Cooperative binding of substrate

The Hill Equation Describes the Behavior of Enzymes That Exhibit Cooperative Binding of Substrate... 

The symmetry model (fig. 2.4) of allostery can describe the cooperative binding of substrate to enzyme (homotropic effect), as well as the influence of effector molecules on the activity of enzymes (heterotropic effect). 

This equation embodies all the features of positive cooperative binding of substrate and the effect of this upon biocatalytic rate. Given the power terms, this equation is decidedly not identical with the Michaelis-Menten equation (8.8) However, an alternative and equally important biocatalytic equation can be derived from Equation (8.30) with a little more work and a few simple assumptions. First, let us assume that cooperative binding is sufficiently positive that terms in [S] are eliminated from Equation (8.30). Second, let us define Vmax according to... 

Q Sequential model of cooperative binding of substrate S to an allosteric enzyme. Binding substrate to one subunit induces the other subunit to adopt the R state, which has a higher affinity for substrate. 

Supramolecular chemistry has been a very popular research topic for three decades now. Most applications are foreseen in sensors and opto-electronical devices. Supramolecular catalysis often refers to the combination of a catalyst with a synthetic receptor molecule that preorganizes the substrate-catalyst complex and has also been proposed as an important possible application. The concept, which has proven to be powerful in enzymes, has mainly been demonstrated by chemists that investigated hydrolysis reactions. Zinc and copper in combination with cyclodextrins as the receptor dramatically enhance the rate ofhydrolysis. So far, the ample research devoted to transition metal catalysis has not been extended to supramolecular transition metal catalysis. A rare example of such a supramolecular transition metal catalyst was the results of the joined efforts of the groups of Nolte and Van Leeuwen [SO], They reported a basket-shaped molecule functionalized with a catalytically active rhodium complex that catalyzed hydrogenation reactions according to the principles of enzymes. The system showed substrate selectivity, Michaelis Menten kinetics and rate enhancement by cooperative binding of substrate molecules. The hydroformylation of allyl catachol substrates resulted in a complex mixture of products. 

The relationship between substrate concentration ([S]) and reaction velocity (v, equivalent to the degree of binding of substrate to the active site) is, in the absence of cooperativity, usually hyperbolic in nature, with binding behavior complying with the law of mass action. However, the equation describing the hyperbolic relationship between v and [S] can be simple or complex, depending on the enzyme, the identity of the substrate, and the reaction conditions. Quantitative analyses of these v versus [S] relationships are referred to as enzyme kinetics. 

Cooperative binding of the synthetic substrate bis(p-nitrophenyl) phosphate and of a protein inhibitor (see Sections III,D,2 and 3) might also be considered as an indirect indication of a dimeric structure. 

There are exceptions to Michaelis-Menten behaviour. For example allosteric enzymes which instead of a hyperbolic curve in a Lversus [S] graph yield a sigmoidal plot (the behaviour is rather like non-catalytic allosteric proteins, such as haemoglobin, Section 2.5. This type of curve can indicate cooperative binding of the substrate to the enzyme. We have discussed cooperativity in Section 1.5 (see also Section 10.4.3). In addition, regulatory molecules can further alter the activity of allosteric enzymes. 

Figures 5.11A and B show the characteristic sigmoid curves obtained as a result of interaction between the substrate site, the stimulating modulator site, and the inhibitory modulator site for K and M classes of enzymes. The curves in the absence of modulators are homotropic effects caused by cooperative binding of the substrate. Heterotropic modulators, which can be either positive or negative in their actions, are molecules other than the substrate.

Negative cooperativity. You have isolated a dimeric enzyme that contains two identical active sites. The binding of substrate to one active site decreases the substrate affinity of the other active site. Which allosteric model best accounts for this negative cooperativity ... 

Figure 10.3 ATCase displays sigmoidal kinetics. A plot of product formation as a function of substrate concentration produces a sigmoidal curve because the binding of substrate to one active site increases the activity at the other active sites. Thus, the enzyme shows cooperativity.

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