u l l u u l l

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村桥康
5 years ago
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2 u l l u u l l

3 DNA u u

4 Cystic Fibrosis u u

5 CF u u

6 CF

7 CF ATP u u u

8 CF u u

9 CF CFTR

10 CF CFTR

11 CF

12 u u

13 u l u l u l

14 1 u l l l l

15 u l l l l l l n n

17 l l l n Ø l n n

19 u

20 u

22 : minnumcoins(m-1) + 1 minnumcoins(m) = min of minnumcoins(m-3) + 1 minnumcoins(m-7) + 1

23 minnumcoins(m-c 1 ) + 1 minnumcoins(m) = min of minnumcoins(m-c 2 ) + 1 minnumcoins(m-c d ) + 1

24 1. RecursiveChange(M,c,d) 2. if M = 0 3. return 0 4. bestnumcoins ß infinity 5. for i ß 1 to d 6. if M c i 7. numcoins ß RecursiveChange(M c i, c, d) 8. if numcoins + 1 < bestnumcoins 9. bestnumcoins ß numcoins return bestnumcoins

25 RecursiveChange

26 Value Min # of coins

27 Value Min # of coins

28 Value Min # of coins

29 u u u

30 1. DPChange(M,c,d) 2. bestnumcoins 0 ß 0 3. for m ß 1 to M 4. bestnumcoins m ß infinity 5. for i ß 1 to d 6. if m c i 7. if bestnumcoins m ci + 1 < bestnumcoins m 8. bestnumcoins m ß bestnumcoins m ci return bestnumcoins M

31 DPChange c = (1,3,7) M = 9

32 2

33 * * * * * * * * * * * *

34 u u u

35 promising start, but leads to bad choices!

36 j 0 1 i S 0,1 = S 1,0 = 5

37 j i S 0,2 = S 1,1 = S 2,0 = 8

38 MT(n,m) if n=0 or m=0 return MT(n,m) x ß MT(n-1,m)+ length of the edge from (n- 1,m) to (n,m) y ß MT(n,m-1)+ length of the edge from (n,m-1) to (n,m) return max{x,y}

39 i 0 j S 3,0 = S 1,2 = S 2,1 = S 3,0 = 8

40 i 0 j S 1,3 = S 2,2 = greedy alg. fails! 9 S 3,1 = 9

41 j i S 2,3 = S 3,2 = 9

42 i 0 j S 3,3 = 16

43 u s i, j = max s i-1, j + weight of the edge between (i-1, j) and (i, j) s i, j-1 + weight of the edge between (i, j-1) and (i, j) u u

45 u u u c) a) b)

47 A 2 A 3 A 1 B u s B = max of s A1 + weight of the edge (A 1, B) s A2 + weight of the edge (A 2, B) s A3 + weight of the edge (A 3, B)

48 DAG u l l u l

49 DAG

50 DAG su 1 + u 1 s v = max of su 2 + u 2 su 3 + u 3 l

53 u l u v : A T A T A T A T w : T A T A T A T A

54 u v : A T A T A T A T -- w : -- T A T A T A T A u

55 (Edit Distance) u

56 Hamming distance always compares i -th letter of v with i -th letter of w V = ATATATAT W = TATATATA Hamming distance: d(v, w)=8 Computing Hamming distance is a trivial task. vs

57 vs Hamming distance always compares i -th letter of v with i -th letter of w V = ATATATAT W = TATATATA Hamming distance: d(v, w)=8 Just one shift Make it all line up Computing Hamming distance is a trivial task Edit distance may compare i -th letter of v with j -th letter of w V = - ATATATAT W = TATATATA Edit distance: d(v, w)=2 Computing edit is a non-trivial task

58 Hamming distance always compares i -th letter of v with i -th letter of w V = ATATATAT W = TATATATA Hamming distance: d(v, w)=8 vs Edit distance may compare i -th letter of v with j -th letter of w V = - ATATATAT W = TATATATA Edit distance: d(v, w)=2 (one insertion and one deletion) How to find what j goes with what i???

59 à TGCATAT à TGCATA à TGCAT à ATGCAT à ATCCAT à ATCCGAT

60 TGCATAT à ATCCGAT in 4 steps TGCATAT à (insert A at front) ATGCATAT à (delete 6 th T) ATGCATA à (substitute G for 5 th A) ATGCGTA à (substitute C for 3 rd G) ATCCGAT (Done)

61 TGCATAT à ATCCGAT in 4 steps TGCATAT à (insert A at front) ATGCATAT à (delete 6 th T) ATGCATA à (substitute G for 5 th A) ATGCGTA à (substitute C for 3 rd G) ATCCGAT (Done) Can it be done in 3 steps???

62 (alignment) V = ATCTGATG W = TGCATAC match n = 8 m = 7 mismatch V W A T C T G A T G T G C A T A C deletion insertion

63 u v : w : A T CT GA T T GCA T A u m = 7 n = 6 v w A T -- G T T A T -- A T C G T -- A -- C 4 matches 2 insertions 2 deletions

64 u

65 A T _ G T T A T _ A T C G T _ A _ C (0,0), (1,1), (2,2), (2,3), (3,4), (4,5), (5,5), (6,6), (7,6), (7,7)

66 v= AT_GTTAT_ w= ATCGT_A_C (0,0), (1,1), (2,2), (2,3), (3,4), (4,5), (5,5), (6,6), (7,6), (7,7)

67 v= AT_GTTAT_ w= ATCGT_A_C v= AT_GTTAT_ w= ATCG_TA_C

68 0 1 5

69 u l l l l

70 LCS i coords: 0 elements of v elements of w j coords: A T -- C -- T G A T C -- T G C A T -- A -- C (0,0)à (1,0)à (2,1)à (2,2)à (3,3)à (3,4)à (4,5)à (5,5)à (6,6)à (7,6)à (8,7) LCS: TCTAC positions in v: positions in w: 2 < 3 < 4 < 6 < 8 1 < 3 < 5 < 6 < 7

71 LCS

72 i T 0 1 j A T C T G A T C G C 2 3 A T A C 7

73 LCS i T 0 1 j A T C T G A T C G C 2 3 A T A C 7

74 LCS i 0 j A T C T G A T C T G C A T A C 7

75 LCS u i-1,j -1 i-1,j s i-1,j + 0 s i,j = MAX s i,j s i-1,j , if v i = w i,j -1 j i,j

76 LCS u

77 LCS S i,j = S i-1, j-1 max S i-1, j S i, j-1 ç value from NW +1, if v i = w j ç value from North (top) ç value from West (left)

78 LCS v i = w j, s i,j = s i-1,j-1 +1 s 2,2 = [s 1,1 = 1] + 1 s 2,5 = [s 1,4 = 1] + 1 s 4,2 = [s 3,1 = 1] + 1 s 5,2 = [s 4,1 = 1] + 1 s 7,2 = [s 6,1 = 1] + 1

79 LCS

80 LCS 1. LCS(v,w) 2. for i ß 1 to n 3. s i,0 ß 0 4. for j ß 1 to m 5. s 0,j ß 0 6. for i ß 1 to n 7. for j ß 1 to m 8. s i-1,j 9. s i,j ß max s i,j s i-1,j-1 + 1, if v i = w j 11. if s i,j = s i-1,j 12. b i,j ß if s i,j = s i,j if s i,j = s i-1,j return (s n,m, b)

81 Printing LCS: 1. PrintLCS(b,v,i,j) 2. if i = 0 or j = 0 3. return 4. if b i,j = 5. PrintLCS(b,v,i-1,j-1) 6. print v i 7. else 8. if b i,j = 9. PrintLCS(b,v,i-1,j) 10. else 11. PrintLCS(b,v,i,j-1)

82 u u u LCS

83 LCS : u l l l u l l l l

84 µ

85 u l l A C C T G A G A G A C G T G G C A G 70%

86 u l l l

87 u l l à à u l l à à

88 (Scoring Matrix) u l l

89 A R N K A R N K à

90 l R ( x, y R) = q l R ( x, y M) i x i = i p j x i y q i y j

91 u u = = i y x y x i y i x i y x i i i i i i i i q q p q q p R y x R M y x R ), ( ), ( ) log( ), ( ),, ( b a ab i i i q q p b a s y x s S = =

92 u l l u l l

93 PAM u l l l

94 PAM X u l u Ala Arg Asn Asp Cys Gln Glu Gly His Ile Leu Lys... A R N D C Q E G H I L K... Ala A Arg R Asn N Asp D Cys C Gln Q Trp W Tyr Y Val V

95 BLOSUM u l u l

96 BLOSUM

97 u u l l l

98 --T -CC-C-AGT -TATGT-CAGGGGACACG A-GCATGCAGA-GAC AATTGCCGCC-GTCGT-T-TTCAG----CA-GTTATG T-CAGAT--C tcccagttatgtcaggggacacgagcatgcagagac aattgccgccgtcgttttcagcagttatgtcagatc

99 Local alignment Global alignment

100 u u u

101 u u l

102 Local alignment Global alignment

103

104

105

106

107

108 -

109 u 0 s i,j = max s i-1,j-1 + δ (v i, w j ) s i-1,j + δ (v i, -) s i,j-1 + δ (-, w j ) (Smith-Waterman )

110 n n n n

111 u u l = b a ab b a b a b a b a p q q q q b a s q q,, log ), ( = i i i i x Q x P x P Q P H ) ( ) ( )log ( ) (

112 Affine Gap Penalties) u u u l l l l

113 u l l u

114 -ρ - x *σ

115

116 δ δ ρ σ δ ρ δ δ σ

117 s i,j = max s i,j = max s i-1,j - σ s i-1,j (ρ+σ) s i,j-1 - σ s i,j-1 (ρ+σ) ß ß s i,j = s i-1,j-1 + δ (v i, w j ) max s i,j s i,j ß ß

118 l l l δ s 0 -ρ s -ρ 0 s -σ l -σ

119 u u u l l l l

120 u u u u u u u

121 ) ( ), ( ) ( ), ( ) ( ), ( ), ( ) ( ), ( ), ( R P R y x P M P M y x P M P M y x P y x P M P M y x P y x M P + = = '), ( 1 ) ( ), ( ) / ( ), ( 1 ) ( ), ( ) / ( ), ( ' ' s e e R P R y x P M P M y x P R P R y x P M P M y x P S S = σ + = + = ) ) ( ) ( log( ) ), ( ), ( log( ' R P M P R y x P M y x P s + =

122 u u ) exp( ) ( ( u) x N KNe x M P λ ) ( 1 ) ( ) ( S E S e S x P Kmne S E = > = λ λ mn T S log + >

123

124 u l l l

125 u l l

126 u l l l

127 l n n n l

128 l l n n n n n

129 u u A -- T G C A A T -- C -- A T G C

130 A -- T G C A A T -- C -- A T G C

131 A -- T G C A A T -- C -- A T G C

132 A -- T G C A A T -- C A T G C (0,0,0) (1,1,0) (1,2,1) (2,3,2) (3,3,3) (4,4,4)

133 u u u

134 2 3 V W 2-D 3-D

135 2 3

136 3 (i-1,j-1,k-1) (i-1,j,k-1) (i-1,j-1,k) (i-1,j,k) (i,j-1,k-1) (i,j,k-1) (i,j-1,k) (i,j,k)

137 s i,j,k = max s i-1,j-1,k-1 + δ(v i, w j, u k ) s i-1,j-1,k + δ (v i, w j, _ ) s i-1,j,k-1 + δ (v i, _, u k ) s i,j-1,k-1 + δ (_, w j, u k ) s i-1,j,k + δ (v i, _, _) s i,j-1,k + δ (_, w j, _) s i,j,k-1 + δ (_, _, u k ) cube diagonal: no indels face diagonal: one indel edge diagonal: two indels δ(x, y, z) is an entry in the 3-D scoring matrix

138 u u u

139 ClustalW u u u

140 u v 1 v 2 v 3 v 4 v 1 - v v v (.17 =17 % )

141 v 1 v 2 v 3 v 4 v 1 - v v v v 1 v 3 v 4 v 2 : v 1,3 = alignment (v 1, v 3 ) v 1,3,4 = alignment((v 1,3 ),v 4 ) v 1,2,3,4 = alignment((v 1,3,4 ),v 2 )

142 u u u FOS_RAT FOS_MOUSE FOS_CHICK FOSB_MOUSE FOSB_HUMAN PEEMSVTS-LDLTGGLPEATTPESEEAFTLPLLNDPEPK-PSLEPVKNISNMELKAEPFD PEEMSVAS-LDLTGGLPEASTPESEEAFTLPLLNDPEPK-PSLEPVKSISNVELKAEPFD SEELAAATALDLG----APSPAAAEEAFALPLMTEAPPAVPPKEPSG--SGLELKAEPFD PGPGPLAEVRDLPG-----STSAKEDGFGWLLPPPPPPP LPFQ PGPGPLAEVRDLPG-----SAPAKEDGFSWLLPPPPPPP LPFQ.. : **. :.. *:.* *. * **:

143 u

144 u u

145 u u

146 u u

147 u l u

148 vs

149 Simultaneous correlation Time-delayed correlation Inverted correlation

150 Local alignment between pairs of expression profiles u u u M ( x, y ) = i j x i y j u E i j = max( Ei 1, j 1 + M D, ij i, j = max( Di 1, j 1 M ij,0),0)

151 Results

152 Results

153 Results

154

tbjx0121ZW.PDF

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