Useful equation for calculating binding constants from CD data.
These equations are set up for use with SigmaPlot but can easily
be modified to work with other plotting programs.
I. Fit data to the Hill equation.
[Parameters]
;Modify these values for your data
n=.15 ;vmax
h=2 ;Hill Coefficient
k=100 ;association constant divided by 10^6
C=.010 ;constant to offset data if it doesn't pass though
the origin.
[Variables]
x=col(1) ;ligand concentration in micromolar
y=col(2) ;change in CD, absorbance, rate etc.
[Equations]
u=n*k^h*(x^h)
d=1+(k^h*(x^h))
f=u/d +C
fit f to y; fit calculated binding curve to raw data
II. Calculate the association constant of an enzyme-ligand
complex assuming a tight binding
model.
[Parameters]
; modify these initial values to fit your data.
M=10 ;Amax
k=100 ; ka association constant (divided by 10^6)
nbs=1 ; number of binding sites
[Variables]
x=col(1); ligand concentration in micromolar
y=col(2); spectral change at each ligand concentration
[Equations]
n=1/nbs
P=1; protein concentration in micromolar
q=(1+(n*k*x)+(k*P))/(2*k*P)
r=((1+(n*k*x)+k*P)/(2*k*P))^2
s=(n*x/P)
f=M*(q-sqrt(r-s))
fit f to y; fit calculated to observed spectral change.