Rate Theory for Driven Complex Biosystems: Stochastic Modelling and Computer Simulations

The present proposal for renewal comprises two major themes which relate to different aspects of biocomplexity. Namely, we plan to study (i) time-dependent features of neuronal coding and (ii) stochastic transport properties of bio-particles through bottlenecks. These two objectives are accessible by related theoretical modellings and similar numerical simulation techniques. In particular, in both aspects the non-linear stochastic dynamics are described in terms of few temporal or spatial-temporal relevant variables. Fluctuations induce escape processes from stable manifolds of the state variables describing their passage across dynamical thresholds, free energy or entropic barriers or physical bottlenecks. These escape events, being driven by non-stationary or non-Markovian noises define the principal unifying theme and, within a rate theory framework, constitute a new conceptual approach of modelling and simulating complex (bio-)systems.