On the molecular mechanism of facilitated oxygen diffusion by haemoglobin and myoglobin

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Abstract
The equation suggested by Wyman (1966) to explain the facilitated diffusion of oxygen in a haemoglobin solution is studied. The results for myoglobin are also given. A singular perturbation approach is used which, in this particular situation, reduces the problem from that of solving a nonlinear second-order differential equation to that of solving an algebraic quadratic one. The method also suggests functional forms for the dependence of the fractional saturation of the protein on the oxygen concentrations at the surfaces of the layer of solution through which the oxygen diffuses. The variation in the concentration of free oxygen and the fractional saturation within the layer of solution are given for haemoglobin and myoglobin. The results are consistent with those found experimentally by Wittenberg (1966). A physical implication of the mathematical solution is that the haemoglobin or myoglobin is essentially everywhere in equilibrium with the oxygen in solution. Although this has been conjectured in the past, for example by Wyman (1966), it is motivated here by the mathematics.