The Totally Asymmetric Simple Exclusion Process (TASEP) is a classical stochastic process which has
been used to model transport phenomena in various non-equilibrium particle systems in statistical
physics, traffic systems, and biology. In the context of mRNA translation, we have recently studied
a generalized version of this process, called the inhomogeneous ℓ-TASEP, to provide analytical
formulas for the general statistics associated with the particle current and density. More
precisely, our methods rely on solving a non-linear PDE that generalizes the Burgers’ equation and
describes the average dynamics of the current. This PDE is derived from considering the process in
the so-called “hydrodynamic limit”, obtained as the lattice size gets large. These results have the
advantage of enabling an immediate quantification of the process and its phase diagram as a
function of the different parameters associated with it, which is impossible to achieve via
conventional stochastic simulations.
To help mathematicians, physicists and biologists visualize these results and apply them in other
contexts, we have developed the present software, which provides a user-friendly and easy-to-run
graphical user interface. We provide a stand-alone version available for download at this address:
https://github.com/songlab-cal/EGGTART
For any input values of particle size, entrance rate, exit rate, and site-specific hopping rates,
CIVET enables a complete visualization and extraction of the main quantities of interest associated
with the transport process, such as the current, density, and a full description of the phase
diagram associated with different types of traffic behavior. The scope of our visualization might
be of interest not only to researchers primarily studying interacting particle and transport
systems, but also mathematicians and physicists working in PDEs and dynamical systems, as it leads
to identify major shocks, rarefaction waves and ultimately the stationary density achieved in the
long time limit for a general conservation law.
Accompanying our software, we provide a user manual which contains an introduction and
description of the general features of the software. This manual also contains a tutorial
that helps to understand the main properties of the TASEP, and should be used with the demo
.csv input files provided with the software. The
manual and .csv files can be downloaded at the same address as the software.
Keywords | transport phenomena, stochastic processes, PDE, l-TASEP (Totally Asymmetric Simple Exclusion Process) |
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