Ligand Binding
1. Summary of Key
Equations / Relationships
E + S Û ES ; Kd = [E][S]/[ES] and Ka = 1/ Kd
So = S + ES; Eo = E + ES
If So >> Eo , then S ~ So then Kd [ES] = [Eo – ES][So]
[ES] = EoSo/(Kd + So); define Fraction of sites occupied q = [ES]/Eo = So/(Kd + So)
thus Kd = So when q = 0.5
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Recall from your enzyme kinetics;
[ES] = Eo(So/(Kd + So)) is similar to v = Vmax (So/(KM + So))
and KM = So when v/Vmax = 0.5
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2.
Manipulations of Equation
a) double reciprocal plot 1/q = Kd/ So + 1 ; plot 1/q vs. 1 / So
b) Scatchard Plot: q = So/(Kd + So) or qKd + qSo = So or q = 1 - qKd /So
plot q vs. q/So slope = - Kd
3.
Competitive Binding
q = Ao/(Kd + Ao) but with a competitive “B” present, Kd = Kd,A (1 + [B]/Kd,B)
à replot apparent Kd to obtain Kd.B