An Account of Models of Molecular Circuits for Associative Learning with Reinforcement Effect and Forced Dissociation

The development of synthetic biology has enabled massive progress in biotechnology and in approaching research questions from a brand-new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo, and in silico have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great interest to understand how associative learning is formed at the molecular circuit level. Mathematical models are increasingly used to predict the behaviours of molecular circuits. Fernando's model, which is one of the first works in this line of research using the Hill equation, attempted to design a synthetic circuit that mimics Hebbian learning in a neural network architecture. In this article, we carry out indepth computational analysis of the model and demonstrate that the reinforcement effect can be achieved by choosing the proper parameter values. We also construct a novel circuit that can demonstrate forced dissociation, which was not observed in Fernando's model. Our work can be readily used as reference for synthetic biologists who consider implementing circuits of this kind in biological systems.