Learning capacity and function of stochastic reaction networks

Biochemical reaction networks are expected to encode an efficient representation of the function of cells in a variable environment. It is thus important to see how these networks do learn and implement such representations. The first step in this direction is to characterize the function and learning capabilities of basic artificial reaction networks. In this study, we consider multilayer networks of reversible reactions that connect two layers of signal and response species through an intermediate layer of hidden species. We introduce a stochastic learning algorithm that updates the reaction rates based on the correlation values between reaction products and responses. Our findings indicate that the function of networks with random reaction rates, as well as their learning capacity for random signal-response activities, are critically determined by the number of reactants and reaction products. Moreover, the stored patterns exhibit different levels of robustness and qualities as the reaction rates deviate from their optimal values in a stochastic model of defect evolution. These findings can help suggest network modules that are better suited to specific functions, such as amplifiers or dampeners, or to the learning of biologically relevant signal-response activities.