在热涨落驱动下，生物膜和蛋白等生物大分子跨越势垒而形成的微观构象变化涉及大量微观生物进程。由于势垒的阻碍，这类变化需要微观意义下极长的等待时间，是典型的稀有事件，为直接模拟带来困难。结合分子模拟的自由能计算是研究这类问题的主要方法。然而，寻找将这类复杂的高维动力学进行有效降维的反应坐标具有的本质困难，从而严重地约束了自由能计算的应用。本项目中，申请人将在已有工作的基础上，发展并完善一套新的自由能计算框架，其基本步骤包括（1）寻找自由能鞍点；（2）获取转移路径；（3）沿转移路径进行伞抽样和自由能分析。该方法本质上是一维采样。项目发展的自由能鞍点算法可用于快速发现反应坐标的缺陷和寻找新反应坐标。因此，新方法将大大节省自由能计算的计算复杂度，加快研究进程。这一计算框架将用于小分子跨膜渗透和膜-肽相互作用这一复杂而重要的问题中，通过自由能计算为药物设计进行初筛，为理解相关生物进程提供支持。

Microscopic conformational changes of bio-membranes and biomolecules such as proteins plays the key role in a large number of microscopic biological processes. During such conformational changes, the system usually need to cross free energy barrier under thermal fluctuations. As a result, such changes require extremely long waiting times in the microscopic sense, which are typical rare events that present difficulties for direct simulation. Free energy calculations combined with molecular modeling are the main methods for studying such problems. However, it is inherently difficult to find the reaction coordinates that effectively describes such complex high-dimensional dynamics. This lead to severely constraint in the application of free energy calculation. In this project, the applicant will develop and improve a new framework for free energy calculations based on the existing work. The new framework involves the following steps: (1) Find the saddle point of the free energy function; (2) Obtain the transition path; (3) Perform umbrella sampling and free energy analysis along the transition path. This method is essentially one-dimensional sampling. Furthermore, the saddle point algorithm that will be developed in this project can be used to quickly detect drawbacks of reaction coordinates and find new reaction coordinates. Therefore, the new method will greatly reduce the computational complexity of free energy calculations and speed up the applications. This computational framework will be applied in the study of complex and important problems such as the transmembrane permeation of small molecules and membrane-peptide interactions. Our work will shed light in drug designing and the understanding of membrane-related biological processes.