Chapter 7, Problem 1P

The following data describe the binding of oxygen to human myoglobin at $\text{37°C}$ .

From these data, estimate (a) $P_{50}$ and (b) the fraction saturation of myoglobin at $\text{30 mm}$

Hg, the partial pressure of ${\text{O}}_2$ in venous blood.

Interpretation Introduction

Interpretation: The value of $P_{50}$ needs to be calculated from the given data.

Concept Introduction: The hemoglobin capacity of oxygen is 1.34 mL per gram of oxygen gas. This capacity increases the total capacity of blood oxygen 70 times comparing to the dissolved oxygen in the blood. In mammals, the hemoglobin molecule can carry maximum of 4 oxygen molecules.

Explanation of Solution

The data given is as follows:

$P_{{\text{O}}_{\text{2}}}\left(\text{mm Hg}\right)$	$Y_{{\text{O}}_{\text{2}}}$
0.5	0.161
1	0.277
2	0.434
3	0.535
4	0.605
6	0.697
8	0.754
12	0.821
20	0.885

The graph between $P_{{\text{O}}_{\text{2}}}$ and $Y_{{\text{O}}_{\text{2}}}$ is plotted as follows:

  

The value of $P_{50}$ is calculated as follows:

For the above graph, the trending line equation is represented as follows:

  $y=0.2075\ln (x)+0.3014$

Putting the value of $Y_{{\text{O}}_{\text{2}}}$ equal to 0.50 thus,

  $0.5=0.2075\ln (p)+0.3014$

Or,

  $\begin{array}{l}\ln p=\frac{0.5-0.3014}{0.2075}\\ p=e^{0.957}\\ =2.6\text{ mm Hg}\end{array}$

Thus, the partial pressure is approximately 2.6 mm Hg.

Interpretation Introduction

Interpretation: The fraction of saturation of myoglobin at 30 mm Hg partial pressure of oxygen needs to be determined.

Concept Introduction: The hemoglobin capacity of oxygen is 1.34 mL per gram of oxygen gas. This capacity increases the total capacity of blood oxygen 70 times comparing to the dissolved oxygen in the blood. In mammals, the hemoglobin molecule can carry maximum of 4 oxygen molecules.

Explanation of Solution

The fraction of saturation at partial pressure 30 mm Hg is represented in the graph as follows:

  

On extrapolated, the value of $\theta$ will be approximately 0.95. Thus, the fraction saturation of myoglobin at 30 mm Hg is 0.95.