Combining sampling from multiple trials
=======================================

| Erika McCarthy\ :sup:`1`, Şölen Ekesan\ :sup:`1`, and Darrin M.
  York\ :sup:`1`
| :sup:`1`\ Laboratory for Biomolecular Simulation Research, Institute
  for Quantitative Biomedicine and Department of Chemistry and Chemical
  Biology, Rutgers University, Piscataway, NJ 08854, USA

Learning objectives
-------------------

- Analyze combined umbrella sampling for a 1-dimenional reaction using NDFES to generate a PMF from multiple trials

Relevant literature
-------------------

- `Catalytic mechanism and pH dependence of a methyltransferase ribozyme
  (MTR1) from computational
  enzymology <https://academic.oup.com/nar/article/51/9/4508/7127216?login=true>`__
- `Surface-Accelerated String Method for Locating Minimum Free Energy
  Paths <https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c01401>`__
- `Extension of the Variational Free Energy Profile and Multistate
  Bennett Acceptance Ratio Methods for High-Dimensional Potential of
  Mean Force Profile
  Analysis <https://pubs.acs.org/doi/10.1021/acs.jpca.1c00736>`__


Generating a combined PMF
-------------------------

Often times one may break sampling into mulitple trials and create a PMF based on the total combined sampling. .You have been provided the output multiple trials that must be copied to the working directory.

Create a directory called combined_analysis.

List the contents of your working directory. It should be structured as
follows:

.. code-block:: bash

      [user@cluster] cp -r /expanse/projects/qstore/amber_ws/tutorials/QMMM_DFTB3_MTR1/1D/ouputs/t{2..8} ./
      [user@cluster] ls
      combined_analysis  t1  t2  t3  t4  t5  t6  t7  t8  


The structur files have been removed from the output directories for
the sake of file size, but these would have been generated by the
simulations and are not required for analysis. We want to combine the
metafiles from all of the trial directories.


Run the following command to generate metafile.all:

.. code-block:: bash

      [user@cluster] cd combined_analysis
      [user@cluster] ndfes-CombineMetafiles.py -o metafile.all ../t{1..8}/analysis/metafile 

Run the following command to generate metafile.all.chk:

.. code-block:: bash

      [user@cluster] ndfes_omp --mbar -w 0.15 --nboot 0 -c metafile.all.chk metafile.all  

This will generate metafile.all.chk. Finally, we will generate the path
file for the entire PMF.


Run the following command to generate the path file:

.. code-block:: bash

      [user@cluster] ndfes-path_omp --chk metafile.all.chk --ipath metafile.all --npathpts 32 --nsplpts 400 --opath path_all

The ndfes commands are also given in combined_analysis.sh, but for the
sake of understanding the role of each program they have been run one at
a time.

Plot the PMF with xmgrace:

.. code-block:: bash

      [user@cluster] xmgrace -block path_all.rbf.0.dat -bxy 3:4  

| 

.. container::

   .. figure:: /_static/files/ModularTutorials/MTR1_QMMM/PMF_combined.png
      :alt: Figure 3

      **Figure 3.** PMF as a function of reaction coordinate value from
      simulation of all 32 umbrella windows.

Now we can see the full PMF. From this we see that the free energy
barrier for this reaction is ~30 kcal/mol, which is quite high. In 1
dimension it is very clear what the path is from reactants to products,
and we can plot the free energy as a function of a single coordinate.
However, if more reaction coordinates are involved, the path from
reactant to product is less clear. In the following sections you will
see how the use of more reaction coordinates can better model this
reaction.