Lecture 20 Summary

The sequential model for allostery was formulated by Daniel Koshland and coworkers, as an extension of his earlier idea of induced fit as a mode of enzyme-substrate recognition.

We discuss heterotropic effects in hemoglobin such as 2,3-bisphosphoglycerate binding and the Bohr effect, and how they constitute physiological adaptations. Included in our discussion is the molecular basis for transfer of oxygen from mother to fetus, and the contribution of the Bohr effect and carbonic anhydrase in the transport of CO₂ from the respiring peripheral tissues to the pulmonary interface.

Mathematical models for allostery

The mathematical treatment of cooperative ligand binding: The Hill equation and plots. The concerted or Monod-Wyman-Changeux (MWC) model.

Diagram of ligand binding to protein modeled by two states, T (low affinity) and R (high affinity).

Exercise: Show, using the definitions of L, L₁, K_d^T, and K_d^R, and the thermodynamic cycle of the diagram at left to show that L₁ = c L₀, where c = K_d^R/ K_d^T.

The Hill coefficient

The number n in the Hill equation is known as the Hill coefficient. The Hill coefficient provides a quantitative measure of cooperativity, and can be thought of as the hypothetical number of ligand molecules that would have to bind to the protein, in an all-or-none fashion, to give the observed slope in a Hill plot of experimental binding data. We derived the Hill equation at left with the assumption that only apo and fully occupied protein molecules contribute to the binding equilibrium. Myoglobin of course yields a Hill coefficient of 1.0, while hemoglobin binding of oxygen gives a Hill coefficient of 2.8.

Chemical basis of the Bohr effect

The Bohr effect is an example of a heterotropic effect in an allosteric protein.

The role of the Bohr effect and carbonic anhydrase in transport of CO₂ from peripheral tissues to pulmonary interface.

HbS and sickle cell disease

A variant of the β chain of Hb has a substitution of the glutamate residue at position 6. The residue in place of glutamate is valine, and this mutation is denoted as E6V in standard nomenclature for mutant proteins. The substitution creates the possibility for the valine residue to dock into a hydrophobic patch formed by residues Phe85 and Leu88 when the heterotetramer is in the deoxy form. The interaction occurs between tetramers and each tetramer can make two contacts with other tetramers, one with Val6 and another involving Phe85/Leu88. Thus, the deoxy form of this mutant hemoglobin tends to form abnormal polymeric forms that grow into insoluble fibrous structures that damage erythrocytes.

Learning objectives

• Describe the heterotropic effects of 2,3-bisphosphoglycerate binding and the Bohr effect in hemoglobin and explain their physiological roles.
• Describe how mathematical models can be used to quantify, predict, or fit data for cooperative binding or kinetics.
• Describe the features of the MWC (concerted) model.
• Exercise: Use a graphing program such as Excel to investigate the binding curves produced by the mathematical form of the concerted/MWC model, contrasting it with the hyperbolic form, and noting the effects of changing parameter (n, L, c) values.

Page updated, 11-07-09

References

1. Information Center for Sickle Cell and Thalassemic Disorders. (hosted by Harvard Medical School and Brigham and Women's Hospital)