二次规划方法拟合蛋白质复合物的电子密度图
Quadratic Programming Approach to Fit Protein Complexes into Electron Density Maps
摘要：
本文研究了蛋白质复合物的电子密度图拟合问题。它们由转换成重叠矩阵的高分辨率cryoEM密度图表示，并部分显示了复合物的结构。一般的目的是确定所有蛋白质在其中的位置。这个问题是NP难的，因为它属于复合物的一组离散状态的组合优化领域。我们介绍了二次规划方法的问题。为了找到一个近似解，我们将密度映入成一个重叠矩阵，这通常是不确定的。由于矩阵是不定的，相应的二次型的最优化问题是非凸的。为了处理最优化问题的非凸性，我们使用不同的凸松弛来找到哪一组蛋白质最小化二次型最好。
英文摘要：
The paper investigates the problem of fitting protein complexes into electron density maps. They are represented by high-resolution cryoEM density maps converted into overlapping matrices and partly show a structure of a complex. The general purpose is to define positions of all proteins inside it. This problem is known to be NP-hard, since it lays in the field of combinatorial optimization over a set of discrete states of the complex. We introduce quadratic programming approaches to the problem. To find an approximate solution, we convert a density map into an overlapping matrix, which is generally indefinite. Since the matrix is indefinite, the optimization problem for the corresponding quadratic form is non-convex. To treat non-convexity of the optimization problem, we use different convex relaxations to find which set of proteins minimizes the quadratic form best.
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