Job: Local Refinement

At a glance

Refine a volume or a part of a volume to high resolution by incorporating existing pose information to prevent significant deviation from a known good alignment.

• Use particles from an alignment with existing gold-standard half sets

• Create a mask with a soft edge to focus the refinement on a subvolume

• Generally a user-selected fulcrum position produces best results

• Impose a Gaussian prior to regularize the problem when the subvolume is small or the input alignment is already of medium- to high-quality

Description

Local Refinement is a technique for generating a single 3D volume from a stack of particle images, like Homogeneous or Non-Uniform refinement. However, where Homogeneous and Non-Uniform refinements discard pre-existing alignment information, Local Refinement incorporates information from previous alignments from upstream jobs. This presents several advantages:

• Sub-regions which are too small to align on their own may be improved by Local Refinement

• Information about the rotation and translation needed to align the consensus volume compared to the desired sub-region provides information about flexibility

• Combined with other job types, Local Refinement enables advanced workflows for investigation of pseudosymmetry or symmetry with flexibility

In each iteration of a local refinement, the volume is masked. Then, the algorithm finds the optimal pose of the masked subvolume within the given search extent of rotations around a fulcrum and translations for each particle image. The map is updated using the new poses, and the process continues.

Local Refinement should be your first choice when attempting to resolve two subdomains which are flexible relative to each other but internally rigid. For example, the head and foot regions of the Yeast U4/U6.U5 tri-snRNP (spliceosome) bend around flexible hinges, but are otherwise relatively rigid. Local refinement significantly improved map quality for those domains.

If the domains undergo continuous deformations or conformational changes, algorithms like 3D Variability Analysis or 3D Flexible Refinement might produce better results.

Inputs

Particles

Unlike other refinement jobs, particle inputs to Local Refinement must have been previously aligned in 3D, and must have a FSC half-set split. These conditions are satisfied by, for example, Homogeneous or Non-Uniform refinement.

Particles can also be provided from a Particle Subtraction job, but subtraction is not required.

Particle Subtraction and Local Refinement

Particle subtraction attempts to accommodate the fact that we cannot apply a mask to our particle images. It subtracts a projection of the excluded regions of a map from the particle images, leaving behind the parts of the image corresponding to what we want to align. Because this subtraction requires projection of the information in our volume by the pose of the particle, it requires a high-quality initial alignment to work properly. See the Particle Subtraction job page for more detail.

Volume

Local Refinement accepts any volume with half maps as an input.

Mask

Local Refinement requires a mask that includes the region to refine. Note that the mask does not necessarily have to exclude anything — a mask covering the entire volume is acceptable.

Ensure that your mask has a sufficiently soft edge to avoid ringing artifacts. For more information on mask creation, please see the relevant guide page.

Outputs

Volume

The refined sub-volume is not masked. It is possible that new features will become visible which are outside the mask if they are rigidly associated with the refined sub-volume.

Particles

Particles are output with new poses.

Mask

If dynamic masking is enabled, the refined mask is output. Otherwise the mask is the same as the input.

Commonly Adjusted Parameters

Alignment parameters

The alignment parameters control how much the sub-volume is rotated during the search for its optimal pose. Broadly speaking, the search extent should be large enough to capture the range of motion of the sub-volume, but small enough that the prior alignment information is still useful in preventing overfitting.

Use pose/shift Gaussian prior during alignment

A Gaussian prior penalizes poses far from the initial value.

If true, during each iteration, poses far from the input pose are softly penalized. This increases stability while still allowing for an alignment far from the input, if the score is sufficiently high.

When this option is enabled, two additional settings are available to control the standard deviation of the prior over rotation and shifts, respectively. Wider standard deviations “weaken” the prior, while tighter ones increase the penalty on poses far from the input.

Generally, your prior should follow your expected distribution of the particles. For instance, when refining a highly flexible domain, wide shifts are appropriate. On the other hand, when improving detail in well-aligned, rigid region of the target a prior as small as 3° or 2 Å may work best.

Regardless of the width of the Gaussian, no poses outside the search extent will be considered. If priors are enabled, then the search extents are given a default value of three times the prior standard deviations, for both the rotation and shift priors.

For small masks or low SNR data, the use of these priors is encouraged to help increase stability and reduce overfitting.

Search Extents

Search extents control the maximum displacements of the sub-volume.

These parameters set the maximum distance from the starting alignment that the sub-volume will be rotated (Rotation search extent) or translated (Shift search extent) in degrees and Å, respectively.

Re-centering

Recentering controls whether each iteration searches a region around the input pose or the optimal pose found in the previous iteration.

In each iteration, the sub-volume is assigned a new pose (rotation and shift). These settings control whether future iterations should start from the input pose (False) or the updated pose (True) for the rotations and shifts, respectively.

If either of these settings are set to True, we strongly recommend that a pose/shift Gaussian prior is applied to the alignments to prevent particles from drifting far from their initial pose in early iterations.

These settings re-center both the search grid and the Gaussian prior, if applied.

Some users have reported increased alignment quality when turning both re-centering and Gaussian priors on.

Fulcrum Location

The two default fulcrum locations (left: mask_center; middle: box_center) and a user-defined fulcrum (right).

Local refinement requires a fulcrum about which it will rotate the search volume while aligning to particles. By default, this is the center of the input mask. It can also be set to the center of the box (the fulcrum for all other refinements).

Additionally, you can specify an exact fulcrum location. This can be entered as a triplet of coordinates with the suffix px or A to indicate the triplet is being specified in pixels or Angstroms, respectively. Specify this coordinate in x, y, z order, with 0, 0, 0 px or 0, 0, 0 Acorresponding to the corner of the box.

For an example of fulcrum selection, see the tri-snRNP case study.

Fulcrum Location

The choice of a fulcrum location is an important parameter to consider. An inappropriate fulcrum location can exaggerate or dampen the expected results of a given rotation by coupling it with a translation. See Improper search extents and/or fulcrum position for more information.

Refinement parameters

Marginalization

Enabling marginalization allows for insertion of particle images at multiple poses, weighted by the likelihood of that pose. Marginalization can improve results when the target is smaller, when overfitting occurs, or when the particle stack still contains some noisy outliers.

Non-Uniform Refinement Enable

Enable cross-validation-optimal filtering, as in a Non-Uniform Refinement. This can significantly improve results for membrane proteins or other targets with disordered regions.

Symmetry

Enforce point-group symmetry. Note that this parameter uses the box center, regardless of the choice of fulcrum. We recommend performing symmetry expansion rather than using this setting, as symmetry expansion can accommodate minor breaks in symmetry.

Mask

When set to static, use the input mask. When set to dynamic, perform dynamic masking to re-generate a mask at each iteration of refinement. We generally recommend static masking to avoid mask-based overfitting.

If dynamic masking is used, the following parameters influence mask generation:

• Regions of the map with a value greater than the Dynamic mask threshold are included in the mask.

• Dynamic mask near and far control the distance in Å from the thresholded map edge to begin and end the soft edge, respectively.

Minimize over per-particle scale

When enabled, optimize the per-particle scale at each refinement iteration. In general, this should be kept off due to the instability of particle scale when considering a masked subregion compared to the full particle image.

Initial lowpass resolution

The input map will be low-pass filtered to this resolution before the first iteration. Subsequent iterations will be filtered to the GSFSC resolution.

The initial lowpass resolution can be an important parameter to tune. The default value of 12 Å is conservative. If the input particles are already well-aligned, lowpass filtering worsens alignments in the initial iterations by discarding good alignment information. At best, this results in slightly longer job runtimes as the initial iteration is spent getting back to the quality of the input alignments. At worst, for smaller regions of the particle which are difficult to initially align, the particles may shift too far from their input alignments and never recover the quality of the initial alignments.

We recommend that this value is set to the local resolution for the sub-volume to be refined (which can be determined with a Local Resolution Estimation job). If the sub-volume to be refined is large and well-aligned, a heuristic of 1–2 Å higher value (that is, worse resolution) than the GSFSC resolution may also give good results.

Common Problems

Masking artifacts

As discussed in Mask Selection and Creation, any time a mask “cuts through” density, a soft edge is absolutely essential. In practice, it is often best to try several widths of dilation and padding to find the optimal combination.

Masked subvolume too small

Since local refinement uses the masked volume to search for the proper pose, if the masked subregion is too small there will not be enough information for a high-quality alignment. If the angle and shifts change by a large amount and the sub-volume becomes noisy and low-quality, this is a likely culprit.

Small sub-volumes do not provide enough information for reliable alignment, resulting in noisy, over-fitted results.

If a small volume must be masked and aligned, this problem can be somewhat mitigated by imposing a Gaussian prior on the shifts and rotations. With this prior, poses receive a penalty to their score which increases the further the pose is from the input pose. The smaller the standard deviation of the Gaussian, the harsher the penalty. Penalizing large shifts in this way can reduce overfitting of small sub-volumes.

Generally, your prior should follow your expected distribution of the particles. For instance, when refining a highly flexible domain, wide shifts are appropriate. On the other hand, when improving detail in well-aligned, rigid region of the target a prior as small as 3° or 2 Å may work best.

Pose and shift change histograms are expected to be peaked relatively close to 0, and to decay outward. A large proportion of particles near the right extreme of the histograms indicates poor alignability, which may be alleviated by the use of a gaussian prior or a larger mask. The example histograms above illustrate an overfitted, poorly-aligned sub-volume (blue) and a well-regularized alignment of the same particles (grey) using a Gaussian prior and larger subvolume.

Improper search extents and/or fulcrum position

Ideally, the distribution of angle and shift changes is smooth after the final iteration of local refinement. If either distribution has peaks, especially if those peaks are at the furthest extent of the search range, the refinement may benefit from an increased search range.

A poor choice of fulcrum position may also result in peaks in the angle and shift change plots. A fulcrum position that is far away from the true point about which the sub-volume rotates requires a large translation to correct the alignment. Therefore, especially where large shifts are observed, optimizing the fulcrum may prove beneficial.

Rotation about a fulcrum that is far from the true center of rotation results in an additional shift. This may result in poor alignment.

Image Recentering

In some cases, users have reported that re-centering the images using Volume Alignment Tools significantly improves the results of Local Refinement. If the results of a Local Refinement are unexpectedly poor this may be one possible solution.

Common Next Steps

A local refinement often provides the best possible map for a given rigid sub-volume. If the volume improves, creating a mask around the new features may iteratively increase map quality.

If after local refinement you suspect that the aligned sub-volume may have some heterogeneity, 3D Classification will quickly tease apart discrete conformations in your aligned sub-volume. Using the mask from your Local Refinement job and a solvent mask around the whole map will likely provide the best results.

Example Workflow

Case Study: Yeast U4/U6.U5 tri-snRNP