{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercise: Molecular Dynamics with OpenMM – Solution"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-02T08:41:57.017179Z",
"start_time": "2020-07-02T08:41:56.478203Z"
}
},
"outputs": [],
"source": [
"from IPython.core.display import display, HTML\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import simtk.openmm as mm # Main OpenMM functionality\n",
"import simtk.openmm.app as app # Application layer (handy interface)\n",
"import simtk.unit as unit # Unit/quantity handling"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-02T08:41:59.476097Z",
"start_time": "2020-07-02T08:41:59.451380Z"
}
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Jupyter notebook configuration\n",
"display(HTML(\"\"))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-02T08:41:59.700080Z",
"start_time": "2020-07-02T08:41:59.647628Z"
},
"run_control": {
"marked": true
}
},
"outputs": [],
"source": [
"# matplotlib configuration\n",
"mpl.rc_file(\"../../matplotlibrc\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inspect the system"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Go to the website of the [RCSB protein data bank](https://www.rcsb.org/)\n",
"and download the *solution NMR structure of a small peptide* with the PDB-ID 6a5j as .pdb-textfile.\n",
"Open the .pdb-file with the text editor of your choice\n",
"and identify the section in which the molecular structure is described."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ How many residues and atoms does the molecule have?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*The peptide has 13 residues and 260 atoms.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Ways to find out:* \n",
" - *Inspect the .pdb text file*\n",
" - *Load the .pdb file with a molecule viewer (VMD)*\n",
" - *Load the .pdb file with OpenMM*"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:33:28.191465Z",
"start_time": "2020-06-30T07:33:27.935342Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"molecule = app.PDBFile(\"md_openmm/6a5j.pdb\")\n",
"molecule.topology"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - Parse the .pdb file with Python"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T07:41:44.043154Z",
"start_time": "2020-07-01T07:41:44.027736Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The structure contains:\n",
" 13 residues:\n",
" ILE LYS LYS ILE LEU SER LYS ILE LYS LYS LEU LEU LYS\n",
"\n",
" 260 atoms\n",
"\n",
" 20 frames\n",
"\n"
]
}
],
"source": [
"with open(\"md_openmm/6a5j.pdb\") as pdbfile:\n",
" print(\"The structure contains:\")\n",
" atom_count = 0 # How many atoms?\n",
" model_count = 0 # How many frames?\n",
" for line in pdbfile:\n",
" if line.startswith(\"SEQRES\"):\n",
" print(f\" {line.split()[3]} residues:\")\n",
" print(f\" {' '.join(line.split()[4:])}\\n\")\n",
" continue\n",
" if line.startswith(\"MODEL\"):\n",
" model_count += 1\n",
" atom_count = 0\n",
" continue\n",
" if line.startswith(\"ATOM\"):\n",
" atom_count += 1\n",
" continue\n",
" print(f\" {atom_count} atoms\\n\")\n",
" print(f\" {model_count} frames\\n\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __b)__ Copy the atom definitions for the second amino acid residue and include it in your report."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T07:49:27.799754Z",
"start_time": "2020-07-01T07:49:27.776698Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ATOM 22 N LYS A 2 -7.295 3.130 -0.024 1.00 0.08 N\n",
"ATOM 23 CA LYS A 2 -6.396 2.084 -0.500 1.00 0.07 C\n",
"ATOM 24 C LYS A 2 -6.593 0.793 0.291 1.00 0.08 C\n",
"ATOM 25 O LYS A 2 -6.656 0.809 1.521 1.00 0.09 O\n",
"ATOM 26 CB LYS A 2 -4.934 2.531 -0.384 1.00 0.08 C\n",
"ATOM 27 CG LYS A 2 -4.546 3.653 -1.334 1.00 0.11 C\n",
"ATOM 28 CD LYS A 2 -3.114 4.126 -1.099 1.00 0.12 C\n",
"ATOM 29 CE LYS A 2 -3.033 5.105 0.061 1.00 0.62 C\n",
"ATOM 30 NZ LYS A 2 -3.301 4.453 1.372 1.00 1.15 N\n",
"ATOM 31 H LYS A 2 -6.928 3.882 0.486 1.00 0.19 H\n",
"ATOM 32 HA LYS A 2 -6.625 1.895 -1.537 1.00 0.09 H\n",
"ATOM 33 HB2 LYS A 2 -4.750 2.865 0.626 1.00 0.10 H\n",
"ATOM 34 HB3 LYS A 2 -4.298 1.682 -0.589 1.00 0.10 H\n",
"ATOM 35 HG2 LYS A 2 -4.633 3.296 -2.350 1.00 0.13 H\n",
"ATOM 36 HG3 LYS A 2 -5.218 4.485 -1.184 1.00 0.12 H\n",
"ATOM 37 HD2 LYS A 2 -2.484 3.270 -0.879 1.00 0.56 H\n",
"ATOM 38 HD3 LYS A 2 -2.756 4.613 -1.994 1.00 0.49 H\n",
"ATOM 39 HE2 LYS A 2 -2.043 5.536 0.080 1.00 1.15 H\n",
"ATOM 40 HE3 LYS A 2 -3.759 5.890 -0.097 1.00 1.06 H\n",
"ATOM 41 HZ1 LYS A 2 -2.685 3.624 1.493 1.00 1.67 H\n",
"ATOM 42 HZ2 LYS A 2 -4.292 4.147 1.422 1.00 1.71 H\n",
"ATOM 43 HZ3 LYS A 2 -3.118 5.123 2.147 1.00 1.58 H\n"
]
}
],
"source": [
"print_residue = 2\n",
"with open(\"md_openmm/6a5j.pdb\") as pdbfile:\n",
" for line in pdbfile:\n",
" if not line.startswith(\"ATOM\"):\n",
" continue\n",
" if int(line[22:26]) < print_residue:\n",
" continue\n",
" if int(line[22:26]) > print_residue:\n",
" break\n",
" print(line.strip())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Open the .pdb-file in VMD.\n",
"\n",
" - __c)__ How many structures are contained in the file?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*The .pdb-file contains 20 structures.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __d)__ Set the background colour to white and remove the axis icon.\n",
"Visualise the peptide structure in a representation that emphasises the secondary structure (e.g. *NewCartoon*, *NewRibbons*, ...) and choose *Secondary Structure* as colouring method.\n",
"Visualise the side chain of lysines in the structure in a representation that shows bonds and atoms (e.g. *Licorice*, *CPK*, ...) and color them by chemical element.\n",
"Render an image of the first structure frame and include it in your\n",
"report."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __e)__ The structure file contains hydrogens. What is the total charge of the peptide?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Rational approach__ *The peptide has 6 lysine residues in its sequence. All lysine side chains are protonated and the total charge of the molecule is +6*."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Forcefield approach__ *Get the total charge of the system from the partial charges of the atoms:*"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:33:36.621320Z",
"start_time": "2020-06-30T07:33:36.334920Z"
}
},
"outputs": [],
"source": [
"forcefield = app.ForceField(\"amber14/protein.ff14SB.xml\")\n",
"system = forcefield.createSystem(molecule.topology)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:33:37.154969Z",
"start_time": "2020-06-30T07:33:37.139706Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\n",
"\n",
"\n"
]
}
],
"source": [
"for force in system.getForces():\n",
" print(type(force))\n",
" if isinstance(force, mm.openmm.NonbondedForce):\n",
" # For charges, we are only interested in the non-bonded forces\n",
" nonbonded = force"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A non-bonded force entry of an atom looks like this:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:34:09.098321Z",
"start_time": "2020-06-30T07:34:09.084371Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[Quantity(value=0.0311, unit=elementary charge),\n",
" Quantity(value=0.3249998523775958, unit=nanometer),\n",
" Quantity(value=0.7112800000000001, unit=kilojoule/mole)]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nonbonded.getParticleParameters(0)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:33:38.642730Z",
"start_time": "2020-06-30T07:33:38.638591Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Partial charge 0.0311 e\n",
"Minimum energy distance 0.3249998523775958 nm\n",
"Minimum energy 0.7112800000000001 kJ/mol\n"
]
}
],
"source": [
"force_description = zip(\n",
" [\"Partial charge\", \"Minimum energy distance\", \"Minimum energy\"],\n",
" nonbonded.getParticleParameters(0)\n",
")\n",
"\n",
"for desc, comp in force_description:\n",
" print(f\"{desc:<26} {comp}\")"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:33:40.437126Z",
"start_time": "2020-06-30T07:33:40.429946Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"5.999999999999995"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"total_charge = 0.\n",
"for i in range(nonbonded.getNumParticles()):\n",
" nb_i = clePnonbonded.getPartiarameters(i)\n",
" total_charge += nb_i[0].value_in_unit(unit.elementary_charge)\n",
"total_charge"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2020-06-30T07:35:42.178777Z",
"start_time": "2020-06-30T07:35:42.164249Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"round(total_charge)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Prepare the structure"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Save the first structure included in the .pdb-file to a new separate\n",
".pdb file, e.g. *conf.pdb*. We want to use this frame as\n",
"starting structure for our simulation.\n",
"Use OpenMM to load the structure into memory."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Ways to achieve this:* \n",
" - *Copy the ATOM entries for MODEL 1 manually to a new file*\n",
" - *Use File > Save Coordinates dialog in VMD*\n",
" - *Parse the file with Python*"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:00:13.657571Z",
"start_time": "2020-07-01T08:00:13.638562Z"
}
},
"outputs": [],
"source": [
"with open(\"md_openmm/6a5j.pdb\") as pdbfile:\n",
" with open(\"md_openmm/conf.pdb\", 'w') as newfile:\n",
" model_count = 0\n",
" for line in pdbfile:\n",
" if line.startswith(\"MODEL\"):\n",
" model_count += 1\n",
" if model_count > 1:\n",
" break\n",
" continue\n",
" if not line.startswith(\"ATOM\"):\n",
" continue\n",
" newfile.write(line)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-02T08:42:08.207761Z",
"start_time": "2020-07-02T08:42:08.142822Z"
}
},
"outputs": [],
"source": [
"molecule = app.PDBFile(\"md_openmm/conf.pdb\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ Investigate the topology attribute of the loaded molecule. How many covalent bonds are present?"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-02T08:42:54.695050Z",
"start_time": "2020-07-02T08:42:54.665385Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"print(molecule.topology)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __b)__ We want to simulate the molecule using the AMBER 14SB force field in TIP3P water. Create a forcefield object suitable for this purpose."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:29.004956Z",
"start_time": "2020-07-01T08:39:28.795742Z"
}
},
"outputs": [],
"source": [
"forcefield = app.ForceField(\n",
" \"amber14/protein.ff14SB.xml\",\n",
" \"amber14/tip3p.xml\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __c)__ Our structure file does not include solvent and has a non-zero total charge. Put the molecule in a cubic water box with a minimum distance of 1 nm to the box boarders. Make sure that also counter ions are added to neutralise the system."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"model = app.Modeller(molecule.topology, molecule.positions)\n",
"model.addSolvent(\n",
" forcefield,\n",
" padding=1 * unit.nanometer,\n",
" neutralize=True\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __d)__ Save the modified structure (peptide plus solvent and ions) to a .pdb-file.\n",
"Load the structure into VMD and visualise the peptide as before. Additionally show ions as van-der-Waals spheres and water molecules within a distance of 2 Å in the *Licorice* representation. __Optional__ Add a transparent surface representation (e.g. *QuickSurf*) for the peptide."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"molecule.positions = model.getPositions()\n",
"molecule.topology = model.getTopology()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"with open(\"md_openmm/solv.pdb\", \"w\") as file_:\n",
" molecule.writeFile(\n",
" molecule.topology, molecule.positions,\n",
" file=file_\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Setup"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ Create a system object from the topology of the solvated peptide with the forcefield you setup earlier. Use H-bonds constraints, and PME for nonbonded interactions (cutoff 1 nm)."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:22.211165Z",
"start_time": "2020-07-01T08:39:21.733922Z"
}
},
"outputs": [],
"source": [
"molecule = app.PDBFile(\"md_openmm/solv.pdb\")"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:34.024830Z",
"start_time": "2020-07-01T08:39:33.765468Z"
}
},
"outputs": [],
"source": [
"system = forcefield.createSystem(\n",
" molecule.topology,\n",
" nonbondedMethod=app.PME,\n",
" nonbondedCutoff=1 * unit.nanometer,\n",
" constraints=app.HBonds\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __b)__ We want to simulate in the *NVT* ensemble. Add an Andersen thermostat to the system to keep the temperature at 300 K (coupling rate 1/ps)."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:36.297499Z",
"start_time": "2020-07-01T08:39:36.279060Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"5"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"system.addForce(\n",
" mm.AndersenThermostat(300 * unit.kelvin, 1 / unit.picosecond)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __c)__ We want to propagate the simulation using a Verlet integrator in timesteps of 2 fs (we need a contraint tolerance of 0.00001). Setup a simulation object with the solvated topology, the system and the integrator. Use `\"CPU\"` as the simulation platform."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:40.913769Z",
"start_time": "2020-07-01T08:39:40.880457Z"
}
},
"outputs": [],
"source": [
"integrator = mm.VerletIntegrator(2.0*unit.femtoseconds)\n",
"integrator.setConstraintTolerance(0.00001)\n",
"\n",
"simulation = app.Simulation(\n",
" molecule.topology, # Topology\n",
" system, # System\n",
" integrator, # Integrator\n",
" mm.Platform.getPlatformByName('CPU') # Platform\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:10:45.239892Z",
"start_time": "2020-07-01T08:10:45.225072Z"
}
},
"source": [
"*How to figure out which platform to use?*"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:14:01.518063Z",
"start_time": "2020-07-01T08:14:01.503579Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n_platforms = mm.Platform.getNumPlatforms() # How many platforms are supported?\n",
"n_platforms"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:14:23.611169Z",
"start_time": "2020-07-01T08:14:23.591267Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reference\n",
"CPU\n"
]
}
],
"source": [
"for i in range(n_platforms):\n",
" print(mm.Platform.getPlatform(i).getName())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __d)__ Add the current atomic positions of the solvated peptide to the context of the simulation."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"simulation.context.setPositions(molecule.positions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Energy minimisation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ Minimise the energy of the system. Save the new positions to a .pdb-file."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"simulation.minimizeEnergy()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"state = simulation.context.getState(getPositions=True)\n",
"molecule.positions = state.getPositions()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"with open(\"md_openmm/min.pdb\", \"w\") as file_:\n",
" molecule.writeFile(\n",
" molecule.topology, molecule.positions,\n",
" file=file_\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ Open the structure in VMD and render an image the same way as in the last step in which the original and the minimised atoms are overlaid. Choose different colors for the two states. Can you see the difference?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Equilibration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ We now want to equilibrate our system in the *NVT* ensemble for 100 ps. Add a state reporter to the simulation object that reports the total and potential energy and the temperature at every picosecond and write it to a file (e.g. `equilibration.log`)."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:39:57.642065Z",
"start_time": "2020-07-01T08:39:57.114149Z"
}
},
"outputs": [],
"source": [
"molecule = app.PDBFile(\"md_openmm/min.pdb\")\n",
"simulation.context.setPositions(molecule.positions)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"run_length = 50000 # 50000 * 2 fs = 100 ps\n",
"simulation.reporters.append(\n",
" app.StateDataReporter(\n",
" \"md_openmm/equilibration.log\", 500, step=True,\n",
" potentialEnergy=True, totalEnergy=True,\n",
" temperature=True, progress=True,\n",
" remainingTime=True, speed=True,\n",
" totalSteps=run_length,\n",
" separator='\\t')\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __b)__ Run the simulation. It should take about 10 minutes to complete on a processor with 4 cores. Reduce the number of steps, if it takes much longer on your hardware."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"run_control": {
"marked": false
}
},
"outputs": [],
"source": [
"simulation.step(run_length)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __c)__ Plot the energies against the simulation time step."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:38:21.270030Z",
"start_time": "2020-07-01T08:38:21.259710Z"
}
},
"outputs": [],
"source": [
"pot_e = []\n",
"tot_e = []\n",
"temperature = []\n",
"\n",
"with open(\"md_openmm/equilibration.log\") as file_:\n",
" for line in file_:\n",
" if line.startswith(\"#\"):\n",
" continue\n",
" pot_e_, tot_e_, temperature_ = line.split()[2:5]\n",
" pot_e.append(float(pot_e_))\n",
" tot_e.append(float(tot_e_))\n",
" temperature.append(float(temperature_))\n",
" \n",
" # Alternative solution:\n",
" # for l, v in zip((pot_e, tot_e, temperature), line.split()[2:5]):\n",
" # l.append(float(v))\n",
"\n",
"t = range(1, 101)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:38:30.851767Z",
"start_time": "2020-07-01T08:38:29.482167Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.plot(t, [x / 1000 for x in pot_e], label=\"potential\")\n",
"ax.plot(t, [x / 1000 for x in tot_e], label=\"total\")\n",
"\n",
"ax.set(**{\n",
" \"xlabel\": \"time / ps\",\n",
" \"xlim\": (0, 100),\n",
" \"ylabel\": \"energy / 10$^{3}$ kJ mol$^{-1}$\"\n",
" })\n",
"\n",
"ax.legend(\n",
" framealpha=1,\n",
" edgecolor=\"k\",\n",
" fancybox=False\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __d)__ Plot the temperature against the simulation time step."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:38:41.262117Z",
"start_time": "2020-07-01T08:38:40.980821Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0, 0.5, 'temperature / K'), (0, 100), Text(0.5, 0, 'time / ps')]"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.plot(t, temperature)\n",
"\n",
"ax.set(**{\n",
" \"xlabel\": \"time / ps\",\n",
" \"xlim\": (0, 100),\n",
" \"ylabel\": \"temperature / K\"\n",
" })"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __e)__ Save the current state of the simulation to an .xml-file."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"simulation.saveState(\"md_openmm/eq.xml\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Production"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __a)__ Load the state of the equilibrated system into the simulation object."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"ExecuteTime": {
"end_time": "2020-07-01T08:40:08.197285Z",
"start_time": "2020-07-01T08:40:08.114918Z"
}
},
"outputs": [],
"source": [
"simulation.loadState(\"md_openmm/eq.xml\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __b)__ Reset the simulation reporters. Let's now assume we want to simulate the system for 100 ns. Add a state reporter to the simulation object that reports the potential energy every 10 ps and writes it to a file (e.g. `simulation.log`). Add a structure reporter that saves the current atom positions to a .pdb-file every 10 ps."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"simulation.reporters = []\n",
"\n",
"run_length = 50000000 # 50000000 * 2 fs = 100 ns\n",
"simulation.reporters.append(\n",
" app.StateDataReporter(\n",
" \"md_openmm/simulation.log\", 5000, step=True,\n",
" potentialEnergy=True,\n",
" temperature=True, progress=True,\n",
" remainingTime=True, speed=True,\n",
" totalSteps=run_length,\n",
" separator='\\t')\n",
" )\n",
"\n",
"simulation.reporters.append(\n",
" app.PDBReporter('run.pdb', 5000)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __c)__ The simulation can easily take several days to finish, depending on the used hardware, so you do not have to run it yourself completely. Just start the simulation to see if everything works and run it until the first structure has been saved by the structure reporter (after 10 ps)."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"run_control": {
"marked": false
}
},
"outputs": [],
"source": [
"simulation.step(5100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - __d)__ Open the saved .pdb-file in VMD. Render an image that shows only the peptide in a representation which emphasises the secondary structure and compares the original to the minimised and the current conformation. Align the structures (e.g. using the *RMSD Trajectory Tool*)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.10"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}