Tackling Hysteresis in Conformational Sampling: How to Be Forgetful with MEMENTO

Abstract

The structure of proteins has long been recognized 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 steered MD (SMD) 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 utilizes 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 SMD 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 SMD 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.

The mechanism of mammalian proton-coupled peptide transporters

“…If the CV is not optimal, problems can manifest in the form of hysteresis (starting-state dependence) when moving between known end-states. (Lichtinger and Biggin, 2023) This is the case for the PepT2 OCC↔OF transition with the simple tip-CV illustrated in figure 2a. Using either metadynamics or SMD with replica-exchange umbrella sampling (REUS), the end-state from which the simulations were started is always favoured in the resulting potential of mean force (PMF), with the hysteresis effect totalling ≈ 40 kcal mol −1 for each method (figure S6).…”

“…We have recently proposed the MEMENTO method for history-independent path generation between given end-states. ( Lichtinger and Biggin, 2023 ) In short, protein coordinates are morphed, followed by reconstructing an ensemble of structures at each morphing intermediate using MODELLER. Monte-Carlo simulated annealing with an energy function based on between-intermediate RMSD values then finds a smooth path through these ensembles.…”

“…Using the trajectory data from our 1D-PMFs, we derived 2D CVs via a PCA-based approach we have previously described for LEUT. ( Lichtinger and Biggin, 2023 ) We pooled all sampling collected in 1D-REUS runs along the tip-CV for apo OCC↔OF (and equivalently for OCC↔IF. The same procedure was taken for these trajectories, and we will only explicitly write about OCC↔OF in the following paragraph).…”

Converging PMF Calculations of Antibiotic Permeation across an Outer Membrane Porin with Subkilocalorie per Mole Accuracy

“…Our key assessment of convergence was given by the comparison of PMFs obtained after constant-velocity pulling simulations in forward or reverse directions, here corresponding to PP-to-EC or EC-to-PP directions, respectively. Because PMF calculations frequently suffer from hysteresis problems, comparing PMFs obtained after forward and reverse pulling provides a highly sensitive test for convergence. − In addition, for each pulling direction (PP-to-EC or EC-to-PP), we computed PMFs from two independent sets of US windows initiated from two independent pulling simulations. Comparing the latter PMFs provides an additional quality test but may not reveal hysteresis problems that are, in our experience, a major matter of concern during US simulations of biomolecules.…”

“…By averaging all EC-to-PP and PP-to-EC PMF replicates in Figure 8B, we obtained the PMF with 95% confidence intervals below 1 kcal/mol for orientation 2 (Figure 7, magenta curve). The PMF for orientation 2 reveals a marked free-energy minimum at the channel center at z = −0.1 nm, where fosmidomycin forms simultaneous hydrogen bonds with Arg 59 , Arg 60 , and Ser 125 (Figure 7, left panel).…”