Group-Theoretic Methods in Protein Structure Determina-n

描述(由申请人提供)：这是一项将群论和(非对易)调和分析的技术应用于结构生物学的计算方面的建议。将开发和实施新的算法，以解决以下问题：在不事先知道Saupe排列张量的情况下，从未分配的剩余偶极耦合中从头确定蛋白质结构；快速最小化多结构域蛋白质的分子替换的“旋转函数”；从低温电子显微镜的投影中从头确定电子密度。我们的统一方法将这些问题转化为有限群和李群上的极小化问题和快速泛函计算，对于这些问题，我们需要将梯度下降和FFT等方法推广到群值环境中。我们的团队结合了数学、工程和生物学方面的专业知识，这是在这一高度交叉的学科中取得进展所必需的。 蛋白质结构的确定是理解蛋白质功能和分子设计的核心问题。这对于健康和环境科学在与“特制药物”相关的努力方面的进步是绝对关键的--即开发针对人类、动物或植物的靶向疗法。我们的努力有可能通过为实验者提供用于比较分子结构的新的和有效的技术来改造高通量技术。我们方法的新奇之处在于它专注于在生命科学的背景下使用群论和群表示理论(调和分析)的工具。这一建议的一个特别吸引人的方面是理论与实践之间的密切联系。我们的跨学科团队将数学、计算、生物和工程技能结合在一起，因此它能够做好准备，在一个本质上是多学科的问题上取得进展，并利用这些领域中的每一个。

DESCRIPTION (provided by applicant): This is a proposal to bring techniques from group theory and (noncommutative) harmonic analysis to bear on computational aspects of structural biology. Novel algorithms will be developed and implemented in order to address the following problems: de novo determination of protein structure from unassigned residual dipolar couplings without a prior knowledge of the Saupe alignment tensor; rapid minimization of the "rotation function" for molecular replacement of multi-domain proteins; de novo determination of electron densities from projections in cryo-electron-microscopy. Our unified approach casts these as minimization problems and fast functional evaluations on finite and Lie groups, for which we will need to generalize methods such as gradient descent and FFTs to the group-valued setting. Our team combines expertise in mathematics, engineering, and biology necessary to make progress in this highly interdisciplinary subject. The problem of protein structure determination is central to the understanding of protein function and molecular design. This is absolutely critical to the progress of the health and environmental sciences in regards to efforts related to "designer drugs" - i.e., the development of targeted therapies, be they for humans, animals, or plants. Our efforts have the potential to remake high-throughput techniques by providing experimentalists with new and efficient techniques for the comparison of molecular structures. The novelty of our approach is in its focus on the use of the tools of group theory and group representation theory (harmonic analysis) in this life sciences setting. A particularly attractive aspect of this proposal is the close connection between theory and practice. Our interdisciplinary team combines mathematical, computational, biological, and engineering skills - so that it is well-poised to make progress on a problem that is inherently multidisciplinary and one that draws on each of these areas