Bifurcations of a Positive Feedback Loop with Partial Binding

초록

The positive feedback loop with cooperative binding of the auto-regulatory transcription factor molecules, is the simplest form of a genetic regulatory network (GRN) that can exhibit bistable behavior. The steady states of such systems have been analyzed, but only under the simplifying assumption that the protein molecules bind to the gene simultaneously. In this work, I consider a positive feedback loop where two molecules of the gene product bind to the gene, but one molecule at a time, to activate its own production. I find an analytic expression for the stable fixed point of the corresponding rate equation, and obtain the full phase diagram. Both the model with one-molecule binding and the model with the simultaneous binding of two molecules are shown to be the special limits of the current model. Moreover, the current model exhibits novel bifurcation behavior unseen in previous models.

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