Chapter 7, Problem 16P

Interpretation Introduction

(a)

Interpretation:

The graph of the given data to form an oxygen-binding curve is to be plotted. The oxygen partial pressure at which the given hemoglobin is half-saturated is to be stated. Whether oxygen binding seems to be cooperative or not on the basis of the curve is to be stated.

Concept introduction:

Proteins are the biomolecules which are composed of the long chain of amino acid residues. The protein which contains oxygen and is present in the red blood cells in the body is known as hemoglobin. It contains iron as well.

Answer to Problem 16P

The plot of the given data to form an oxygen-binding curve is shown below.

The oxygen partial pressure at which the given hemoglobin is half-saturated is $p_{{\text{O}}_{\text{2}}}=10\text{torr}$. Oxygen binding is very less or non cooperative.

Explanation of Solution

On the basis of the given data for oxygen-binding for lamprey hemoglobin, the graph of fractional saturation versus partial pressure of oxygen is plotted as follows:

At the oxygen partial pressure, $p_{{\text{O}}_{\text{2}}}=10\text{torr}$ and at $Y=0.5$, the given hemoglobin is half-saturated. The saturation of hemoglobin increases with increasing partial pressure.

Thus, this plot between partial pressure of oxygen $p_{{\text{O}}_{\text{2}}}$ and fractional saturation $Y$ shows that oxygen binding seems to be very less cooperative.

Interpretation Introduction

(b)

Interpretation:

A hill plot by using the given data is to be stated. Whether the hill plot shows any evidence for cooperativity or not is to be stated. The information about the hill coefficient is to be explained.

Concept introduction:

Proteins are the biomolecules which are composed of the long chain of amino acid residues. The protein which contains oxygen and is present in the red blood cells in the body is known as hemoglobin. It contains iron as well.

The hill equation indicates the two close equations which show the binding of a ligand with the macromolecule.

Answer to Problem 16P

A hill plot by using the given data is shown as,

This plot show little bit cooperativity in the center of the curve and its hill coefficient is $1.3$.

Explanation of Solution

The equation that is used to show the hill equation is given as,

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

Here,

$Y$ is the fractional saturation.

$p{\text{O}}_2^n$ is the partial pressure of oxygen.

$p{\text{O}}_{50}^n$ is the partial pressure of oxygen at half saturation of hemoglobin.

The values of$\log \left(\frac{Y}{1-Y}\right)$ for $Y=0.0060$ is calculated as,

$\log \left(\frac{0.0060}{1-0.0060}\right)=-2.22$

Similarly, for $Y=0.0124$, the value of $\log \left(\frac{Y}{1-Y}\right)$ is $-1.901$, for $Y=0.0190$, the value of $\log \left(\frac{Y}{1-Y}\right)$ is $-1.713$, for $Y=0.0245$, the value of $\log \left(\frac{Y}{1-Y}\right)$ is $-1.6$, for $Y=0.0307$, the value of $\log \left(\frac{Y}{1-Y}\right)$ is $-1.5$. Similarly, all the values of $Y=0.0380$ to $Y=0.970$ will be evaluated till $Y=0.970$, the value of $\log \left(\frac{Y}{1-Y}\right)$ is $1.51$.

The value of $\log$

$\left(p{\text{O}}_2\right)$ for $p{\text{O}}_2=0.1$ is calculated as,

$\log \left(0.1\right)=-1$

Similarly, for $p{\text{O}}_2=0.2$, the value of $\log$

$\left(p{\text{O}}_2\right)$ is $-0.699$, for $p{\text{O}}_2=0.3$, the value of $\log$

$\left(p{\text{O}}_2\right)$ is $-0.523$, for $p{\text{O}}_2=0.4$, the value of $\log$

$\left(p{\text{O}}_2\right)$ is $-0.398$, for $p{\text{O}}_2=0.5$, the value of $\log$

$\left(p{\text{O}}_2\right)$ is $-0.301$. Similarly, all the values of $p{\text{O}}_2=0.6$ to $p{\text{O}}_2=200$ will be evaluated till $p{\text{O}}_2=200$ for which the value of $\log$

$\left(p{\text{O}}_2\right)$ is $2.30$.

With the help of the given data for oxygen-binding for lamprey hemoglobin, the plot between $\log \left(\frac{Y}{1-Y}\right)$ and $\log$$\left(p{\text{O}}_2\right)$

The value of slope $n$ is coming out to be $1.3$ for the given hill plot. This plot shows the very little cooperativity at the central part of the plot having $n=1.3$.

The hill coefficient for the graph is $n=1.3$.

Interpretation Introduction

(c)

Interpretation:

A model that is used to explain the observed cooperativity in oxygen binding by lamprey hemoglobin is to be stated.

Concept introduction:

Proteins are the biomolecules which are composed of the long chain of amino acid residues. The protein which contains oxygen and is present in the red blood cells in the body is known as hemoglobin. It contains iron as well.

Answer to Problem 16P

A model that is used to explain the observed cooperativity in oxygen binding by lamprey hemoglobin suggests that binding of oxygen with any monomer is easier as compared to binding of first oxygen with deoxygenated dimer.

Explanation of Solution

It is given that lamprey hemoglobin produces oligomers in the deoxygenated state. These oligomers were primarily dimmers in the deoxygenated state. These dimers are having low affinity for oxygen as compared to monomers. The cooperativity in oxygen binding is shown only if the dissociation of dimmers into two monomers occurs after the binding of first oxygen atom with a dimer. In this model, the binding of oxygen with every monomer is very easy as compared to the binding between first oxygen and the deoxy dimer.