Data-guided Multi-Map variables for ensemble refinement of molecular movies

Abstract

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the 3-dimensional electron density of a protein, as it would be determined by cryo-EM or X-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous densitydriven molecular dynamics methodologies that determine only the best map-model fits, our work uses the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along reaction coordinates derived from electron densities can serve to induce conformational transitions between known intermediates. The simulated pathways appear reversible, with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein DataBank. We find that the best quantitative agreement with experimental freeenergy differences is obtained using medium resolution (∼5 Å) density information coupled to comparatively large structural transitions. Practical considerations for generating transitions with multiple intermediate atomic density distributions are also discussed.2

Molecular Dynamics to Predict Cryo-EM: Capturing Transitions and Short-Lived Conformational States of Biomolecules

“…This can improve the description of the free energy landscape associated with conformational changes of proteins and nucleic acids, as the cryo-EM map can be used as a reference for the conformational ensemble. Such approach, based on Multi-Map variable method, was very recently released for NAMD ( Vant et al, 2020 ). The initial results for both the steered-MD simulations and free energy methods are encouraging, with the free energy profiles for the conformational transitions comparable to those determined using high-resolution structures as a reference.…”

Protein Conformational States—A First Principles Bayesian Method

“…Adenylate kinase (ADK) converts ATP, ADP, and AMP by closing around substrate molecules [ 20 ]. The transition from closed to open was simulated in Reference [ 5 ] using steered molecular dynamics on a reaction coordinate interpolating between the electron density maps of PDB IDs 1AKE (Reference [ 20 ], closed) and 4AKE (Reference [ 2 ], open). The simulation data we used did not contain ligands, but did contain water and ions.…”

“…A chaperone protein assists transformation of large, hydrophobic proteins from initial, linear, to folded shapes [ 4 ]. X-ray and cryo electron-microscopy reveals conformations with small motions on the 1–5 Ångstrom level for those proteins that crystallize [ 5 ]. Neutron scattering and nuclear magnetic resonance structures of room temperature proteins show greater shape variability, but are usually able to classify structures into a few ‘canonical’ structures.…”

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments

“…CVs have also been used with enhanced sampling techniques, such as umbrella sampling 32 or metadynamics 33 , which bias the simulation along the CVs to more efficiently explore the conformational space for extracting the free-energy landscape. Along these lines, several methods 34 , 35 have been proposed to extract free energies from MD simulations with CVs that use 3D maps instead of directly using the individual particles.…”