Cooperative enzymes

The cooperative binding of O2 by hemoglobin and the allosteric effects in many enzymes require interaction between sites that are widely separated in space. The MWC model was proposed in 1965 to incorporate allosteric and conformational effects in an explanation of enzyme cooperativity. The seminal observation was that most cooperative proteins have several identical subunits (protomers) in each molecule (oligomer) this situation is imperative for binding cooperativity. The MWC model is defined as follows ... 

An analysis of the influence of enzyme cooperativity in the mathematical model of product activated oscillatory glycolysis reaction was made by Goldbetter and Venieratos (1980). They established the relationship between the instabilities and the value of the Hill coefficient in the allosteric model for phosphofructokinase. 

IIIF) Goldbetter, A., Venieratos, D. Analysis of the Role of Enzyme Cooperativity in... 

The analytical expression (2.28) allows us to establish an explicit link between enzyme cooperativity and instability of the steady state. This expression also permits us to determine the periodic variation of enzyme cooperativity in the course of oscillations. 

Fig. 2.24. Role of enzyme cooperativity in the mechanism of oscillations. The curves yield the Hill coefficient, Hh, at steady state (eqn (2.28)) as a function of the allosteric constant L, for increasing values of the number of enzyme subunits (n = 2 to 8). On each cin e, the dashed domain denotes the instability of the steady state (Goldbeter Venieratos, 1980).

The existence of two time scales within the system lowers the threshold of cooperativity required for oscillations. As indicated in fig. 2.27, oscillations can indeed occur for values of the Hill coefficient close to unity when the product concentration varies more rapidly than that of the substrate. The importance of enzyme cooperativity in the mechanism of oscillations appears to be reduced in these conditions. 

The linear stability analysis of eqns (2.30) shows that the domain of instability of the unique steady state is larger than in the case of a linear sink of product. The main effect of the Michaelian sink of product is, however, to allow the occurrence of sustained oscillations in the absence of enzyme cooperativity - but not of autocatalytic regulation (Goldbeter Dupont, 1990). 

If, as shown by the analysis of the situation of a Michaelian sink of reaction product, enzyme cooperativity is not a necessary prerequisite for sustained glycolytic oscillations, the analysis of the model nevertheless indicates that the nonlinearity associated with enzyme cooperativity favours periodic behaviour and, in most circumstances, remains essential for its occurrence. 

The detailed analysis of the model for the product-activated allosteric enzyme allowed a precise quantification of the role played by enzyme cooperativity in glycolytic oscillations (see chapter 2). However, the analysis of a slightly modified model in which the sink of the product becomes Michaelian - i.e. saturable - instead of linear, showed (see section 2.7) that oscillations can occur even if the allosteric enzyme contains a single subunit existing in two conformational states. Enzyme cooperativity is therefore not a condition sine qua non for oscillations to occur weaker nonlinearities, of the Michaelian type, distributed over several reactions of the system, can thus cooperate to raise its global... 

Goldbeter, A. 1977. On the role of enzyme cooperativity in metabolic oscillations. Analysis of the Hill coefficient in a model for glycolytic periodicities. Biophys. Chem. 6 95-9. 

Goldbeter, A. D. Venieratos. 1980. Analysis of the role of enzyme cooperativity in the mechanism of metabolic oscillations. J. Mol. Biol. 138 137-44. 

Relationship between membrane lipid fluidity and enzyme cooperativity a) Changes in fatty acid composition... 

Not all enzymes show the simple hyperbolic dependence of rate of reaction on substrate concentration shown in Figure 2.8. Some enzymes consist of several separate protein chains, each with an active site. In many such enzymes, the binding of substrate to one active site causes changes in the conformation not only of that active site, but of the whole multi-subunit array. This change in conformation affects the other active sites, altering the ease with which substrate can bind to the other active sites. This is cooperativity — the different subunits of the complete enzyme cooperate with each other. Because there is a change in the conformation (or shape) of the enzyme molecule, the phenomenon is also called allostericity (from the Greek for different shape ), and such enzymes are called allosteric enzymes. 

The capacities for cooperativity and allosteric regulation elevate enzymes from the level of simple catalysts to that of the regulators of metabolism. In fact, cooperativity and allosteric regulation share a common mechanism—the alteration of the properties of the catalytic site by binding of a ligand to a second site on the enzyme. Cooperativity may be thought of as the homotropic interaction of identical catalytic sites, and allostery as the heterotropic interaction of a catalytic site and a dissimilar site which binds an allosteric modifier. 

At this point, it should be mentioned that experimental examples apart from hemoglobin are more related to the cooperative effects of molecules and not directly involved in the reaction, such as activators and inhibitors. Thus, treatment of enzyme cooperativity should incorporate the influence of modifiers. 

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