The plot below has two curves (A, B) that show the fractional occupancy of hemoglobin and myoglobin by oxygen as a function of the amount of oxygen.

The two reactions are

i. $$\mathrm{E} + \mathrm{S} \rightleftharpoons \mathrm{ES}$$ and​

ii. $$\mathrm{E} + n\mathrm{S} \rightleftharpoons \mathrm{ES}_n$$​​

where S is $$O_2$$ and E is myoglobin or hemoglobin

The equations that could be used to fit the two curves are:

I. $$Y_{\alpha} = \frac{[\mathrm{O}_2]^n}{K + [\mathrm{O}_2]^n}$$​​

II. $$Y_{\alpha} = \frac{(p\mathrm{O}_2)^n}{K + (p\mathrm{O}_2)^n}\qquad \text{where } K = \frac{[\mathrm{E}][\mathrm{S}]^n}{[\mathrm{ES}_n]}$$​​

III. $$Y_{\alpha} = \frac{[\mathrm{O}_2]}{K + [\mathrm{O}_2]}$$​​

IV. $$Y_{\alpha} = \frac{(p\mathrm{O}_2)}{K + (p\mathrm{O}_2)}\qquad \text{where } K = \frac{[\mathrm{E}][\mathrm{S}]}{[\mathrm{ES}]}$$

$$Y_{O2}$$ is the fraction of oxygen-binding sites occupied by oxygen. $$pO_2$$ is partial pressure of oxygen.

From the options given below, select the option with the right curve (A,B), reaction (i, ii) and equation/s (I, II, III, IV) that describe oxygen binding to hemoglobin and myoglobin.

Correct option is A

(a) Myoglobin: curve A, reaction i, equations III and IV. Hemoglobin: curve B, reaction ii, equations I and II.

Sol. Let's break down the given information:

• Curve A is characteristic of myoglobin. The graph shows a hyperbolic curve that is typical for myoglobin because it binds oxygen in a non-cooperative manner. As the oxygen concentration increases, myoglobin binds oxygen in a steady, almost linear fashion, indicating a hyperbolic binding curve.

• Curve B represents hemoglobin, which shows a sigmoidal (S-shaped) curve, indicating cooperative binding. As the first molecule of oxygen binds to hemoglobin, the molecule undergoes a conformational change that makes it easier for subsequent oxygen molecules to bind. This cooperativity is reflected in the sigmoidal curve.

  ​Myoglobin binds oxygen using the reaction i (E + S ↔ ES) and its equation is described by equation III, where the fraction of binding sites occupied by oxygen (Y_o) is given by the relationship $$Y_o = \frac{[O_2]^n}{K + [O_2]^n}$$ where K is the dissociation constant and n is the Hill coefficient, which reflects the degree of cooperativity. Since myoglobin binds oxygen non-cooperatively, n = 1.

  Hemoglobin binds oxygen cooperatively, described by reaction ii (E + nS ↔ ES_n), and the equation used to describe this cooperativity is equation I: $$Y_o = \frac{(pO_2)^n}{K + (pO_2)^n}$$ where n is greater than 1 due to the cooperative binding of oxygen.

  Thus, the correct combination is:

  • Myoglobin: curve A, reaction i, equations III and IV.

  • Hemoglobin: curve B, reaction ii, equations I and II.

  Information Booster:  

  • Curve A (Myoglobin): Myoglobin is a monomeric protein that binds oxygen non-cooperatively, which results in a hyperbolic curve. This indicates that as oxygen binds, the affinity remains constant throughout the binding process. The Hill coefficient (n = 1) reflects this non-cooperative binding.

  • Curve B (Hemoglobin): Hemoglobin is a tetrameric protein that exhibits cooperative binding, which leads to a sigmoidal curve. The binding of the first oxygen molecule increases the affinity for the next molecules of oxygen, resulting in a steep rise in oxygen binding as the partial pressure of oxygen increases. The Hill coefficient (n > 1) reflects this positive cooperativity.

  • Reaction i and ii:

    • Reaction i: Describes the binding of a single molecule of oxygen to myoglobin, with a simple reversible reaction where oxygen binds to the myoglobin protein in a non-cooperative manner.

    • Reaction ii: Describes the cooperative binding of oxygen to hemoglobin, where binding of oxygen increases the affinity of hemoglobin for additional oxygen molecules.

    • Additional Information:  

  • Equations III and IV:

    • Equation III: This is used to describe myoglobin's binding of oxygen, which follows a simple hyperbolic model.

    • Equation IV: This could also describe the binding of oxygen in a non-cooperative manner, fitting with myoglobin’s behavior.

  • Equations I and II:

    • Equation I: Describes the cooperative binding of oxygen to hemoglobin, represented by a sigmoidal curve.

    • Equation II: Another way of describing the cooperative oxygen binding in hemoglobin, which takes into account the cooperative nature of oxygen binding to hemoglobin.

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