Mathematical comparison of memory functions between mutual activation and repression networks in a stochastic environment

Biological memory is a ubiquitous function that can generate a sustained response to a transient inductive stimulus. To better understand this function, we must consider the mechanisms by which different structures of genetic networks achieve memory. Here, we investigated two competitive gene regulatory network models: the regulated mutual activation network (MAN) and the regulated mutual repression network (MRN). Stochasticity deteriorated the persistence of memory of both the MAN and the MRN. Mathematical comparison by simulation and theoretical analysis identified functional differences in the stochastic memory between the competitive models: specifically, the MAN provided much more robust, persistent memory than the MRN. The stochastic persistent memory pattern of the MAN can be adjusted by changing the binding strength of the activators, whereas the MRN required highly cooperative and strong binding repressors for robust memory.