Question

The following results represent the oxygen binding activity of purified myoglobin,

purified hemoglobin, and hemoglobin in human blood cells.

pO2 (Torr)	Fraction of purified myoglobin with O2	pO2 (Torr)	Fraction of purified hemoglobin with O2	pO2 (Torr)	Fraction of hemoglobin in red blood cells with O2
0.5	0.161	0.1	.00315	10.6	0.10
1.0	0.277	0.35	.0099	19.5	0.30
2.0	0.434	0.794	.0306	27.4	0.50
3.0	0.535	1.748	.0909	37.5	0.70
4.0	0.605	2.884	.24	50.4	0.85
6.0	0.697	4.467	.50	77.3	0.96
8.0	0.754	5.75	.76	92.3	0.98
12	0.821	7.94	.909
20	0.885	12.88	.969
		29.51	.99
		67.60	.997

Based on the data shown in the Table, determine the Hill coefficients of purified myoglobin, purified hemoglobin, and hemoglobin in red blood cells.

Answer 1

Answer:

• Equation for Hill coficient = Y/1-Y = (pO₂/P₅₀)ⁿ
• Taking the log of both side : log(Y/1-Y)= n(log pO₂)- n(log P₅₀)
• Where Y = Fractional saturation of heamoglobin & 1-Y = free Heamoglobin

For purified Mayoglobin the Hill cofficient is-

• n (pO₂/P₅₀) = n(log pO₂)-  n(log P₅₀) , here n=1
• 1(log 20)- 1(log 2) = 1(1.30) - 1(0.30) =1 Hill cofficient n =1

For purified Heamoglobin the Hill cofficient is-

• n log(pO₂/P₅₀)=  n(log pO₂)-  n(log P₅₀) , here n=4
• 4(log 67.60)- 4(log 4.46) = 4(1.82) - 4(0.64)
• 7.28 - 2.56 = 4.72 Hill cofficient n =4.72

For purified Heamoglobin in blood the Hill cofficient is-

• n log(pO₂/P₅₀)=  n(log pO₂)-  n(log P₅₀) , here n=4
• 4(log 92.3)- 4(log 27.4) = 4(1.69) - 4(1.43)
• 6.76 - 5.72 =1.04 Hill cofficient n =1.04
• n=1 describes no cooperative

n>1 describes positive cooperativity ( 1 ligand binding faciliates other)

n<1 describes negative cooperativity (1 ligand binding inhibits other binding)

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