Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations

The underlying molecular mechanisms of metabolic and genetic regulations are computationally identical and can be described by a finite state Markov process. We establish a common computational model for both regulations based on the stationary distribution of the Markov process with the aim of establishing a unified, quantitative model of general biological regulations. Various existing results regarding intracellular regulations are derived including the classical Michaelis-Menten equation and its generalization to more complex allosteric enzymes in a systematic way. The notion of probability flow is introduced to distinguish the equilibrium stationary distribution from the non-equilibrium one; it plays a crucial role in the analysis of stationary state equations. A graphical criterion to guarantee the existence of an equilibrium stationary distribution is derived, which turns out to be identical to the classical Wegscheider condition. Simple graphical methods to compute the equilibrium and non-equilibrium stationary distributions are derived based crucially on the probability flow, which dramatically simplifies the classical methods still used in enzymology.