"""
Quatfit routines for PDB2PQR
This module is used to find the coordinates of a new
atom based on a reference set of
coordinates and a definition set of coordinates.
Original Code by David J. Heisterberg
The Ohio Supercomputer Center
1224 Kinnear Rd.
Columbus, OH 43212-1163
(614)292-6036
djh@osc.edu djh@ohstpy.bitnet ohstpy::djh
Translated to C from fitest.f program and interfaced with
Xmol program by Jan Labanowski, jkl@osc.edu jkl@ohstpy.bitnet
ohstpy::jkl
----------------------------
PDB2PQR -- An automated pipeline for the setup, execution, and analysis of
Poisson-Boltzmann electrostatics calculations
Copyright (c) 2002-2010, Jens Erik Nielsen, University College Dublin;
Nathan A. Baker, Washington University in St. Louis; Paul Czodrowski &
Gerhard Klebe, University of Marburg
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the names of University College Dublin, Washington University in
St. Louis, or University of Marburg nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
OF THE POSSIBILITY OF SUCH DAMAGE.
----------------------------
"""
__date__ = "28 February 2006"
__author__ = "David Heisterberg, Jan Labanowski, Jens Erik Nielsen, Todd Dolinsky"
import math
from utilities import *
def findCoordinates(numpoints, refcoords, defcoords, defatomcoords):
"""
Driver for the quaternion file. Provide the coordinates as inputs
and obtain the coordinates for the new atom as output.
Parameters
numpoints: The number of points in each list (int)
refcoords: The reference coordinates, a list of lists of form
[x,y,z] (list)
defcoords: The definition coordinates, a list of lists of form
[x,y,z] (list)
defatomcoords: The definition coordinates for the atom to be
placed in the reference frame (list)
Returns
newcoords: The coordinates of the new atom in the
reference frame (list)
"""
refcenter, fitcenter, rotation = qfit(numpoints, refcoords, defcoords)
newcoords = qtransform(1, defatomcoords, refcenter, fitcenter, rotation)
# Only return the first coordinates
return newcoords[0]
def qtransform(numpoints, defcoords, refcenter, fitcenter, rotation):
"""
Transform the set of defcoords using the reference center, the fit
center, and a rotation matrix.
Parameters
numpoints: The number of points in each list (int)
defcoords: Definition coordinates (list)
refcenter: The reference center (list)
defcenter: The definition center (list)
rotation: The rotation matrix (list)
Returns
newcoords: The coordinates of the new point (list)
"""
if numpoints == 1:
defcoords = [defcoords]
fitcoords = translate(numpoints, defcoords, fitcenter, 1)
rotated = rotmol(numpoints, fitcoords, rotation)
newcoords = translate(numpoints, rotated, refcenter, 2)
return newcoords
def qfit(numpoints, refcoords, defcoords):
"""
Method for getting new atom coordinates from sets of reference
and definition coordinates.
Parameters
numpoints: The number of points in each list (int)
refcoords: List of reference coordinates, with each set
a list of form [x,y,z] (list)
defcoords: List of definition coordinates, with each set
a list of form [x,y,z] (list)
"""
nrot = 30
refcenter, refcoords = center(numpoints, refcoords)
defcenter, defcoords = center(numpoints, defcoords)
q, u = qtrfit(numpoints, defcoords, refcoords, nrot)
rotated = rotmol(numpoints, defcoords, u)
newcoords = translate(numpoints, rotated, refcenter, 2)
return refcenter, defcenter, u
def qchichange(initcoords, refcoords, angle):
"""
Change the chiangle of the reference coordinate using the
initcoords and the given angle
Parameters
initcoords: Coordinates based on the point and basis atoms
(one dimensional list)
difchi : The angle to use (float)
refcoords : The atoms to analyze (list of many coordinates)
Returns
newcoords : The new coordinates of the atoms (list of many coords)
"""
# Initialize
L,R = [],[]
for i in range(3):
L.append(0.0)
R.append([0.0,0.0,0.0])
# Convert to radians and normalize
radangle = math.pi * angle/180.0
normalized = normalize(initcoords)
L[0] = normalized[0]
L[1] = normalized[1]
L[2] = normalized[2]
# Construct the rotation matrix
R[0][0] = math.cos(radangle) + L[0]*L[0] * (1.0 - math.cos(radangle))
R[1][1] = math.cos(radangle) + L[1]*L[1] * (1.0 - math.cos(radangle))
R[2][2] = math.cos(radangle) + L[2]*L[2] * (1.0 - math.cos(radangle))
R[1][0] = L[0]*L[1]*(1.0 - math.cos(radangle)) - L[2] * math.sin(radangle)
R[2][0] = L[0]*L[2]*(1.0 - math.cos(radangle)) + L[1] * math.sin(radangle)
R[0][1] = L[1]*L[0]*(1.0 - math.cos(radangle)) + L[2] * math.sin(radangle)
R[2][1] = L[1]*L[2]*(1.0 - math.cos(radangle)) - L[0] * math.sin(radangle)
R[0][2] = L[2]*L[0]*(1.0 - math.cos(radangle)) - L[1] * math.sin(radangle)
R[1][2] = L[2]*L[1]*(1.0 - math.cos(radangle)) + L[0] * math.sin(radangle)
numpoints = len(refcoords)
newcoords = rotmol(numpoints, refcoords, R)
return newcoords
def rotmol(numpoints, x, u):
"""
Rotate a molecule
Parameters
numpoints: The number of points in the list (int)
x: The input coordinates (list)
u: The left rotation matrix (list)
Returns
out: The rotated coordinates out=u * x (list)
"""
out = []
for i in range(numpoints):
out.append([])
out[i].append(u[0][0] *x[i][0] + u[1][0] * x[i][1] + u[2][0] * x[i][2])
out[i].append(u[0][1] *x[i][0] + u[1][1] * x[i][1] + u[2][1] * x[i][2])
out[i].append(u[0][2] *x[i][0] + u[1][2] * x[i][1] + u[2][2] * x[i][2])
return out
def qtrfit(numpoints, defcoords, refcoords, nrot):
"""
Find the quaternion, q, [and left rotation matrix, u] that minimizes
| qTXq - Y | ^ 2 [|uX - Y| ^ 2]
This is equivalent to maximizing Re (qTXTqY)
The left rotation matrix, u, is obtained from q by
u = qT1q
Parameters
numpoints: The number of points in each list (int)
defcoords: List of definition coordinates, with each set
a list of form [x,y,z] (list)
refcoords: List of fitted coordinates, with each set
a list of form [x,y,z] (list)
nrot : The maximum number of jacobi sweeps
Returns
q : The best-fit quaternion
u : The best-fit left rotation matrix
"""
xxyx = 0.0
xxyy = 0.0
xxyz = 0.0
xyyx = 0.0
xyyy = 0.0
xyyz = 0.0
xzyx = 0.0
xzyy = 0.0
xzyz = 0.0
q = []
c = []
for i in range(numpoints):
xxyx = xxyx + defcoords[i][0] * refcoords[i][0]
xxyy = xxyy + defcoords[i][0] * refcoords[i][1]
xxyz = xxyz + defcoords[i][0] * refcoords[i][2]
xyyx = xyyx + defcoords[i][1] * refcoords[i][0]
xyyy = xyyy + defcoords[i][1] * refcoords[i][1]
xyyz = xyyz + defcoords[i][1] * refcoords[i][2]
xzyx = xzyx + defcoords[i][2] * refcoords[i][0]
xzyy = xzyy + defcoords[i][2] * refcoords[i][1]
xzyz = xzyz + defcoords[i][2] * refcoords[i][2]
for i in range(4):
c.append([])
for j in range(4):
c[i].append(0.0)
c[0][0] = xxyx + xyyy + xzyz
c[0][1] = xzyy - xyyz
c[1][1] = xxyx - xyyy - xzyz
c[0][2] = xxyz - xzyx
c[1][2] = xxyy + xyyx
c[2][2] = xyyy - xzyz - xxyx
c[0][3] = xyyx - xxyy
c[1][3] = xzyx + xxyz
c[2][3] = xyyz + xzyy
c[3][3] = xzyz - xxyx - xyyy
d,v = jacobi(c, nrot) # diagonalize c
for i in range(4):
q.append(v[i][3])
u = q2mat(q)
return q,u
def jacobi(a, nrot):
"""
Jacobi diagonalizer with sorted output, only good for 4x4 matrices
Parameters
a: Matrix to diagonalize (4x4 list)
nrot: Maximum number of sweeps
Returns
d: Eigenvalues
v: Eigenvectors
"""
v = []
d = []
for j in range(4):
d.append(0)
v.append([])
for i in range(4):
v[j].append(0.0)
v[j][j] = 1.0
d[j] = a[j][j]
for l in range(nrot):
dnorm = 0.0
onorm = 0.0
for j in range(4):
dnorm = dnorm + abs(d[j])
for i in range(j):
onorm = onorm + abs(a[i][j])
if dnorm != 0:
if onorm/dnorm <= 1e-12: break
for j in range(1,4):
for i in range(j):
b = a[i][j]
if abs(b) > 0.0:
dma = d[j] - d[i]
if abs(dma) + abs(b) <= abs(dma):
t = b / dma
else:
q = 0.5 * dma/b
t = 1.0/(abs(q) + math.sqrt(1 + q*q))
if q < 0:
t = t * -1
c = 1.0/math.sqrt(t*t + 1)
s = t*c
a[i][j] = 0.0
for k in range(i):
atemp = c * a[k][i] - s * a[k][j]
a[k][j] = s * a[k][i] + c * a[k][j]
a[k][i] = atemp
for k in range(i+1 ,j):
atemp = c * a[i][k] - s * a[k][j]
a[k][j] = s * a[i][k] + c * a[k][j]
a[i][k] = atemp
for k in range(j+1, 4):
atemp = c * a[i][k] - s * a[j][k]
a[j][k] = s * a[i][k] + c * a[j][k]
a[i][k] = atemp
for k in range(4):
vtemp = c * v[k][i] - s * v[k][j]
v[k][j] = s * v[k][i] + c * v[k][j]
v[k][i] = vtemp
dtemp = c*c*d[i] + s*s*d[j] - 2.0*c*s*b
d[j] = s*s*d[i] + c*c*d[j] + 2.0*c*s*b
d[i] = dtemp
nrot = l
for j in range(3):
k = j
dtemp = d[k]
for i in range(j+1,4):
if d[i] < dtemp:
k = i
dtemp = d[k]
if k > j:
d[k] = d[j]
d[j] = dtemp
for i in range(4):
dtemp = v[i][k]
v[i][k] = v[i][j]
v[i][j] = dtemp
return d,v
def q2mat(q):
"""
Generate a left rotation matrix from a normalized quaternion
Parameters
q: The normalized quaternion (list)
Returns
u: The rotation matrix (2-dimensional list)
"""
u = []
for i in range(3):
u.append([])
for j in range(3):
u[i].append(0.0)
u[0][0] = q[0]*q[0] + q[1]*q[1] - q[2]*q[2] - q[3]*q[3]
u[0][1] = 2.0 * (q[1] * q[2] - q[0] * q[3])
u[0][2] = 2.0 * (q[1] * q[3] + q[0] * q[2])
u[1][0] = 2.0 * (q[2] * q[1] + q[0] * q[3])
u[1][1] = q[0]*q[0] - q[1]*q[1] + q[2]*q[2] - q[3]*q[3]
u[1][2] = 2.0 * (q[2] * q[3] - q[0] * q[1])
u[2][0] = 2.0 *(q[3] * q[1] - q[0] * q[2])
u[2][1] = 2.0 * (q[3] * q[2] + q[0] * q[1])
u[2][2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3]
return u
def center(numpoints, refcoords):
"""
Center a molecule using equally weighted points
Parameters
numpoints: Number of points
refcoords: List of reference coordinates, with each set
a list of form [x,y,z] (list)
Returns
refcenter: Center of the set of points (list)
relcoords: Moved refcoords relative to refcenter (list)
"""
refcenter = []
relcoords = []
for i in range(3):
refcenter.append(0.0)
for i in range(numpoints):
refcenter[0] += refcoords[i][0]
refcenter[1] += refcoords[i][1]
refcenter[2] += refcoords[i][2]
for i in range(3):
refcenter[i] = refcenter[i] / numpoints
for i in range(numpoints):
relcoords.append([])
relcoords[i].append(refcoords[i][0] - refcenter[0])
relcoords[i].append(refcoords[i][1] - refcenter[1])
relcoords[i].append(refcoords[i][2] - refcenter[2])
return refcenter, relcoords
def translate(numpoints, refcoords, center, mode):
"""
Translate a molecule using equally weighted points
Parameters
numpoints: Number of points
refcoords: List of reference coordinates, with each set
a list of form [x,y,z] (list)
center: Center of the system(list)
mode: If 1, center will be subtracted from refcoords
If 2, center will be added to refcoords
Returns
relcoords: Moved refcoords relative to refcenter (list)
"""
relcoords = []
if mode == 1:
modif = -1
elif mode == 2:
modif = 1
for i in range(numpoints):
relcoords.append([])
relcoords[i].append(refcoords[i][0] + modif * center[0])
relcoords[i].append(refcoords[i][1] + modif * center[1])
relcoords[i].append(refcoords[i][2] + modif * center[2])
return relcoords
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