Tackling hysteresis in conformational sampling — how to be forgetful with MEMENTO

Abstract

The structure of proteins has long been recognised to hold the key to understanding and engineering their function, and rapid advances in structural biology (and protein structure prediction) are now supplying researchers with an ever-increasing wealth of structural information. Most of the time, however, structures can only be determined in free energy minima, one at a time. While conformational flexibility may thus be inferred from static end-state structures, their interconversion mechanisms - a central ambition of structural biology - are often beyond the scope of direct experimentation. Given the dynamical nature of the processes in question, many studies have attempted to explore conformational transitions using molecular dynamics (MD). However, ensuring proper convergence and reversibility in the predicted transitions is extremely challenging. In particular, a commonly used technique to map out a path from a starting to a target conformation called targeted MD (tMD) can suffer from starting-state dependence (hysteresis) when combined with techniques such as umbrella sampling (US) to compute the free energy profile of a transition. Here, we study this problem in detail on conformational changes of increasing complexity. We also present a new, history-independent approach that we term 'MEMENTO' (Morphing End states by Modelling Ensembles with iNdependent TOpologies) to generate paths that alleviate hysteresis in the construction of conformational free energy profiles. MEMENTO utilises template-based structure modelling to restore physically reasonable protein conformations based on coordinate interpolation (morphing) as an ensemble of plausible intermediates, from which a smooth path is picked. We compare tMD and MEMENTO on well-characterized test cases (the toy peptide deca-alanine and the enzyme adenylate kinase) before discussing its use in more complicated systems (the kinase P38α and the bacterial leucine transporter LeuT). Our work shows that for all but the simplest systems tMD paths should not in general be used to seed umbrella sampling or related techniques, unless the paths are validated by consistent results from biased runs in opposite directions. MEMENTO, on the other hand performs well as a flexible tool to generate intermediate structures for umbrella sampling. We also demonstrate that extended end-state sampling combined with MEMENTO can aid the discovery of collective variables on a case-by-case basis.

Converging PMF calculations of antibiotic permeation across an outer membrane porin with sub-kilocalorie per mole accuracy

“…Because PMF calculations frequently suffer from hysteresis problems, comparing PMFs obtained after forward and reverse pulling provides a highly sensitive test for convergence. [47][48][49] In addition, for each pulling direction (PP-to-EC or EC-to-PP), we computed PMFs from two independent set of US windows initiated from two independent pulling simulations. Comparing the latter PMFs provides an additional quality test, but it may not reveal hysteresis problems that are, in our experience, a major matter of concern during US simulations of biomolecules.…”