AMBER TI Tutorials

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Introduction to TIMD

This is a TIMD tutorial based on the tutorial written by Thomas Steinbrecher. But some important changes have been made to suit the current AMBER 10 version according to Miranda's tutorial from Simmerling's lab.

And this is my own version of TIMD of the T4-L99A enzyme, the results are a little different from Thomas' results due to some changes in the parameters. Always remember that the experimental value is the absolute criteria.

In this tutorial, free energy calculations will be used to calculate the relative binding free energy of two simple ligands, benzene and phenol to the T4-lysozyme mutant L99A. Free energies will be computed by using the thermodynamic integration facilities of the sander program. A modified van-der-Waals equation (softcore potentials) are used to ensure smooth free energy curves.

Thermodynamic cycle and Method

To calculate the binding energy difference between two ligands, look at the thermodynamic cycle on the left.

TI calculations compute the free energy difference between two states A and B by coupling them via a parameters λ that serves as an additional, nonspatial coordinate. This λ formalism allows the free energy difference between the states to be computed as in the equation shown on the right.

λ formalism for thermodynamic integration

From the pictures above, you can see that Processes A and B represent the binding of two different ligands to a protein, while processes C and D are transformations from one ligand to the other while it is bound to the protein (C) or simply solvated in water (D).

Since Δ GC-Δ GD = Δ GA-Δ GB, TI calculations can be used to compute relative binding free energies, making them useful tools in drug design or lead optimization applications.

Preparation for setup of the T4 L99A System

The two ligands were sketched and parametrized with gaff atom types and resp charges were generated using antechamber on gaussian03 output files. (Please refer to a basic AMBER tutorial on how to use the antechamber tools to parametrize a ligand. The benzene and phenol molecules were saved in two OFF-libraries (benz.lib and phen.lib) for further use. The screenshot shows that C6 was selected as the position bearing the hydroxyl group in phenol.

You can get the OFF-libraries from Shun or just download it from the following links:benz.lib and phen.lib.

We are going to use the X-ray structure of T4-L99A from the pdb (after stripping water molecules and unneeded heteroatoms from it: pdb file) as basis to set up our simulation files. Generally, you can strip the waters and other unneeded molecules in another software, but here the modified pdb file is already provided.

We will use two runs of leap to produce four sets of parameter and restart files, containing both ligands in the protein bound and solvated states.

Notice if there are sharp changes in the TIMD process, more sets of parameter and restart files are required(generally 6 sets). For example, in Miranda's tutorial, she has 3 sets of topology/coordinate files for each transformation: two 'original' endpoint files generated directly from crystal/MD structures, one 'fake' endpoint file generated by mutating one 'original' endpoint file. Thus totally 6 sets of files for her tutorial.

tleap to generate sets of parameter and restart files

We will use two runs of leap to produce four set of parameter and restart files, containing both ligands in the protein bound and solvated states. The first leap run (input file) will produce pdb files of the solvated und neutralized benzene complex and of the benzene ligand in water (complex.pdb and ligand.pdb). From these two additional pdb files are made by renaming the BNZ molecule to PHN and deleting H6 (t4_phn.pdb and phn.pdb).

The script for first tleap run:

source leaprc.ff03
source leaprc.gaff
loadoff benz.lib

complex = loadpdb 181L_mod.pdb
solvatebox complex TIP3PBOX 12
addions complex Cl- 0
savepdb complex complex.pdb

ligand = copy BNZ
solvatebox ligand TIP3PBOX 12
savepdb ligand ligand.pdb


These four pdb files are then used in a second leap run (input file) to generate the *.prm and *.rst files. This yields 4 parameter and 4 rst files.

The script for second tleap run:

source leaprc.ff03
source leaprc.gaff
loadoff benz.lib
loadoff phen.lib

complex = loadpdb complex.pdb
setbox complex vdw
savepdb complex t4_bnz_leap.pdb
saveamberparm complex t4_bnz.prm t4_bnz.rst

ligand = loadpdb ligand.pdb
setbox ligand vdw
savepdb ligand bnz_leap.pdb
saveamberparm ligand bnz.prm bnz.rst

complex = loadpdb t4_phn.pdb
setbox complex vdw
savepdb complex t4_phn_leap.pdb
saveamberparm complex t4_phn.prm t4_phn.rst

ligand = loadpdb phn.pdb
setbox ligand vdw
savepdb ligand phn_leap.pdb
saveamberparm ligand phn.prm phn.rst

Start Structures Results and scripts preparation

After the following steps, you should already have 4 sets of starting structures for the system. Now we should focus on the scripts used to run the thermodynamics integration.

you can get these sets of files from Shun, or download them from the Thomas site.

There are totally 6 directories for you to make a 3-step change in 2 different environments. Moreover, in each directory, you should do 3 steps for a complete simulation: minimization, equilibration, production.

In this case, we will do:

  • 500 steps of steepest descent minimization (the only kind working with TI)
  • 50 ps of density equilibration (equilibrating T and δ at the same time is not very good form, but we'll get away with it here
  • 200 ps of NPT production MD to collect dV/dλ data

The following is a short description of the script:

minimization:

COMMENT: this is a minimization
 &cntrl
  imin = 1,     ntx = 1,
  maxcyc=500,
  ntpr = 100,
  ntf = 2,      ntc = 2,
  ntb = 1,      cut = 9.0,
  icfe=1,       clambda = 0.${X},
  ifsc=0,
  crgmask='${mask0}',
 &end

equilibration

density equilibration
 &cntrl
  imin = 0,     ntx = 1,        irest = 0,
  ntpr = 2500,  ntwr = 10000,   ntwx = 0,
  ntf = 2,      ntc = 2,
  ntb = 2,      cut = 9.0,
  nstlim = 25000,       dt = 0.002,
  temp0 = 300.0,        ntt = 3,        gamma_ln = 5,
  ntp = 1,      pres0 = 1.0,    taup = 0.2,
  icfe=1,       clambda = 0.${X},
  ifsc=0,
  crgmask='${mask0}',
 &end


production

NPT production
 &cntrl
  imin = 0,     ntx = 5,        irest = 1,
  ntpr = 10000, ntwr = 100000,  ntwx = 10000,
  ntf = 2,      ntc = 2,
  ntb = 2,      cut = 9.0,
  nstlim = 100000,      dt = 0.002,
  temp0 = 300.0,        ntt = 3,        gamma_ln = 2,
  ntp = 1,      pres0 = 1.0,    taup = 2.0,
  icfe=1,       clambda = 0.${X},
  ifsc=0,
  crgmask='${mask0}',
 &end

Remember to change the masks in your actual scripts. The masks here make it easy to reuse the scripts.

When the softcore potential algorithms are activated, the scripts are a little different.

Setup and run MD

I would create 6 directories to run the Thermodynamics Integration Molecular Dynamics separately.

3 steps: removing the charges from benzene, VDW change from benzene to phenol, adding the charges to phenol.

2 environments: unbound water environment and bound with T4 L99A environment.

For the second step which is VDW change from benzene to phenol, some important changes have been made. In AMBER 10, a new kind of method is used: softcore potentials algorithm. Using this algorithm removes the requirement to prepare "dummy" atoms and allows two parameter/top files to have different atoms.

Several things to notice when run the molecular dynamics:

  • you can use different numbers of windows. But when you use the new windows, the original windows' simulation data could also be used.
  • running the minimization separatesly for the VDW change step. Because in this step, only 2 processors could be used to run the minimizations. You can use more processors for the equilibrium and production steps.
  • Make sure to always use Langevin when you are applying soft core potential, for this is a requirement in AMBER manual.
  • ntf should equal 1 for all softcore part. Otherwise, there would be errors or crashes in the SANDER module.
  • Set proper time for the simulations to run. Generally, TIMD will take a lot of time. The with_t4 environment will take much more time for running a simulation. In this example, we use the following setups as Thomas:
    • 500 steps of steepest descent minimization (the only kind working with TI)
    • 50 ps of density equilibration (equilibrating T and δ at the same time is not very good form, but we'll get away with it here
    • 200 ps of NPT production MD to collect dV/dλ data

So the total computing time on seawulf is about 4 hours for no_t4_part, 48 hours for with_t4_part.


the bash scripts for running the simulations on the seawulf are listed below:

no_t4_step1: no_t4_step1_inputgen.bash

no_t4_step2: no_t4_step2_min.bash, no_t4_step2_equiprod.bash

no_t4_step3: no_t4_step3_inputgen.bash

with_t4_step1: with_t4_step1_inputgen.bash

with_t4_step2: with_t4_step2_min.bash, with_t4_step2_equiprod.bash

with_t4_step3: with_t4_step3_inputgen.bash

Post-processing

After running the simulations on the seawulf cluster, you still have plenty of work to do. The analyze of the data is not so straight and you need to write linux scripts using python or perl to extract the data.

I write a python extraction scripts myself to extract the data DVDL and rms data like the following file TIMD_extraction.py. Your should read and know how it works: in that case, you could know how to modify it for your use.

For the integration calculation, Thomas has a PERL script. I have rewritten it by python. You can use or modify both of them according to your needs. The basic direction for writing the integration scripts is to get the width or weight of each lambda value; then you can use the width to calculate everything. Notice that the DV/DL values for Lambda 0 and 1 are just estimations from the adjacent points.

some scripts for analysis:

To use the extraction script, read the instructions in the code carefully, and set the filename variable as you need.

Get the lambda, DVDL, and rms information from the extraction report data; output in the format that could be used for integration

Integration is done using simple error estimation, you can modify the script to use Gaussian error estimation.

Graphs From the Data

Here I will show you the DVDL-lambda data I get from my simulation results. The graph is according to the format of Thomas' tutorials. T4 TIMD results.jpg

T4 data result.jpg

This is the final result of my simulation.

You would find that the main energy difference comes from the step2. This is an interesting phenomenon. Thomas' comment: "One would have expected that the loss of solvation on the polar hydroxyl group might strongly influence the relative binding free energies, but from this calculations, the main difference seems to be the sterical effect of accomodating the bulkier hydroxyl group in the binding site, with electrostatics playing a minor role. This result might however change if the calculation would be refined further."

You can make your own comment from the results. The ability to analyze data is as important as the ability to generate data. ==

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