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Diffusion theory can be applied to antibodies attaching to ligand sites

Published online by Cambridge University Press:  17 February 2009

D. P. Wilson and
D. L. S. McElwain
D. P. Wilson
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane Qld 4001, Australia; e-mail: s.mcelwain@qut.edu.au.
D. L. S. McElwain
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane Qld 4001, Australia; e-mail: s.mcelwain@qut.edu.au.
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Abstract

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Humoral immunity is that aspect of specific immunity that is mediated by B lymphocytes and involves the neutralising of disease-producing microorganisms, called pathogens, by means of antibodies attaching to the pathogen's binding sites. This inhibits the pathogen's entry into target cells. We present a master equation in both discrete and in continuous form for a ligand bound at n sites becoming a ligand bound at m sites in a given interaction time. To track the time-evolution of the antibody-ligand interaction, it is shown that the process is most easily treated classically and that in this case the master equation can be reduced to an equivalent one-dimensional diffusion equation. Thus well-known diffusion theory can be applied to antibody-ligand interactions. We consider three distinct cases depending on whether the probability of antibody binding compared to the probability of dissociation is relatively large, small or comparable, and numerical solutions are given.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005, pp. 495 - 505
Copyright
Copyright © Australian Mathematical Society 2005

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