Multisubstrate kinetics

In real situations, there are complex cases such as in biological waste water treatment and fermentation technology (complex media with multiple carbon sources, e.g., molasses, worts, metabolic intermediates, vitamins, etc.) that cannot be treated with the simple model equations fi = fi s) given in Sect. 5.3. In the course of a growth process in a complex medium, the valuable, easily utilized components are exhausted after a short time. For use of the remaining 

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Further drawbacks associated with the direct linear plot include the fact that this analysis does not readily lend itself to standard computerized graphing methods (for example, use of GraphPad Prism), although specialized software is available (Henderson, 1993). Of course, one of the major advantages of the direct linear plot is the ability to obtain kinetic constants by eye, without the need for a computer. However, for presentation purposes, the use of graphing software is still desirable. Furthermore, any behavior more complicated than simple, single substrate kinetics - for example, turnover in the presence of an inhibitor, or multisubstrate kinetics - caimot readily be shown on a direct linear plot. This is in contrast with the flexibility afforded by nonhnear regression approaches. 

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 ... 

Fe-S clusters in 862 multisubstrate, kinetics of 464,465 oligomeric 475,497 pacemaker 535—537 processive action 602 prochiral centers 478-481 proofreading 482... 

It would be desirable to determine all binding constants from the simple experiments, but values for K, a, and [j cannot be obtained without performing more complex experiments. More importantly, the observation of partial inhibition or activation indicates that multisubstrate kinetic mechanisms are likely to be involved, and care should be taken in the interpretation of the data and the design of future experiments. 

Figure 5.48. Multisubstrate kinetics for a two-substrate reaction (a) Concentration/ time diagram for strictly sequential substrate utilization (diauxic growth), (b) Partly overlapping and partly sequential substrate use. (c) Simultaneous substrate utilization. Sum-type kinetics are often applied in (b) and (c).

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. 

Guha, S., Peters, C. A. and Jaffe, P. R. (1999). Multisubstrate biodegradation kinetics of naphthalene, phenanthrene, and pyrene mixtures, Biotechnol. Bioeng., 65, 491-499. 

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... 

A. J. Hanekom, Generic kinetic equations for modeling multisubstrate reactions in computa tional systems biology. Master s thesis, Stellenbosch University (2006). 

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. 

The use of Haldane relationships to verify the magnitude of the equilibrium constant or, conversely, to determine (or verify) one of the kinetic parameters requires that aU constants be measured under the same experimental conditions (eg., temperature, pH, buffer species, ionic strength, free metal ion concentrations, etc) If not, the Haldane relationship has no meaning. In addition, kinetic data are often limited in precision, unlike equilibrium measurements. For multisubstrate reactions, there are at least two different Haldane relationships. Thus,... 

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)... 

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