SGER: Global Minimum Determination by Underestimation: Application to Protein-Ligand Docking

提出了两种新的算法来预测计算生物学中Rn中能量表面函数的全局最小值。这样的函数的特征在于具有非常大数量的局部最小值，其中该数量通常随n呈指数增长。例如，这种类型的能量表面出现在计算药物设计中的蛋白质-配体对接中。全局最小值的位置决定了蛋白质表面对接配体（药物）最有可能的位置。这项研究基于早期的结果，假设能量表面是盆形的，具有许多局部最小值。该方法利用凸二次函数逼近能量面，低估了能量面的大量局部极小值，并在L1范数下使误差最小化.结果表明，在许多情况下，这个凸函数的唯一最小值是一个很好的预测的全球最小的能量surface.Intellectual优点：我们建议建立在这个早期的工作，开发两个新的和更有效的算法。第一个将确定一个二次低估函数，其中函数Hessian的特征值满足指定的下限和上限。这包括凸二次曲面作为特殊情况.在一些重要的情况下，能量面不是盆形的，而是包含相对少量的明显的局部极小值，以及大量相对浅的局部极小值。明显的局部最小值的位置是未知的，但其中之一是全局最小值。第二个新算法将确定一个低估的功能，其中包括一个小数目的负高斯的总和。与二次函数一样，所有高斯的位置和形状将通过在大量局部最小值处最小化近似误差来确定。预测的全球最低点的能量表面，然后给出的位置，高斯与最小函数值在其center.Impact：这两个算法将开发，实施和测试现实的计算模型的蛋白质配体对接能量表面，并提供，按照大学的政策，被用作计算机辅助药物设计软件包的关键组成部分之一。

It is proposed to develop two new algorithms for predicting the global minimum of energy surface functions in Rn arising in computational biology. Such functions are characterized by having a very large number of local minima, where the number typically grows exponentially with n. Energy surfaces of this type arise, for example, in protein-ligand docking in computational drug design. The location of the global minimum determines the most likely location of the docked ligand (drug) on the protein surface.This research is based on earlier results where it is assumed that the energy surface is basin-shaped, with many local minima. The energy surface was approximated by a convex quadratic function which underestimated a large number of local minima of the energy surface, and minimized the error in theL1 norm. It was shown that in many cases the unique minimum of this convex function was a good predictor of the global minimum of the energy surface.Intellectual Merit: We propose to build on this earlier work by developing two new and more efficient algorithms. The first will determine a quadratic underestimating function where the eigenvalues of the function Hessian satisfy specified lower and upper bounds. This includes the convex quadraticas a special case. In some important cases the energy surface, rather than being basin-shaped, contains a relatively small number of pronounced local minima, in addition to a large number relatively shallow local minima. The location of the pronounced local minima is not known, but one of them is the global minimum. The second proposed new algorithm will determine an underestimating function which consists of the sum of a small number of negative Gaussians. The location and shape of all Gaussians will be determined,as with the quadratic function, by minimizing the approximation error at a large number of local minima. The predicted global minimum point of the energy surface is then given by the location of that Gaussian with the minimum function value at its center.Impact: These two algorithms will be developed, implemented and tested on realistic computational models of protein-ligand docking energy surfaces, and made available, in accordance with University policy, to be used as one of the key components of a computer-aided drug design software package.