def random_ellipsoid(box, size, min_axis):
# return a random ellipsoid record of the form:
# [ ELLIPSOID, x_pos, y_pos, z_pos, size, x0, y0, z0, x1, y1, z2, x2, y2, z2 ]
# where the xyz vectors are orthogonal and of length 1.0 or less.
box = box - size
tmp0 = cpv.random_vector()
tmp1 = cpv.random_vector()
tmp2 = cpv.cross_product(tmp1, tmp0)
tmp3 = cpv.cross_product(tmp1, tmp2)
tmp4 = cpv.cross_product(tmp2, tmp3)
tmp2 = cpv.normalize(tmp2)
tmp3 = cpv.normalize(tmp3)
tmp4 = cpv.normalize(tmp4)
primary = cpv.scale(tmp2, random())
secondary = cpv.scale(tmp3,random())
tertiary = cpv.scale(tmp4,random())
factor = 1.0 / max( cpv.length(primary), cpv.length(secondary), cpv.length(tertiary))
primary = cpv.scale(primary, factor)
secodary = cpv.scale(secondary, factor)
tertiary = cpv.scale(tertiary, factor)
return [ ELLIPSOID,
size + random() * box, size + random() * box, size + random() * box,
max(random() * size, min_axis),
] + primary + secondary + tertiary
def visualize_orientation(direction,
center=[0.0] * 3,
scale=1.0,
symmetric=False,
color='green',
color2='red'):
'''
DESCRIPTION
Draw an arrow. Helper function for "helix_orientation" etc.
'''
from pymol import cgo
color_list = cmd.get_color_tuple(color)
color2_list = cmd.get_color_tuple(color2)
if symmetric:
scale *= 0.5
end = cpv.add(center, cpv.scale(direction, scale))
radius = 0.3
obj = [cgo.SAUSAGE]
obj.extend(center)
obj.extend(end)
obj.extend([
radius,
0.8,
0.8,
0.8,
])
obj.extend(color_list)
if symmetric:
start = cpv.sub(center, cpv.scale(direction, scale))
obj.append(cgo.SAUSAGE)
obj.extend(center)
obj.extend(start)
obj.extend([
radius,
0.8,
0.8,
0.8,
])
obj.extend(color2_list)
coneend = cpv.add(
end, cpv.scale(direction, 4.0 * radius / cpv.length(direction)))
obj.append(cgo.CONE)
obj.extend(end)
obj.extend(coneend)
obj.extend([
radius * 1.75,
0.0,
])
obj.extend(color_list * 2)
obj.extend([
1.0,
1.0, # Caps
])
cmd.load_cgo(obj, get_unused_name('oriVec'), zoom=0)
def pdbBox(line):
''' Parses a gro box line and returns a pdb CRYST1 line '''
from math import degrees
from chempy.cpv import length, get_angle
v = [10*float(i) for i in line.split()] + 6*[0] # Padding for rectangular boxes
v1, v2, v3 = (v[0], v[3], v[4]), (v[5], v[1], v[6]), (v[7], v[8], v[2])
a = length(v1)
b = length(v2)
c = length(v3)
alpha = degrees(get_angle(v2, v3))
beta = degrees(get_angle(v1, v3))
gamma = degrees(get_angle(v1, v2))
return _pdbBoxLine % (a, b, c, alpha, beta, gamma)
def pdbBox(line):
''' Parses a gro box line and returns a pdb CRYST1 line '''
from math import degrees
from chempy.cpv import length, get_angle
v = [10*float(i) for i in line.split()] + 6*[0] # Padding for rectangular boxes
v1, v2, v3 = (v[0], v[3], v[4]), (v[5], v[1], v[6]), (v[7], v[8], v[2])
a = length(v1)
b = length(v2)
c = length(v3)
alpha = degrees(get_angle(v2, v3))
beta = degrees(get_angle(v1, v3))
gamma = degrees(get_angle(v1, v2))
return _pdbBoxLine % (a, b, c, alpha, beta, gamma)
def visualize_orientation(direction, center=[0.0]*3, scale=1.0, symmetric=False, color='green', color2='red'):
'''
DESCRIPTION
Draw an arrow. Helper function for "helix_orientation" etc.
'''
from pymol import cgo
color_list = cmd.get_color_tuple(color)
color2_list = cmd.get_color_tuple(color2)
if symmetric:
scale *= 0.5
end = cpv.add(center, cpv.scale(direction, scale))
radius = 0.3
obj = [cgo.SAUSAGE]
obj.extend(center)
obj.extend(end)
obj.extend([
radius,
0.8, 0.8, 0.8,
])
obj.extend(color_list)
if symmetric:
start = cpv.sub(center, cpv.scale(direction, scale))
obj.append(cgo.SAUSAGE)
obj.extend(center)
obj.extend(start)
obj.extend([
radius,
0.8, 0.8, 0.8,
])
obj.extend(color2_list)
coneend = cpv.add(end, cpv.scale(direction, 4.0*radius/cpv.length(direction)))
obj.append(cgo.CONE)
obj.extend(end)
obj.extend(coneend)
obj.extend([
radius * 1.75,
0.0,
])
obj.extend(color_list * 2)
obj.extend([
1.0, 1.0, # Caps
])
cmd.load_cgo(obj, get_unused_name('oriVec'), zoom=0)
def scramble(self,mode):
if self.cmd.count_atoms(self.sculpt_object):
sc_tmp = "_scramble_tmp"
if mode == 0:
self.cmd.select(sc_tmp,self.sculpt_object+
" and not (fixed or restrained)")
if mode == 1:
self.cmd.select(sc_tmp,self.sculpt_object+
" and not (fixed)")
extent = self.cmd.get_extent(sc_tmp)
center = self.cmd.get_position(sc_tmp)
radius = 1.25*cpv.length(cpv.sub(extent[0],extent[1]))
self.cmd.alter_state(self.cmd.get_state(), sc_tmp,
"(x,y,z)=rsp(pos,rds)",
space= { 'rsp' : cpv.random_displacement,
'pos' : center,
'rds' : radius })
self.cmd.delete(sc_tmp)
def scramble(self,mode):
if self.cmd.count_atoms(self.sculpt_object):
sc_tmp = "_scramble_tmp"
if mode == 0:
self.cmd.select(sc_tmp,self.sculpt_object+
" and not (fixed or restrained)")
if mode == 1:
self.cmd.select(sc_tmp,self.sculpt_object+
" and not (fixed)")
extent = self.cmd.get_extent(sc_tmp)
center = self.cmd.get_position(sc_tmp)
radius = 1.25*cpv.length(cpv.sub(extent[0],extent[1]))
self.cmd.alter_state(self.cmd.get_state(), sc_tmp,
"(x,y,z)=rsp(pos,rds)",
space= { 'rsp' : cpv.random_displacement,
'pos' : center,
'rds' : radius })
self.cmd.delete(sc_tmp)
def helix_orientation_hbond(selection, visualize=1, cutoff=3.5, quiet=0):
'''
DESCRIPTION
Get the center and direction of a helix as vectors. Will only work
for alpha helices and gives slightly different results than
helix_orientation. Averages direction of O(i)->N(i+4) hydrogen bonds.
USAGE
helix_orientation selection [, visualize [, cutoff]]
ARGUMENTS
cutoff = float: maximal hydrogen bond distance {default: 3.5}
SEE ALSO
helix_orientation
'''
visualize, quiet, cutoff = int(visualize), int(quiet), float(cutoff)
stored.x = dict()
cmd.iterate_state(STATE, '(%s) and name N+O' % (selection),
'stored.x.setdefault(resv, dict())[name] = x,y,z')
vec_list = []
for resi in stored.x:
resi_other = resi + 4
if 'O' in stored.x[resi] and resi_other in stored.x:
if 'N' in stored.x[resi_other]:
vec = cpv.sub(stored.x[resi_other]['N'], stored.x[resi]['O'])
if cpv.length(vec) < cutoff:
vec_list.append(vec)
if len(vec_list) == 0:
print 'warning: count == 0'
raise CmdException
vec = _vec_sum(vec_list)
vec = cpv.normalize(vec)
return _common_orientation(selection, vec, visualize, quiet)
def helix_orientation_hbond(selection, visualize=1, cutoff=3.5, quiet=0):
'''
DESCRIPTION
Get the center and direction of a helix as vectors. Will only work
for alpha helices and gives slightly different results than
helix_orientation. Averages direction of O(i)->N(i+4) hydrogen bonds.
USAGE
helix_orientation selection [, visualize [, cutoff]]
ARGUMENTS
cutoff = float: maximal hydrogen bond distance {default: 3.5}
SEE ALSO
helix_orientation
'''
visualize, quiet, cutoff = int(visualize), int(quiet), float(cutoff)
stored.x = dict()
cmd.iterate_state(STATE, '(%s) and name N+O' % (selection),
'stored.x.setdefault(resv, dict())[name] = x,y,z')
vec_list = []
for resi in stored.x:
resi_other = resi + 4
if 'O' in stored.x[resi] and resi_other in stored.x:
if 'N' in stored.x[resi_other]:
vec = cpv.sub(stored.x[resi_other]['N'], stored.x[resi]['O'])
if cpv.length(vec) < cutoff:
vec_list.append(vec)
if len(vec_list) == 0:
print 'warning: count == 0'
raise CmdException
vec = _vec_sum(vec_list)
vec = cpv.normalize(vec)
return _common_orientation(selection, vec, visualize, quiet)
def compute_surface_normals():
'''
Compute average normals from all adjacent triangles
on each vertex
'''
from functools import reduce
# don't use cpv.normalize which has an RSMALL4 limit
normalize = lambda v: cpv.scale(v, 1. / cpv.length(v))
for face in table['face']:
if 'vertex_index' in face:
indices = face['vertex_index']
elif 'vertex_indices' in face:
indices = face['vertex_indices']
else:
return
f_vert = [vertices[i] for i in indices]
f_xyz = [(v['x'], v['y'], v['z']) for v in f_vert]
try:
normal = normalize(cpv.cross_product(
cpv.sub(f_xyz[1], f_xyz[0]),
cpv.sub(f_xyz[2], f_xyz[1])))
except ZeroDivisionError:
continue
for v in f_vert:
v.setdefault('normals', []).append(normal)
for v in vertices:
try:
v['nx'], v['ny'], v['nz'] = normalize(
reduce(cpv.add, v.pop('normals')))
except (KeyError, ZeroDivisionError):
continue
def compute_surface_normals():
'''
Compute average normals from all adjacent triangles
on each vertex
'''
from functools import reduce
# don't use cpv.normalize which has an RSMALL4 limit
normalize = lambda v: cpv.scale(v, 1. / cpv.length(v))
for face in table['face']:
if 'vertex_index' in face:
indices = face['vertex_index']
elif 'vertex_indices' in face:
indices = face['vertex_indices']
else:
return
f_vert = [vertices[i] for i in indices]
f_xyz = [(v['x'], v['y'], v['z']) for v in f_vert]
try:
normal = normalize(cpv.cross_product(
cpv.sub(f_xyz[1], f_xyz[0]),
cpv.sub(f_xyz[2], f_xyz[1])))
except ZeroDivisionError:
continue
for v in f_vert:
v.setdefault('normals', []).append(normal)
for v in vertices:
try:
v['nx'], v['ny'], v['nz'] = normalize(
reduce(cpv.add, v.pop('normals')))
except (KeyError, ZeroDivisionError):
continue
def angle_between_domains(selection1, selection2, method='align',
state1=STATE, state2=STATE, visualize=1, quiet=1):
'''
DESCRIPTION
Angle by which a molecular selection would be rotated when superposing
on a selection2.
Do not use for measuring angle between helices, since the alignment of
the helices might involve a rotation around the helix axis, which will
result in a larger angle compared to the angle between helix axes.
USAGE
angle_between_domains selection1, selection2 [, method ]
ARGUMENTS
selection1 = string: atom selection of first helix
selection2 = string: atom selection of second helix
method = string: alignment command like "align" or "super" {default: align}
EXAMPLE
fetch 3iplA 3iplB, async=0
select domain1, resi 1-391
select domain2, resi 392-475
align 3iplA and domain1, 3iplB and domain1
angle_between_domains 3iplA and domain2, 3iplB and domain2
SEE ALSO
align, super, angle_between_helices
'''
import math
try:
import numpy
except ImportError:
print ' Error: numpy not available'
raise CmdException
state1, state2 = int(state1), int(state2)
visualize, quiet = int(visualize), int(quiet)
if cmd.is_string(method):
try:
method = cmd.keyword[method][0]
except KeyError:
print 'no such method:', method
raise CmdException
mobile_tmp = get_unused_name('_')
cmd.create(mobile_tmp, selection1, state1, 1, zoom=0)
try:
method(mobile=mobile_tmp, target=selection2, mobile_state=1,
target_state=state2, quiet=quiet)
mat = cmd.get_object_matrix(mobile_tmp)
except:
print ' Error: superposition with method "%s" failed' % (method.__name__)
raise CmdException
finally:
cmd.delete(mobile_tmp)
try:
# Based on transformations.rotation_from_matrix
# Copyright (c) 2006-2012, Christoph Gohlke
R33 = [mat[i:i+3] for i in [0,4,8]]
R33 = numpy.array(R33, float)
# direction: unit eigenvector of R33 corresponding to eigenvalue of 1
w, W = numpy.linalg.eig(R33.T)
i = w.real.argmax()
direction = W[:, i].real
# rotation angle depending on direction
m = direction.argmax()
i,j,k,l = [
[2,1,1,2],
[0,2,0,2],
[1,0,0,1]][m]
cosa = (R33.trace() - 1.0) / 2.0
sina = (R33[i, j] + (cosa - 1.0) * direction[k] * direction[l]) / direction[m]
angle = math.atan2(sina, cosa)
angle = abs(math.degrees(angle))
except:
print ' Error: rotation from matrix failed'
raise CmdException
if not quiet:
try:
# make this import optional to support running this script standalone
from .querying import centerofmass, gyradius
except (ValueError, ImportError):
gyradius = None
try:
# PyMOL 1.7.1.6+
centerofmass = cmd.centerofmass
except AttributeError:
centerofmass = lambda s: cpv.scale(cpv.add(*cmd.get_extent(s)), 0.5)
center1 = centerofmass(selection1)
center2 = centerofmass(selection2)
print ' Angle: %.2f deg, Displacement: %.2f angstrom' % (angle, cpv.distance(center1, center2))
if visualize:
center1 = numpy.array(center1, float)
center2 = numpy.array(center2, float)
center = (center1 + center2) / 2.0
if gyradius is not None:
rg = numpy.array(gyradius(selection1), float)
else:
rg = 10.0
h1 = numpy.cross(center2 - center1, direction)
h2 = numpy.dot(R33, h1)
h1 *= rg / cpv.length(h1)
h2 *= rg / cpv.length(h2)
for pos in [center1, center2, center1 + h1, center1 + h2]:
cmd.pseudoatom(mobile_tmp, pos=list(pos), state=1)
# measurement object for angle and displacement
name = get_unused_name('measurement')
cmd.distance(name, *['%s`%d' % (mobile_tmp, i) for i in [1,2]])
cmd.angle(name, *['%s`%d' % (mobile_tmp, i) for i in [3,1,4]])
# CGO arrow for axis of rotation
visualize_orientation(direction, center1, rg, color='blue')
cmd.delete(mobile_tmp)
return angle
def angle_between_domains(selection1,
selection2,
method='align',
state1=STATE,
state2=STATE,
visualize=1,
quiet=1):
'''
DESCRIPTION
Angle by which a molecular selection would be rotated when superposing
on a selection2.
Do not use for measuring angle between helices, since the alignment of
the helices might involve a rotation around the helix axis, which will
result in a larger angle compared to the angle between helix axes.
USAGE
angle_between_domains selection1, selection2 [, method ]
ARGUMENTS
selection1 = string: atom selection of first helix
selection2 = string: atom selection of second helix
method = string: alignment command like "align" or "super" {default: align}
EXAMPLE
fetch 3iplA 3iplB, bsync=0
select domain1, resi 1-391
select domain2, resi 392-475
align 3iplA and domain1, 3iplB and domain1
angle_between_domains 3iplA and domain2, 3iplB and domain2
SEE ALSO
align, super, angle_between_helices
'''
import math
try:
import numpy
except ImportError:
print(' Error: numpy not available')
raise CmdException
state1, state2 = int(state1), int(state2)
visualize, quiet = int(visualize), int(quiet)
if cmd.is_string(method):
try:
method = cmd.keyword[method][0]
except KeyError:
print('no such method:', method)
raise CmdException
mobile_tmp = get_unused_name('_')
cmd.create(mobile_tmp, selection1, state1, 1, zoom=0)
try:
method(mobile=mobile_tmp,
target=selection2,
mobile_state=1,
target_state=state2,
quiet=quiet)
mat = cmd.get_object_matrix(mobile_tmp)
except:
print(' Error: superposition with method "%s" failed' %
(method.__name__))
raise CmdException
finally:
cmd.delete(mobile_tmp)
try:
# Based on transformations.rotation_from_matrix
# Copyright (c) 2006-2012, Christoph Gohlke
R33 = [mat[i:i + 3] for i in [0, 4, 8]]
R33 = numpy.array(R33, float)
# direction: unit eigenvector of R33 corresponding to eigenvalue of 1
w, W = numpy.linalg.eig(R33.T)
i = w.real.argmax()
direction = W[:, i].real
# rotation angle depending on direction
m = direction.argmax()
i, j, k, l = [[2, 1, 1, 2], [0, 2, 0, 2], [1, 0, 0, 1]][m]
cosa = (R33.trace() - 1.0) / 2.0
sina = (R33[i, j] +
(cosa - 1.0) * direction[k] * direction[l]) / direction[m]
angle = math.atan2(sina, cosa)
angle = abs(math.degrees(angle))
except:
print(' Error: rotation from matrix failed')
raise CmdException
if not quiet:
try:
# make this import optional to support running this script standalone
from .querying import centerofmass, gyradius
except (ValueError, ImportError):
gyradius = None
try:
# PyMOL 1.7.1.6+
centerofmass = cmd.centerofmass
except AttributeError:
centerofmass = lambda s: cpv.scale(cpv.add(*cmd.get_extent(s)),
0.5)
center1 = centerofmass(selection1)
center2 = centerofmass(selection2)
print(' Angle: %.2f deg, Displacement: %.2f angstrom' %
(angle, cpv.distance(center1, center2)))
if visualize:
center1 = numpy.array(center1, float)
center2 = numpy.array(center2, float)
center = (center1 + center2) / 2.0
if gyradius is not None:
rg = numpy.array(gyradius(selection1), float)
else:
rg = 10.0
h1 = numpy.cross(center2 - center1, direction)
h2 = numpy.dot(R33, h1)
h1 *= rg / cpv.length(h1)
h2 *= rg / cpv.length(h2)
for pos in [center1, center2, center1 + h1, center1 + h2]:
cmd.pseudoatom(mobile_tmp, pos=list(pos), state=1)
# measurement object for angle and displacement
name = get_unused_name('measurement')
cmd.distance(name, *['%s`%d' % (mobile_tmp, i) for i in [1, 2]])
cmd.angle(name, *['%s`%d' % (mobile_tmp, i) for i in [3, 1, 4]])
# CGO arrow for axis of rotation
visualize_orientation(direction, center1, rg, color='blue')
cmd.delete(mobile_tmp)
return angle
