Mathematical Sciences: "Markov Dependence in Statistics andInformation Theory and Statistical Problems in Physical Mapping"

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One of the main goals of the Human Genome Project is to produce physical maps of the human chromosomes. Such maps are important steps on the path to the complete sequencing of chromosomes, and have other important applications, such as assisting in the localizing of disease genes. A common method for constructing physical maps is based on fingerprinting random clones. The proposed research uses information theory notions to quantify information needed for the completion of a physical map, and information obtained from random clone data. Maximizing the mutual information between a configuration variable and data is also proposed as a design criterion to select the hybridization probability parameter. Numerical and analytic approximations to the criterion will be considered in the simple pairwise comparison case, on which most current physical mapping strategies are based. Optimal values of the parameter can then be obtained using these approximations. Finally, it will be addressed how to utilize mapping information to localize positions of genes of interest on the chromosomes. The proposed research is on applying information theory to physical mapping problems arising from the Human Genome Project. An information-theoretic approach is proposed to address certain problems arising from physical mapping in the Human Genome Project. The goals of a physical map will be clarified and we will answer questions regarding the amount of information we need for and the amount we learn about the map. A 3-clone approach is expected to extract more information out of mapping data than from 2-clone data, and the possibility of using mapping data to locate genes of biological interest will be better understood.