Branching process models in cellular population dynamics

描述（由申请人提供）：本提案的总体目标是应用和开发一类称为一般分支过程的随机模型，用于涉及细胞群体动力学的各种生物/生物医学应用。这些模型将用于解释数据，估计参数，评估特定假设并进行预测。具体项目有：（1）与癌症治疗相关的细胞群体的增殖性;（2）与衰老过程以及癌症治疗相关的端粒动力学;（3）与食品微生物学相关的细菌停滞期估计;以及与退行性遗传病相关的三个项目：（4）线粒体DNA中有害突变的积累，（5）具有相互冲突的选择水平的细胞群体，其中一种类型的DNA可能在细胞内受到青睐，但在细胞间不受选择，以及（6）有害突变积累的“棘轮”过程。 在生物学中，特别是在细胞群体动力学中，非常需要数学建模和定量数据分析。虽然不同的数学方法已经采取了许多这些问题，分支过程似乎能够提供很大的改进，因为它们是固有的随机性，考虑到细胞周期时间，突变等的自然随机性，并且它们在概念上是明确的，从个体水平上的行为建模开始，例如通过建模细胞周期和估计相关参数。拟议的研究旨在开发生物学上合理的模型和估计技术，并提高计算和估计的准确性。1 公共卫生相关性：这里提出用数学方法解决的生物医学问题都与公共卫生相关。细胞群体去分化的问题与癌症治疗有关，端粒缩短的问题与衰老过程有关，也与癌症治疗有关，细菌滞后期估计的问题与食品安全有关，突变积累的问题与遗传疾病有关。提出的数学方法（一般分支过程），以改善建模和估计在这些问题中涉及的细胞群体过程。1

DESCRIPTION (provided by applicant): The overarching goal of this proposal is to apply and develop a class of stochastic models known as general branching processes for various biological/biomedical applications that involve cellular population dynamics. These models will be used to explain data, estimate parameters, assess specific hypotheses, and make predictions. Specific projects are: (1) asynchronicity in cell populations, relevant to cancer therapy; (2) telomere dynamics, relevant to processes of aging and also to cancer therapy; (3) bacterial lag phase estimation, relevant to food microbiology; and three projects relevant to degenerative genetic disease: (4) accumulation of deleterious mutations in mitochondrial DNA, (5) cell populations with conflicting levels of selection where one type of DNA may be favored inside the cell but not for selection among cells, and (6) the "ratchet" process of accumulation of harmful mutations. There is a great need for mathematical modeling and quantitative data analysis in biology in general, and in cellular population dynamics in particular. Although different mathematical approaches have been taken to many of these problems, branching processes seem to be able to offer great improvement in that they are inherently stochastic, taking into account the natural randomness in cell cycle times, mutations, etc. and that they are conceptually clear, starting from modeling behavior on the individual level, for example by modeling the cell cycle and estimating relevant parameters. The proposed research is intended to develop models and estimation techniques that are biologically sound and improve accuracy in computation and estimation. 1 PUBLIC HEALTH RELEVANCE: The biomedical problems that are here proposed to be addressed with mathematical methods are all relevant to public health. The problem of desynchronization of cell populations is relevant to cancer therapy, the problem of shortening of telomeres is relevant to processes of aging and also to cancer therapy, the problem of bacterial lag phase estimation is relevant to food safety, and the problems of accumulation of mutations is relevant to genetic disease. The proposed mathematical methods (general branching processes) are conjectured to improve modeling and estimation in the cellular population processes involved in these problems. 1