Scripts: angles.py

# Chimera Python script to compute angles between dynactin axis and microtuble axes
# projected to the 2d planes containing the microtubule axis and dynactin centroid
# and the plane contining the microtubule axis that is perpendicular to that plane.

cm = (0,0,0)    # Microtubule axis point
am = (0,0,1)    # Microtubule axis vector

cd = (7.5,10.8,-5.6)    # Dynactin centroid in dynactin map coordinate system (Angstroms)
ad = (.8,.7,.2)         # Dynactin long axis vector in dynactin map coord system.

# Convert dynactin coordinates to microtubule coordinates
from chimera import openModels
mmodel, dmodel = openModels.list()      # Assuming microtubule model #0, dynactin model #1
print "Using microtubule model", mmodel.name, "dynactin model", dmodel.name

# Find transformation from dynactin model coordinates to camera coordinates
# then camera coordinates to microtuble coordinates.
import Matrix as M
tf = M.multiply_matrices(M.xform_matrix(mmodel.openState.xform.inverse()),
                         M.xform_matrix(dmodel.openState.xform))
cdm = M.apply_matrix(tf, cd)    # Dynactin centroid in microtubule map coordinate system
adm = M.apply_matrix_without_translation(tf, ad)        # Dynactin axis in microtubule map coordinate system
adm = M.normalize_vector(adm)   # Make sure axis is unit length vector

# Make coordinate system for microtubule with z-axis along cylinder axis,
# and yz plane containing dynactin center
from numpy import subtract
mx,my,mz = M.orthonormal_frame(zaxis = am, ydir = subtract(cdm, cm))

# Now measure dynactin axis angle in microtubule yz plane and xz planes.
from math import atan2, pi
ayz = atan2(M.inner_product(my, adm), M.inner_product(mz, adm))
axz = atan2(M.inner_product(mx, adm), M.inner_product(mz, adm))

print('Dynactin axis orientation: %.1f degrees from microtubule axis, %.1f degrees transverse to microtuble axis'
      % (ayz * 180/pi, axz * 180/pi))