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ペアワイズアラインメント

ペアワイズアラインメントとは

  • 2本のDNAの塩基配列(タンパク質のアミノ酸配列)を比較する方法の一つ
  • バイオインフォマティクスでは最も基本的な解析手法

なぜDNA配列の比較をするのか¶

  1. DNAの機能を知りたい(∵ DNAの配列が似ていると機能が似ている)
  2. DNAのどの部分が重要かを知りたい。(∵ 「保存されている=重要」だと考えられる)
  3. 生物の進化系統樹を知りたい
  4. 新型シーケンサーで読まれたDNAの由来を知りたい

DNAの変異や新型シークエンサーの読み取りエラーでは長さが異なることがあるので、長さの変化を考慮し効率の良い動的計画法を用いる

アラインメントの種類 説明 例
グローバルアラインメント 2本の配列の全体をアラインメントする。 Needleman-Wunsch
ローカルアラインメント 2本の配列の似ている部分を検出し、その部分をアランメントする Smith-Waterman

実装¶

各種アラインメントを実装していく。なお、全てAffine gap penaltyを利用する。

In [1]:
from kerasy.Bio.alignment import NeedlemanWunshGotoh, SmithWaterman, BackwardNeedlemanWunshGotoh
In [2]:
# サンプル配列
seqX = "GGAGTGAGGGGAGCAGTTGGGCTGAAGATGGTCAACGCCGAGGGAACGGTAAAGGCGACGGAGCTGTGGCAGACCTGGCTTCCTAACCACGTCCCGTGTTTTGCGGCTCCGCGAGGACTG"
seqY = "CGCATGCGGAGTGAGGGGAGCAGTTGGGAACAGATGGTCCCGCCGAGGGACCGGTGGGCAGACGGGGCCAGCTGTGGCAGACACTGGCTTCTAACCACCGAACGTTCTTTCCGCTCCGC"

Needleman-Wunsch-Gotoh¶

自作のモジュール(kerasy.Bio.alignment.NeedlemanWunshGotoh)を使ってアラインメントをします。

In [3]:
model = NeedlemanWunshGotoh()
In [4]:
model.align(seqX, seqY)
 Needleman-Wunsh-Gotoh 
Alignment score: 14.0

|parameter            |value|
-----------------------------
|match                |    1|
|mimatch              |   -1|
|gap opening penalty  |    5|
|gap extension penalty|    1|
===============================================================
X: -------GGAGTGAGGGGAGCAGTTGGGCTGAAGATGGTCAACGCCGAGGGAACGGTAAA
Y: CGCATGCGGAGTGAGGGGAGCAGTTGGG-AACAGATGGTC-CCGCCGAGGGACCGGT-GG

X: GGCGACGG----AGCTGTGGCAGAC-CTGGCTTCCTAACCACGTCCCGTGTTTTGCGGCT
Y: GCAGACGGGGCCAGCTGTGGCAGACACTGGCTT-CTAACCACCGAACGT-TCTTTCCGCT

X: CCGCGAGGACTG
Y: CCGC--------
===============================================================

Smith-Waterman¶

自作のモジュール(kerasy.Bio.alignment.SmithWaterman)を使ってアラインメントをします。

In [5]:
model = SmithWaterman()
In [6]:
model.align(seqX, seqY)
 Smith-Waterman 
Alignment score: 37.0

|parameter            |value|
-----------------------------
|match                |    1|
|mimatch              |   -1|
|gap opening penalty  |    5|
|gap extension penalty|    1|
===============================================================
Aligned positions: X[0,111] Y[7,118]
X: GGAGTGAGGGGAGCAGTTGGGCTGAAGATGGTCAACGCCGAGGGAACGGTAAAGGCGACG
Y: GGAGTGAGGGGAGCAGTTGGG-AACAGATGGTC-CCGCCGAGGGACCGGT-GGGCAGACG

X: G----AGCTGTGGCAGAC-CTGGCTTCCTAACCACGTCCCGTGTTTTGCGGCTCCGC
Y: GGGCCAGCTGTGGCAGACACTGGCTT-CTAACCACCGAACGT-TCTTTCCGCTCCGC
===============================================================

制約付きアラインメント¶

  • $x_i$ と $y_j$ がアラインされるという制約下で最大のアラインメントスコアを求める。
  • 全てのパターンを列挙すると $\mathcal{O}(n^2m^2)$ の時間がかかるが、後ろ向きアラインメントと組み合わせることで全てのパターンを $\mathcal{O}(nm)$ で計算可能。
    • 前向き:xiとyjがアラインされる時の、iまでとjまでの配列の最大アラインメントスコアを保持。
    • 後ろ向き:xiとyjがアラインされる時の、i+1以降とj+1以降の配列の最大アラインメントスコアを保持。

Needleman-Wunsch-Gotohの逆向きアラインメントは(kerasy.Bio.alignment.BackwardNeedlemanWunshGotoh)に定義してあります。

In [7]:
model_forward  = NeedlemanWunshGotoh()
model_backward = BackwardNeedlemanWunshGotoh()
In [8]:
model_forward.align(seqX,seqY,memorize=True)
 Needleman-Wunsh-Gotoh 
Alignment score: 14.0

|parameter            |value|
-----------------------------
|match                |    1|
|mimatch              |   -1|
|gap opening penalty  |    5|
|gap extension penalty|    1|
===============================================================
X: -------GGAGTGAGGGGAGCAGTTGGGCTGAAGATGGTCAACGCCGAGGGAACGGTAAA
Y: CGCATGCGGAGTGAGGGGAGCAGTTGGG-AACAGATGGTC-CCGCCGAGGGACCGGT-GG

X: GGCGACGG----AGCTGTGGCAGAC-CTGGCTTCCTAACCACGTCCCGTGTTTTGCGGCT
Y: GCAGACGGGGCCAGCTGTGGCAGACACTGGCTT-CTAACCACCGAACGT-TCTTTCCGCT

X: CCGCGAGGACTG
Y: CCGC--------
===============================================================
In [9]:
model_backward.align(seqX,seqY,memorize=True)
 Backward Needleman-Wunsh-Gotoh 
Alignment score: 14.0

|parameter            |value|
-----------------------------
|match                |    1|
|mimatch              |   -1|
|gap opening penalty  |    5|
|gap extension penalty|    1|
===============================================================
X: -------GGAGTGAGGGGAGCAGTTGGGCTGAAGATGGTCAACGCCGAGGGAACGGTAAA
Y: CGCATGCGGAGTGAGGGGAGCAGTTGGGAACA-GATGGTCC-CGCCGAGGGACCGGTGG-

X: GGCGACGG----AGCTGTGGCAGAC-CTGGCTTCCTAACCACGTCCCGTGTTTTGCGGCT
Y: GCAGACGGGGCCAGCTGTGGCAGACACTGGCTTC-TAACCACCGAACGTTCTTTCCG-CT

X: CCGCGAGGACT
Y: CCGC-------
===============================================================
In [10]:
k=3
n=len(seqX)+1
m=len(seqY)+1
In [11]:
M = model_forward.DP.reshape((k,n,m))[0,1:,1:]
bM = model_backward.DP.reshape((k,n,m))[0,1:,1:]
In [12]:
A = M+bM
In [13]:
# 上の配列を見れば、seqX[0] と seqY[7] がアラインされている時に最大スコア14を取ることがわかるので、それを確かめる。
print(A[0,7])
14.0
In [14]:
# 可視化のために pandas を使用。
import pandas as pd
pd.set_option('display.max_rows', m)
pd.set_option('display.max_columns', n)
In [15]:
df = pd.DataFrame(A)
In [16]:
df
Out[16]:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
0 12.0 10.0 8.0 8.0 8.0 10.0 8.0 14.0 7.0 2.0 1.0 -4.0 -5.0 -10.0 -11.0 -14.0 -17.0 -20.0 -25.0 -26.0 -31.0 -34.0 -35.0 -38.0 -39.0 -40.0 -41.0 -44.0 -49.0 -50.0 -51.0 -54.0 -55.0 -60.0 -63.0 -64.0 -67.0 -70.0 -71.0 -72.0 -75.0 -76.0 -79.0 -76.0 -81.0 -80.0 -83.0 -84.0 -89.0 -92.0 -93.0 -94.0 -95.0 -98.0 -101.0 -100.0 -103.0 -106.0 -111.0 -112.0 -113.0 -118.0 -117.0 -118.0 -119.0 -122.0 -125.0 -128.0 -129.0 -132.0 -133.0 -138.0 -141.0 -142.0 -147.0 -148.0 -150.0 -156.0 -156.0 -159.0 -160.0 -163.0 -164.0 -167.0 -170.0 -171.0 -174.0 -177.0 -180.0 -181.0 -184.0 -187.0 -190.0 -193.0 -194.0 -197.0 -198.0 -201.0 -200.0 -203.0 -206.0 -209.0 -210.0 -211.0 -214.0 -217.0 -218.0 -221.0 -224.0 -225.0 -228.0 -229.0 -230.0 -235.0 -238.0 -241.0 -242.0 -243.0 -246.0
1 5.0 12.0 8.0 6.0 6.0 8.0 8.0 8.0 14.0 5.0 2.0 -1.0 -4.0 -7.0 -10.0 -11.0 -14.0 -17.0 -22.0 -25.0 -26.0 -33.0 -34.0 -35.0 -38.0 -39.0 -40.0 -41.0 -44.0 -49.0 -50.0 -53.0 -54.0 -57.0 -62.0 -63.0 -64.0 -67.0 -70.0 -71.0 -72.0 -75.0 -76.0 -79.0 -76.0 -81.0 -80.0 -83.0 -84.0 -89.0 -92.0 -93.0 -94.0 -95.0 -98.0 -101.0 -100.0 -103.0 -106.0 -111.0 -112.0 -113.0 -118.0 -117.0 -118.0 -119.0 -122.0 -125.0 -128.0 -131.0 -132.0 -135.0 -140.0 -141.0 -144.0 -147.0 -148.0 -150.0 -157.0 -156.0 -159.0 -160.0 -163.0 -166.0 -169.0 -170.0 -171.0 -174.0 -179.0 -180.0 -183.0 -186.0 -189.0 -192.0 -193.0 -194.0 -197.0 -200.0 -201.0 -200.0 -203.0 -206.0 -211.0 -210.0 -211.0 -216.0 -217.0 -220.0 -223.0 -224.0 -227.0 -228.0 -229.0 -232.0 -237.0 -240.0 -243.0 -242.0 -243.0
2 2.0 3.0 10.0 8.0 6.0 6.0 6.0 6.0 6.0 14.0 3.0 0.0 -3.0 -4.0 -9.0 -12.0 -13.0 -16.0 -17.0 -24.0 -27.0 -26.0 -31.0 -34.0 -35.0 -38.0 -41.0 -42.0 -41.0 -44.0 -47.0 -48.0 -53.0 -54.0 -59.0 -60.0 -65.0 -64.0 -67.0 -68.0 -69.0 -70.0 -75.0 -76.0 -79.0 -76.0 -83.0 -80.0 -85.0 -84.0 -89.0 -90.0 -91.0 -96.0 -95.0 -98.0 -101.0 -100.0 -105.0 -106.0 -111.0 -112.0 -113.0 -116.0 -117.0 -118.0 -121.0 -122.0 -125.0 -126.0 -131.0 -134.0 -137.0 -140.0 -143.0 -146.0 -149.0 -150.0 -150.0 -157.0 -156.0 -159.0 -158.0 -163.0 -166.0 -169.0 -172.0 -171.0 -176.0 -177.0 -180.0 -183.0 -184.0 -187.0 -190.0 -193.0 -192.0 -197.0 -198.0 -201.0 -200.0 -203.0 -204.0 -209.0 -210.0 -213.0 -214.0 -217.0 -220.0 -221.0 -224.0 -225.0 -228.0 -231.0 -234.0 -237.0 -238.0 -241.0 -242.0
3 -1.0 2.0 3.0 8.0 6.0 6.0 4.0 6.0 6.0 4.0 14.0 1.0 0.0 -5.0 -4.0 -9.0 -12.0 -13.0 -18.0 -17.0 -24.0 -29.0 -26.0 -31.0 -34.0 -35.0 -38.0 -41.0 -42.0 -41.0 -44.0 -49.0 -48.0 -55.0 -56.0 -59.0 -60.0 -65.0 -64.0 -67.0 -68.0 -69.0 -70.0 -75.0 -76.0 -79.0 -76.0 -83.0 -80.0 -85.0 -84.0 -89.0 -90.0 -91.0 -96.0 -95.0 -98.0 -101.0 -100.0 -105.0 -106.0 -111.0 -112.0 -113.0 -116.0 -117.0 -118.0 -121.0 -122.0 -127.0 -126.0 -133.0 -136.0 -137.0 -142.0 -143.0 -146.0 -150.0 -151.0 -150.0 -157.0 -156.0 -159.0 -160.0 -165.0 -166.0 -169.0 -172.0 -171.0 -176.0 -179.0 -182.0 -185.0 -186.0 -187.0 -192.0 -193.0 -192.0 -197.0 -198.0 -201.0 -202.0 -205.0 -204.0 -209.0 -212.0 -213.0 -216.0 -217.0 -220.0 -223.0 -224.0 -225.0 -230.0 -233.0 -236.0 -239.0 -238.0 -241.0
4 -4.0 -3.0 0.0 1.0 8.0 4.0 4.0 2.0 4.0 4.0 2.0 14.0 1.0 -2.0 -5.0 -6.0 -11.0 -14.0 -15.0 -20.0 -19.0 -22.0 -27.0 -26.0 -29.0 -34.0 -35.0 -38.0 -41.0 -42.0 -41.0 -46.0 -49.0 -50.0 -53.0 -58.0 -61.0 -60.0 -63.0 -64.0 -67.0 -66.0 -69.0 -68.0 -75.0 -76.0 -79.0 -76.0 -83.0 -80.0 -85.0 -84.0 -87.0 -92.0 -91.0 -94.0 -95.0 -100.0 -103.0 -100.0 -105.0 -106.0 -109.0 -112.0 -113.0 -116.0 -119.0 -118.0 -121.0 -124.0 -127.0 -128.0 -131.0 -136.0 -137.0 -142.0 -145.0 -148.0 -148.0 -153.0 -150.0 -155.0 -156.0 -159.0 -160.0 -165.0 -168.0 -169.0 -170.0 -171.0 -176.0 -177.0 -182.0 -185.0 -186.0 -189.0 -190.0 -193.0 -192.0 -197.0 -198.0 -201.0 -202.0 -205.0 -204.0 -207.0 -210.0 -211.0 -214.0 -215.0 -220.0 -221.0 -224.0 -227.0 -228.0 -233.0 -234.0 -237.0 -238.0
5 -7.0 -4.0 -3.0 -2.0 -1.0 8.0 2.0 4.0 4.0 2.0 4.0 2.0 14.0 1.0 0.0 -3.0 -6.0 -9.0 -14.0 -15.0 -20.0 -21.0 -20.0 -25.0 -26.0 -29.0 -32.0 -33.0 -36.0 -39.0 -40.0 -43.0 -44.0 -49.0 -52.0 -53.0 -56.0 -59.0 -60.0 -61.0 -64.0 -65.0 -64.0 -67.0 -66.0 -73.0 -74.0 -77.0 -76.0 -81.0 -78.0 -83.0 -84.0 -85.0 -90.0 -91.0 -92.0 -95.0 -98.0 -101.0 -98.0 -103.0 -106.0 -107.0 -110.0 -111.0 -114.0 -117.0 -118.0 -121.0 -122.0 -127.0 -130.0 -131.0 -136.0 -137.0 -140.0 -144.0 -147.0 -146.0 -151.0 -150.0 -153.0 -156.0 -159.0 -160.0 -163.0 -166.0 -169.0 -170.0 -173.0 -176.0 -179.0 -182.0 -183.0 -184.0 -187.0 -190.0 -191.0 -190.0 -195.0 -198.0 -201.0 -200.0 -203.0 -206.0 -207.0 -210.0 -213.0 -214.0 -217.0 -218.0 -219.0 -224.0 -227.0 -230.0 -233.0 -232.0 -235.0
6 -10.0 -9.0 -6.0 -3.0 -4.0 -1.0 6.0 2.0 2.0 4.0 2.0 2.0 2.0 14.0 1.0 -2.0 -5.0 -8.0 -9.0 -14.0 -17.0 -18.0 -23.0 -20.0 -23.0 -28.0 -31.0 -34.0 -33.0 -34.0 -37.0 -38.0 -43.0 -44.0 -49.0 -52.0 -55.0 -56.0 -57.0 -58.0 -61.0 -64.0 -66.0 -62.0 -65.0 -66.0 -71.0 -74.0 -77.0 -76.0 -79.0 -76.0 -81.0 -84.0 -85.0 -88.0 -91.0 -94.0 -97.0 -96.0 -99.0 -98.0 -101.0 -104.0 -107.0 -110.0 -113.0 -114.0 -115.0 -116.0 -121.0 -124.0 -127.0 -130.0 -133.0 -136.0 -139.0 -141.0 -142.0 -147.0 -146.0 -149.0 -148.0 -153.0 -156.0 -159.0 -162.0 -163.0 -166.0 -167.0 -170.0 -173.0 -174.0 -177.0 -180.0 -183.0 -182.0 -187.0 -188.0 -191.0 -190.0 -193.0 -196.0 -199.0 -200.0 -203.0 -204.0 -207.0 -210.0 -211.0 -214.0 -215.0 -218.0 -221.0 -224.0 -227.0 -228.0 -231.0 -232.0
7 -13.0 -10.0 -9.0 -8.0 -5.0 -2.0 -1.0 6.0 2.0 0.0 4.0 0.0 2.0 1.0 14.0 3.0 0.0 -3.0 -8.0 -9.0 -14.0 -17.0 -18.0 -22.0 -18.0 -21.0 -26.0 -29.0 -32.0 -33.0 -34.0 -37.0 -38.0 -43.0 -46.0 -47.0 -50.0 -53.0 -54.0 -55.0 -58.0 -59.0 -64.0 -64.0 -60.0 -63.0 -66.0 -69.0 -72.0 -75.0 -76.0 -77.0 -74.0 -79.0 -82.0 -83.0 -86.0 -89.0 -94.0 -95.0 -96.0 -97.0 -98.0 -99.0 -102.0 -105.0 -108.0 -111.0 -112.0 -115.0 -116.0 -121.0 -124.0 -125.0 -130.0 -131.0 -134.0 -139.0 -139.0 -142.0 -145.0 -146.0 -147.0 -150.0 -153.0 -154.0 -157.0 -160.0 -163.0 -164.0 -167.0 -170.0 -173.0 -176.0 -177.0 -180.0 -181.0 -184.0 -185.0 -186.0 -189.0 -192.0 -193.0 -194.0 -197.0 -200.0 -201.0 -204.0 -207.0 -208.0 -211.0 -212.0 -213.0 -218.0 -221.0 -224.0 -225.0 -226.0 -229.0
8 -16.0 -13.0 -12.0 -11.0 -10.0 -5.0 -4.0 -1.0 6.0 0.0 2.0 2.0 2.0 0.0 3.0 14.0 3.0 0.0 -5.0 -6.0 -11.0 -14.0 -15.0 -18.0 -21.0 -16.0 -21.0 -26.0 -29.0 -30.0 -31.0 -34.0 -35.0 -40.0 -41.0 -44.0 -47.0 -50.0 -51.0 -52.0 -55.0 -56.0 -59.0 -64.0 -62.0 -60.0 -61.0 -66.0 -69.0 -72.0 -75.0 -74.0 -75.0 -74.0 -79.0 -80.0 -83.0 -86.0 -91.0 -92.0 -93.0 -96.0 -95.0 -96.0 -99.0 -102.0 -105.0 -108.0 -109.0 -112.0 -113.0 -118.0 -121.0 -122.0 -127.0 -128.0 -131.0 -135.0 -138.0 -137.0 -142.0 -143.0 -144.0 -147.0 -150.0 -151.0 -154.0 -157.0 -160.0 -161.0 -164.0 -167.0 -170.0 -173.0 -174.0 -177.0 -178.0 -179.0 -182.0 -183.0 -186.0 -189.0 -190.0 -191.0 -194.0 -197.0 -198.0 -201.0 -204.0 -205.0 -208.0 -209.0 -210.0 -215.0 -218.0 -221.0 -222.0 -223.0 -226.0
9 -19.0 -16.0 -15.0 -14.0 -13.0 -8.0 -7.0 -4.0 -1.0 4.0 2.0 0.0 2.0 0.0 2.0 3.0 14.0 3.0 -2.0 -3.0 -8.0 -11.0 -12.0 -17.0 -16.0 -19.0 -16.0 -21.0 -26.0 -27.0 -28.0 -31.0 -32.0 -37.0 -40.0 -39.0 -44.0 -47.0 -48.0 -49.0 -52.0 -53.0 -58.0 -57.0 -62.0 -62.0 -58.0 -61.0 -66.0 -69.0 -72.0 -73.0 -72.0 -75.0 -74.0 -77.0 -80.0 -83.0 -88.0 -89.0 -90.0 -95.0 -94.0 -93.0 -96.0 -99.0 -102.0 -105.0 -106.0 -109.0 -110.0 -115.0 -118.0 -119.0 -124.0 -125.0 -128.0 -132.0 -133.0 -136.0 -137.0 -140.0 -141.0 -144.0 -147.0 -148.0 -151.0 -154.0 -157.0 -158.0 -161.0 -164.0 -167.0 -170.0 -171.0 -174.0 -175.0 -178.0 -177.0 -180.0 -183.0 -186.0 -187.0 -188.0 -191.0 -194.0 -195.0 -198.0 -201.0 -202.0 -205.0 -206.0 -207.0 -212.0 -215.0 -218.0 -219.0 -220.0 -223.0
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Published
Oct 1, 2019
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Oct 1, 2019
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情報基礎実験(浅井)
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  • 情報基礎実験(浅井) 13
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