Chemical Forums
Specialty Chemistry Forums => Biochemistry and Chemical Biology Forum => Topic started by: Epimetheus on January 14, 2016, 08:28:47 AM
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I've been looking at the Michaleis-Menten constant, Km, being zero from a mathematical perspective and it doesn't make any sense - i.e it breaks the Michaleis-Menten equation (the velocity of a reaction becomes undefined).
But does having a Km=0 make any physical sense? Is it possible - does the model need amending to take into account zero values?
Thanks for any insight.
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Consider a very simple system involving E, ES, and three rate constants. The definition of Km in terms of rate constants is that it is equal to (k-1 + k2)/k1.
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Indeed, so Km=0 would imply K-1=-Kcat.
However, deriving the MM equation at various stages requires us dividing by Km, and so Km must strictly not be zero for the derivation to make sense..
Also if we let Km=S (as we would to find that Km is half Vmax) then the velocity is also undefined.
Hence, i cannot make sense of it mathematically. But does Km=0 make sense physically?
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Indeed, so Km=0 would imply K-1=-Kcat.
This does not sound correct. Both k-1 and k2would have to be zero, in order for Km to be zero.
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How so?
We have:
Km = (K-1 + K2)/K1 =0
Hence we only need the numerator to sum to zero for this to be true, i.e: K-1 + K2 = 0.
Which implies K-1=-K2.
K-1 = -K2 = 0 is just one possibility.
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Rate constants cannot be negative numbers.
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Ah yes. Excellent.
Then Km cannot be zero as there wouldn't be a MM reaction taking place at all.