Stochastic Automata Networks and Tensors with Application to Chemical Kinetics

Often, given a system of biochemical reactions, it is useful to be able to predict the system’s future state from the initial quantities of the involved molecules. There are methodologies for developing such predictions, ranging from simple approaches such as Monte Carlo simulations to more sophisticated higher-order tensors and stochastic automata networks. Many revolve around solving the chemical master equation that arises in the modeling of the underlying biochemical kinetics. This work considers the case of dealing with the resulting high-dimensional data and shows how tensor representations allow us to cope with the “curse of dimensionality” that significantly complicates such problems. A key outcome in this work is the demonstration of the inherent differences and similarities between two prominent modeling methods, by computational examples on one hand and a mathematical proof on the other hand. Applications where biochemical reactions occur are found in a variety of scenarios, including enzyme kinetics and genetics. Tensor-based solutions may have applications in dealing with many other high dimensional data outside of strictly chemical reaction systems.