Driven lattice gases: models for intracellular transport

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.