Coexistence of Deterministic and Stochastic Bistability in a 1-D Birth-Death Process with Hill Type Nonlinear Birth Rates
The paper shows that, for a specific 1 − D birth-death process, the parameter ranges for the existence of the deterministic bistability exactly coincide with the parameter ranges for the existence of the stochastic bistability, namely bimodality. The considered 1 − D birth-death process is a reduced model of TMG induced lactose operon of Escherichia coli in which the birth rate for intra cellular TMG molecules is of Hill type. As opposed to the results reported by some works for other 1 − D birth-death processes in the literature, such as the observation called Keizer paradox, no bistability without bimodality and also no bimodality without bistability are obtained for any set of model parameters. Bistability without bimodality is observed to occur only when invalid calculations of steady-state probabilities due to i) big number problems related to very small probabilities corresponding to troughs between two peaks and/or ii) inappropriately low choice of molecule numbers are not prevented.
KeywordsChemical Master Equation Molecule Number Biochemical Reaction Network Hill Type Bistability Range
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