Hill's cooperativity
5th Reaction
Reminder:
A + B <--> AB
Ka=Keq=[AB]/[A][B]=1/Kd
θ=[AB]/([AB]+[A])=[B]/([B]+Kd)
MWC Model (Cooperativity)
A + nB <--> ABn
Ka=Keq=[ABn]/[A][B]n=1/Kd
θ=[B]n/([B]n+Kd)
log(θ/(1- θ))=nlog(B)-log(kd) …Hill's equation
Suppression mediated by cI:
ρ + nCI <--> ρ:CIn (k+, k-)
Keq=Ka=[ρ:CIn]/[ρ][CI]n
Si ρ0=[ρ]+[ρ:CIn]
… ρ0=[ρ]+Keq[ρ][CI]n
=> ρ= (ρ0/Keq)/((1/keq)+[CI]n)
Flow= k+[ρ][CI]n = K+((ρ0/Keq)/((1/Keq)+[CI]n))[CI]n
Flow= k+([ρ0]/Keq) [CI]n / ((1/Keq)+[CI]n)
=> Vm= k+([ρ0]/Keq) & Kp=1/Keq=Kd
So:
Keq = exp( -ΔG / R T )
k+ = (KB/h) T exp( -ΔG / R T ) = (KB/h) T Keq
Keq= |
2.89517E+17 |
|
|
KB= |
1.38E-23 |
J/K |
k+= |
1.79764E+30 |
/s |
|
h= |
6.63E-34 |
J s |
|
|
|
|
R= |
1.9872 |
cal/(K mol) |
ΔG= |
-23810 |
cal/mol |
|
T= |
298 |
K |
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