SECTION 3

Reweighting

The final stage of our calculation is to use probability generated by TASS simulation to get the free energy surface. But in TASS simulation we have applied MTD bias in 33 umbrella windows which will give biased probability distribution. We need to get unbiased probability distribution by reweighting and then patching all the umbrella windows using Weighted Histogram Analysis Method (WHAM).

Following instructions are given to reweight and generate free energy surface:

  • Compile the metadynamics unbiasing code.
$ gfortran mtd_reweighting_tass.f
  • Prepare the input files (COLVAR, HILLS, run.sh).

If one is using PLUMED for running simulations output files can be directly used. (Remove commented lines from COLVAR and HILLS file.)

COLVAR file should have following information :

<Time> <CV1(ϕ1)> <CV2 (ϕ2)> <CV3 (ψ1)> <CV4 (ψ2)>

HILLS file should have the following information: 

<Time> <Hill position> <Hill width> <Hill height>

run.sh has following information:

-T0:     (value in K) temperature of physical system. (Default: 300 K)
-T:      (value in K) temperature of auxiliary variable. (Default: 300 K)
-dT:     (value in K) ΔT parameter used in WT-MTD. (Default:1500 K)
-tmin:   step number in COLVAR file, from which reweighting should start (Default:1)
-tmax :  step number in COLVAR file, at which reweighting should stop (Default: total number of steps in COLVAR file)
-grid:   <gridmin1> <gridmax1> <gridsize1> of CV1,<gridmin2> <gridmax2> <gridsize2> of CV2,……
-pfrqMD: Number of steps after which COLVAR file is updates
-dtMTD:  Number of steps used to update bias in WTMTD
    • Run command run.sh for processing files from different umbrella windows.
$ sh run.sh

Output file: Probability file (Pu.dat). Rename it as PROB_i, where "i" is the umbrella index. These PROB files contains probability of (Φ1, Ψ1, Φ2, Ψ2).

  • Collect all the PROB_i files in a folder PROB. These PROB_i are the input for WHAM analysis.
  • Compile the WHAM code.
$ mpif90 wham_tass_2D.f90 -o wham_PLUMED_4D.x
  • Prepare WHAM input files (whaminput, input).

input file contain following information:

<No. of CVs> <No. of umbrella windows> <Temperature of auxiliary variable>
<gridmin1> <gridmax1> <gridsize1> of CV1,
<gridmin2> <gridmax2> <gridsize2> of CV2,
…….

Temperature of auxiliary system should be provided in Kelvin. Here, grid information should be same as used during MTD unbiasing.

whaminput file contains following information:

<Convergence criteria>
<Probability file name of umbrella window 1>
<Position of umbrella window> <Force constant> <No of steps used for MTD unbiasing> of umbrella window 1
<Probability file name of umbrella window 2>
<Position of umbrella window> <Force constant> <No of steps used for MTD unbiasing> of umbrella window 2
…..
<Probability file name of umbrella window h>
<Position of umbrella window> <Force constant> <No of steps used for MTD unbiasing> of umbrella window h

  • Run the executable (wham_PLUMED_4D.x). 
$ mpirun –np 8 wham_PLUMED_4D.x (Running on 8 processors)

or

$ ./wham_PLUED_4D.x

Input file: PROB_i, whaminput, input

Output file: free_energy, which contains the free energies.

We can project the reconstructed the 5-dimensional free energy surface on (Φ1, Φ2) plane. Here, energy is in kcal/mol.


The convergence along Φ1 and Φ2 is as follows: