Local Algorithms for Minimizing the Force Field for 3D Representation of Macromolecules

• Published in: Computational mathematics and mathematical physics 2019-12, Vol.59 (12), p.1994-2008
• Main Authors: Yakovlev, P. A., Anikin, A. S., Bol’shakova, O. A., Gasnikov, A. V., Gornov, A. Yu, Ermak, T. V., Makarenko, D. V., Morozov, V. P., Neterebskii, B. O.
• Format: Article
• Language: English
• Subjects: Algorithms; Complex formation; Complexity; Computational Mathematics and Numerical Analysis; Energy conservation; Macromolecules; Mathematics; Mathematics and Statistics; Molecular docking; Optimization; Proteins; Quasi Newton methods
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542519120030

The majority of problems in structural computational biology require minimization of the energy function (force field) defined on the molecule geometry. This makes it possible to determine properties of molecules, predict the correct arrangement of protein chains, find the best molecular docking for complex formation, verify hypotheses concerning the protein design, and solve other problems arising in modern drug development. In the case of low-molecular compounds (consisting of less than 250 atoms), the problem of finding the geometry that minimizes the energy function is well studied. The minimization of macromolecules (in particular, proteins) consisting of tens of thousands of atoms is more difficult. However, a distinctive feature of statements of these problems is that initial approximations that are close to the solution are often available. Therefore, the original problem can be formulated as a problem of nonconvex optimization in the space of about variables. The complexity of computing the function and its gradient is quadratic in the number variables. A comparative analysis of gradient-free methods with gradient-type methods (gradient descent, fast gradient descent, conjugate gradient, and quasi-Newton methods) in their GPU implementations is carried out.