Standard model of a binary digit of memory with multiple covalent modifications in a cell

A model system of ordinary differential equations describing cyanobacteria’s circadian rhythm by use of a binary digit of memory induced by multiple covalent modification in a cell level is considered. It is mathematically rigorously proved that this system possesses bifurcation structure of hysteresis type in 1-site model. We apply it to the cyanobacterial circadian rhythm to make comparisons between some important biochemical experimental results and our simulations. These show very good agreement to elucidate theoretically fine skeleton structure with memory reinforcement effect in cell level.