Résumé:

Résumé: Pour le transport et la répartition d'objets, de personnes etc, les voies de transport sont typiquement organisés en réseau. Les transports publiques, le réseau ferroviaire et les autoroutes en témoignent à l'échelle d'une ville ou d'un pays. Mais il en va de même à d'autres échelles, et la répartition active de constituants moléculaires dans une cellule vivante, cruciale pour sa survie, est un exemple d'une complexité particulière. Ici, le gros du travail est effectué par des moteurs moléculaires, qui se déplacent sur les fibres interconnectés du cytosquelette. Un modèle minimaliste peut être construit à partir de l'idée de réseaux aléatoires sur lesquels se déroule un transport stochastique hors équilibre, par exemple basé sur le TASEP ("Totally Asymmetric Exclusion Process"). L'analyse de tels modèles permet de mettre en place une méthodologie pour comprendre le rôle du transport sur réseau, d'apprécier le rôle des branchements dans de tels processus, et d'apprendre en passant beaucoup de physique sur les processus stochastiques hors équilibre.

Résumé:

One important role which the cytoskeleton plays in cells is to provide a network of filaments along which molecular motors can procede. This provides an essential mechanism by which a cell can establish transport of cargos over distances of the order of the cell size. The details of how such motors achieve procession along the biofilaments constituting the cytoskeleton are very complex indeed, but much of their behaviour (including collective aspects of the transport) can be described in terms of well-established models, such as the Totally Asymmetric Transport Process (TASEP) or similar. These are well-studied on single filaments. Recent work has allowed us to establish a framework to transpose this understanding to an overall network of interconnected filaments, mimicking the cytoskeleton. We discuss how new aspects of heterogeneity arise on the network scale, and we aOne important role which the cytoskeleton plays in cells is to provide a network of filaments along which molecular motors can procede. This provides an essential mechanism by which a cell can establish transport of cargos over distances of the order of the cell size. The details of how such motors achieve procession along the biofilaments constituting the cytoskeleton are very complex indeed, but much of their behaviour (including collective aspects of the transport) can be described in terms of well-established models, such as the Totally Asymmetric Transport Process (TASEP) or similar. These are well-studied on single filaments. Recent work has allowed us to establish a framework to transpose this understanding to an overall network of interconnected filaments, mimicking the cytoskeleton. We discuss how new aspects of heterogeneity arise on the network scale, and we argue that they are generic to many types of transport on networks. We also present very recent ideas for incorporating more complex features aimed at applying the approach to cytoskeletal transport in particular. rgue that they are generic to many types of transport on networks. We also present very recent ideas for incorporating more complex features aimed at applying the approach to cytoskeletal transport in particular.

Ref HAL: hal-00617509_v1
DOI: 10.1103/PhysRevLett.107.068702
WoS: 000293562900005
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78 Citations
Résumé:

We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices crucially modifies the transport features of a network: irregular networks involve homogeneous segments and have a bimodal distribution of edge densities, whereas regular networks are dominated by shocks leading to a unimodal density distribution. The proposed numerical approach of solving for mean-field transport on networks provides a general framework for studying TASEP on large networks, and is expected to generalize to other transport processes.

Commentaires: arXiv:1105.2905v2; see also highlight in Physical Review Focus http://focus.aps.org/story/v28/st6

Ref HAL: hal-00504393_v1
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Résumé:

In this paper we rationalize relevant features of totally asymmetric simple exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle–hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.

Ref HAL: hal-00364561_v1
Ref Arxiv: 0812.3559
Ref. & Cit.: NASA ADS
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Résumé:

Using molecular dynamics computer simulations we investigate the agingdynamics of a gel. We start from a fractal structure generated by the DLCA-DEFalgorithm, onto which we then impose an interaction potential consisting of ashort-range attraction as well as a long-range repulsion. After relaxing thesystem at T=0, we let it evolve at a fixed finite temperature. Depending on thetemperature T we find different scenarios for the aging behavior. For T>0.2 thefractal structure is unstable and breaks up into small clusters which relax toequilibrium. For T<0.2 the structure is stable and the dynamics slows down withincreasing waiting time. At intermediate and low T the mean squareddisplacement scales as t^{2/3} and we discuss several mechanisms for thisanomalous time dependence. For intermediate T, the self-intermediate scatteringfunction is given by a compressed exponential at small wave-vectors and by astretched exponential at large wave-vectors. In contrast, for low T it is astretched exponential for all wave-vectors. This behavior can be traced back toa subtle interplay between elastic rearrangements, fluctuations of chain-likefilaments, and heterogeneity.

Commentaires: 30 pages, 25 figures

Ref HAL: hal-00504391_v1
DOI: 10.1088/0953-8984/20/29/295213
WoS: 000257325900033
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12 Citations
Résumé:

We investigate a totally asymmetric simple exclusion process (TASEP) on a periodic hexagonal lattice with a single unit cell. We first explain the resulting stationary density profiles and the resulting fundamental current–density relation in terms of mean-field arguments. For intermediate overall densities, transport through one of the segments saturates in a maximum current phase, whereas the others develop domain walls of fixed height but fluctuating position. Via kinetic Monte Carlo simulations we focus on and fully characterize their non-equilibrium and stochastic phenomenology. We invoke a picture of anticorrelated domain wall dynamics, which we visualize as a diffusing obstruction of constant size (‘jam'). The role of the boundary conditions is discussed by comparing the periodic lattice carrying a fixed number of particles to a system coupled to reservoirs at open boundaries which is periodic only on average. We highlight the differences in their dynamics based on a novel visualization of domain wall motion at an intermediate ‘mesoscopic' timescale.