Algorithms for local optimization of OPLS energy for large protein structures

TL;DR

This paper explores and compares various local optimization algorithms, including gradient-based and gradient-free methods, for energy minimization of large protein structures using the OPLS force field, demonstrating their effectiveness on real biological data.

Contribution

It introduces a practical comparison of optimization methods tailored for large protein energy minimization, emphasizing GPU implementation and real data application.

Findings

Fast gradient descent with line-search is efficient on GPU.

Conjugate gradient and LBFGS methods perform well for large molecules.

The methods successfully optimize real protein structures from BIOCAD.

Abstract

Many problems arise in computational biology can be reduced to the minimization of energy function, that determines on the geometry of considered molecule. The solution of this problem allows in particular to solve folding and docking problems in structural biology. For the small molecules this problem is well solved. But for the large molecules ($10^4$ atoms and more) this is still an open problem. In this work we consider energy minimization problem (OPLS force field) for the large molecules but with good enough initial (starting) point. In the paper one can find a biological explanation of this assumption. Due to this assumption we reduce the global optimization problem to the local one. We compare different methods: gradient-free methods, gradient type methods (gradient method, fast gradient method, conjugate gradients (CG), LBFGS), high-order (tensor) methods. We observe that the most convenient ones in GPU realization are fast gradient descent with special line-search and CG (Polak--Ribiere--Polyak), LBFGS (memory = 3 iteration). Finally, we demonstrate how all these method work on real data set provided by BIOCAD.