title: Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics.
abstract: 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.
authors.affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. nsinitsyn@lanl.gov
authors.forename: N A
authors.initials: NA
authors.lastname: Sinitsyn
authors.forename: I
authors.initials: I
authors.lastname: Nemenman
mesh_terms: D000465:Algorithms; D001419:Bacteria / Q000254:growth & development; D001686:Biological Phenomena / Q000502:physiology*; D007700:Kinetics; D008954:Models, Biological; D008956:Models, Chemical; D013269:Stochastic Processes; D013997:Time Factors