HetMM: A Michaelis-Menten model for non-homogeneous enzyme mixtures

The Michaelis-Menten model requires its reaction velocities to be measured from a preparation of homogeneous enzymes, with identical or near-identical catalytic activities. However, there are many cases where enzyme preparations do not satisfy this condition, or where one may wish to test the validity of this assumption. We introduce a kinetic model that relaxes this requirement, by assuming there are an unknown number of enzyme species drawn from an unknown probability distribution. This model features one additional parameter over the Michaelis-Menten model, describing the standard deviation of this distribution. We show that the assumption of homogeneity is usually sufficient even in non-homogeneous solutions, and only fails under extreme conditions where Km spans orders of magnitude. We validate this method through simulation studies, demonstrating the method does not overfit to random noise, despite its increase in dimensionality. The two models can be accurately discriminated between even with moderate levels of experimental error. We applied this model to three homogeneous and three heterogeneous biological systems, showing that the standard and heterogeneous models outperform in either case, respectively. Lastly, we show that heterogeneity is not readily distinguished from negatively-cooperative binding under the Hill model. These two fundamentally distinct properties - inequality in catalytic ability and interference between binding sites - give similar Michaelis-Menten curves that are not readily resolved without further experimentation. Our method allows testing for homogeneity and performing parameter inference in a Bayesian framework, and is available online in the user-friendly HetMM package at https://github.com/jordandouglas/HetMM .