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