def getOrderParamq(subPos, Pos, BoxDims, lowCut=0.0, highCut=8.0):
"""Finds angles for 4 nearest neighbors of each water and returns for all waters the
tetrahedral order parameter, q, used by Errington and Debenedetti (2001).
Inputs:
subPos - positions of set of atoms to measure tetrahedrality of (may be different, subset, or same as Pos)
Pos - positions of ALL atoms that can make tetrahedral configurations (needed if subPos not same as Pos)
BoxDims - current box dimensions to account for periodicity
lowCut - lower cutoff for nearest-neighbor shell (default 0.0)
highCut - higher cutoff for nearest-neighbor shell used to find 4 nearest neighbors
Outputs:
qVals - returns an order parameter value for each water
distNeighbs - returns distances from central oxygen to 4 nearest neighbors
"""
#Set-up array to hold results
qVals = np.zeros(len(subPos))
distNeighbs = np.zeros((len(subPos), 4))
#Find nearest neighbors for ALL atoms in subPos
#But make sure using efficient algorithm...
#If subPos is same as Pos, use allnearneighbors instead
if np.array_equal(subPos, Pos):
nearNeighbs = wl.allnearneighbors(Pos, BoxDims, lowCut,
highCut).astype(bool)
else:
nearNeighbs = wl.nearneighbors(subPos, Pos, BoxDims, lowCut,
highCut).astype(bool)
#Loop over each position in subPos, finding angle made with the closest 4 neighbors, then q
for (i, apos) in enumerate(subPos):
#Make sure have nearest neighbors...
if np.sum(nearNeighbs[i]) > 0:
thisPos = wl.reimage(Pos[nearNeighbs[i]], apos, BoxDims)
thisDists = np.linalg.norm(thisPos - apos, axis=1)
sortInds = np.argsort(thisDists)
newPos = thisPos[sortInds][:4]
distNeighbs[i, :] = thisDists[sortInds][:4]
#below returns symmetric, square array (zero diagonal)
tempAng = wl.tetracosang(apos, newPos, BoxDims)
#Only want half of array, flattened
angVals = tempAng[np.triu_indices(len(tempAng), k=1)]
#Now compute q for this set of angles
qVals[i] = 1.0 - (3.0 / 8.0) * np.sum(
(np.cos(angVals * np.pi / 180.0) + (1.0 / 3.0))**2)
#Return all of the order parameter values
return qVals, distNeighbs
def getCosAngs(subPos, Pos, BoxDims, lowCut=0.0, highCut=3.413):
"""This is called getCosAngs, but actually just returns the angles themselves (faster to convert
from cos(theta) to theta in Fortran)
Inputs:
subPos - positions of set of atoms to measure tetrahedrality of (may be different, subset, or same as Pos)
Pos - positions of ALL atoms that can make tetrahedral configurations (needed if subPos not same as Pos)
BoxDims - current box dimensions to account for periodicity
lowCut - lower cutoff for nearest-neighbor shell (default 0.0)
highCut - higher cutoff for nearest-neighbor shell (default 3.413 - see Chaimovich, 2014, but should really
change to reflect first peak in g(r) for the chosen water model)
Outputs:
angVals - all angle values for current configuration of positions supplied
numAngs - number of angles for each central oxygen atom (i.e. number neighbors factorial)
This is useful for finding which angles belong to which central oxygens
This return value was added on 07/09/2017, so any code using this function
before then will break, unfortunately, but the fix is easy.
"""
#Set-up array to hold angle results and stack as go... list increases in size!
angVals = np.array([])
numAngs = np.zeros(len(subPos))
#Find nearest neighbors for ALL atoms in subPos
#But make sure using efficient algorithm...
#If subPos is same as Pos, use allnearneighbors instead
if np.array_equal(subPos, Pos):
nearNeighbs = wl.allnearneighbors(Pos, BoxDims, lowCut,
highCut).astype(bool)
else:
nearNeighbs = wl.nearneighbors(subPos, Pos, BoxDims, lowCut,
highCut).astype(bool)
#Loop over each position in subPos, finding angle made with all neighbor pairs
for (i, apos) in enumerate(subPos):
#Make sure have nearest neighbors...
if len(Pos[nearNeighbs[i]]) > 0:
#below returns symmetric, square array (zero diagonal)
tempAng = wl.tetracosang(apos, Pos[nearNeighbs[i]], BoxDims)
#Only want half of array, flattened
angVals = np.hstack(
(angVals, tempAng[np.triu_indices(len(tempAng),
k=1)].tolist()))
numAngs[i] = tempAng.shape[0]
return angVals, numAngs
def doSimDynamics(top,
systemRef,
integratorRef,
platform,
prop,
temperature,
scalexy=False,
inBulk=False,
state=None,
pos=None,
vels=None,
nSteps=10000000):
#Input a topology object, reference system, integrator, platform, platform properties,
#and optionally state file, positions, or velocities
#If state is specified including positions and velocities and pos and vels are not None, the
#positions and velocities from the provided state will be overwritten
#Does NPT, stopping periodically to run NVE to compute dynamics
#Only the NPT simulation will be saved, not the NVE
#Copy the reference system and integrator objects
system = copy.deepcopy(systemRef)
integrator = copy.deepcopy(integratorRef)
#For NPT, add the barostat as a force
#If not in bulk, use anisotropic barostat
if not inBulk:
system.addForce(
mm.MonteCarloAnisotropicBarostat(
(1.0, 1.0, 1.0) * u.bar,
temperature, #Temperature should be SAME as for thermostat
scalexy, #Set with flag for flexibility
scalexy,
True, #Only scale in z-direction
250 #Time-steps between MC moves
))
#If in bulk, have to use isotropic barostat to avoid any weird effects with box changing dimensions
else:
system.addForce(mm.MonteCarloBarostat(1.0 * u.bar, temperature, 250))
#Create new simulation object for NPT simulation
sim = app.Simulation(top.topology, system, integrator, platform, prop,
state)
#Also create copies and simulation object for the NVE we will be running
systemNVE = copy.deepcopy(systemRef)
integratorNVE = mm.VerletIntegrator(2.0 * u.femtoseconds)
integratorNVE.setConstraintTolerance(1.0E-08)
simNVE = app.Simulation(top.topology, systemNVE, integratorNVE, platform,
prop)
#Set the particle positions in the NPT simulation
if pos is not None:
sim.context.setPositions(pos)
#Apply constraints before starting the simulation
sim.context.applyConstraints(1.0E-08)
#Check starting energy decomposition if want
#decompEnergy(sim.system, sim.context.getState(getPositions=True))
#Initialize velocities if not specified
if vels is not None:
sim.context.setVelocities(vels)
else:
try:
testvel = sim.context.getState(getVelocities=True).getVelocities()
print(
"Velocities included in state, starting with 1st particle: %s"
% str(testvel[0]))
#If all the velocities are zero, then set them to the temperature
if not np.any(testvel.value_in_unit(u.nanometer / u.picosecond)):
print(
"Had velocities, but they were all zero, so setting based on temperature."
)
sim.context.setVelocitiesToTemperature(temperature)
except:
print("Could not find velocities, setting with temperature")
sim.context.setVelocitiesToTemperature(temperature)
#Set up the reporter to output energies, volume, etc.
sim.reporters.append(
app.StateDataReporter(
'prod_out.txt', #Where to write - can be stdout or file name (default .csv, I prefer .txt)
500, #Number of steps between writes
step=True, #Write step number
time=True, #Write simulation time
potentialEnergy=True, #Write potential energy
kineticEnergy=True, #Write kinetic energy
totalEnergy=True, #Write total energy
temperature=True, #Write temperature
volume=True, #Write volume
density=False, #Write density
speed=True, #Estimate of simulation speed
separator=
' ' #Default is comma, but can change if want (I like spaces)
))
#Set up reporter for printing coordinates (trajectory)
sim.reporters.append(
NetCDFReporter(
'prod.nc', #File name to write trajectory to
500, #Number of steps between writes
crds=True, #Write coordinates
vels=True, #Write velocities
frcs=False #Write forces
))
#Identify solute indices and water oxygen indices
soluteInds = []
owInds = []
hw1Inds = []
hw2Inds = []
for res in top.residues:
if res.name not in ['OTM', 'CTM', 'STM', 'NTM', 'SOL']:
for atom in res.atoms:
soluteInds.append(atom.idx)
elif res.name == 'SOL':
for atom in res.atoms:
if atom.name == 'OW':
owInds.append(atom.idx)
elif atom.name == 'HW1':
hw1Inds.append(atom.idx)
elif atom.name == 'HW2':
hw2Inds.append(atom.idx)
print("Solute indices:")
print(soluteInds)
#print("Water oxygen indices:")
#print(owInds)
#print("Water hydrogen (1st) indices:")
#print(hw1Inds)
#print("Water hydrogen (2nd) indices:")
#print(hw2Inds)
#Define cutoffs for solute solvation shells
solShell1Cut = 0.55 #nanometers from all solute atoms (including hydrogens)
solShell2Cut = 0.85
#Create array to store the dynamic information of interest every 0.2 ps (100 steps) for 50 ps
calcSteps = 100
calcTotSteps = 25000
numWats = np.zeros(
(int(calcTotSteps / calcSteps) + 1, 2)
) #Number waters that started in shell that are in shell at later time
dipCorrs = np.zeros((int(calcTotSteps / calcSteps) + 1,
2)) #Dipole correlation in both solute shells
#Start running dynamics
print("\nRunning NPT simulation with interspersed NVE to find dynamics...")
sim.context.setTime(0.0)
stepChunk = 5000 #Run NVE for 50 ps to find dynamics every 10 ps
countSteps = 0
while countSteps < nSteps:
countSteps += stepChunk
sim.step(stepChunk)
#Record the simulation state so can kick off the NVE simulation
thisState = sim.context.getState(getPositions=True, getVelocities=True)
#Get solute and water oxygen coordinates after wrapping around the solute
coords = thisState.getPositions(asNumpy=True)
boxDims = np.diagonal(thisState.getPeriodicBoxVectors(asNumpy=True))
wrapCOM = np.average(coords[soluteInds], axis=0)
coords = wl.reimage(coords, wrapCOM, boxDims) - wrapCOM
solCoords = coords[soluteInds]
owCoords = coords[owInds]
hw1Coords = coords[hw1Inds]
hw2Coords = coords[hw2Inds]
#Figure out which waters are in the solute solvation shells
shell1BoolMat = wl.nearneighbors(solCoords, owCoords, boxDims, 0.0,
solShell1Cut)
shell1Bool = np.array(np.sum(shell1BoolMat, axis=0), dtype=bool)
shell2BoolMat = wl.nearneighbors(solCoords, owCoords, boxDims,
solShell1Cut, solShell2Cut)
shell2Bool = np.array(np.sum(shell2BoolMat, axis=0), dtype=bool)
#Count number of waters in each shell (will need for averaging)
thisCount1 = int(np.sum(shell1Bool))
thisCount2 = int(np.sum(shell2Bool))
#print("Found %i waters in shell1"%thisCount1)
#print("Found %i waters in shell2"%thisCount2)
#Loop over waters in shells and compute dipole vectors as references
refDipoles1 = np.zeros((thisCount1, 3))
refDipoles2 = np.zeros((thisCount2, 3))
for k, pos in enumerate(owCoords[shell1Bool]):
thisOHvecs = wl.reimage(
[hw1Coords[shell1Bool][k], hw2Coords[shell1Bool][k]], pos,
boxDims) - pos
thisDip = -0.5 * (thisOHvecs[0] + thisOHvecs[1])
refDipoles1[k] = thisDip / np.linalg.norm(thisDip)
for k, pos in enumerate(owCoords[shell2Bool]):
thisOHvecs = wl.reimage(
[hw1Coords[shell2Bool][k], hw2Coords[shell2Bool][k]], pos,
boxDims) - pos
thisDip = -0.5 * (thisOHvecs[0] + thisOHvecs[1])
refDipoles2[k] = thisDip / np.linalg.norm(thisDip)
#Set up the NVE simulation
simNVE.context.setState(thisState)
simNVE.context.setTime(0.0)
#Loop over taking steps to computed dynamics
countStepsNVE = 0
while countStepsNVE <= calcTotSteps:
calcState = simNVE.context.getState(getPositions=True)
#Get solute and water oxygen coordinates after wrapping around the solute
coords = calcState.getPositions(asNumpy=True)
wrapCOM = np.average(coords[soluteInds], axis=0)
coords = wl.reimage(coords, wrapCOM, boxDims) - wrapCOM
solCoords = coords[soluteInds]
owCoords = coords[owInds]
hw1Coords = coords[hw1Inds]
hw2Coords = coords[hw2Inds]
#Count waters that started in each shell that are now in the shell at this time
#No absorbing boundaries
thisbool1Mat = wl.nearneighbors(solCoords, owCoords, boxDims, 0.0,
solShell1Cut)
thisbool1 = np.array(np.sum(thisbool1Mat, axis=0), dtype=bool)
thisbool2Mat = wl.nearneighbors(solCoords, owCoords, boxDims,
solShell1Cut, solShell2Cut)
thisbool2 = np.array(np.sum(thisbool2Mat, axis=0), dtype=bool)
numWats[int(countStepsNVE / calcSteps),
0] += int(np.sum(thisbool1 * shell1Bool))
numWats[int(countStepsNVE / calcSteps),
1] += int(np.sum(thisbool2 * shell2Bool))
#Loop over waters in shells and compute dipole vectors for this configuration
#Adding to sum that we will normalize to find average at each time point
for k, pos in enumerate(owCoords[shell1Bool]):
thisOHvecs = wl.reimage(
[hw1Coords[shell1Bool][k], hw2Coords[shell1Bool][k]], pos,
boxDims) - pos
thisDip = -0.5 * (thisOHvecs[0] + thisOHvecs[1])
thisDip /= np.linalg.norm(thisDip)
dipCorrs[int(countStepsNVE / calcSteps),
0] += (np.dot(thisDip, refDipoles1[k]) /
float(thisCount1))
for k, pos in enumerate(owCoords[shell2Bool]):
thisOHvecs = wl.reimage(
[hw1Coords[shell2Bool][k], hw2Coords[shell2Bool][k]], pos,
boxDims) - pos
thisDip = -0.5 * (thisOHvecs[0] + thisOHvecs[1])
thisDip /= np.linalg.norm(thisDip)
dipCorrs[int(countStepsNVE / calcSteps),
1] += (np.dot(thisDip, refDipoles2[k]) /
float(thisCount2))
simNVE.step(calcSteps)
countStepsNVE += calcSteps
#Finish normalizing dipole correlations (really cosine of angle between dipole vector at different times)
numWats /= float(int(nSteps / stepChunk))
dipCorrs /= float(int(nSteps / stepChunk))
print("Normalizing factor for finding averages: %f" %
float(int(nSteps / stepChunk)))
#And save the final state of the NPT simulation in case we want to extend it
sim.saveState('nptDynamicsState.xml')
#And return the dipole correlations and times at which they were computed
timeVals = 0.002 * np.arange(0.0, calcTotSteps + 0.0001, calcSteps)
return numWats, dipCorrs, timeVals
def main(args):
print time.ctime(time.time())
#Get topology file we're working with
topFile = args[0]
#And figure out if we're dealing with solute at surface or in bulk
if (args[1] == 'True'):
inBulk = True
else:
inBulk = False
if (args[2] == 'True'):
doReweight = True
else:
doReweight = False
#Read in topology file now to get information on solute atoms
top = pmd.load_file(topFile)
soluteInds = []
for res in top.residues:
if res.name not in ['OTM', 'CTM', 'STM', 'NTM', 'SOL']:
for atom in res.atoms:
soluteInds.append(atom.idx)
#Now define how we compute three-body angles with bins and cut-off
#Shell cut-off
shellCut = 3.32 #1st minimum distance for TIP4P-Ew water at 298.15 K and 1 bar
#Number of angle bins
nAngBins = 100 #500
#Define bin centers (should be nBins equally spaced between 0 and 180)
angBinCents = 0.5 * (np.arange(0.0, 180.001, 180.0/nAngBins)[:-1] + np.arange(0.0, 180.001, 180.0/nAngBins)[1:])
#And distance bins for local oxygen-oxygen RDF calculation
#(really distance histograms from central oxygens - can normalize however we want, really)
distBinWidth = 0.05
nDistBins = int(shellCut / distBinWidth)
distBins = np.arange(0.0, nDistBins*distBinWidth+0.00001, distBinWidth)
distBinCents = 0.5 * (distBins[:-1] + distBins[1:])
#Define the size of the probes used for assessing density fluctuations near solute
probeRadius = 3.3 # radius in Angstroms; the DIAMETER of a methane so assumes other atoms methane-sized
#And bins for numbers of waters in probes
probeBins = np.arange(0.0, 21.00001, 1.0)
nProbeBins = len(probeBins) - 1 #Will use np.histogram, which includes left edge in bin (so if want up to 20, go to 21)
#And will record number waters in each solvation shell (histograms of)
shellBins = np.arange(0.0, 251.00001, 1.0) #probably way too many bins, but don't want to run out
nShellBins = len(shellBins) - 1
#Should we do 2D histogram for angles and distances?
#Or also do 2D histogram for number of waters in probe and three-body angle?
#Interesting if make probe radius same size as three-body angle cutoff?
#Finally, also define the bins for computing RDFs of waters near all solute atoms
#Will use to define 1st and 2nd solvation shells
rdfBinWidth = 0.2
rdfMax = 12.00
rdfBins = np.arange(0.0, rdfMax+0.000001, rdfBinWidth)
rdfBinCents = 0.5 * (rdfBins[:-1] + rdfBins[1:])
nRDFBins = len(rdfBinCents)
rdfBinVols = (4.0*np.pi/3.0)*(rdfBins[1:]**3 - rdfBins[:-1]**3)
bulkDens = 0.0332 #Roughly right for TIP4P-EW at 298.15 K and 1 bar in inverse Angstroms cubed
#Need to create a variety of arrays to hold the data we're interested in
#Will record distributions in both 1st and 2nd solvation shells
shellCountsCoupled = np.zeros((nShellBins, 2)) #Histograms for numbers of waters in hydration shells of solutes
probeHistsCoupled = np.zeros((nProbeBins, 2)) #Histograms for numbers waters in probes in 1st and 2nd hydration shells
angHistsCoupled = np.zeros((nAngBins, 2)) #Histograms of three-body angles for water oxygens within solvation shells
distHistsCoupled = np.zeros((nDistBins, 2)) #Histograms of distances to water oxygens from central oxygens
solRDFsCoupled = np.zeros((nRDFBins, len(soluteInds))) #RDFs between each solute atom and water oxygens
shellCountsDecoupled = np.zeros((nShellBins, 2)) #Same as above, but decoupled state, not coupled state
probeHistsDecoupled = np.zeros((nProbeBins, 2))
angHistsDecoupled = np.zeros((nAngBins, 2))
distHistsDecoupled = np.zeros((nDistBins, 2))
solRDFsDecoupled = np.zeros((nRDFBins, len(soluteInds)))
#First need configuration weights to use in computing average quantities
#But only do if we're using a simuation with an expanded ensemble
if doReweight:
if inBulk:
weightsCoupled, weightsDecoupled = getConfigWeightsBulk(kB=1.0, T=1.0)
#Using 1 for kB and T because alchemical_output.txt should already have potential energies in kBT
simDirs = ['.']
else:
weightsCoupled, weightsDecoupled = getConfigWeightsSurf()
simDirs = ['Quad_0.25X_0.25Y', 'Quad_0.25X_0.75Y', 'Quad_0.75X_0.25Y', 'Quad_0.75X_0.75Y']
else:
weightsCoupled = np.array([])
weightsDecoupled = np.array([])
simDirs = ['.']
#To correctly match weights up to configurations, need to count frames from all trajectories
countFrames = 0
#Next, want to loop over all trajectories and compute RDFs from solute atoms to water oxygens
#Will use this to define solvation shells for finding other properties
#Actually, having looked at RDFs, just use 5.5 for first shell and 8.5 for second shell...
#AND use all atoms, including hydrogens, which have LJ interactions in GAFF2, to define shells
#Actually now only using heavy atoms... but when look at RDFs, examine all atoms
for adir in simDirs:
if doReweight:
#Before loading trajectory, figure out how many frames to exclude due to weight equilibration
alcDat = np.loadtxt(adir+'/alchemical_output.txt')
startTime = alcDat[0, 1]
startFrame = int(startTime) - 1
else:
startFrame = 0
top = pmd.load_file(topFile)
top.rb_torsions = pmd.TrackedList([]) #This is just for SAM systems so that it doesn't break pytraj
top = pt.load_parmed(top, traj=False)
traj = pt.iterload(adir+'/prod.nc', top, frame_slice=(startFrame, -1))
if not doReweight:
weightsCoupled = np.hstack((weightsCoupled, np.ones(len(traj))))
weightsDecoupled = np.hstack((weightsDecoupled, np.ones(len(traj))))
print("\nTopology and trajectory loaded from directory %s" % adir)
owInds = top.select('@OW')
soluteInds = top.select('!(:OTM,CTM,STM,NTM,SOL)')
print("\n\tFound %i water oxygens" % len(owInds))
print("\tFound %i solute atoms" % len(soluteInds))
for i, frame in enumerate(traj):
if i%1000 == 0:
print "On frame %i" % i
boxDims = np.array(frame.box.values[:3])
currCoords = np.array(frame.xyz)
#Wrap based on soluate atom center of geometry and get coordinates of interest
wrapCOM = np.average(currCoords[soluteInds], axis=0)
currCoords = wl.reimage(currCoords, wrapCOM, boxDims) - wrapCOM
owCoords = currCoords[owInds]
solCoords = currCoords[soluteInds]
#Loop over solute atoms and find pair-distance histograms with water oxygens
for j, acoord in enumerate(solCoords):
solRDFsCoupled[:,j] += (weightsCoupled[countFrames+i]
* wl.pairdistancehistogram(np.array([acoord]), owCoords, rdfBinWidth, nRDFBins, boxDims))
solRDFsDecoupled[:,j] += (weightsDecoupled[countFrames+i]
* wl.pairdistancehistogram(np.array([acoord]), owCoords, rdfBinWidth, nRDFBins, boxDims))
#Note that pairdistancehistogram is right-edge inclusive, NOT left-edge inclusive
#In practice, not a big difference
countFrames += len(traj)
#Finish by normalizing RDFs properly
for j in range(len(soluteInds)):
solRDFsCoupled[:,j] /= rdfBinVols #bulkDens*rdfBinVols
solRDFsDecoupled[:,j] /= rdfBinVols #bulkDens*rdfBinVols
if not doReweight:
solRDFsCoupled /= float(countFrames)
solRDFsDecoupled /= float(countFrames)
#And save to file
np.savetxt('solute-OW_RDFs_coupled.txt', np.hstack((np.array([rdfBinCents]).T, solRDFsCoupled)),
header='RDF bins (A) solute atom-OW RDF for solute atom indices %s'%(str(soluteInds)))
np.savetxt('solute-OW_RDFs_decoupled.txt', np.hstack((np.array([rdfBinCents]).T, solRDFsDecoupled)),
header='RDF bins (A) solute atom-OW RDF for solute atom indices %s'%(str(soluteInds)))
print("\tFound RDFs for water oxygens from solute indices.")
solShell1Cut = 5.5 #Angstroms from all solute atoms (including hydrogens)
solShell2Cut = 8.5
#And now that we know how many frames, we can assign real weights if not reweighting
if not doReweight:
weightsCoupled /= float(countFrames)
weightsDecoupled /= float(countFrames)
#Reset countFrames so get weights right
countFrames = 0
#Repeat looping over trajectories to calculate water properties in solute solvation shell
for adir in simDirs:
if doReweight:
#Before loading trajectory, figure out how many frames to exclude due to weight equilibration
alcDat = np.loadtxt(adir+'/alchemical_output.txt')
startTime = alcDat[0, 1]
startFrame = int(startTime) - 1
else:
startFrame = 0
top = pmd.load_file(topFile)
top.rb_torsions = pmd.TrackedList([]) #This is just for SAM systems so that it doesn't break pytraj
top = pt.load_parmed(top, traj=False)
traj = pt.iterload(adir+'/prod.nc', top, frame_slice=(startFrame, -1))
print("\nTopology and trajectory loaded from directory %s" % adir)
owInds = top.select('@OW')
soluteInds = top.select('!(:OTM,CTM,STM,NTM,SOL)&!(@H=)')
surfInds = top.select('(:OTM,CTM,STM,NTM)&!(@H=)') #For probe insertions, also include solute and surface heavy atoms
print("\n\tFound %i water oxygens" % len(owInds))
print("\tFound %i solute heavy atoms" % len(soluteInds))
print("\tFound %i non-hydrogen surface atoms" % len(surfInds))
if len(surfInds) == 0:
surfInds.dtype=int
for i, frame in enumerate(traj):
#if i%10 == 0:
# print "On frame %i" % i
boxDims = np.array(frame.box.values[:3])
currCoords = np.array(frame.xyz)
#Wrap based on soluate atom center of geometry and get coordinates of interest
wrapCOM = np.average(currCoords[soluteInds], axis=0)
currCoords = wl.reimage(currCoords, wrapCOM, boxDims) - wrapCOM
owCoords = currCoords[owInds]
solCoords = currCoords[soluteInds]
surfCoords = currCoords[surfInds]
#Now get solvent shells around solute
shell1BoolMat = wl.nearneighbors(solCoords, owCoords, boxDims, 0.0, solShell1Cut)
shell1Bool = np.array(np.sum(shell1BoolMat, axis=0), dtype=bool)
shell2BoolMat = wl.nearneighbors(solCoords, owCoords, boxDims, solShell1Cut, solShell2Cut)
shell2Bool = np.array(np.sum(shell2BoolMat, axis=0), dtype=bool)
#And add weight to histogram for numbers of waters in shells
thisCount1 = int(np.sum(shell1Bool))
shellCountsCoupled[thisCount1, 0] += weightsCoupled[countFrames+i]
shellCountsDecoupled[thisCount1, 0] += weightsDecoupled[countFrames+i]
thisCount2 = int(np.sum(shell2Bool))
shellCountsCoupled[thisCount2, 1] += weightsCoupled[countFrames+i]
shellCountsDecoupled[thisCount2, 1] += weightsDecoupled[countFrames+i]
#And compute water properties of solvent shells, first 3-body angles
thisAngs1, thisNumAngs1 = wp.getCosAngs(owCoords[shell1Bool], owCoords, boxDims, highCut=shellCut)
thisAngHist1, thisAngBins1 = np.histogram(thisAngs1, bins=nAngBins, range=[0.0, 180.0], density=False)
angHistsCoupled[:,0] += weightsCoupled[countFrames+i] * thisAngHist1
angHistsDecoupled[:,0] += weightsDecoupled[countFrames+i] * thisAngHist1
thisAngs2, thisNumAngs2 = wp.getCosAngs(owCoords[shell2Bool], owCoords, boxDims, highCut=shellCut)
thisAngHist2, thisAngBins2 = np.histogram(thisAngs2, bins=nAngBins, range=[0.0, 180.0], density=False)
angHistsCoupled[:,1] += weightsCoupled[countFrames+i] * thisAngHist2
angHistsDecoupled[:,1] += weightsDecoupled[countFrames+i] * thisAngHist2
#And ow-ow pair distance histograms in both shells as well
thisDistHist1 = wl.pairdistancehistogram(owCoords[shell1Bool], owCoords, distBinWidth, nDistBins, boxDims)
distHistsCoupled[:,0] += weightsCoupled[countFrames+i] * thisDistHist1
distHistsDecoupled[:,0] += weightsDecoupled[countFrames+i] * thisDistHist1
thisDistHist2 = wl.pairdistancehistogram(owCoords[shell2Bool], owCoords, distBinWidth, nDistBins, boxDims)
distHistsCoupled[:,1] += weightsCoupled[countFrames+i] * thisDistHist2
distHistsDecoupled[:,1] += weightsDecoupled[countFrames+i] * thisDistHist2
#Next compute distributions of numbers of waters in probes centered within each shell
#To do this, create random grid of points in SQUARE that encompasses both shells
#Then only keep points within each shell based on distance
#Square will be based on shell cutoffs and min and max coordinates in each dimension of solute
minSolX = np.min(solCoords[:,0]) - solShell2Cut
maxSolX = np.max(solCoords[:,0]) + solShell2Cut
minSolY = np.min(solCoords[:,1]) - solShell2Cut
maxSolY = np.max(solCoords[:,1]) + solShell2Cut
minSolZ = np.min(solCoords[:,2]) - solShell2Cut
maxSolZ = np.max(solCoords[:,2]) + solShell2Cut
thisGridX = minSolX + np.random.random(500)*(maxSolX - minSolX)
thisGridY = minSolY + np.random.random(500)*(maxSolY - minSolY)
thisGridZ = minSolZ + np.random.random(500)*(maxSolZ - minSolZ)
thisGrid = np.vstack((thisGridX, thisGridY, thisGridZ)).T
gridBoolMat1 = wl.nearneighbors(solCoords, thisGrid, boxDims, 0.0, solShell1Cut)
gridBool1 = np.array(np.sum(gridBoolMat1, axis=0), dtype=bool)
thisNum1 = wl.probegrid(np.vstack((owCoords, surfCoords, solCoords)), thisGrid[gridBool1], probeRadius, boxDims)
thisProbeHist1, thisProbeBins1 = np.histogram(thisNum1, bins=probeBins, density=False)
probeHistsCoupled[:,0] += weightsCoupled[countFrames+i] * thisProbeHist1
probeHistsDecoupled[:,0] += weightsDecoupled[countFrames+i] * thisProbeHist1
gridBoolMat2 = wl.nearneighbors(solCoords, thisGrid, boxDims, solShell1Cut, solShell2Cut)
gridBool2 = np.array(np.sum(gridBoolMat2, axis=0), dtype=bool)
thisNum2 = wl.probegrid(np.vstack((owCoords, surfCoords, solCoords)), thisGrid[gridBool2], probeRadius, boxDims)
thisProbeHist2, thisProbeBins2 = np.histogram(thisNum2, bins=probeBins, density=False)
probeHistsCoupled[:,1] += weightsCoupled[countFrames+i] * thisProbeHist2
probeHistsDecoupled[:,1] += weightsDecoupled[countFrames+i] * thisProbeHist2
countFrames += len(traj)
#Should have everything we need, so save to text files
np.savetxt('solute_shell_hists.txt',
np.hstack((np.array([shellBins[:-1]]).T, shellCountsCoupled, shellCountsDecoupled)),
header='Histograms of numbers of waters in first and second solute solvation shells with solvent in coupled (columns 2, 3) and decoupled (columns 4, 5) states')
np.savetxt('solute_probe_hists.txt',
np.hstack((np.array([probeBins[:-1]]).T, probeHistsCoupled, probeHistsDecoupled)),
header='Number waters in probe histograms in first and second solute solvation shells with solvent in coupled (columns 2, 3) and decoupled (columns 4, 5) states')
np.savetxt('solute_ang_hists.txt',
np.hstack((np.array([angBinCents]).T, angHistsCoupled, angHistsDecoupled)),
header='3-body angle histograms in first and second solute solvation shells with solvent in coupled (columns 2, 3) and decoupled (columns 4, 5) states')
np.savetxt('solute_pair_hists.txt',
np.hstack((np.array([distBinCents]).T, distHistsCoupled, distHistsDecoupled)),
header='O-O pair-distance histograms in first and second solute solvation shells with solvent in coupled (columns 2, 3) and decoupled (columns 4, 5) states')
print time.ctime(time.time())
def computeSphericalFourierCoeffs(subPos,
Pos,
BoxDims,
lowCut=0.0,
highCut=3.413,
minDegree=0,
maxDegree=12):
"""Computes the vectors of Fourier coefficients for each degree of a spherical harmonic expansion
as described by Keys, Iacovella, and Glotzer, 2011. subPos is treated as the central atoms,
while Pos should include the atoms that may potentially be neighbors.
Inputs:
subPos - positions of atoms to treat as the central atoms
Pos - positions of all other atoms, which will be considered for neighbor-searching; can be same as subPos
BoxDims - box dimensions so that minimum images may be used
lowCut - (default 0.0) the lower cutoff for the radial shell
highCut - (default 3.413) the upper cutoff for the radial shell
minDegree - (default 0) the minimum spherical harmonic degree (l)
maxDegree - (default 12) the maximum spherical harmonic degree (l)
Outputs:
coeffVecs - a len(subPos) x (1 + maxDegree - minDegree) x (2*maxDegree + 1) matrix
For each central atom in subPos, a matrix of the complex-valued vectors (as rows)
is provided. This still allows magnitudes to be easily evaluated, since real and
imaginary parts of zero will contribute nothing to the magnitude
numNeighbs - number of neighbors for each water molecule (necessary to compute global order parameters
or coefficients by multiplying by this and the dividing by the total of the waters
to "average" over)
"""
#Set up the output matrix now since know size
coeffVecs = np.zeros(
(len(subPos), 1 + maxDegree - minDegree, 2 * maxDegree + 1),
dtype=complex)
#And array to return number of neighbors for each water
numNeighbs = np.zeros(len(subPos), dtype='float16')
#Would be nice to combine neighbor searching with 3-body angle computation or H-bonding code
#But then harder to efficiently implement different cutoffs...
#So that might be too ambitious
#Find neighbors within cutoff for ALL atoms in subPos
#But make sure using efficient algorithm...
#If subPos is same as Pos, use allnearneighbors instead
if np.array_equal(subPos, Pos):
nearNeighbs = wl.allnearneighbors(Pos, BoxDims, lowCut,
highCut).astype(bool)
else:
nearNeighbs = wl.nearneighbors(subPos, Pos, BoxDims, lowCut,
highCut).astype(bool)
#Loop over each position in subPos and find neighbor positions in spherical coordinates
for (i, apos) in enumerate(subPos):
#Make sure have nearest neighbors...
if len(Pos[nearNeighbs[i]]) > 0:
tempPos = wl.reimage(Pos[nearNeighbs[i]], apos, BoxDims) - apos
numNeighbs[i] = len(tempPos)
#Compute radial distances... unfortunate that have to do this again, but maybe improve later
rdists = np.linalg.norm(tempPos, axis=1)
#And get polar and azimuthal angles
polarang = np.arccos(tempPos[:, 2] / rdists)
azimang = np.arctan2(
tempPos[:, 1], tempPos[:, 0]
) #Using special arctan2 function to get quadrant right
#Now compute Fourier coefficient vectors (i.e. have complex-valued component of coefficient vector
#associated with each m value, where m = -l, -l+1, ... , l)
#Loop over the desired number of coefficients to compute
for l in range(minDegree, maxDegree + 1):
thisvec = np.zeros(2 * l + 1, dtype=complex)
#Also note that have one vector for each neighbor, so must loop over neighbors
for j in range(len(tempPos)):
thisvec += sph_harm(np.arange(-l, l + 1), l, azimang[j],
polarang[j])
thisvec /= len(tempPos)
#And compute the magnitude of this vector of complex numbers
coeffVecs[i, l - minDegree, :(2 * l + 1)] = thisvec
return coeffVecs, numNeighbs
def main(args):
print('\nReading in files and obtaining LJ information...')
#First read in topology and trajectory
topFile = args[0]
trajFile = args[1]
top = pmd.load_file(topFile)
trajtop = copy.deepcopy(top)
trajtop.rb_torsions = pmd.TrackedList(
[]) #Necessary for SAM systems so doesn't break pytraj
trajtop = pt.load_parmed(trajtop, traj=False)
traj = pt.iterload(trajFile, top=trajtop)
#Next use parmed to get LJ parameters for all atoms in the solute, as well as water oxygens and surface atoms
#While go, also collect dictionaries of atomic indices associated with each atom type
#Will have to check separately when looking at overlaps with solute
soluteLJ = []
soluteInds = []
dictOtherLJ = {}
dictOtherInds = {}
for res in top.residues:
if res.name not in ['OTM', 'CTM', 'STM', 'NTM', 'SOL']:
for atom in res.atoms:
soluteInds.append(atom.idx)
soluteLJ.append([atom.sigma, atom.epsilon])
else:
for atom in res.atoms:
if not atom.type in dictOtherInds:
dictOtherInds[atom.type] = [atom.idx]
else:
dictOtherInds[atom.type].append(atom.idx)
if not atom.type in dictOtherLJ:
dictOtherLJ[atom.type] = np.array(
[atom.sigma, atom.epsilon])
soluteLJ = np.array(soluteLJ)
print(soluteLJ)
#Use Lorentz-Berthelot combining rules to get LJ parameters between each solute atom and a water oxygen
dictMixLJ = {}
for i in range(soluteLJ.shape[0]):
for akey in dictOtherLJ:
dictMixLJ['%i_%s' % (i, akey)] = np.array([
0.5 * (soluteLJ[i, 0] + dictOtherLJ[akey][0]),
np.sqrt(soluteLJ[i, 1] * dictOtherLJ[akey][1])
])
for key, val in dictMixLJ.iteritems():
print("%s, %s" % (key, str(val.tolist())))
print(
'\nDetermining hard-sphere radii for all combinations of solute and other system atoms...'
)
#Next compute hard-sphere radii by integrating according to Barker and Hendersen, Weeks, etc.
#In order to this right, technically using WCA potential, not LJ
hsRadii = {}
rvals = np.arange(0.0, 50.005, 0.005)
betaLJ = 1.0 / ((1.9872036E-03) * 298.15)
for i in range(soluteLJ.shape[0]):
for akey in dictOtherLJ:
[thisSig, thisEps] = dictMixLJ['%i_%s' % (i, akey)]
if thisEps == 0.0:
hsRadii['%i_%s' % (i, akey)] = 0.0
continue
thisRmin = thisSig * (2.0**(1.0 / 6.0))
thisSigdRmin6 = (thisSig / thisRmin)**6
thisPotRmin = 4.0 * thisEps * ((thisSigdRmin6**2) - thisSigdRmin6)
thisSigdR6 = (thisSig / rvals)**6
thisPotVals = 4.0 * thisEps * (
(thisSigdR6**2) - thisSigdR6) - thisPotRmin
thisPotVals[np.where(rvals >= thisRmin)] = 0.0
thisPotVals *= betaLJ
thisIntegrand = 1.0 - np.exp(-thisPotVals)
thisIntegrand[0] = 1.0
hsRadii['%i_%s' % (i, akey)] = simps(thisIntegrand, rvals)
#Need to multiply by two because will use atom centers to check overlap? Is Rhs distance between centers?
for key, val in hsRadii.iteritems():
print("%s, %f" % (key, val))
#Keep track of hard-sphere radii with water oxygens specially
solOWhsRadii = np.zeros(soluteLJ.shape[0])
for i in range(soluteLJ.shape[0]):
solOWhsRadii[i] = hsRadii['%i_OW_tip4pew' %
i] #Only using TIP4P/EW here
print('\nStarting loop over trajectory...')
#Now loop over trajectory and check if solute is overlapping with any waters OR surface atoms
#Will create a distribution of overlapping atoms
numOverlap = np.arange(101.0)
countOverlap = np.zeros(len(numOverlap))
#And also track average solute volume that we're trying to insert
solVol = 0.0
countFrames = 0
print('')
for frame in traj:
if countFrames % 100 == 0:
print("On frame %i" % countFrames)
countFrames += 1
boxDims = np.array(frame.box.values[:3])
currCoords = np.array(frame.xyz)
#Get solute coordinates and make sure solute is whole
#Then get solute coordinates relative to first solute atom
#Don't need any other wrapping because wl.nearneighbors will do its own wrapping
solCoords = currCoords[soluteInds]
solRefCoords = wl.reimage(solCoords, solCoords[0],
boxDims) - solCoords[0]
#While we have the coordinates nice, compute solute volume
#Do this based on hard-sphere radii to water oxygens, which is the most likely case anyway
solVol += np.sum(wl.spherevolumes(solRefCoords, solOWhsRadii, 0.1))
#Will shift the solute first atom (and others too) to a number of random locations
#Since applying restraint (if have surface) Z is drawn from the distribution we want
#X and Y can be drawn more easily from uniform distributions, so do this to randomize solute position
numRandXY = 1000
randX = np.random.random(numRandXY) * boxDims[0]
randY = np.random.random(numRandXY) * boxDims[1]
#And will keep track of number of overlapping atoms for each solute random position
thisTotOverlap = np.zeros(numRandXY, dtype=int)
#Loop over all non-solute atoms in the system by atom type
for akey, val in dictOtherInds.iteritems():
#For this specific atom type, need to keep track of WHICH neighbors overlapping
#And need to do for EACH solute atom
#Don't want to double-count if two solute atoms both overlap the same other atom
overlapBool = np.zeros((numRandXY, len(val)), dtype=int)
#Now loop over each solute atom
for i, coord in enumerate(solRefCoords):
thisRadius = hsRadii['%i_%s' % (i, akey)]
if thisRadius == 0.0:
continue
#Define coordinates of the current solute atom we're working with
#So setting first atom to random XY position, then shifting by distance to first atom
hsCoords = np.zeros((numRandXY, 3))
hsCoords[:, 0] = coord[0] + randX
hsCoords[:, 1] = coord[1] + randY
hsCoords[:, 2] = coord[2] + solCoords[0, 2]
#Identify boolean for overlapping atoms and add to overall boolean for overlap
#Note that want OR operation, so adding boolean arrays
overlapBool += wl.nearneighbors(hsCoords, currCoords[val],
boxDims, 0.0, thisRadius)
#For this non-solute atom type, add number of atoms overlapping with ANY solute atom
thisTotOverlap += np.sum(np.array(overlapBool, dtype=bool), axis=1)
thisBins = np.arange(np.max(thisTotOverlap) + 1)
countOverlap[thisBins] += np.bincount(thisTotOverlap)
print(countOverlap.tolist())
print('Hard-sphere solute insertion probability: %f' %
(-np.log(countOverlap[0] / np.sum(countOverlap))))
#Save the distribution to file
np.savetxt(
'HS-solute_overlap_hist.txt',
np.vstack((numOverlap, countOverlap)).T,
header=
'Number of non-solute atoms overlapping Histogram count')
solVol /= float(len(traj))
print(
'Average solute hard-sphere volume (based on water oxygen LJ params): %f'
% (solVol))