Multisubstrate enzymes, kinetics

Unconsumed substrates are treated as substrates or essential activators in deriving rate equations and studying detailed mechanisms. Nonetheless, one must indicate whether an unconsumed substrate (U) remains bound to the enzyme or not (in this case, U also becomes an unaltered product) in the reaction scheme. In practice, unconsumed substrates are likely to be involved in all the typical multisubstrate kinetic mechanisms Only one case is illustrated here, namely that the unconsumed substrate Su activates catalysis when bound in a rapid-equilibrium ordered mechanism ... 

Enzyme production kinetics in SSF have the potential to be quite complex, with complex patterns of induction and repression resulting from the multisubstrate environment. As a result, no mechanistic model of enzyme production in SSF has yet been proposed. Ramesh et al. [120] modeled the production of a-amylase and neutral protease by Bacillus licheniformis in an SSF system. They showed that production profiles of the two enzymes could be described by the logistic equation. However, although they claimed to derive the logistic equation from first principles, the derivation was based on a questionable initial assumption about the form of the equation describing product formation kinetics They did not justify why the rate of enzyme production should be independent of biomass concentration but directly proportional to the multiple of the enzyme concentration and the substrate concentration. As a result their equation must be considered as simply empirical. 

When there is more than one substrate (see Multisubstrate enzymes), the kinetics may be second order (or pseudo-second-order. See Cleland s short notation). The equation for a second order reaction is A + B iib P, where kj is the bimolecular rate constant, and V = k2[A][B], All chemical reactions are reversible andd eventually reach an equilibrium in which the rates of the forward and reverse reactions are equal. 

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed Bi-Bi reactions) are considered below. 

Restricting ourselves to the rapid equilibrium approximation (as opposed to the steady-state approximation) and adopting the notation of Cleland [158 160], the most common enzyme-kinetic mechanisms are shown in Fig. 8. In multisubstrate reactions, the number of participating reactants in either direction is designated by the prefixes Uni, Bi, or Ter. As an example, consider the Random Bi Bi Mechanism, depicted in Fig. 8a. Following the derivation in Ref. [161], we assume that the overall reaction is described by vrbb = k+ [EAB — k EPQ. Using the conservation of total enzyme... 

MULTISUBSTRATE SYSTEMS. Wong and Hanes were probably among the first to suggest that alternative substrates may be useful in mechanistic studies. Fromm s laboratory was the first to use and extend the theory of alternative substrate inhibition to address specific questions about multisubstrate enzyme kinetic mechanisms. Huang demonstrated the advantages of a constant ratio approach when dealing with alternative substrate kinetics. 

While requiring the availability of competitive inhibitors for each of the substrates, Fromm s use of competitive inhibitors to distinguish multisubstrate enzyme kinetic pathways represents the most powerful initial rate method. See Alternative Substrate Inhibition... 

Data analysis flow chart, 240, 314-315 data point number requirements, 240, 314 determination of enzyme kinetic parameters multisubstrate, 240, 316-319 single substrate, 240, 314-316 enzyme mechanism testing, 240, 322 evaluation of binding processes, 240, 319321 file transfer protocol site, 240, 312 instructions for use, 240, 312-313. 

Fromm and Cleland provide valuable discussions of the utility of Haldane relations in excluding certain kinetic reaction mechanisms based on a numerical evaluation of the constants on each side of the equal sign in the Haldane relation. If the equality is maintained, the candidate mechanism is consistent with the observed rate parameter data. Obviously, one must be concerned about the quality of experimentally derived estimates of rate parameters, because chemists have frequently observed that thermodynamic data (such as equilibrium constants) are often more accurate and precise than kinetically derived parameters. See Haldane Relations for Multisubstrate Enzymes... 

Rose and co-workers first demonstrated that a proteo-lyzed form of hexokinase forms a sticky (or sluggishly dissociable) complex with glucose. The generalized application of this approach to the kinetic characterization of multisubstrate enzymes has been treated in detail. See also Partition Coefficient Radiospecific Activity Stickiness... 

Initial rate enzyme kinetics are useful in defining the order of substrate binding interactions in multisubstrate... 

Experiments designed to reach conclusions about an enzyme-catalyzed reaction by examining how one or more products of the reaction alter the kinetic behavior of the enzyme. The diagnostic value of these approaches can be limited by formation of E substrate product abortive complexes in multisubstrate mechanisms. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

Multidrug resistance protein 417 Multilamellar vesicles (liposomes) 392 Multiple attack concept 606 Multisubstrate enzymes, kinetics of 464 Muramic acid (Mur) 165s Murein 170,428,429s. See also Peptidoglycan Musci 29 Muscle(s)... 

Second order reactions 458 Secondary kinetic isotope effect 592, 600 on fumarate hydratase 684 Secondary plots for kinetics of multisubstrate enzymes 465 Secondary structure 63... 

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 most common enzymatic reactions are those with two or more substrates and as many products. But many of the simpler single-substrate schemes are valuable for the development of kinetic ideas concerning effects of pH, temperature, etc., on enzyme reaction rates. Although the mechanisms of multisubstrate reactions are complicated, their kinetics can often be described by an equation of the form ... 

While such a study might have been carried out with conventional methods, the use of HPLC facilitated the work considerably by allowing all reactants and products to be measured in one analysis. Clearly, the HPLC assay method should be considered when the kinetics of a multisubstrate enzyme reaction are to be studied. 

Vrzheshch PV, Varfolomeev SD. Steady-state kinetics of multisubstrate enzymatic reactions - inactivation of the enzyme in the course of reaction. Biochemistry (Moscow) 1985 50 125-32. 

Equations for the initial velocity of an enzyme-catalyzed reaction, such as the Michaelis-Menten equation, can provide useful parameters for describing or comparing enzymes. However, many multisubstrate enzymes, such as glucokinase, have kinetic patterns that do not fit the Michaelis-Menten model (or do so under non-physiologic conditions). The Michaelis-Menten model is also inapplicable to enzymes present in a higher concentration than their substrates. Nonetheless, the term K is still used for these enzymes to describe the approximate concentration of substrate at which velocity equals Y2 V ax-... 

S Additional information <3, 7> (<3> enzyme exists in different conformational states with different substrate kinetic properties [9] <3> presumably one common nucleoside acceptor site [15] <3> purine deoxynucleo-side activity inseparably associated with deoxycytidine kinase protein [16] <3> several isozymes cytosolic deoxycytidine kinase I and II, plus mitochondrial isozyme [10] <3> multisubstrate enzyme, that also phos-phorylates purine deoxyribonucleotides [9] <7> enzyme has two separate active sites for deoxycytidine and deoxyadenosine activity [22] <3> reacts with both enantiomers of -deoxycytidine, -deoxyguanidine, -deoxyadenosine, and a-D-deoxycytidine is also substrate [31] <3> reacts with both enantiomers of jS-deoxyadenosine, j3-arabinofuranosyl-adenine and jd-deoxyguanine ]34] <3> remarkably relaxed enantioselectivity with respect to cytidine derivatives in p configuration [36] <3> lack of enantioselectivity for D- and L-analogues of cytidine and adenosine [43]) [9, 10, 15, 16, 22, 31, 34, 43]... 

S ATP -I- deoxycytidine <1, 3, 4, 8> (<3> deoxycytidine kinase is a multisubstrate enzyme that also phosphorylates deoxyadenosine, it exists in different conformational states with different substrate kinetic properties... 

One can probably guess that in relation to reality, the reaction examples of the illustration or of equation (3-73) are much simplified. Many enzymes of known function catalyze reactions involving more than one substrate. The mechanisms can be quite complex, however, the rate laws do generally follow the form of equation (3-73) if the composition of only one substrate is varied at one time. A good discussion of such multisubstrate enzyme-catalyzed reactions is given by Plowman [K.M. Plowman, Enzyme Kinetics, McGraw-Hill Book Co., New York, NY, (1972)]. There is a strong family resemblance between these enzymatic sequences and those encountered in the detailed collision theory of Benson and Axworthy in Chapter 1. 

The steady-state kinetic treatment of multisubstrate random enzyme reactions gives rise to the forward rate equation of higher order in substrate terms that reflect the number of substrate addition in the formation of intermediary complexes. The transformations are nonlinear. For example, the steady-state treatment of the random bi bi reaction gives, in a coefficient form ... 

The steady-state kinetics of monosubstrate enzyme reactions has been described in Chapter 3. However, tme monosubstrate reactions are quite rare in nature and are restricted only to some isomerases and epimerases. The majority of enzyme reactions are multisubstrate reactions, with two or three substrates and one, two, or three products of reaction (lUBMB, 1992). 

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