Dr. Bence Melykuti (Postdoc with MechEng at UCSB)

Title: Searching for a diffusion process model for chemical reaction kinetics: the chemical Langevin equation and beyond

Abstract: Our objective is to examine the standard Ito stochastic differential equation (SDE) model for (bio)chemical reaction kinetics, the chemical Langevin equation (CLE). By the connection between the martingale problem and the existence of a weak solution for an SDE, we can formulate the CLE in alternative, weakly equivalent forms. We explore what the minimum number of Brownian motions necessary for an equivalent formulation is and discuss the corresponding underlying geometrical structure. We find another formulation that speeds up numerical simulation. We also show that in terms of first and second moments, the CLE appears to be the best Ito SDE model for reaction kinetics. We highlight that in its original form, the variables of the CLE can become negative with positive probability. This leads to the open question whether there exists a nonnegativity-preserving, continuous stochastic model for reaction kinetics, and whether it is driven by standard Brownian motion or something else.