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sequencing.py
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sequencing.py
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from copy import deepcopy
from collections import defaultdict, OrderedDict
from operator import itemgetter
from itertools import permutations
def composition(k, text):
"""
decompose a string into a sequence of overlapping k-mers
>>> list(composition(5, 'CAATCCAAC'))
['CAATC', 'AATCC', 'ATCCA', 'TCCAA', 'CCAAC']
>>> list(composition(5, 'AAAAAACGAT'))
['AAAAA', 'AAAAA', 'AAAAC', 'AAACG', 'AACGA', 'ACGAT']
"""
n = len(text)
for i in xrange(n - k + 1):
yield text[i:i+k]
def compose_from_sorted_kmers(kmers):
"""
compose original string from overlapping k-mers composition sequence
>>> compose_from_sorted_kmers(['ACCGA', 'CCGAA', 'CGAAG', 'GAAGC', 'AAGCT'])
'ACCGAAGCT'
"""
result, kmers = kmers[0], kmers[1:]
k = len(result)
for kmer in kmers:
assert kmer[0:k-1] == result[-k+1:]
result += kmer[-1]
return result
def overlap_graph(kmers):
"""
For each k-mer in a sequence, generate a list of overlapping k-mers from it
>>> overlap_graph(['ATGCG', 'GCATG', 'CATGC', 'AGGCA', 'GGCAT'])
[('GCATG', ['CATGC']), ('CATGC', ['ATGCG']), ('AGGCA', ['GGCAT']), ('GGCAT', ['GCATG'])]
>>> overlap_graph(['AAAAA', 'AAAAA', 'AAAAC', 'AAACG', 'AACGA', 'ACGAT'])
[('AAAAA', ['AAAAA', 'AAAAC']), ('AAAAA', ['AAAAA', 'AAAAC']), ('AAAAC', ['AAACG']), ('AAACG', ['AACGA']), ('AACGA', ['ACGAT'])]
>>> overlap_graph(['AAAAA', 'AAAAA', 'AAAAC', 'AAACG', 'AACGA', 'ACGAA', 'CGAAA', 'GAAAA', 'AAAAA', 'AAAAT'])
[('AAAAA', ['AAAAA', 'AAAAC', 'AAAAA', 'AAAAT']), ('AAAAA', ['AAAAA', 'AAAAC', 'AAAAA', 'AAAAT']), ('AAAAC', ['AAACG']), ('AAACG', ['AACGA']), ('AACGA', ['ACGAA']), ('ACGAA', ['CGAAA']), ('CGAAA', ['GAAAA']), ('GAAAA', ['AAAAA', 'AAAAA', 'AAAAC', 'AAAAA', 'AAAAT']), ('AAAAA', ['AAAAA', 'AAAAA', 'AAAAC', 'AAAAT'])]
"""
result = []
for i in range(len(kmers)):
kmer = kmers[i]
k = len(kmer)
ovp = []
for j in range(len(kmers)):
if i != j:
kkmer = kmers[j]
if kkmer[0:k-1] == kmer[-k+1:]:
ovp.append(kkmer)
if ovp:
result.append((kmer, ovp))
return result
def debruijn_graph(k, text):
"""
Builds the de Bruijn graph of a sequence
>>> debruijn_graph(5, 'AAAAAACGAT')
[('AAAA', ['AAAA', 'AAAA', 'AAAC']), ('AAAC', ['AACG']), ('AACG', ['ACGA']), ('ACGA', ['CGAT'])]
>>> debruijn_graph(5, 'AGAAAACGAT')
[('AAAA', ['AAAC']), ('AAAC', ['AACG']), ('AACG', ['ACGA']), ('ACGA', ['CGAT']), ('AGAA', ['GAAA']), ('GAAA', ['AAAA'])]
>>> debruijn_graph(4, 'AAGATTCTCTAAGA')
[('AAG', ['AGA', 'AGA']), ('AGA', ['GAT']), ('ATT', ['TTC']), ('CTA', ['TAA']), ('CTC', ['TCT']), ('GAT', ['ATT']), ('TAA', ['AAG']), ('TCT', ['CTA', 'CTC']), ('TTC', ['TCT'])]
>>> debruijn_graph(2, 'TAATGCCATGGGATGTT')
[('A', ['A', 'T', 'T', 'T']), ('C', ['A', 'C']), ('G', ['A', 'C', 'G', 'G', 'T']), ('T', ['A', 'G', 'G', 'G', 'T'])]
"""
kmers = composition(k, text)
return debruijn_graph_from_kmers(k, kmers)
def debruijn_graph_from_kmers(k, kmers):
"""
de Bruijn graph from ramdonly ordered kmers
>>> import random
>>> results = []
>>> for k, text in [(5, 'AAAAAACGAT'), (5, 'AGAAAACGAT'), (4, 'AAGATTCTCTAAGA'), (2, 'TAATGCCATGGGATGTT')]:
... kmers = list(composition(k, text))
... random.shuffle(kmers)
... results.append(debruijn_graph_from_kmers(k, kmers) == debruijn_graph(k, text))
>>> all(results)
True
"""
debruijn_nodes = defaultdict(list)
for kmer in kmers:
debruijn_nodes[kmer[:k-1]].append(kmer[1:])
return [(d, sorted(dd)) for d, dd in sorted(debruijn_nodes.items(), key=itemgetter(0))]
def walk_cycle(adjacency_map, starting_node=None):
"""
Find the first cycle in the given eulerian adjacency list
>>> walk_cycle(OrderedDict([(0, [3]), (1, [0]), (2, [1, 6]), (3, [2]), (4, [2]), (5, [4]), (6, [5, 8]), (7, [9]), (8, [7]), (9, [6])]))
[0, 3, 2, 6, 8, 7, 9, 6, 5, 4, 2, 1, 0]
>>> walk_cycle(OrderedDict([(0, [3]), (1, [0]), (2, [6, 1]), (3, [2]), (4, [2]), (5, [4]), (6, [8, 5]), (7, [9]), (8, [7]), (9, [6])]))
[0, 3, 2, 1, 0]
"""
if starting_node is not None:
result = [starting_node]
else:
for node in adjacency_map.iterkeys():
result = [node]
break
while True:
next_nodes = adjacency_map[result[-1]]
result.append(next_nodes.pop())
if not next_nodes:
adjacency_map.pop(result[-2])
if result[-1] == result[0]:
break
return result
class CloseLink(object):
pass
close_link = CloseLink()
def euler_path(adjacency_map, path_permutations=0):
"""
>>> euler_path(OrderedDict([(0, [3]), (1, [0]), (2, [6, 1]), (3, [2]), (4, [2]), (5, [4]), (6, [8, 5]), (7, [9]), (8, [7]), (9, [6])]))
[6, 5, 4, 2, 1, 0, 3, 2, 6, 8, 7, 9, 6]
>>> euler_path(OrderedDict([(0, [2]), (1, [3]), (2, [1]), (3, [0, 4]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]))
[6, 7, 8, 9, 6, 3, 0, 2, 1, 3, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1]), (3, [0, 4, 5]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]))
[6, 7, 8, 9, 6, 3, 0, 3, 5, 0, 2, 1, 3, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1, 4]), (3, [0, 4, 5]), (4, [2]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]))
[6, 7, 8, 9, 6, 3, 4, 2, 1, 3, 0, 3, 5, 0, 2, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1, 4]), (3, [0, 4, 5]), (4, [2]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]), 1)
[6, 7, 8, 9, 6, 3, 5, 0, 3, 4, 2, 1, 3, 0, 2, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1, 4]), (3, [0, 4, 5]), (4, [2]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]), 2)
[6, 7, 8, 9, 6, 3, 0, 2, 4, 2, 1, 3, 5, 0, 3, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1, 4]), (3, [0, 4, 5]), (4, [2]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]), 3)
[6, 7, 8, 9, 6, 3, 5, 0, 3, 0, 2, 4, 2, 1, 3, 4]
>>> euler_path(OrderedDict([(0, [2, 3]), (1, [3]), (2, [1, 4]), (3, [0, 4, 5]), (4, [2]), (5, [0]), (6, [3, 7]), (7, [8]), (8, [9]), (9, [6])]), 9)
Traceback (most recent call last):
...
AssertionError
"""
adjacency_map = deepcopy(adjacency_map)
for node, next_nodes in adjacency_map.iteritems():
if path_permutations > 0:
permuted_next_nodes = permutations(next_nodes)
permuted_next_nodes.next()
for next_nodes in permuted_next_nodes:
path_permutations -= 1
adjacency_map[node] = list(next_nodes)
if path_permutations == 0:
break
assert path_permutations == 0
inverse_adjacency_map = defaultdict(list)
for node, next_nodes in adjacency_map.iteritems():
for next_node in next_nodes:
inverse_adjacency_map[next_node].append(node)
first_node = last_node = None
for node, next_nodes in adjacency_map.iteritems():
if len(next_nodes) > len(inverse_adjacency_map.get(node, [])):
first_node = node
break
for node, next_nodes in inverse_adjacency_map.iteritems():
if len(next_nodes) > len(adjacency_map.get(node, [])):
last_node = node
adjacency_map.setdefault(last_node, []).append(close_link)
adjacency_map[close_link] = [first_node]
break
cycle = walk_cycle(adjacency_map)
while True:
for i, node in enumerate(cycle):
if node in adjacency_map:
cycle = cycle[i:-1] + cycle[0:i]
cycle.extend(walk_cycle(adjacency_map, starting_node=node))
break
else:
break
for i, node in enumerate(cycle):
if node == close_link:
cycle = cycle[i+1:] + cycle[1:i]
break
return cycle
def sequence_from_kmers(k, kmers):
"""
>>> sequence_from_kmers(4, ['CTTA', 'ACCA', 'TACC', 'GGCT', 'GCTT', 'TTAC'])
'GGCTTACCA'
"""
adjacency_map = OrderedDict(debruijn_graph_from_kmers(k, kmers))
return compose_from_sorted_kmers(euler_path(adjacency_map))
def universal_string(k):
kmers = [bin(i)[2:].zfill(k) for i in range(2**k)]
return sequence_from_kmers(k, kmers)
def universal_circular_string(k):
kmers = [bin(i)[2:].zfill(k) for i in range(2**k)]
debruijn = dict(debruijn_graph_from_kmers(k, kmers))
return compose_from_sorted_kmers(euler_path(debruijn)[:-k+1])
def gapped_pairs_composition(k, d, text):
"""
>>> list(gapped_pairs_composition(3, 1, 'TAATGCCATGGGATGTT'))
[('TAA', 'GCC'), ('AAT', 'CCA'), ('ATG', 'CAT'), ('TGC', 'ATG'), ('GCC', 'TGG'), ('CCA', 'GGG'), ('CAT', 'GGA'), ('ATG', 'GAT'), ('TGG', 'ATG'), ('GGG', 'TGT'), ('GGA', 'GTT')]
"""
queue = []
nlen = d + k + 1
for kmer in composition(k, text):
queue.append(kmer)
if len(queue) == nlen:
yield queue.pop(0), kmer
def compose_from_sorted_gapped_pairs(d, paired_kmers):
"""
>>> compose_from_sorted_gapped_pairs(1, [('TAA', 'GCC'), ('AAT', 'CCA'), ('ATG', 'CAT'), ('TGC', 'ATG'), ('GCC', 'TGG'), ('CCA', 'GGG'), ('CAT', 'GGA'), ('ATG', 'GAT'), ('TGG', 'ATG'), ('GGG', 'TGT'), ('GGA', 'GTT')])
'TAATGCCATGGGATGTT'
>>> compose_from_sorted_gapped_pairs(2, [('GACC', 'GCGC'), ('ACCG', 'CGCC'), ('CCGA', 'GCCG'), ('CGAG', 'CCGG'), ('GAGC', 'CGGA')])
'GACCGAGCGCCGGA'
>>> compose_from_sorted_gapped_pairs(3, [('GTG', 'GTG'), ('TGG', 'TGA'), ('GGT', 'GAG'), ('GTC', 'AGA'), ('TCG', 'GAT'), ('CGT', 'ATG'), ('GTG', 'TGT'), ('TGA', 'GTT'), ('GAG', 'TTG'), ('AGA', 'TGA')])
'GTGGTCGTGAGATGTTGA'
"""
k = len(paired_kmers[0][0])
resultP = compose_from_sorted_kmers(map(itemgetter(0), paired_kmers))
resultS = compose_from_sorted_kmers(map(itemgetter(1), paired_kmers))
if resultP[k+d:] == resultS[:-k-d]:
return resultP + resultS[-k-d:]
def debruijn_graph_from_gapped_pairs(k, paired_kmers):
return debruijn_graph_from_kmers(k, map(itemgetter(0), paired_kmers)), debruijn_graph_from_kmers(k, map(itemgetter(1), paired_kmers))
def euler_path_for_gapped_pairs(k, d, prefix_adjacency_map, suffix_adjacency_map):
permutations = 0
while True:
peuler_path = euler_path(prefix_adjacency_map, permutations)
seuler_path = euler_path(suffix_adjacency_map)
if peuler_path[k+d:] == seuler_path[:-k-d]:
break
else:
permutations += 1
return zip(peuler_path, seuler_path)
def sequence_from_gapped_pairs(k, d, paired_kmers):
"""
>>> sequence_from_gapped_pairs(4, 2, [('GAGA', 'TTGA'), ('TCGT', 'GATG'), ('CGTG', 'ATGT'), ('TGGT', 'TGAG'), ('GTGA', 'TGTT'), ('GTGG', 'GTGA'), ('TGAG', 'GTTG'), ('GGTC', 'GAGA'), ('GTCG', 'AGAT')])
'GTGGTCGTGAGATGTTGA'
"""
adjacency_maps = debruijn_graph_from_gapped_pairs(k, paired_kmers)
epath = euler_path_for_gapped_pairs(k, d, OrderedDict(adjacency_maps[0]), OrderedDict(adjacency_maps[1]))
return compose_from_sorted_gapped_pairs(d + 1, epath)