Abstract
Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of substrates, which is known as the progress curve assay. However, this canonical approach works in limited conditions, such as when there is a large excess of substrate over enzyme. Even when this condition is satisfied, the identifiability of parameters is not always guaranteed, and often not verifiable in practice. To overcome such limitations of the canonical approach for the progress curve assay, here we propose a Bayesian approach based on an equation derived with the total quasi-steady-state approximation. In contrast to the canonical approach, estimates obtained with this proposed approach exhibit little bias for any combination of enzyme and substrate concentrations. Importantly, unlike the canonical approach, an optimal experiment to identify parameters with certainty can be easily designed without any prior information. Indeed, with this proposed design, the kinetic parameters of diverse enzymes with disparate catalytic efficiencies, such as chymotrypsin, fumarase, and urease, can be accurately and precisely estimated from a minimal amount of timecourse data. A publicly accessible computational package performing such accurate and efficient Bayesian inference for enzyme kinetics is provided.
Highlights
Because enzymes can modulate biochemical reaction rates by selectively catalyzing specific substrates[1], they play fundamental roles in metabolism, signal transduction, and cell regulation, and their malfunction can cause serious diseases[2,3]
Note that both assays require prior knowledge of KM, which gives rise to the conundrum that, in order to estimate KM, the approximate value of KM needs to be known. To overcome such limits on the inference using the model based on the MM equation, which is referred to as the sQ model, here we propose an alternative approach
Where KM =/kf is the Michaelis-Menten constant and kcat is the catalytic constant. This sQ model derived with the standard QSSA has been widely used to estimate the kinetic parameters, KM and kcat from the progress curve of the product[8–11,23,25]
Summary
Because enzymes can modulate biochemical reaction rates by selectively catalyzing specific substrates[1], they play fundamental roles in metabolism, signal transduction, and cell regulation, and their malfunction can cause serious diseases[2,3]. The progress curve assay requires less data to estimate parameters than the initial velocity assay does. Since both assays are based on the MM equation, they should be performed only when the MM equation is valid, that is, when the enzyme concentration is a much lower than the sum of the substrate concentration and the KM7,14 (see below for more details). For the progress curve assay, the initial substrate concentration is recommended to be at a similar level to KM23,25 Note that both assays require prior knowledge of KM, which gives rise to the conundrum that, in order to estimate KM, the approximate value of KM needs to be known
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