I am trying to model a system with negative cooperativity between ligand and receptor, and I have data for dissociation constants, hill constant as well as the rate of forward reaction (which I am assuming to be constant for my purpose). Using hill equation
Frac. of ligand bound = [L]^n/(Kd + [L]^n)
and substituting Kd with Koff/Kon, where Koff is reverse rate constant and Kon is forward rate constant, will I be able to calculate Koff at each time step if I have value for Kon? Or am I making any any mistakes?
Thank you very much in advance.
The Hill equation relates to a chemical equilibrium with Koff is a constant .
At equilibrium ,then , you could calculate Koff from the equation, as
Koff = Kon ([L] ^n/ theta - [L]^n ) where theta = frac of ligand bound.
not sure what you mean by Koff varying with time.
Hi Arjun,
Kd in your equation is an apparent dissociation constant, you must use the microscopic dissociation constant KD insead, so the Hill equation for your purpose is
theta = [L]^n / (Kd^n + [L]^n)
This yields, after rearrangement:
Koff^n = Kon^n ( [L]^n (1-theta)/theta)
So, you can try with this correction, beware of the power of n on the rate constants.
I guess you wanna calculate koff for the applied concentrations and not "time steps".
Best,
Karoly
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