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Created November 4, 2014 09:26
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Simple De Bruijn Graph implementation courtesy of Ben Langmead
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DeBruijnGraph.ipynb
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"cells": [
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"cell_type": "markdown",
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"source": [
"#### Simple De Bruijn Graph implementation courtesy of Ben Langmead\n",
"\n",
"(see the [Sources](https://github.com/lexnederbragt/INF-BIOx121_fall2014_de_novo_assembly/blob/master/Sources.md) document for original source and license of this code)\n",
"\n",
"How to use this notebook:\n",
"\n",
"* 'activate' cells by clicking on them with the mouse (you will see a blinking cursor)\n",
"* execute cells by pressing the ctrl and enter keys simultaneously\n",
"* you can also execute code by pressing shift + enter, this will activate the next cell\n",
"\n",
"Execute the first few cells until the one that generates the first plot. This will load the necessary python code."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"class DeBruijnGraph:\n",
" ''' De Bruijn directed multigraph built from a collection of\n",
" strings. User supplies strings and k-mer length k. Nodes\n",
" are k-1-mers. An Edge corresponds to the k-mer that joins\n",
" a left k-1-mer to a right k-1-mer. '''\n",
" \n",
" @staticmethod\n",
" def chop(st, k):\n",
" ''' Chop string into k-mers of given length '''\n",
" # workaround for the fact that length of the sequences\n",
" # in the nodes was one less than size of k in the original implementation\n",
" # as suggested by Katie Dean\n",
" k = k + 1\n",
" for i in xrange(0, len(st)-(k-1)):\n",
" yield (st[i:i+k], st[i:i+k-1], st[i+1:i+k])\n",
" \n",
" class Node:\n",
" ''' Node representing a k-1 mer. Keep track of # of\n",
" incoming/outgoing edges so it's easy to check for\n",
" balanced, semi-balanced. '''\n",
" \n",
" def __init__(self, km1mer):\n",
" self.km1mer = km1mer\n",
" self.nin = 0\n",
" self.nout = 0\n",
" \n",
" def isSemiBalanced(self):\n",
" return abs(self.nin - self.nout) == 1\n",
" \n",
" def isBalanced(self):\n",
" return self.nin == self.nout\n",
" \n",
" def __hash__(self):\n",
" return hash(self.km1mer)\n",
" \n",
" def __str__(self):\n",
" return self.km1mer\n",
" \n",
" def __init__(self, strIter, k, circularize=False):\n",
" ''' Build de Bruijn multigraph given string iterator and k-mer\n",
" length k '''\n",
" self.G = {} # multimap from nodes to neighbors\n",
" self.nodes = {} # maps k-1-mers to Node objects\n",
" for st in strIter:\n",
" if circularize:\n",
" st += st[:k-1]\n",
" for kmer, km1L, km1R in self.chop(st, k):\n",
" nodeL, nodeR = None, None\n",
" if km1L in self.nodes:\n",
" nodeL = self.nodes[km1L]\n",
" else:\n",
" nodeL = self.nodes[km1L] = self.Node(km1L)\n",
" if km1R in self.nodes:\n",
" nodeR = self.nodes[km1R]\n",
" else:\n",
" nodeR = self.nodes[km1R] = self.Node(km1R)\n",
" nodeL.nout += 1\n",
" nodeR.nin += 1\n",
" self.G.setdefault(nodeL, []).append(nodeR)\n",
" # Iterate over nodes; tally # balanced, semi-balanced, neither\n",
" self.nsemi, self.nbal, self.nneither = 0, 0, 0\n",
" # Keep track of head and tail nodes in the case of a graph with\n",
" # Eularian walk (not cycle)\n",
" self.head, self.tail = None, None\n",
" for node in self.nodes.itervalues():\n",
" if node.isBalanced():\n",
" self.nbal += 1\n",
" elif node.isSemiBalanced():\n",
" if node.nin == node.nout + 1:\n",
" self.tail = node\n",
" if node.nin == node.nout - 1:\n",
" self.head = node\n",
" self.nsemi += 1\n",
" else:\n",
" self.nneither += 1\n",
" \n",
" def nnodes(self):\n",
" ''' Return # nodes '''\n",
" return len(self.nodes)\n",
" \n",
" def nedges(self):\n",
" ''' Return # edges '''\n",
" return len(self.G)\n",
" \n",
" def hasEulerianWalk(self):\n",
" ''' Return true iff graph has Eulerian walk. '''\n",
" return self.nneither == 0 and self.nsemi == 2\n",
" \n",
" def hasEulerianCycle(self):\n",
" ''' Return true iff graph has Eulerian cycle. '''\n",
" return self.nneither == 0 and self.nsemi == 0\n",
" \n",
" def isEulerian(self):\n",
" ''' Return true iff graph has Eulerian walk or cycle '''\n",
" # technically, if it has an Eulerian walk\n",
" return self.hasEulerianWalk() or self.hasEulerianCycle()\n",
" \n",
" def eulerianWalkOrCycle(self):\n",
" ''' Find and return sequence of nodes (represented by\n",
" their k-1-mer labels) corresponding to Eulerian walk\n",
" or cycle '''\n",
" assert self.isEulerian()\n",
" g = self.G\n",
" if self.hasEulerianWalk():\n",
" g = g.copy()\n",
" g.setdefault(self.tail, []).append(self.head)\n",
" # graph g has an Eulerian cycle\n",
" tour = []\n",
" src = g.iterkeys().next() # pick arbitrary starting node\n",
" \n",
" def __visit(n):\n",
" while len(g[n]) > 0:\n",
" dst = g[n].pop()\n",
" __visit(dst)\n",
" tour.append(n)\n",
" \n",
" __visit(src)\n",
" tour = tour[::-1][:-1] # reverse and then take all but last node\n",
" \n",
" if self.hasEulerianWalk():\n",
" # Adjust node list so that it starts at head and ends at tail\n",
" sti = tour.index(self.head)\n",
" tour = tour[sti:] + tour[:sti]\n",
" \n",
" # Return node list\n",
" return map(str, tour)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"class DeBruijnPlot(DeBruijnGraph):\n",
" def to_dot(self, weights=False):\n",
" \"\"\" Write dot representation to given filehandle. If 'weights'\n",
" is true, label edges corresponding to distinct k-1-mers\n",
" with weights, instead of writing a separate edge for each\n",
" copy of a k-1-mer. \"\"\"\n",
" dot_str = []\n",
" dot_str.append(\"digraph \\\"DeBruijn graph\\\" {\\n\")\n",
" dot_str.append(\" bgcolor=\\\"transparent\\\";\\n\")\n",
" for node in self.G.iterkeys():\n",
" lab = node.km1mer\n",
" dot_str.append(\" %s [label=\\\"%s\\\"] ;\\n\" % (lab, lab))\n",
" for src, dsts in self.G.iteritems():\n",
" srclab = src.km1mer\n",
" if weights:\n",
" weightmap = {}\n",
" if weights:\n",
" for dst in dsts:\n",
" weightmap[dst] = weightmap.get(dst, 0) + 1\n",
" for dst, v in weightmap.iteritems():\n",
" dstlab = dst.km1mer\n",
" dot_str.append(\" %s -> %s [label=\\\"%d\\\"] ;\\n\" % (srclab, dstlab, v))\n",
" else:\n",
" for dst in dsts:\n",
" srclab = src.km1mer\n",
" dstlab = dst.km1mer\n",
" dot_str.append(\" %s -> %s [label=\\\"\\\"] ;\\n\" % (srclab, dstlab))\n",
" dot_str.append(\"}\\n\")\n",
" return ''.join(dot_str)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%install_ext https://raw.githubusercontent.com/cjdrake/ipython-magic/master/gvmagic.py"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Installed gvmagic.py. To use it, type:\n",
" %load_ext gvmagic\n"
]
}
],
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"cell_type": "code",
"collapsed": false,
"input": [
"%load_ext gvmagic"
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"language": "python",
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"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"####Exercise 1: simple De Bruijn graph\n",
"\n",
"Do the exercise by execute the code cell below.\n",
"\n",
"Let's first generate a really simple De Bruijn graph of a short read 'GCTGATCGATTT' with kmer size 4 \n",
"\n",
"* study the graph and see if it indeed encodes the read\n",
"* now change the kmer size to 3 and again trace the read: what happened?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%dotobj DeBruijnPlot(['GCTGATCGATTT'], 3)"
],
"language": "python",
"metadata": {},
"outputs": [
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"output_type": "display_data",
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"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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"<!-- Generated by graphviz version 2.36.0 (20140111.2315)\n",
" -->\n",
"<!-- Title: DeBruijn graph Pages: 1 -->\n",
"<svg width=\"178pt\" height=\"404pt\"\n",
" viewBox=\"0.00 0.00 178.00 404.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
"<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 400)\">\n",
"<title>DeBruijn graph</title>\n",
"<!-- ATC -->\n",
"<g id=\"node1\" class=\"node\"><title>ATC</title>\n",
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"<text text-anchor=\"middle\" x=\"48\" y=\"-373.8\" font-family=\"Times,serif\" font-size=\"14.00\">ATC</text>\n",
"</g>\n",
"<!-- TCG -->\n",
"<g id=\"node7\" class=\"node\"><title>TCG</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"29\" cy=\"-306\" rx=\"27.1951\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"29\" y=\"-301.8\" font-family=\"Times,serif\" font-size=\"14.00\">TCG</text>\n",
"</g>\n",
"<!-- ATC&#45;&gt;TCG -->\n",
"<g id=\"edge1\" class=\"edge\"><title>ATC&#45;&gt;TCG</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M43.4006,-360.055C41.2535,-352.145 38.6465,-342.54 36.2439,-333.688\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"39.5544,-332.523 33.557,-323.789 32.7988,-334.357 39.5544,-332.523\"/>\n",
"</g>\n",
"<!-- CGA -->\n",
"<g id=\"node2\" class=\"node\"><title>CGA</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"28\" cy=\"-234\" rx=\"28.1721\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"28\" y=\"-229.8\" font-family=\"Times,serif\" font-size=\"14.00\">CGA</text>\n",
"</g>\n",
"<!-- GAT -->\n",
"<g id=\"node3\" class=\"node\"><title>GAT</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"85\" cy=\"-162\" rx=\"26.9548\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"85\" y=\"-157.8\" font-family=\"Times,serif\" font-size=\"14.00\">GAT</text>\n",
"</g>\n",
"<!-- CGA&#45;&gt;GAT -->\n",
"<g id=\"edge2\" class=\"edge\"><title>CGA&#45;&gt;GAT</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M40.6501,-217.465C48.1035,-208.311 57.6775,-196.554 66.0214,-186.307\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"68.7849,-188.456 72.3852,-178.492 63.3569,-184.036 68.7849,-188.456\"/>\n",
"</g>\n",
"<!-- GAT&#45;&gt;ATC -->\n",
"<g id=\"edge3\" class=\"edge\"><title>GAT&#45;&gt;ATC</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M83.9293,-180.098C81.8425,-209.7 76.4002,-272.289 65,-324 63.0773,-332.721 60.3271,-342.053 57.5976,-350.419\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"54.233,-349.442 54.3353,-360.036 60.862,-351.691 54.233,-349.442\"/>\n",
"</g>\n",
"<!-- ATT -->\n",
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"</g>\n",
"<!-- GAT&#45;&gt;ATT -->\n",
"<g id=\"edge4\" class=\"edge\"><title>GAT&#45;&gt;ATT</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" points=\"88.5001,-118.104 85,-108.104 81.5001,-118.104 88.5001,-118.104\"/>\n",
"</g>\n",
"<!-- TTT -->\n",
"<g id=\"node9\" class=\"node\"><title>TTT</title>\n",
"<ellipse fill=\"none\" stroke=\"black\" cx=\"85\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
"<text text-anchor=\"middle\" x=\"85\" y=\"-13.8\" font-family=\"Times,serif\" font-size=\"14.00\">TTT</text>\n",
"</g>\n",
"<!-- ATT&#45;&gt;TTT -->\n",
"<g id=\"edge5\" class=\"edge\"><title>ATT&#45;&gt;TTT</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M85,-71.6966C85,-63.9827 85,-54.7125 85,-46.1124\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" points=\"88.5001,-46.1043 85,-36.1043 81.5001,-46.1044 88.5001,-46.1043\"/>\n",
"</g>\n",
"<!-- CTG -->\n",
"<g id=\"node5\" class=\"node\"><title>CTG</title>\n",
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"<text text-anchor=\"middle\" x=\"141\" y=\"-301.8\" font-family=\"Times,serif\" font-size=\"14.00\">CTG</text>\n",
"</g>\n",
"<!-- TGA -->\n",
"<g id=\"node8\" class=\"node\"><title>TGA</title>\n",
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"</g>\n",
"<!-- CTG&#45;&gt;TGA -->\n",
"<g id=\"edge6\" class=\"edge\"><title>CTG&#45;&gt;TGA</title>\n",
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"</g>\n",
"<!-- GCT -->\n",
"<g id=\"node6\" class=\"node\"><title>GCT</title>\n",
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"<text text-anchor=\"middle\" x=\"141\" y=\"-373.8\" font-family=\"Times,serif\" font-size=\"14.00\">GCT</text>\n",
"</g>\n",
"<!-- GCT&#45;&gt;CTG -->\n",
"<g id=\"edge7\" class=\"edge\"><title>GCT&#45;&gt;CTG</title>\n",
"<path fill=\"none\" stroke=\"black\" d=\"M141,-359.697C141,-351.983 141,-342.712 141,-334.112\"/>\n",
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"</g>\n",
"<!-- TCG&#45;&gt;CGA -->\n",
"<g id=\"edge8\" class=\"edge\"><title>TCG&#45;&gt;CGA</title>\n",
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"</g>\n",
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"<g id=\"edge9\" class=\"edge\"><title>TGA&#45;&gt;GAT</title>\n",
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"####Exercise 2: simple overlap\n",
"\n",
"The following command will generate the De Bruijn graph with k = 4 for two reads that have some overlap:\n",
"\n",
"```\n",
"GCTGATCGATTT \n",
" CGATTTTCGGCGAA\n",
"```\n",
"\n",
"* find the two reads again in the graph: which nodes represent the overlap?\n",
"* change k from 4 to 5, to 6, to 7, to 8, what happens?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%dotobj DeBruijnPlot(['GCTGATCGATTT', 'CGATTTTCGGCGAA'], 4)"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"\n",
"####Exercise 3: overlap and an internal repeat\n",
"\n",
"* these two reads overlap, but also have short repeat: the sequence `ATCGA` is present in both reads\n",
"\n",
"```\n",
"GCTGATCGATTT\n",
" CGATTTTATCGAAA\n",
"```\n",
"\n",
"* what happened with the repeat? And the overlap?\n",
"* change k from 4 to 5, to 6, to 7, to 8, what happens?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%dotobj DeBruijnPlot(['GCTGATCGATTT', 'CGATTTTATCGAAA'], 4)"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"####Exercise 4: resolving a repeat\n",
"\n",
"The following sequence has two copies of the `ATCGA` repeat\n",
"\n",
"Decrease and increase the kmer size stepwise\n",
"* at what kmer size is the repeat resolved?\n",
"* why this kmer size?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%dotobj DeBruijnPlot(['GCTGATCGATATGGATTTTATCGAAAAGTCGTAGTC'], 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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"</g>\n",
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"<g id=\"edge5\" class=\"edge\"><title>GTAGT&#45;&gt;TAGTC</title>\n",
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"</g>\n",
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"<g id=\"edge6\" class=\"edge\"><title>AGTCG&#45;&gt;GTCGT</title>\n",
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"</g>\n",
"<!-- TCGTA&#45;&gt;CGTAG -->\n",
"<g id=\"edge7\" class=\"edge\"><title>TCGTA&#45;&gt;CGTAG</title>\n",
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"</g>\n",
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"<g id=\"edge8\" class=\"edge\"><title>GATCG&#45;&gt;ATCGA</title>\n",
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"</g>\n",
"<!-- TTTTA&#45;&gt;TTTAT -->\n",
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"</g>\n",
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"<g id=\"edge10\" class=\"edge\"><title>TGGAT&#45;&gt;GGATT</title>\n",
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"</g>\n",
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"<g id=\"edge12\" class=\"edge\"><title>CGATA&#45;&gt;GATAT</title>\n",
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"<!-- CTGAT -->\n",
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"</g>\n",
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"</g>\n",
"<!-- AAGTC&#45;&gt;AGTCG -->\n",
"<g id=\"edge14\" class=\"edge\"><title>AAGTC&#45;&gt;AGTCG</title>\n",
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"<!-- CGAAA -->\n",
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"</g>\n",
"<!-- GAAAA -->\n",
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"</g>\n",
"<!-- CGAAA&#45;&gt;GAAAA -->\n",
"<g id=\"edge15\" class=\"edge\"><title>CGAAA&#45;&gt;GAAAA</title>\n",
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"</g>\n",
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"<g id=\"edge18\" class=\"edge\"><title>ATATG&#45;&gt;TATGG</title>\n",
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"</g>\n",
"<!-- GCTGA&#45;&gt;CTGAT -->\n",
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"</g>\n",
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}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"####Exercise 5: read with error\n",
"\n",
"* these two reads are identical, except for a one base 'error' in the second one\n",
"\n",
"```\n",
"GCTGATCGATTT\n",
"GCTGATAGATTT\n",
"```\n",
"\n",
"* create the graph with kmer size 5 and *5 copies* of the first read\n",
"* add *one copy* of the second read (again, kmer size 5)\n",
"* explain the graph\n",
"* increase the kmer size"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%dotobj DeBruijnPlot(['GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATAGATTT'], 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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}
],
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}
],
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}
]
}
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