The biochemical systems equation is a compact equation of nonlinear differential equations for describing a kinetic model for any network of coupled biochemical reactions and transport processes.
The equation is expressed in the following form:
The notation for the dependent variable x varies among authors. For example, some authors use s, indicating species. x is used here to match the state space notation used in control theory but either notation is acceptable.
 is the stoichiometry matrix which is an  by  matrix of stoichiometry coefficient.  is the number of species and  the number of biochemical reactions. The notation for  is also variable. In constraint-based modeling the symbol  tends to be used to indicate stoichiometry. However in biochemical dynamic modeling and sensitivity analysis,  tends to be in more common use to indicate number. In the chemistry domain, the symbol used for the stoichiometry matrix is highly variable though the symbols S and N have been used in the past. 
 is an n-dimensional column vector of reaction rates, and  is a p-dimensional column vector of parameters.