Dehydrogenases steady-state kinetics

We have dealt so far with enzymes that react with a single substrate only. The majority of enzymes, however, involve two substrates. The dehydrogenases, for example, bind both NAD+ and the substrate that is to be oxidized. Many of the principles developed for the single-substrate systems may be extended to multisubstrate systems. However, the general solution of the equations for such systems is complicated and well beyond the scope of this book. Many books devoted almost solely to the detailed analysis of the steady state kinetics of multisubstrate systems have been published, and the reader is referred to these for advanced study.11-14 The excellent short accounts by W. W. Cleland15 and K. Dalziel16 are highly recommended. 

The steady-state kinetic studies of liver alcohol dehydrogenase (12.5 nM) are performed. The initial rates (v in /rM/rnin) with varying substrate concentrations in both directions (forward for ethanol oxidation and reverse for ethanal reduction) are given below. Evaluate their kinetic parameters and equilibrium constant. 

Steenkamp, D. J., and Mallinson, J., 1976, Trimethylamine dehydrogenase from a methy-lotrophic bacterium I. Isolation and steady-state kinetics. Biochim. Biophys. Acta. 429 705n719. 

The main parts of this scheme were proposed earlier by Theorell and co-workers 119,291) on the basis of inhibitor binding and steady-state kinetic studies. Other suggested mechanisms based on general acid-base catalysis 297), reduction of the enzyme 362), or direct participation of histidine 363) or cysteine 364) in the hydride transfer step are highly unlikely in view of the crystallographic and kinetic results reviewed in this chapter. Contrary to expectations the mechanism described here is in most details very different from that proposed for lactic dehydrogenase 126). 

What this really means is that the ternary complex has such a transitory existence that it never makes up a significant fraction of the total amount of enzyme. Steady-state kinetics concerns itself only with those complexes which, by their existence, detectably alter the pattern of dependence of reaction rate on substrate concentration. The Theorell-Chance mechanism may be seen perhaps as a manifestation of highly effective catalysis. Certainly, in the case of the enzyme for which it was first described, horse liver alcohol dehydrogenase, the mechanism is obeyed for good substrates i.e. short-chain primary alcohols with secondary alcohols, which are poor substrates, the ternary complex becomes kinetically significant - because it works less well [44]. 

A detailed thermod5mamic analysis was performed with lactate dehydrogenase, in the lactate — p5mivate direction, by means of steady-state kinetics and presteady-state kinetic methods, by Laidler and Peterman (1979). A particularly detailed kinetic studies of the energetics of two multistep enzymes, triose-phosphate isomerase and prohne racemase, has been described by the research team of Albery and Knowles (Albery Knowles, 1976, 1986 Knowles, 1991). Apart from these examples, very few complete thermodynamic analyses have been performed with reactions involving more than one substrate or more than one intermediate in reaction. 

Kato N, Sahm H, Wagner F (1979) Steady-state kinetics of formaldehyde dehydrogenase and formate dehydrogenase from a methanol-utilizing yeast, Candida boidinii. Biochim Biophys Acta Enzymol 566 12-20... 

Shone CC, Fromm H J (1981) Steady-state and pre-steady-state kinetics of coenzyme A linked aldehyde dehydrogenase from Escherichia coli. Biochemistry... 

Fig. 6.63 Illustration of (A) and (B) convex biphasic behavior for the model in Fig. 6.61. (From W. Min, L Jiang, X.S. Xle, Chem. Asian J. 5 (2010) 1129. Copyright 2010 Wiley.) (C) Example of concave biphasic behavior showing negative cooperativity in the steady-state kinetics of sugar oxidation by soluble quinoprotein glucose dehydrogenase from Acinetobacter calcoaceticus. (From A.J.J. Olsthoorn, T. Otsuku, J.A. Duine, FEBS J. 255 (1998) 255-261. Copyright 1998 Federation of European Biochemical Societies).

Yang and Schulz also formulated a treatment of coupled enzyme reaction kinetics that does not assume an irreversible first reaction. The validity of their theory is confirmed by a model system consisting of enoyl-CoA hydratase (EC 4.2.1.17) and 3-hydroxyacyl-CoA dehydrogenase (EC 1.1.1.35) with 2,4-decadienoyl coenzyme A as a substrate. Unlike the conventional theory, their approach was found to be indispensible for coupled enzyme systems characterized by a first reaction with a small equilibrium constant and/or wherein the coupling enzyme concentration is higher than that of the intermediate. Equations based on their theory can allow one to calculate steady-state velocities of coupled enzyme reactions and to predict the time course of coupled enzyme reactions during the pre-steady state. 

We start our analysis of the TCA cycle kinetics by examining the predicted steady state production of NADH as a function of the NAD and ADP concentrations. From Equation (6.31) we see that there can be no net flux through the TCA cycle when concentration of either NAD or ADP, which serve as substrates for reactions in the cycle, is zero. Thus when the ratios [ATP]/[ADP] and [NADH]/[NAD] are high, we expect the TCA cycle reaction fluxes to be inhibited by simple mass action. In addition, the allosteric inhibition of several enzymes (for example inhibition of pyruvate dehydrogenase by NADH and ACCOA) has important effects. 

To understand how the TCA cycle responds kinetically to changes in demand, we can examine the predictions in time-dependent reaction fluxes in response to changes in the primary controlling variable NAD. Figure 6.4 plots predicted reaction fluxes for pyruvate dehydrogenase, aconitase, fumarase, and malate dehydrogenase in response to an instantaneous change in NAD. The initial steady state is obtained... 

Harris, T. K., and Davidson, V. L., 1993a, A new kinetic model for the steady-state reactions of the quinoprotein methanol dehydrogenase from Paracoccus-denitrificans. Biochemistry 32 4362n4368. 

Bloomfield, V., Peller, L., Alberty, R. A. (l%2b). Multiple intermediates in steady-state enzyme kinetics III. Analysis of the kinetics of some reactions catalyzed by dehydrogenases. J. Amer. Chem. Soc. 84,4375-4384. 

Nicotinamide-nucleotide-linked dehydrogenases were among the earliest two-substrate enzymes to be subjected to detailed kinetic study by steady-state 1-3) and rapid reaction techniques (4), and provided much of the original stimulus for the necessary extension of kinetic theory already developed for one-substrate and hydrolytic enzymes S-8). This was partly because of the convenience and precision with which rates can be measured by means of the light absorption or fluorescence emission 9-11) of the reduced coenzymes and because of the changes of these properties which accompany the binding of reduced coenzymes to many dehydrogenases 12,13). 

Kinetic data (steady-state and rapid reaction) can be used to identify the sequence of enzyme-containing complexes as substrates are converted to products, and to identify the rates of some or all of the elementary steps in the overall reaction. For instance, in a two-substrate reaction such as that catalyzed by lactate dehydrogenase (lactate+ NAD <- pyruvate+NADH), it can be shown that the... 

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