Modified limiting dilution analysis : a mathematical model with biological interpretation Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/g445ch766

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  • A mathematical model of Limiting Dilution Analysis for two limiting parameters is presented and investigated. Limiting Dilution Analysis is a microbiological cell assay developed for immunological application. In the given case we deal with the interaction between B lymphocytes, macrophage derived factor and T-independent antigens. The state of the art is that quantitative statements are only possible if one cell type (in general the B cells) is limiting and all others are in excess present. The basis for this thesis is a set of experiments in which B cells and macrophage derived factor are limiting and all other involved cells and factors are in saturating amounts present. It is shown that so far presented suggestions on modeling Limiting Dilution Analysis for two limiting cell-types are not suitable for this problem. Further, a mathematical model based on data is presented and interpreted in immunological terms with the help of a set of partial differential equations. The basis for the interpretation of the model are changes in affinity and saturation effects, both not incorporated in the so far presented models of the assay. In particular the relevance of mathematical interpretation of this process for the identification of new concepts as the saturation effects is stressed. The model of partial differential equations is highly non-linear but offers the possibility of interpreting the highly interrelated processes apart from each other.
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