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generate.py
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#!/usr/bin/env python
"""
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing author: Oliver Henrich (University of Strathclyde, Glasgow)
------------------------------------------------------------------------- */
"""
"""
Import basic modules
"""
import sys, os, timeit
from timeit import default_timer as timer
start_time = timer()
"""
Try to import numpy; if failed, import a local version mynumpy
which needs to be provided
"""
try:
import numpy as np
except:
print >> sys.stderr, "numpy not found. Exiting."
sys.exit(1)
"""
Check that the required arguments (box offset and size in simulation units
and the sequence file were provided
"""
try:
box_offset = float(sys.argv[1])
box_length = float(sys.argv[2])
infile = sys.argv[3]
except:
print >> sys.stderr, "Usage: %s <%s> <%s> <%s>" % (sys.argv[0], \
"box offset", "box length", "file with sequences")
sys.exit(1)
box = np.array ([box_length, box_length, box_length])
"""
Try to open the file and fail gracefully if file cannot be opened
"""
try:
inp = open (infile, 'r')
inp.close()
except:
print >> sys.stderr, "Could not open file '%s' for reading. \
Aborting." % infile
sys.exit(2)
# return parts of a string
def partition(s, d):
if d in s:
sp = s.split(d, 1)
return sp[0], d, sp[1]
else:
return s, "", ""
"""
Define the model constants
"""
# set model constants
PI = np.pi
POS_BASE = 0.4
POS_BACK = -0.4
EXCL_RC1 = 0.711879214356
EXCL_RC2 = 0.335388426126
EXCL_RC3 = 0.52329943261
"""
Define auxillary variables for the construction of a helix
"""
# center of the double strand
CM_CENTER_DS = POS_BASE + 0.2
# ideal distance between base sites of two nucleotides
# which are to be base paired in a duplex
BASE_BASE = 0.3897628551303122
# cutoff distance for overlap check
RC2 = 16
# squares of the excluded volume distances for overlap check
RC2_BACK = EXCL_RC1**2
RC2_BASE = EXCL_RC2**2
RC2_BACK_BASE = EXCL_RC3**2
# enumeration to translate from letters to numbers and vice versa
number_to_base = {1 : 'A', 2 : 'C', 3 : 'G', 4 : 'T'}
base_to_number = {'A' : 1, 'a' : 1, 'C' : 2, 'c' : 2,
'G' : 3, 'g' : 3, 'T' : 4, 't' : 4}
# auxillary arrays
positions = []
a1s = []
a3s = []
quaternions = []
newpositions = []
newa1s = []
newa3s = []
basetype = []
strandnum = []
bonds = []
"""
Convert local body frame to quaternion DOF
"""
def exyz_to_quat (mya1, mya3):
mya2 = np.cross(mya3, mya1)
myquat = [1,0,0,0]
q0sq = 0.25 * (mya1[0] + mya2[1] + mya3[2] + 1.0)
q1sq = q0sq - 0.5 * (mya2[1] + mya3[2])
q2sq = q0sq - 0.5 * (mya1[0] + mya3[2])
q3sq = q0sq - 0.5 * (mya1[0] + mya2[1])
# some component must be greater than 1/4 since they sum to 1
# compute other components from it
if q0sq >= 0.25:
myquat[0] = np.sqrt(q0sq)
myquat[1] = (mya2[2] - mya3[1]) / (4.0*myquat[0])
myquat[2] = (mya3[0] - mya1[2]) / (4.0*myquat[0])
myquat[3] = (mya1[1] - mya2[0]) / (4.0*myquat[0])
elif q1sq >= 0.25:
myquat[1] = np.sqrt(q1sq)
myquat[0] = (mya2[2] - mya3[1]) / (4.0*myquat[1])
myquat[2] = (mya2[0] + mya1[1]) / (4.0*myquat[1])
myquat[3] = (mya1[2] + mya3[0]) / (4.0*myquat[1])
elif q2sq >= 0.25:
myquat[2] = np.sqrt(q2sq)
myquat[0] = (mya3[0] - mya1[2]) / (4.0*myquat[2])
myquat[1] = (mya2[0] + mya1[1]) / (4.0*myquat[2])
myquat[3] = (mya3[1] + mya2[2]) / (4.0*myquat[2])
elif q3sq >= 0.25:
myquat[3] = np.sqrt(q3sq)
myquat[0] = (mya1[1] - mya2[0]) / (4.0*myquat[3])
myquat[1] = (mya3[0] + mya1[2]) / (4.0*myquat[3])
myquat[2] = (mya3[1] + mya2[2]) / (4.0*myquat[3])
norm = 1.0/np.sqrt(myquat[0]*myquat[0] + myquat[1]*myquat[1] + \
myquat[2]*myquat[2] + myquat[3]*myquat[3])
myquat[0] *= norm
myquat[1] *= norm
myquat[2] *= norm
myquat[3] *= norm
return np.array([myquat[0],myquat[1],myquat[2],myquat[3]])
"""
Adds a strand to the system by appending it to the array of previous strands
"""
def add_strands (mynewpositions, mynewa1s, mynewa3s):
overlap = False
# This is a simple check for each of the particles where for previously
# placed particles i we check whether it overlaps with any of the
# newly created particles j
print >> sys.stdout, "## Checking for overlaps"
for i in xrange(len(positions)):
p = positions[i]
pa1 = a1s[i]
for j in xrange (len(mynewpositions)):
q = mynewpositions[j]
qa1 = mynewa1s[j]
# skip particles that are anyway too far away
dr = p - q
dr -= box * np.rint (dr / box)
if np.dot(dr, dr) > RC2:
continue
# base site and backbone site of the two particles
p_pos_back = p + pa1 * POS_BACK
p_pos_base = p + pa1 * POS_BASE
q_pos_back = q + qa1 * POS_BACK
q_pos_base = q + qa1 * POS_BASE
# check for no overlap between the two backbone sites
dr = p_pos_back - q_pos_back
dr -= box * np.rint (dr / box)
if np.dot(dr, dr) < RC2_BACK:
overlap = True
# check for no overlap between the two base sites
dr = p_pos_base - q_pos_base
dr -= box * np.rint (dr / box)
if np.dot(dr, dr) < RC2_BASE:
overlap = True
# check for no overlap between backbone site of particle p
# with base site of particle q
dr = p_pos_back - q_pos_base
dr -= box * np.rint (dr / box)
if np.dot(dr, dr) < RC2_BACK_BASE:
overlap = True
# check for no overlap between base site of particle p and
# backbone site of particle q
dr = p_pos_base - q_pos_back
dr -= box * np.rint (dr / box)
if np.dot(dr, dr) < RC2_BACK_BASE:
overlap = True
# exit if there is an overlap
if overlap:
return False
# append to the existing list if no overlap is found
if not overlap:
for p in mynewpositions:
positions.append(p)
for p in mynewa1s:
a1s.append (p)
for p in mynewa3s:
a3s.append (p)
# calculate quaternion from local body frame and append
for ia in xrange(len(mynewpositions)):
mynewquaternions = exyz_to_quat(mynewa1s[ia],mynewa3s[ia])
quaternions.append(mynewquaternions)
return True
"""
Returns the rotation matrix defined by an axis and angle
"""
def get_rotation_matrix(axis, anglest):
# The argument anglest can be either an angle in radiants
# (accepted types are float, int or np.float64 or np.float64)
# or a tuple [angle, units] where angle is a number and
# units is a string. It tells the routine whether to use degrees,
# radiants (the default) or base pairs turns.
if not isinstance (anglest, (np.float64, np.float32, float, int)):
if len(anglest) > 1:
if anglest[1] in ["degrees", "deg", "o"]:
#angle = np.deg2rad (anglest[0])
angle = (np.pi / 180.) * (anglest[0])
elif anglest[1] in ["bp"]:
angle = int(anglest[0]) * (np.pi / 180.) * (35.9)
else:
angle = float(anglest[0])
else:
angle = float(anglest[0])
else:
angle = float(anglest) # in degrees (?)
axis = np.array(axis)
axis /= np.sqrt(np.dot(axis, axis))
ct = np.cos(angle)
st = np.sin(angle)
olc = 1. - ct
x, y, z = axis
return np.array([[olc*x*x+ct, olc*x*y-st*z, olc*x*z+st*y],
[olc*x*y+st*z, olc*y*y+ct, olc*y*z-st*x],
[olc*x*z-st*y, olc*y*z+st*x, olc*z*z+ct]])
"""
Generates the position and orientation vectors of a
(single or double) strand from a sequence string
"""
def generate_strand(bp, sequence=None, start_pos=np.array([0, 0, 0]), \
dir=np.array([0, 0, 1]), perp=False, double=True, rot=0.):
# generate empty arrays
mynewpositions, mynewa1s, mynewa3s = [], [], []
# cast the provided start_pos array into a numpy array
start_pos = np.array(start_pos, dtype=float)
# overall direction of the helix
dir = np.array(dir, dtype=float)
if sequence == None:
sequence = np.random.randint(1, 5, bp)
# the elseif here is most likely redundant
elif len(sequence) != bp:
n = bp - len(sequence)
sequence += np.random.randint(1, 5, n)
print >> sys.stderr, "sequence is too short, adding %d random bases" % n
# normalize direction
dir_norm = np.sqrt(np.dot(dir,dir))
if dir_norm < 1e-10:
print >> sys.stderr, "direction must be a valid vector, \
defaulting to (0, 0, 1)"
dir = np.array([0, 0, 1])
else: dir /= dir_norm
# find a vector orthogonal to dir to act as helix direction,
# if not provided switch off random orientation
if perp is None or perp is False:
v1 = np.random.random_sample(3)
v1 -= dir * (np.dot(dir, v1))
v1 /= np.sqrt(sum(v1*v1))
else:
v1 = perp;
# generate rotational matrix representing the overall rotation of the helix
R0 = get_rotation_matrix(dir, rot)
# rotation matrix corresponding to one step along the helix
R = get_rotation_matrix(dir, [1, "bp"])
# set the vector a1 (backbone to base) to v1
a1 = v1
# apply the global rotation to a1
a1 = np.dot(R0, a1)
# set the position of the fist backbone site to start_pos
rb = np.array(start_pos)
# set a3 to the direction of the helix
a3 = dir
for i in range(bp):
# work out the position of the centre of mass of the nucleotide
rcdm = rb - CM_CENTER_DS * a1
# append to newpositions
mynewpositions.append(rcdm)
mynewa1s.append(a1)
mynewa3s.append(a3)
# if we are not at the end of the helix, we work out a1 and rb for the
# next nucleotide along the helix
if i != bp - 1:
a1 = np.dot(R, a1)
rb += a3 * BASE_BASE
# if we are working on a double strand, we do a cycle similar
# to the previous one but backwards
if double == True:
a1 = -a1
a3 = -dir
R = R.transpose()
for i in range(bp):
rcdm = rb - CM_CENTER_DS * a1
mynewpositions.append (rcdm)
mynewa1s.append (a1)
mynewa3s.append (a3)
a1 = np.dot(R, a1)
rb += a3 * BASE_BASE
assert (len (mynewpositions) > 0)
return [mynewpositions, mynewa1s, mynewa3s]
"""
Main function for this script.
Reads a text file with the following format:
- Each line contains the sequence for a single strand (A,C,G,T)
- Lines beginning with the keyword 'DOUBLE' produce double-stranded DNA
Ex: Two ssDNA (single stranded DNA)
ATATATA
GCGCGCG
Ex: Two strands, one double stranded, the other single stranded.
DOUBLE AGGGCT
CCTGTA
"""
def read_strands(filename):
try:
infile = open (filename)
except:
print >> sys.stderr, "Could not open file '%s'. Aborting." % filename
sys.exit(2)
# This block works out the number of nucleotides and strands by reading
# the number of non-empty lines in the input file and the number of letters,
# taking the possible DOUBLE keyword into account.
nstrands, nnucl, nbonds = 0, 0, 0
lines = infile.readlines()
for line in lines:
line = line.upper().strip()
if len(line) == 0:
continue
if line[:6] == 'DOUBLE':
line = line.split()[1]
length = len(line)
print >> sys.stdout, "## Found duplex of %i base pairs" % length
nnucl += 2*length
nstrands += 2
nbonds += (2*length-2)
else:
line = line.split()[0]
length = len(line)
print >> sys.stdout, \
"## Found single strand of %i bases" % length
nnucl += length
nstrands += 1
nbonds += length-1
# rewind the sequence input file
infile.seek(0)
print >> sys.stdout, "## nstrands, nnucl = ", nstrands, nnucl
# generate the data file in LAMMPS format
try:
out = open ("data.oxdna", "w")
except:
print >> sys.stderr, "Could not open data file for writing. Aborting."
sys.exit(2)
lines = infile.readlines()
nlines = len(lines)
i = 1
myns = 0
noffset = 1
for line in lines:
line = line.upper().strip()
# skip empty lines
if len(line) == 0:
i += 1
continue
# block for duplexes: last argument of the generate function
# is set to 'True'
if line[:6] == 'DOUBLE':
line = line.split()[1]
length = len(line)
seq = [(base_to_number[x]) for x in line]
myns += 1
for b in xrange(length):
basetype.append(seq[b])
strandnum.append(myns)
for b in xrange(length-1):
bondpair = [noffset + b, noffset + b + 1]
bonds.append(bondpair)
noffset += length
# create the sequence of the second strand as made of
# complementary bases
seq2 = [5-s for s in seq]
seq2.reverse()
myns += 1
for b in xrange(length):
basetype.append(seq2[b])
strandnum.append(myns)
for b in xrange(length-1):
bondpair = [noffset + b, noffset + b + 1]
bonds.append(bondpair)
noffset += length
print >> sys.stdout, "## Created duplex of %i bases" % (2*length)
# generate random position of the first nucleotide
cdm = box_offset + np.random.random_sample(3) * box
# generate the random direction of the helix
axis = np.random.random_sample(3)
axis /= np.sqrt(np.dot(axis, axis))
# use the generate function defined above to create
# the position and orientation vector of the strand
newpositions, newa1s, newa3s = generate_strand(len(line), \
sequence=seq, dir=axis, start_pos=cdm, double=True)
# generate a new position for the strand until it does not overlap
# with anything already present
start = timer()
while not add_strands(newpositions, newa1s, newa3s):
cdm = box_offset + np.random.random_sample(3) * box
axis = np.random.random_sample(3)
axis /= np.sqrt(np.dot(axis, axis))
newpositions, newa1s, newa3s = generate_strand(len(line), \
sequence=seq, dir=axis, start_pos=cdm, double=True)
print >> sys.stdout, "## Trying %i" % i
end = timer()
print >> sys.stdout, "## Added duplex of %i bases (line %i/%i) in %.2fs, now at %i/%i" % \
(2*length, i, nlines, end-start, len(positions), nnucl)
# block for single strands: last argument of the generate function
# is set to 'False'
else:
length = len(line)
seq = [(base_to_number[x]) for x in line]
myns += 1
for b in xrange(length):
basetype.append(seq[b])
strandnum.append(myns)
for b in xrange(length-1):
bondpair = [noffset + b, noffset + b + 1]
bonds.append(bondpair)
noffset += length
# generate random position of the first nucleotide
cdm = box_offset + np.random.random_sample(3) * box
# generate the random direction of the helix
axis = np.random.random_sample(3)
axis /= np.sqrt(np.dot(axis, axis))
print >> sys.stdout, \
"## Created single strand of %i bases" % length
newpositions, newa1s, newa3s = generate_strand(length, \
sequence=seq, dir=axis, start_pos=cdm, double=False)
start = timer()
while not add_strands(newpositions, newa1s, newa3s):
cdm = box_offset + np.random.random_sample(3) * box
axis = np.random.random_sample(3)
axis /= np.sqrt(np.dot(axis, axis))
newpositions, newa1s, newa3s = generate_strand(length, \
sequence=seq, dir=axis, start_pos=cdm, double=False)
print >> sys.stdout, "## Trying %i" % (i)
end = timer()
print >> sys.stdout, "## Added single strand of %i bases (line %i/%i) in %.2fs, now at %i/%i" % \
(length, i, nlines, end-start,len(positions), nnucl)
i += 1
# sanity check
if not len(positions) == nnucl:
print len(positions), nnucl
raise AssertionError
out.write('# LAMMPS data file\n')
out.write('%d atoms\n' % nnucl)
out.write('%d ellipsoids\n' % nnucl)
out.write('%d bonds\n' % nbonds)
out.write('\n')
out.write('4 atom types\n')
out.write('1 bond types\n')
out.write('\n')
out.write('# System size\n')
out.write('%f %f xlo xhi\n' % (box_offset,box_offset+box_length))
out.write('%f %f ylo yhi\n' % (box_offset,box_offset+box_length))
out.write('%f %f zlo zhi\n' % (box_offset,box_offset+box_length))
out.write('\n')
out.write('Masses\n')
out.write('\n')
out.write('1 3.1575\n')
out.write('2 3.1575\n')
out.write('3 3.1575\n')
out.write('4 3.1575\n')
# for each nucleotide print a line under the headers
# Atoms, Velocities, Ellipsoids and Bonds
out.write('\n')
out.write(\
'# Atom-ID, type, position, molecule-ID, ellipsoid flag, density\n')
out.write('Atoms\n')
out.write('\n')
for i in xrange(nnucl):
out.write('%d %d %22.15le %22.15le %22.15le %d 1 1\n' \
% (i+1, basetype[i], \
positions[i][0], positions[i][1], positions[i][2], \
strandnum[i]))
out.write('\n')
out.write('# Atom-ID, translational, rotational velocity\n')
out.write('Velocities\n')
out.write('\n')
for i in xrange(nnucl):
out.write("%d %22.15le %22.15le %22.15le %22.15le %22.15le %22.15le\n" \
% (i+1,0.0,0.0,0.0,0.0,0.0,0.0))
out.write('\n')
out.write('# Atom-ID, shape, quaternion\n')
out.write('Ellipsoids\n')
out.write('\n')
for i in xrange(nnucl):
out.write(\
"%d %22.15le %22.15le %22.15le %22.15le %22.15le %22.15le %22.15le\n" \
% (i+1,1.1739845031423408,1.1739845031423408,1.1739845031423408, \
quaternions[i][0],quaternions[i][1], quaternions[i][2],quaternions[i][3]))
out.write('\n')
out.write('# Bond topology\n')
out.write('Bonds\n')
out.write('\n')
for i in xrange(nbonds):
out.write("%d %d %d %d\n" % (i+1,1,bonds[i][0],bonds[i][1]))
out.close()
print >> sys.stdout, "## Wrote data to 'data.oxdna'"
print >> sys.stdout, "## DONE"
# call the above main() function, which executes the program
read_strands (infile)
end_time=timer()
runtime = end_time-start_time
hours = runtime/3600
minutes = (runtime-np.rint(hours)*3600)/60
seconds = (runtime-np.rint(hours)*3600-np.rint(minutes)*60)%60
print >> sys.stdout, "## Total runtime %ih:%im:%.2fs" % (hours,minutes,seconds)

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