Hierarchy of models: from qualitative to quantitative analysis of circadian rhythms in cyanobacteria

Abstract

A hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations' models derived from the PWA model. This hierarchy provides different levels of approximation of the biological system and, crucially, allows the use of theoretical tools to more exactly analyze and understand the mechanisms of the system. The Kai ABC oscillator, which is at the core of the cyanobacterial circadian rhythm, is analyzed as a case study, showing how several fundamental properties-order of oscillations, synchronization when mixing oscillating samples, structural robustness, and entrainment by external cues-can be obtained from basic mechanisms.