Moduli Spaces of Polygons with Applications to Protein-Macrocycle Docking

合成大环(MC)因其作为治疗药物的潜力而受到越来越多的关注。除了有望成为治疗药物外，MC还因其复杂的拓扑结构而具有极大的数学兴趣。然而，由于多种原因，目前还缺乏有效的方法来模拟MC及其蛋白质靶标的3D复合体。对于目前用于对接小的非环状药物分子的方法来说，MCS太大和太复杂。对于蛋白质-蛋白质对接的方法来说，它们也太灵活了。这个项目的目标是开发几何方法来有效地模拟大分子的顺应性相互作用，也称为柔性对接问题。目前的方法是基于暴力直接计算机模拟。分子的大小和要探索的空间的狭小性质使这些都不切实际。用于大环结构建模的软件BRIKARD和分子对接套件CLUSPRO中使用的高效精确分析方法将通过开发数学结构结合成一种新的对接协议，能够有效地处理灵活的配体蛋白质对接。由此产生的软件将立即用于制药业的大环药物设计领域。此外，分子灵活性和机器人学之间的联系为创建简单的模型提供了丰富的基础，这些模型将用于向高中生介绍机器人学、灵活性和分子建模的基本概念。蛋白质-大环对接的核心是在全球范围内寻找能量最小值，这是一个具有挑战性的问题，因为搜索空间的高维度、崎岖的能量环境和高昂的能量函数评估成本。大循环形状空间的非平凡结构有效地阻碍了使用当前方法对蛋白质-大循环相互作用的成功建模。这一障碍将通过用适当的流形描述与不同程度的分子柔性相对应的构象空间来克服。搜索将通过引入黎曼度量来适当权衡配体-蛋白质旋转-平移和环状配体灵活性来指导。能量项也将被纳入，以解释配体和结合口袋的空间相互作用。这将允许对低能量区域进行有效采样，从而避免联合构象空间的高能量区域。由此产生的混合方法将从粗粒度全局采样开始，以确定蛋白质-配体形状空间的有前景的区域，随后是使用更详细的评分函数的中期调整和优化，最后是定向精细重采样以获得高分辨率结构。创建的对接框架将适用于广泛的任务，包括无约束的配体对接和蛋白质环建模。智力上的优点包括：(I)理解具有固定边长和角度的欧氏空间R3中的多边形模空间，(Ii)为搜索蛋白质-配体复合体中的相对位置和顺应性形状变化而得出适当的权重，以及(Iii)改进一般对接协议的有效性。最终的软件将作为开源软件发布，并通过广泛使用的CLUSPRO服务器免费提供。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Synthetic Macrocycles (MCs) are receiving increased attention for their potential as therapeutic agents. Beside their promise as therapeutics, MCs also have great mathematical interest due to their complex topological structure. However, for several reasons effective methods for modeling 3D complexes of MCs and their protein targets are lacking. MCs are too large and complex for current methods used for docking small non-cyclic drug molecules. They are also too flexible for methods of protein-protein docking. The goal of this project is to develop geometrical methods to efficiently model the compliant interaction of macromolecules, also known as the Flexible Docking Problem. Current methods are based on brute force direct computer simulations. The large size of the molecules and the confined nature of the space to be explored renders these impractical. The efficient exact analytical methodologies used in the software BRIKARD for macrocycle structure modeling and in the molecular docking suite CLUSPRO will be combined through the development of mathematical structures into a new docking protocol, capable of efficiently handling flexible ligand protein docking. The resulting software will find immediate use in the pharmaceutical industry in the area of macrocyclic drug design. Moreover, the connection between molecular flexibility and robotics offers a rich ground for creating simple models that will be used for outreach activities introducing high school students to basic ideas of robotics, flexibility and molecular modeling.At the heart of protein-macrocycle docking lies a global search for an energy minimum, a challenging problem due to high dimensionality of the search space, rugged energy landscape, and high cost of energy function evaluation. The non-trivial structure of macrocycle shapespace effectively precludes successful modeling of protein-macrocycle interactions using current methods. This obstacle will be overcome by describing conformational spaces corresponding to different degrees of molecular flexibility by appropriate manifolds. The search will be guided by introducing a Riemannian metric to properly weigh ligand-protein rotation-translations and cyclic ligand flexibility. Energetic terms will also be incorporated to account for steric interactions of the ligand and binding pocket. This will allow efficient sampling of low energy regions, avoiding high energy areas of the joint conformational space. The resulting hybrid method will begin with coarse grained global sampling to identify promising areas of protein-ligand shapespace, followed by medium-range adjustments and optimization using more detailed scoring functions, and, finally, targeted fine resampling to obtain high resolution structures. The docking framework created will be applicable to a broad spectrum of tasks including unconstrained ligand docking and protein loop modeling. Intellectual merits include: (i) understanding moduli spaces of polygons in Euclidean space R3 with fixed side lengths and angles, (ii) deriving proper weights for searches in the relative placement and compliant shape changes in a protein-ligand complex, and (iii) improvement of effectiveness of general docking protocols. The resulting software will be released as open source and made freely available through the widely used CLUSPRO server.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.