Focus Documentation

Maximum likelihood is an algorithm that finds a set of underlying parameters which maximize the likelihood of the observed particle images. wise The optimization targets include the statistical parameters of translation, rotation, and noise. The algorithm here accomplishes a single particle processing strategy (Fig.), where the unit cells are extracted from 2d crystals. The profile of unbending provides the initial approximate positions of the unit cells.

Maximum Likelihood Algorithm

Choose if a Single Particle reconstruction, e.g. using Maximum Likelihood, should run in addition or the unbending prorams, or not.

Choose if the Single Particle 2D result should be used in 2dx_merge. If not, then the Fourier-filtered result from the Unbending will be used instead.

Chose if the amplitude correction should be done before (whole image) or after the windowing into a particle stack.

Choose if the the next reference should be determined using a maximum likelihood processing, or using the cross-correlation alignment.

Maximum Likelihood Parameters

Following dimensions are measured in pixels

This is the size of the first windowed particles, before ML and CTF correction. Cut two or three times the final window size.

This is the dimension of the particles extracted from 2D crystals. The center coordinates of windows are from the profile of unbending, which give the approximate location of unit cells. The window size should be larger than one unit cell to obtain the complete structure, an accurate relation with the unit cell dimension is not required though. On the other hand, large windows including multiple unit cells may have inner translation and rotation, which should be avoided in the case of badly ordered crystals.

This is the final window size for the cropped particles, e.g. 120. In Pixels.

This is the inner window size for the final cropped particles. If those particles should be pasted into a slightly larger frame with a border set to the mean value, then set this value here to the inner window diameter, e.g. 110. Otherwise, use here the same diameter as for ML_realcellxy_outer.

The size of the mask applied to the reference.

A switch determines the thresholding methods of selecting the particles to be aligned.

• ML_absolute_threshold: All the particles with correlation coefficients beyond this value are selected.
• ML_relative_threshold: The particles are sorted by the correlation coefficients, and the top percentages of them are selected.

A switch determines how to get the initial reference.

Average reference: The average of all the particles produces the initial reference.

Noise reference: A pure noise image is the initial reference. There is not any bias in the initial reference. This setting surprising gives good results in many cases, especially when the average reference is not reliable.

Random reference: Randomly take any particle as the initial reference. This is not a good option in some cases.

If whitening is applied prior to the ML, noise at high frequencies may be amplified. A low-pass filter can help to prevent unreliable alignment at high frequencies.

A switch defines the low pass filter shape.

none: no low-pass filtering.

Gaussian: A Gaussian filtering is applied.

Sharp cutoff: Frequency components beyond the cutoff point are set to zero.

The radius takes value in (0,0.5). The value of “0.0” means no low-pass filtering is applied.

The scale of downsampling in Fourier space. 1: no down sampling; n: crop the 1/n radius center area in the Fourier space. Use e.g. 1.

This flag indicates if whitening is applied to the crystal image before the ML process.

This flag indicates if CTF correction is applied to the crystal image to generate the final map.

The unit cell symmetrization is applied to the reference in each iteration of the ML processing. Only rotational symmetry would be used. (eg. 1,2,3,4,6). Apply rotational symmetrization only when the phase origin is reliable.

This set of angle parameters determines the in-plane rotation alignment in the ML. (from, to, step) are the minimum & maximum rotation angles, and the increment steps. Use 0.0, 0.0, 1.0 for no angle search.

Termination criteria of the ML processing

The maximum number of iterations that the ML process is allowed to do. One of the joint conditions for terminating ML, eg 50.

This is an indicator of the convergence of translation and rotation. The ML process will terminate if the parameters converges, which means the parameter (translation and rotation) change between two consecutive iterations is smaller than the criterion.

The amplitudes of the final map is scaled to restore the attenuated signals at high frequencies.

B factor in the exponential envelop function. Normally negative, use eg -500.

To prevent the B-factor from amplifying unreliable high frequency information, the envelop function is combined with the FSC. This is the factor to weight the envelop function and the FSC in refining the final map. The range is 0.0-1.0.