Ilya Nemenman

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  Stochastic processes in the adiabatic limit: applications to biochemistry and population genetics
  Ilya Nemenman
  Stochastic biochemical systems and population genetics models are described by similar mathematical equations, and hence similar phenomena should be observed in both systems. Here we focus on stochastic kinetics with time scale separation. We show how to integrate out the fast degrees of freedom, while rigorously preserving their effects on the fluctuations of slower variables. This procedure allows to speed up simulation of kinetic networks and reveals a number of interesting phenomena, previously unobserved in the context of classical stochastic kinetics. One of the most interesting is the emergence of geometric phases, which we show may have substantial effects on, in particular, the frequency of fixation of new mutations in slowly variable environments.
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  Robust completion time distributions in complex biological networks
  Ilya Nemenman
  Ilya Nemenman, Physics, Emory University
  
  Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. I will present a characterization of the first passage (completion) time distributions for such processes. I will argue that, for a wide class of biochemical kinetics systems related to kinetic proofreading, the completion time time behavior simplifies as the system size grows: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. This robust simplification of completion time distributions is independent of many microscopic details of the signaling systems and can be utilized for efficient control of cellular response properties. Even further simplifications are possible when one considers dynamics of many coupled kinetic proofreading enabled receptors, which can attain low activation noise with robust mean time to activation.