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Kinetics of enzymes with iso-mechanisms: analysis of product inhibition.

ABSTRACT: Isomerizations of free enzyme can be detected in kinetic patterns of product inhibition when the isomerization is partially rate-limiting. The kinetic pattern is non-competitive, owing to binding of substrate and product to different forms of free enzyme. This adds an additional term to the rate equation, sometimes represented as KSP. Several kineticists have noted that, as the rate of isomerization becomes high in relation to catalytic turnover, the intercept effect will become small, KSP will approach infinity, and the pattern will look competitive. Britton [(1973) Biochem. J. 133, 255-261] asserted that KSP will also approach infinity when the rate of isomerization becomes low. This second assertion is incorrect and can be traced to the particular model and graphical representation used to examine KSP as a function of relative rate constants. The function portrayed as a parabola with two roots for KSP is, instead, a straight line with one root. The algebraic condition justifying the second root obtains in the limit of zero in the rate of reaction and thus is not experimentally relevant, and the appearance of competitive inhibition, based on KSP alone, is not valid. Using a more general model, new equations are derived and presented which provide direct calculations of the apparent rate constants for free enzyme isomerizations from product-inhibition data when the equilibrium of the isomerization is near 1, and useful limits for the rate constants when greater than or less than 1.

SUBMITTER: Rebholz KL

PROVIDER: S-EPMC1137703 | biostudies-other | 1993 Dec

REPOSITORIES: biostudies-other

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Project description:The phenyl + ethylene (C6H5 + C2H4) reaction network was explored experimentally and theoretically to understand the temperature dependence of the reaction kinetics and product distribution under various temperature and pressure conditions. The flash photolysis apparatus combining laser absorbance spectroscopy (LAS) and time-resolved molecular beam mass spectrometry (MBMS) was used to study reactions on the C8H9 potential energy surface (PES). In LAS experiments, 505.3 nm laser light selectively probed C6H5 decay, and we measured the total C6H5 consumption rate coefficients in the intermediate temperature region (400-800 K), which connects previous experiments performed in high-temperature (pyrolysis) and low-temperature (cavity-ring-down methods) regions. From the quantum chemistry calculations by Tokmakov and Lin using the G2M(RCC5)//B3LYP method, we constructed a kinetic model and estimated phenomenological pressure-dependent rate coefficients, k(T, P), with the Arkane package in the reaction mechanism generator. The MBMS experiments, performed at 600-800 K and 10-50 Torr, revealed three major product peaks: m/z = 105 (adducts, mostly 2-phenylethyl radical, but also 1-phenylethyl radical, ortho-ethyl phenyl radical, and a spiro-fused ring radical), 104 (styrene, co-product with a H atom), and 78 (benzene, co-product with C2H3 radical). Product branching ratios were predicted by the model and validated by experiments for the first time. At 600 K and 10 Torr, the yield ratio of the H-abstraction reaction (forming benzene + C2H3) is measured to be 1.1% and the H-loss channel (styrene + H) has a 2.5% yield ratio. The model predicts 1.0% for H-abstraction and 2.3% for H-loss, which is within the experimental error bars. The branching ratio and formation of styrene increase at high temperature due to the favored formally direct channel (1.0% at 600 K and 10 Torr, 5.8% at 800 K and 10 Torr in the model prediction) and the faster β-scission reactions of C8H9 isomers. The importance of pressure dependence in kinetics is verified by the increase in the yield of the stabilized adduct from radical addition from 80.2% (800 K, 10 Torr) to 88.9% (800 K, 50 Torr), at the expense of styrene + H. The pressure-dependent model developed in this work is well validated by the LAS and MBMS measurements and gives a complete picture of the C6H5 + C2H4 reaction.

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Kinetics of enzymes with iso-mechanisms: analysis of product inhibition.

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