Multisubstrate systems

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. 

The method is not as useful with multisubstrate systems however, Cornish-Bowden and EndrenyE have presented a robust regression method to treat data with more parameters. 

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. 

While almost all synthetically useful catalytic reactions involve two reactants it will be best to first illustrate this graphical approach using a unimolecular process and the way it can be affected by inhibitors. After this some different types of bisubstrate reactions will be discussed. More detailed analyses of the kinetics of multisubstrate systems have been published in texts 13 and... 

It often becomes necessary in biochemical reactions to continuously add one (or more) substrate(s), a nutrient, or any regulating compound to a batch reactor, from which there is no continuous removal of product. A reactor in which this is accomplished is conventionally termed the semibatch reactor (Chapter 4) but is referred to as a fed-batch reactor in biochemical language. The fed-batch mode of operation is very useful when an optimum concentration of the substrate (or one of the substrates in a multisubstrate system) or of a particular nutrient is desirable. This can be achieved by imposing an optimal feed policy. 

Yoon et al. (1977), Aris and Humphrey (1977), and Knorre (1976) derived generalized Monod equations for multisubstrate systems, based on the following sequence of reactions ... 

Numerous hydrolaseotalyzed KRs of various secondary alcohols were performed in continuous-flow mode (Figure 9.8 and Table 9.6). The bioimprinting effect in sol-gel immobilization of various lipases (Lipase AK, Lipase PS, CaLB, and CrL) was studied (116]. The performance of the immobilized biocatalysts were characterized by enantiomer selective acylation of various racemic secondary alcohols in two different multisubstrate systems (mix A rac-23a,c-e and mix B rac-23b and roc-23i) in batch and continuous-flow mode. The synthetic usefiilness of the best biocatalysts was demonstrated by the KR of racemic l-(thiophen-2-yl)ethanol (rac-23j) in batch and continuous-flow systems [116]. 

When the concentration of one substrate is made variable, while all the others are held constant or at saturation (>10 K ), such a multisubstrate system usually reduces to a practical single-substrate system that obeys Michaelis-Menten kinetics. It is through such a reduced, single-variable system that most steady-state kinetics are used to evaluate kinetic parameters and to distinguish between various reaction mechanisms. 

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

Occasionally, one may also wish to use an auxiliary enzyme not as an assay system but strictly as a means for maintaining the steady-state concentration of a primary reactant in a multisubstrate reaction system. For instance, acetate kinase (and its substrate acetyl phosphate) or creatine kinase (and its substrate creatine phos-... 

DERIVATION OF MORE COMPLICATED RATE EQUATIONS. So far, the rate equations that describe one-substrate enzyme systems have been fairly simple, and the usual algebraic manipulations of substitution and/or addition of simultaneous equations have permitted us to obtain the pertinent rate law. When the number of steps increases and especially when there are branched pathways involved, these manual methods become cumbersome, and more systematic procedures are required. The next two sections should allow the reader to develop a working knowledge of effective methods for obtaining multisubstrate enzyme rate expressions. 

In the Briggs-Haldane steady-state treatment of a one-substrate enzyme system, the Michaelis constant, usually symbolized by, is ( 2 + k3)/ki. For more complex reactions (e.g., with several substrates and/or isomerization steps), the Michaelis constant for a given substrate is a more complex collection of rate constants. For a multisubstrate enzyme having substrates A and B, the Michaelis constants are usually symbolized by and, by and, or by and, respectively. 

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. 

The National Science Foundation is sponsoring a study led by Dr. Richard Bartha of Rutgers University on the multisubstrate biodegradation kinetics of PAHs from creosote, coal tar, and diesel fuel. The relative biodegradabilities and substrate interactions of PAHs in sole and multi-substrate systems will be determined and related to dissolution kinetics processes governing bioavailability. An integrated mathematical model of the behavior of PAHs in NAPL-contaminated soils will be developed and validated. 

The catalytic reaction of lipases follow the so called ping-pong bi-bi mechanism, a double displacement mechanism. This is a special multisubstrate reaction in which, for a two-substrate, two-product (i.e., bi-bi) system, an enzyme reacts with one substrate to form a product and a modified enzyme, the latter then reacting with a second substrate to form a second, final product, and regenerating the original enzyme (ping-pong). 

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. 

Chem. Descrip. Zinc orthophosphate complex CAS 7779-90-0 EINECS/ELINCS 231-143-9 Uses Corrosion Inhibitor, pigment, universal tannin stain for multisubstrate water-based systems, direct-to-metal finishes, high-gloss systems, and thin-film applies. 

The kinetics of many enzymes such as kinases and polymerases involve two or more substrates and products. Such multisubstrate enzymes present far more complex kinetics than the Michaelis—Menten type because of the order of substrate and/or product interactions with the enzyme. For the formulation of detailed rate equations for multisubstrate enzyme systems, interested readers should consult the treatises on enzyme kinetics (110,118). 

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