Exhaustive Analysis for the Effects of a Feedback Regulation on the Bi-Stability in Cellular Signaling Systems

摘要

Cellular signaling systems regulate biochemical reactions operating in cells for various functions. The regulatory mechanisms have been recently studied intensively since the malfunction of the regulation is thought to be one of the substantial causes of cancer formation. However, it is rather difficult to develop the theoretical framework for investigation of the regulatory mechanisms due to their complexity and nonlinearity. In this study, more general approach is proposed for elucidation of emergence of the bi-stability in cellular signaling systems by construction of mathematical models for a class of cellular signaling systems and the exhaustive simulation analysis over the variation of network architectures and the values of parameters. The model system is formulated as regulatory network in which every node represents an activation-inactivation cyclic reaction for respective constituent enzyme of the network and the regulatory interactions between the reactions are depicted by arcs between nodes. The emergence of the stable equilibrium point in steady states of the network is analyzed with the Michaelis-Menten reaction scheme as the reaction mechanism in each cyclic reaction. The analysis is performed for all variations of the regulatory networks comprised of two nodes, three nodes, and four nodes with a single feedback regulation loop. The ratios and the aspects of the emergence of the stable equilibrium points are analyzed over the exhaustive combinations of the parameter values for each node with the common Michaelis constant for the regulatory networks. It is revealed that the shorter feedback length is favorable for bi-stability. Furthermore, the bi-stability and the oscillation is more likely to develop in the case of low value of the Michaelis constant than in the case of high value, implying that the condition of the higher saturation levels, which induces stronger nonlinearity. In addition to these results, the analysis for the parameter regions yielding the bi-stability and the oscillation are presented.