Algorithms for local optimization of OPLS energy for large protein structures

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.