To solve for the concentration of all components appearing in any general biochemical reaction as in (), the Michaelis–Menten kinetics for an enzymatic reaction are coupled with the Monod kinetics for biomass dynamics. The most general case is to assume that the enzyme concentration is proportional to the biomass concentration and that the reaction is not in quasi-steady state. These hypotheses lead to the following system of equations
with , and where  is the concentration of the most limiting substrate in each reaction i, z is the enzyme yield coefficient, Y is the yield coefficient expressing the biomass gain per unit of released product and  is the biomass mortality rate.