Speaker: Dan Daniel Erdmann-Pham, UC Berkeley
Abstract: On a molecular level, a gene's typical journey from DNA to functional protein is governed by a number of coupled interacting particle systems whose dynamics determine the gene's ultimate abundance, stability and viability. Analyzing these systems is thus a prerequisite for understanding and predicting gene expression at large, but often complicated by the presence of long-range correlations, possibly non-equilibrium dynamics, and the high dimensionality of couplings between them.
In this talk, we will focus on one of the most central such processes, the so-called inhomogeneous l-TASEP, used to approximate a form of stochastic, driven transport of particle-like objects on finite lattices. While simplified versions of the TASEP have been thoroughly studied as model systems in non-equilibrium statistical mechanics and for their unexpected connections to random matrix theory and the nascent KPZ universality class, the tools and ideas developed therein tend to not transfer easily to the most general TASEP setup necessary for describing gene expression. We begin to bridge this gap by establishing the hydrodynamic limit of the inhomogeneous l-TASEP, describing the process on an LLN-type scale, and use it to obtain closed-form formulae for particle densities and currents, as well as a characterization of the associated phase diagram. With these in hand, we formulate a set of design principles to optimize gene expression regulation, corroborate such principles on data, and give a perspective on where our results stand in the greater picture of understanding the gene expression ecosystem as a whole.