Related Experiment Video
Updated: Jan 24, 2026
Application of Stopped-flow Kinetics Methods to Investigate the Mechanism of Action of a DNA Repair Protein
Published on: March 31, 2010
Results on stochastic reaction networks with non-mass action kinetics
David F Anderson1, Tung D Nguyen1
1Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, WI 53706, USA.
Abstract:
In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons [1]. That work spurred a number of followup analyses. In 2015, Anderson, Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in [1], and proved it is a well known Lyapunov function [2]. In 2016, Cappelletti and Wiuf showed the converse of the main result in [1]: if a reaction network with stochastic mass action kinetics admits a stationary distribution that is a product of Poissons, then the deterministic model is complex balanced [3]. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in [1] are non-explosive (so the stationary distribution characterizes the limiting behavior). In this paper, we generalize each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics.
Related Concept Videos
02:05SN1 Reaction: Kinetics
However, Sir Christopher Ingold and Edward D. Hughes, who studied the kinetics of various nucleophilic substitution reactions, noticed that a tertiary alkyl halide does undergo a nucleophilic substitution reaction in the presence of a weak nucleophile. While studying the substitution...
02:14SN2 Reaction: Kinetics
In a chemical reaction, a relationship exists between the concentration of reactants and the rate at which the reaction proceeds. The study to measure this relationship is known as the kinetics of a chemical reaction. Kinetic studies are used to deduce the rate law of a chemical reaction, which provides information about the species involved during the transition state of the rate-determining step. Thus, kinetic studies help to derive the mechanism of a...
02:45E2 Reaction: Kinetics and Mechanism
02:46E1 Reaction: Kinetics and Mechanism
03:07Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy
01:19Enzyme Kinetics
Scientists typically study enzyme kinetics with a fixed amount of enzyme in the controlled environment of a test tube. When more reactant, or substrate, is...