Generalizing Michaelis-Menten Theory to Account for Substrate Heterogeneity

Abstract

Enzymes are typically analyzed under the assumption of homogeneous substrates, yet many biological, biotechnological, and industrial reactions involve chemically or physically heterogeneous substrates. Here we present a theoretical framework showing that mixtures of non-identical substrates at steady state still follow the Michaelis-Menten (MM) rate law, yielding apparent parameters [Formula] that depend on the mean and variance of the underlying energy distributions. This mathematical identity with the classical MM form can bias interpretation of fitted parameters and conceal mechanistic diversity. We show that variance in substrate energetics can shift [Formula] and [Formula] as strongly as changes in mean binding or activation energies, making substrate heterogeneity an independent but hidden design axis. Numerical simulations of 500 coupled Michaelis-Menten reactions--each representing a distinct substrate--validated the closed-form expressions for the apparent parameters. Analysis of 43220 curated BRENDA entries quantified the kinetic spread in enzymology, and our framework shows that realistic substrate heterogeneity gives comparable variability. Our framework extends the MM theory to heterogeneous substrates by adding a single, physically interpretable variance term to the classical equations. This enables inference of hidden heterogeneity from bulk fits and positions substrate pretreatment as a complementary optimization axis alongside conventional enzyme engineering for enzymes acting on heterogeneous substrates.