Given the biochemical network:
where  and  are fixed species to ensure the system is open. The system equation can be written as:
So that:
The elements of the rate vector will be rate equations that are functions of one or more species  and parameters, p. In the example, these might be simple mass-action rate laws such as  where  is the rate constant parameter. The particular laws chosen will depend on the specific system under study. Assuming mass-action kinetics, the above equation can be written in complete form as: