A substrate binds 100 times as tightly to the R state of an allosteric enzyme as

Question

A substrate binds 100 times as tightly to the R state of an allosteric enzyme as to its T state. Assume that the concerted model applies to this enzyme.

a) By what factor does the binding of one substrate molecule per enzyme molecule alter the ratio of the concentrations of enzyme molecules in the R and T states?

b) Suppose that L, the ratio of [T] to [R] in the absence of substrate, is 10-7 and that the enzyme contains four binding sites for substrate. What is the ratio of enzyme molecules in the R state to those in the T state in the presence of saturating amounts of substrate, assuming that the concerted model is obeyed?

Explanation / Answer

(a) 100.

The change in the [R]/[T] ratio on binding one substrate molecule must be the same as the ratio of the substrate affinities of the two forms

(b) 10.

The binding of four substrate molecules changes the [R]/[T] by a factor of 1004 = 108. The ratio in the absence of substrate is 10-7. Hence, the ratio in the fully liganded molecule is 108

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