Impacts of statistical feedback on the flexibility-accuracy trade-offin biological systems

Biological systems possess the ability to adapt quickly andadequately to both environmental and internal changes. This vital ability cannot be explained in terms ofconventional stochastic processes because such processes arecharacterized by atrade-off between flexibility and accuracy, that is, they either show shorttransition times (large Kramers escape rates) to broad steady-statedistributions or long transition times to sharply peaked distributions. To develop a stochastic theory for systemsexhibiting both flexibility and accuracy, we study systems under the impact of white noise multiplied with anaccordant statistical measure, here the probability density. Thisresults in negative feedback and circular causality: the more probable a stable state the lessit will be affected by noise and, conversely, the less a stable state is affected by noisethe more probable it is. Using nonlinear Fokker-Planckequations, steady states are computed via transformations ofsolutions of the corresponding linear Fokker-Planck equations. Transients reveal rapidly evolving and sharply peaked probability densities and thus mimic systems characterized by both flexibility and accuracy.