# Foster 5/15/06
# gnuplot script to generate quadratic form of binding equation
# At: total concentration of molecule A
# Bt: total concentration of molecule B (titrant)
# Af: free concentation of A
# Bf: free B
# Kd: dissociation constant
# N: nuber of binding sites in A
# fb: fraction bound
print "Binding equation"
print "# At: total concentration of A
print "# Af: free concentatio of B
print "# Bt: total B
print "# Bf: free B
print "# Kd: dissociation constant
print "# N: nuber of binding sites
print "fb: fraction bound
pause -1 "press return to continue
At = 1e-6
Bt = 1e-6
Kd = 1e-6
# signal from free a, ab complex
Sa = 10; Sab = 100
AB(x) = (Kd+At+x - ((Kd+x+At)**2 - 4*x*At)**0.5)/2
fb(x) = AB(x)/At
s(x) = Sa + (Sab-Sa)*fb(x)
plot fb(x)