segmentmodel.py

import numpy as np
import random
from arbdmodel import PointParticle, ParticleType, Group, ArbdModel
from coords import rotationAboutAxis, quaternion_from_matrix, quaternion_to_matrix
from nonbonded import *
from copy import copy, deepcopy
from nbPot import nbDnaScheme

from scipy.special import erf
import scipy.optimize as opt
from scipy import interpolate

from CanonicalNucleotideAtoms import canonicalNtFwd, canonicalNtRev, seqComplement
from CanonicalNucleotideAtoms import enmTemplateHC, enmTemplateSQ, enmCorrectionsHC

import pdb
"""
TODO:
 + fix handling of crossovers for atomic representation
 + map to atomic representation
    + add nicks
    - handle circular dna
    - transform ssDNA nucleotides 
    - shrink ssDNA
    - shrink dsDNA backbone
    - make orientation continuous
    - sequence
 + ensure crossover bead potentials aren't applied twice 
 - remove performance bottlenecks
 - test for large systems
 - assign sequence
 - ENM
 - rework location class Location 
 - document
"""

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 segments
        # 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.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):
        self.connection = connection # TODO weakref? 

    def __repr__(self):
        if self.on_fwd_strand:
            on_fwd = "on_fwd_strand"
        else:
            on_fwd = "on_rev_strand"
        # return "<Location in {} at contour {} {} with connection {}>".format( self.container.name, self.address, self.on_fwd_strand, self.connection )
        # return "<Location {} in {} at contour {} {} with connection {}>".format( self.type_, self.container.name, self.address, on_fwd, self.connection )
        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")
        
# class ConnectableElement(Transformable):
class ConnectableElement():
    """ Abstract base class """
    ## TODO: eliminate mutable default arguments
    def __init__(self, connection_locations=[], 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_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):
        ## TODO fix circular references        
        A,B = [connection.A, connection.B]
        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 = []

    def get_contour_position(self,seg):
        assert( isinstance(seg,Segment) )
        if seg == self.parent:
            return self.contour_position
        else:
            ## TODO replace with something more elegant
            for c,A,B in self.parent.get_connections_and_locations():
                if A.particle is self and B.container is seg:
                    nt = np.abs( (self.contour_position - A.address)*A.container.num_nts )
                    if B.address < 0.5:
                        return B.address-nt/seg.num_nts
                    else:
                        return B.address+nt/seg.num_nts
            ## ERROR
            print("")
            for c,A,B in self.parent.get_connections_and_locations():
                print("  ",c.type_)
                print(A,B)
                print(A.particle,self)
                print(B.container,seg)
            print("")
            import pdb
            pdb.set_trace()
            raise Exception("Did not find location for particle {} in Segment {}".format(self,seg))

## 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_nts, 
                 start_position = np.array((0,0,0)),
                 end_position = None, 
                 segment_model = None):

        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.num_nts = int(num_nts)
        if end_position is None:
            end_position = np.array((0,0,self.distance_per_nt*num_nts)) + start_position
        self.start_position = start_position
        self.end_position = end_position

        ## Set up interpolation for positions
        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.sequence = 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_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):
        if self.start_orientation is not None:
            # axis = self.start_orientation.dot( np.array((0,0,1)) )
            if self.quaternion_spline_params is None:
                axis = self.contour_to_tangent(s)
                orientation = rotationAboutAxis( axis, s*self.twist_per_nt*self.num_nts, normalizeAxis=True )
                ## TODO: ensure this is correct
                # orientation = self.start_orientation.dot(orientation) # .dot( self.start_orientation )
                orientation = orientation.dot( self.start_orientation )
            else:
                q = interpolate.splev(s, self.quaternion_spline_params)
                q = q/np.linalg.norm(q)
                orientation = quaternion_to_matrix(q)
                
        else:
            orientation = None
        return orientation

    def get_contour_sorted_connections_and_locations(self):
        sort_fn = lambda c: c[1].address
        cl = self.get_connections_and_locations()
        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_nts)]
        else:
            assert(len(self.sequence) == self.num_nts) # 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):
        """ 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)
        if self.local_twist:
            orientation = self.contour_to_orientation(contour_position)
            ## TODO: move this code (?)
            if orientation is None:
                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_nts, normalizeAxis=True )
                # orientation = rot.dot(orientation)
            else:
                orientation = orientation
                            
        else:
            raise NotImplementedError

        # key = self.sequence
        # if self.ntAt5prime is None and self.ntAt3prime is not None: key = "5"+key
        # if self.ntAt5prime is not None and self.ntAt3prime is None: key = key+"3"
        # if self.ntAt5prime is None and self.ntAt3prime is None: key = key+"singlet"

        key = seq

        ## TODO
        if not is_fwd:
            nt_dict = canonicalNtFwd
        else:
            nt_dict = canonicalNtRev
        atoms = nt_dict[ key ].duplicate() # TODO: clone
                        
        # print( atoms.orientation, orientation )
        # atoms.orientation = atoms.orientation.dot( orientation )
        atoms.orientation = orientation.dot(atoms.orientation)
        atoms.position = pos

        ## TODO: scale positions
        return atoms
        
    def add_location(self, nt, type_, on_fwd_strand=True):
        ## Create location if needed, add to segment
        c = nt/(self.num_nts-1)
        assert(c >= 0 and c <= 1)
        assert(c*(self.num_nts-1) == round(c*(self.num_nts-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):
        address = nt/(self.num_nts-1)
        locations = [l for l in self.get_locations("5prime") if
                     l.address == address and
                     l.on_fwd_strand == on_fwd_strand] 
        if len(locations) == 0:
            self.add_location(nt,"5prime",on_fwd_strand)

    def add_3prime(self, nt, on_fwd_strand=True):
        address = nt/(self.num_nts-1) # TODO: put into a fn call
        locations = [l for l in self.get_locations("3prime") if
                     l.address == address and
                     l.on_fwd_strand == on_fwd_strand] 
        if len(locations) == 0:
            self.add_location(nt,"3prime",on_fwd_strand)

    def get_5prime_locations(self):
        """ Returns tuple of contour_position and direction of strand
        True represents a strand whose 5-to-3 direction increases with contour
        """
        return [l for l in self.get_locations("5prime")]
        raise NotImplementedError # TODO

    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 get_end_of_strand(self, contour_pos, is_fwd):
        """ Walks through locations, checking for crossovers """

        ## Iterate through locations
        # for l in self.locations:
        def loc_iter():
            locations = sorted(self.locations, key=lambda l:l.address)
            if is_fwd:
                for l in locations:
                    yield l
            else:
                for l in locations[::-1]:
                    yield l
            
        for l in loc_iter():
            # if l.particle is None:
            #     pos = l.address
            # else:
            #     pos = l.particle.get_contour_position()          
            pos = l.address

            ## DEBUG
            # if self.name == "1-0" and is_fwd == False:
            #     import pdb
            #     pdb.set_trace()

            ## Skip locations encountered before our strand
            if is_fwd:
                if pos <= contour_pos: continue
            elif pos >= contour_pos: continue

            ## Stop if we found the 3prime end
            if l.on_fwd_strand == is_fwd and l.type_ == "3prime":
                return 1*is_fwd, 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("from {}, connection {} to {}".format(contour_pos,l,B))
                return pos, B.container, B.address, B.on_fwd_strand
                
            ## Stop at other strand crossovers so basepairs line up
            elif c.type_ == "crossover":
                # print("pausing at {}".format(l))
                return pos, l.container, pos, is_fwd

        ## 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 connected beads?
        i = np.argmin((cs - contour_position)**2)

        return self.beads[i]

    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:
            print("WARNING: DEBUG")
            tmp = []
            for c in new_children:
                if c not in tmp:
                    tmp.append(c)
            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, etcl) 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]
        for b in existing_beads:
            assert(b.parent is not None)

        ## Add ends if they don't exist yet
        ## TODO: what about 1 nt segments?
        if len(existing_beads) == 0 or existing_beads[0].get_contour_position(self) > 0:
            b = self._generate_one_bead(0, 0)
            existing_beads = [b] + existing_beads
        if existing_beads[-1].get_contour_position(self) < 1:
            b = self._generate_one_bead(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)]

            # 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 )
            ds = e_ds / (num_beads+1)
            nts = ds*self.num_nts
            eb1.num_nts += 0.5*nts
            eb2.num_nts += 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.intrahelical_neighbors.append(eb1)
                eb1.intrahelical_neighbors.append(last)
            last = eb1
            for j in range(num_beads):
                s = ds*(j+1) + s0
                b = self._generate_one_bead(s,nts)

                last.intrahelical_neighbors.append(b)
                b.intrahelical_neighbors.append(last)
                last = b
                tmp_children.append(b)

        last.intrahelical_neighbors.append(eb2)
        eb2.intrahelical_neighbors.append(last)

        if eb2.parent == self:
            tmp_children.append(eb2)
        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_nts, start_position = np.array((0,0,0)),
                 end_position = None, 
                 segment_model = None,
                 local_twist = False,
                 num_turns = None,
                 start_orientation = None):
        
        self.helical_rise = 10.44
        self.distance_per_nt = 3.4
        Segment.__init__(self, name, num_nts, 
                         start_position,
                         end_position, 
                         segment_model)

        self.local_twist = local_twist
        if num_turns is None:
            num_turns = float(num_nts) / self.helical_rise
        self.twist_per_nt = float(360 * num_turns) / num_nts

        if start_orientation is None:
            start_orientation = np.array(((1,0,0),(0,1,0),(0,0,1)))
        self.start_orientation = start_orientation

        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
        self.quaternion_spline_params = None


    ## 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]):
        """ Add a crossover between two helices """
        ## Validate other, nt, other_nt
        ##   TODO

        ## Create locations, connections and add to segments
        c = nt/(self.num_nts-1)
        assert(c >= 0 and c <= 1)
        
        def get_loc(seg, address, on_fwd_strand):
            loc = None
            for l in seg.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( seg, address=address, type_="crossover", on_fwd_strand=on_fwd_strand )
            return loc

        loc = get_loc(self, c, strands_fwd[0])

        c = other_nt/(other.num_nts-1)
        assert(c >= 0 and c <= 1)
        other_loc = get_loc( other, c, strands_fwd[1] )
        self._connect(other, Connection( loc, other_loc, type_="crossover" ))

    ## 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_ )
        ## Create and add connection
        end1.container._connect( end2.container, Connection( end1, end2, type_=type_ ) )

    def _get_num_beads(self, contour, max_basepairs_per_bead, max_nucleotides_per_bead):
        return int(contour*self.num_nts // max_basepairs_per_bead)

    def get_3prime_locations(self):
        ## TODO test
        return self.get_locations("3prime")

    def get_5prime_locations(self):
        ## TODO test
        return self.get_locations("5prime")
        locs = []
        
        ## Add ends of segment if they aren't connected
        cl = self.get_connections_and_locations()
        connlocs = [A for c,A,B in cl]
        if self.start5 not in connlocs:
            locs.append((0,True)) # TODO
        if self.end5 not in connlocs:
            locs.append((1,False)) # TODO
        
        ## TODO Add nicks
        return locs
        
    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)
            opos = pos + orientation.dot( np.array((Segment.orientation_bond.r0,0,0)) )
            o = SegmentParticle( Segment.orientation_particle, opos, nts,
                                 num_nts=nts, parent=self )
            bead = SegmentParticle( Segment.dsDNA_particle, pos, name="DNA",
                                    num_nts=nts, parent=self, 
                                    orientation_bead=o,
                                    contour_position=contour_position )

        else:
            bead = SegmentParticle( Segment.dsDNA_particle, pos, name="DNA",
                                    num_nts=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_nts, start_position = np.array((0,0,0)),
                 end_position = None, 
                 segment_model = None):

        self.distance_per_nt = 5
        Segment.__init__(self, name, num_nts, 
                         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_3end(self, end5, force_connection=False):
        self._connect_end( end5,  _5_to_3 = False, force_connection = force_connection )

    def connect_5end(self, end3, force_connection=False):
        self._connect_end( end3,  _5_to_3 = True, force_connection = force_connection )

    def _connect_end(self, other, _5_to_3, force_connection):
        assert( isinstance(other, Location) )
        if _5_to_3 == True:
            my_end = self.end5
            assert( other.type_ == "end3" )
        else:
            my_end = self.end3
            assert( other.type_ == "end5" )

        self._connect( other.container, Connection( my_end, other, type_="intrahelical" ) )

    def _get_num_beads(self, contour, max_basepairs_per_bead, max_nucleotides_per_bead):
        return int(contour*self.num_nts // max_nucleotides_per_bead)

    def get_5prime_locations(self):
        locs = []
        
        ## Add ends of segment if they aren't connected
        cl = self.get_connections_and_locations()
        connLocs = [A for c,A,B in cl]
        if self.start not in connLocs:
            locs.append((0,True)) # TODO

        return locs

    def _generate_one_bead(self, contour_position, nts):
        pos = self.contour_to_position(contour_position)
        b = SegmentParticle( Segment.ssDNA_particle, pos, 
                             name="NAS",
                             num_nts=nts, parent=self,
                             contour_position=contour_position )
        self._add_bead(b)
        return b

    
class StrandInSegment(Group):
    """ Class that holds atomic model, maps to segment """
    
    def __init__(self, segment, start, end, is_fwd):
        """ start/end should be provided expressed as contour_length, is_fwd tuples """
        Group.__init__(self)
        self.num_nts = 0
        # self.sequence = []
        self.segment = segment
        self.start = start
        self.end = end
        self.is_fwd = is_fwd

        ## TODO: get sequence (from segment?)        
        nts = np.abs(end-start)*(segment.num_nts-1)+1
        self.num_nts = int(round(nts))
        assert( np.abs(self.num_nts-nts) < 0.001 )

        # print(" Creating {}-nt StrandInSegment in {} from {} to {} {}".format(self.num_nts, segment.name, start, end, is_fwd))

    def get_sequence(self):
        """ return 5-to-3 """
        seg = self.segment
        nt0 = self.start*(seg.num_nts-1)          # TODO: should it ever be .end?
        assert( nt0 == round(nt0) )
        nt0 = int(nt0)
        assert( (self.end-self.start) >= 0 or not self.is_fwd )
        if self.is_fwd:
            return [seqComplement[seg.sequence[nt]] for nt in range(nt0,nt0+self.num_nts)]
        else:
            return [seg.sequence[nt] for nt in range(nt0,nt0-self.num_nts,-1)]

class Strand(Group):
    """ Class that holds atomic model, maps to segments """
    def __init__(self, segname = None):
        Group.__init__(self)
        self.num_nts = 0
        self.children = self.strand_segments = []
        self.segname = segname

    ## TODO disambiguate names of functions
    def add_dna(self, segment, start, end, is_fwd):
        """ start/end should be provided expressed as contour_length, is_fwd tuples """
        s = StrandInSegment( segment, start, end, is_fwd )
        self.add( s )
        self.num_nts += s.num_nts

    def set_sequence(self,sequence):
        ## validate input
        assert( np.all( [i in ('A','T','C','G') for i in sequence] ) )

        ## set sequence on each segment
        for s in self.children:
            seg = s.segment
            ...

        ...

    # def get_sequence(self):
    #     sequence = []
    #     for ss in self.strand_segments:
    #         sequence.extend( ss.get_sequence() )

    #     assert( len(sequence) >= self.num_nts )
    #     ret = ["5"+sequence[0]] +\
    #           sequence[1:-1] +\
    #           [sequence[-1]+"3"]
    #     assert( len(ret) == self.num_nts )
    #     return ret

    def generate_atomic_model(self):
        last = None
        resid = 1
        for s in self.strand_segments:
            seg = s.segment
            contour = np.linspace(s.start,s.end,s.num_nts)
            for c,seq in zip(contour,s.get_sequence()):
                if s.is_fwd:
                    nt = seg._generate_atomic_nucleotide( c, s.is_fwd, seq ) # TODO add sequence,termini
                else:
                    nt = seg._generate_atomic_nucleotide( c, s.is_fwd, "A" )

                s.add(nt)
                ## Join last basepairs
                if last is not None:
                    o3,c3,c4,c2,h3 = [last.atoms_by_name[n] 
                                      for n in ("O3'","C3'","C4'","C2'","H3'")]
                    p,o5,o1,o2,c5 = [nt.atoms_by_name[n] 
                                     for n in ("P","O5'","O1P","O2P","C5'")]
                    self.add_bond( o3, p, None )
                    self.add_angle( c3, o3, p, None )
                    for x in (o5,o1,o2):
                        self.add_angle( o3, p, x, None )
                        self.add_dihedral(c3, o3, p, x, None )
                    for x in (c4,c2,h3):
                        self.add_dihedral(x, c3, o3, p, None )
                    self.add_dihedral(o3, p, o5, c5, None)
                nt.__dict__['resid'] = resid
                resid += 1
                last = nt

class SegmentModel(ArbdModel):
    def __init__(self, segments=[], local_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 bonded potentials

        self._generate_bead_model( max_basepairs_per_bead, max_nucleotides_per_bead, local_twist)

        self.useNonbondedScheme( nbDnaScheme )


    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( items )
        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)
        if key not in self._bonded_potential:
            if type_ == "bond":
                self._bonded_potential[key] = HarmonicBond(kSpring,d, rRange=(0,500), 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):
        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 ):
        ## TODO: test
        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

    """ Mapping between different resolution models """
    def _clear_beads(self):
        for s in self.segments:
            s.clear_all()
        self.clear_all(keep_children=True)
        assert( len([b for b in self]) == 0 )
        locParticles = []
        # for c,A,B in self.get_connections():
        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):
        """ Set new function for each segments functions
        contour_to_position and contour_to_orientation """

        for s in self.segments:
            ## TODO: may need to make spline on helices continuously differentiable
            # beads = s.beads # [b for b in s.beads]
            beads = list(set(s.beads + [A.particle for c,A,B in s.get_connections_and_locations("intrahelical")]))
            ## 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]
            contours = [b.get_contour_position(s) for b in beads]

            cb = sorted( zip(contours,beads), key=lambda a:a[0] )
            beads = [b for c,b in cb] 
            contours = [c for c,b in cb] 

            ids = [b.idx for b in beads]
            
            """ Get positions """
            positions = bead_coordinates[ids,:].T

            ## TODO: determine whether having beads is an issue 
            try:
                tck, u = interpolate.splprep( positions, u=contours, s=0, k=3 )
            except:
                tck, u = interpolate.splprep( positions, u=contours, s=0, k=1 )

            s.position_spline_params = tck

            """ Get twist """
            cb = [e for e in cb 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
                    angleVec = o.position - b.position
                    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 )
                    # quats.append( quaternion_from_matrix( np.array([t,y,angleVec])) )
                    q = quaternion_from_matrix( np.array([angleVec,y,t]).T)

                    if lastq is not None:
                        if q.dot(lastq) < 0:
                            q = -q
                    quats.append( q )

                quats = np.array(quats)
                try:
                    tck, u = interpolate.splprep( quats.T, u=contours, s=0, k=3 )
                except:
                    tck, u = interpolate.splprep( quats.T, u=contours, s=0, k=1 )
                s.quaternion_spline_params = tck

            ## TODO: set twist

    def _generate_bead_model(self,
                             max_basepairs_per_bead = 7,
                             max_nucleotides_per_bead = 4,
                             local_twist=False):

        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_nts-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, generate beads at appropriate locations
        for c,A,B in self.get_connections("intrahelical"):
            s1,s2 = [l.container for l in (A,B)]
            if isinstance(s1,DoubleStrandedSegment) and isinstance(s2,DoubleStrandedSegment):
                ## TODO be more elegant!
                if A.on_fwd_strand == False: continue # TODO verify this avoids double-counting
                assert( A.particle is None )
                assert( B.particle is None )

                ## TODO: offload the work here to s1
                a1,a2 = [l.address   for l in (A,B)]
                a1,a2 = [a - (0.5/s.num_nts) if a == 0 else a + (0.5/s.num_nts) for a,s in zip((a1,a2),(s1,s2))]

                b = s1._generate_one_bead(a1,0)
                A.particle = B.particle = b

            else:
                ## TODO fix this for ssDNA vs dsDNA (maybe a1/a2 should be calculated differently)
                a1,a2 = [l.address   for l in (A,B)]
                a1,a2 = [a - (0.5/s.num_nts) if a == 0 else a + (0.5/s.num_nts) for a,s in zip((a1,a2),(s1,s2))]
                if isinstance(s2,DoubleStrandedSegment):
                    b = s2._generate_one_bead(a2,0)
                else:
                    b = s1._generate_one_bead(a1,0)
                A.particle = B.particle = b

        """ 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)]

            b = s1.get_nearest_bead(a1)
            if b is not None and np.abs(b.contour_position-a1)*s1.num_nts < 1.9:
                ## combine beads
                b.contour_position = 0.5*(b.contour_position + a1) # avg position
                A.particle = b
            else:
                A.particle = s1._generate_one_bead(a1,0)

            b = s2.get_nearest_bead(a2)
            if b is not None and np.abs(b.contour_position-a2)*s2.num_nts < 1.9:
                ## combine beads
                b.contour_position = 0.5*(b.contour_position + a2) # avg position
                B.particle = b
            else:
                B.particle = s2._generate_one_bead(a2,0)

        """ 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():
        #    ...

        """ 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
                continue
            else:
                for b in (b1,b2): assert( b is not None )
                b1.intrahelical_neighbors.append(b2)
                b2.intrahelical_neighbors.append(b1)

        """ Reassign bead types """
        if self.DEBUG: print("Assigning bead types")
        beadtype_s = dict()
        for segment in segments:
            for b in segment:
                b.num_nts = np.around( b.num_nts, decimals=1 )
                key = (b.type_.name[0].upper(), b.num_nts)
                if key in beadtype_s:
                    b.type_ = beadtype_s[key]
                else:
                    t = deepcopy(b.type_)
                    if key[0] == "D":
                        t.__dict__["nts"] = b.num_nts*2
                    elif key[0] == "S":
                        t.__dict__["nts"] = b.num_nts
                    elif key[0] == "O":
                        t.__dict__["nts"] = b.num_nts
                    else:
                        raise Exception("TODO")
                    # print(t.nts)
                    t.name = t.name + "%03d" % (10*t.nts)
                    beadtype_s[key] = b.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:
            parent = self._getParent(b1,b2)