At the microscopic level, the dynamics of arbitrary networks of chemical reactions can be modeled as jump Markov processes whose sample paths converge, in the limit of large number of molecules, to the solutions of a set of algebraic ordinary differential equations. Fluctuations around these asymptotic trajectories and the corresponding phase transitions can in principle be studied through large deviations theory in path space, also called Wentzell-Freidlin (W-F) theory. However, the specific form of the jump rates for this family of processes does not, in general, satisfy the standard regularity assumptions imposed by such theory.
In this talk, I will first introduce some results in chemical reaction network theory, connecting the dynamical properties of these dynamical systems to the structure of the underlying network of reactions. I will then discuss sufficient stability and nondegeneracy conditions on the given family of Markov jump processes to obtain the desired large deviations estimates, and show how these conditions can be translated into structural ones, in the spirit of the results introduced earlier, facilitating their verification for large metabolic networks.