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