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UBC Theses and Dissertations

Mathematical models of immunity Mathewson, Donald Jeffrey


A cross-linking model for the activation of the A cell or immune accessory cell as a function of certain extracellular conditions is developed to determine the valency of the specific factor receptor on the A cell surface. It is found that such a determination can be made based on the FWHM of cross-linking curves which differ by a full order of magnitude between the bivalent receptor case and the monovalent receptor case. This determination can be made provided one can obtain accurate values for the equilibrium constants which characterize the system and provided that activation and IL-1 secretion is a linear function of cross-linking. It is also found that a determination of valence can be made if the equilibrium constants are such that substantial one receptor bridge formation takes place (one antibody molecule bound on both ends by the same receptor). This one-receptor bridge formation only takes place if the receptor is bivalent, and it presents itself in the cross-linking curve in a very distinctive manner. A second network model described as an ecological competition model of steady state lymphocyte populations is presented. This model, known as the symmetrical network theory is analysed numerically by integration of the differential equations and shown to provide a reasonable qualitative picture of the immune system's stable steady states, and offer a glimpse of state switching.

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