Mathematical algorithm development for the analysis of receptor binding kinetics, immunoglobulin A genetics, codon usage, protein domain boundaries, and other biological phenomena

This thesis documents the development of several computational algorithms and methods in the fields of bioinformatics and computational biology. The first problem studied is that of codon usage in prokaryotes. A series of calculations was performed on codon usage data from 101 completely sequenced prokaryotes (both bacteria and archae bacteria) to help us graphically understand how these organisms use codons and to give us clues about what drives their codon bias. The second study aimed to develop an algorithm for identifying domain boundaries in protein sequences using only the information contained in those sequences. We developed an algorithm that identifies amino acid patterns that appear to be enriched at domain boundaries, builds a database of these patterns, and uses them to score unknown sequences. In the process of developing the algorithm, we identified some unusual features of some amino acids themselves that may shed light on some ontological questions regarding the need for all 20 amino acids (e.g. what are the functional differences between closely related amino acids like aspartic acid and glutamic acid). The third project was to search the human expressed sequence tag (EST) database for polymorphisms of immunoglobulin A (IgA) genes. In particular, we were out to identify not single nucleotide polymorphisms (or SNP's, something that has already been done in several important studies), but groups of amino acid changes that might be coordinated on the same set of EST's for some functional purpose. The three just described studies fall under the rubric of bioinformatics. On the computational biology side, we developed various tools for the fitting and validation of differential equation models to the binding kinetics of human immunoglobulin (antibodies) to mouse neonatal Fc receptor (FcRn). Understanding of the Fc-FcRn interaction has been shown to be critical to predicting the in vivo half-life of antibodies. Unable to validate the standard model of the interaction that had been established by other authors for slightly different systems (human Fc on human FcRn or mouse on mouse), we built more complex models (involving three or more binding “sites” on the single receptor), with more independent variables (time of binding, time of dissociation, ligand concentration, pH of binding, pH of dissociation, etc.), with more diagnostic tools (e.g. a variance model to compute the Schwarz criterion, tools for designing D-optimal experiments, etc.) to allow us to assess the quality of our fits. The large array of tools developed should help in the continuing study of Fc-FcRn interactions, and in the study of other complex receptor-ligand system.