import pdb
import numpy as np
import random
from .model.arbdmodel import PointParticle, ParticleType, Group, ArbdModel
from .coords import rotationAboutAxis, quaternion_from_matrix, quaternion_to_matrix
from .model.nonbonded import *
from copy import copy, deepcopy
from .model.nbPot import nbDnaScheme
from scipy.special import erf
import scipy.optimize as opt
from scipy import interpolate
from .model.CanonicalNucleotideAtoms import canonicalNtFwd, canonicalNtRev, seqComplement
from .model.CanonicalNucleotideAtoms import enmTemplateHC, enmTemplateSQ, enmCorrectionsHC
# import pdb
"""
TODO:
+ fix handling of crossovers for atomic representation
+ map to atomic representation
+ add nicks
+ transform ssDNA nucleotides
- shrink ssDNA
+ shrink dsDNA backbone
+ make orientation continuous
+ sequence
- handle circular dna
+ ensure crossover bead potentials aren't applied twice
+ remove performance bottlenecks
- test for large systems
+ assign sequence
+ ENM
- rework Location class
- remove recursive calls
- document
- add unit test of helices connected to themselves
"""
class CircularDnaError(Exception):
pass
class ParticleNotConnectedError(Exception):
pass
class Location():
""" Site for connection within an object """
def __init__(self, container, address, type_, on_fwd_strand = True):
## TODO: remove cyclic references(?)
self.container = container
self.address = address # represents position along contour length in segment
# assert( type_ in ("end3","end5") ) # TODO remove or make conditional
self.on_fwd_strand = on_fwd_strand
self.type_ = type_
self.particle = None
self.connection = None
self.is_3prime_side_of_connection = None
self.prev_in_strand = None
self.next_in_strand = None
self.combine = None # some locations might be combined in bead model
def get_connected_location(self):
if self.connection is None:
return None
else:
return self.connection.other(self)
def set_connection(self, connection, is_3prime_side_of_connection):
self.connection = connection # TODO weakref?
self.is_3prime_side_of_connection = is_3prime_side_of_connection
def get_nt_pos(self):
try:
pos = self.container.contour_to_nt_pos(self.address, round_nt=True)
except:
if self.address == 0:
pos = 0
elif self.address == 1:
pos = self.container.num_nt-1
else:
raise
return pos
def __repr__(self):
if self.on_fwd_strand:
on_fwd = "on_fwd_strand"
else:
on_fwd = "on_rev_strand"
return "<Location {}.{}[{:.2f},{:d}]>".format( self.container.name, self.type_, self.address, self.on_fwd_strand)
class Connection():
""" Abstract base class for connection between two elements """
def __init__(self, A, B, type_ = None):
assert( isinstance(A,Location) )
assert( isinstance(B,Location) )
self.A = A
self.B = B
self.type_ = type_
def other(self, location):
if location is self.A:
return self.B
elif location is self.B:
return self.A
else:
raise Exception("OutOfBoundsError")
def delete(self):
self.A.container.connections.remove(self)
self.B.container.connections.remove(self)
self.A.connection = None
self.B.connection = None
def __repr__(self):
return "<Connection {}--{}--{}]>".format( self.A, self.type_, self.B )
# class ConnectableElement(Transformable):
class ConnectableElement():
""" Abstract base class """
def __init__(self, connection_locations=None, connections=None):
if connection_locations is None: connection_locations = []
if connections is None: connections = []
## TODO decide on names
self.locations = self.connection_locations = connection_locations
self.connections = connections
def get_locations(self, type_=None, exclude=()):
locs = [l for l in self.connection_locations if (type_ is None or l.type_ == type_) and l.type_ not in exclude]
counter = dict()
for l in locs:
if l in counter:
counter[l] += 1
else:
counter[l] = 1
assert( np.all( [counter[l] == 1 for l in locs] ) )
return locs
def get_location_at(self, address, on_fwd_strand=True, new_type="crossover"):
loc = None
if (self.num_nt == 1):
# import pdb
# pdb.set_trace()
## Assumes that intrahelical connections have been made before crossovers
for l in self.locations:
if l.on_fwd_strand == on_fwd_strand and l.connection is None:
assert(loc is None)
loc = l
# assert( loc is not None )
else:
for l in self.locations:
if l.address == address and l.on_fwd_strand == on_fwd_strand:
assert(loc is None)
loc = l
if loc is None:
loc = Location( self, address=address, type_=new_type, on_fwd_strand=on_fwd_strand )
return loc
def get_connections_and_locations(self, connection_type=None, exclude=()):
""" Returns a list with each entry of the form:
connection, location_in_self, location_in_other """
type_ = connection_type
ret = []
for c in self.connections:
if (type_ is None or c.type_ == type_) and c.type_ not in exclude:
if c.A.container is self:
ret.append( [c, c.A, c.B] )
elif c.B.container is self:
ret.append( [c, c.B, c.A] )
else:
import pdb
pdb.set_trace()
raise Exception("Object contains connection that fails to refer to object")
return ret
def _connect(self, other, connection, in_3prime_direction=None):
## TODO fix circular references
A,B = [connection.A, connection.B]
if in_3prime_direction is not None:
A.is_3prime_side_of_connection = not in_3prime_direction
B.is_3prime_side_of_connection = in_3prime_direction
A.connection = B.connection = connection
self.connections.append(connection)
other.connections.append(connection)
l = A.container.locations
if A not in l: l.append(A)
l = B.container.locations
if B not in l: l.append(B)
# def _find_connections(self, loc):
# return [c for c in self.connections if c.A == loc or c.B == loc]
class SegmentParticle(PointParticle):
def __init__(self, type_, position, name="A", segname="A", **kwargs):
self.name = name
self.contour_position = None
PointParticle.__init__(self, type_, position, name=name, segname=segname, **kwargs)
self.intrahelical_neighbors = []
self.other_neighbors = []
self.locations = []
def get_intrahelical_above(self):
""" Returns bead directly above self """
# assert( len(self.intrahelical_neighbors) <= 2 )
for b in self.intrahelical_neighbors:
if b.get_contour_position(self.parent) > self.contour_position:
return b
def get_intrahelical_below(self):
""" Returns bead directly below self """
# assert( len(self.intrahelical_neighbors) <= 2 )
for b in self.intrahelical_neighbors:
if b.get_contour_position(self.parent) < self.contour_position:
return b
def _neighbor_should_be_added(self,b):
if type(self.parent) != type(b.parent):
return True
c1 = self.contour_position
c2 = b.get_contour_position(self.parent)
if c2 < c1:
b0 = self.get_intrahelical_below()
else:
b0 = self.get_intrahelical_above()
if b0 is not None:
c0 = b0.get_contour_position(self.parent)
if np.abs(c2-c1) < np.abs(c0-c1):
## remove b0
self.intrahelical_neighbors.remove(b0)
b0.intrahelical_neighbors.remove(self)
return True
else:
return False
return True
def make_intrahelical_neighbor(self,b):
add1 = self._neighbor_should_be_added(b)
add2 = b._neighbor_should_be_added(self)
if add1 and add2:
# assert(len(b.intrahelical_neighbors) <= 1)
# assert(len(self.intrahelical_neighbors) <= 1)
self.intrahelical_neighbors.append(b)
b.intrahelical_neighbors.append(self)
def get_nt_position(self, seg):
""" Returns the "address" of the nucleotide relative to seg in
nucleotides, taking the shortest (intrahelical) contour length route to seg
"""
if seg == self.parent:
return seg.contour_to_nt_pos(self.contour_position)
else:
pos = self.get_contour_position(seg)
return seg.contour_to_nt_pos(pos)
def get_contour_position(self,seg):
if seg == self.parent:
return self.contour_position
else:
cutoff = 30*3
target_seg = seg
## depth-first search
## TODO cache distances to nearby locations?
def descend_search_tree(seg, contour_in_seg, distance=0, visited_segs=None):
nonlocal cutoff
if visited_segs is None: visited_segs = []
if seg == target_seg:
# pdb.set_trace()
## Found a segment in our target
sign = (contour_in_seg == 1) - (contour_in_seg == 0)
assert( sign in (1,-1) )
if distance < cutoff: # TODO: check if this does anything
cutoff = distance
return [[distance, contour_in_seg+sign*seg.nt_pos_to_contour(distance)]], [(seg, contour_in_seg, distance)]
if distance > cutoff:
return None,None
ret_list = []
hist_list = []
## Find intrahelical locations in seg that we might pass through
for c,A,B in seg.get_connections_and_locations("intrahelical"):
if B.container in visited_segs: continue
dx = seg.contour_to_nt_pos( A.address, round_nt=False ) - seg.contour_to_nt_pos( contour_in_seg, round_nt=False)
dx = np.abs(dx)
results,history = descend_search_tree( B.container, B.address,
distance+dx, visited_segs + [seg] )
if results is not None:
ret_list.extend( results )
hist_list.extend( history )
return ret_list,hist_list
results,history = descend_search_tree(self.parent, self.contour_position)
if results is None or len(results) == 0:
raise Exception("Could not find location in segment") # TODO better error
return sorted(results,key=lambda x:x[0])[0][1]
# nt_pos = self.get_nt_position(seg)
# return seg.nt_pos_to_contour(nt_pos)
def update_position(self, contour_position):
self.contour_position = contour_position
self.position = self.parent.contour_to_position(contour_position)
if 'orientation_bead' in self.__dict__:
o = self.orientation_bead
o.contour_position = contour_position
orientation = self.parent.contour_to_orientation(contour_position)
if orientation is None:
print("WARNING: local_twist is True, but orientation is None; using identity")
orientation = np.eye(3)
o.position = self.position + orientation.dot( np.array((Segment.orientation_bond.r0,0,0)) )
def __repr__(self):
return "<SegmentParticle {} on {}[{:.2f}]>".format( self.name, self.parent, self.contour_position)
## TODO break this class into smaller, better encapsulated pieces
class Segment(ConnectableElement, Group):
""" Base class that describes a segment of DNA. When built from
cadnano models, should not span helices """
"""Define basic particle types"""
dsDNA_particle = ParticleType("D",
diffusivity = 43.5,
mass = 300,
radius = 3,
)
orientation_particle = ParticleType("O",
diffusivity = 100,
mass = 300,
radius = 1,
)
# orientation_bond = HarmonicBond(10,2)
orientation_bond = HarmonicBond(30,1.5, rRange = (0,500) )
ssDNA_particle = ParticleType("S",
diffusivity = 43.5,
mass = 150,
radius = 3,
)
def __init__(self, name, num_nt,
start_position = None,
end_position = None,
segment_model = None):
if start_position is None: start_position = np.array((0,0,0))
Group.__init__(self, name, children=[])
ConnectableElement.__init__(self, connection_locations=[], connections=[])
self.resname = name
self.start_orientation = None
self.twist_per_nt = 0
self.beads = [c for c in self.children] # self.beads will not contain orientation beads
self._bead_model_generation = 0 # TODO: remove?
self.segment_model = segment_model # TODO: remove?
self.strand_pieces = dict()
for d in ('fwd','rev'):
self.strand_pieces[d] = []
self.num_nt = int(num_nt)
if end_position is None:
end_position = np.array((0,0,self.distance_per_nt*num_nt)) + start_position
self.start_position = start_position
self.end_position = end_position
## Set up interpolation for positions
self._set_splines_from_ends()
self.sequence = None
def __repr__(self):
return "<{} {}[{:d}]>".format( type(self), self.name, self.num_nt )
def _set_splines_from_ends(self):
a = np.array([self.start_position,self.end_position]).T
tck, u = interpolate.splprep( a, u=[0,1], s=0, k=1)
self.position_spline_params = tck
self.quaternion_spline_params = None
def clear_all(self):
Group.clear_all(self) # TODO: use super?
self.beads = []
for c,loc,other in self.get_connections_and_locations():
loc.particle = None
def contour_to_nt_pos(self, contour_pos, round_nt=False):
nt = contour_pos*(self.num_nt) - 0.5
if round_nt:
assert( np.isclose(np.around(nt),nt) )
nt = np.around(nt)
return nt
def nt_pos_to_contour(self,nt_pos):
return (nt_pos+0.5)/(self.num_nt)
def contour_to_position(self,s):
p = interpolate.splev( s, self.position_spline_params )
if len(p) > 1: p = np.array(p).T
return p
def contour_to_tangent(self,s):
t = interpolate.splev( s, self.position_spline_params, der=1 )
t = (t / np.linalg.norm(t,axis=0))
return t.T
def contour_to_orientation(self,s):
assert( isinstance(s,float) or isinstance(s,int) or len(s) == 1 ) # TODO make vectorized version
if self.quaternion_spline_params is None:
axis = self.contour_to_tangent(s)
axis = axis / np.linalg.norm(axis)
rotAxis = np.cross(axis,np.array((0,0,1)))
rotAxisL = np.linalg.norm(rotAxis)
zAxis = np.array((0,0,1))
if rotAxisL > 0.001:
theta = np.arcsin(rotAxisL) * 180/np.pi
if axis.dot(zAxis) < 0: theta = 180-theta
orientation0 = rotationAboutAxis( rotAxis/rotAxisL, theta, normalizeAxis=False ).T
else:
orientation0 = np.eye(3) if axis.dot(zAxis) > 0 else \
rotationAboutAxis( np.array((1,0,0)), 180, normalizeAxis=False )
orientation = rotationAboutAxis( axis, self.twist_per_nt*self.contour_to_nt_pos(s), normalizeAxis=False )
orientation = orientation.dot(orientation0)
else:
q = interpolate.splev( s, self.quaternion_spline_params )
if len(q) > 1: q = np.array(q).T # TODO: is this needed?
orientation = quaternion_to_matrix(q)
return orientation
def get_contour_sorted_connections_and_locations(self,type_):
sort_fn = lambda c: c[1].address
cl = self.get_connections_and_locations(type_)
return sorted(cl, key=sort_fn)
def randomize_unset_sequence(self):
bases = list(seqComplement.keys())
# bases = ['T'] ## FOR DEBUG
if self.sequence is None:
self.sequence = [random.choice(bases) for i in range(self.num_nt)]
else:
assert(len(self.sequence) == self.num_nt) # TODO move
for i in range(len(self.sequence)):
if self.sequence[i] is None:
self.sequence[i] = random.choice(bases)
def _get_num_beads(self, max_basepairs_per_bead, max_nucleotides_per_bead ):
raise NotImplementedError
def _generate_one_bead(self, contour_position, nts):
raise NotImplementedError
def _generate_atomic_nucleotide(self, contour_position, is_fwd, seq, scale):
""" Seq should include modifications like 5T, T3 Tsinglet; direction matters too """
# print("Generating nucleotide at {}".format(contour_position))
pos = self.contour_to_position(contour_position)
orientation = self.contour_to_orientation(contour_position)
""" deleteme
## TODO: move this code (?)
if orientation is None:
import pdb
pdb.set_trace()
axis = self.contour_to_tangent(contour_position)
angleVec = np.array([1,0,0])
if axis.dot(angleVec) > 0.9: angleVec = np.array([0,1,0])
angleVec = angleVec - angleVec.dot(axis)*axis
angleVec = angleVec/np.linalg.norm(angleVec)
y = np.cross(axis,angleVec)
orientation = np.array([angleVec,y,axis]).T
## TODO: improve placement of ssDNA
# rot = rotationAboutAxis( axis, contour_position*self.twist_per_nt*self.num_nt, normalizeAxis=True )
# orientation = rot.dot(orientation)
else:
orientation = orientation
"""
key = seq
nt_dict = canonicalNtFwd if is_fwd else canonicalNtRev
atoms = nt_dict[ key ].generate() # TODO: clone?
atoms.orientation = orientation.dot(atoms.orientation)
if isinstance(self, SingleStrandedSegment):
if scale is not None and scale != 1:
for a in atoms:
a.position = scale*a.position
a.beta = 0
atoms.position = pos - atoms.atoms_by_name["C1'"].collapsedPosition()
else:
if scale is not None and scale != 1:
if atoms.sequence in ("A","G"):
r0 = atoms.atoms_by_name["N9"].position
else:
r0 = atoms.atoms_by_name["N1"].position
for a in atoms:
if a.name[-1] in ("'","P","T"):
a.position = scale*(a.position-r0) + r0
a.beta = 0
atoms.position = pos
return atoms
def add_location(self, nt, type_, on_fwd_strand=True):
## Create location if needed, add to segment
c = self.nt_pos_to_contour(nt)
assert(c >= 0 and c <= 1)
# TODO? loc = self.Location( address=c, type_=type_, on_fwd_strand=is_fwd )
loc = Location( self, address=c, type_=type_, on_fwd_strand=on_fwd_strand )
self.locations.append(loc)
## TODO? Replace with abstract strand-based model?
def add_5prime(self, nt, on_fwd_strand=True):
if isinstance(self,SingleStrandedSegment):
on_fwd_strand = True
self.add_location(nt,"5prime",on_fwd_strand)
def add_3prime(self, nt, on_fwd_strand=True):
if isinstance(self,SingleStrandedSegment):
on_fwd_strand = True
self.add_location(nt,"3prime",on_fwd_strand)
def get_3prime_locations(self):
return sorted(self.get_locations("3prime"),key=lambda x: x.address)
def get_5prime_locations(self):
## TODO? ensure that data is consistent before _build_model calls
return sorted(self.get_locations("5prime"),key=lambda x: x.address)
def iterate_connections_and_locations(self, reverse=False):
## connections to other segments
cl = self.get_contour_sorted_connections_and_locations()
if reverse:
cl = cl[::-1]
for c in cl:
yield c
## TODO rename
def _add_strand_piece(self, strand_piece):
""" Registers a strand segment within this object """
## TODO use weakref
d = 'fwd' if strand_piece.is_fwd else 'rev'
## Validate strand_piece (ensure no clashes)
for s in self.strand_pieces[d]:
l,h = sorted((s.start,s.end))
for value in (strand_piece.start,strand_piece.end):
assert( value < l or value > h )
## Add strand_piece in correct order
self.strand_pieces[d].append(strand_piece)
self.strand_pieces[d] = sorted(self.strand_pieces[d],
key = lambda x: x.start)
## TODO rename
def get_strand_segment(self, nt_pos, is_fwd, move_at_least=0.5):
""" Walks through locations, checking for crossovers """
# if self.name in ("6-1","1-1"):
# import pdb
# pdb.set_trace()
move_at_least = 0
## Iterate through locations
# locations = sorted(self.locations, key=lambda l:(l.address,not l.on_fwd_strand), reverse=(not is_fwd))
def loc_rank(l):
nt = l.get_nt_pos()
## optionally add logic about type of connection
return (nt, not l.on_fwd_strand)
# locations = sorted(self.locations, key=lambda l:(l.address,not l.on_fwd_strand), reverse=(not is_fwd))
locations = sorted(self.locations, key=loc_rank, reverse=(not is_fwd))
# print(locations)
for l in locations:
# TODOTODO probably okay
if l.address == 0:
pos = 0.0
elif l.address == 1:
pos = self.num_nt-1
else:
pos = self.contour_to_nt_pos(l.address, round_nt=True)
## DEBUG
## Skip locations encountered before our strand
# tol = 0.1
# if is_fwd:
# if pos-nt_pos <= tol: continue
# elif nt_pos-pos <= tol: continue
if (pos-nt_pos)*(2*is_fwd-1) < move_at_least: continue
## TODO: remove move_at_least
if np.isclose(pos,nt_pos):
if l.is_3prime_side_of_connection: continue
## Stop if we found the 3prime end
if l.on_fwd_strand == is_fwd and l.type_ == "3prime":
# print(" found end at",l)
return pos, None, None, None, None
## Check location connections
c = l.connection
if c is None: continue
B = c.other(l)
## Found a location on the same strand?
if l.on_fwd_strand == is_fwd:
# print(" passing through",l)
# print("from {}, connection {} to {}".format(nt_pos,l,B))
Bpos = B.get_nt_pos()
return pos, B.container, Bpos, B.on_fwd_strand, 0.5
## Stop at other strand crossovers so basepairs line up
elif c.type_ == "crossover":
if nt_pos == pos: continue
# print(" pausing at",l)
return pos, l.container, pos+(2*is_fwd-1), is_fwd, 0
raise Exception("Shouldn't be here")
# print("Shouldn't be here")
## Made it to the end of the segment without finding a connection
return 1*is_fwd, None, None, None
def get_nearest_bead(self, contour_position):
if len(self.beads) < 1: return None
cs = np.array([b.contour_position for b in self.beads]) # TODO: cache
# TODO: include beads in connections?
i = np.argmin((cs - contour_position)**2)
return self.beads[i]
def _get_atomic_nucleotide(self, nucleotide_idx, is_fwd=True):
d = 'fwd' if is_fwd else 'rev'
for s in self.strand_pieces[d]:
try:
return s.get_nucleotide(nucleotide_idx)
except:
pass
raise Exception("Could not find nucleotide in {} at {}.{}".format( self, nucleotide_idx, d ))
def get_all_consecutive_beads(self, number):
assert(number >= 1)
## Assume that consecutive beads in self.beads are bonded
ret = []
for i in range(len(self.beads)-number+1):
tmp = [self.beads[i+j] for j in range(0,number)]
ret.append( tmp )
return ret
def _add_bead(self,b,set_contour=False):
if set_contour:
b.contour_position = b.get_contour_position(self)
# assert(b.parent is None)
if b.parent is not None:
b.parent.children.remove(b)
self.add(b)
self.beads.append(b) # don't add orientation bead
if "orientation_bead" in b.__dict__: # TODO: think of a cleaner approach
o = b.orientation_bead
o.contour_position = b.contour_position
if o.parent is not None:
o.parent.children.remove(o)
self.add(o)
self.add_bond(b,o, Segment.orientation_bond, exclude=True)
def _rebuild_children(self, new_children):
# print("_rebuild_children on %s" % self.name)
old_children = self.children
old_beads = self.beads
self.children = []
self.beads = []
if True:
## TODO: remove this if duplicates are never found
# print("Searching for duplicate particles...")
## Remove duplicates, preserving order
tmp = []
for c in new_children:
if c not in tmp:
tmp.append(c)
else:
print(" DUPLICATE PARTICLE FOUND!")
new_children = tmp
for b in new_children:
self.beads.append(b)
self.children.append(b)
if "orientation_bead" in b.__dict__: # TODO: think of a cleaner approach
self.children.append(b.orientation_bead)
# tmp = [c for c in self.children if c not in old_children]
# assert(len(tmp) == 0)
# tmp = [c for c in old_children if c not in self.children]
# assert(len(tmp) == 0)
assert(len(old_children) == len(self.children))
assert(len(old_beads) == len(self.beads))
def _generate_beads(self, bead_model, max_basepairs_per_bead, max_nucleotides_per_bead):
""" Generate beads (positions, types, etc) and bonds, angles, dihedrals, exclusions """
## TODO: decide whether to remove bead_model argument
## (currently unused)
## First find points between-which beads must be generated
# conn_locs = self.get_contour_sorted_connections_and_locations()
# locs = [A for c,A,B in conn_locs]
# existing_beads = [l.particle for l in locs if l.particle is not None]
# if self.name == "S001":
# pdb.set_trace()
existing_beads0 = {l.particle for l in self.locations if l.particle is not None}
existing_beads = sorted( list(existing_beads0), key=lambda b: b.get_contour_position(self) )
for b in existing_beads:
assert(b.parent is not None)
## Add ends if they don't exist yet
## TODOTODO: test 1 nt segments?
if len(existing_beads) == 0 or existing_beads[0].get_nt_position(self) >= 0.5:
# if len(existing_beads) > 0:
# assert(existing_beads[0].get_nt_position(self) >= 0.5)
b = self._generate_one_bead( self.nt_pos_to_contour(0), 0)
existing_beads = [b] + existing_beads
if existing_beads[-1].get_nt_position(self)-(self.num_nt-1) < -0.5:
b = self._generate_one_bead( self.nt_pos_to_contour(self.num_nt-1), 0)
existing_beads.append(b)
assert(len(existing_beads) > 1)
## Walk through existing_beads, add beads between
tmp_children = [] # build list of children in nice order
last = None
for I in range(len(existing_beads)-1):
eb1,eb2 = [existing_beads[i] for i in (I,I+1)]
assert( eb1 is not eb2 )
# if np.isclose(eb1.position[2], eb2.position[2]):
# import pdb
# pdb.set_trace()
# print(" %s working on %d to %d" % (self.name, eb1.position[2], eb2.position[2]))
e_ds = eb2.get_contour_position(self) - eb1.get_contour_position(self)
num_beads = self._get_num_beads( e_ds, max_basepairs_per_bead, max_nucleotides_per_bead )
## Ensure there is a ssDNA bead between dsDNA beads
if num_beads == 0 and isinstance(self,SingleStrandedSegment) and isinstance(eb1.parent,DoubleStrandedSegment) and isinstance(eb2.parent,DoubleStrandedSegment):
num_beads = 1
## TODO similarly ensure there is a dsDNA bead between ssDNA beads
ds = e_ds / (num_beads+1)
nts = ds*self.num_nt
eb1.num_nt += 0.5*nts
eb2.num_nt += 0.5*nts
## Add beads
if eb1.parent == self:
tmp_children.append(eb1)
s0 = eb1.get_contour_position(self)
if last is not None:
last.make_intrahelical_neighbor(eb1)
last = eb1
for j in range(num_beads):
s = ds*(j+1) + s0
# if self.name in ("51-2","51-3"):
# if self.name in ("31-2",):
# print(" adding bead at {}".format(s))
b = self._generate_one_bead(s,nts)
last.make_intrahelical_neighbor(b)
last = b
tmp_children.append(b)
last.make_intrahelical_neighbor(eb2)
if eb2.parent == self:
tmp_children.append(eb2)
# if self.name in ("31-2",):
# pdb.set_trace()
self._rebuild_children(tmp_children)
def _regenerate_beads(self, max_nts_per_bead=4, ):
...
class DoubleStrandedSegment(Segment):
""" Class that describes a segment of ssDNA. When built from
cadnano models, should not span helices """
def __init__(self, name, num_bp, start_position = np.array((0,0,0)),
end_position = None,
segment_model = None,
local_twist = False,
num_turns = None,
start_orientation = None,
twist_persistence_length = 90 ):
self.helical_rise = 10.44
self.distance_per_nt = 3.4
Segment.__init__(self, name, num_bp,
start_position,
end_position,
segment_model)
self.num_bp = self.num_nt
self.local_twist = local_twist
if num_turns is None:
num_turns = float(num_bp) / self.helical_rise
self.twist_per_nt = float(360 * num_turns) / num_bp
if start_orientation is None:
start_orientation = np.eye(3) # np.array(((1,0,0),(0,1,0),(0,0,1)))
self.start_orientation = start_orientation
self.twist_persistence_length = twist_persistence_length
self.nicks = []
self.start = self.start5 = Location( self, address=0, type_= "end5" )
self.start3 = Location( self, address=0, type_ = "end3", on_fwd_strand=False )
self.end = self.end3 = Location( self, address=1, type_ = "end3" )
self.end5 = Location( self, address=1, type_= "end5", on_fwd_strand=False )
# for l in (self.start5,self.start3,self.end3,self.end5):
# self.locations.append(l)
## Set up interpolation for azimuthal angles
a = np.array([self.start_position,self.end_position]).T
tck, u = interpolate.splprep( a, u=[0,1], s=0, k=1)
self.position_spline_params = tck
## TODO: initialize sensible spline for orientation
## Convenience methods
## TODO: add errors if unrealistic connections are made
## TODO: make connections automatically between unconnected strands
def connect_start5(self, end3, type_="intrahelical", force_connection=False):
if isinstance(end3, SingleStrandedSegment):
end3 = end3.end3
self._connect_ends( self.start5, end3, type_, force_connection = force_connection )
def connect_start3(self, end5, type_="intrahelical", force_connection=False):
if isinstance(end5, SingleStrandedSegment):
end5 = end5.start5
self._connect_ends( self.start3, end5, type_, force_connection = force_connection )
def connect_end3(self, end5, type_="intrahelical", force_connection=False):
if isinstance(end5, SingleStrandedSegment):
end5 = end5.start5
self._connect_ends( self.end3, end5, type_, force_connection = force_connection )
def connect_end5(self, end3, type_="intrahelical", force_connection=False):
if isinstance(end3, SingleStrandedSegment):
end3 = end3.end3
self._connect_ends( self.end5, end3, type_, force_connection = force_connection )
def add_crossover(self, nt, other, other_nt, strands_fwd=(True,False), nt_on_5prime=True, type_="crossover"):
""" Add a crossover between two helices """
## Validate other, nt, other_nt
## TODO
if isinstance(other,SingleStrandedSegment):
other.add_crossover(other_nt, self, nt, strands_fwd[::-1], not nt_on_5prime)
else:
## Create locations, connections and add to segments
c = self.nt_pos_to_contour(nt)
assert(c >= 0 and c <= 1)
loc = self.get_location_at(c, strands_fwd[0])
c = other.nt_pos_to_contour(other_nt)
# TODOTODO: may need to subtract or add a little depending on 3prime/5prime
assert(c >= 0 and c <= 1)
other_loc = other.get_location_at(c, strands_fwd[1])
self._connect(other, Connection( loc, other_loc, type_=type_ ))
if nt_on_5prime:
loc.is_3prime_side_of_connection = False
other_loc.is_3prime_side_of_connection = True
else:
loc.is_3prime_side_of_connection = True
other_loc.is_3prime_side_of_connection = False
## Real work
def _connect_ends(self, end1, end2, type_, force_connection):
## TODO remove self?
## validate the input
for end in (end1, end2):
assert( isinstance(end, Location) )
assert( end.type_ in ("end3","end5") )
assert( end1.type_ != end2.type_ )
## Remove other connections involving these points
if end1.connection is not None:
print("WARNING: reconnecting {}".format(end1))
end1.connection.delete()
if end2.connection is not None:
print("WARNING: reconnecting {}".format(end2))
end2.connection.delete()
## Create and add connection
if end2.type_ == "end5":
end1.container._connect( end2.container, Connection( end1, end2, type_=type_ ), in_3prime_direction=True )
else:
end2.container._connect( end1.container, Connection( end2, end1, type_=type_ ), in_3prime_direction=True )
def _get_num_beads(self, contour, max_basepairs_per_bead, max_nucleotides_per_bead):
# return int(contour*self.num_nt // max_basepairs_per_bead)
return int(contour*(self.num_nt**2/(self.num_nt+1)) // max_basepairs_per_bead)
def _generate_one_bead(self, contour_position, nts):
pos = self.contour_to_position(contour_position)
if self.local_twist:
orientation = self.contour_to_orientation(contour_position)
if orientation is None:
print("WARNING: local_twist is True, but orientation is None; using identity")
orientation = np.eye(3)
opos = pos + orientation.dot( np.array((Segment.orientation_bond.r0,0,0)) )
# if np.linalg.norm(pos) > 1e3:
# pdb.set_trace()
assert(np.linalg.norm(opos-pos) < 10 )
o = SegmentParticle( Segment.orientation_particle, opos, name="O",
contour_position = contour_position,
num_nt=nts, parent=self )
bead = SegmentParticle( Segment.dsDNA_particle, pos, name="DNA",
num_nt=nts, parent=self,
orientation_bead=o,
contour_position=contour_position )
else:
bead = SegmentParticle( Segment.dsDNA_particle, pos, name="DNA",
num_nt=nts, parent=self,
contour_position=contour_position )
self._add_bead(bead)
return bead
class SingleStrandedSegment(Segment):
""" Class that describes a segment of ssDNA. When built from
cadnano models, should not span helices """
def __init__(self, name, num_nt, start_position = None,
end_position = None,
segment_model = None):
if start_position is None: start_position = np.array((0,0,0))
self.distance_per_nt = 5
Segment.__init__(self, name, num_nt,
start_position,
end_position,
segment_model)
self.start = self.start5 = Location( self, address=0, type_= "end5" ) # TODO change type_?
self.end = self.end3 = Location( self, address=1, type_ = "end3" )
# for l in (self.start5,self.end3):
# self.locations.append(l)
def connect_end3(self, end5, force_connection=False):
self._connect_end( end5, _5_to_3 = True, force_connection = force_connection )
def connect_5end(self, end3, force_connection=False): # TODO: change name or possibly deprecate
self._connect_end( end3, _5_to_3 = False, force_connection = force_connection )
def _connect_end(self, other, _5_to_3, force_connection):
assert( isinstance(other, Location) )
if _5_to_3 == True:
seg1 = self
seg2 = other.container
end1 = self.end3
end2 = other
# assert( other.type_ == "end5" )
if (other.type_ is not "end5"):
print("Warning: code does not prevent connecting 3prime to 3prime, etc")
else:
seg1 = other.container
seg2 = self
end1 = other
end2 = self.end5
# assert( other.type_ == "end3" )
if (other.type_ is not "end3"):
print("Warning: code does not prevent connecting 3prime to 3prime, etc")
## Remove other connections involving these points
if end1.connection is not None:
print("WARNING: reconnecting {}".format(end1))
end1.connection.delete()
if end2.connection is not None:
print("WARNING: reconnecting {}".format(end2))
end2.connection.delete()
conn = Connection( end1, end2, type_="intrahelical" )
seg1._connect( seg2, conn, in_3prime_direction=True )
def add_crossover(self, nt, other, other_nt, strands_fwd=(True,False), nt_on_5prime=True, type_='sscrossover'):
""" Add a crossover between two helices """
## Validate other, nt, other_nt
## TODO
## TODO: fix direction
# c1 = self.nt_pos_to_contour(nt)
# # TODOTODO
# ## Ensure connections occur at ends, otherwise the structure doesn't make sense
# # assert(np.isclose(c1,0) or np.isclose(c1,1))
# assert(np.isclose(nt,0) or np.isclose(nt,self.num_nt-1))
if nt == 0:
c1 = 0
elif nt == self.num_nt-1:
c1 = 1
else:
raise Exception("Crossovers can only be at the ends of an ssDNA segment")
loc = self.get_location_at(c1, True)
if other_nt == 0:
c2 = 0
elif other_nt == other.num_nt-1:
c2 = 1
else:
c2 = other.nt_pos_to_contour(other_nt)
if isinstance(other,SingleStrandedSegment):
## Ensure connections occur at opposing ends
assert(np.isclose(other_nt,0) or np.isclose(other_nt,self.num_nt-1))
other_loc = other.get_location_at( c2, True )
# if ("22-2" in (self.name, other.name)):
# pdb.set_trace()
if nt_on_5prime:
self.connect_end3( other_loc )
else:
other.connect_end3( self )
else:
assert(c2 >= 0 and c2 <= 1)
other_loc = other.get_location_at( c2, strands_fwd[1] )
if nt_on_5prime:
self._connect(other, Connection( loc, other_loc, type_="sscrossover" ), in_3prime_direction=True )
else:
other._connect(self, Connection( other_loc, loc, type_="sscrossover" ), in_3prime_direction=True )
def _get_num_beads(self, contour, max_basepairs_per_bead, max_nucleotides_per_bead):
return int(contour*(self.num_nt**2/(self.num_nt+1)) // max_basepairs_per_bead)
# return int(contour*self.num_nt // max_nucleotides_per_bead)
def _generate_one_bead(self, contour_position, nts):
pos = self.contour_to_position(contour_position)
b = SegmentParticle( Segment.ssDNA_particle, pos,
name="NAS",
num_nt=nts, parent=self,
contour_position=contour_position )
self._add_bead(b)
return b
class StrandInSegment(Group):
""" Represents a piece of an ssDNA strand within a segment """
def __init__(self, segment, start, end, is_fwd):
""" start/end should be provided expressed in nt coordinates, is_fwd tuples """
Group.__init__(self)
self.num_nt = 0
# self.sequence = []
self.segment = segment
self.start = start
self.end = end
self.is_fwd = is_fwd
nts = np.abs(end-start)+1
self.num_nt = int(round(nts))
assert( np.isclose(self.num_nt,nts) )
segment._add_strand_piece(self)
def _nucleotide_ids(self):
nt0 = self.start # seg.contour_to_nt_pos(self.start)
assert( np.abs(nt0 - round(nt0)) < 1e-5 )
nt0 = int(round(nt0))
assert( (self.end-self.start) >= 0 or not self.is_fwd )
direction = (2*self.is_fwd-1)
return range(nt0,nt0 + direction*self.num_nt, direction)
def get_sequence(self):
""" return 5-to-3 """
# TODOTODO test
seg = self.segment
if self.is_fwd:
return [seg.sequence[nt] for nt in self._nucleotide_ids()]
else:
return [seqComplement[seg.sequence[nt]] for nt in self._nucleotide_ids()]
def get_contour_points(self):
c0,c1 = [self.segment.nt_pos_to_contour(p) for p in (self.start,self.end)]
return np.linspace(c0,c1,self.num_nt)
def get_nucleotide(self, idx):
""" idx expressed as nt coordinate within segment """
lo,hi = sorted((self.start,self.end))
if self.is_fwd:
idx_in_strand = idx - lo
else:
idx_in_strand = hi - idx
assert( np.isclose( idx_in_strand , int(round(idx_in_strand)) ) )
assert(idx_in_strand >= 0)
return self.children[int(round(idx_in_strand))]
class Strand(Group):
""" Represents an entire ssDNA strand from 5' to 3' as it routes through segments """
def __init__(self, segname = None, is_circular = False):
Group.__init__(self)
self.num_nt = 0
self.children = self.strand_segments = []
self.segname = segname
self.is_circular = is_circular
## TODO disambiguate names of functions
def add_dna(self, segment, start, end, is_fwd):
""" start/end are given as nt """
if np.abs(start-end) <= 0.9:
print( "WARNING: segment constructed with a very small number of nts ({})".format(np.abs(start-end)) )
# import pdb
# pdb.set_trace()
for s in self.strand_segments:
if s.segment == segment and s.is_fwd == is_fwd:
# assert( s.start not in (start,end) )
# assert( s.end not in (start,end) )
if s.start in (start,end) or s.end in (start,end):
raise CircularDnaError("Found circular DNA")
s = StrandInSegment( segment, start, end, is_fwd )
self.add( s )
self.num_nt += s.num_nt
def set_sequence(self,sequence): # , set_complement=True):
## validate input
assert( len(sequence) >= self.num_nt )
assert( np.all( [i in ('A','T','C','G') for i in sequence] ) )
seq_idx = 0
## set sequence on each segment
for s in self.children:
seg = s.segment
if seg.sequence is None:
seg.sequence = [None for i in range(seg.num_nt)]
if s.is_fwd:
for nt in s._nucleotide_ids():
seg.sequence[nt] = sequence[seq_idx]
seq_idx += 1
else:
for nt in s._nucleotide_ids():
seg.sequence[nt] = seqComplement[sequence[seq_idx]]
seq_idx += 1
# def get_sequence(self):
# sequence = []
# for ss in self.strand_segments:
# sequence.extend( ss.get_sequence() )
# assert( len(sequence) >= self.num_nt )
# ret = ["5"+sequence[0]] +\
# sequence[1:-1] +\
# [sequence[-1]+"3"]
# assert( len(ret) == self.num_nt )
# return ret
def link_nucleotides(self, nt5, nt3):
parent = nt5.parent if nt5.parent is nt3.parent else self
o3,c3,c4,c2,h3 = [nt5.atoms_by_name[n]
for n in ("O3'","C3'","C4'","C2'","H3'")]
p,o5,o1,o2,c5 = [nt3.atoms_by_name[n]
for n in ("P","O5'","O1P","O2P","C5'")]
parent.add_bond( o3, p, None )
parent.add_angle( c3, o3, p, None )
for x in (o5,o1,o2):
parent.add_angle( o3, p, x, None )
parent.add_dihedral(c3, o3, p, x, None )
for x in (c4,c2,h3):
parent.add_dihedral(x, c3, o3, p, None )
parent.add_dihedral(o3, p, o5, c5, None)
def generate_atomic_model(self, scale, first_atomic_index):
last = None
resid = 1
## TODO relabel "strand_segment"
strand_segment_count = 0
for s in self.strand_segments:
strand_segment_count += 1
seg = s.segment
contour = s.get_contour_points()
# if s.end == s.start:
# pdb.set_trace()
# assert(s.end != s.start)
assert( s.num_nt == 1 or (np.linalg.norm( seg.contour_to_position(contour[-1]) - seg.contour_to_position(contour[0]) ) > 0.1) )
for c,seq in zip(contour,s.get_sequence()):
if last is None and not self.is_circular:
seq = "5"+seq
if strand_segment_count == len(s.strand_segments) and c == 1 and not self.is_circular:
seq = seq+"3"
nt = seg._generate_atomic_nucleotide( c, s.is_fwd, seq, scale )
# if s.is_fwd:
# else:
# nt = seg._generate_atomic_nucleotide( c, s.is_fwd, "A" )
s.add(nt)
## Join last basepairs
if last is not None:
self.link_nucleotides(last,nt)
nt.__dict__['resid'] = resid
resid += 1
last = nt
nt._first_atomic_index = first_atomic_index
first_atomic_index += len(nt.children)
if self.is_circular:
self.link_nucleotides(last,self.strand_segments[0].children[0])
return first_atomic_index
def update_atomic_orientations(self,default_orientation):
last = None
resid = 1
for s in self.strand_segments:
seg = s.segment
contour = s.get_contour_points()
for c,seq,nt in zip(contour,s.get_sequence(),s.children):
orientation = seg.contour_to_orientation(c)
## TODO: move this code (?)
if orientation is None:
axis = seg.contour_to_tangent(c)
angleVec = np.array([1,0,0])
if axis.dot(angleVec) > 0.9: angleVec = np.array([0,1,0])
angleVec = angleVec - angleVec.dot(axis)*axis
angleVec = angleVec/np.linalg.norm(angleVec)
y = np.cross(axis,angleVec)
orientation = np.array([angleVec,y,axis]).T
nt.orientation = orientation.dot(default_orientation) # this one should be correct
class SegmentModel(ArbdModel):
def __init__(self, segments=[], local_twist=True, escapable_twist=True,
max_basepairs_per_bead=7,
max_nucleotides_per_bead=4,
dimensions=(1000,1000,1000), temperature=291,
timestep=50e-6, cutoff=50,
decompPeriod=10000, pairlistDistance=None,
nonbondedResolution=0,DEBUG=0):
self.DEBUG = DEBUG
if DEBUG > 0: print("Building ARBD Model")
ArbdModel.__init__(self,segments,
dimensions, temperature, timestep, cutoff,
decompPeriod, pairlistDistance=None,
nonbondedResolution=0)
# self.max_basepairs_per_bead = max_basepairs_per_bead # dsDNA
# self.max_nucleotides_per_bead = max_nucleotides_per_bead # ssDNA
self.children = self.segments = segments
self._bonded_potential = dict() # cache for bonded potentials
self._generate_bead_model( max_basepairs_per_bead, max_nucleotides_per_bead, local_twist, escapable_twist)
self.useNonbondedScheme( nbDnaScheme )
self.useTclForces = False
self._generate_strands()
def get_connections(self,type_=None,exclude=()):
""" Find all connections in model, without double-counting """
added=set()
ret=[]
for s in self.segments:
items = [e for e in s.get_connections_and_locations(type_,exclude=exclude) if e[0] not in added]
added.update([e[0] for e in items])
ret.extend( list(sorted(items,key=lambda x: x[1].address)) )
return ret
def _recursively_get_beads_within_bonds(self,b1,bonds,done=()):
ret = []
done = list(done)
done.append(b1)
if bonds == 0:
return [[]]
for b2 in b1.intrahelical_neighbors:
if b2 in done: continue
for tmp in self._recursively_get_beads_within_bonds(b2, bonds-1, done):
ret.append( [b2]+tmp )
return ret
def _get_intrahelical_beads(self,num=2):
## TODO: add check that this is not called before adding intrahelical_neighbors in _generate_bead_model
assert(num >= 2)
ret = []
for s in self.segments:
for b1 in s.beads:
for bead_list in self._recursively_get_beads_within_bonds(b1, num-1):
assert(len(bead_list) == num-1)
if b1.idx < bead_list[-1].idx: # avoid double-counting
ret.append([b1]+bead_list)
return ret
def _get_intrahelical_angle_beads(self):
return self._get_intrahelical_beads(num=3)
def _get_potential(self, type_, kSpring, d, max_potential = None):
key = (type_, kSpring, d, max_potential)
if key not in self._bonded_potential:
assert( kSpring >= 0 )
if type_ == "bond":
self._bonded_potential[key] = HarmonicBond(kSpring,d, rRange=(0,1200), max_potential=max_potential)
elif type_ == "angle":
self._bonded_potential[key] = HarmonicAngle(kSpring,d, max_potential=max_potential)
# , resolution = 1, maxForce=0.1)
elif type_ == "dihedral":
self._bonded_potential[key] = HarmonicDihedral(kSpring,d, max_potential=max_potential)
else:
raise Exception("Unhandled potential type '%s'" % type_)
return self._bonded_potential[key]
def get_bond_potential(self, kSpring, d):
assert( d > 1 )
return self._get_potential("bond", kSpring, d)
def get_angle_potential(self, kSpring, d):
return self._get_potential("angle", kSpring, d)
def get_dihedral_potential(self, kSpring, d, max_potential=None):
while d > 180: d-=360
while d < -180: d+=360
return self._get_potential("dihedral", kSpring, d, max_potential)
def _getParent(self, *beads ):
if np.all( [b1.parent == b2.parent
for b1,b2 in zip(beads[:-1],beads[1:])] ):
return beads[0].parent
else:
return self
def _get_twist_spring_constant(self, sep):
""" sep in nt """
kT = 0.58622522 # kcal/mol
twist_persistence_length = 90 # set semi-arbitrarily as there is a large spread in literature
## <cos(q)> = exp(-s/Lp) = integrate( cos[x] exp(-A x^2), {x, 0, pi} ) / integrate( exp(-A x^2), {x, 0, pi} )
## Assume A is small
## int[B_] := Normal[Integrate[ Series[Cos[x] Exp[-B x^2], {B, 0, 1}], {x, 0, \[Pi]}]/
## Integrate[Series[Exp[-B x^2], {B, 0, 1}], {x, 0, \[Pi]}]]
## Actually, without assumptions I get fitFun below
## From http://www.annualreviews.org/doi/pdf/10.1146/annurev.bb.17.060188.001405
## units "3e-19 erg cm/ 295 k K" "nm" =~ 73
Lp = twist_persistence_length/0.34
fitFun = lambda x: np.real(erf( (4*np.pi*x + 1j)/(2*np.sqrt(x)) )) * np.exp(-1/(4*x)) / erf(2*np.sqrt(x)*np.pi) - np.exp(-sep/Lp)
k = opt.leastsq( fitFun, x0=np.exp(-sep/Lp) )
return k[0][0] * 2*kT*0.00030461742
def extend(self, other, copy=True):
assert( isinstance(other, SegmentModel) )
if copy:
for s in other.segments:
self.segments.append(deepcopy(s))
else:
for s in other.segments:
self.segments.append(s)
self._clear_beads()
def update(self, segment , copy=False):
assert( isinstance(segment, Segment) )
if copy:
segment = deepcopy(segment)
self.segments.append(segment)
self._clear_beads()
""" Mapping between different resolution models """
def _clear_beads(self):
for s in self.segments:
s.clear_all()
self.clear_all(keep_children=True)
## Check that it worked
assert( len([b for b in self]) == 0 )
locParticles = []
for s in self.segments:
for c,A,B in s.get_connections_and_locations():
for l in (A,B):
if l.particle is not None:
locParticles.append(A.particle)
assert( len(locParticles) == 0 )
assert( len([b for s in self.segments for b in s.beads]) == 0 )
def _update_segment_positions(self, bead_coordinates): # TODO: rename to update_splines
""" Set new function for each segments functions
contour_to_position and contour_to_orientation """
for s in self.segments:
# if s.name == "61-1":
# pdb.set_trace()
cabs = s.get_connections_and_locations("intrahelical")
if np.any( [B.particle is None for c,A,B in cabs] ):
print( "WARNING: none type found in connection, skipping" )
cabs = [e for e in cabs if e[2].particle is not None]
beads = set(s.beads + [A.particle for c,A,B in cabs])
if len(beads) <= 1:
pdb.set_trace()
## Add nearby beads
for c,A,B in cabs:
## TODOTODO test?
filter_fn = lambda x: x is not None and x not in beads
bs = list( filter( filter_fn, B.particle.intrahelical_neighbors ) )
beads.update(bs)
for i in range(3):
bs = list( filter( filter_fn, [n for b in bs for n in b.intrahelical_neighbors] ) )
beads.update(bs)
beads = list(beads)
## Skip beads that are None (some locations were not assigned a particle to avoid double-counting)
# beads = [b for b in beads if b is not None]
beads = list(filter(lambda x: x is not None, beads))
if isinstance(s, DoubleStrandedSegment):
beads = list(filter(lambda x: x.type_.name[0] == "D", beads))
contours = []
for b in beads:
try:
# if s.name == "61-1" and b.parent.name == "60-1":
# pdb.set_trace()
## might fail if s is an entire segment away
contours.append(b.get_contour_position(s))
except:
## ignore failed attempts
beads.remove(b)
contours = [b.get_contour_position(s) for b in beads]
contours = np.array(contours, dtype=np.float16) # deliberately use low precision
contours,ids = np.unique(contours, return_index=True)
if np.any( (contours[:-1] - contours[1:])**2 < 1e-8 ):
pdb.set_trace()
## TODO: keep closest beads beyond +-1.5 if there are fewer than 2 beads
tmp = []
dist = 1
while len(tmp) < 5 and dist < 3:
tmp = [ci for ci in zip(contours,ids) if np.abs(ci[0]-0.5) < dist]
dist += 0.1
if len(tmp) <= 1:
raise Exception("Failed to fit spline into segment {}".format(s))
contours = [ci[0] for ci in tmp]
ids = [ci[1] for ci in tmp]
# cb = sorted( zip(contours,beads), key=lambda a:a[0] )
# beads = [b for c,b in cb]
# contours = [c for c,b in cb]
beads = [beads[i] for i in ids]
ids = [b.idx for b in beads]
if len(beads) <= 1:
pdb.set_trace()
""" Get positions """
positions = bead_coordinates[ids,:].T
# print("BEADS NOT IN {}:".format(s))
# for b,c in filter(lambda z: z[0] not in s.beads, zip(beads,contours)):
# print(" {}[{:03f}]: {:0.3f}".format(b.parent.name, b.contour_position, c) )
ret = interpolate.splprep( positions, u=contours, s=0, k=1, full_output=1 )
tck = ret[0][0]
ret = interpolate.splprep( positions, u=contours, s=0, k=1, full_output=1 )
tck2 = ret[0][0]
assert( tck[0][0] == tck2[0][0] )
# if len(beads) < 8:
# ret = interpolate.splprep( positions, u=contours, s=0, k=1, full_output=1 )
# tck = ret[0][0]
# if ret[2] > 0:
# pdb.set_trace()
# else:
# try:
# ret = interpolate.splprep( positions, u=contours, s=0, k=3, full_output=1 )
# tck = ret[0][0]
# if ret[2] > 0:
# pdb.set_trace()
# except:
# ret = interpolate.splprep( positions, u=contours, s=0, k=1, full_output=1 )
# tck = ret[0][0]
# if ret[2] > 0:
# pdb.set_trace()
s.position_spline_params = tck
""" Get twist """
cb = [e for e in zip(contours,beads) if 'orientation_bead' in e[1].__dict__]
beads = [b for c,b in cb]
contours = [c for c,b in cb]
ids = [b.idx for b in beads]
# if 'orientation_bead' in beads[0].__dict__:
if len(beads) > 3:
tangents = s.contour_to_tangent(contours)
quats = []
lastq = None
for b,t in zip(beads,tangents):
o = b.orientation_bead
# positions
# angleVec = o.position - b.position
angleVec = bead_coordinates[o.idx,:] - bead_coordinates[b.idx,:]
angleVec = angleVec - angleVec.dot(t)*t
angleVec = angleVec/np.linalg.norm(angleVec)
y = np.cross(t,angleVec)
assert( np.abs(np.linalg.norm(y) - 1) < 1e-2 )
q = quaternion_from_matrix( np.array([angleVec,y,t]).T)
# q = quaternion_from_matrix( np.array([angleVec,y,t]))
if lastq is not None:
if q.dot(lastq) < 0:
q = -q
quats.append( q )
lastq = q
# pdb.set_trace()
quats = np.array(quats)
# tck, u = interpolate.splprep( quats.T, u=contours, s=3, k=3 ) ;# cubic spline not as good
tck, u = interpolate.splprep( quats.T, u=contours, s=0, k=1 )
s.quaternion_spline_params = tck
def _generate_bead_model(self,
max_basepairs_per_bead = 7,
max_nucleotides_per_bead = 4,
local_twist=False,
escapable_twist=True):
segments = self.segments
for s in segments:
s.local_twist = local_twist
""" Simplify connections """
# d_nt = dict() #
# for s in segments:
# d_nt[s] = 1.5/(s.num_nt-1)
# for s in segments:
# ## replace consecutive crossovers with
# cl = sorted( s.get_connections_and_locations("crossover"), key=lambda x: x[1].address )
# last = None
# for entry in cl:
# c,A,B = entry
# if last is not None and \
# (A.address - last[1].address) < d_nt[s]:
# same_type = c.type_ == last[0].type_
# same_dest_seg = B.container == last[2].container
# if same_type and same_dest_seg:
# if np.abs(B.address - last[2].address) < d_nt[B.container]:
# ## combine
# A.combine = last[1]
# B.combine = last[2]
# ...
# # if last is not None:
# # s.bead_locations.append(last)
# ...
# last = entry
# del d_nt
""" Generate beads at intrahelical junctions """
if self.DEBUG: print( "Adding intrahelical beads at junctions" )
## Loop through all connections, generating beads at appropriate locations
for c,A,B in self.get_connections("intrahelical"):
s1,s2 = [l.container for l in (A,B)]
# if s1.name in ("49-3","49-4") and s2.name in ("49-3","49-4"):
# if s1.name in ("51-2","51-3") and s2.name in ("51-2","51-3"):
# pdb.set_trace()
# print("Working on {}".format(c))
## TODO be more elegant!
# if isinstance(s1, DoubleStrandedSegment) and isinstance(s2, DoubleStrandedSegment) and A.on_fwd_strand == False: continue
# if isinstance(s1, DoubleStrandedSegment) and isinstance(s2, DoubleStrandedSegment) and A.on_fwd_strand == False: continue
## if A.on_fwd_strand == False: continue # TODO verify this avoids double-counting
## TODO determine whether any logic is needed to prevent double-counting
assert( A.particle is None )
assert( B.particle is None )
## TODO: offload the work here to s1
# TODOTODO
a1,a2 = [l.address for l in (A,B)]
# a1,a2 = [a - s.nt_pos_to_contour(0.5) if a == 0 else a + s.nt_pos_to_contour(0.5) for a,s in zip((a1,a2),(s1,s2))]
for a in (a1,a2):
assert( np.isclose(a,0) or np.isclose(a,1) )
# a1,a2 = [a - s.nt_pos_to_contour(0) if a == 0 else a + s.nt_pos_to_contour(0) for a,s in zip((a1,a2),(s1,s2))]
## TODO improve this for combinations of ssDNA and dsDNA (maybe a1/a2 should be calculated differently)
b = None
if isinstance(s1,DoubleStrandedSegment):
b = s1.get_nearest_bead(a1)
if b is not None:
if np.abs(b.get_nt_position(s1) - s1.contour_to_nt_pos(a1)) > 0.5:
b = None
if b is None and isinstance(s2,DoubleStrandedSegment):
b = s2.get_nearest_bead(a2)
if b is not None:
if np.abs(b.get_nt_position(s2) - s2.contour_to_nt_pos(a2)) > 0.5:
b = None
if b is not None and b.parent not in (s1,s2):
b = None
if b is None:
## need to generate a bead
if isinstance(s2,DoubleStrandedSegment):
b = s2._generate_one_bead(a2,0)
else:
b = s1._generate_one_bead(a1,0)
A.particle = B.particle = b
b.locations.extend([A,B])
# pdb.set_trace()
""" Generate beads at other junctions """
for c,A,B in self.get_connections(exclude="intrahelical"):
s1,s2 = [l.container for l in (A,B)]
if A.particle is not None and B.particle is not None:
continue
# assert( A.particle is None )
# assert( B.particle is None )
## TODO: offload the work here to s1/s2 (?)
a1,a2 = [l.address for l in (A,B)]
if A.particle is None:
b = s1.get_nearest_bead(a1)
if b is not None and s1.contour_to_nt_pos(np.abs(b.contour_position-a1)) < min(max_basepairs_per_bead, max_nucleotides_per_bead)*0.5:
## combine beads
b.update_position( 0.5*(b.contour_position + a1) ) # avg position
else:
b = s1._generate_one_bead(a1,0)
A.particle = b
b.locations.append(A)
if B.particle is None:
b = s2.get_nearest_bead(a2)
if b is not None and s2.contour_to_nt_pos(np.abs(b.contour_position-a2)) < min(max_basepairs_per_bead, max_nucleotides_per_bead)*0.5:
## combine beads
b.update_position( 0.5*(b.contour_position + a2) ) # avg position
else:
b = s2._generate_one_bead(a2,0)
B.particle = b
b.locations.append(B)
""" Some tests """
for c,A,B in self.get_connections("intrahelical"):
for l in (A,B):
if l.particle is None: continue
assert( l.particle.parent is not None )
""" Generate beads in between """
if self.DEBUG: print("Generating beads")
for s in segments:
s._generate_beads( self, max_basepairs_per_bead, max_nucleotides_per_bead )
# """ Combine beads at junctions as needed """
# for c,A,B in self.get_connections():
# ...
# ## Debug
# all_beads = [b for s in segments for b in s.beads]
# positions = np.array([b.position for b in all_beads])
# dists = positions[:,np.newaxis,:] - positions[np.newaxis,:,:]
# ids = np.where( np.sum(dists**2,axis=-1) + 0.02**2*np.eye(len(dists)) < 0.02**2 )
# print( ids )
# pdb.set_trace()
""" Add intrahelical neighbors at connections """
for c,A,B in self.get_connections("intrahelical"):
b1,b2 = [l.particle for l in (A,B)]
if b1 is b2:
## already handled by Segment._generate_beads
pass
else:
for b in (b1,b2): assert( b is not None )
b1.make_intrahelical_neighbor(b2)
""" Reassign bead types """
if self.DEBUG: print("Assigning bead types")
beadtype_s = dict()
def _assign_bead_type(bead, num_nt, decimals):
num_nt0 = bead.num_nt
bead.num_nt = np.around( np.float32(num_nt), decimals=decimals )
key = (bead.type_.name[0].upper(), bead.num_nt)
if key in beadtype_s:
bead.type_ = beadtype_s[key]
else:
t = deepcopy(bead.type_)
t.__dict__["nts"] = bead.num_nt*2 if t.name[0].upper() in ("D","O") else bead.num_nt
t.name = t.name + "%03d" % (t.nts*10**decimals)
print( "{} --> {} ({})".format(num_nt0, bead.num_nt, t.name) )
beadtype_s[key] = bead.type_ = t
# (cluster_size[c-1])
import scipy.cluster.hierarchy as hcluster
beads = [b for s in segments for b in s if b.type_.name[0].upper() in ("D","O")]
data = np.array([b.num_nt for b in beads])[:,np.newaxis]
order = int(2-np.log10(2*max_basepairs_per_bead)//1)
try:
clusters = hcluster.fclusterdata(data, float(max_basepairs_per_bead)/500, criterion="distance")
cluster_size = [np.mean(data[clusters == i]) for i in np.unique(clusters)]
except:
clusters = np.arange(len(data))+1
cluster_size = data.flatten()
for b,c in zip(beads,clusters):
_assign_bead_type(b, cluster_size[c-1], decimals=order)
beads = [b for s in segments for b in s if b.type_.name[0].upper() in ("S")]
data = np.array([b.num_nt for b in beads])[:,np.newaxis]
order = int(2-np.log10(max_nucleotides_per_bead)//1)
try:
clusters = hcluster.fclusterdata(data, float(max_nucleotides_per_bead)/500, criterion="distance")
cluster_size = [np.mean(data[clusters == i]) for i in np.unique(clusters)]
except:
clusters = np.arange(len(data))+1
cluster_size = data.flatten()
for b,c in zip(beads,clusters):
_assign_bead_type(b, cluster_size[c-1], decimals=order)
# for bead in [b for s in segments for b in s]:
# num_nt0 = bead.num_nt
# # bead.num_nt = np.around( np.float32(num_nt), decimals=decimals )
# key = (bead.type_.name[0].upper(), bead.num_nt)
# if key in beadtype_s:
# bead.type_ = beadtype_s[key]
# else:
# t = deepcopy(bead.type_)
# t.__dict__["nts"] = bead.num_nt*2 if t.name[0].upper() in ("D","O") else bead.num_nt
# # t.name = t.name + "%03d" % (t.nts*10**decimals)
# t.name = t.name + "%.16f" % (t.nts)
# print( "{} --> {} ({})".format(num_nt0, bead.num_nt, t.name) )
# beadtype_s[key] = bead.type_ = t
""" Update bead indices """
self._countParticleTypes() # probably not needed here
self._updateParticleOrder()
""" Add intrahelical bond potentials """
if self.DEBUG: print("Adding intrahelical bond potentials")
dists = dict() # intrahelical distances built for later use
intra_beads = self._get_intrahelical_beads()
if self.DEBUG: print(" Adding %d bonds" % len(intra_beads))
for b1,b2 in intra_beads:
# assert( not np.isclose( np.linalg.norm(b1.collapsedPosition() - b2.collapsedPosition()), 0 ) )
if np.linalg.norm(b1.collapsedPosition() - b2.collapsedPosition()) < 1:
print("WARNING: some beads are very close")
parent = self._getParent(b1,b2)
## TODO: could be sligtly smarter about sep
sep = 0.5*(b1.num_nt+b2.num_nt)
conversion = 0.014393265 # units "pN/AA" kcal_mol/AA^2
if b1.type_.name[0] == "D" and b2.type_.name[0] == "D":
elastic_modulus_times_area = 1000 # pN http://markolab.bmbcb.northwestern.edu/marko/Cocco.CRP.02.pdf
d = 3.4*sep
k = conversion*elastic_modulus_times_area/d
else:
## TODO: get better numbers our ssDNA model
elastic_modulus_times_area = 800 # pN http://markolab.bmbcb.northwestern.edu/marko/Cocco.CRP.02.pdf
d = 5*sep
k = conversion*elastic_modulus_times_area/d
# print(sep,d,k)
if b1 not in dists:
dists[b1] = dict()
if b2 not in dists:
dists[b2] = dict()
# dists[b1].append([b2,sep])
# dists[b2].append([b1,sep])
dists[b1][b2] = sep
dists[b2][b1] = sep
# dists[[b1,b2]] = dists[[b2,b1]] = sep
bond = self.get_bond_potential(k,d)
parent.add_bond( b1, b2, bond, exclude=True )
# for s in self.segments:
# sepsum = 0
# beadsum = 0
# for b1 in s.beads:
# beadsum += b1.num_nt
# for bead_list in self._recursively_get_beads_within_bonds(b1, 1):
# assert(len(bead_list) == 1)
# if b1.idx < bead_list[-1].idx: # avoid double-counting
# for b2 in bead_list:
# if b2.parent == b1.parent:
# sepsum += dists[b1][b2]
# sepsum += sep
# print("Helix {}: bps {}, beads {}, separation {}".format(s.name, s.num_nt, beadsum, sepsum))
""" Add intrahelical angle potentials """
if self.DEBUG: print("Adding intrahelical angle potentials")
for b1,b2,b3 in self._get_intrahelical_angle_beads():
## TODO: could be slightly smarter about sep
sep = 0.5*b1.num_nt+b2.num_nt+0.5*b3.num_nt
parent = self._getParent(b1,b2,b3)
kT = 0.58622522 # kcal/mol
if b1.type_.name[0] == "D" and b2.type_.name[0] == "D" and b3.type_.name[0] == "D":
## <cos(q)> = exp(-s/Lp) = integrate( x^4 exp(-A x^2) / 2, {x, 0, pi} ) / integrate( x^2 exp(-A x^2), {x, 0, pi} )
## <cos(q)> ~ 1 - 3/4A
## where A = k_spring / (2 kT)
k = 1.5 * kT * (1.0 / (1-np.exp(-float(sep)/147))) * 0.00030461742; # kcal_mol/degree^2
if local_twist:
## TODO optimize this paramter
k *= 0.5 # halve because orientation beads have similar springs
angle = self.get_angle_potential(k,180)
o1,o2,o3 = [b.orientation_bead for b in (b1,b2,b3)]
parent.add_angle( o1, o2, o3, angle )
else:
## TODO: get correct number from ssDNA model
k = 1.5 * kT * (1.0 / (1-np.exp(-float(sep)/3))) * 0.00030461742; # kcal_mol/degree^2
angle = self.get_angle_potential(k,180)
parent.add_angle( b1, b2, b3, angle )
""" Add intrahelical exclusions """
if self.DEBUG: print("Adding intrahelical exclusions")
beads = dists.keys()
def _recursively_get_beads_within(b1,d,done=()):
ret = []
for b2,sep in dists[b1].items():
if b2 in done: continue
if sep < d:
ret.append( b2 )
done.append( b2 )
tmp = _recursively_get_beads_within(b2, d-sep, done)
if len(tmp) > 0: ret.extend(tmp)
return ret
exclusions = set()
for b1 in beads:
exclusions.update( [(b1,b) for b in _recursively_get_beads_within(b1, 20, done=[b1])] )
if self.DEBUG: print("Adding %d exclusions" % len(exclusions))
for b1,b2 in exclusions:
parent = self._getParent(b1,b2)
parent.add_exclusion( b1, b2 )
""" Twist potentials """
if local_twist:
if self.DEBUG: print("Adding twist potentials")
for b1 in beads:
if "orientation_bead" not in b1.__dict__: continue
for b2,sep in dists[b1].items():
if "orientation_bead" not in b2.__dict__: continue
if b2.idx < b1.idx: continue # Don't double-count
p1,p2 = [b.parent for b in (b1,b2)]
o1,o2 = [b.orientation_bead for b in (b1,b2)]
parent = self._getParent( b1, b2 )
""" Add heuristic 90 degree potential to keep orientation bead orthogonal """
k = (1.0/2) * 1.5 * kT * (1.0 / (1-np.exp(-float(sep)/147))) * 0.00030461742; # kcal_mol/degree^2
pot = self.get_angle_potential(k,90)
parent.add_angle(o1,b1,b2, pot)
parent.add_angle(b1,b2,o2, pot)
## TODO: improve this
twist_per_nt = 0.5 * (p1.twist_per_nt + p2.twist_per_nt)
angle = sep*twist_per_nt
if angle > 360 or angle < -360:
print("WARNING: twist angle out of normal range... proceeding anyway")
# raise Exception("The twist between beads is too large")
k = self._get_twist_spring_constant(sep)
if escapable_twist:
pot = self.get_dihedral_potential(k,angle,max_potential=1)
else:
pot = self.get_dihedral_potential(k,angle)
parent.add_dihedral(o1,b1,b2,o2, pot)
def k_angle(sep):
return 1.5 * kT * (1.0 / (1-np.exp(-float(sep)/147))) * 0.00030461742; # kcal_mol/degree^2
def k_xover_angle(sep):
return 0.5 * k_angle(sep)
def add_local_crossover_orientation_potential(b1,b2,is_parallel=True):
u1,u2 = [b.get_intrahelical_above() for b in (b1,b2)]
d1,d2 = [b.get_intrahelical_below() for b in (b1,b2)]
k = k_xover_angle(sep=1)
pot = self.get_angle_potential(k,120)
if 'orientation_bead' in b1.__dict__:
o = b1.orientation_bead
self.add_angle( o,b1,b2, pot )
if 'orientation_bead' in b2.__dict__:
o = b2.orientation_bead
self.add_angle( b1,b2,o, pot )
if 'orientation_bead' in b1.__dict__:
t0 = -90 if A.on_fwd_strand else 90
if not is_parallel: t0 *= -1
o1 = b1.orientation_bead
if u2 is not None and isinstance(u2.parent,DoubleStrandedSegment):
k = k_xover_angle( dists[b2][u2] )
pot = self.get_dihedral_potential(k,t0)
self.add_dihedral( o1,b1,b2,u2, pot )
elif d2 is not None and isinstance(d2.parent,DoubleStrandedSegment):
k = k_xover_angle( dists[b2][d2] )
pot = self.get_dihedral_potential(k,-t0)
self.add_dihedral( o1,b1,b2,d2, pot )
if 'orientation_bead' in b2.__dict__:
t0 = -90 if B.on_fwd_strand else 90
if not is_parallel: t0 *= -1
o2 = b2.orientation_bead
if u1 is not None and isinstance(u1.parent,DoubleStrandedSegment):
k = k_xover_angle( dists[b1][u1] )
pot = self.get_dihedral_potential(k,t0)
self.add_dihedral( o2,b2,b1,u1, pot )
elif d1 is not None and isinstance(d1.parent,DoubleStrandedSegment):
k = k_xover_angle( dists[b1][d1] )
pot = self.get_dihedral_potential(k,-t0)
self.add_dihedral( o2,b2,b1,d1, pot )
""" Add connection potentials """
for c,A,B in self.get_connections("terminal_crossover"):
## TODO: use a better description here
b1,b2 = [loc.particle for loc in (c.A,c.B)]
# pot = self.get_bond_potential(4,18.5)
pot = self.get_bond_potential(4,12)
self.add_bond(b1,b2, pot)
dotProduct = b1.parent.contour_to_tangent(b1.contour_position).dot(
b2.parent.contour_to_tangent(b2.contour_position) )
## Add potential to provide a particular orinetation
if local_twist:
add_local_crossover_orientation_potential(b1,b2, is_parallel=dotProduct > 0)
""" Add connection potentials """
for c,A,B in self.get_connections("sscrossover"):
b1,b2 = [loc.particle for loc in (c.A,c.B)]
## TODO: improve parameters
pot = self.get_bond_potential(4,6)
self.add_bond(b1,b2, pot)
## Add potentials to provide a sensible orientation
## TODO refine potentials against all-atom simulation data
"""
u1,u2 = [b.get_intrahelical_above() for b in (b1,b2)]
d1,d2 = [b.get_intrahelical_below() for b in (b1,b2)]
k_fn = k_angle
if isinstance(b1.parent,DoubleStrandedSegment):
a,b,c = (d1,b1,b2) if d1.parent is b1.parent else (u1,b1,b2)
else:
a,b,c = (d2,b2,b1) if d2.parent is b2.parent else (u2,b2,b1)
"""
# pot = self.get_angle_potential( k_fn(dists[a][b]), 120 ) # a little taller than 90 degrees
# self.add_angle( a,b,c, pot )
# o = b.orientation_bead
# angle=3
# pot = self.get_angle_potential( 1, 0 ) # a little taller than 90 degrees
# self.add_angle( a,b,c, pot )
dotProduct = b1.parent.contour_to_tangent(b1.contour_position).dot(
b2.parent.contour_to_tangent(b2.contour_position) )
if local_twist:
add_local_crossover_orientation_potential(b1,b2, is_parallel=dotProduct > 0)
crossover_bead_pots = set()
for c,A,B in self.get_connections("crossover"):
b1,b2 = [loc.particle for loc in (A,B)]
## Avoid double-counting
if (b1,b2,A.on_fwd_strand,B.on_fwd_strand) in crossover_bead_pots: continue
crossover_bead_pots.add((b1,b2,A.on_fwd_strand,B.on_fwd_strand))
crossover_bead_pots.add((b2,b1,B.on_fwd_strand,A.on_fwd_strand))
pot = self.get_bond_potential(4,18.5)
self.add_bond(b1,b2, pot)
## Get beads above and below
u1,u2 = [b.get_intrahelical_above() for b in (b1,b2)]
d1,d2 = [b.get_intrahelical_below() for b in (b1,b2)]
dotProduct = b1.parent.contour_to_tangent(b1.contour_position).dot(
b2.parent.contour_to_tangent(b2.contour_position) )
if dotProduct < 0:
tmp = d2
d2 = u2
u2 = tmp
a = None
if u1 is not None and u2 is not None:
t0 = 0
a,b,c,d = (u1,b1,b2,u2)
elif d1 is not None and d2 is not None:
t0 = 0
a,b,c,d = (d1,b1,b2,d2 )
elif d1 is not None and u2 is not None:
t0 = 180
a,b,c,d = (d1,b1,b2,u2)
elif u1 is not None and d2 is not None:
t0 = 180
a,b,c,d = (u1,b1,b2,d2)
if a is not None:
k = k_xover_angle( dists[b][a]+dists[c][d] )
pot = self.get_dihedral_potential(k,t0)
self.add_dihedral( a,b,c,d, pot )
if local_twist:
add_local_crossover_orientation_potential(b1,b2, is_parallel=dotProduct > 0)
## TODOTODO check that this works
for crossovers in self.get_consecutive_crossovers():
if local_twist: break
## filter crossovers
new_cl = []
lastParticle = None
for cl in crossovers:
c,A,B,d = cl
if A.particle is not lastParticle:
new_cl.append(cl)
lastParticle = A.particle
crossovers = new_cl
for i in range(len(crossovers)-2):
c1,A1,B1,dir1 = crossovers[i]
c2,A2,B2,dir2 = crossovers[i+1]
s1,s2 = [l.container for l in (A1,A2)]
sep = A1.particle.get_nt_position(s1) - A2.particle.get_nt_position(s2)
sep = np.abs(sep)
n1,n2,n3,n4 = (B1.particle, A1.particle, A2.particle, B2.particle)
"""
<cos(q)> = exp(-s/Lp) = integrate( cos[x] exp(-A x^2), {x, 0, pi} ) / integrate( exp(-A x^2), {x, 0, pi} )
Assume A is small
int[B_] := Normal[Integrate[ Series[Cos[x] Exp[-B x^2], {B, 0, 1}], {x, 0, \[Pi]}]/
Integrate[Series[Exp[-B x^2], {B, 0, 1}], {x, 0, \[Pi]}]]
Actually, without assumptions I get fitFun below
"""
## From http://www.annualreviews.org/doi/pdf/10.1146/annurev.bb.17.060188.001405
## units "3e-19 erg cm/ 295 k K" "nm" =~ 73
Lp = s1.twist_persistence_length/0.34 # set semi-arbitrarily as there is a large spread in literature
fitFun = lambda x: np.real(erf( (4*np.pi*x + 1j)/(2*np.sqrt(x)) )) * np.exp(-1/(4*x)) / erf(2*np.sqrt(x)*np.pi) - np.exp(-sep/Lp)
k = opt.leastsq( fitFun, x0=np.exp(-sep/Lp) )
k = k[0][0] * 2*kT*0.00030461742
t0 = sep*s1.twist_per_nt # TODO weighted avg between s1 and s2
# pdb.set_trace()
if A1.on_fwd_strand: t0 -= 120
if dir1 != dir2:
A2_on_fwd = not A2.on_fwd_strand
else:
A2_on_fwd = A2.on_fwd_strand
if A2_on_fwd: t0 += 120
# t0 = (t0 % 360
# if n2.idx == 0:
# print( n1.idx,n2.idx,n3.idx,n4.idx,k,t0,sep )
pot = self.get_dihedral_potential(k,t0)
self.add_dihedral( n1,n2,n3,n4, pot )
# ## remove duplicate potentials; ## TODO ensure that they aren't added twice in the first place?
# self.remove_duplicate_terms()
def walk_through_helices(segment, direction=1, processed_segments=None):
"""
First and last segment should be same for circular helices
"""
assert( direction in (1,-1) )
if processed_segments == None:
processed_segments = set()
def segment_is_new_helix(s):
return isinstance(s,DoubleStrandedSegment) and s not in processed_segments
new_s = None
s = segment
## iterate intrahelically connected dsDNA segments
while segment_is_new_helix(s):
conn_locs = s.get_contour_sorted_connections_and_locations("intrahelical")[::direction]
processed_segments.add(new_s)
new_s = None
new_dir = None
for i in range(len(conn_locs)):
c,A,B = conn_locs[i]
## TODO: handle change of direction
# TODOTODO
address = 1*(direction==-1)
if A.address == address and segment_is_new_helix(B.container):
new_s = B.container
assert(B.address in (0,1))
new_dir = 2*(B.address == 0) - 1
break
yield s,direction
s = new_s # will break if None
direction = new_dir
# if new_s is None:
# break
# else:
# s = new_s
# yield s
## return s
def get_consecutive_crossovers(self):
## TODOTODO TEST
crossovers = []
processed_segments = set()
for s1 in self.segments:
if not isinstance(s1,DoubleStrandedSegment):
continue
if s1 in processed_segments: continue
s0,d0 = list(SegmentModel.walk_through_helices(s1,direction=-1))[-1]
# s,direction = get_start_of_helices()
tmp = []
for s,d in SegmentModel.walk_through_helices(s0,-d0):
if s == s0 and len(tmp) > 0:
## end of circular helix, only add first crossover
cl_list = s.get_contour_sorted_connections_and_locations("crossover")
if len(cl_list) > 0:
tmp.append( cl_list[::d][0] + [d] )
else:
tmp.extend( [cl + [d] for cl in s.get_contour_sorted_connections_and_locations("crossover")[::d]] )
processed_segments.add(s)
crossovers.append(tmp)
return crossovers
def set_sequence(self, sequence, force=True):
if force:
self.strands[0].set_sequence(sequence)
else:
try:
self.strands[0].set_sequence(sequence)
except:
...
for s in self.segments:
s.randomize_unset_sequence()
def _generate_strands(self):
self.strands = strands = []
""" Ensure unconnected ends have 5prime Location objects """
for seg in self.segments:
## TODO move into Segment calls
five_prime_locs = sum([seg.get_locations(s) for s in ("5prime","crossover","terminal_crossover")],[])
three_prime_locs = sum([seg.get_locations(s) for s in ("3prime","crossover","terminal_crossover")],[])
def is_start_5prime(l):
return l.get_nt_pos() < 1 and l.on_fwd_strand
def is_end_5prime(l):
return l.get_nt_pos() > seg.num_nt-2 and not l.on_fwd_strand
def is_start_3prime(l):
return l.get_nt_pos() < 1 and not l.on_fwd_strand
def is_end_3prime(l):
return l.get_nt_pos() > seg.num_nt-2 and l.on_fwd_strand
if seg.start5.connection is None:
if len(list(filter( is_start_5prime, five_prime_locs ))) == 0:
seg.add_5prime(0) # TODO ensure this is the same place
if 'end5' in seg.__dict__ and seg.end5.connection is None:
if len(list(filter( is_end_5prime, five_prime_locs ))) == 0:
seg.add_5prime(seg.num_nt-1,on_fwd_strand=False)
if 'start3' in seg.__dict__ and seg.start3.connection is None:
if len(list(filter( is_start_3prime, three_prime_locs ))) == 0:
seg.add_3prime(0,on_fwd_strand=False)
if seg.end3.connection is None:
if len(list(filter( is_end_3prime, three_prime_locs ))) == 0:
seg.add_3prime(seg.num_nt-1)
# print( [(l,l.get_connected_location()) for l in seg.locations] )
# addresses = np.array([l.address for l in seg.get_locations("5prime")])
# if not np.any( addresses == 0 ):
# ## check if end is connected
# for c,l,B in self.get_connections_and_locations():
# if c[0]
""" Build strands from connectivity of helices """
def _recursively_build_strand(strand, segment, pos, is_fwd, mycounter=0, move_at_least=0.5):
seg = segment
history = []
while True:
mycounter+=1
if mycounter > 10000:
import pdb
pdb.set_trace()
#if seg.name == "22-1" and pos > 140:
# if seg.name == "22-2":
# import pdb
# pdb.set_trace()
end_pos, next_seg, next_pos, next_dir, move_at_least = seg.get_strand_segment(pos, is_fwd, move_at_least)
try:
strand.add_dna(seg, pos, end_pos, is_fwd)
except CircularDnaError:
## Circular DNA was found
break
except:
print("Unexpected error:", sys.exc_info()[0])
raise
if next_seg is None:
return
else:
history.append((seg,pos,is_fwd))
seg,pos,is_fwd = (next_seg, next_pos, next_dir)
for seg in self.segments:
locs = seg.get_5prime_locations()
if locs is None: continue
# for pos, is_fwd in locs:
for l in locs:
# print("Tracing",l)
# TODOTODO
pos = seg.contour_to_nt_pos(l.address, round_nt=True)
is_fwd = l.on_fwd_strand
s = Strand()
_recursively_build_strand(s, seg, pos, is_fwd)
# print("{} {}".format(seg.name,s.num_nt))
strands.append(s)
## Trace circular DNA
def strands_cover_segment(segment, is_fwd=True):
direction = 'fwd' if is_fwd else 'rev'
nt = 0
for sp in segment.strand_pieces[direction]:
nt += sp.num_nt
return nt == segment.num_nt
def find_nt_not_in_strand(segment, is_fwd=True):
fwd_str = 'fwd' if is_fwd else 'rev'
def check(val):
assert(val >= 0 and val < segment.num_nt)
print("find_nt_not_in_strand({},{}) returning {}".format(
segment, is_fwd, val))
return val
if is_fwd:
last = -1
for sp in segment.strand_pieces[fwd_str]:
if sp.start-last > 1:
return check(last+1)
last = sp.end
return check(last+1)
else:
last = segment.num_nt
for sp in segment.strand_pieces[fwd_str]:
if last-sp.end > 1:
return check(last-1)
last = sp.start
return check(last-1)
def add_strand_if_needed(seg,is_fwd):
if not strands_cover_segment(seg, is_fwd):
pos = nt = find_nt_not_in_strand(seg, is_fwd)
s = Strand(is_circular = True)
_recursively_build_strand(s, seg, pos, is_fwd)
strands.append(s)
for seg in self.segments:
add_strand_if_needed(seg,True)
if isinstance(seg, DoubleStrandedSegment):
add_strand_if_needed(seg,False)
self.strands = sorted(strands, key=lambda s:s.num_nt)[::-1]
def check_strands():
dsdna = filter(lambda s: isinstance(s,DoubleStrandedSegment), self.segments)
for s in dsdna:
nt_fwd = nt_rev = 0
for sp in s.strand_pieces['fwd']:
nt_fwd += sp.num_nt
for sp in s.strand_pieces['rev']:
nt_rev += sp.num_nt
assert( nt_fwd == s.num_nt and nt_rev == s.num_nt )
# print("{}: {},{} (fwd,rev)".format(s.name, nt_fwd/s.num_nt,nt_rev/s.num_nt))
check_strands()
## relabel segname
counter = 0
for s in self.strands:
if s.segname is None:
s.segname = "D%03d" % counter
counter += 1
def _assign_basepairs(self):
## Assign basepairs
for seg in self.segments:
if isinstance(seg, DoubleStrandedSegment):
strands1 = seg.strand_pieces['fwd'] # already sorted
strands2 = seg.strand_pieces['rev']
nts1 = [nt for s in strands1 for nt in s.children]
nts2 = [nt for s in strands2 for nt in s.children[::-1]]
assert(len(nts1) == len(nts2))
for nt1,nt2 in zip(nts1,nts2):
## TODO weakref
nt1.basepair = nt2
nt2.basepair = nt1
def _update_orientations(self,orientation):
for s in self.strands:
s.update_atomic_orientations(orientation)
def _write_atomic_ENM(self, prefix, lattice_type=None):
## TODO: ensure atomic model was generated already
if lattice_type is None:
lattice_type = self.lattice_type
if lattice_type == "square":
enmTemplate = enmTemplateSQ
elif lattice_type == "honeycomb":
enmTemplate = enmTemplateHC
else:
raise Exception("Lattice type '%s' not supported" % self.latticeType)
## TODO: allow ENM to be created without first building atomic model
noStackPrime = 0
noBasepair = 0
with open("%s.exb" % prefix,'w') as fh:
# natoms=0
for seg in self.segments:
## Continue unless dsDNA
if not isinstance(seg,DoubleStrandedSegment): continue
for strand_piece in seg.strand_pieces['fwd'] + seg.strand_pieces['rev']:
for nt1 in strand_piece.children:
other = []
nt2 = nt1.basepair
if strand_piece.is_fwd:
other.append((nt2,'pair'))
nt2 = nt2.get_intrahelical_above()
if nt2 is not None and strand_piece.is_fwd:
## TODO: check if this already exists
other.append((nt2,'paircross'))
nt2 = nt1.get_intrahelical_above()
if nt2 is not None:
other.append((nt2,'stack'))
nt2 = nt2.basepair
if nt2 is not None and strand_piece.is_fwd:
other.append((nt2,'cross'))
for nt2,key in other:
"""
if np.linalg.norm(nt2.position-nt1.position) > 7:
import pdb
pdb.set_trace()
"""
key = ','.join((key,nt1.sequence[0],nt2.sequence[0]))
for n1, n2, d in enmTemplate[key]:
d = float(d)
k = 0.1
if lattice_type == 'honeycomb':
correctionKey = ','.join((key,n1,n2))
assert(correctionKey in enmCorrectionsHC)
dk,dr = enmCorrectionsHC[correctionKey]
k = float(dk)
d += float(dr)
i = nt1._get_atomic_index(name=n1)
j = nt2._get_atomic_index(name=n2)
fh.write("bond %d %d %f %.2f\n" % (i,j,k,d))
# print("NO STACKS found for:", noStackPrime)
# print("NO BASEPAIRS found for:", noBasepair)
## Loop dsDNA regions
push_bonds = []
processed_segs = set()
## TODO possibly merge some of this code with SegmentModel.get_consecutive_crossovers()
for segI in self.segments: # TODOTODO: generalize through some abstract intrahelical interface that effectively joins "segments", for now interhelical bonds that cross intrahelically-connected segments are ignored
if not isinstance(segI,DoubleStrandedSegment): continue
## Loop over dsDNA regions connected by crossovers
conn_locs = segI.get_contour_sorted_connections_and_locations("crossover")
other_segs = list(set([B.container for c,A,B in conn_locs]))
for segJ in other_segs:
if (segI,segJ) in processed_segs:
continue
processed_segs.add((segI,segJ))
processed_segs.add((segJ,segI))
## TODO perhaps handle ends that are not between crossovers
## Loop over ordered pairs of crossovers between the two
cls = filter(lambda x: x[-1].container == segJ, conn_locs)
cls = sorted( cls, key=lambda x: x[1].get_nt_pos() )
for cl1,cl2 in zip(cls[:-1],cls[1:]):
c1,A1,B1 = cl1
c2,A2,B2 = cl2
ntsI1,ntsI2 = [segI.contour_to_nt_pos(A.address) for A in (A1,A2)]
ntsJ1,ntsJ2 = [segJ.contour_to_nt_pos(B.address) for B in (B1,B2)]
ntsI = ntsI2-ntsI1+1
ntsJ = ntsJ2-ntsJ1+1
assert( np.isclose( ntsI, int(round(ntsI)) ) )
assert( np.isclose( ntsJ, int(round(ntsJ)) ) )
ntsI,ntsJ = [int(round(i)) for i in (ntsI,ntsJ)]
## Find if dsDNA "segments" are pointing in same direction
## could move this block out of the loop
tangentA = segI.contour_to_tangent(A1.address)
tangentB = segJ.contour_to_tangent(B1.address)
dot1 = tangentA.dot(tangentB)
tangentA = segI.contour_to_tangent(A2.address)
tangentB = segJ.contour_to_tangent(B2.address)
dot2 = tangentA.dot(tangentB)
if dot1 > 0.5 and dot2 > 0.5:
...
elif dot1 < -0.5 and dot2 < -0.5:
## TODO, reverse
...
print("Warning: {} and {} are on antiparallel helices (not yet implemented)... skipping".format(A1,B1))
continue
else:
print("Warning: {} and {} are on helices that do not point in similar direction... skipping".format(A1,B1))
continue
## Go through each nucleotide between the two
for ijmin in range(min(ntsI,ntsJ)):
i=j=ijmin
if ntsI < ntsJ:
j = int(round(float(ntsJ*i)/ntsI))
elif ntsJ < ntsI:
i = int(round(float(ntsI*j)/ntsJ))
ntI_idx = int(round(ntsI1+i))
ntJ_idx = int(round(ntsJ1+j))
## Skip nucleotides that are too close to crossovers
if i < 11 or j < 11: continue
if ntsI2-ntI_idx < 11 or ntsJ2-ntJ_idx < 11: continue
## Find phosphates at ntI/ntJ
for direction in [True,False]:
try:
i = segI._get_atomic_nucleotide(ntI_idx, direction)._get_atomic_index(name="P")
j = segJ._get_atomic_nucleotide(ntJ_idx, direction)._get_atomic_index(name="P")
push_bonds.append((i,j))
except:
# print("WARNING: could not find 'P' atom in {}:{} or {}:{}".format( segI, ntI_idx, segJ, ntJ_idx ))
...
print("PUSH BONDS:", len(push_bonds))
if not self.useTclForces:
with open("%s.exb" % prefix, 'a') as fh:
for i,j in push_bonds:
fh.write("bond %d %d %f %.2f\n" % (i,j,1.0,31))
else:
flat_push_bonds = list(sum(push_bonds))
atomList = list(set( flat_push_bonds ))
with open("%s.forces.tcl" % prefix,'w') as fh:
fh.write("set atomList {%s}\n\n" %
" ".join([str(x-1) for x in atomList]) )
fh.write("set bonds {%s}\n" %
" ".join([str(x-1) for x in flat_push_bonds]) )
fh.write("""
foreach atom $atomList {
addatom $atom
}
proc calcforces {} {
global atomList bonds
loadcoords rv
foreach i $atomList {
set force($i) {0 0 0}
}
foreach {i j} $bonds {
set rvec [vecsub $rv($j) $rv($i)]
# lassign $rvec x y z
# set r [expr {sqrt($x*$x+$y*$y+$z*$z)}]
set r [getbond $rv($j) $rv($i)]
set f [expr {2*($r-31.0)/$r}]
vecadd $force($i) [vecscale $f $rvec]
vecadd $force($j) [vecscale [expr {-1.0*$f}] $rvec]
}
foreach i $atomList {
addforce $i $force($i)
}
}
""")
def set_dimensions_from_structure( self, padding_factor=1.5, isotropic=False ):
positions = []
for s in self.segments:
positions.append(s.contour_to_position(0))
positions.append(s.contour_to_position(0.5))
positions.append(s.contour_to_position(1))
positions = np.array(positions)
dx,dy,dz = [(np.max(positions[:,i])-np.min(positions[:,i])+30)*padding_factor for i in range(3)]
if isotropic:
dx = dy = dz = max((dx,dy,dz))
self.dimensions = [dx,dy,dz]
def _generate_atomic_model(self, scale=1):
self.children = self.strands
first_atomic_index = 0
for s in self.strands:
first_atomic_index = s.generate_atomic_model(scale,first_atomic_index)
self._assign_basepairs()
return
## Angle optimization
angles = np.linspace(-180,180,180)
score = []
for a in angles:
o = rotationAboutAxis([0,0,1], a)
sum2 = count = 0
for s in self.strands:
s.update_atomic_orientations(o)
for s1,s2 in zip(s.strand_segments[:-1],s.strand_segments[1:]):
nt1 = s1.children[-1]
nt2 = s2.children[0]
o3 = nt1.atoms_by_name["O3'"]
p = nt2.atoms_by_name["P"]
sum2 += np.sum((p.collapsedPosition()-o3.collapsedPosition())**2)
count += 1
score.append(sum2/count)
print(angles[np.argmin(score)])
print(score)