If I know that the free energy barrier of the first step of a enzymatic reaction has increased (And I know by how much) but the other steps remain unchanged may I infer from this any kind of accurate information into how this change should effect the specific activity of Kcat of the enzyme?
If kcat is the rate constant for the enzyme-catalyzed reaction and Ea is the activation energy of the catalyzed reaction, then kcat is proportional to e(-Ea/RT), or ln(kcat) is proportional to -Ea/RT. Thus, if Ea increases, kcat decreases, and you can calculate the proprtional decrease based on the known change in Ea.
Hi there,
If the reaction scheme you are working on is the Michaelis Menten one :
E+SES--->E+P
then kcat acts only at the second step (ES---> E+P). Therefore I would say kcat remains unchanged if the first step is the only affected (Kd increased).
Hi:
it is an interesting question of enzyamology with great importance of science. It is concerned to the relation between protein conformational change and enzyme activity.
first of all, your assumption is wrong. if first step of enzyamtic reaction is altered, other parameters of enzyamtic reaction (or step) will be changed also whatever small it is.
my theory has given a reasonable answer to your question, see my papers: Zhao Q. dynamic model of enzymes action. Protein Pept Lett. 2011, 18.92-99 . Qinyi Zhao Allodynamic Regulation of Protein Activity, Quantum Matter 2, 144-152 (2013)
Hi,
To add some more comments to Dominique answer, to answer your question Gary you need to know what is the rate-limiting step of your reaction.
The kcat of an enzyme reflects that rate-limiting step. I do not know on what kind of enzymes you are working but, if it is a Glycoside hydrolase, most of the time the rate-limiting step is the deglycosylation step (2nd one) (unless you are studying mutants, in which case the rate-limiting step might not be the same as the wild-type). Therefore the Ea of the first step in such case can not be related to kcat.
However, for glycoside hydrolases the kcat/Km is an approximation of the firs step (glycosylation), that you can then relate to Ea of the first step.
The answer to your question strongly depends on the enzyme model which you use, or better to say which is valid in your reaction.
MM scheme is just one of them (and it is definitely wrong in principle) and as it was already pointed out in that model the first reaction is not the rate limiting usually.
So your question as it is cannot be answered.
Csaba
Bastien and Csaba are correct, your question can be properly answered only by knowing the type of reaction you are studying, the steps involved and, above all, which step(s) is (are) actually rate-limiting.
If your 'first step' is the rate limiting step , then the reasoning put forward by Adam applies. But if some later step is much slower to begin with, then a modest rise in the energetic barrier for the first step may have no consequences for the overall reaction rate.
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