Abstract

Protein molecular conformation is an important and challenging problem in biophysics. It is to recover the structure of proteins based on limited information such as noised distances, lower and upper bounds on some distances between atoms. In this paper, based on the recent progress in numerical algorithms for Euclidean distance matrix (EDM) optimization problems, we propose a EDM model for protein molecular conformation. We reformulate the problem as a rank-constrained least squares problem with linear equality constraints, box constraints, as well as a cone constraint. Due to the nonconvexity of the problem, we develop a majorized penalty approach to solve the problem. We apply the accelerated block coordinate descent algorithm proposed in Sun et al. (SIAM J Optim 26(2):1072–1100, 2016) to solve the resulting subproblem. Extensive numerical results demonstrate the efficiency of the proposed model.

中文翻译：

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蛋白质分子构象的欧氏距离矩阵模型

摘要

蛋白质分子构象是生物物理学中一个重要且具有挑战性的问题。它是基于有限的信息（例如，噪声距离，原子之间的某些距离的上下限）来恢复蛋白质的结构。本文基于欧氏距离矩阵（EDM）优化问题数值算法的最新进展，提出了蛋白质分子构象的EDM模型。我们将该问题重新表述为具有线性等式约束，框形约束以及圆锥形约束的秩约束最小二乘问题。由于问题的非凸性，我们开发了一种广义罚分法来解决该问题。我们应用了Sun等人提出的加速块坐标下降算法。（SIAM J Optim 26（2）：1072-1100，2016年）解决由此产生的子问题。大量的数值结果证明了该模型的有效性。