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@ljmartin
Created September 16, 2023 09:31
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<ForceField>
<AtomTypes>
<Type name="metha-C" class="O" element="C" mass="16.04"/>
</AtomTypes>
<Residues>
<Residue name="UME">
<Atom name="C" type="metha-C"/>
</Residue>
</Residues>
<NonbondedForce coulomb14scale="0.833333" lj14scale="0.5">
<Atom type="metha-C" charge="0.0" sigma="0.373" epsilon="1.230096"/>
</NonbondedForce>
</ForceField>
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "a5c83e4d-eb40-46be-950e-fcb3b4622c37",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning: importing 'simtk.openmm' is deprecated. Import 'openmm' instead.\n"
]
}
],
"source": [
"from simtk.openmm.app import *\n",
"from simtk.openmm import *\n",
"from simtk.unit import *\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import tqdm"
]
},
{
"cell_type": "markdown",
"id": "16e120cf-5f28-4b9f-8a42-8802436afe14",
"metadata": {},
"source": [
"# set up a single united atom methane system\n",
"Start with basically a single LJ particle, and solvate it in water. \n",
"\n",
"Why this system? It's just a test system, used in by Chodera & Shirts in:\n",
"- Replica exchange and expanded ensemble simulations as Gibbs sampling: Simple improvements for enhanced mixing\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "4391009a-33be-46ed-8b52-1acc1e75d9c7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pdb = PDBFile('single_methane.pdb')\n",
"forcefield = ForceField('amber14/tip3pfb.xml', './methane.xml')\n",
"\n",
"modeller=Modeller(pdb.topology, pdb.positions)\n",
"modeller.addSolvent(forcefield, padding=1*nanometer)\n",
"\n",
"system = forcefield.createSystem(modeller.topology, nonbondedMethod=CutoffPeriodic,\n",
" nonbondedCutoff=0.8*nanometer, constraints=HBonds, ewaldErrorTolerance=1e-5)\n",
"\n",
"TEMPERATURE=283*kelvin\n",
"PRESSURE = 1*atmosphere\n",
"TIMESTEP = 2*femtoseconds\n",
"\n",
"barostat = MonteCarloBarostat(PRESSURE, TEMPERATURE)\n",
"system.addForce(barostat)"
]
},
{
"cell_type": "markdown",
"id": "05b6428b-a9b7-448e-a452-70f47f96c514",
"metadata": {},
"source": [
"# add a force to scale the LJ interaction between methane and water\n",
"\n",
"the below just deletes the methane's epsilon from the `NonbondedForce`, while adding a `CustomNonbondedForce` to apply the Lennard-Jones potential between the methane particle and all the water particles. \n",
"\n",
"The `CustomNonbondedForce` has a global parameter that we can switch off to remove the LJ interactions completely. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "04265b7a-6374-4be2-934b-7c879acfb61d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"forces = { force.__class__.__name__ : force for force in system.getForces() }\n",
"nbforce = forces['NonbondedForce']\n",
"\n",
"# Add a CustomNonbondedForce to handle only alchemically-modified interactions\n",
"alchemical_particles = set([0])\n",
"chemical_particles = set(range(system.getNumParticles())) - alchemical_particles\n",
"\n",
"\n",
"##softcore lennard jones: <-- not needed in the SAI approach!\n",
"\n",
"#energy_function = 'lambda*4*epsilon*x*(x-1.0); x = (sigma/reff_sterics)^6;'\n",
"#energy_function += 'reff_sterics = sigma*(0.5*(1.0-lambda) + (r/sigma)^6)^(1/6);'\n",
"#energy_function += 'sigma = 0.5*(sigma1+sigma2); epsilon = sqrt(epsilon1*epsilon2);'\n",
"\n",
"\n",
"#normal lennard jone:\n",
"energy_expression = \"sterics;\"\n",
"energy_expression += \"sterics=scalingFactor*4*epsilon*((sigma/r)^12 - (sigma/r)^6);\"\n",
"energy_expression += \"epsilon = sqrt(epsilon1*epsilon2);\"\n",
"energy_expression += \"sigma = 0.5*(sigma1+sigma2);\"\n",
"\n",
"custom_force = openmm.CustomNonbondedForce(energy_expression)\n",
"custom_force.addGlobalParameter('scalingFactor', 1.0)\n",
"custom_force.addPerParticleParameter('sigma')\n",
"custom_force.addPerParticleParameter('epsilon')\n",
"custom_force.setNonbondedMethod(2)\n",
"custom_force.setCutoffDistance(0.8*nanometer)\n",
"custom_force.setForceGroup(1)\n",
"\n",
"for index in range(system.getNumParticles()): #must add all particles to any nonbonded force\n",
" [charge, sigma, epsilon] = nbforce.getParticleParameters(index)\n",
" custom_force.addParticle([sigma, epsilon]) #charge isn't added because it isn't used.\n",
" \n",
"custom_force.addInteractionGroup(alchemical_particles, chemical_particles)\n",
"system.addForce(custom_force)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "49479a82-91bd-4dc8-984b-8d14ef04a597",
"metadata": {},
"outputs": [],
"source": [
"#remove the methane from the original nonbondedforce by setting it's charge and epsilon parameter to zero:\n",
"nbforce.setParticleParameters(0, 0*elementary_charge, 1*nanometer, 0*kilojoules_per_mole)\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "7326083a-fde9-4f09-b4e1-e14838a965be",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"energy is: -14211.412847552809 kJ/mol\n"
]
}
],
"source": [
"#finally, create the Simulation object:\n",
"\n",
"integrator = LangevinIntegrator(TEMPERATURE, 1/picosecond, TIMESTEP)\n",
"\n",
"platform = Platform.getPlatformByName('OpenCL')\n",
"prop = {'OpenCLPrecision':'single'}\n",
"\n",
"simulation = Simulation(modeller.topology, system, integrator, platform, prop)\n",
"simulation.context.setPositions(modeller.positions)\n",
"simulation.context.setVelocitiesToTemperature(TEMPERATURE)\n",
"\n",
"PDBFile.writeFile(modeller.topology, modeller.positions, file=open('methane.pdb', 'w'))\n",
"simulation.reporters.append(DCDReporter('methane.dcd', 1000))\n",
"\n",
"\n",
"simulation.minimizeEnergy()\n",
"\n",
"print('energy is:', simulation.context.getState(getEnergy=True).getPotentialEnergy())\n"
]
},
{
"cell_type": "markdown",
"id": "9f35db94-3989-4a4a-bc3f-988d8f0e86ff",
"metadata": {},
"source": [
"# Equilibrate the box before doing a calculation"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "ee6d9176-74df-4f15-adf2-74fbc5f84f3b",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/jh/02165y2n7kq2y5ychxtzcjm40000gn/T/ipykernel_30658/2688709138.py:4: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
"Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
" for _ in tqdm.tqdm_notebook(range(300)):\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "5e0974df2d4f4927a3d4ebb5649539ab",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/300 [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pes = list()\n",
"group_p=list()\n",
"vol = list()\n",
"for _ in tqdm.tqdm_notebook(range(300)):\n",
" simulation.step(100)\n",
" state = simulation.context.getState(getEnergy=True)\n",
" pe = state.getPotentialEnergy()\n",
" v = state.getPeriodicBoxVolume() \n",
" pes.append(pe)\n",
" vol.append(v)\n",
" \n",
" \n",
" state = simulation.context.getState(getEnergy=True, groups={1})\n",
" p = state.getPotentialEnergy()\n",
" group_p.append(p)\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "78c81e85-579a-447d-ba5f-e0d804632cce",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,2)\n",
"\n",
"fig.set_figwidth(15)\n",
"fig.set_figheight(5)\n",
"\n",
"ax[0].plot([i/kilojoule*mole for i in pes])\n",
"ax[0].set_ylabel('PE')\n",
"ax[1].plot([i.value_in_unit(nanometer**3) for i in vol])\n",
"ax[1].set_ylabel('Volume')\n",
"\n",
"#we check visually that it's equilibrated, and can then save the positions and velocities. \n",
"state = simulation.context.getState(getPositions=True, getVelocities=True)\n",
"\n",
"equilibrated_positions = state.getPositions()\n",
"equilibrated_velocities = state.getVelocities()\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c53a5244-ffba-4a5b-a930-03953409625e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fe33901a260>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#plot just the energy of the methane nonbonded interactions:\n",
"fig, ax = plt.subplots()\n",
"\n",
"fig.set_figwidth(10)\n",
"fig.set_figheight(5)\n",
"\n",
"ax.plot([i/kilojoule*mole for i in group_p])\n"
]
},
{
"cell_type": "markdown",
"id": "8375b42a-f68e-48ed-9b9e-df8ceed63533",
"metadata": {},
"source": [
"# Let's go. \n",
"We'll do two simulations, and collect 100 samples in each. The first has a fully-interacting methane, i.e. a \"real\" particle. At point, we'll also calculate what the energies would have been if the real particle was actually a \"ghost\" particle, aka dummy atom, aka annihilated particle.\n",
"\n",
"Then we'll do the same thing but the coordinates will be sampled from the \"ghost\" particle regime, while also calculating energies with a \"real\" particle. \n",
"\n",
"This second situation presents a problem! The real particle will sometimes overlap with a water molecule. Since we use the regular LJ potential in the SAI approach, this leads to stupidly high repulsive energies coming from the LJ force. If we had charges, too, then we'd have stupidly high Coulomb potentials, too. \n",
"\n",
"To demonstrate this, we'll use PyMBAR to estimate the free energy difference between the two states. I use the `u_kn` setting, so we just have a matrix of shape (2, 200) - that is, two possible potentials, with 200 samples from configuration space, where each xyz sample is used to calculate the 2 energies. \n",
"\n",
"I'll assume that the energies are uncorrelated in this situation because it's a simple system. If this assumption is violated, we should have error estimates that are _too small_ - i.e. it doesn't invalidate the point here. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "68037181-63ae-478a-8a8f-b88024bf7903",
"metadata": {},
"outputs": [],
"source": [
"u_kn = [ [], [] ] "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "fcee3386-e0cc-4cee-853f-4807a087c8de",
"metadata": {
"scrolled": true,
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 300/300 [04:33<00:00, 1.10it/s]\n"
]
}
],
"source": [
"def getEnergyAt(simulation, scalefactor):\n",
" currFactor = simulation.context.getParameter('scalingFactor')\n",
" simulation.context.setParameter('scalingFactor', scalefactor)\n",
" \n",
" state = simulation.context.getState(getEnergy=True)\n",
" nrg = state.getPotentialEnergy()._value\n",
" \n",
" #return the simulation to whwatever state it was in before we got it.\n",
" simulation.context.setParameter('scalingFactor', currFactor)\n",
" \n",
" return nrg\n",
"\n",
"\n",
"#scale factor of 1 means fully interacting. \n",
"#so to avoid popping into existence, we'll start with a real particle, \n",
"#and then afterwards, make it ghost. \n",
"for i in tqdm.tqdm(range(300)):\n",
" simulation.step(1500)\n",
"\n",
" nrg = getEnergyAt(simulation, 1)\n",
" u_kn[0].append(nrg)\n",
" \n",
" nrg = getEnergyAt(simulation, 0)\n",
" u_kn[1].append(nrg)\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "5e4d1c1a-f122-4cc4-9f0f-6f9939681d5a",
"metadata": {
"scrolled": true,
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 300/300 [04:37<00:00, 1.08it/s]\n"
]
}
],
"source": [
"#now pop it out of existence. \n",
"#and sample for another 100 configurations in this new potential. \n",
"simulation.context.setParameter('scalingFactor', 0)\n",
"for i in tqdm.tqdm(range(300)):\n",
" simulation.step(1500)\n",
"\n",
" nrg = getEnergyAt(simulation, 1)\n",
" u_kn[0].append(nrg)\n",
" \n",
" nrg = getEnergyAt(simulation, 0)\n",
" u_kn[1].append(nrg)"
]
},
{
"cell_type": "markdown",
"id": "2f3a0735-78ec-469e-8fba-cc4e26747c5e",
"metadata": {},
"source": [
"# note a few extremely large energies \n",
"Even though the dynamics aren't affect (i.e. we didn't have explosions!) in practice, the large energies makes it difficult to achieve overlap beween the two states. If we had smoothly interpolated using intermediate lambda states, the start and end points would _also_ not have overlap - but they would have intermediate states that allow an overlapping path. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "810e8f93-5405-4eaa-9239-452c849a5835",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fe2d84a5d20>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(u_kn[0])\n",
"plt.plot(u_kn[1])"
]
},
{
"cell_type": "markdown",
"id": "5b6232f1-a05c-4099-981c-ba7196da9c33",
"metadata": {},
"source": [
"# Finally, calculate free energy difference. \n",
"Observe that it's too big compared to an alchemical lambda schedule using either MBAR or serialized tempering (see graph at end of notebook [at this link here](https://github.com/ljmartin/generalized_tempering/blob/master/fe_of_hydration/fe_of_hydration.ipynb) - I was expecting about 5 kT)\n",
"\n",
"Note also that the overlap between the states is <<< 0.01% "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "b9797c90-4524-45d5-b049-17e5cb6b4209",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning on use of the timeseries module: If the inherent timescales of the system are long compared to those being analyzed, this statistical inefficiency may be an underestimate. The estimate presumes the use of many statistically independent samples. Tests should be performed to assess whether this condition is satisfied. Be cautious in the interpretation of the data.\n",
"WARNING:pymbar.mbar_solvers:\n",
"****** PyMBAR will use 64-bit JAX! *******\n",
"* JAX is currently set to 32-bit bitsize *\n",
"* which is its default. *\n",
"* *\n",
"* PyMBAR requires 64-bit mode and WILL *\n",
"* enable JAX's 64-bit mode when called. *\n",
"* *\n",
"* This MAY cause problems with other *\n",
"* Uses of JAX in the same code. *\n",
"******************************************\n",
"\n"
]
}
],
"source": [
"\n",
"from pymbar import MBAR"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "ea149cd4-b522-47ea-9888-f5aa753688ef",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:pymbar.mbar_solvers:\n",
"******* JAX 64-bit mode is now on! *******\n",
"* JAX is now set to 64-bit mode! *\n",
"* This MAY cause problems with other *\n",
"* uses of JAX in the same code. *\n",
"******************************************\n",
"\n"
]
},
{
"data": {
"text/plain": [
"{'Delta_f': array([[ 0. , -21.45163334],\n",
" [ 21.45163334, 0. ]]),\n",
" 'dDelta_f': array([[ 0. , 15891.54028413],\n",
" [15892.19949939, 0. ]])}"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"result = MBAR(u_kn, [300, 300])\n",
"result.compute_free_energy_differences()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "bae46193-f75b-4167-b306-fbe5ecf7f53b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'scalar': 2.640010432486406e-11,\n",
" 'eigenvalues': array([1., 1.]),\n",
" 'matrix': array([[1.00000000e+00, 1.27341258e-11],\n",
" [1.27341258e-11, 1.00000000e+00]])}"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"overlaps = result.compute_overlap()\n",
"overlaps"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "3ec83787-3496-4fc2-89a6-a183c3536057",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.00000000e+00, 1.27341258e-11],\n",
" [1.27341258e-11, 1.00000000e+00]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"overlaps['matrix']"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4929dff7-08a8-43cc-8e6b-92c516d967f5",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
REMARK 1 CREATED WITH OPENMM 7.1.1, 2018-04-06
CRYST1 24.668 24.668 24.668 90.00 90.00 90.00 P 1 1
HETATM 1 C UME B 1 13.603 1.517 15.610 1.00 0.00 C
END
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