What is Allostery and cooperativity? — Biology

Definition 7.9 University Biology — Year 3 · Chapter 7 — Structural Biology of Proteins

A protein is allosteric when the binding of a ligand at one site changes the affinity of another site, through a change of conformation transmitted across the molecule. When the two sites bind the same ligand and the effect is positive, binding is cooperative: the fractional saturation $Y$ rises with ligand concentration as a sigmoid rather than a hyperbola, described empirically by the Hill equation $Y = [S]^{n_{H}}/(K^{n_{H}} + [S]^{n_{H}})$ with a Hill coefficient $n_{H} > 1$ (haemoglobin: $n_{H} \approx 2.8$ for its four sites; myoglobin, one site: $n_{H} = 1$ ). Haemoglobin exists in two quaternary conformations, the T state (tense, low affinity, favoured when no oxygen is bound) and the R state (relaxed, high affinity), and switches between them as a whole; protons, carbon dioxide and 2,3-bisphosphoglycerate stabilise T and so lower the affinity — the Bohr effect, by which working tissue, acid and warm, takes more oxygen from the blood.

Oxygen saturation of haemoglobin computed from the Monod–Wyman–Changeux equation with the parameters of the example (red), against a single-site carrier of the same half-saturation pressure (blue). Between lung and working muscle the cooperative carrier unloads nearly twice as much.

Examples

Example 7.11 (Haemoglobin in numbers)

Take $n = 4$ , $K_{R} = 1\,\mathrm{mmHg}$ , $c = 0.01$ (so $K_{T} = 100\,\mathrm{mmHg}$ ) and $L = 3\times 10^{5}$ . At the partial pressure of oxygen in arterial blood, $100\,\mathrm{mmHg}$ , $\alpha = 100$ and $Y = 0.97$ ; at $40\,\mathrm{mmHg}$ , the venous value at rest, $Y = 0.78$ ; at $26\,\mathrm{mmHg}$ , $Y = 0.52$ — the model reproduces the half-saturation pressure of $26\,\mathrm{mmHg}$ ; at $20\,\mathrm{mmHg}$ , in an exercising muscle, $Y = 0.35$ . A non-cooperative carrier of the same half-saturation pressure would give $100/126 = 0.79$ in the lungs and $20/46 = 0.43$ in the muscle, unloading $0.36$ of its capacity where haemoglobin unloads $0.62$ . Cooperativity is what makes a carrier that loads fully at one pressure and unloads mostly at a pressure only five times lower.

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