The correct answer is (1) Myoglobin: curve A, reaction i, equations III and IV. Hemoglobin: curve B, reaction ii, equations I and II.

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Introduction

Oxygen transport proteins in vertebrates—hemoglobin and myoglobin—exhibit distinct patterns in oxygen binding, which can be mathematically described by different kinetic and equilibrium equations. Interpreting their binding curves reveals crucial insights into cooperativity, molecular structure, and physiological function. This guide explains how equations relate to sigmoidal and hyperbolic curves, the underlying biochemistry of hemoglobin and myoglobin, and how to choose the correct models for each.

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Understanding the Curves

• Curve A (Hyperbolic): Typical of myoglobin, a monomeric protein binding oxygen non-cooperatively.

• Curve B (Sigmoidal): Typical of hemoglobin, a tetrameric protein binding oxygen with positive cooperativity.

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Reactions and Equations

Myoglobin

• Monomeric binding (reaction i): $E+S\rightleftharpoons ES$

• Binding equations:

  • Equation III: YO2=[O2]K+[O2]YO2=K+[O2][O2]

  • Equation IV: YO2=pO2K+pO2YO2=K+pO2pO2

Both describe hyperbolic saturation kinetics, typical for single binding-site proteins.

Hemoglobin

• Oligomeric, cooperative binding (reaction ii): E+nS⇌ESnE+nS⇌ESn

• Binding equations:

  • Equation I: YO2=[O2]nK+[O2]nYO2=K+[O2]n[O2]n

  • Equation II: YO2=(pO2)nK+(pO2)nYO2=K+(pO2)n(pO2)n

These are Hill equations, describing the sigmoidal kinetics of cooperative (multi-site) binding in hemoglobin.

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Connecting Curves to Biochemistry

• Myoglobin:

  • Single subunit (monomer), one oxygen-binding site.

  • Binds oxygen independently.

  • Response is hyperbolic due to simple saturation kinetics.

• Hemoglobin:

  • Four subunits (tetramer), four oxygen-binding sites.

  • Each oxygen binding increases affinity for subsequent binding—a classic case of positive cooperativity.

  • Sigmoidal, “S-shaped,” oxygen saturation curve.

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Summary Table

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Conclusion

The correct mapping is:

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

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

This match is rooted in the biochemical principles of ligand binding, protein structure, and cooperativity, offering essential insights for competitive exams and advanced biochemistry.