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bioRxiv · 10.1101/2022.11.28.518182

Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition

Murugan, R.
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Abstract

We derive approximate expressions under various conditions of validity over both pre- and post-steady state regimes of the velocity-substrate-inhibitor spaces of the Michaelis-Menten enzyme kinetic schemes with fully and partial competitive inhibition. Our refinement over the currently available standard quasi steady state approximations (sQSSA) seems to be valid over wide range of enzyme to substrate and enzyme to inhibitor ratios. Further, we show that under certain conditions the enzyme-inhibitor-substrate system can exhibit temporally well-separated two different steady states with respect to both enzyme-substrate and enzyme-inhibitor complexes. We define the ratios fS = vmax/(KMS + e0) and fI = umax/(KMI + e0) as the acceleration factors with respect to the catalytic conversion of substrate and inhibitor into their respective products. Here KMS and KMI are the Michaelis-Menten parameters associated with the binding of substrate and inhibitor with the enzyme, vmax and umax are the respective maximum reaction velocities and e0, s0, and i0 are total enzyme, substrate and inhibitor levels. When (fS / fI) < 1, then enzyme-substrate complex will show multiple steady states subsequently reaches the full-fledged steady state only after the depletion of enzyme-inhibitor complex. When (fS / fI) > 1, then the enzyme-inhibitor complex will show multiple steady states and subsequently reaches the full-fledged steady state only after the depletion of enzyme-substrate complex. This complex behavior exclusively when (fS / fI) = 1 is the root cause of large amount of error in the estimation of various kinetic parameters both in the cases of fully and partial competitive inhibition schemes using the sQSSA methods. Remarkably, we show that our refined expressions for the reaction velocities over enzyme-substrate-inhibitor space can control this error more significantly than the currently available sQSSA velocity expressions.

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Murugan, R.. 2022-11-28. Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition. https://doi.org/10.1101/2022.11.28.518182

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