Mathematical Biology seminar Tory Richardson University of Utah "Fast DNA target finding by facilitated diffusion" Tuesday, February 24 1-2pm in LCB 215 Abstract: I will present a stochastic model for facilitated diffusion, the mechanism by which regulatory proteins locate short, specific binding sequences within a much larger DNA substrate. The search alternates between two modes: a slow, one-dimensional exploration along DNA and a fast, three-dimensional excursion through the surrounding cytosol. In the model, proteins switch randomly between these states until the target is reached, and this intermittency can substantially shorten target-finding times relative to single-mode descriptions. In many settings, experimentally relevant timescales are controlled by extreme events, in particular, the minimum first-passage time to the target among many independent proteins. Using short-time asymptotics of the first-passage distribution, I will identify distinct regimes for these extreme statistics and show how the fastest target-finding time depends on protein copy number N and the switching rates between search modes. Incorporating extreme first-passage behavior can also reconcile discrepancies between observed binding times and predictions from earlier models.