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. / Graduation date: 1994
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/36763 |
| Date | 04 April 1994 |
| Creators | Maier, Stefan H. |
| Contributors | Magana, Mario E. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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