In Case study 4.4, we discussed the role of hemoglobin in...

In Case study 4.4, we discussed the role of hemoglobin in regulating the pH of blood. Now we explore the mechanism of regulation in detail. (a) If we denote the protonated and deprotonated forms of hemoglobin as HbH and $\mathrm{Hb}^{-}$, respectively, then the proton transfer equilibria for deoxygenated and fully oxygenated hemoglobin can be written as: $$ \begin{aligned} & \mathrm{HbH} \rightleftarrows \mathrm{Hb}^{-}+\mathrm{H}^{+} \quad \mathrm{pK}_{\mathrm{a}}=6.62 \\ & \mathrm{HbHO}_2 \rightleftarrows \mathrm{HbO}_2^{-}+\mathrm{H}^{+} \quad \mathrm{pK}_{\mathrm{a}}=8.18 \end{aligned} $$ where we take the view (for the sake of simplicity) that the protein contains only one acidic proton. (i) What fraction of deoxygenated hemoglobin is deprotonated at $\mathrm{pH}=7.4$, the value for normal blood? (ii) What fraction of oxygenated hemoglobin is deprotonated at $\mathrm{pH}=7.4$ ? (iii) Use your results from parts (a.i) and (a.ii) to show that deoxygenation of hemoglobin is accompanied by the uptake of protons by the protein. (b) It follows from the discussion in Case study 4.4 and part (a) that the exchange of $\mathrm{CO}_2$ for $\mathrm{O}_2$ in tissue is accompanied by complex proton transfer equilibria: the release of $\mathrm{CO}_2$ into blood produces hydronium ions that can be bound tightly to hemoglobin once it releases $\mathrm{O}_2$. These processes prevent changes in the pH of blood. To treat the problem more quantitatively, let us calculate the amount of $\mathrm{CO}_2$ that can be transported by blood without a change in pH from its normal value of 7.4. (i) Begin by calculating the amount of hydronium ion bound per mole of oxygenated hemoglobin molecules at $\mathrm{pH}=7.4$. (ii) Now calculate the amount of hydronium ion bound per mole of deoxygenated hemoglobin molecules at $\mathrm{pH}=7.4$. (iii) From your results for parts (b.i) and (b.ii), calculate the amount of hydronium ion that can be bound per mole of hemoglobin molecules as a result of the release of $\mathrm{O}_2$ by the fully oxygenated protein at $\mathrm{pH}=7.4$. (iv) Finally, use the result from part (b.iii) to calculate the amount of $\mathrm{CO}_2$ that can be released into the blood per mole of hemoglobin molecules at $\mathrm{pH}=7.4$.

In Case study 4.4, we discussed the role of hemoglobin in regulating the pH of blood. Now we explore the mechanism of regulation in detail.
(a) If we denote the protonated and deprotonated forms of hemoglobin as HbH and $\mathrm{Hb}^{-}$, respectively, then the proton transfer equilibria for deoxygenated and fully oxygenated hemoglobin can be written as:
$$
\begin{aligned}
& \mathrm{HbH} \rightleftarrows \mathrm{Hb}^{-}+\mathrm{H}^{+} \quad \mathrm{pK}_{\mathrm{a}}=6.62 \\
& \mathrm{HbHO}_2 \rightleftarrows \mathrm{HbO}_2^{-}+\mathrm{H}^{+} \quad \mathrm{pK}_{\mathrm{a}}=8.18
\end{aligned}
$$
where we take the view (for the sake of simplicity) that the protein contains only one acidic proton. (i) What fraction of deoxygenated hemoglobin is deprotonated at $\mathrm{pH}=7.4$, the value for normal blood? (ii) What fraction of oxygenated hemoglobin is deprotonated at $\mathrm{pH}=7.4$ ? (iii) Use your results from parts (a.i) and (a.ii) to show that deoxygenation of hemoglobin is accompanied by the uptake of protons by the protein.
(b) It follows from the discussion in Case study 4.4 and part (a) that the exchange of $\mathrm{CO}_2$ for $\mathrm{O}_2$ in tissue is accompanied by complex proton transfer equilibria: the release of $\mathrm{CO}_2$ into blood produces hydronium ions that can be bound tightly to hemoglobin once it releases $\mathrm{O}_2$. These processes prevent changes in the pH of blood. To treat the problem more quantitatively, let us calculate the amount of $\mathrm{CO}_2$ that can be transported by blood without a change in pH from its normal value of 7.4. (i) Begin by calculating the amount of hydronium ion bound per mole of oxygenated hemoglobin molecules at $\mathrm{pH}=7.4$. (ii) Now calculate the amount of hydronium ion bound per mole of deoxygenated hemoglobin molecules at $\mathrm{pH}=7.4$. (iii) From your results for parts (b.i) and (b.ii), calculate the amount of hydronium ion that can be bound per mole of hemoglobin molecules as a result of the release of $\mathrm{O}_2$ by the fully oxygenated protein at $\mathrm{pH}=7.4$. (iv) Finally, use the result from part (b.iii) to calculate the amount of $\mathrm{CO}_2$ that can be released into the blood per mole of hemoglobin molecules at $\mathrm{pH}=7.4$.

Key Concepts

Bohr Effect

The Bohr effect is the physiological phenomenon where changes in blood pH and carbon dioxide concentration influence hemoglobin's affinity for oxygen. A decrease in pH (increased proton concentration) leads to reduced oxygen affinity, facilitating oxygen release in tissues, while the binding of oxygen in the lungs promotes proton release. This reciprocal relationship is a key mechanism in efficient gas exchange and pH regulation.

CO2 Transport and Proton Transfer Mechanisms

The interplay between carbon dioxide transport and proton transfer is central to maintaining blood pH. As tissues produce CO2, it is converted to bicarbonate and protons, and the binding of these protons to hemoglobin prevents significant pH changes. This mechanism, involving complex equilibria among CO2, H+, and the different forms of hemoglobin, ensures efficient removal of CO2 and stabilization of blood pH during respiration.

Buffering Capacity of Blood

Buffering capacity refers to the ability of a solution, such as blood, to resist changes in pH upon the addition of acids or bases. Hemoglobin functions as an important buffer in blood by binding or releasing protons in response to changes in pH, thereby helping maintain a stable pH environment critical for physiological processes.

pKa and Acid-Base Equilibrium

pKa is the negative logarithm of the acid dissociation constant and represents the pH at which half of the acidic groups are deprotonated. It plays a key role in determining the equilibrium state of protonation for molecules. In the context of hemoglobin, different pKa values associated with its oxygenated and deoxygenated forms illustrate how shifting oxygen affinity influences proton binding.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a fundamental tool in acid-base chemistry that relates the pH of a solution to the pKa of an acid and the ratio of its deprotonated to protonated forms. It is particularly useful for calculating the fraction of a molecule that is deprotonated or protonated at a given pH, which is critical in understanding hemoglobin's behavior in different oxygenation states.

Protonation Equilibria

This concept refers to the reversible transfer of protons (H+) between chemical species, such as between different forms of hemoglobin. The equilibrium determines the relative amounts of protonated and deprotonated forms based on the environmental pH and the intrinsic acid dissociation constant (pKa) of the acidic groups involved.

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