Question

The data below show the binding of oxygen to squid hemocyanin. Determine from a Hill plot whether the binding is cooperative and estimate the minimum number of subunits in the molecule.

pO2 (mm)

1.13 5.55 7.72 10.72 31.71 71.87 100.5 123.3 136.7 166.8 203.2 262.2 327.0 452.8 566.9 736.7

Percent Saturation

0.30 1.33 1.92 3.51 8.37 18.96 32.90 47.80 55.7 67.3 73.4 79.4 83.4 87.5 89.2 91.3

Answer 1

log (Y/1-Y) = nlog L - log Kd

A plot of log (Y/1-Y) vs log L is called a Hill plot, where n is the Hill coefficient.   This equation is of the form:  
y = mx + b which will be a straight line with slope n and y intercept of - log Kd. When n = 1, as it would be with Mb or Hb whichever site oxygen binds to each site with the same affinity does not depend on of the number of other oxygens bound to other sites, the Hill plot is linear with a slope of 1. Solving for the x intercept (when the y axis variable is 0) in equations 7 gives:

8)   0 = nlog L -log Kd, or nlogL = log Kd, or log L = (logKd)/n.

The X intercept is when the dependent variable "y" value is 0. This occurs when Y/(1-Y) = 1, which occurs at half fractional saturation. (Remember log 1 = log 10⁰ = 0)

Substituting equation 4 (Kd = P₅₀ⁿ) into (7) and (8) gives
(9) log (Y/1-Y) = nlog L - n log P₅₀- the Hill Equation with P₅₀ instead of Kd,
(10) 0 = nlog L -nlog P₅₀, or nlogL = nlog P₅₀, or log L = logP₅₀.