Control analysis of enzyme mechanisms in terms of the classical steady-state description.

The algebraic rate equations of steady-state enzyme kinetics generally allow the derivation of analytical expressions for the distribution of rate control among the elementary reactions defined by the kinetic mechanism. It is shown that these analytical expressions complete the macroscopic (probabilistic) description of enzyme-catalysed chemical reactions without involving any assumption at the microscopic (molecular) level. By also surveying some directly relevant results of the graph theoretical treatment of enzyme mechanisms, it is shown that control analysis is an integral part of steady-state enzyme kinetics.

[Gluten enteropathy]. / Gluten-enteropathia.

In this case report has been shown 32-old women patient. She was received on Department of Internal medicine of State Hospital "Sarajevo" because of prostration, weight loss (more than 20 kg) and frequently, abundant diarrheas. Clinical treatment, including biopsy of small intestine, referred on gluten-enteropathy. In war-stricken Sarajevo, when major part of food were bread, macaroni and pies, obviously there was perception of sensibility on gluten in this women who hadn't got any similar problem for her life. After adequate diet without gluten, on the control examination two month later, we can hardly recognize our patient. She can get more than 20 kg, without mental depression and would be married soon.

How to derive flux control coefficients from the rate equations of classical enzyme kinetics.

A recent report by Brown and Cooper demonstrated the usefulness of calculating "flux control coefficients" for each of the rate constants involved in the assumed kinetic mechanism of a single enzyme. The calculations of Brown and Cooper involved numerical differentiation. The present article substantiates this report by showing that the numerical results of Brown and Cooper can also be obtained in an explicit form. The analytical equations given establish the relationship between rigorously specified overall rate processes and "elementary rate constants," both being defined by the rate equations of classical enzyme kinetics. It is shown that analytical flux control coefficients can be obtained for all types of rate processes considered in classical enzyme kinetics, including, "initial rates," equilibrium exchange reactions, and reactions at limiting levels of substrate (and/or product) saturation. By restricting the discussion to strictly consecutive (ordered, unbranched, linear) mechanisms, the line of reasoning can be presented in a relatively simple form. The main conclusions are the following: (a) It is advantageous to carry out the analysis in terms of paired (conjugated) control coefficients. (b) Flux control analysis of "elementary rate constants" does not require any extra kinetic argument. (c) Neither the immediate aim nor the results of the presented type of analysis are directly relevant to theories of metabolic control. On the contrary, the type of control analysis considered completes classical enzyme kinetics with a new facet. (d) For illustrating its usefulness, the concept of flux control coefficients is applied to the problem of optimization of enzyme activity.

Control analysis of single enzyme sequences with abortive complexes and random substrate binding.

Single-enzyme reactions involving abortive complexes, and random sequences, respectively, are subjected to control analysis. Explicit analytical expressions are presented which cover these kinetic behaviors. The latter are based (1) on the concept of control coefficients which measure the sensitivity of flux with respect to rate constants, and (2) on the classical steady state rate equations. The methods include both a graph theoretic approach and computer-aided derivation of algebraic expressions. Some conclusions are derived from the analysis of simple models. It is demonstrated (1) that abortive complexes exert no kinetic (as opposed to equilibrium) control over steady state flux; (2) the sum of the paired flux control coefficients for each step in the catalytic cycle, as well as the sum of the flux control coefficients for the unidirectional steps which emanate from each enzyme species, is equal to unity in a random sequence; (3) in the case of a random reaction sequence, the numerator terms of the rate equation exert an effect in the paired flux control coefficients for those steps in the random portion of the reaction sequence.

Kinetic barriers under steady-state conditions.

It is shown by analysis of a numerical example that kinetic barrier diagrams [Südi (1991) Biochem. J. 276; 265-268] are also useful for displaying the phenomenological resistance of an enzymic turnover to net chemical fluxes observed under steady-state conditions. Most importantly, a new additivity rule is revealed by net flux profiles, which refers to limiting ('ideal') conditions. The rule states that the net fluxes that one obtains under initial steady-state conditions are strictly identical with the overall flux in the corresponding equilibrium system. This finding amounts to defining the relation between unidirectional fluxes and net fluxes, and explains why the total 'one-way flux resistance' to the overall reaction at chemical equilibrium on the one hand, and the 'net flux resistance' to both initial steady-state reactions on the other hand, have to be equal. The conclusions are claimed to be generally valid for consecutive chemical reactions.

How to draw kinetic barrier diagrams for enzyme-catalysed reactions.

A modified way to construct kinetic barrier diagrams is presented. Although the diagram superficially resembles a free-energy profile, it is independent of any conception derived from transition-state theory. Some simple calculations referring to the lactate dehydrogenase turnover reaction at equilibrium demonstrate self-consistency of the diagram and its direct relevance to the results of numerical simulations of the detailed course of enzyme-catalysed reactions.

Kinetic analysis of experiments involving the single turnover of an enzyme.

The complete solution to the kinetic equation for nucleotide fluorescence quenching on addition of pyruvate to the late dehydrogenase-NADH complex modifies previous interpretations of such experiments.

Chiral recognition of prochiral centres and general acid-base catalysis. Necessarily interrelated manifestations of active-site structure.

On the basis of Ogston's [(1948) Nature (London) 162, 963] argument, the following conclusions are indicated by the stereochemistry of the reversible oxidation of glycollate by lactate dehydrogenase: (1) general acid-base catalysis is involved in the reaction; (2) the transformation of enzyme-bound (tetrahedral) substrate into enzyme-bound (trigonal) product involves a conformational transition of the enzyme-coenzyme complex.

On the catalytic activity of chemically modified enzymes involving two or more substrates and products.

Catalytic activity of both native and chemically modified enzymes are numerically expressed in the literature with either kmax (= V/[ET]), or ke (=(V/[ET])/Km), if they refer to a one-substrate one-product reaction. Higher-order catalytic constants of the k'E type have not so far been calculated for enzyme reactions involving two or more substrates and products. a) It is shown here how such higher-order k'E-values can be calculated from easily obtainable experimental information; whatever the number of substrates and products, and even if binding of substrates and release of products follow a branched pathway. b) k'E-Values define the specific rate with which free substrates are converted by the enzyme into free products. Their dimensions (M-ns-1) are defined by the number of substrates (n). k'E-Values refer to the same process as the catalytic constants generally used in physical organic chemistry. c) The required experimental information is mainly based on steady state parameters of the V'- and K'm-types, supplemented with equilibrium and fast kinetic studies of straightforward substrate binding reactions. d) It is shown that higher-order k'E-values always involve the "Haldane problem" of the chemical reaction step. On the other hand, k'E-values are independent of the rate of release of all but the first product in the overall reaction. e) The so-called "Haldane relations" are shown to be determined by the way in which k'E-values can be calculated from V' and K'm-type experimental parameters. f) A number of theoretical considerations indicate that catalytic of the k'E-type are much more suitable for expressing the catalytic activity of chemically modified enzymes than maximal velocities are. This conclusion is demonstrated by a comparison of k'E- and k'max-values of some recently described modified forms of alcohol dehydrogenase.

The role of product release in enzyme catalysis.

Conceptual definitions of maximal velocity and the Michaelis constant are provided that do not involve the assumption of any rate-determining step. The experimental basis of those definitions is a combination of pre-steady state and steady state kinetic observations.

The lactate dehydrogenase--reduced nicotinamide--adenine dinucleotide--pyruvate complex. Kinetics of pyruvate binding and quenching of coeznyme fluorescence.

The stopped-flow kinetic studies described in this and the following paper (Südi, 1974) demonstrate that a Haldane-type description of the reversible lactate dehydrogenase reaction presents an experimentally feasible task. Combined results of these two papers yield numerical values for the six rate constants defined by the following equilibrium scheme, where E represents lactate dehydrogenase: [Formula: see text] The experiments were carried out at pH8.4 at a relatively low temperature (6.3 degrees C) with the pig heart enzyme. Identification of the above two intermediates and determination of the corresponding rate constants actually involve four series of independent observations in these studies, since (a) the reaction can be followed in both directions, and (b) both the u.v. absorption and the fluorescence of the coenzymes are altered in the reaction, and it is shown that these two spectral changes do not occur simultaneously. Kinetic observations made in the reverse direction are reported in this paper. It is demonstrated that the fluorescence of NADH can no longer be observed in the ternary complex E(NADH) (Pyr). Even though the oxidation-reduction reaction rapidly follows the formation of this complex, the numerical values of k(-4) (8.33x10(5)m(-1).s(-1)) and k(+4) (222s(-1)) are easily obtained from a directly observed second-order reaction step in which fluorescent but not u.v.-absorbing material is disappearing. U.v.-absorption measurements do not clearly resolve the subsequent oxidation-reduction step from the dissociation of lactate. It is shown that this must be due partly to the instrumental dead time, and partly to a low transient concentration of E(NAD+) (Lac) in the two-step sequential reaction in which the detectable disappearance of u.v.-absorbing material takes place. It is estimated that about one-tenth of the total change in u.v. absorption is due to a ;burst reaction' in which E(NAD+) (Lac) is produced, and this estimation yields, from k(obs.)=120s(-1), k(-2)=1200s(-1).

Macroscopic rate constants involved in the formation and interconversion of the two central enzyme--substrate complexes of the lactate dehydrogenase turnover.

The preceding paper (Südi, 1974) reports partial success in describing the conversion of E(NADH) plus pyruvate into E(NAD+) plus lactate in terms of a simple Haldane-type scheme which involves two intermediates (E(NADH) (Pyr) and E(NAD+) (Lac)), where E represents lactate dehydrogenase. This information is completed here by reporting kinetic results obtained by carrying out the same reaction in the opposite direction. The combined results of these two papers confirm the findings of Holbrook & Gutfreund (1973) that the observed spectral changes do take place at the level of resolution of this simple two-intermediate scheme. The following numerical values for the rate (and equilibrium) constants involved in their formation and decomposition are reported: [Formula: see text] It is shown that although the precision of estimation of some of these numerical values is subject to some experimental uncertainty, their derivation from direct experimental observations only involves the principle of microscopic reversibility. This paper describes stopped-flow kinetic observations made with E(NAD+) and lactate as the two reactants. It is shown that fluorescence and u.v.-absorption measurements yield the same experimental rate constant for the last reaction step in which E(NADH) is generated. On the other hand, the generation of E(NADH) (Pyr) can only be indirectly observed, as a less than stoicheiometric ;burst', and by u.v.-absorption measurements only. It is shown that the stoicheiometry of this partial ;burst reaction', and a pre-equilibrium factor in the directly observed rate of E(NADH)-production, yield equivalent information about the reversible oxidation-reduction step. It is further shown that the pre-equilibrium factor that is involved in the generation of E(NADH) can be determined because k(+4)=222s(-1) is already known (Südi, 1974). Since the fluorescence measurements yield much more precise estimations, and their interpretation is considered by the author to be free of ambiguity, the presented quantitative analysis is based on the fluorescence observations.