# Mass action kinetics

**Mass action kinetics** is a kinetic scheme for chemical reaction networks which says that the rate of a chemical reaction is proportional to the product of the concentrations of the reacting chemical species. It was first formulated by Cato Maximilian Guldberg and Peter Waage in the 1860's ^{[1]}. It remains one of the most common kinetic assumptions used by chemists, biologists, and mathematicians.

## Deterministic modeling

In the ordinary differential equation modeling of chemical reaction networks, the assumption of mass-action kinetics produces polynomial vector fields. For example, consider the reaction given by

If we let and denote the concentrations of *A* and *B* respectively, then the reaction occurs at a rate proportional to . That is to say, we have

where is the (fixed) proportionality rate (or *rate constant*) associated with the reaction. Since each instance of the reaction produces a net decrease of one molecule of *A* and *B* each, and an increase of one molecule of *C*, we can model the reaction as

## Stochastic modeling

## References

- ↑ C.M. Guldberg and P. Waage, Studies Concerning Affinity,
*C. M. Forhandlinger: Videnskabs-Selskabet i Christiana*(1864), 35