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.

Figure 1

(a) Steered MD (SMD) between DFG-in and DFG-out conformations of P38α. Bidirectional steers on the RMSD to the respective target configuration, projected on the difference of RMSDs (DRMSD). (b) Replica-exchange umbrella sampling (REUS) on the obtained transition paths shows strong hysteresis. (c) Schematic representation of the problem of orthogonal degrees of freedom (DOFs) in SMD. (d) Schematic overview of the MEMENTO procedure, fixing unphysical morphing intermediates by template-based modelling.

Figure 2

(a) MEMENTO windows 0, 7, 15, and 23 after linear morphing, showing unphysical geometry in the intermediates. (b) The same windows after MODELLER processing, re-adding caps and pdb2gmx processing. Unphysical geometry is now fixed. (c) PMF of deca-alanine unfolding in water, sampled by 1D REUS along the end-to-end distance. The shaded area is the range of PMFs observed when taking only the first 60%, the last 60%, and the full sampling, which gives an indication of error and convergence. (d) Convergence of triplicate REUS simulations from SMD and MEMENTO paths. Both methods yield paths that converge on comparable time scales for deca-alanine, though convergence is inherently stochastic.

Figure 3

(a) An overview of the domain motions in the ADK open ↔ closed conformational change. (b) Representations of MEMENTO ADK intermediates 0, 7, 15 and 23, displaying the required domain motion. (c and d) PMFs from 1D-REUS of the ADK conformational change along the LID–NMP CV, with paths from (c) MEMENTO and (d) SMD. Shaded areas are the ranges of PMFs observed when taking only the first 60%, the last 60%, and the full sampling.

Figure 4

(a) An alternative closed-state identified by clustering trajectories from 1D-REUS with MEMENTO paths. The LID domain is closed while the NMP domain remains open. (b) PMF from 2D-REUS along the LID–CORE and NMP–CORE CVs, with MEMENTO paths connecting the closed, open, and alternative closed states. Crosses indicate the REUS window starting frames, connected in sequence. (c) AP5A inhibitor binding pose in the 1AKE crystal structure, illustrating how the negative ligand charge is accommodated by multiple positively charged protein residues. (d) PMF from 2D-REUS in the presence of AP5A, displaying a switch of the conformational preference to the closed state.

Figure 5

(a) Overview of the P38α system, highlighting DFG-in and DFG-out states. (b) 1D-REUS along the DRMSD CV from MEMENTO paths, showing big differences between replicates. Shaded area is the range of PMFs observed when taking only the first 60%, the last 60%, and the full sampling. (c) PCA results, showing the two CVs obtained for 2D-REUS sampling. (d) 2D-REUS along PCA-CVs with MEMENTO paths. Crosses indicate the REUS window starting frames, connected in sequence. (e and f) 2D-REUS from SMD paths, in the (e) DFG-in → DFG-out and (f) DFG-out → DFG-in directions.

Figure 6

(a) Overview of the IF and OCC structures of LeuT, and pore radius profiles calculated with CHAP. (b) Illustration of the closing motion of TM1, before (green) and after (pink) 1 μs unbiased MD. (c) 1D-REUS along the DRMSD CV from MEMENTO paths, showing big differences between replicates. Shaded area is the range of PMFs observed when taking only the first 60%, the last 60%, and the full sampling. (d) PCA results, showing the two CVs obtained for further sampling. (e and f) 2D-REUS from (e) MEMENTO and (f) SMD paths. Crosses indicate the REUS window starting frames, connected in sequence.