Driven lattice gases: models for intracellular transport
Intracellular transport phenomena, such as kinesins and myosins moving\nalong cytoskeletal filaments or ribosomes along messenger RNA, can be\nmodeled by one-dimensional driven lattice gases. Among these, the\nTotally Asymmetric Simple Exclusion Process (TASEP), has been\nextensively used. It describes a system of particles hopping in a\npreferred direction with hard core interaction. The goal of this\nthesis is to explore the relevance of some features that are missed by\nthis simple model, such as the exchange of particles between molecular\ntrack and the cytoplasm, the extended molecular structure of each\nmotor, and the interaction of motors with imperfections on the track\nacting as road blocks for intracellular traffic.\n\nRecent studies have taken into account particle exchange between the\ntrack and bulk solution (Langmuir kinetics). It was found that this\nviolation of current conservation along the track leads to phase\ncoexistence regions in the phase diagram not present in the TASEP. We\nhave extended these studies in two ways. First, motivated by the fact\nthat many molecular motors are dimers, we study how the stationary\nproperties of the system (density profile and phase behavior) change\nupon replacing monomers with extended particles. Analytical refined\nand generalized mean field theory, supported by numerical Monte Carlo\nsimulations, give a detailed description of the phase diagram. Our\nstudy proves that the extension gives quantitative but not qualitative\nchanges in the phase diagram, showing that the picture obtained in the\ncase of monomers is robust upon considering extended particles.\nSecond, motivated by the presence of structural imperfections of the\ntrack that act as road blocks, we study the influence of an isolated\ndefect characterized by a reduced hopping rate on the non-equilibrium\nsteady state. We explore the phase behavior in the full parameter\nrange and find that the phase diagram changes qualitatively as\ncompared to the case without defects, showing new phase coexistence\nregions. In particular above a certain threshold strength of the\ndefect, its presence induces a macroscopic change in the density\nprofile. The regions where the defect is relevant (called bottleneck\nphases) are identified and studied.\n\nIn the second part of the thesis we investigate the dynamical features\nof these models. First we concentrate on the dynamics of the simple\nTASEP, for which a complete analysis was missing. We use a technique\nborrowed from solid state physics, the Boltzmann-Langevin method, to\ngive a full description of the correlation function in the whole\nparameter space. Finally we study the dynamics of a tracer particle\nin a TASEP with on-off kinetics. We observe that it is possible to\nreconstruct the density profile from the velocity of the tracer\nparticle and we propose to perform single molecule experiments with\nfluorescently labelled molecular motors to explore the density profile\nand ultimately test the phase behavior predicted in this thesis.