Effects of a Positive Feedback Loop upon the Stability of Bi-Connected Elementary Biochemical Reaction Cycles

We explored the stability transitions of a biochemical reaction network that were induced by a positive feedback loop (PFL) through kinetics-based mathematical modeling, and identified a novel role of the PFL. First, we proposed the elementary reaction loop (ERL) as a building block of biochemical networks. Then, we analyzed the effects of a PFL upon the responses of a bi-connected ERL (bc-ERL) by exploring the stability of the steady-state equations of the bc-ERL and bc-ERL/PFL in the parameter space. Although previously, the bc-ERL was theoretically predicted to be bistable even in the absence of a PFL, we identified all types of conceivable stability transitions induced by the PFL herein. Thus, this is the first report of the transition from bistability (bc-ERL) to monostability (bc-ERL/PFL) (i.e., the b → m transition), for which the origin was the significantly lower Michaelis-Menten constant in the PFL. The biological roles of the b → m transition are discussed.