Group-Theoretic Methods in Protein Structure Determina-n

描述（由申请人提供）： 这是一个建议，使技术从群论和（非交换）谐波分析承担计算方面的结构生物学。将开发和实施新的算法，以解决以下问题：从头确定蛋白质结构的未分配的残余偶极耦合没有事先知道的Saupe对齐张量;快速最小化的“旋转函数”的分子置换的多域蛋白质;从头确定的电子密度从投影在冷冻电子显微镜。我们的统一方法将这些问题转化为有限群和李群上的最小化问题和快速函数求值，为此我们需要将梯度下降和FFT等方法推广到群值设置。我们的团队结合了数学，工程和生物学方面的专业知识，以便在这个高度跨学科的学科中取得进展。 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。这对健康和环境科学在与"设计药物"有关的努力方面的进步绝对至关重要--即，靶向治疗的发展，无论是对人类，动物还是植物。我们的努力有可能通过为实验人员提供新的有效的分子结构比较技术来改造高通量技术。 我们的方法的新颖之处在于它的重点是在这个生命科学设置的群论和群表示理论（谐波分析）的工具的使用。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。 我们的跨学科团队结合了数学，计算，生物和工程技能-因此，它准备好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