beadModel.py

# -*- coding: utf-8 -*-
from datetime import datetime
from cadnano.cnenum import PointType
from math import pi,sqrt,exp,floor
import numpy as np
from scipy.special import erf
import scipy.optimize as opt
import os, sys, subprocess

import nbPot
from coords import minimizeRmsd, quaternionToMatrix3, rotationAboutAxis


class HarmonicPotential():
    def __init__(self, k, r0, rRange=(0,50), resolution=0.1, maxForce=None, prefix="potentials/"):
        self.k = k
        self.r0 = r0
        self.maxForce = maxForce
        self.rRange = rRange
        self.prefix = prefix
        self.periodic = False
        self.type = "None"
        self._kscale = None
        self._init_hook()

    def filename(self):
        # raise NotImplementedError("Not implemented")
        return "%s%s-%.3f-$.3f.dat" % (self.prefix, self.type,
                                       self.k*self._kscale, self.r0)

    def write_file(self):
        r = np.arange( self.rRange[0], 
                       self.rRange[1]+self.resolution, 
                       self.resolution )
        dr = r-self.r0

        if self.periodic == True:
            rSpan = self.rRange[1]-self.rRange[0]
            assert(rSpan > 0)
            dr = np.mod( dr+0.5*rSpan, rSpan) - 0.5*rSpan 

        u = 0.5*self.k*dr**2

        if self.maxForce is not None:
            assert(self.maxForce > 0)
            f = np.diff(u)/np.diff(r)
            f[f>maxForce] = maxForce
            f[f<-maxForce] = -maxForce
            u[0] = 0
            u[1:] = np.cumsum(f*np.diff(r))
        np.savetxt( self.filename(), np.array([r, u]).T, fmt="%f" )

    def __hash__(self):
        assert(self.type != "None")
        return hash((self.type, self.k, self.r0, self.rRange, self.resolution, self.maxForce, self.prefix, self.periodic))

    def __eq__(self, other):
        for a in ("type", "k", "r0", "rRange", "resolution", "maxForce", "prefix", "periodic"):
            if self.__dict__[a] != other.__dict__[a]:
                return False
        return True

class NonBonded(HarmonicPotential):
    def _init_hook(self):
        self.type = "nonbonded"
        self._kscale = 1.0

class Bond(HarmonicPotential):
    def _init_hook(self):
        self.type = "bond"
        self._kscale = 1.0

class Angle(HarmonicPotential):
    def _init_hook(self):
        self.type = "angle"
        self._kscale = (180.0/pi)**2

class Dihedral(HarmonicPotential):
    def _init_hook(self):
        self.periodic = True
        self.type = "dihedral"
        self._kscale = (180.0/pi)**2

class Node():
    def __init__(self, helix, pos, type="dsDNA"):
        self.helix    = helix
        self.position = np.array(pos)
        self.initialPosition = np.array(pos)
        self.type     = type
        self.nodeAbove = None
        self.nodeBelow = None
        self.xovers = []
        self.ssXovers = []
        self.idx = helix.model.numParticles
        helix.model.numParticles += 1

    def addNodeAbove(self, node, separation):
        assert(self.nodeAbove is None)
        self.nodeAbove = node
        self.nodeAboveSep = separation # bp
    def addNodeBelow(self, node, separation):
        assert(self.nodeBelow is None)
        self.nodeBelow = node
        self.nodeBelowSep = separation # bp

    def addXover(self, node, fwds, double=False):
        ## TODO: what is meant by polarity?
        self.xovers.append( (node,fwds,double) )

    def addSsXover(self, node, fwds):
        self.ssXovers.append( (node,fwds) )
    
    def getNodesAbove(self,numNodes,inclusive=False):
        assert( type(numNodes) is int and numNodes > 0 )

        nodeList,sepList = [[],[]]
        n = self
        if inclusive:
            nodeList.append(n)

        for i in range(numNodes):
            if n.nodeAbove is None: break
            n = n.nodeAbove
            nodeList.append(n)
            sepList.append(n.nodeBelowSep)
            
        return nodeList,sepList

    def getNodesBelow(self,numNodes,inclusive=False):
        assert( type(numNodes) is int and numNodes > 0 )

        nodeList,sepList = [[],[]]
        n = self
        if inclusive:
            nodeList.append(n)

        for i in range(numNodes):
            if n.nodeBelow is None: break
            n = n.nodeBelow
            nodeList.append(n)
            sepList.append(n.nodeBelowSep)
            
        return nodeList,sepList

class helix():
    def __init__(self, model, part, hid):
        self.model = model
        self.props = part.getModelProperties().copy() # TODO: maybe move this out of here
        self.nodes = dict()
        self.hid = hid

        if self.props.get('point_type') == PointType.ARBITRARY:
            # TODO add code to encode Parts with ARBITRARY point configurations
            raise NotImplementedError("Not implemented")
        else:
            vh_props, origins = part.helixPropertiesAndOrigins()
            for x in vh_props:
                self.props[x] = vh_props[x][hid]

            self.origin = origins[hid]
            x,y = self.origin
            self.zIdxToPos = lambda idx: (x*10,y*10,-3.4*idx)


    def addNode(self, zIdx, strandOccupancies):
        ## Determine what kind of node we are making
        i = int(round(zIdx))
        if i in strandOccupancies[0] and i in strandOccupancies[1]:
            type = "dsDNA"
        elif i in strandOccupancies[0] or i in strandOccupancies[1]:
            # type = "dsDNA"
            type = "ssDNA"
        else:
            raise Exception( "Attempt to add a node at %d where there is no DNA!\n Strand at indeces: %s" % (i,strandOccupancies) )
        ## Add the node
        n = Node(self, self.zIdxToPos(zIdx), type)
        if zIdx in self.nodes:
            raise Exception("Attempted to add a node in the same location (%d:%.1f) twice!" % (self.hid,zIdx))
        self.nodes[zIdx] = n

        ## Update ordered list of nodes 
        if self.model.particles is not None:
            model.buildOrderedParticlesList()

        return n

    def getOrigin(self):
        return self.origin

    def __iter__(self):
        for x in sorted(self.nodes.items(), key=lambda x: x[0]):
            yield x
    
class beadModel():

    def __init__(self, part, twistPersistenceLength=75.0, maxBpsPerDNode=4, maxNtsPerSNode=2):
        self.numParticles = 0
        self.helices = dict()
        self.particles = None
        self.particleTypeCounts = None

        # self._nbParams = set()
        self._bondParams = set()
        self._angleParams = set()
        self._dihedralParams = set()

        self._nbParamFiles = []
        self._bondParamFiles = set()
        self._angleParamFiles = set()
        self._dihedralParamFiles = set()

        self.twistPersistenceLength = twistPersistenceLength


        self._buildModel(part, maxBpsPerDNode, maxNtsPerSNode)
        
        ## Post process the model
        self.buildOrderedParticlesList()
        self._setTypes()
        self._countParticleTypes()
        self.buildOrderedParticlesList()

    def __iter__(self):
        for x in sorted(self.helices.items(), key=lambda x: x[0]):
            yield x

    def buildOrderedParticlesList(self):
        ## Create ordered list
        particles = [(n,hid,zid) for hid,hlx in self for zid,n in hlx]        
        self.particles = sorted(particles, key=lambda x: (x[0].type, x[0].idx))
        
        ## Update node indices
        for p,i in zip(self.particles,range(self.numParticles)):
            p[0].idx = i
            
        self.initialCoords = np.array([p[0].initialPosition for p in self.particles])
        self._nodeHids = np.array([p[1] for p in self.particles])

    def _setTypes(self):
        for p,hid,zid in self.particles:
            bps = []
            if p.nodeAbove is not None: bps.append(p.nodeAboveSep)
            if p.nodeBelow is not None: bps.append(p.nodeBelowSep)
            if bps == []: bps = [3]
            p.bps = 10*np.mean(bps)

            if p.type == "ssDNA":
                p.bps *= 0.5

            p.bps = int(round(p.bps))
            p.type = "%s%d" % (p.type[0], p.bps)

    def _countParticleTypes(self):
        particleTypeCounts = dict()
        for p in self.particles:
            t = p[0].type
            if t in particleTypeCounts:
                particleTypeCounts[t] += 1
            else:
                particleTypeCounts[t] = 1
        self.particleTypeCounts = particleTypeCounts

    def addHelix(self, part, hid):
        h = helix(self,part,hid)
        self.helices[hid] = h
        return h
    
    def _helixStrandsToEnds(self, helixStrands):

        """Utility method to convert cadnano strand lists into list of
        indices of terminal points"""

        endLists = [[],[]]
        for endList, strandList in zip(endLists,helixStrands):
            lastStrand = None
            for s in strandList:
                if lastStrand is None:
                    ## first strand
                    endList.append(s[0])
                elif lastStrand[1] != s[0]-1: 
                    assert( s[0] > lastStrand[1] )
                    endList.extend( [lastStrand[1], s[0]] )
                lastStrand = s
            if lastStrand is not None:
                endList.append(lastStrand[1])
        return endLists
    
    def simulate(self, outputPrefix, outputDirectory='output', numSteps=100000000, timestep=100e-6, gpu=0, arbd=None):
        assert(type(gpu) is int)
        # assert(type(numSteps) is int)
        if outputDirectory == '': outputDirectory='.'
            
        if arbd is None:
            for path in os.environ["PATH"].split(os.pathsep):
                path = path.strip('"')
                fname = os.path.join(path, "arbd")
                if os.path.isfile(fname) and os.access(fname, os.X_OK):
                    arbd = fname
                    break

        if not os.path.exists(arbd):
            raise Exception("ARBD was not found")
        if not os.path.isfile(arbd):
            raise Exception("ARBD was not found")
        if not os.access(arbd, os.X_OK):
            raise Exception("ARBD is not executable")

        if not os.path.exists(outputDirectory):
            os.makedirs(outputDirectory)
        elif not os.path.isdir(outputDirectory):
            raise Exception("outputDirectory '%s' is not a directory!" % outputDirectory)
            

        self.writePdb( outputPrefix + ".pdb" )
        self.writePsf( outputPrefix + ".psf" )
        self.writeArbdFiles( outputPrefix, numSteps=numSteps, timestep=timestep )

        env = os.environ.copy()
        env["CUDA_DEVICE_ORDER"] = "PCI_BUS_ID"

        ## http://stackoverflow.com/questions/18421757/live-output-from-subprocess-command
        # cmd = "%s -g %d %s.bd %s/%s" % (arbd, gpu, outputPrefix, outputDirectory, outputPrefix)
        # cmd = (arbd, (-g %d %s.bd %s/%s" % (gpu, outputPrefix, outputDirectory, outputPrefix))
        cmd = (arbd, '-g', "%d" % gpu, "%s.bd" % outputPrefix, "%s/%s" % (outputDirectory, outputPrefix))
        cmd = tuple(str(x) for x in cmd)

        print("Running ARBD with: %s" % " ".join(cmd))
        process = subprocess.Popen(cmd, env=env, stdout=subprocess.PIPE, universal_newlines=True)
        for line in process.stdout:
        # for line in iter(process.stdout.readline, b''):
            sys.stdout.write(line)
            sys.stdout.flush()
            # sys.stdout.write(line.decode(sys.stdout.encoding))
    
    # -------------------------- #
    # Methods for building model #
    # -------------------------- #
    def _buildModel(self, part, maxBpsPerDNode, maxNtsPerSNode):
        # maxVhelixId = part.getIdNumMax()
        
        props = part.getModelProperties().copy()
        # print(props)

        if props.get('point_type') == PointType.ARBITRARY:
            # TODO add code to encode Parts with ARBITRARY point configurations
            raise NotImplementedError("Not implemented")
        else:
            vh_props, origins = part.helixPropertiesAndOrigins()
            # print(' VIRTUAL HELICES:', vh_props)
            # # print(' ORIGINS:', origins)
            # group_props['virtual_helices'] = vh_props
            # group_props['origins'] = origins
            
        ## TODO: compartmentalize following
        ## Loop over virtual helices and build lists of strands 
        vh_list = []
        strand_list = []
        xover_list = []
        numHID = part.getIdNumMax() + 1
        for id_num in range(numHID):
            offset_and_size = part.getOffsetAndSize(id_num)
            if offset_and_size is None:
                # add a placeholder
                vh_list.append((id_num, 0))
                strand_list.append(None)
                # prop_list.append(None)
            else:
                offset, size = offset_and_size
                vh_list.append((id_num, size))
                fwd_ss, rev_ss = part.getStrandSets(id_num)
                # for s in fwd_ss:
                #     print(' VHELIX %d fwd_ss:' % id_num, s)
                fwd_idxs, fwd_colors  = fwd_ss.dump(xover_list)
                rev_idxs, rev_colors  = rev_ss.dump(xover_list)
                strand_list.append((fwd_idxs, rev_idxs))

                # if id_num < 2:
                #     print( fwd_idxs )
                #     for s in fwd_ss:
                #         print( s.insertionsOnStrand() )
                
                ## prop_list.append((fwd_colors, rev_colors))
                # for s in strand_list:
                #     print( s )
                

        ## Get dictionary of insertions 
        allInsertions = part.insertions()

        ## Expand strand_lists for crossover filtering 
        expandedStrandList = []
        for fwdRevStrands in strand_list:
            tmp = []
            if fwdRevStrands is not None:
                for strands in fwdRevStrands:
                    fwdOrRev = []
                    for a,b in strands: fwdOrRev.extend(range(a,b+1))
                    tmp.append(fwdOrRev)
            expandedStrandList.append(tmp)

        ## Find crossovers involving ssDNA and dsDNA
        ssXoList, dsXoList, extraInterhelicalBondList = [[],[],[]]
        for entry in xover_list:
            h1,f1,z1,h2,f2,z2 = entry
            if strand_list[h1] is None or strand_list[h2] is None:
                print("WARNING: crossover to empty helix")
                continue

            ds1 = z1 in expandedStrandList[h1][0] and z1 in expandedStrandList[h1][1]
            ds2 = z2 in expandedStrandList[h2][0] and z2 in expandedStrandList[h2][1]

            occ1Above = z1+1 in expandedStrandList[h1][0] or z1+1 in expandedStrandList[h1][1]
            occ2Above = z2+1 in expandedStrandList[h2][0] or z2+1 in expandedStrandList[h2][1]

            occ1Below = z1-1 in expandedStrandList[h1][0] or z1-1 in expandedStrandList[h1][1]
            occ2Below = z2-1 in expandedStrandList[h2][0] or z2-1 in expandedStrandList[h2][1]

            if ((not occ1Above) and (not occ2Below)) or \
               ((not occ1Below) and (not occ2Above)):
                extraInterhelicalBondList.append(entry)
            else:
                if ds1 and ds2:
                    dsXoList.append(entry)
                else:
                    ssXoList.append(entry)

        ## Build dictionary of dsDNA crossovers
        xoDicts = [dict() for i in range(numHID)]
        for hid1 in range(numHID):
            tmp = xoDicts[hid1]
            for hid2 in range(numHID):
                allXos       = {(z1,z2,f1,f2) for h1,f1,z1,h2,f2,z2 in dsXoList if h1 == hid1 and h2 == hid2}
                allXos.update( {(z2,z1,f2,f1) for h1,f1,z1,h2,f2,z2 in dsXoList if h2 == hid1 and h1 == hid2} )
                allXos = sorted(list(allXos), key = lambda x: (x[0],x[1]))

                ## Replace each double-crossover with a single one
                excludedXos, extraXos = [set(),set()]
                for i in range(len(allXos)):
                    xoi = allXos[i]
                    for j in range(i+1,len(allXos)):
                        xoj = allXos[j]
                        if xoj[0] - xoi[0] > 2: break
                        if xoi[0]+1 == xoj[0] and xoi[1]+1 == xoj[1] and \
                           xoi[2]   == xoj[2] and xoi[3]   == xoj[3]:
                            excludedXos.add(xoi)
                            excludedXos.add(xoj)
                            extraXos.add( (xoi[0]+0.5,xoi[1]+0.5,xoi[2],xoi[3]) )
                xos = {xo for xo in allXos if xo not in excludedXos}
                xos.update(extraXos)
            
                ## Set dictionary entry
                xos = list(xos)
                if len(xos) > 0:
                    tmp[hid2] = xos

        ## Build dictionary of dsDNA crossovers
        xoDicts = [dict() for i in range(numHID)]
        for hid1 in range(numHID):
            tmp = xoDicts[hid1]
            for hid2 in range(numHID):
                allXos       = {(z1,z2,f1,f2) for h1,f1,z1,h2,f2,z2 in dsXoList if h1 == hid1 and h2 == hid2}
                allXos.update( {(z2,z1,f2,f1) for h1,f1,z1,h2,f2,z2 in dsXoList if h2 == hid1 and h1 == hid2} )
                allXos = sorted(list(allXos), key = lambda x: (x[0],x[1]))

                ## Replace each double-crossover with a single one
                excludedXos, extraXos = [set(),set()]
                for i in range(len(allXos)):
                    xoi = allXos[i]
                    for j in range(i+1,len(allXos)):
                        xoj = allXos[j]
                        if xoj[0] - xoi[0] > 2: break
                        if xoi[0]+1 == xoj[0] and xoi[1]+1 == xoj[1] and \
                           xoi[2]   == xoj[2] and xoi[3]   == xoj[3]:
                            excludedXos.add(xoi)
                            excludedXos.add(xoj)
                            extraXos.add( (xoi[0]+0.5,xoi[1]+0.5,xoi[2],xoi[3]) )
                xos = {xo for xo in allXos if xo not in excludedXos}
                xos.update(extraXos)
            
                ## Set dictionary entry
                xos = list(xos)
                if len(xos) > 0:
                    tmp[hid2] = xos

        ## Build dictionary of ssDNA crossovers
        ssXoDicts = [dict() for i in range(numHID)]
        for hid1 in range(numHID):
            tmp = ssXoDicts[hid1]
            for hid2 in range(numHID):
                xos       = {(z1,z2,f1,f2) for h1,f1,z1,h2,f2,z2 in ssXoList if h1 == hid1 and h2 == hid2}
                xos.update( {(z2,z1,f2,f1) for h1,f1,z1,h2,f2,z2 in ssXoList if h2 == hid1 and h1 == hid2} )
                xos = sorted(list(xos), key = lambda x: (x[0],x[1]))
                ## Set dictionary entry
                if len(xos) > 0:
                    tmp[hid2] = xos

        ## Build helices 
        for hid in range(numHID):
            # print("Working on helix",hid)
            
            helixStrands = strand_list[hid]
            if helixStrands is None: 
                continue

            ## Build list of tuples containing (idx,length) of insertions/skips
            insertions = sorted( [(i[0],i[1].length()) for i in allInsertions[hid].items()],
                                 key=lambda x: x[0] )
            
            ## Build list of strand ends and list of mandatory node locations
            ends1,ends2 = self._helixStrandsToEnds(helixStrands)
            # xoZids = [x for x in xoDicts2[hid].keys()]

            ## Find crossovers for this helix
            xoZids = [x[1] for h0 in range(hid) if hid in xoDicts[h0] for x in xoDicts[h0][hid]]
            xoZids.extend([x[0] for hid2,xos in xoDicts[hid].items() for x in xos])
            xoZids.extend([x[1] for h0 in range(hid) if hid in ssXoDicts[h0] for x in ssXoDicts[h0][hid]])
            xoZids.extend([x[0] for hid2,xos in ssXoDicts[hid].items() for x in xos])
            reqNodeZids = sorted(list(set( ends1 + ends2 + xoZids ) ) )
            
            ## Build lists of which nt sites are occupied in the helix
            strandOccupancies = [ [x for i in range(0,len(e),2) 
                                   for x in range(e[i],e[i+1]+1)] 
                                  for e in (ends1,ends2) ]
            
           
            ## Build helix by adding nodes
            beadHelix = self.addHelix(part,hid)
            if hid in ():
                print("%d nodes:" %hid,reqNodeZids)
                print("orig xos:",[xo for xo in xover_list if xo[0] == hid or xo[3] == hid])
                print("xosZids:", sorted(xoZids) )
                print("strandOccupancy1:",strandOccupancies[0])
                print("strandOccupancy2:",strandOccupancies[1])

            prevNode = None
            for i in range( len(reqNodeZids)-1 ):
                zid1,zid2 = reqNodeZids[i:i+2]
                
                ## Check that there are nts between zid1 and zid2 before adding nodes
                zMid = int(0.5*(zid1+zid2))
                if zMid in strandOccupancies[0] and zMid in strandOccupancies[1]:
                    ## dsDNA
                    maxBpsPerNode = maxBpsPerDNode
                if zMid in strandOccupancies[0] or zMid in strandOccupancies[1]:
                    ## ssDNA
                    maxBpsPerNode = maxNtsPerSNode
                else:
                    continue

                numBps = zid2-zid1
                # if numBps < 2:
                #     print(hid,zid1,zid2)
                # assert(numBps >= 1)

                for ins_idx,length in insertions:
                    ## TODO: ensure placement of insertions is correct
                    ##   (e.g. are insertions at the ends handled correctly?)
                    if ins_idx < zid1:
                        continue
                    if ins_idx >= zid2:
                        break
                    numBps += length

                # if numBps = 0:
                #     print("WARNING: found stretch of DNA with 0 length; skipping")
                #     next

                nodesBetween = round( float(numBps-1)/maxBpsPerNode )
                if nodesBetween < 0: 
                    nodesBetween = 0
                bpsPerNode = float(numBps)/(nodesBetween+1)
                if bpsPerNode == 0: 
                    bpsPerNode = 0.1
                zidPerNode = float(zid2-zid1)/(nodesBetween+1)

                try:
                    if prevNode is None:
                        prevNode = beadHelix.addNode( zid1, strandOccupancies )

                    for i in range(nodesBetween):
                        node = beadHelix.addNode( zid1+(i+1)*zidPerNode, strandOccupancies )
                        self._connectNodes(prevNode, node, bpsPerNode)
                        prevNode = node

                    node = beadHelix.addNode( zid2, strandOccupancies )
                    self._connectNodes(prevNode, node, bpsPerNode)
                except:
                    print(hid,zid1,zid2,nodesBetween,bpsPerNode)
                    raise Exception("ERROR")

                prevNode = None
                if (int(floor(zid2+1)) in strandOccupancies[0]) or \
                   (int(floor(zid2+1)) in strandOccupancies[1]):
                    prevNode = node

        ## Add extra intrahelical bonds
        ## Add crossovers
        for entry in extraInterhelicalBondList:
            h1,f1,z1,h2,f2,z2 = entry
            n1 = self.helices[h1].nodes[z1]
            n2 = self.helices[h2].nodes[z2]

            try:
                self._connectNodes(n1,n2,1)
            except:
                assert(True)
            try:
                self._connectNodes(n2,n1,1)
            except:
                assert(True)
                    

        ## Add crossovers
        for hid1 in range(numHID):
            for hid2, xos in xoDicts[hid1].items():
                for xo in xos:
                    self._addCrossover(hid1,hid2,xo)

        ## Add ssDNA xovers    
        for hid1 in range(numHID):
            for hid2, xos in ssXoDicts[hid1].items():
                for xo in xos:
                    self._addSsCrossover(hid1,hid2,xo)


        return

    def _connectNodes(self, below, above, sep):
        below.addNodeAbove(above, sep)
        above.addNodeBelow(below, sep)
        
    def _addCrossover(self, hid1, hid2, xo):
        zid1, zid2, isFwd1, isFwd2 = xo
        node1 = self.helices[hid1].nodes[zid1]
        node2 = self.helices[hid2].nodes[zid2]

        ## TODO add polarity
        polarity = 0
        node1.addXover(node2, (isFwd1, isFwd2))
        node2.addXover(node1, (isFwd2, isFwd1))

    def _addSsCrossover(self, hid1, hid2, xo):
        zid1, zid2, isFwd1, isFwd2 = xo
        node1 = self.helices[hid1].nodes[zid1]
        node2 = self.helices[hid2].nodes[zid2]

        ## TODO add polarity
        polarity = 0
        node1.addSsXover(node2, isFwd1)
        node2.addSsXover(node1, isFwd2)

    def addModel(self, model):
        assert( isinstance(model, type(self)) )

        hidOffset = max( self.helices.keys() ) + 1
        # nidOffset = self.numParticles
        for hid,h in model:
            self.helices[hid+hidOffset] = h

        self.numParticles += model.numParticles

        self.buildOrderedParticlesList()
        self._setTypes()
        self._countParticleTypes()


    def backmap(self, simplerModel, simplerModelCoords, 
                dsDnaHelixNeighborDist=50, dsDnaAllNeighborDist=30,
                ssDnaHelixNeighborDist=20, ssDnaAllNeighborDist=15):

        ## Assign each bead to a bead in simplerModel
        mapToSimplerModel = dict()
        cgWeight = dict()
        for hDict,cgHDict in zip(self,simplerModel):
            assert(hDict[0] == cgHDict[0])
            h,cgH = [x[1] for x in (hDict,cgHDict)] # get helix

            zIdxs = np.array( sorted([i for i,b in cgH]) )
            for i,b in h:
                cgi = np.searchsorted(zIdxs,i,side='left',sorter=None)
                cgi, = [zIdxs[x] if x < len(zIdxs) else zIdxs[-1] for x in (cgi,)]
                mapToSimplerModel[b.idx] = [cgH.nodes[x] for x in (cgi,)]
                
        ## Find new axis and position of each bead using neighborhood
        beads = [b for h in self for i,b in h[1].nodes.items()]

        ## Find transformation for each bead of simplerModel
        trans = dict()
        for b in list(set([b for i,bs in mapToSimplerModel.items() for b in bs])):
            helixCutoff = dsDnaHelixNeighborDist if b.type[0] == 'd' else ssDnaHelixNeighborDist
            allCutoff = dsDnaAllNeighborDist if b.type[0] == 'd' else ssDnaAllNeighborDist

            def positionsAreLinear(pos):
                if len(pos) == 0: return False
                center = np.mean(pos,axis=0)
                cPos = pos-center
                return np.sum( np.abs( np.linalg.eig( cPos.T.dot(cPos) )[0] ) > 1e-3 ) == 3

            ids = []
            attempts = 0
            posOld = []
            while len(ids) <= 3 or not positionsAreLinear(posOld):
                if attempts > 15: raise Exception("Too many attempts to find a neighborhood for backmaping bead %d" % b.idx)
                ids = simplerModel._getNeighborhoodIds(b, simplerModelCoords, helixCutoff, allCutoff)
                posOld = np.array( [simplerModel.particles[i][0].initialPosition for i in ids] )
                allCutoff *= 1.2
                attempts+=1

            if attempts > 1:
                print("Warning, increased allCutoff to",allCutoff)

            posNew = np.array( [simplerModelCoords[i] for i in ids] )
            trans[b.idx] = minimizeRmsd( posOld, posNew )

        ## Optionally smooth orientations
            
        ## Apply transformation to each bead of self
        for b in beads:
            cgb, = mapToSimplerModel[b.idx]
            cgi = cgb.idx
            r0 = simplerModel.particles[cgi][0].initialPosition
            R,c0,c1 = trans[cgi]
            b.position = (b.initialPosition - r0).dot(R) + simplerModelCoords[cgi]
            assert( np.all(np.isreal( b.position )) )
        

    def _getNeighborhoodIds(self, bead, coords, helixCutoff=50, allCutoff=np.sqrt(35)):
        i = bead.idx

        coords0 = self.initialCoords
        # print(coords0[i,:])
        coordsI = np.outer(coords0[i,:],np.ones([len(coords0),1])).T
        dr2Initial = np.sum((coords0 - coordsI)**2, axis=-1)
        dr2Final = np.sum((coords - coords[i,:])**2, axis=-1)
        
        ## Include all in same helix within 5 nm of bead after simulation        
        ret = list( np.where( (dr2Final < helixCutoff**2) * (self._nodeHids == bead.helix.hid) )[0] )
        ret = list( np.where( (dr2Final < helixCutoff**2) * (self._nodeHids == bead.helix.hid) * (dr2Initial < 100**2) )[0] )

        ## Include all within 3.5 nm both before AND after simulation
        ret.extend( list( np.where( (dr2Final < allCutoff**2) * (dr2Initial < allCutoff**2) )[0] ) )
        return sorted(list(set(ret)))

    # -------------------------- #
    # Methods for querying model #
    # -------------------------- #
    def _getIntrahelicalNodeSeries(self,seriesLen):
        nodeSeries = set() 
        for hid,hlx in self:
            for zid,n in hlx:
                nodeList,sepList = n.getNodesAbove(seriesLen-1, inclusive = True)
                if len(nodeList) == seriesLen:
                    nodeList = tuple(nodeList)
                    sepList = tuple(sepList)
                    nodeSeries.add( tuple((nodeList,sepList)) )
        return nodeSeries

    def _getIntrahelicalBonds(self):
        return self._getIntrahelicalNodeSeries(2)

    def _getIntrahelicalAngles(self):
        return self._getIntrahelicalNodeSeries(3)

    def _getCrossoverBonds(self):
        return { ((n, xo[0]), xo[1])
                 for hid,hlx in self
                 for zid,n in hlx for xo in n.xovers if n.idx < xo[0].idx }

    def _getSsCrossoverBonds(self):
        return { ((n, xo[0]), xo[1]) 
                 for hid,hlx in self
                 for zid,n in hlx for xo in n.ssXovers if n.idx < xo[0].idx }


    def _getCrossoverAnglesAndDihedrals(self):
        angles,dihedrals = [set(),set()]
        contiguousCrossovers = []

        for hid,hlx in self.helices.items():
            crossovers = []
            bpsBetween = 0
            for zid,n in hlx:
                ## Search for contiguous crossovers
                if n.nodeBelow is None or n.type[0] != "d":
                    ## Found ssDNA or a gap; reset search
                    if len(crossovers) > 0:
                        contiguousCrossovers.append(crossovers)
                    crossovers = []
                    bpsBetween = 0

                if n.nodeBelow is not None:
                    bpsBetween += n.nodeBelowSep
                if len(n.xovers) > 0:
                    crossovers.append( (n,bpsBetween) )

            if len(crossovers) > 0:
                contiguousCrossovers.append(crossovers)

        ## Process contiguousCrossovers
        for crossovers in contiguousCrossovers:
            for i in range(len(crossovers)-1):
                ni,bpi = crossovers[i]
                # for j in range(i+1,len(crossovers)):
                for j in range(i+1,i+2): # Just look at adjacent crossovers
                    assert(j == i+1)
                    nj,bpj = crossovers[j]
                    bpsBetween = bpj-bpi
                    if bpsBetween < 60:
                        for xo1 in ni.xovers:
                            for xo2 in nj.xovers:
                                assert( bpsBetween != 0 )
                                angles.add( ((xo1[0], ni, nj), bpsBetween) )
                                angles.add( ((ni, nj, xo2[0]), bpsBetween) )
                                dihedrals.add( ((xo1[0], ni, nj, xo2[0]), bpsBetween, xo1[1], xo2[1]) )
                    else:
                        break
        return angles, dihedrals
        

    def _removeIntrahelicalConnectionsBeyond(self, cutoff):
        bonds = self._getIntrahelicalBonds()
        for b in bonds:
            n1,n2 = b[0]
            r2 = np.sum( (n1.position - n2.position)**2 )
            if r2 > cutoff**2:
                if n1.nodeAbove == n2:
                    assert(n2.nodeBelow == n1)
                    n1.nodeAbove = None
                    n2.nodeBelow = None
                elif n2.nodeAbove == n1:
                    assert(n1.nodeBelow == n2)
                    n1.nodeBelow = None
                    n2.nodeAbove = None
                else:
                    raise

    def _removeCrossoversBeyond(self, cutoff):
        for hid,hlx in self:
            for zid,n1 in hlx:
                newXovers = []
                for xo in n1.xovers:
                    n2 = xo[0]
                    r2 = np.sum( (n1.position - n2.position)**2 )
                    if r2 < cutoff**2:
                        newXovers.append(xo)
                n1.xovers = newXovers

        for hid,hlx in self:
            for zid,n1 in hlx:
                newXovers = []
                for xo in n1.ssXovers:
                    n2 = xo[0]
                    r2 = np.sum( (n1.position - n2.position)**2 )
                    if r2 < cutoff**2:
                        newXovers.append(xo)
                n1.ssXovers = newXovers

    def _getBonds(self):
        bonds = self._getIntrahelicalBonds()
        bonds.update( self._getCrossoverBonds() )
        bonds.update( self._getSsCrossoverBonds() )
        return bonds


    # -------------------------- #
    # Methods for prinitng model #
    # -------------------------- #
    def writePdb(self, filename):
        with open(filename,'w') as fh:
            ## Write header
            fh.write("CRYST1    1000.    1000.    1000.  90.00  90.00  90.00 P 1           1\n")

            ## Write coordinates
            formatString = "ATOM  {:>5d} {:^4s}{:1s}{:3s} {:1s}{:>5s}   {:8.3f}{:8.3f}{:8.3f}{:6.2f}{:6.2f}{:2s}{:2f}\n"
            for n,hid,zid in self.particles:
                ## http://www.wwpdb.org/documentation/file-format-content/format33/sect9.html#ATOM
                idx = n.idx
                name = n.type
                resname = name[:3]
                chain = "A"
                charge = 0
                occ = hid
                beta = zid
                x,y,z = [x for x in n.position]
                
                assert(idx < 1e5)
                resid = "{:<4d}".format(idx)

                fh.write( formatString.format(
                    idx, name[:1], "", resname, chain, resid, x, y, z, occ, beta, "", charge ))
        return
        
    def writePsf(self, filename):
        with open(filename,'w') as fh:
            ## Write header
            fh.write("PSF NAMD\n\n") # create NAMD formatted psf
            
            ## ATOMS section
            idx=1
            for hid,hlx in self:
                for x in hlx:
                    idx += 1

            fh.write("{:>8d} !NATOM\n".format(idx-1))

            ## From vmd/plugins/molfile_plugin/src/psfplugin.c
            ## "%d %7s %10s %7s %7s %7s %f %f"
            formatString = "{idx:>8d} {segname:7s} {resid:<10s} {resname:7s}" + \
                           " {name:7s} {type:7s} {charge:f} {mass:f}\n"
            for n,hid,zid in self.particles:
                idx = n.idx + 1
                data = dict(
                    idx     = idx,
                    segname = "A",
                    resid   = "%d%c%c" % (idx," "," "), # TODO: work with large indeces
                    name    = n.type[:1],
                    resname = n.type[:3],
                    type    = n.type[:1],
                    charge  = 0,
                    mass    = 100,
                )
                fh.write(formatString.format( **data ))
            fh.write("\n")

            ## Write out bonds
            bonds = self._getBonds()
            fh.write("{:>8d} !NBOND\n".format(len(bonds)))
            counter = 0
            for n,seps in bonds:
                fh.write( "{:d} {:d} ".format(n[0].idx+1,n[1].idx+1) )
                counter += 1
                if counter == 3:
                    fh.write("\n")
                    counter = 0
            fh.write("\n")

        return

    def writeArbdFiles(self, prefix, numSteps=100000000, timestep=100e-6):
        ## TODO: save and reference directories and prefixes using member data
        d = "potentials"
        self._writeArbdCoordFile( prefix + ".coord.txt" )
        self._writeArbdBondFile(  prefix, directory = d )
        self._writeArbdAngleFile( prefix, directory = d )
        self._writeArbdDihedralFile( prefix, directory = d )
        self._writeArbdExclFile(  prefix + ".excludes.txt" )
        self._writeArbdPotentialFiles( prefix, directory = d )
        self._writeArbdConf( prefix, numSteps, timestep )
        
    def _writeArbdCoordFile(self, filename):
        with open(filename,'w') as fh:
            for n,hid,zid in self.particles:
                fh.write("%f %f %f\n" % tuple(x for x in n.position))
        
    def _writeArbdConf(self, prefix, numSteps=100000000, timestep=100e-6 ):
        ## TODO: raise exception if _writeArbdPotentialFiles has not been called
        filename = "%s.bd" % prefix
        with open(filename,'w') as fh:
            fh.write("""# seed 1234
timestep %f
steps %d
numberFluct 0
interparticleForce 1
fullLongRange 0
temperature 291
electricField 0.0

outputPeriod 10000
outputEnergyPeriod 10000
outputFormat dcd

decompPeriod 100000
cutoff 40.0
pairlistDistance 80
""" % (timestep, numSteps))
            
            for x in self.getParticleTypesAndCounts():
                fh.write("\nparticle %s\nnum %d\n" % x)
                ## TODO: look up better values in dictionary for particle types
                fh.write("gridFile null.dx\ndiffusion 100\n")

            fh.write("\ninputCoordinates %s.coord.txt\n"  % prefix )
            if os.path.exists("test.0.restart"):
                fh.write("restartCoordinates test.0.restart\n" )
            fh.write("""\n## Interaction potentials
tabulatedPotential  1
## The i@j@file syntax means particle type i will have NB interactions with particle type j using the potential in file
""")
            for pair,f in zip(self._particleTypePairIter(), self._nbParamFiles):
                i,j,t1,t2 = pair
                fh.write("tabulatedFile %d@%d@%s\n" % (i,j,f))


            fh.write("\n")
            for f in self._bondParamFiles:
                fh.write("tabulatedBondFile %s\n" % f)

            fh.write("\n")
            for f in self._angleParamFiles:
                fh.write("tabulatedAngleFile %s\n" % f)