Scripts: microtubule.py

#
# Make a geometric model of a microtubule in Chimera 1.8
#
def microtubule_model(path,                             # points used for cubic spline
                      radius = 90.0,                    # microtubule center to tubulin center (Angstroms)
                      monomer_spacing = 40.0,           # distance along protofilament (Angstroms)
                      number_of_protofilaments = 13,    
                      rise_per_turn = -3,               # number of monomers (negative for left hand helix)
                      colors = ((.7,.7,.6,1),(.4,.4,.5,1))):

  spt = smooth_path(path, monomer_spacing)              # points and tangents
  pt = equispaced_points(spt, monomer_spacing)
  f = path_coordinate_frames(pt)
  pl = helix_subunit_placements(f, radius, monomer_spacing, number_of_protofilaments, rise_per_turn)
  r = 0.5*monomer_spacing
  col = [colors[0]]*number_of_protofilaments + [colors[1]]*number_of_protofilaments
  s = place_spheres(pl, r, col)
  s.name = 'microtubule'
  return s

def smooth_path(path, spacing):

  from Matrix import distance
  seg_lengths = [distance(path[i],path[i+1]) for i in range(len(path)-1)]
  subdiv = max(0, int(max(seg_lengths) / spacing) - 1)
  from VolumePath import spline
  pt = spline.natural_cubic_spline(path, subdiv, return_tangents = True)
  return pt

# Modified code from VolumeFilter/unbend.py to also intepolate tangents.
def equispaced_points(points_and_tangents, spacing):

  pt = points_and_tangents
  ept = [pt[0]]
  from VolumePath import spline
  arcs = spline.arc_lengths([p for p,t in pt])
  d = spacing
  from Matrix import linear_combination, normalize_vector
  for i, a in enumerate(arcs):
    while a > d:
      f = (d - arcs[i-1]) / (arcs[i] - arcs[i-1])
      (p0,t0),(p1,t1) = pt[i-1],pt[i]
      p = linear_combination((1-f), p0, f, p1)
      t = normalize_vector(linear_combination((1-f), t0, f, t1))
      ept.append((p,t))
      d += spacing
  return ept

def path_coordinate_frames(pt):

  from VolumePath import tube
  f = tube.extrusion_transforms(pt)
  return f

def helix_subunit_placements(f, radius, subunit_spacing, subunits_per_turn, rise_per_turn):

  pl = []
  import Matrix as M
  for tf in f:
    for i in range(subunits_per_turn):
      a = i * (360.0/subunits_per_turn) # degrees
      dz = subunit_spacing*i*float(rise_per_turn)/subunits_per_turn
      stf = M.multiply_matrices(tf,
                                M.translation_matrix((0,0,dz)),
                                M.rotation_transform((0,0,1),a),
                                M.translation_matrix((radius,0,0)))
      pl.append(stf)
  return pl

def place_spheres(pl, radius, colors = [(.7,.7,.7,1)]):

  from _surface import SurfaceModel
  s = SurfaceModel()

  # Sphere geometry
  from Icosahedron import icosahedron_triangulation
  va, ta = icosahedron_triangulation(radius, subdivision_levels = 2, sphere_factor = 1)
  na = va.copy()
  import Matrix
  Matrix.normalize_vectors(na)
#  va[:,0] *= 0.5       # Flatten
  va[:,1] *= 1.1

  for i,tf in enumerate(pl):
    rgba = colors[i%len(colors)]
    p = s.addPiece(va, ta, rgba)
    p.normals = na
    p.placement = tf

  return s

def test():
  path = ((0,0,0), (0,0,500), (50,0,1000), (0,50,1500))
  s = microtubule_model(path)
  from chimera import openModels
  openModels.add([s])

test()