The rate of substrate utilization is related to the specific growth rate as
where
: X is the total biomass (since the specific growth rate μ is normalized to the total biomass),
: Y is the yield coefficient.
r is negative by convention.
In some applications, several terms of the form [S] / (K + [S]) are multiplied together where more than one nutrient or growth factor has the potential to be limiting (e.g. organic matter and oxygen are both necessary to heterotrophic bacteria). When the yield coefficient, being the ratio of mass of microorganisms to mass of substrate utilized, becomes very large, this signifies that there is deficiency of substrate available for utilization.