Adult haemoglobin has and Hill coefficient

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Cooperativity: zippers, melting and allosteric binding

Problem

Adult haemoglobin has

p_{50}^{\text{adult}} = 26\,\mathrm{mmHg}

and Hill coefficient

n_H = 2.8

. Two points read off a foetal-blood binding curve are

Y=0.142

p=10\,\mathrm{mmHg}

and

Y=0.889

p=40\,\mathrm{mmHg}

. ((a)) Fit the Hill function to the two foetal points: plot

\ln[Y/(1-Y)]

against

\ln p

, and find the foetal Hill coefficient and

p_{50}^{\text{foetal}}

. ((b)) Compute the fractional saturation

Y

of adult and of foetal haemoglobin at the placental oxygen partial pressure

p=20\,\mathrm{mmHg}

, using the Hill function

Y=p^{n_H}/(p_{50}^{n_H}+p^{n_H})

with the adult values and your fitted foetal values. ((c)) Repeat the calculation for both carriers treated as non-cooperative, independent sites of the same respective

p_{50}

values (i.e.

n_H=1

), at the same pressure

p=20\,\mathrm{mmHg}

. ((d)) Compare the saturation difference (foetal minus adult) in the cooperative case with that in the independent-site case, and explain briefly how the difference in

p_{50}

allows foetal blood to pick up oxygen released by maternal (adult) haemoglobin at the placenta.

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