Abstract
Wyman's equation for facilitated diffusion of a ligand through a solution slab containing a carrier is recast and solved by means of a regular perturbation expansion in the parameter representing the driving force for facilitation. This new solution is complementary to the previously exploited singular perturbation solution due to Murray and represents facilitation in the low facilitation parameter regime. The most significant physical realization of this regime occurs when there is a large affinity between ligand and carrier, as in the carbon monoxide-hemoglobin system.
The validity domains of the regular perturbation solution and the singular perturbation solution of Mitchell and Murray and Rubinow and Dembo are delineated. The equation for facilitated diffusion is solved numerically for parameter values appropriate to the oxygen-myoglobin experiments of Wittenberg, and to the carbon monoxide-hemoglobin experiments of Mochizuki and Forster, and Wittenberg. This solution provides a norm for comparison of the utility of the perturbation solutions.
We show how the theory explains the apparent contradiction between the positive observations of Mochizuki and Forster and the negative observations of Wittenberg on facilitation of carbon monoxide transport through a slab of hemoglobin solution.
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Supported in part by the National Science Foundation under Grant No. PCM77-03344
In partial fulfillment of the Ph.D. degree at Cornell University
Professor S. I. Rubinow has passed away on February 22, 1981
Computations were performed at the Courant Mathematics and Computing Laboratory, supported by DOE under contract #EY-76-C-02-3077.
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Nedelman, J., Rubinow, S.I. Facilitated diffusion of oxygen and carbon monoxide in the large affinity regime. J. Math. Biol. 12, 73–90 (1982). https://doi.org/10.1007/BF00275204
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DOI: https://doi.org/10.1007/BF00275204