Bayesian Analysis of Shapes and Curves with Applications in Structural Bioinformatics

这项研究涉及新的概率和贝叶斯统计模型的发展，用于分析生物大分子的三维结构。第二个重点是统计方法的发展，用于表征分子在外力作用下的生物力学行为，例如在细胞蛋白质（例如分子马达）的研究中以及生物工程（例如纳米级传感）和材料科学（例如智能材料和生物启发材料）的问题中出现。重点是蛋白质结构和蛋白质力响应曲线的比较建模和分类。随机模型的三维形状的探索动机的困难，定量比较复杂的蛋白质结构信息。贝叶斯技术开发的未解决的问题，匹配未标记的点集，使用扩展的技术，从统计形状分析领域。计算算法，使这些技术实用的高通量搜索的生物分子科学家也是本研究的一个主要重点，并开发了几个方向，涉及精确算法，蒙特卡罗采样技术，快速近似的基础上几何算法。这项研究的第二个组成部分涉及贝叶斯模型的误差变量回归和功能数据分析技术的力延伸曲线测量单分子。功能数据分析的贝叶斯分层随机效应模型的发展，沿着贝叶斯计算的有效算法的发展，进行。这种统计方法的研究是广泛的适用性，但所有的工作显然是由生物医学科学和生物分子工程的重要跨学科应用的动机和直接相关。该研究构成了随机建模在计算生物学，生物信息学和计算化学中的应用的重要进展，并将为参与这些领域的科学研究人员和工程师提供统一的理论框架和实用的数据分析技术和软件工具。这些进步对于在这一领域工作的统计学家以及需要新的数据分析和预测建模方法和工具的领域科学家来说非常重要。

This research involves development of new probabilistic and Bayesian statistical models for the analysis of three-dimensional structures of biological macromolecules. A secondary focus is the development of statistical methods for characterizing the biomechanical behavior of molecules under applied forces such as arise in the study of cellular proteins (e.g. molecular motors) and in problems of bioengineering (e.g. nano-scale sensing") and materials science (e.g. smart materials and biologically inspired materials). The emphasis is on comparative modeling and classification of protein structures and protein force-response curves. Stochastic models of three-dimensional shapes are explored motivated by the difficulties in quantitative comparison of complex structural information of proteins. Bayesian techniques are developed for unsolved problems of matching unlabeled point sets using extensions of techniques from the area of statistical shape analysis. Computational algorithms for making these techniques practical for high-throughput searching by biomolecular scientists are also a major focus of this research, and several directions are developed involving exact algorithms, Monte Carlo sampling techniques, and rapid approximations based on geometric algorithms. A second component of this research involves Bayesian models for errors-in-variables regression and functional data analysis techniques for force-extension curves measured on single molecules. The development of Bayesian hierarchical random-effects models for functional data analysis, along with development of efficient algorithms for Bayesian computations, is carried out. This statistical methodology research is of broad applicability, but all work is clearly motivated by and directly relevant to significant interdisciplinary applications in biomedical science and biomolecular engineering. The research constitutes important advances in stochastic modeling for applications in computational biology, bioinformatics, and computational chemistry, and will provide both unified theoretical frameworks and practical data analysis techniques and software tools for scientific researchers and engineers involved in these areas. Such advances will be important to statisticians working in this area, as well as domain scientists in need of new methodology and tools for data analysis and predictive modeling.