Helical symmetry

Symmetrizing a particle

Helical operator syntax

Symmetrizing a helical particle can be done with the usual tool dsym:

 vh = dsym(v,<operator>);

where operator represents any symmetry operator. The syntax for helical operators is:

 h [<phi>,<dz>,<repetitions[optional]>,<rotational symmetry[optional]>] 

Here:

• phi is the angular increment in degrees
• dz is the axial rise in pixels
• the number of repetitions (defaults to the maximum definible for a given volume).
  Can be passed as 0 to force Dynamo to create a default value.
• additional Cn rotation to account for n-start helices.

Example:

 vh = dsym(v,'h[15.6,4.7]');
 vh = dsym(v,'h[15.6,4.7,5]');       % uses 5 repetitions
 vh = dsym(v,'h[15.6,4.7,5,8]');    % uses 5 repetitions and adds a C8 symmetrization
 vh = dsym(v,'h[15.6,4.7,0,8]');    % computes internally the maximal number of repetitions

Using symmetrization in alignment projects

The simplest way is to input one operator with the syntax described #Helical operator syntax above in the Numerical settings area of the dcm GUI.

This allows to impose a given symmetrization. In order to estimate the symmetry, you will need to create a plugin.

Estimating the helical symmetry of a density map

You can use the command dynamo_symmetry_scan.

This command operates by creating a matrix of symmetrization opertors, and comparing the transformed volumes with the original one. The transform that produces the highest cross correlation is considered the best match.

Number of repetitions

Symmetrization of a volume is computed by applying onto the original volume the transformation (phi,dz) repeatedly in both directions a number of times (called repetitions). The transformed volumes are averaging together. For instance, 17 repetitions imply 8 subsequent applications of (phi,dz) to the original volume and 8 applications of -(phi,dz).

Each time (phi,dz) is applied, the transformed volume will have a "bottom" of dz layers of pixels that are undefined: (they correspond to the theoretically part of the infinite helix below our volume). The averaging procedure will discard contributions of such pixels. As a result, the central area of the symmetrized volume will be representing contributions of more transformed volumes, attaining thus a higher SNR.

If the user does not specify a number of repetitions, Dynamo will take the maximal number of repetitions for the given volume. If the volume is of size N pixels and the operator carries an axial rise of dz pixels, the maximal number of translations along the z axis is floor(N/dz)