Michaelis-Menten constant zero?

[Prometheus]

I've been looking at the Michaelis-Menten constant, Km, being zero from a mathematical perspective and it doesn't make any sense - i.e. it breaks the Michaelis-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.

[andrewcellini]

I've been looking at the Michaelis-Menten constant, Km, being zero from a mathematical perspective and it doesn't make any sense - i.e. it breaks the Michaelis-Menten equation (the velocity of a reaction becomes undefined).

wouldn't the velocity always be at Vmax?

 

assume Km = 0

 

V = Vmax/(Km + )

 

V = Vmax /(0 + ) = Vmax/ = Vmax

 

edit: after thinking about it i don't think this would happen as I just showed above.I forgot that is defined as Km = (Kr + Kcat)/Kf, Kr is the constant of the reverse of binding substrate to the enzyme. Kr and Kcat are positive real numbers, so for Km to be zero they would both have to be zero. and because Vmax = Kcat*[E] where E is the concentration of enzyme (held constant), if Kcat is 0 Vmax is 0 and thus V = 0 when Km = 0.

But does having a Km=0 make any physical sense?

it has a great affinity for whatever substrate it acts on, that's for sure, but i've not been able to come across papers where, given the conditions in the experiment, the Km was equal to zero.

 

edit: i'm not sure what physical sense to make of it given my addition to my answer above.

Edited January 15, 2016 by andrewcellini

[Prometheus]

In addition to that you have to divide through by Km at some point deriving the Michaelis-Menten equation, which if zero would be undefined.

 

I ask because the BRENDA database has some Km (and Kcat, Kcat/Km) values of zero and before i wrote it off as truncation or experimental error i just wanted to check if it made any sense.

[andrewcellini]

In addition to that you have to divide through by Km at some point deriving the Michaelis-Menten equation, which if zero would be undefined.

the derivation in my textbook (Biochemistry 8th ed Campbell and Farrell) and also on this website (http://www.bgu.ac.il/~aflaloc/BioHTML/Goodies/DeriveMMEqn.html) would have you dividing by Km + S

 

to make this short (and to start somewhat in the middle) you would be at ([E] - [ES])/[ES] = Km

 

Km[ES] = [E] -[ES]

(Km+)[ES] = [E]

[ES] = [E]/(Km + )

Edited January 15, 2016 by andrewcellini

[Prometheus]

The derivation i followed was similar, but for one bit.

 

From the steady-state approximation: k_-1[ES] + k_cat[ES] = k₁[E]

 

and: K_m = (k_-1 + k_cat)/k₁

 

we get:[ES] = [E]/K_m

 

Which is why i thought Km could not be zero for the MM to be valid.

[andrewcellini]

lol duh, this slipped my mind too; that's what i get for starting in the middle of the derivation. the total enzyme is conserved, so the concentration of the enzyme [E] = [E]0 - [ES], where [E]0 is the initial concentration. substitute that in for [E] in your equation and you should arrive at what i got.

Edited January 16, 2016 by andrewcellini

[Xalatan]

Km is a measure of enzyme affinity for the substrate, the definition being the substrate concentration when reaction velocity is 1/2 Vmax.

 

So, having a Km of 0 does not make physical sense because enzymatic affinity cannot be infinite; the substrate concentration at 1/2 Vmax cannot be zero because at least some substrate is needed for the reaction to proceed.

[andrewcellini]

Prometheus, what enzyme were you looking at on BRENDA? the enzyme with the smallest Km that i've found was "site-specific DNA-methyltransferase (adenine-specific)" with a Km of 0.00000000000001 mM for DNA Adenine

 

http://www.brenda-enzymes.org/literature.php?e=2.1.1.72&r=676217

[Prometheus]

I was looking at all of them - some 35000. Used a python script to extract all the parameters. I presumed there was just some truncation error when extracting the data but since i know nothing of MM kinetics i just wanted to confirm it has no physical meaning. I'm satisfied now it is just truncation error. Thanks for the help.