[2] Techniques in coupled enzyme assays

doi:10.1016/0076-6879(79)63004-5

Methods in Enzymology

Volume 63, 1979, Pages 22-42

https://doi.org/10.1016/0076-6879(79)63004-5 Get rights and content

Abstract

The amount of auxiliary enzyme to be added to a assay system utilizing a single coupled reaction can be calculated from $V_{2} = −2.303 log (1 − F_{p})K_{p} t$ based on McClure's³ analysis where V₂ is the number of units of E₂, F_p is the desired fraction of the steady-state reaction of the primary enzyme to be measured, K_p is the Michaelis constant for P for E₂, and t is the desired lag time. Alternatively the method of Storer and Cornish-Bowden⁸ used Eq. (17) $t^{∗} = φK_{p} υ$ where $t^{∗}$ is the transient time, K_p is above, and v₁ is the highest velocity of the primary enzyme to be measured. A value for φ is calculated at a specified time, and from Table I the ratio $υ_{1} V_{2}$ is determined for a specified $v_{2} v_{1}$ ratio.

A plot of product (Q) appearance versus time allows evaluation of the steady-state intermediate product level (P_ss) and the lag time as a check on the assumptions for the above equations. A check should always be done to assure that the assays are linear with a reasonable lag time.

Storer and Cornish-Bowden's⁸ treatment can be applied to systems with several coupling enzymes, and the nomogram of McClure (Fig. 3) is useful for a two-auxiliary enzyme system.

A check should always be done by adding a small amount of the primary enzyme product and determining that it reacts very rapidly with the assay enzymes, ensuring that the assay system is actually working.

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The determination of a substrate or enzyme activity by coupling one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course expressions valid under the quasi-steady-state and reactant stationary state assumptions. In this paper, the dynamical behavior of coupled enzyme catalyzed reaction mechanisms is studied by analysis of the phase-plane. We analyze two types of time-dependent slow manifolds – Sisyphus and Laelaps manifolds – that occur in the asymptotically autonomous vector fields that arise from enzyme coupled reactions. Projection onto slow manifolds yields various reduced models, and we present a geometric interpretation of the slow/fast dynamics that occur in the phase–planes of these reactions.
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In this case, the secondary reaction step (2) is known as the indicator reaction. Traditionally, coupled enzyme assays are designed so that the product of the non-observable reaction is a substrate for the secondary enzyme in the indicator reaction (see [6] for specific applications). While this type of assay is well-studied [7–10], in vitro assays that consist of a zymogen activation step have not been analyzed with the same degree of interest.
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[2] Techniques in coupled enzyme assays

Abstract

FEBS Lett.

Biochim. Biophys. Acta

J. Theor. Biol.

Anal. Biochem.

Anal. Biochem.

J. Biol. Chem.

Biochem. Z.

An Introduction to the Study of Enzymes