Robustness Analysis of Intracellular Oscillators with Application to the Circadian Clock

Abstract: Periodic oscillations underlie many intracellular functions, such as circadian time keeping, cell cycle control and locomotor pattern generation in nerve cells. These intracellular oscillations are generated in intricate biochemical reaction networks involving genes, proteins and other biochemical components. In most cases, robust oscillations are of pivotal importance for the organism, i.e., the oscillations must be maintained in the presence of internal and external perturbations.Model based analysis of robustness in intracellular oscillators has attracted considerable attention in recent years. The analysis has almost exclusively been based on either complete removal of network components, e.g., single genes, or perturbation of model parameters. In this thesis, a control theoretic approach to analyze structural robustness of intracellular oscillators is proposed. The method is based on adding dynamic perturbations to the network interactions. Determination of the smallest perturbation translating the underlying steady-state into a Hopf bifurcation point is used to quantify the robustness. The method can be used to determine critical substructures within the overall network and to identify specific network fragilities. Also, an approach to nonlinear model reduction based on the robustness analysis is proposed.The proposed robustness analysis method is applied to elucidate mechanisms underlying robust oscillations in circadian clocks. Circadian clocks, molecular oscillators generating 24 hour rhythms in many organisms, are known to display a striking robustness towards internal and external perturbations. The underlying networks involve a large number of genes that are transcribed into mRNA which produce proteins subsequently regulating the activity of other genes, together forming an intricate network with a large number of embedded feedback loops. An often recurring hypothesis is that the interlocked feedback loop structure of circadian clocks serves the purpose of robustness. From analysis of several recently published models of circadian clocks, it is found in this thesis that the robustness of circadian clocks primarily results from a high gain in a single gene regulatory feedback loop generating the oscillations. This gain can be elevated by additional feedback loops, involving either gene regulation or post-translational feedback, but a similar robustness can be achieved by simply increasing the amplification within the master feedback loop.