Novel Approaches to Empirical Force Field Models in Molecular Modeling via Multidimensional Scaling

该项目侧重于确定生物分子结构的新计算方法，这对于我们理解蛋白质等生物分子如何发挥其功能至关重要。这种对功能的理解反过来又影响了疾病诊断和治疗技术的发展。确定生物分子结构的一种广泛使用的方法是利用力场模型计算分子势能的最小值。势能解释了原子间键的拉伸、键角的变形以及非键原子之间的相互作用（如静电力）等特征。令人感兴趣的是具有非常低势能的分子结构，因为生物分子将自己折叠成倾向于最小化势能的形状：大自然是一个优化器。一种方法是通过应用计算技术系统地改变原子的位置来降低势能，从而寻求物理上有意义的分子构型。将计算算法应用于能量最小化时，会遇到一个严重的困难，即搜索需要在通往低势能构型的路上经过高势能构型。例如，原子彼此靠近时，由于排斥力的作用，势能会增加。最小化算法很难处理这种情况，因为它们不能事先确定允许势能的增加最终会导致能量较低的配置。因此，算法可能会停留在使附近构型的势能最小的结构上，而不是在整个结构上，并且没有物理意义。本项目探索了一种解决这一困难的新方法。我们用原子间的距离，而不是原子的位置来提出问题，用这些距离来重写势能。粗略地说，我们的方法对应于添加每个原子的虚拟副本，每个副本对应一个其他原子。当然，我们还必须添加一些条件，以确保一个原子的所有虚拟副本最终合并为一个原子。然而，我们使用的条件可以在能量最小化过程的中间步骤中放松，并且只有在我们接近解决方案时才强制执行。这种方法得益于向搜索空间添加大量额外维度。打个比方，想象一下从芝加哥开始寻找北美的最低点——死亡谷。作为纯粹的地球旅行者，我们可能会被愚弄，停在落基山脉脚下或大盐湖周围的局部低点，就像优化算法可能会停在局部能量最小化处一样。但是，如果我们放宽陆路旅行的要求，允许乘飞机旅行，那么我们就可以越过地面上的局部极小值，到达理想的目的地。初步测试表明，我们的方法极大地改善了众所周知的麻烦的能量项的行为。该项目将研究其在分子结构测定中的用途，并将研究其扩展到其他应用，如药物对接和寻找化学反应的过渡机制。

The project focuses on new computational methods for the determination of biomolecular structure, which is crucial to our understanding of how biomolecules such as proteins perform the functions they do. This functional understanding, in turn, figures in the development of techniques for disease diagnosis and treatment. A widely used approach to determining the structure of biomolecules is the minimization of the molecule''s potential energy, computed using a force-field model. The potential energy accounts for such features as the stretching of bonds between atoms, the deformation of bond angles, and the interactions of non-bonded atoms (e.g., electrostatic forces). Of interest are molecular configurations that have very low potential energies, since biomolecules fold themselves into shapes that tend to minimize the potential energy: Nature is an optimizer. One seeks physically meaningful molecular configurations by applying computational techniques to systematically vary the locations of the atoms to reduce the potential energy. A serious difficulty encountered when applying computational algorithms to energy minimization arises when the search needs to move through configurations with high potential energies on the way to configurations with low potential energies. For instance, moving atoms close past one another increases the potential energy due to repulsive forces. Minimization algorithms have difficulty dealing with this situation since they cannot be sure in advance that allowing increases in potential energy will ultimately lead to configurations with lower energy. As a consequence, algorithms may halt at structures that minimize the potential energy only among nearby configurations, but not overall, and are not of physical interest. This project explores a new approach to address this difficulty. We pose the problem in terms of the interatomic distances, rather than the locations of the atoms, rewriting the potential energy in terms of these distances. Roughly speaking, our approach corresponds to adding fictitious copies of each atom, one for each of the other atoms. Of course, we must also add conditions that ensure that all the fictitious copies of an atom ultimately coalesce into a single atom. However, we use conditions that can be relaxed at intermediate steps of the energy minimization process and are only enforced as we approach a solution. This approach benefits from adding a large number of extra dimensions to the search space. As an analogy, imagine a search for the lowest point in North America, Death Valley, starting from Chicago. As purely earthbound voyagers we might be fooled into stopping at a local low point at the foot of the Rockies or around the Great Salt Lake, just as optimization algorithms might halt at local energy minimizers. But if we relax the requirement of traveling by land and allow travel by air, then we can pass over local minimizers on the ground to arrive at the desired destination. Preliminary tests have shown that our approach greatly improves the behavior of the more notoriously troublesome energy terms. This project will investigate its use for molecular structure determination and will examine extensions to other applications such as drug docking and finding transition mechanisms for chemical reactions.