College of Liberal Arts & Sciences

# Math Biology Seminar

**Abstract: **

A crucial stage in the production of proteins from the information encoded in the genes is called translation. During this stage, complex molecular machines, called ribosomes, bind to the mRNA and "read" it in a sequential manner. In 2011, Reuveni et al. suggested a nonlinear dynamical model for this process called the Ribosome Flow Model (RFM). The RFM can be derived as a mean-field approximation of an important model from non-equilibrium statistical physics called the Totally Asymmetric Simple Exclusion Process (TASEP). In this talk, we analyze the RFM using tools from systems and control theory including contraction theory, monotone systems theory, the analytic theory of continued fractions, Perron-Frobenius theory, and convex analysis. We detail several biological implications of the analysis and compare them to known experimental results. Joint work with Tamir Tuller (Tel Aviv University), Alexander Ovseevich (Institute for Problems in Mechanics, Moscow), and Eduardo D. Sontag (Northeastern University).