9 research outputs found
Far-from-equilibrium transport with constrained resources
The totally asymmetric simple exclusion process (TASEP) is a well studied
example of far-from-equilibrium dynamics. Here, we consider a TASEP with open
boundaries but impose a global constraint on the total number of particles. In
other words, the boundary reservoirs and the system must share a finite supply
of particles. Using simulations and analytic arguments, we obtain the average
particle density and current of the system, as a function of the boundary rates
and the total number of particles. Our findings are relevant to biological
transport problems if the availability of molecular motors becomes a
rate-limiting factor.Comment: 14 pages, 7 figures, uses iopart12.clo and iopart.cl
Competition between Multiple Totally Asymmetric Simple Exclusion Processes for a Finite Pool of Resources
Using Monte Carlo simulations and a domain wall theory, we discuss the effect
of coupling several totally asymmetric simple exclusion processes (TASEPs) to a
finite reservoir of particles. This simple model mimics directed biological
transport processes in the presence of finite resources, such as protein
synthesis limited by a finite pool of ribosomes. If all TASEPs have equal
length, we find behavior which is analogous to a single TASEP coupled to a
finite pool. For the more generic case of chains with different lengths,
several unanticipated new regimes emerge. A generalized domain wall theory
captures our findings in good agreement with simulation results.Comment: 14 pages, 13 figures, v2: minor change
Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources
We revisit a totally asymmetric simple exclusion process (TASEP) with open
boundaries and a global constraint on the total number of particles [Adams, et.
al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles
into the lattice depends on the number available in the reservoir. Thus, the
total occupation on the lattice feeds back into its filling process. Although a
simple domain wall theory provided reasonably good predictions for Monte Carlo
simulation results for certain quantities, it did not account for the
fluctuations of this feedback. We generalize the previous study and find
dramatically improved predictions for, e.g., the density profile on the lattice
and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change
Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process
To synthesize proteins in a cell, an mRNA has to work with a finite pool of
ribosomes. When this constraint is included in the modeling by a totally
asymmetric simple exclusion process (TASEP), non-trivial consequences emerge.
Here, we consider its effects on the power spectrum of the total occupancy,
through Monte Carlo simulations and analytical methods. New features, such as
dramatic suppressions at low frequencies, are discovered. We formulate a theory
based on a linearized Langevin equation with discrete space and time. The good
agreement between its predictions and simulation results provides some insight
into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change
Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
The phenomenon of protein synthesis has been modeled in terms of totally
asymmetric simple exclusion processes (TASEP) since 1968. In this article, we
provide a tutorial of the biological and mathematical aspects of this approach.
We also summarize several new results, concerned with limited resources in the
cell and simple estimates for the current (protein production rate) of a TASEP
with inhomogeneous hopping rates, reflecting the characteristics of real genes.Comment: 25 pages, 7 figure