Nonexclusive binding coefficient

Parameters c and L are, respectively, the nonexclusive binding coefficient of the substrate and the allosteric constant of the enzyme (Monod et al, 1965). The enzyme represents a perfect K system when 0=1, i.e. when the R and T states possess the same catalytic activity and differ only by their affinity for the substrate (c < 1). When c = 1 and 0<1, the enzyme behaves as a perfect V system. In the general case of a K-V system, parameters c and 0 are both less than unity. Parameters L and c markedly influence the degree of cooperativity of the enzyme. 

Linear stability analysis permits the construction of stability diagrams as a function of the main parameters of the model. Such diagrams are represented in fig. 2.12 as a function of the nonexclusive binding coefficient of the substrate, c, and of the allosteric constant, L for two values... 

Fig. 2.12. Stability diagram for the allosteric model with positive feedback, as a function of the nonexclusive binding coefficient c and of the allosteric constant L, for (a) = 10 and (b) e = 10". System (2.7) admits a unique steady state. This state is stable in domain I and unstable in domain II in the latter domain, the system evolves towards a limit cycle. For parameter values corresponding to domain III no steady state is reached as the substrate can only accumulate in the course of time (Goldbeter Lefever, 1972).

Equations (13.28) are obtained with the aid of the rapid equilibrium assumptions, from the distribution of complexes the dissociation constants and Kp are disguised as c, the nonexclusive binding coefficient ... 

On the other hand, in the presence of a saturating concentration of an activator, X, that binds exclusively to the R state, the enzyme whl be driven entirely to the R state. This time [A] is equal at half the maximal rate of reaction. From these two estimations, the nonexclusive binding coefficient, c, is calculated from... 

A useful parameter sometimes reported in kinetic studies is the nonexclusive binding coefficient (c). This coefficient is defined as the ratio of the intrinsic enzyme-substrate dissociation constants for the enzyme in the R... 

A lower value of the nonexclusive binding coefficient is associated with a higher cooperativity, and therefore sigmoidicity, of the velocity curves. A lower value of this coefficient implies a decreased affinity of the T state for substrate relative to the R state. If the enzyme in the T state does not bind substrate kj = oo), c = 0. 

This analysis predicts that the addition of a negative effector should not inhibit the oscillations in the case of an exclusive binding of the substrate to the R state of the enzyme. As indicated in fig. 2.26, indeed, the curve H vs L loses its bell shape when coefficient c 0 the degree of cooperativity remains maximal at large values of the allosteric constant so that the steady state remains unstable regardless of the amount of inhibitor added to the system. The fact that an inhibitor of PFK, such as citrate, suppresses glycolytic oscillations would therefore suggest that the substrate binds in a nonexclusive manner to the two conformations of the enzyme. 

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