305 research outputs found
Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates
We analyze the open boundary partially asymmetric exclusion process with
smoothly varying internal hopping rates in the infinite-size, mean field limit.
The mean field equations for particle densities are written in terms of Ricatti
equations with the steady-state current as a parameter. These equations are
solved both analytically and numerically. Upon imposing the boundary conditions
set by the injection and extraction rates, the currents are found
self-consistently. We find a number of cases where analytic solutions can be
found exactly or approximated. Results for from asymptotic analyses for
slowly varying hopping rates agree extremely well with those from extensive
Monte Carlo simulations, suggesting that mean field currents asymptotically
approach the exact currents in the hydrodynamic limit, as the hopping rates
vary slowly over the lattice. If the forward hopping rate is greater than or
less than the backward hopping rate throughout the entire chain, the three
standard steady-state phases are preserved. Our analysis reveals the
sensitivity of the current to the relative phase between the forward and
backward hopping rate functions.Comment: 12 pages, 4 figure
Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions
Totally asymmetric simple exclusion processes on lattices with junctions,
where particles interact with hard-core exclusion and move on parallel lattice
branches that at the junction combine into a single lattice segment, are
investigated. A simple approximate theory, that treats the correlations around
the junction position in a mean-field fashion, is developed in order to
calculate stationary particle currents, density profiles and a phase diagram.
It is shown that there are three possible stationary phases depending on the
state of each of the lattice branch. At first-order phase boundaries, where the
density correlations are important, a modified phenomenological domain-wall
theory, that accounts for correlations, is introduced. Extensive Monte Carlo
computer simulations are performed to investigate the system, and it is found
that they are in excellent agreement with theoretical predictions.Comment: 16 pages, 7 figure
Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes
Kinesins are processive motor proteins that move along microtubules in a
stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent
experiments have investigated the coupling between the individual steps of
single kinesin molecules and ATP hydrolysis, taking explicitly into account
forward steps, backward steps and detachments. A theoretical study of
mechanochemical coupling in kinesins, which extends the approach used
successfully to describe the dynamics of conventional motor proteins, is
presented. The possibility of irreversible detachments of kinesins from the
microtubules is also explicitly taken into account. Using the method of first-
passage times, experimental data on the mechanochemical coupling in kinesins
are fully described using the simplest two-state model. It is shown that the
dwell times for the kinesin to move one step forward or backward, or to
dissociate irreversibly are the same, although the probabilities of these
events are different. It is concluded that the current theoretical view, that
only the forward motion of the motor protein molecule is coupled to ATP
hydrolysis, is consistent with all available experimental observations for
kinesins.Comment: Submitted to Biophysical Journa
Local Inhomogeneity in Asymmetric Simple Exclusion Processes with Extended Objects
Totally asymmetric simple exclusion processes (TASEP) with particles which
occupy more than one lattice site and with a local inhomogeneity far away from
the boundaries are investigated. These non-equilibrium processes are relevant
for the understanding of many biological and chemical phenomena. The
steady-state phase diagrams, currents, and bulk densities are calculated using
a simple approximate theory and extensive Monte Carlo computer simulations. It
is found that the phase diagram for TASEP with a local inhomogeneity is
qualitatively similar to homogeneous models, although the phase boundaries are
significantly shifted. The complex dynamics is discussed in terms of
domain-wall theory for driven lattice systems.Comment: 11 pages, 5 figure
Current reversal and exclusion processes with history-dependent random walks
A class of exclusion processes in which particles perform history-dependent
random walks is introduced, stimulated by dynamic phenomena in some biological
and artificial systems. The particles locally interact with the underlying
substrate by breaking and reforming lattice bonds. We determine the
steady-state current on a ring, and find current-reversal as a function of
particle density. This phenomenon is attributed to the non-local interaction
between the walkers through their trails, which originates from strong
correlations between the dynamics of the particles and the lattice. We
rationalize our findings within an effective description in terms of
quasi-particles which we call front barriers. Our analytical results are
complemented by stochastic simulations.Comment: 5 pages, 6 figure
Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes
Asymmetric exclusion processes for particles moving on parallel channels with
inhomogeneous coupling are investigated theoretically. Particles interact with
hard-core exclusion and move in the same direction on both lattices, while
transitions between the channels is allowed at one specific location in the
bulk of the system. An approximate theoretical approach that describes the
dynamics in the vertical link and horizontal lattice segments exactly but
neglects the correlation between the horizontal and vertical transport is
developed. It allows us to calculate stationary phase diagrams, particle
currents and densities for symmetric and asymmetric transitions between the
channels. It is shown that in the case of the symmetric coupling there are
three stationary phases, similarly to the case of single-channel totally
asymmetric exclusion processes with local inhomogeneity. However, the
asymmetric coupling between the lattices lead to a very complex phase diagram
with ten stationary-state regimes. Extensive Monte Carlo computer simulations
generally support theoretical predictions, although simulated stationary-state
properties slightly deviate from calculated in the mean-field approximation,
suggesting the importance of correlations in the system. Dynamic properties and
phase diagrams are discussed by analyzing constraints on the particle currents
across the channels
Sequence Heterogeneity Accelerates Protein Search for Targets on DNA
The process of protein search for specific binding sites on DNA is
fundamentally important since it marks the beginning of all major biological
processes. We present a theoretical investigation that probes the role of DNA
sequence symmetry, heterogeneity and chemical composition in the protein search
dynamics. Using a discrete-state stochastic approach with a first-passage
events analysis, which takes into account the most relevant physical-chemical
processes, a full analytical description of the search dynamics is obtained. It
is found that, contrary to existing views, the protein search is generally
faster on DNA with more heterogeneous sequences. In addition, the search
dynamics might be affected by the chemical composition near the target site.
The physical origins of these phenomena are discussed. Our results suggest that
biological processes might be effectively regulated by modifying chemical
composition, symmetry and heterogeneity of a genome.Comment: 10 pages, 5 figure
Duality and phase diagram of one dimensional transport
The observation of duality by Mukherji and Mishra in one dimensional
transport problems has been used to develop a general approach to classify and
characterize the steady state phase diagrams. The phase diagrams are determined
by the zeros of a set of coarse-grained functions without the need of detailed
knowledge of microscopic dynamics. In the process, a new class of
nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files
- …