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Pierobon, Paolo (2006): Driven lattice gases: models for intracellular transport. Dissertation, LMU München: Faculty of Physics
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Abstract

Intracellular transport phenomena, such as kinesins and myosins moving along cytoskeletal filaments or ribosomes along messenger RNA, can be modeled by one-dimensional driven lattice gases. Among these, the Totally Asymmetric Simple Exclusion Process (TASEP), has been extensively used. It describes a system of particles hopping in a preferred direction with hard core interaction. The goal of this thesis is to explore the relevance of some features that are missed by this simple model, such as the exchange of particles between molecular track and the cytoplasm, the extended molecular structure of each motor, and the interaction of motors with imperfections on the track acting as road blocks for intracellular traffic. Recent studies have taken into account particle exchange between the track and bulk solution (Langmuir kinetics). It was found that this violation of current conservation along the track leads to phase coexistence regions in the phase diagram not present in the TASEP. We have extended these studies in two ways. First, motivated by the fact that many molecular motors are dimers, we study how the stationary properties of the system (density profile and phase behavior) change upon replacing monomers with extended particles. Analytical refined and generalized mean field theory, supported by numerical Monte Carlo simulations, give a detailed description of the phase diagram. Our study proves that the extension gives quantitative but not qualitative changes in the phase diagram, showing that the picture obtained in the case of monomers is robust upon considering extended particles. Second, motivated by the presence of structural imperfections of the track that act as road blocks, we study the influence of an isolated defect characterized by a reduced hopping rate on the non-equilibrium steady state. We explore the phase behavior in the full parameter range and find that the phase diagram changes qualitatively as compared to the case without defects, showing new phase coexistence regions. In particular above a certain threshold strength of the defect, its presence induces a macroscopic change in the density profile. The regions where the defect is relevant (called bottleneck phases) are identified and studied. In the second part of the thesis we investigate the dynamical features of these models. First we concentrate on the dynamics of the simple TASEP, for which a complete analysis was missing. We use a technique borrowed from solid state physics, the Boltzmann-Langevin method, to give a full description of the correlation function in the whole parameter space. Finally we study the dynamics of a tracer particle in a TASEP with on-off kinetics. We observe that it is possible to reconstruct the density profile from the velocity of the tracer particle and we propose to perform single molecule experiments with fluorescently labelled molecular motors to explore the density profile and ultimately test the phase behavior predicted in this thesis.