Misuse of the Michaelis-Menten rate law for protein interaction networks and its remedy.

Jae Kyoung Kim,Pedro Mendes,John J. Tyson

doi:10.1371/journal.pcbi.1008258

Jae Kyoung Kim, Pedro Mendes + Show 1 more

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https://doi.org/10.1371/journal.pcbi.1008258

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Abstract

For over a century, the Michaelis–Menten (MM) rate law has been used to describe the rates of enzyme-catalyzed reactions and gene expression. Despite the ubiquity of the MM rate law, it accurately captures the dynamics of underlying biochemical reactions only so long as it is applied under the right condition, namely, that the substrate is in large excess over the enzyme-substrate complex. Unfortunately, in circumstances where its validity condition is not satisfied, especially so in protein interaction networks, the MM rate law has frequently been misused. In this review, we illustrate how inappropriate use of the MM rate law distorts the dynamics of the system, provides mistaken estimates of parameter values, and makes false predictions of dynamical features such as ultrasensitivity, bistability, and oscillations. We describe how these problems can be resolved with a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA). Furthermore, we show that the tQSSA can be used for accurate stochastic simulations at a lower computational cost than using the full set of mass-action rate laws. This review describes how to use quasi-steady state approximations in the right context, to prevent drawing erroneous conclusions from in silico simulations.

Highlights

The Michaelis–Menten (MM) rate law has been the dominant paradigm for describing the rates of enzyme-catalyzed reactions for 100 years [1,2,3,4]
Even in such situations outside its range of validity, the MM rate law has frequently beenused to model enzyme-catalyzed reactions. We illustrate how such unjustified use of the MM rate law for protein interaction networks leads to erroneous conclusions. We describe how such errors can often be prevented by replacing the MM rate law with a slightly modified form, based on the “total” quasisteady state approximation, which is generally accurate for any combination of substrate and enzyme concentrations [14,15,16,17,18,19,20,21]
Embedding an ultrasensitive response in a positive feedback loop is a common mechanism for creating a bistable switch [37,38]; modeling zero-order ultrasensitivity based on MM rate laws (Eq 7) in a protein interaction network can generate “phantom” bistability as well

Summary

Introduction

The Michaelis–Menten (MM) rate law has been the dominant paradigm for describing the rates of enzyme-catalyzed reactions for 100 years [1,2,3,4]. MM rate law) as the sQSSA model of a single-substrate enzyme-catalyzed reaction. In the case of low enzyme concentration, both the sQSSA and the tQSSA models provide good estimates of the “true” rate constants when the models are fitted to the progress curve P(t) simulated with the full model (i.e., a “progress-curve assay”) (Fig 1d inset).

Results

Conclusion