Chapter 7, Problem 14P

Interpretation Introduction

(a)

Interpretation:

An oxygen-binding curve for a hypothetical two subunit hemoglobin with $n=1.8$ and $P_{50}=10\text{ torr}$ should be plotted.

Concept introduction:

Hill equation is represented as follows:

$\log \left(\frac{Y}{1-Y}\right)=n\log \left(p{\text{O}}_2\right)-n\log (P_{50})$

Here, Y- fractional saturation

n − a measure of the degree of cooperativity in ligand binding.

P₅₀ − partial pressure of oxygen at which hemoglobin is half saturated.

The Hill plot of log(Y/1-Y) versus log(P₅₀) should be a linear graph with slope of n.

Interpretation Introduction

(b)

Interpretation:

An oxygen-binding curve for shypothetical two subunit hemoglobin with $n=2,\text{ L = 1000, c = 0}{\text{.01 and K}}_R=1\text{ torr}$ should be plotted using concerted model

Concept introduction:

Concerted model equation is written as follows:

$Y=\frac{\alpha {\left(1+\alpha \right)}^{n-1}+Lc\alpha {\left(1+c\alpha \right)}^{n-1}}{{\left(1+\alpha \right)}^n+L{\left(1+c\alpha \right)}^n}$

Here, Y − fractional saturation

a − ratio between the substrate concentration and the dissociation constant for a ligand binding to a single site in R state.

L − The ratio of the concentrations of the T and R states with no ligands bound

c − the ratio between the dissociation constant for a ligand binding to a single site in R state and that of T state.

n − number of binding sites

Also, the ratio can be calculated as follows:

$\alpha =\frac{p{O}_2}{K_R}$

Here,

pO₂ − partial pressure of oxygen

K_R - the dissociation constant for a ligand binding to a single site in R state.