(see the Sources document for original source and license of this code)

How to use this notebook:

- 'activate' cells by clicking on them with the mouse (you will see a blinking cursor)
- execute cells by pressing the ctrl and enter keys simultaneously
- you can also execute code by pressing shift + enter, this will activate the next cell

Execute the first few cells until the one that generates the first plot. This will load the necessary python code.

In [1]:

```
class DeBruijnGraph:
''' De Bruijn directed multigraph built from a collection of
strings. User supplies strings and k-mer length k. Nodes
are k-1-mers. An Edge corresponds to the k-mer that joins
a left k-1-mer to a right k-1-mer. '''
@staticmethod
def chop(st, k):
''' Chop string into k-mers of given length '''
# workaround for the fact that length of the sequences
# in the nodes was one less than size of k in the original implementation
# as suggested by Katie Dean
k = k + 1
for i in xrange(0, len(st)-(k-1)):
yield (st[i:i+k], st[i:i+k-1], st[i+1:i+k])
class Node:
''' Node representing a k-1 mer. Keep track of # of
incoming/outgoing edges so it's easy to check for
balanced, semi-balanced. '''
def __init__(self, km1mer):
self.km1mer = km1mer
self.nin = 0
self.nout = 0
def isSemiBalanced(self):
return abs(self.nin - self.nout) == 1
def isBalanced(self):
return self.nin == self.nout
def __hash__(self):
return hash(self.km1mer)
def __str__(self):
return self.km1mer
def __init__(self, strIter, k, circularize=False):
''' Build de Bruijn multigraph given string iterator and k-mer
length k '''
self.G = {} # multimap from nodes to neighbors
self.nodes = {} # maps k-1-mers to Node objects
for st in strIter:
if circularize:
st += st[:k-1]
for kmer, km1L, km1R in self.chop(st, k):
nodeL, nodeR = None, None
if km1L in self.nodes:
nodeL = self.nodes[km1L]
else:
nodeL = self.nodes[km1L] = self.Node(km1L)
if km1R in self.nodes:
nodeR = self.nodes[km1R]
else:
nodeR = self.nodes[km1R] = self.Node(km1R)
nodeL.nout += 1
nodeR.nin += 1
self.G.setdefault(nodeL, []).append(nodeR)
# Iterate over nodes; tally # balanced, semi-balanced, neither
self.nsemi, self.nbal, self.nneither = 0, 0, 0
# Keep track of head and tail nodes in the case of a graph with
# Eularian walk (not cycle)
self.head, self.tail = None, None
for node in self.nodes.itervalues():
if node.isBalanced():
self.nbal += 1
elif node.isSemiBalanced():
if node.nin == node.nout + 1:
self.tail = node
if node.nin == node.nout - 1:
self.head = node
self.nsemi += 1
else:
self.nneither += 1
def nnodes(self):
''' Return # nodes '''
return len(self.nodes)
def nedges(self):
''' Return # edges '''
return len(self.G)
def hasEulerianWalk(self):
''' Return true iff graph has Eulerian walk. '''
return self.nneither == 0 and self.nsemi == 2
def hasEulerianCycle(self):
''' Return true iff graph has Eulerian cycle. '''
return self.nneither == 0 and self.nsemi == 0
def isEulerian(self):
''' Return true iff graph has Eulerian walk or cycle '''
# technically, if it has an Eulerian walk
return self.hasEulerianWalk() or self.hasEulerianCycle()
def eulerianWalkOrCycle(self):
''' Find and return sequence of nodes (represented by
their k-1-mer labels) corresponding to Eulerian walk
or cycle '''
assert self.isEulerian()
g = self.G
if self.hasEulerianWalk():
g = g.copy()
g.setdefault(self.tail, []).append(self.head)
# graph g has an Eulerian cycle
tour = []
src = g.iterkeys().next() # pick arbitrary starting node
def __visit(n):
while len(g[n]) > 0:
dst = g[n].pop()
__visit(dst)
tour.append(n)
__visit(src)
tour = tour[::-1][:-1] # reverse and then take all but last node
if self.hasEulerianWalk():
# Adjust node list so that it starts at head and ends at tail
sti = tour.index(self.head)
tour = tour[sti:] + tour[:sti]
# Return node list
return map(str, tour)
```

In [2]:

```
class DeBruijnPlot(DeBruijnGraph):
def to_dot(self, weights=False):
""" Write dot representation to given filehandle. If 'weights'
is true, label edges corresponding to distinct k-1-mers
with weights, instead of writing a separate edge for each
copy of a k-1-mer. """
dot_str = []
dot_str.append("digraph \"DeBruijn graph\" {\n")
dot_str.append(" bgcolor=\"transparent\";\n")
for node in self.G.iterkeys():
lab = node.km1mer
dot_str.append(" %s [label=\"%s\"] ;\n" % (lab, lab))
for src, dsts in self.G.iteritems():
srclab = src.km1mer
if weights:
weightmap = {}
if weights:
for dst in dsts:
weightmap[dst] = weightmap.get(dst, 0) + 1
for dst, v in weightmap.iteritems():
dstlab = dst.km1mer
dot_str.append(" %s -> %s [label=\"%d\"] ;\n" % (srclab, dstlab, v))
else:
for dst in dsts:
srclab = src.km1mer
dstlab = dst.km1mer
dot_str.append(" %s -> %s [label=\"\"] ;\n" % (srclab, dstlab))
dot_str.append("}\n")
return ''.join(dot_str)
```

In [3]:

```
%install_ext https://raw.githubusercontent.com/cjdrake/ipython-magic/master/gvmagic.py
```

In [4]:

```
%load_ext gvmagic
```

Do the exercise by execute the code cell below.

Let's first generate a really simple De Bruijn graph of a short read 'GCTGATCGATTT' with kmer size 4

- study the graph and see if it indeed encodes the read
- now change the kmer size to 3 and again trace the read: what happened?

In [6]:

```
%dotobj DeBruijnPlot(['GCTGATCGATTT'], 3)
```

The following command will generate the De Bruijn graph with k = 4 for two reads that have some overlap:

```
GCTGATCGATTT
CGATTTTCGGCGAA
```

- find the two reads again in the graph: which nodes represent the overlap?
- change k from 4 to 5, to 6, to 7, to 8, what happens?

In [ ]:

```
%dotobj DeBruijnPlot(['GCTGATCGATTT', 'CGATTTTCGGCGAA'], 4)
```

- these two reads overlap, but also have short repeat: the sequence
`ATCGA`

is present in both reads

```
GCTGATCGATTT
CGATTTTATCGAAA
```

- what happened with the repeat? And the overlap?
- change k from 4 to 5, to 6, to 7, to 8, what happens?

In [ ]:

```
%dotobj DeBruijnPlot(['GCTGATCGATTT', 'CGATTTTATCGAAA'], 4)
```

The following sequence has two copies of the `ATCGA`

repeat

Decrease and increase the kmer size stepwise

- at what kmer size is the repeat resolved?
- why this kmer size?

In [8]:

```
%dotobj DeBruijnPlot(['GCTGATCGATATGGATTTTATCGAAAAGTCGTAGTC'], 5)
```

- these two reads are identical, except for a one base 'error' in the second one

```
GCTGATCGATTT
GCTGATAGATTT
```

- create the graph with kmer size 5 and
*5 copies*of the first read - add
*one copy*of the second read (again, kmer size 5) - explain the graph
- increase the kmer size

In [10]:

```
%dotobj DeBruijnPlot(['GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATCGATTT','GCTGATAGATTT'], 5)
```