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UBC Theses and Dissertations

Studies of the immune network based on shape-space and distance coefficient Royer, Sophie


A selective history of immunology is first presented that tells about the development of the theories of “acquired immunity”, from the early observations of the phenomenon of immunity in the Roman times until the long debate ending in the late 1960’s between the proponents of the theories of “cellular immunity” and those of the theories of “humoral immunity”. Some theories of antibody formation are also reviewed up to the “clonal selection theory”. Then the “immune network hypothesis” and some of the models that it engendered are explained, with a focus on a particular model due to Hoffmann and his co-workers: the N-dimensional network model. A short history of the attempts to model the “affinity” distribution and various choices of “connectivity” matrices is presented, focussed on a particular one: a connectivity matrix based on a one-dimensional “shape space”. The ± shape-space ¹, a shape-space formulated by Segel and Perelson, is reviewed and a “new shape-space without shape zero”, the Δ shape-space, is introduced in which “complementarity” relationships between clones differ from the ones in the + shapespace. Some analysis and numerical simulations of the two different versions of shapespace embedded in Hoffmann’s N-dimensional network are shown, which are the first simulations of the model to have ever been be done with non-Boolean affinities. The concept of a “distance coefficient” is reviewed, analyzed and developed further for its use with non-Boolean affinities. The first numerical simulations of the distance coefficients to have ever been done are presented and analyzed, embedded in Hoffmann’s N-dimensional network model with Boolean and non-Boolean affinities. ¹The author’s renaming of the original shape-space of Segel and Perelson.

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