: Application to mRNA translation rate estimation

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the messenger ribonucleic acid (mRNA) during translation. Although this model has been widely studied in the past, the extent of collision between particles and the average distance between a particle to its nearest neighbor have not been quantified explicitly. We provide here a theoretical analysis of such quantities via the distribution of isolated particles. In the classical form of the model in which each particle occupies only a single site, we obtain an exact analytic solution using the matrix ansatz. We then employ a refined mean-field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from Saccharomyces cerevisiae suggests a potential bias against the detection of nearby ribosomes with a gap distance of less than approximately three codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate associated with collisions can be robustly estimated and show that approximately 1% of the translating ribosomes get obstructed.

Topology-dependent density optima for efficient simultaneous network exploration

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimize this process: How many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimized at a searcher density that is well predicted by the spectral gap. Furthermore, we find that nonequilibrium processes, realized through the addition of bias, can support significantly increased density optima. Our results suggest alternative hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.

Reactions, diffusion, and volume exclusion in a conserved system of interacting particles

Complex biological and physical transport processes are often described through systems of interacting particles. The effect of excluded volume on these transport processes has been well studied; however, the interplay between volume exclusion and reactions between heterogenous particles is less well studied. In this paper we develop a framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. We consider simple reactions (unimolecular and bimolecular) that conserve the total number of particles. From an off-lattice microscopic individual-based model we use the Fokker-Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions that require particle contact the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parametrization to experimental data than existing models.

Self-organized system-size oscillation of a stochastic lattice-gas model

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

Jamming and condensation in one-dimensional driven flow

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially condensed phase is the most interesting, compared to that in the original SB problem.

Interference of two codirectional exclusion processes in the presence of a static bottleneck: A biologically motivated model

We develop a two-species exclusion process with a distinct pair of entry and exit sites for each species of rigid rods. The relatively slower forward stepping of the rods in an extended bottleneck region, located in between the two entry sites, controls the extent of interference of the codirectional flow of the two species of rods. The relative positions of the sites of entry of the two species of rods with respect to the location of the bottleneck are motivated by a biological phenomenon. However, the primary focus of the study here is to explore the effects of the interference of the flow of the two species of rods on their spatiotemporal organization and the regulations of this interference by the extended bottleneck. By a combination of mean-field theory and computer simulation, we calculate the flux of both species of rods and their density profiles as well as the composite phase diagrams of the system. If the bottleneck is sufficiently stringent, then some of the phases become practically unrealizable, although not ruled out on the basis of any fundamental physical principle. Moreover, the extent of suppression of flow of the downstream entrants by the flow of the upstream entrants can also be regulated by the strength of the bottleneck. We speculate on the possible implications of the results in the context of the biological phenomenon that motivated the formulation of the theoretical model.

Braess paradox in a network of totally asymmetric exclusion processes

We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-length ratios.

On-site residence time in a driven diffusive system: Violation and recovery of a mean-field description

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using domain wall theory, we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP+LK), and TASEP coupled to mutually interactive LK (TASEP+MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.

Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state

Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.

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

Using the totally asymmetric simple-exclusion-process and mean-field transport theory, we investigate the transport in closed random networks with simple crossing topology-two incoming, two outgoing segments, as a model for molecular motor motion along biopolymer networks. Inspired by in vitro observation of molecular motor motion, we model the motor behavior at the intersections by introducing different exit rates for the two outgoing segments. Our simulations of this simple network reveal surprisingly rich behavior of the transport current with respect to the global density and exit rate ratio. For asymmetric exit rates, we find a broad current plateau at intermediate motor densities resulting from the competition of two subnetwork populations. This current plateau leads to stabilization of transport properties within such networks.

Ribosome recycling induces optimal translation rate at low ribosomal availability

During eukaryotic cellular protein synthesis, ribosomal translation is made more efficient through interaction between the two ends of the messenger RNA (mRNA). Ribosomes reaching the 3′ end of the mRNA can thus recycle and begin translation again on the same mRNA, the so-called ‘closed-loop’ model. Using a driven diffusion lattice model of translation, we study the effects of ribosome recycling on the dynamics of ribosome flow and density on the mRNA. We show that ribosome recycling induces a substantial increase in ribosome current. Furthermore, for sufficiently large values of the recycling rate, the lattice does not transition directly from low to high ribosome density, as seen in lattice models without recycling. Instead, a maximal current phase becomes accessible for much lower values of the initiation rate, and multiple phase transitions occur over a wide region of the phase plane. Crucially, we show that in the presence of ribosome recycling, mRNAs can exhibit a peak in protein production at low values of the initiation rate, beyond which translation rate decreases. This has important implications for translation of certain mRNAs, suggesting that there is an optimal concentration of ribosomes at which protein synthesis is maximal, and beyond which translational efficiency is impaired.

Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory, which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent 1/2 even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.

Minimal model of transcriptional elongation processes with pauses

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

Efficiency at maximum power of motor traffic on networks

We study motor traffic on Bethe networks subject to hard-core exclusion for both tightly coupled one-state machines and loosely coupled two-state machines that perform work against a constant load. In both cases we find an interaction-induced enhancement of the efficiency at maximum power (EMP) as compared to noninteracting motors. The EMP enhancement occurs for a wide range of network and single-motor parameters and is due to a change in the characteristic load-velocity relation caused by phase transitions in the system. Using a quantitative measure of the trade-off between the EMP enhancement and the corresponding loss in the maximum output power we identify parameter regimes where motor traffic systems operate efficiently at maximum power without a significant decrease in the maximum power output due to jamming effects.

Asymmetric simple exclusion process on chains with a shortcut

We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M. Yuan et al. [J. Phys. A 40, 12351 (2007)] to describe directed motion of molecular motors along twisted filaments. We report here unexpected results which revise the previous findings in the case of maximum current through the network. Our theoretical analysis, based on the effective rates' approximation, shows that the second (shunted) segment can exist in both low- and high-density phases, as well as in the coexistence (shock) phase. Numerical simulations demonstrate that the last option takes place in finite-size networks with head and tail chains of equal length, provided the injection and ejection rates at their external ends are equal and greater than one-half. Then the local density distribution and the nearest-neighbor correlations in the middle chain correspond to a shock phase with completely delocalized domain wall. Upon moving the shortcut to the head or tail of the network, the density profile takes a shape typical of a high- or low-density phase, respectively. Surprisingly, the main quantitative parameters of that shock phase are governed by a positive root of a cubic equation, the coefficients of which linearly depend on the probability of choosing the shortcut. Alternatively, they can be expressed in a universal way through the shortcut current. The unexpected conclusion is that a shortcut in the bulk of a single lane may create traffic jams.

Run-and-tumble dynamics in a crowded environment: persistent exclusion process for swimmers

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate α. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as α(-0.5) in both one and two dimensions. For a range of densities, due to cooperative effects, the stopping time scales as T(1d)(0.85) and as T(2d)(0.8), where T(d) is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.

Role of network junctions for the totally asymmetric simple exclusion process

We study the effect of local regulation mechanisms on stochastic network traffic, based on simple examples. Using the totally asymmetric simple exclusion process on a multiloop structure in which several segments share a single junction, we illustrate several mechanisms: (i) additional segments improve transport but the effect saturates due to blockage, (ii) bias reduces the overall transport and leads to several regimes, (iii) "pumping" particles out of the junctions, via a locally increased hopping rate, allows us to compensate the bottlenecks but becomes futile beyond a characteristic rate which we determine. We provide a generic discussion of combinations of these effects, including phase diagrams in terms of the control parameters.

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the noninteracting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.

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.

Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

We report here results on the study of the totally asymmetric simple exclusion process, defined on an open network, consisting of head and tail simple-chain segments with a double-chain section inserted in between. Results of numerical simulations for relatively short chains reveal an interesting feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of particles in that part of the network. In the symmetric case of equal injection and ejection rates α=β>1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high- (low-) density phases of a simple chain. The total bulk density of particles in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

Motor-mediated bidirectional transport along an antipolar microtubule bundle: a mathematical model

Long-distance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis has demonstrated that long-range motility of motors and their endosomal cargo occurs on unipolar microtubules (MTs) near the extremities of the cell. These MTs are bundled into antipolar bundles within the central part of the cell. Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion where dynein drives motility towards MT minus ends and kinesin towards MT plus ends. Although this means that one can easily assign the drivers of bidirectional motion in the unipolar section, the bipolar orientations in the bundle mean that it is possible for either motor to drive motion in either direction. In this paper we use a multilane asymmetric simple exclusion process modeling approach to simulate and investigate phases of bidirectional motility in a minimal model of an antipolar MT bundle. In our model, EE cargos (particles) change direction on each MT with a turning rate Ω and there is switching between MTs in the bundle at the minus ends. At these ends, particles can hop between MTs with rate q(1) on passing from a unipolar to a bipolar section (the obstacle-induced switching rate) or q(2) on passing in the other direction (the end-induced switching rate). By a combination of numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different values of these parameters and of Θ, the overall density of particles within this closed system. We find that even if Θ is low, the system can exhibit a variety of phases with shocks in the density profiles near plus and minus ends caused by queuing of particles. We discuss how the parameters influence the type of particle that dominates active transport in the bundle.

Modeling cytoskeletal traffic: an interplay between passive diffusion and active transport

We introduce the totally asymmetric simple exclusion process with Langmuir kinetics on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales: we find three regimes for steady state transport, corresponding to the scale of the network, of individual segments, or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram.

Efficiency at maximum power of interacting molecular machines

We investigate the efficiency of systems of molecular motors operating at maximum power. We consider two models of kinesin motors on a microtubule: for both the simplified and the detailed model, we find that the many-body exclusion effect enhances the efficiency at maximum power of the many-motor system, with respect to the single motor case. Remarkably, we find that this effect occurs in a limited region of the system parameters, compatible with the biologically relevant range.

Spectra of sparse non-hermitian random matrices: an analytical solution

We present the exact analytical expression for the spectrum of a sparse non-hermitian random matrix ensemble, generalizing two standard results in random-matrix theory: this analytical expression constitutes a non-hermitian version of the Kesten-McKay measure as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs, which are locally treelike. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends in a nonmonotonic way upon the degree of symmetry of the graph edges.

Classical driven transport in open systems with particle interactions and general couplings to reservoirs

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.