Mathematical Sciences: Genome Dynamics: Stochastic Modeling of Variable Gene Copy Numbers

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The principal investigator will extend the modeling of gene amplification to situations in which there is new experimental evidence. Some of the aspects of gene amplification to be considered are integration of extrachromosomal fragments, unequal chromatid exchange, and variable length of repeats in telomeres at the ends of chromosomes. The mathematical models to be used will include branching processes and random walks. The models will be used to estimate the probabilities and transition rates of the events. The principal investigator will develop new mathematical models in genetics. The goals of this work will be to test if mathematical models based on previously proposed informal biological models are sufficient to reproduce experimental observations in quantitative detail, to provide a better understanding of the molecular processes, and to suggest new experiments which would be informative.