Numerical Errors in Minimization Based Binding Energy Calculations

Abstract

This work examines the effect of small input perturbations on binding energies computed from differences between energy minimized structures, such as the Prime MM-GBSA and MOE MM-GB/VI methods. The applied perturbations include translations of the cognate ligand in the binding site by a maximum of 0.1 Å along each coordinate or the permutation of the order of atoms of the cognate ligand without any changes to the atom coordinates. These seemingly inconsequential input changes can lead to as much as 17 kcal/mol differences in the computed binding energy. The calculated binding energies cluster around discrete values, which correspond to specific ligand poses. It appears that the largest variations are observed for target-ligand systems in which there is a possibility for multiple poses with strong hydrogen bonds. The barriers between different poses can appear fractal-like, making it difficult to predict which solution will be produced from a given input. Including protein flexibility in MM-GBSA calculations further increases numerical instability, and the protein strain terms seem to be the major factor contributing to this sensitivity. In such calculations it appears unwise to extend the flexible region beyond 6 Å.

Improved Ligand Binding Energies Derived from Molecular Dynamics: Replicate Sampling Enhances the Search of Conformational Space

“…Further investigation led us to make small variations in the starting coordinates that resulted in significant changes in the calculated MM-PBSA energies for protein/ligand complexes. These effects mirror the chaotic behavior of scores observed by Feher and Williams using standard minimization or docking protocols. − In our lab, Amber versions 10 and 11 displayed similar divergent behavior of the trajectories. In each case, the energy averaged over many MD frames appeared to converge but to different values.…”

The long road to calibrated prediction uncertainty in computational chemistry

“…These include errors due to finite arithmetics implementation of CC codes and, for stochastic methods, to the random errors resulting from finite sampling. For properly implemented and converged methods, numerical errors can often be assumed to be well controlled and negligible against other error sources 8 (except for instances of numerical chaos 49,50 ). However, for most algorithms we are still missing rigorous error bounds 51,52 , and estimation of the amplitude of numerical errors due to finite arithmetics requires computational approaches.…”

“…However, for most algorithms we are still missing rigorous error bounds 51,52 , and estimation of the amplitude of numerical errors due to finite arithmetics requires computational approaches. In the Monte Carlo framework, one observes the effects of tiny perturbations of model inputs 8,49 and/or arithmetic operations [53][54][55] , without need to alter the codes. The use of interval arithmetics has also been proposed 56 , but it might require in-depth recoding, barely an option for legacy CC codes.…”