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aligner.py
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aligner.py
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import prody
import numpy
import MDANM
import random
import hamiltonian
#
# Classes to represent alignment results
#
class GenericAlignmentResult(object):
def __repr__(self):
pass
class RMSDAlignmentResult(GenericAlignmentResult):
def __init__(self, rmsd):
self._rmsd = rmsd
def __repr__(self):
return 'RMSD: {0:.3f}'.format(self._rmsd)
class EnergyAlignmentResult(GenericAlignmentResult):
def __init__(self, energy):
self._energy = energy
def __repr__(self):
return 'Energy: {0:.3f}'.format(self._energy)
#
# Base class for other alignment methods
#
class GenericAligner(object):
def align(self, native, prediction):
self._native = native
self._prediction = prediction
self._check_sizes()
def align_and_color(self, native, prediction):
pass
def _check_sizes(self):
assert len(self._native) == len(self._prediction)
#
# Do alignment based on RMSD
#
class RMSDAligner(GenericAligner):
'''
Do alignment based on RMSD.
'''
def __init__(self):
pass
def align(self, native, prediction):
'''
Align prediction to native.
Returns: the results, the native structure, and the aligned prediction.
'''
GenericAligner.align(self, native, prediction)
self._do_align()
return self._align_results, self._native, self._prediction
def align_and_color(self, native, prediction):
'''
Performs alignment and assigns deviations to B-factor column.
'''
self.align(native, prediction)
self._add_colors()
return self._align_results, self._native, self._prediction
def _do_align(self):
self._transformation = prody.calcTransformation(self._prediction, self._native)
self._transformation.apply(self._prediction)
rmsd = prody.calcRMSD(self._native, self._prediction)
self._align_results = RMSDAlignmentResult(rmsd)
def _add_colors(self):
h_native = prody.HierView(self._native)
h_prediction = prody.HierView(self._prediction)
for (native_res, pred_res) in zip( h_native.iterResidues(), h_prediction.iterResidues() ):
native_coords = native_res.getCoordinates()
pred_coords = pred_res.getCoordinates()
d = numpy.linalg.norm(native_coords - pred_coords)
pred_res.setTempFactors(d)
#
# Do alignment based on energy
#
class EnergyAligner(GenericAligner):
def __init__(self, n_steps = 10000, step_size=0.01):
self.n_steps = 10000
self.step_size = 0.01
def align(self, native, prediction):
'''
Align prediction to native.
Returns: the results, the native structure, and the aligned prediction.
'''
GenericAligner.align(self, native, prediction)
self._x = self._native.getCoordinates()
self._y = self._prediction.getCoordinates()
self._anm = MDANM.MDANM('energy_align')
self._anm.buildHessian(self._native)
self._anm.calcModes(None, zeros=False)
self._do_translation()
self._v = self._anm.getEigenvalues()
self._V = self._anm.getEigenvectors()
quat = numpy.random.normal(0, 1, 4)
quat = quat / numpy.linalg.norm(quat)
self._quat = quat
self._min_energy = None
self._optimize_fit()
self._apply_transformation()
self._align_results = EnergyAlignmentResult(self._min_energy)
return self._align_results, self._native, self._prediction
def align_and_color(self, native, prediction):
'''
Performs alignment and assigns energies to B-factor column.
'''
self.align(native, prediction)
h = hamiltonian.EDENMHamiltonian( self._native.getCoordinates() )
energy = h.evaluate_energy( self._prediction.getCoordinates() )
energy_matrix = h.get_energy_matrix()
atom_energy = numpy.sum(energy_matrix, axis=0)
hier_view = prody.HierView(self._prediction)
for index, residue in enumerate( hier_view.iterResidues() ):
residue.setTempFactors( atom_energy[index] )
return self._align_results, self._native, self._prediction
def _do_translation(self):
weights = 1.0 / prody.calcSqFlucts(self._anm)
#x_mean = numpy.mean(self._x, axis=0)
#y_mean = numpy.mean(self._y, axis=0)
x_mean = calc_average_coords(self._x, weights)
y_mean = calc_average_coords(self._y, weights)
self._x = self._x - x_mean
self._y = self._y - y_mean
self._x_mean = x_mean
self._y_mean = y_mean
def _optimize_fit(self):
min_energy = self._min_energy
for i in range(self.n_steps):
new_quat = self._gen_trial()
rot_mat = _q_to_mat(new_quat)
E = _calc_energy( numpy.dot(self._y, rot_mat), self._x, self._V, self._v)
if min_energy is None:
min_energy = E
self._quat = new_quat
elif E < min_energy:
min_energy = E
self._quat = new_quat
self._min_energy = min_energy
def _apply_transformation(self):
tx = prody.measure.Transformation(numpy.eye(3), -self._x_mean)
tx.apply(self._native)
ty = prody.measure.Transformation(numpy.eye(3), -self._y_mean)
ty.apply(self._prediction)
rot_mat = _q_to_mat(self._quat)
ty = prody.measure.Transformation( rot_mat, numpy.zeros(3) )
ty.apply(self._prediction)
def _gen_trial(self):
dq0 = random.gauss(0, self.step_size)
dq1 = random.gauss(0, self.step_size)
dq2 = random.gauss(0, self.step_size)
dq3 = random.gauss(0, self.step_size)
new = self._quat + numpy.array( (dq0, dq1, dq2, dq3) )
new = new / numpy.linalg.norm(new)
return new
#
# Helper functions
#
def _q_to_mat(quat):
'''
Convert a quaternion to a rotation matrix
'''
q0 = quat[0]
q1 = quat[1]
q2 = quat[2]
q3 = quat[3]
r = numpy.zeros( (3,3) )
r[0,0] = q0*q0 + q1*q1 - q2*q2 - q3*q3
r[0,1] = 2*(q1*q2 + q0*q3)
r[0,2] = 2*(q1*q3 - q0*q2)
r[1,0] = 2*(q1*q2 - q0*q3)
r[1,1] = q0*q0 - q1*q1 + q2*q2 - q3*q3
r[1,2] = 2*(q2*q3 + q0*q1)
r[2,0] = 2*(q1*q3 + q0*q2)
r[2,1] = 2*(q2*q3 - q0*q1)
r[2,2] = q0*q0 - q1*q1 - q2*q2 + q3*q3
return r
def _calc_energy(target_struct, native_struct, normal_modes, spring_constants):
'''
Calculate the energy based on normal modes
'''
d = native_struct - target_struct
d = d.flatten()
P = numpy.dot( d, normal_modes )
E = numpy.dot( P.transpose(), numpy.dot( numpy.diag(spring_constants), P) )
return E
def calc_average_coords(coords, weights):
n_atoms = len(weights)
x_mean = 0.0
y_mean = 0.0
z_mean = 0.0
total_weight=0.0
for i in range(n_atoms):
x_mean += coords[i,0] * weights[i]
y_mean += coords[i,1] * weights[i]
z_mean += coords[i,2] * weights[i]
total_weight += weights[i]
return numpy.array( (x_mean, y_mean, z_mean) ) / total_weight