两全其美：Cartesian和Cayley分子组装构型空间中的均匀采样
Best of Both Worlds: Uniform sampling in Cartesian and Cayley Molecular Assembly Configuration Space
摘要：
EASAL（efficient atlasing and sampling of assembly landscape）是一种用于表征、可视化、采样和计算小分子组装势能面积分的几何方法。EASAL的效率来自于这样一个事实，即小装配景观允许使用所谓的凯莱参数（原子间距离）的几何表示和采样的装配配置空间区域;这导致他们的隔离，凸化，定制采样和系统遍历使用一个全面的拓扑路线图，确保合理覆盖的关键，但狭窄的区域低有效尺寸。然而，这本身是不够的构型熵和其他积分的准确计算，需要估计的自由能和动力学-其中，它是必不可少的，以获得均匀的采样在适当的carnival或模空间参数化。通过两个参数化之间的映射的雅可比矩阵对凯莱采样进行标准调整充满了来自病态雅可比矩阵的挑战。本文形式化和分析这些挑战，提供修改EASAL，确保凯莱采样的优势，同时确保一定的最小距离和覆盖范围之间的关系采样配置-在笛卡尔空间。将修饰的EASAL的性能与基本EASAL进行比较，并提供了人和大鼠胰岛淀粉样多肽（HiAPP、PDB-2KJ 7和RiAPP PDB-2KB 8）二聚化的数据（两者仅在37个残基中的6个残基上不同，但前者聚集成原纤维，而后者不）。
英文摘要：
EASAL (efficient atlasing and sampling of assembly landscapes) is a recently reported geometric method for representing, visualizing, sampling and computing integrals over the potential energy landscape tailored for small molecular assemblies. EASAL's efficiency arises from the fact that small assembly landscapes permit the use of so-called Cayley parameters (inter-atomic distances) for geometric representation and sampling of the assembly configuration space regions; this results in their isolation, convexification, customized sampling and systematic traversal using a comprehensive topological roadmap, ensuring reasonable coverage of crucial but narrow regions of low effective dimension. However, this alone is inadequate for accurate computation of configurational entropy and other integrals, required for estimation of both free energy and kinetics - where it is essential to obtain uniform sampling in appropriate cartesian or moduli space parameterization. Standard adjustment of Cayley sampling via the Jacobian of the map between the two parameterizations is fraught with challenges stemming from an illconditioned Jacobian. This paper formalizes and analyzes these challenges to provide modifications to EASAL that secure the advantages of Cayley sampling while ensuring certain minimum distance and coverage relationships between sampled configurations - in Cartesian space. The modified EASAL's performance is compared with the basic EASAL and the data are presented for Human and Rat Islet Amylin Polypeptide (HiAPP, PDB-2KJ7 and RiAPP PDB-2KB8) dimerization (the two differ in only 6 out of 37 residues, but the former aggregates into fibrils, while the latter does not).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
