Question

Binding of oxygen to an unknown protein The binding of oxygen to an unknown protein suspected of carrying oxygen was measured by following changes in absorbance of heme and corrected to give a % of saturation. The binding data are shown below % saturation 1.1300 0.3000 5.5500 1.3300 7.7200 1.9200 10.720 3.5100 31.710 8.3700 71.870 18.960 100.50 32.900 123.30 47.800 136.70 55.700 166.80 67.300 203.20 73.400 262.20 79.400 327.00 83.400 452.80 87.500 566.90 89.200 736.70 91.300 You would like to determine the number of binding sites. Using a Hill Plot, determine what the minimum number of binding sites is for this new protein. Note: assume that YO, theta % saturation.

Answer 1

consider that X is that unknow protein and it has n binding site. so we can write

$X+nO_2\rightleftharpoons X(O_2)_n$

Therefore, the fractional saturation (Y) of that unknown protein

$Y=\frac{number\,of\, binding\, site\, occupied}{Total\, number\, of\, binding\, site}$

$Y=\frac{(pO_2)^n}{(pO_2)^n +p_{50}}$

or $\frac{Y}{1-Y}=(\frac{pO_2}{p_{50}})^n$

Taking log on both side, we will get

$log(\frac{Y}{1-Y})=nlog({pO_2})+nlog({p_{50}})$

here

$\theta=\frac{Y}{1-Y}$

so the equation become

$log(\theta)=nlog(pO_2) +nlog(p_{50})$

the above equation represent a straight line with slope n.

so we are going to use this eqation to find the number of binding site ,as your problem has given θ and pO₂. I am using microsoft excel to plot the graph between log( θ ) and log(pO₂)

the table is as follow.

Θ	PO2	log(Θ)	log(pO2)
0.3	1.13	-0.52288	0.053078
1.33	5.55	0.123852	0.744293
1.92	7.72	0.283301	0.887617
3.51	10.72	0.545307	1.030195
8.37	31.71	0.922725	1.501196
18.96	71.87	1.277838	1.856548
32.9	100.5	1.517196	2.002166
47.8	123.3	1.679428	2.090963
55.7	136.7	1.745855	2.135769
67.3	166.8	1.828015	2.222196
73.4	203.2	1.865696	2.307924
79.4	262.2	1.899821	2.418633
83.4	327	1.921166	2.514548
87.5	452.8	1.942008	2.655906
89.2	566.9	1.950365	2.753506
91.3	736.7	1.960471	2.867291

and the graph is

y = 0.96x-0.4938 R2 = 0.9684 (0) 0 0.5 2 2.5 3 3.5 1 1.5 log(pO2)

the equation of straight line is y = 0.96x - 0.4938. In which, the slope is 0.96,i.e., n=0.96 (approx 1)

therefore, in the unknown protein, the number of binding site is 1.