AMC-SS: Biochemical Network Models with Next Gen Sequencing

提出的研究旨在开发新的数学和统计结果，以有效地分析基于“深度”DNA测序新分子技术的数据的生化网络模型。该项目将侧重于从纵向物种计数组成的数据中开发基于可能性的生化网络参数和结构估计。关于参数估计，我们将(i)推导保证可识别性和估计器一致性的数据过程条件，以及（ii）考虑用某些其他似然（例如高斯似然）近似部分观察到的生化网络的似然的方法，从而简化推理问题。关于网络结构的发现，我们将发展分析与化学反应网络几何结构相关的代数变化的方法，以便找到与给定数据最一致的化学计量结构。所获得的理论结果将用于开发一个灵活的框架，用于深度测序数据的统计分析。所得到的算法将通过软件实现，并在真实的DNA测序实验中测试其性能。深层（或下一代）测序技术是现代分子生物学的一项革命性的、崭露头角的工具，允许非常精确的高通量测量细胞系统中的DNA和RNA分子计数。如果适当的数学建模和统计分析工具（及其软件实现）广泛可用，下一代技术将使生物学家有可能制定和测试关于各种分子物种的生物化学相互作用的非常具体的假设。由于他的科学背景和他工作的跨学科性质，申请人处于一个独特的位置，以开发和测试这些工具的生物学相关数据，确保这项研究的数学结果被广泛传播到实验生物学家的科学界。通过改变dna测序数据分析的方法，提出的数学研究将对现代遗传学，生态学和人口研究的许多不同领域的实验高通量方法产生广泛的影响。该项目还将在全州和全国范围内进一步促进生物学研究背景下的数学和统计领域以及对年轻研究人员的跨学科培训。

The proposed research aims at developing new mathematical and statistical results needed to efficiently analyze biochemical network models based on data arriving from the new molecular technology of "deep" DNA sequencing. The project will focus on developing likelihood-based estimates of the biochemical network parameters and structure from the data consisting of longitudinal species counts. With respect to parameter estimation, we shall (i) derive conditions on the data process which guarantee identifiability and estimators consistency as well as (ii) consider ways of approximating the likelihood of a partially observed biochemical network with certain other likelihoods (e.g., Gaussian) for which inference problem is simplified. With respect to network structure discovery, we shall develop methods of analyzing algebraic varieties associated with the geometry of chemical reaction networks in order to find stoichometry structure most consistent with given data. The theoretical results obtained will be used to develop a flexible framework for statistical analysis of deep sequencing data. The resulting algorithms will be implemented with software and their performance tested in real DNA sequencing experiments. The deep (or next-gen) sequencing technology is a revolutionary, up-and-coming tool of modern molecular biology, allowing for very precise high-throughput measuring of DNA and RNA molecular counts in cellular systems. The next-gen technology will make it possible for biologists to formulate and test very specific hypothesis about biochemical interactions of various molecular species, provided that the proper mathematical modeling and statistical analysis tools (and their software implementations) will be broadly available. Due to his scientific background and an interdisciplinary nature of his work, the proposer is in a unique position to develop and then test such tools on data of biological relevance, ensuring that the mathematical results of this research are broadly disseminated to the scientific community of experimental biologists. By transforming the methodology for data analysis in DNA-sequencing, the proposed mathematical research will have broad influence on experimental high-throughput methodology in many different areas of modern genetics, ecology, and population studies. The project will also result in further promotion, both statewide and nationally, of the fields of mathematics and statistics in the context of biological research and the interdisciplinary training of young researchers.