Enzyme kinetics multiple-substrate inhibition

Substrates may affect enzyme kinetics either by activation or by inhibition. Substrate activation may be observed if the enzyme has two (or more) binding sites, and substrate binding at one site enhances the alfinity of the substrate for the other site(s). The result is a highly active ternary complex, consisting of the enzyme and two substrate molecules, which subsequently dissociates to generate the product. Substrate inhibition may occur in a similar way, except that the ternary complex is nonreactive. We consider first, by means of an example, inhibition by a single substrate, and second, inhibition by multiple substrates. 

Previous sections of this chapter have focused on developing general principles for enzyme-catalyzed reactions based on analysis of single-substrate enzyme systems. Yet the majority of biochemical reactions involve multiple substrates and products. With multiple binding steps, competitive and uncompetitive binding interactions, and allosteric and covalent activations and inhibitions possible, the complete set of possible kinetic mechanisms is vast. For extensive treatments on a great number of mechanisms, we point readers to Segel s book [183], Here we review a handful of two-substrate reaction mechanisms, with detailed analysis of the compulsory-order ternary mechanism and a cursory overview of several other mechanisms. 

Although the MM equation is a powerful kinetic form to which the vast majority of enzyme kinetics has been fitted, one should not forget the assumptions and limitations of the model. As a basic example, feedback inhibition, whereby the product of the reaction inhibits the enzyme-substrate cooperativity, multiple-substrate reactions, allosteric modifications, and other deviations from the reaction scheme in equation (1) are treated only adequately by the MM formalism under certain experimental conditions. In other words, enzyme kinetics are often bent to conform to the MM formalism for the sake of obtaining a set of parameters easily recognizable by most biochemists. The expUcit mathematical and experimental treatment of reaction mechanisms more complex than that shown in equation (1) is highly involved, although a mathematical automated kinetic equation derivation framework for an arbitrary mechanism has been described in the past (e.g., ref. 6). 

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 regulation of enzymes by metabolites leads to the concept of allostenc regulation. Allosteric means other structure. Allosteric modulators can bind at a site other than the active site in question and cause activation or inhibition. These modulators can include the substrate itself, which binds at another active site in a multi-subunit enzyme. In fact, allosterically modulated enzymes almost always have a complex quaternary structure (multiple subunits) and exhibit non-Michaelis-Menten kinetics. 

Lakshmi and Balasubramanian (1980) showed the presence of a new multiple form of arylsulfohydrolase B in human and monkey brain. Arylsulfohydrolase B, can be separated by DEAE-cellulose chromatography (Mathew and Balasubramanian, 1984). The B, form totally binds to Sephadex G-200 and was not eluted with 1.0 M NaCl, 0.5 M glucose, 0.5 M glucose plus 0.5 M NaCl, 0.5 M KSCN, 1 M urea, or 1% Triton X-100. The treatment of arylsulfohydrolase B with Escherichia coli alkaline phosphatase results in the formation of a less acidic form, presumably due to dephosphorylation. The dephosphorylated form does not bind to DEAE-cellulose. Inorganic phosphate and serine phosphate but not mannose 6-phosphate can inhibit this dephosphorylation. The kinetic properties of the phosphorylated and dephosphorylated arylsulfohydrolase are quite similar. The possibility that arylsulfohydrolase B is a dephosphorylated form of B, has been ruled out by the significant differences between substrate concentration and activity curves of these enzymes. 

The kinetic properties of these multiple forms are quite similar (Farooqui, 1976b). With p-nitrocatechol sulfate as substrate, arylsulfohydrolase B has a value at least three times higher than that of arylsulfohydrolase A. Sulfate ions produce a noncompetitive inhibition of this enzyme with a K value of... 

The on rate, kon, is equivalent to k, and the off rate, off> is equivalent to the sum of all pathways of E-I breakdown, in this case, A i - - k2. It is possible that multiple products are formed, and the rates of formation of these should be included in the koff term. A progress curve or continuous assay is the best way to determine the kon and Ki of an alternate substrate. Addition of an alternate substrate inhibitor to an enzyme assay results in an exponential decrease in rate to some final steady-state turnover of substrate (Fig. 13.1). In an individual assay, both the rate of inhibition (kobs) and the final steady-state rate (C) will depend on the concentration of inhibitor. Care must be taken to have a sufficient excess of inhibitor over enzyme concentration present, since the inhibitor is consumed during the process. Where possible, working at assay conditions well below the of the assay substrate simplifies the kinetics, as the substrate will not interfere in the inhibition. If the... 

An assay for cerebroside sulphatase is based on t.l.c. and the use of tritium-labelled cerebroside sulphate as a substrate. The cerebroside sulphatase activity of the arylsulphatase A in human liver and kidney was investigated using this assay. Kinetic and other evidence suggested that cerebroside sulphatase also possesses arylsulphatase activity, although both activities are manifest by the same active site. Pure human cerebroside sulphatase has been shown to require the presence of bile salts and to be stimulated by manganese chloride. Cerebroside sulphatases isolated from a number of invertebrates are composed of multiple forms that were separated by isoelectric focusing. These enzymes have activities comparable to those from vertebrates, and they also exhibit arylsulphatase activity. Kinetic data (pH optima and Km values etc.) were reported for the enzymes, which were inhibited by nitrocatechol sulphate. 

The kinetic behaviour of a bound enzyme inhibited by the substrate shows multiple steady states within a particular range of concentrations of the substrate in the macroenvironment, provided diffusion to the enzyme is slow. When the substrate has to cross a membrane to reach the enzyme, regulatory schemes showed that the enzyme s activity can be changed dramatically by small variations in substrate concentration, membrane permeability, and the kinetic constants of the enzyme. It was concluded that the regulatory properties of an enzyme in a cell are more effective than suggested by experiments with the enzyme in solution. 

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