Fast and Accurate Comparison of Protein Conformational Ensembles

Abstract

Molecular dynamics (MD) simulations yield varied results based on simulation conditions; therefore, the results must be compared across different conditions. Previous studies have introduced measures to compare two protein conformational ensembles, each containing multiple protein structures, generated via MD simulations. However, existing brute-force algorithms for computing measures, such as the minimum root mean square deviation (RMSD) and average minimum RMSD, require O(nNM)-time, where n denotes the protein length and N and M are the number of structures in each ensemble. This time complexity can be prohibitively slow when comparing two conformational ensembles generated via long MD simulations. We propose three faster heuristic methods—single-direction method, dual-direction method, and all-direction method—for computing the minimum RMSD and average minimum RMSD in O(n(N+M))-time using the SMAWK algorithm. Experiments on an MD simulation dataset with (N, M) =(10,000, 10,000) demonstrated that the all-direction method was the most accurate, while the single-direction method was the fastest among the proposed methods. The all-direction method achieved average approximation ratios of 1.058 and 1.174 for the minimum RMSD and average minimum RMSD, respectively. The mean absolute error for the minimum RMSD using the all-direction method was approximately three times smaller, and that for the average minimum RMSD was approximately 1.6 times smaller compared with that of the single-direction method. The single-direction method was approximately 1,980 times faster than the existing brute-force algorithm in computing the minimum RMSD and average minimum RMSD.