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N Sinitsyn and I Nemenman, Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics. IET Syst Biol 4, 409, 2010. PDF, arXiv.
- The authors generalise the concept of the geometric phase in stochastic kinetics to a non-cyclic evolution. Its application is demonstrated on kinetics of the Michaelis–Menten reaction. It is shown that the non-periodic geometric phase is responsible for the correction to the Michaelis–Menten law when parameters, such as a substrate concentration, are changing with time. The authors apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.