Period Robustness Analysis of Minimal Models for Biochemical Oscillators

Mathematical modeling is a sophisticated method that facilitates the analysis and understanding of complex biological systems, for example, oscillatory systems. In biology, oscillatory systems are found in numerous species ranging from calcium oscillations to circadian rhythms. These oscillators, of autonomous nature, contain complex feedback mechanisms ruled by molecular interactions that determine the physiology and enable spontaneous oscillations. Although previous results using both experimental and theoretical approaches have revealed core molecular network topologies and conditions that allow autonomous oscillations, many important questions remain elusive.;In this thesis, we investigate five different minimal models that may underlie fundamental molecular processes in biological oscillatory systems. We focus on dynamical differences and period maintenance of the models. In particular, we introduce two types of noises into these minimal models and perform numerical bifurcation and period sensitivity analyses.;Our results demonstrate that small wiring modifications lead to substantial dynamical changes and the oscillatory domain is enlarged in models that involve a positive feedback mechanism including a reversible reaction. Additionally, the outcomes from sensitivity analysis in the presence of external or internal noises reveal different rankings in the hierarchy of period robustness of the five minimal models. Ranking of the models is determined by the number of highly sensitive parameters, network topology and/or noise strength. Finally, we demonstrate that minimal models including positive feedback via autocatalysis are more robust than those where positive feedback is exerted through inhibition of degradation regardless of the noise type.;This investigation will be useful to analyze fundamental molecular mechanisms of different biological oscillators. We admit that characteristics of minimal models may be too simple for modeling a detailed behavior of complex biological oscillators. However, our data indicate that these minimal models may be used as building blocks for biochemical oscillators of greater complexity using synthetic biology.