Noise-induced phenomena and complex rhythms: Theoretical considerations, modelling and experimental

Abstract

Combining the unravelling of the molecular bases of functions in time and of organization in space in biology, on the one hand, with nonlinear dynamics as part of theoretical physics, on the other, is promising great progress in basic understanding of nonlinear spatial pattern formation from huge amounts of data becoming available in systems biology. In this chapter, this will be assessed in terms of the tripod (1) experimentation, (2) modelling and (3) theory. (1) As empirical case studies we will mainly use in this chapter spatiotemporal dynamics of crassulacean acid metabolism and stomatal pore regulation by guard cells. These can be documented by, among other techniques, chlorophyll fluorescence imaging. This leads to modelling and theoretical treatment of circadian and ultradian endogenous oscillations. (2) In modelling, maximum models, providing perfectionist "photographic" imaging of nature, are distinguished from minimal models singling out essential domains in the parameter space of systems, with heuristic aims. The latter are explored in approaches based on experiment/theory feedback. (3) Theoretical assessment dwells on the method of cellular automata, which are frameworks for simulating spatiotemporal patterns arising from local interactions. The theoretical concepts developed are based on the examination of stochasticity with the order-generating effects of noise in stochastic resonance and coherence resonance, where intermediate noise intensity generates quasi-rhythmic behaviour of systems from arrythmicity. This merges into a new path towards systems biology, where the huge amount of data currently provided by analytical progress is cast into the concept of universal dynamic principles. We illustrate this new path by using simple models of synchronization, this being one concept which systems biology can then exploit for the construction of advanced models.