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Phase-plane geometries in coupled enzyme assays.

ABSTRACT: 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.

SUBMITTER: Eilertsen J

PROVIDER: S-EPMC6476317 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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Phase-plane geometries in coupled enzyme assays.

Eilertsen Justin J Stroberg Wylie W Schnell Santiago S

Mathematical biosciences 20180924

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 ...[more]

PMID: 30261179

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