Mathematical Sciences: Stochastic Models of Dynamics of DNA Repeats

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9409909 Kimmel The mechanisms of creation and evolution of repeats are important for both theoretical reasons and for understanding the dynamics of recently discovered disorders involving expansion of repeated DNA. We have been engaged for a long time in studies of dynamics of gene amplification and cell populations. We used and refined mathematical tools: multitype branching processes, branching processes with continuous type space, branching random walks and other. We propose two extensions of our modeling. One is dynamics of expansion of arrays of tandem repeats, which can be viewed as the action of a discrete stochastic dynamical system. The second concerns genetic aberrations caused by dynamic expansions of chromosome regions including short multiple tandem repeats of DNA. Both problems are the subject of active research by molecular biologists. The goals of this work will be to test if mathematical models based on qualitative 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. Recent experimental evidence shows that for a fraction of DNA, its amount per cell and its structure are not constant. Much of this rapidly evolving DNA consists of repeated sequences of various length. The mechanisms of creation and evolution of these repeats are important for both theoretical reasons and for understanding the recently discovered disorders involving expansion of repeated DNA. We have been engaged for a long time in building mathematical and statistical models in this field. Now, as more biological information is becoming available, we propose further extensions of our modeling. We managed to enlist collaboration of competent biological consultants. The goals of this work will be to test if mathematical models based on qualitative biological theories are sufficient to reproduce experimental observations in quantitative detail, to provide a better understandin g of the molecular processes, and to suggest new experiments.