To conduct umbrella sampling, one must generate a series of configurations along a reaction coordinate, ζ. Some of these configurations will serve as the starting configurations for the umbrella sampling windows, which are run in independent simulations. The figure below illustrates these principles. The top image illustrates the pulling simulation we will run now, conducted in order to generate a series of configurations along the reaction coordinate. These configurations are extracted after the simulation is complete (dashed arrows in between the top and middle images). The middle image corresponds to the independent simulations conducted within each sampling window, with the center of mass of the free peptide restrained in that window by an umbrella biasing potential. The bottom images shows the ideal result as a histogram of configurations, with neighboring windows overlapping such that a continuous energy function can later be derived from these simulations.

For this example, the reaction coordinate is the z-axis. To generate these configurations, we must pull peptide A away from the protofibril. We will pull over the course of 500 ps of MD, saving snapshots every 1 ps. This setup has been established based on trial-and-error to obtain a reasonable distribution of configurations. In other systems, it may be necessary to save configurations more often, or sufficient to save configurations less often. The idea is to capture enough configurations along the reaction coordinate to obtain regular spacing of the umbrella sampling windows, in terms of center-of-mass distance between peptides A and B, the latter of which is our reference group.

The .mdp file for this pulling can be found here. A brief explanation of the pulling options used is as follows:

; Pull code
pull            = umbrella
pull_geometry   = distance      ; simple distance increase
pull_dim        = N N Y
pull_start      = yes           ; define initial COM distance > 0
pull_ngroups    = 1
pull_group0     = Chain_B
pull_group1     = Chain_A
pull_rate1      = 0.01          ; 0.01 nm per ps = 10 nm per ns
pull_k1         = 1000          ; kJ mol^-1 nm^-2

• pull = umbrella: using a harmonic potential to pull. IMPORTANT: This procedure is NOT umbrella sampling. I used a harmonic potential in order to make qualitative observations about the dissociation pathway in this study. The harmonic potential allows the force to vary according to the nature of the interactions of peptide A with peptide B. That is, the force will build up until certain critical interactions are broken. See our paper for details. For the purposes of generating the initial configurations for umbrella sampling, you can actually use any combination of pull settings (pull and pull_geometry), but when it comes time for the actual umbrella sampling (in the next step) you MUST be using pull = umbrella. It is very important that you do not apply extremely fast pulling rates or extremely strong force constants, which can seriously deform elements of your system. Please refer to paper (particularly the Supporting Information) for how we chose to validate the pull rate used.
• pull_geometry = distance: see the note the in .mdp file; you can also use position or direction, but changes will have to be made to other pulling parameters. This tutorial makes use of a relatively simple example; for more about the different pull_geometry settings, click here.
• pull_dim = N N Y: we are pulling only in the z-dimension. Thus, x and y are set to "no" (N) and z is set to "yes" (Y).
• pull_start = yes: the initial COM distance is the reference distance for the first frame. This is useful because if we are attempting to pull 5.0 nm, converting the initial COM distance to zero (i.e., pull_start = no) makes this interpretation difficult.
• pull_ngroups = 1: we are only applying a pulling force to one group.
• pull_group0 = Chain_B: reference group for pulling.
• pull_group1 = Chain_A: group to which pulling force is applied.
• pull_rate1 = 0.01: the rate at which the "dummy particle" attached to our pull group is moved. This type of pulling is also called "constant velocity" due to the fact that this rate is fixed.
• pull_k1 = 1000: the force constant for pulling.

Remember that #ifdef POSRES_B statement we added to topol_B.itp a while ago? We're going to use it now. By restraining peptide B of the protofibril, we are able to more easily pull peptide A away. Due to the extensive non-covalent interactions between chains A and B, if we did not restrain chain B, we would end up simply towing the whole complex along the simulation box, which wouldn't accomplish much.

We will need to define some custom index groups for this pulling simulation. Use make_ndx:

make_ndx -f npt.gro
(> indicates the make_ndx prompt)
> r 1-27
> name 19 Chain_A
> r 28-54
> name 20 Chain_B
> q

Now, run the continuous pulling simulation:

grompp -f md_pull.mdp -c npt.gro -p topol.top -n index.ndx -t npt.cpt -o pull.tpr
mdrun -s pull.tpr

Again, this procedure will take some time, so run it in parallel if you have the resources available to you. Once this simulation is complete, we will need to extract useful frames for defining the umbrella sampling windows. The easiest way I have found to do this is the following:

1. Define the spacing of the windows (generally 0.1 - 0.2 nm)
2. Extract all the frames from the pulling trajectory that was just produced
3. Measure the COM distance of each of these frames between the reference and pull group
4. Use the selected frames for umbrella sampling input

To extract the frames from your trajectory (traj.xtc), use trjconv:

trjconv -s pull.tpr -f traj.xtc -o conf.gro -sep

A series of coordinate files (conf0.gro, conf1.gro, etc) will be produced, corresponding to each of the frames saved in the continuous pulling simulation. To iteratively call g_dist on all of these (501!) frames that were generated, I have written a Perl script that takes care of this task. It will print a file called "summary_distances.dat" that contains this information. The script can be found here. We will need to make use of the index file again, as well as a text file called "groups.txt," which will be used to select our analysis groups non-interactively. The contents of groups.txt should be:

19
20

The groups.txt file can be created with a plain text editor. Once you have this file, change the .txt file extension of distances.txt (linked above) to .pl and execute the script:

perl distances.pl

Look at the contents of summary.dat to see the progression of COM distance between chain A and chain B over time. Make note of the configurations to be used for umbrella sampling, based on the desired spacing. That is, if you want 0.2-nm spacing, you might find the following lines in summary.dat:

50     0.600
...
100    0.800

You would then use conf50.gro and conf100.gro as the starting configurations of two adjacent umbrella sampling windows. Make note of all the configurations you wish to use before continuing. For the purposes of this tutorial, identifying configurations with 0.2-nm spacing will suffice, although in the original work a different (more detailed) spacing was used.