Mathematical Sciences: Stochastic Models of Dynamics of DNA Repeats

小行星9409909 重复序列的产生和进化机制对于理解最近发现的涉及重复DNA扩展的疾病的动力学和理论原因都很重要。我们长期从事基因扩增和细胞群体动力学的研究。我们使用并改进了数学工具：多型分支过程，连续型空间的分支过程，分支随机游动等。我们提出了两个扩展我们的建模。一个是串联重复序列阵列扩展的动力学，它可以被看作是一个离散随机动力系统的作用。第二种是由染色体区域的动态扩增引起的遗传畸变，包括DNA的短多串联重复序列。这两个问题都是分子生物学家积极研究的主题。这项工作的目标将是测试，如果数学模型的基础上定性生物模型是足够的定量重现实验观察的细节，提供一个更好的理解的分子过程，并建议新的实验。 最近的实验证据表明，对于一小部分DNA，每个细胞的数量和结构都不是恒定的。这种快速进化的DNA大部分由不同长度的重复序列组成。这些重复序列的产生和进化机制对于理论上的原因和理解最近发现的涉及重复DNA扩展的疾病都很重要。长期以来，我们一直致力于建立这一领域的数学和统计模型。现在，随着更多的生物信息变得可用，我们提出了我们的建模的进一步扩展。我们设法争取到了有能力的生物顾问的合作。这项工作的目标将是测试基于定性生物学理论的数学模型是否足以在定量细节上重现实验观察结果，以提供对分子过程的更好理解，并提出新的实验。

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.