Rotation (Euler) angles

[mohamed marzouk]

Hello, 

I attended the great webinar yesterday on BioExcel, and I would like to use MDAnalysis alongside other MD simulation analysis tools like MDtraj.

During my dissociation simulation for protein/DNA complex, the system (protein) rotates (noticed during visual inspection), So I want to quantify this rotation. 

To do so, I want to get the rotation matrix used after alignment to calculate minimized RMSD, from this (Rotation matrix) I can get the angles of rotation. 

I found this MD analysis tutorial  4.2.1.1. RMS-fitting tutorial That shows how to get the rotation matrix.

My Q?

if there any function that can pick up the Euler angles from the rotation matrix?

I am trying to build my code to run all frames of trajectory and calculate the std deviation of these three angles along the whole trajectory. 

If not, can u suggest the other possible ways to obtain these angles ? 

[Oliver Beckstein]

Hi Mohamed,

Welcome to the mailing list and thank you for attending the bioexcel webinar. I think you asked your question there and I suggested you come here.

As you already found out how to get the rotation martrix, look at functions in MDAnalysis.lib.transformations  https://docs.mdanalysis.org/stable/documentation_pages/lib/transformations.html (which is really Christoph Gohlkes transformations package that we are bundling — apparently, it now exists as its own package on pypi https://pypi.org/project/transformations/ ). 

You have to read through the docs to understand how Euler angles are represented – the module is fairly low level and for some reason, not all the docs are actually being built, so looking at the source code  https://github.com/MDAnalysis/mdanalysis/blob/develop/package/MDAnalysis/lib/transformations.py helps.

1) MDAnalysis.lib.transformations.euler_from_matrix() (unfortunately the documentation is missing… see the example code in the docs and the source https://github.com/MDAnalysis/mdanalysis/blob/149eb504e35670568201af28306fa04462f6c100/package/MDAnalysis/lib/transformations.py#L1061 ) : should give you exactly what you want:

a1, a2, a3 =  MDAnalysis.lib.transformations.euler_from_matrix(R, axes=“szxz")

(but check axes convention… I just added the axes keyword as a reminder that it exists!)

2) Not the Euler angles but the rotation axis (vector) and angle: MDAnalysis.lib.transformations.rotation_from_matrix

https://docs.mdanalysis.org/stable/documentation_pages/lib/transformations.html#MDAnalysis.lib.transformations.rotation_from_matrix 

3) MDAnalysis.lib.transformations.decompose_matrix() https://docs.mdanalysis.org/stable/documentation_pages/lib/transformations.html#MDAnalysis.lib.transformations.decompose_matrix will take a 4x4 matrix M (where M[:3, :3] == R and M[:, 3] = M[3, :] == [0, 0, 1]) and give you amongst other things the Euler angles around static (s) x,y, z axes (“sxyz” convention). 

You could write a function that computes the rotation matrix and Euler angles for one frame and then use a similar approach as in https://userguide.mdanalysis.org/stable/examples/analysis/custom_trajectory_analysis.html (see also my other email to the list today https://groups.google.com/g/mdnalysis-discussion/c/nWaRsEh1rww/m/Pmh4QkPsAQAJ ) to get it for your whole trajectory.

Hope this helped!

Oliver

 

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