Fig 1.
Atomic structure models are refined into a cryo-EM density using biasing forces that maximize similarity between model and map.
A refinement/simulation is initialized with an atomic model (orange) and a density map (blue). A model density is generated in each voxel (grey boxes). Voxel-wise similarity scores between model density and cryo-EM density are akin to a noise model (light blue curve). The gradient of the similarity score determines the fitting forces (blue arrows). Together with a molecular dynamics force field (red arrows), the fitting forces enable model coordinate updates (dark orange) that make the model more similar to the density under force field constraints. New model densities are generated iteratively from the updated model in each time step of the simulation until acceptable convergence is reached.
Fig 2.
Similarity score determines ruggedness of the effective refinement potential energy landscape, also when balancing it with structural bias.
From top to bottom: a One-dimensional refinement of a single particle (black circle) towards a Gaussian-shaped density (gray) with inner-product (purple), cross-correlation (ochre), relative-entropy swapped (dark blue) and relative-entropy (green) as similarity scores. b Expanded model with two particles (black circles, x1 smaller and x2 larger) with two amplitude peaks in a one-dimensional density and target distribution (gray), and the resulting two-dimensional effective potential energy landscapes for inner-product, cross-correlation, swapped relative-entropy and relative-entropy similarity measures. c Combination of the similarity measure and force field contribution to the potential energy landscape, exemplified by a harmonic bond that keeps particles at half the distance between the Gaussian centers. For all relative weights of the contributions of the refinement potential and bond potential energy landscape (ratio 1:2 upper panel, 2:1 middle panel, as illustrated by the scale on the left), the relative entropy similarity score produces smooth landscapes with minima at the positions that are expected from the model input.
Fig 3.
Adaptive scaling of contributions from force-field and cryo-EM density data overcomes potential energy barriers without excessive work input.
a Adaptive force scaling heuristically balances force-field and density influence during refinement simulations. b Particle in energy landscape where density similarity increases from left to right along the black curve. For the upper leg alternative, the similarity decreases despite biasing forces (burgundy arrow), which causes the bias strength to be increased. Conversely, in a scenario where the similarity remains high (lower leg), the biasing force will gradually be reduced to allow the system to better sample the local landscape. c Brownian diffusion in a potential with fixed (grey) and adaptive (burgundy) biasing forces, respectively. The constant biasing force is scaled such that both force-adding schemes yield the same average mean first passage time moving from left to right. The relative-entropy approach leads to significantly lower exerted work on the system (area under the grey and burgundy curves, respectively), which reduces perturbation of the dynamics of the system.
Fig 4.
Refinement into noise-free data with adaptive force scaling.
a Aligned (left) and unaligned (right) starting conformations (black sticks) of a helix subject to refinement simulation into a synthetically generated cryo-EM density (gray mesh). b RMSD per residue of the final refined models starting from the aligned conformation compared to the ground truth model underlying the synthetic density map. Each replicate (n=7) is colored by the similarity measure used, inner-product (purple), cross-correlation (ochre), relative-entropy swapped (dark blue), and relative-entropy (green). c RMSD per residue of the final refined models starting from the unaligned conformation compared to the ground truth model underlying the synthetic density map. Each replicate (n=7) is colored by the similarity measure used, inner-product (purple), cross-correlation (ochre), relative-entropy swapped (dark blue), and relative-entropy (green).
Fig 5.
Refinement of an all-atom X-Ray aldolase structure (PDB id 6ALD) into experimental cryo-EM density (EMD-21023).
a Final structure models from density-guided simulations using different similarity scores colored by unaligned root mean square coordinate deviation (RMSD) per residue from the manually built model (PDB id 6V20). b Fourier shell correlation of starting structure (gray line), rigid-body fit of the starting model to the target density (blue) as well as refinement results in the last simulation frame (solid lines). The reported cryo-EM map resolution and 0.143 FSC are indicated with grey lines. c Unweighted FSC average over the course of refinement simulation.
Fig 6.
Refinement of an all-atom GroEL cryo-EM structure (PDB id 5W0S state 1) into experimental cryo-EM density (EMD-8750, additional map 3).
a Final structure models from density-guided simulations using different similarity scores colored by unaligned root mean square coordinate deviation (RMSD) per residue from the deposited model (PDB id 5W0S state 3). b Fourier shell correlation of starting structure (gray line), rigid-body fit of the starting model to the target density (blue) as well as refinement results in the last simulation frame (solid lines) deviations of an equilibrium simulation (dotted lines). c Unweighted FSC average over the course of refinement simulation.
Fig 7.
Cryo-EM data rectifies model distortions with density-guided simulations.
a Distorted starting model RMSD with respect to manually built model (PDB id 6V20). b Final model structure after refinement into a cryo-EM density (EMD-21023) using adaptive force scaling and relative-entropy similarity score. c Close-up of structural features of the final simulation model (green lines) and cryo-EM density (gray mesh). d Fourier shell correlation of starting structure (gray line) as well as refinement results in the last simulation frame (solid lines). The reported cryo-EM map resolution and 0.143 FSC value are indicated with grey lines. e Un-weighted FSC average over the course of a refinement simulation.