Statistical and Computational Problems in Genetics and Molecular Biology

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This proposal addresses a variety of statistical and computational problems that arise in genetics and molecular biology. An important aim of the research project is the training and development of post-doctoral research fellows in this interdisciplinary area. The problems described here are part of our ongoing collaborations with geneticists and molecular biologists from USC and elsewhere. All of them have significant computational and statistical components. We are studying statistical and algorithmic aspects of physical mapping. Among these are optical mapping, by which ordered restriction maps are produced using fluorescence microscopy. The long term aim is the development of an online program that produces such an ordered map. We are analyzing the efficiency of various physical mapping strategies based on variants of sequence-tagged-sites schemes. In particular, we are studying inhomogeneous clone and anchor distributions, the effects of false, ambiguous or missing anchors, and strategies that allow for mixtures of clone walking and random steps. We are developing statistical models for the evolution of genome rearrangements and methods for reconstructing phylogenetic trees from such data. This is motivated in part by data on rearrangements occurring in the promoter of GFAP in the brain. A related project addresses other aspects of phylogenetic tree reconstruction, in particular the effects of dependence among sites when DNA sequence data is used to build the tree. Motivated by data on rRNA promoters, we are also developing algorithms for fitting more detailed evolutionary models when the underlying tree is known. We are investigating the statistics of pattern counts in molecular sequences. These a re frequently used to characterize biological features such as coding regions, regulatory sequences, splice sites and so on. Our focus is on the development of useful computational algorithms for pattern counts when the underlying sequence structure must be estimated from the data. A further project addresses the estimation of deletion rates in mitochondrial genomes in humans. A PCR assay is used to detect whether or not a cell line contains any mitochondria with the deletion. The data comprise the results of the assay on several cell lines. We are developing analogs of the Luria-Delbruck method of fluctuation analysis for estimating the rate of deletions. The results are used to study the role of the deletion in Kearns-Sayre Syndrome patients. We are developing Monte Carlo likelihood methods for inference in genetics, aimed primarily at the study of mitochondrial and nuclear gene variation in humans, and its use in the study of human evolution. One focus is on the estimation of recombination rates, in particular between human disease loci and a variety of marker loci.