Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics

Abstract

We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We 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.

11 pages

References in corpus (3)

• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer
• Geometric Control Over the Motion of Magnetic Domain Walls