.. -*- coding: utf-8 -*-

=========================================
RMSD fitting and analysis of a trajectory
=========================================

Trajectory frames are going to be superimposed to a reference frame in
such a way that the root mean squared distance (RMSD)

.. math::

  \mathrm{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_{a,i} - x_{b,i})^2}

is minimized.


Superposition
=============

In order to more clearly show conformational changes, superimpose all
trajectory frames on the CORE domain using :menuselection:`Extensions
--> Analysis --> RMSD Trajectory Tool`

1. selection widget (starts with ``protein``): enter the selection for
   the CORE domain: ``protein and not (resid 30 to 59 122 to 159)``
2. :guilabel:`Selection Modifiers`: *Backbone*
3. :guilabel:`Reference Mol`: *Top*
4. :guilabel:`RMSD`: calculate RMSD (avg should be about 2.6 Å)
5. :guilabel:`ALIGN`: superimpose all frames to the first frame
6. :guilabel:`RMSD`: calculate RMSD (avg should be about 1.5 Å)
7. :menuselection:`File --> Plot Data` to show CORE backbone RMSD over
   time
8. visualize the trajectory


RMSD analysis
=============

Task: Produce a timeseries of the backbone RMSD of the *whole protein*
as a function of time (using :menuselection:`Extensions --> Analysis
--> RMSD Trajectory Tool`)

Questions:

- What is the maximum RMSD?
- How does the RMSD change when you include

  - all atoms?
  - all heavy atoms (i.e., do not use hydrogens)?

- Does your RMSD result depend on the previous superposition step?
- Is the result consistent with the previous result of your `RMSD
  analysis of the static structures`_?

.. _`RMSD analysis of the static structures`:
  https://becksteinlab.physics.asu.edu/pages/courses/2016/PHY542/practicals/vmd/structure/domains.html