When a protein does not show cooperativity, the value of n is 1. How does this a

Question

When a protein does not show cooperativity, the value of n is 1. How does this affect the efficiency of oxygen delivery versus the case with a cooperative protein, where the value of n is greater than 1 but less than the maximum number of binding sites? To answer this question, calculate Y in the lungs when p50 23 torr, pO2 97 torr, and n 1. Then, calculate Y in the capillaries, where pO2 26 torr, p50 23, and n is still 1. What is the overall efficiency (expressed as a percent to the ncarest ones) betwcen the fractional saturation in the lungs minus the fractional saturation in the tissues?

Explanation / Answer

Hill equation is used to quantify the cooperative binding of a ligand to a molecule. It is represented as:

Y/1-Y=(pO2/p50)n

Y= (1-Y) * (pO2/p50)n= (pO2/p50)n - (pO2/p50)n *Y

Solving for Y

Y= (pO2/p50)n/1+(pO2/p50)n

Hence,

Y (fractional saturation) = (pO2)n / (p50)n + (pO2)n

n= Hill coefficient or Hill constant.

In lungs, p50=23 torr, pO2=97 torr, n=1

Ylungs= (97)1/(23)1 +(97)1

Ylungs= 97/23+97=0.8083

In capillaries p50=23 torr, pO2=26 torr, n=1

Ycapillaries= (26)1/(23)1 +(26)1

Ycapillaries= 26/23+26=0.5306

Efficiency of oxygen delivery= (Ylungs - Ycapillaries) = (0.8083-0.5306) = 0.2777

Overall Efficiency= 0.2777*100= 27.77%

Suppose n=2.8 at these same conditions, anumber greater than 1.

In lungs, p50=23 torr, pO2=97 torr, n=2.8

Ylungs= (97)2.8/(23)2.8 +(97)2.8

Ylungs= 365561.84/6498.87+365561.84 =0.9825

In capillaries p50=23 torr, pO2=26 torr, n=2.8

Ycapillaries= (26)2.8/(23)2.8 +(26)2.8

Ycapillaries= 9160.63/6498.87+9160.63 = 0.5850

Efficiency of oxygen delivery= (Ylungs - Ycapillaries) = (0.9825-0.5850) = 0.3975

Overall Efficiency= 0.3975*100= 39.75%

Oxygen delivery is 39.75% and 27.77% at n=2.8 and n=1 respectively. Hence, the protein can carry oxygen away from the lungs more efficiently at n=2.8. The protein is 98.25% saturated at p02=98% and n=2.8 while it is only 80.83% saturated at n=1. Oxygen efficiency is higher when n is greater than 1.

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