New Mathematical Methods for Protein Loop Modeling

描述（由申请人提供）：该项目旨在开发新的数学方法来更好地模拟蛋白质的环区。环区缺乏二级结构，根据氨基酸序列预测其三维构象是蛋白质结构和功能研究的主要挑战之一。环通常是蛋白质生物作用机制的位点。学习这些生物机制需要能够有效地对这些构象进行采样的数学和计算方法。由于其固有的灵活性，环路区域可能具有各种各样的形状，并且通过纯粹的随机搜索来发现低自由能的生物学相关构象可能是令人望而却步的。适当约束的发现和有效的结合可以显著地减少构象搜索问题，使其易于计算。Coutsias和Dill小组已经就这些问题合作发表了10年的文章，并为各种软件贡献了一些当前最先进的方法。本文提出：(1)对现有的施加闭环约束的方法进行概括，以统一的形式来处理任意的空间和其他物理或几何约束；(2)更深入地发展数学，将约束环闭合算法的数值分析与多元多项式系统的基本代数和几何性质联系起来；(3)将静态约束方法与高斯网络动力学方法相结合，有效地处理动力学问题；(4)结合对约束构象空间的拓扑和几何性质的更深入理解，通过开发新的协同移动集进一步提高效率和覆盖范围；(5)将它们应用于几个生物学上重要的环路建模问题。如果成功，该项目中开发的方法将有助于更好地理解生物作用机制和计算药物发现，其中配体与蛋白质的结合通常取决于其与环的相互作用。公共卫生相关性：可靠的计算机测定蛋白质中的环结构具有巨大的实际应用：它不仅可以预测控制生物过程的环构象-例如抗原识别，信号转导和酶活性位点门控-而且还可以重新设计蛋白质中关键位置的环以实现新功能。

DESCRIPTION (provided by applicant): This project is to develop new mathematical methods to better model the loop regions of proteins. Loop regions lack secondary structure and predicting their 3-dimensional conformation from amino acid sequences is one of the main challenges in the study of protein structure and function. Loops are often the sites of the biological mechanisms of action of a protein. Learning these biological mechanisms requires mathematical and computational methods that can sample these conformations efficiently. Due to their inherent flexibility, loop regions may assume a vast variety of shapes and discovering the biologically relevant conformations of low free energy by purely random search can be prohibitive. The discovery and efficient incorporation of appropriate constraints can dramatically reduce the conformational search problem and make it tractable to computation. The Coutsias and Dill groups have published collaboratively on these problems for ten years and contributed some of the current state-of-the-art methods to various software. Here it is proposed: (1) to generalize current state of the art methods for imposing loop closure constraints to treat arbitrary steric and other physical or geometrical constraints in a unified formalism; (2) to develop the mathematics more deeply, relating the numerical analysis of constrained loop closure algorithms to the underlying algebraic and geometric properties of multivariate polynomial systems; (3) to combine our static constraint methods with Gaussian Net dynamics methods to treat dynamics efficiently too ; (4) to further increase the efficiencies and coverings through the development of novel concerted move sets combined with a deeper understanding of the topological and geometrical properties of constrained conformation spaces, and (5) to apply them to several biologically important loop modeling problems. If successful, the methods developed in this project will be useful for better understanding biological mechanisms of action and for computational drug discovery, where ligand binding to a protein often depends on its interactions with loops. PUBLIC HEALTH RELEVANCE: Reliable computer determination of the structures of loops in proteins has enormous practical applications: It enables not only prediction of loop conformations controlling biological processes - such as antigen recognition, signal transduction, and enzyme active site gating - but also reengineering of loops at critical locations in proteins for new functions.