Positive Dynamical Networks in Neuronal Regulation: How Tunable Variability Coexists with Robustness

Neuronal systems exhibit highly stable and tunable behaviors in spite of huge variability at the molecular component level and in spite of persistent physiological and pathological perturbations. How is this robust flexibility achieved? Homeostatic integral control has been shown to be key in reconciling variability with stability, but the explanatory model used lacks basic robustness properties to perturbations. We suggest that positive molecular regulatory networks may play a major role in reconciling stability, variability and robustness. The idea we propose is that integral control happens along the dominant direction of the network. This slow direction generates a strongly attractive, and thus robust, subspace along which almost perfect homeostatic regulation can be achieved. Fluctuations of relevant molecular variables along this positive dominant subspace explain how big, positively-correlated variations of biophysical parameters (as measured in experiments) are compatible with robust regulation, thus explaining flexibility. Because of robustness, the properties of the positive network can be subject to slower tuning processes (like the circadian rhythm), which provides a biologically plausible basis for tunable variability to be compatible with robust regulation. The relevance of the proposed regulation model for control-theoretical approaches to neurological diseases is also discussed.