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Metastable dynamics: rare events in cell biology

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SDB - Stochastic dynamical systems in biology: numerical methods and applications

I will discuss an emerging framework where the extensive and powerful toolbox of deterministic dynamical systems can be used to study an important class of noise induced stochastic phenomena, called metastable dynamics. Consider two trajectories: one deterministic and one perturbed by weak noise, each having the same initial conditions. A single fluctuation is very unlikely to perturb the stochastic trajectory very far from the deterministic trajectory, and on short time scales the two remain close. On long time scales, both trajectories approach a stable steady state.  Given enough time, it is possible for a rare sequence of fluctuations to perturb the stochastic trajectory far enough that it moves toward a different steady state. Hence, a stable steady state for a deterministic system becomes a metastable state under the influence of weak noise. I will discuss two applications in biology.   1. The first application is epigenetic switching in gene circuits, the biological problem that first motivated my research. It has been known for decades that gene expression is strongly influenced by random forces within the cell. Rare events driven by noise can cause a dramatic shift in the way a gene is expressed, which can radically alter the state of a cell. One example is an altered state that imparts antibiotic resistance to e-coli bacteria. I will show that diffusion approximations, widely used to study gene expression systems, are inaccurate and unreliable for metastable phenomena. As an alternative, I will propose a far more accurate direct method that eliminates the need for a diffusion approximation.   2. The second application is spontaneous neural activity. Intrinsic noise from molecular fluctuations of voltage-gated ion channels cause spontaneous activity that propagates into and affects local network function.  A spontaneous action potential is a physical example of a new type of first-exit-time problem: the random time to initiate an excitable event in an excitable system with a single fixed point. Using a metastable phase plane analysis, I will show how noise induced excitable events in the stochastic Morris-Leccar model are initiated through a predictable sequence of events. In other words, a single mechanism explains how spontaneous activity is generated. Moreover, the generating mechanism contradicts the current understanding of this phenomena.  It is widely believed that spontaneous activity in most neurons is driven primarily by fast sodium channels, because these channels govern the fast initiation stage of an action potential. Potassium channels respond much more slowly and are responsible for reseting the membrane voltage at the final stage of the action potential. Contrary to the standard paradigm, metastable dynamics predicts that the primary driving force behind spontaneous initiation is the slow potassium channel noise.

This talk is part of the Isaac Newton Institute Seminar Series series.

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