AMC-SS: Biochemical Network Models with Next Gen Sequencing

这项拟议的研究旨在开发有效分析生化网络模型所需的新的数学和统计结果，该模型基于来自新的分子技术--“深度”DNA测序--的数据。该项目将侧重于根据纵向物种计数的数据对生化网络参数和结构进行基于似然的估计。在参数估计方面，我们将(I)导出保证可辨识性和估计器一致性的数据处理条件，以及(Ii)考虑用某些其他似然(例如，高斯)来逼近部分观测生化网络的似然的方法，从而简化推理问题。在网络结构发现方面，我们将发展分析与化学反应网络几何有关的代数变体的方法，以便找到与给定数据最一致的化学结构。获得的理论结果将被用来开发一个灵活的框架，用于对深度测序数据进行统计分析。生成的算法将用软件实现，并在真实的DNA测序实验中测试它们的性能。深度(或下一代)测序技术是现代分子生物学的一种革命性的、新兴的工具，可以非常精确地高通量测量细胞系统中的DNA和RNA分子计数。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化相互作用的非常具体的假设，前提是适当的数学建模和统计分析工具(及其软件实现)将广泛可用。由于他的科学背景和工作的跨学科性质，建议人处于独特的地位，可以开发这种工具，然后在具有生物学相关性的数据上进行测试，确保这项研究的数学结果被广泛传播给实验生物学家的科学界。通过改变DNA测序中的数据分析方法，拟议的数学研究将对现代遗传学、生态学和种群研究的许多不同领域的实验性高通量方法学产生广泛影响。该项目还将在生物研究和青年研究人员的跨学科培训方面，在全州和全国范围内进一步促进数学和统计领域的发展。

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.