abstract: The open-boundary totally asymmetric simple exclusion process (TASEP) with extended particles is an interacting particle system on the lattice of length N, where particles of size l are injected at the left, move (under particle exclusion) to the right at site-specific rates, and leave the lattice with at characteristic rates at the end.
Its versatility and tractability have made the TASEP an attractive stochastic process in various communities: While the homogeneous and near-homogeneous 1−TASEP have been explored by mathematicians and physicists in the context of KPZ universality and non-equilibrium phase transitions, more complex versions of it have found application in modeling processes like molecular transport, gene expression and traffic dynamics.
Despite much progress, when particles are of extended size l > 1 and move at site-dependent rates (as in most biological processes), theoretically analyzing the behavior of the system and the associated phase diagram has remained elusive. Here we present such an analysis in the hydrodynamic limit. Upon deriving the general PDE satisfied by the density of particles, we characterize the associated phase diagram and show that its boundaries are determined by four quantities only; namely the particle size l, and the first, the last, and the minimum hopping rates along the lattice. For each region of the phase diagram, our closed-form formulas for the flux and site-specific particle density agree well with Monte Carlo simulations.
We will apply our theoretical work on a data set of ribosome profiles measured during protein synthesis, illustrating how the underlying biological mechanisms optimize for production rates and costs by judicious choice of relevant parameters.