Transcription

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15 DNA pol RNA pol ARS trna Ribosome DNA mrna Protein Transcription Translation Replication

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17 A B Acceptor stem D-loop T C loop Anticodon loop Variable loop

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25 Relative trna gene copy number box codons 3 box codons 4 box codons 6 box codons A A A A A V V A AG AG A AGG A V A L AG AGA L Relative codon frequency

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31 i j c a o ac c a c c =[o 1,...,o 64 ] o o C a C a k a L A A 1 ˆr C A c a C a k a o ac L F a f ac r ac a a c a a c a c a

32 g c = o c o c c C g o ac g ac = o ac a A c C a f ac = o ac c C a o ac f r ac = 1 k a o ac c C a o ac = o ac o a k a r

33 w ac o ac w ac = c C a o ac

34 = o o o = c C o c C C o = o e o e o o e e e = a A n a o a k a

35 o a a o a a k a f f = a A F a ( a, a ) F a a a a a ( ) a ( a, a )= ac c C a f ac,f B(z z all ) = ( ) ( )

36 = { c C } = (, ) E c = f c e c f c e c = b 1 b 2 b 3 c

37 L L L L w ac w ac = f ac e ac w f ac e ac = b 1 b 2 b 3 b i i L =( wc(i)) 1 1 L = ( L i=1 L wc(i)) i=1

38 w ac = ( L w c (i) ) 1 L = ( 1 L w c (i) ) L i=1 i=1 = ( 1 L L i=1 o ac(i)) ( 1 L L i=1 o a, (i)) = ( 1 o c w c ) o c C w c = o c E[o c ] E[o c ] o c c E[o c ] (b 1 b 2 b 3 )

39 = ( 1 o c C w c ) 1 wc w c = w 0 c w +1 c w +2 c

40 c w c = f c fc fc fc c = 1 wc o c C w W c c t c W c = t (1 s ct )T ct s ct T ct t c W c W ac wac = W ac c C a W c w n = ( 1 ) o c wc o c C

41 s ct = U U σ U U U = M( ) M( ) = o! (o c!) c C c C f oc c

42 o c f c o c o = a A B a o a o o a a o B a B a = (o c e c )2 e c c C a χ 2 o c e c c χ 2 χ 2

43 χ 2 = 1 o a A o ac k 1 a k c C a 1 a o ac c a k a a χ 2 Z a f ac Z a = o a c C a fac 2 1 o a 1 N a = Z 1 a N a k a N a Z a k K = k K n k N a=k N a=k = 1 N a n k a K k

44 > Z Z k=3 = 1 ( 2 ( 1) 1 2 +( Z k=2 3Z k=4 3 ) 1 +( 3 5Z k=6 5 ) 1) = a A N a χ 2

45 X x 1,x 2,...x k X = I(o c ) c C a o c c C a a I( ) 1 o c 1 0 o =[5, 4, 0, 1] x a p x 2 k 1 [p 1,p 2,p 1 +p 2,p 3,...,p 1 +p p k ] 1 T i+1 = T i n 1 n n n = T n 1 1 T = QΛQ T Λ n = QΛ (n 1) Q T 1

46 p 1 p 2 p 1 p 1 D 0 p T Compute new state vector s p 2 p 1 +p 2 p T 1 +p 2 c 1 p 3 p 1 +p 3 p 2 +p 3 p 1 +p 2 +p 3 Repeat until end of sequence p 2 p 3 p 1 +p 3 p 2 +p 3 p 1 +p 2 +p 3 Sum the state vector c 2 c 3 s 1 s i+1 s n D 2 k 1 k = D n p z (z) =p x (x) p y (y) = i {k y,...,k} p x (i) p y (k i + 1) k p z p x + p y 1 k 1 x + y 1 x y

47 n = i o a > 0 i=1 x = a A x a x n nk =1 P (X x),

48 = a A F a E a F a E a H a (H a )= 2 k a E a = H a (H a ) = H a 2 k a H a a H a = f ac 2 f ac c C a a n H a = p a (c)p a (c c ) ka p a (c c ), i=2 p a (c) c p a (c c ) c c a

49 (H a )= o 1 k a. E a = (H a) H a (H a ) = 2 k a H a 2 k a = a A F a E a

50 p c c p c f c = c C f c p c = o + o o + o

51 =1 2p

52 = o o o = 1 M a K L a A L M a K M a M a =2 o ac o ac e ac c C a e ac K K = 1 (k a 1) 1 L 2 a A 1 /2 =

53 S k k S a = 1 k a (k a 1) c C a (r ac 1) 2 r ac k a a = a A F a S a F a 1/18

54 v(c) c 9 v(c) = (A(c i ),A(c)) i=1 A(c) d

55 β i i(g) g i E i (c) i c β 1 β 3

56 w ac w ac = o ac o ac o ac o ac

57 = 2 G(G 1) G i,j {1 ( (i), (j) )}

58 (x x)/s x s x / x Normalized mean CAI Fop CBI Nc Coefficient of variation CAI Fop CBI Nc GC content GC content (x x)/s x s x / x

59 Normalized mean CAI Fop CBI Nc Coefficient of variation CAI Fop CBI Nc Length Length

60 Normalized mean CAI Fop CBI Nc log CV CAI Fop CBI Nc Fraction of 4 & 6 degenerate codons Fraction of 4 & 6 degenerate codons d i d i 1 d = 1 2 {( 1 2 )0, ( 1 2 )1, ( 1 2 )2, ( 1 2 )3 } { 8 15, 4 15, 2 15, 1 15 }

61 Normalized mean CAI Fop CBI Nc log CV CAI Fop CBI Nc Degree of codon discrepancy Degree of codon discrepancy Y = a A F a Y a F a Y a

62 Normalized mean CAI Fop CBI Nc log CV CAI Fop CBI Nc Degree of amino acid discrepancy Degree of amino acid discrepancy = a A φ F a A φ F a

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64 k s

65 k s k s d = k s [ ] k d [ ]. dt k s = k d [ ] [ ] k d = 2/t 1 2 k s k d

66 Transcription [mrna] Translation [Protein] Protein turnover mrna decay k s k d k s k d

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71 A Bias towards reuse (standard deviations) Distance between codons (number of intervening amino acids) B C D

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76 16 A B C Frequency Standard Deviations Standard Deviations Standard Deviations <

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80 Slow translation (GFP1) Rapid translation (GFP2) Rapid translation (GFP2) Slow translation (GFP1)

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82 Alanine normal autocorrelation shuffled within gene shuffled within genome Arginine Glycine Isoleucine 20 Leucine 20 Proline Serine Threonine percent deviation from expected Valine distance between codons (number of intervening amino acids) All >

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84 S. cerevisiae 15 C. glabrata 10 D. melanogaster A. gossypii 10 A. thaliana 15 H. sapiens percent deviation from expected 5 0 S. pombe distance between codons (number of intervening amino acids) C. elegans

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88 61 Anticodon-codon mapping AA-tRNA charging mrna trnas Amino acids Genetic code

89 B Anticodon A Anticodon Codon Codon A(I) U A U G C G C U A U A C G C G

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92 π t e E j e ij =1 E T j t ij =1 T α β

93 π = [π 1,π 2 ] λ = {E,T,π} O P (O λ) P = P (O i λ), i P (O λ) P (λ O) P (M) P (O)

94 1 t 2 12 t trna AGC trna UGC 11 t 22 t e e 21 e 22 e 11 e 12 e 13 e 23 e 24 GCU GCC GCA GCG t π e x i i x i = c i n c c,

95 n c i n c = r c t r, t r c i c n c =( 1 /4)/( 1 /4 + 1 /3) = 3 /7 x i i i γx 2 i + ɛ i γ ɛ i Z =(X E[X])/σ X

96 AGC UGC trna 11 5 GCU GCC Codon GCA GCG trna 11 R 2 = p = Ala UGC Ala AGC Reading = = γx 2 + e s X s = i C ij X ij, i j, C ij +1 1 j

97 Consecutive codon GCU GCC GCA GCG GCU Leading codon GCC GCA GCG s n =(s s)/( s s)

98 ˆp = r +1 n +1, n r

99 1.0 Normalized Score CC REG HMM

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101 Number of predictions Diffr. to random +/- HMM REG CC

102 a b c d e f a a a a a a a a a a a e e e d c b f

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104 2nd 1st T C A G Val Met Ile Leu Leu Phe T C A G GmAA ncm 5 UmAA m 5 CAA GAG UAG IAU A CAU init CAU IAC ncm 5 UAC CAC Ala Thr Pro Ser IGA ncm 5 UGA CGA AGG ncm 5 UGG IGU ncm 5 UGU CAU IGC ncm 5 UGC His Stop Tyr Glu Asp Lys Asn Gln G A GUG mcm 5 s 2 UUG CUG GUU mcm 5 s 2 UUU CUU GUC mcm 5 s 2 UUC CUC Gly Arg Ser Arg Trp Stop Cys GCA CmCA ICG CCG GCU mcm 5 UCU CCU GCC mcm 5 UCC CCC 2nd 3rd T C A G T C A G T C A G T C A G

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108 Anticodon A G U C Pyr Pur Ile 4-box Gly ψ ψ

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113 All Pairs All x All Comparison Candidate Pairs Formation of Stable Pairs Stable Pairs Verification of Stable Pairs Verified Pairs Clustering of Orthologs Group Pairs Broken Pairs Orthologous Groups >

114 l ( a 1, a 2 ) >l ( s 1, s 2 ) a 1 a 2 s 1 s 2 l d d + d

115 Triangle test [%] Domain test [%] Number of orthologous relations Fraction of genes with same number of domains Fraction of genes that pass triangle test Length Tolerance Orthologous relations [10 6 ] l

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117 No Tolerance Tolerance Score BBH RBH Distance RSD SP i, i j, j d j d >k σ 2 (d j d ) d i d >k σ 2 (d i d ) d k σ 2 (d j d )=σ 2 (d j )+σ 2 (d ) (d j,d ) k k

118 A x y 1? y 2 B C z x y 1 y 2 z x y 1 y 2 D z x d > 0 y 1 y 2 d

119 d d = d + d + d + d d d > 0 k k 1 2 d d d d

120 90 Fraction of SP passing test [%] l = 0.70 l = 0.65 l = 0.60 l = SP tolerance 2.4 l = 0.50 A B C x 1 y 2 dx 1 z 2 dy 2 z 1 dx 1 z 1 d y2 z 2 x 1 y 2 x 1 x 2 z 1 z 2 y 1 y 2 z 1 z 2 z 1 z 2

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122 Fraction of VP passing test [%] l = 0.61, k SP = 1.81 l = 0.72, k SP = 1.67 l = 0.58, k SP = VP tolerance

123 A 800 w B x y w 1 x 1 z 1 z 2 y 2 z 1 z 2

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125 = Paralogs = Orthologs AP CP SP VP GP BP = SP minus VP Relative Amount [%] CP SP VP GP Type of Connection

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128 Number of members Class All Bacteria Firmicutes Eukaryota Archaea Vertebrates Mammalia Group Size Genomes Orthologs Ave. groupsize Full

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131 Codon 1st position T C A G Codon 2nd position T C A G Phe Leu Leu Ile Met + Init Val Ser Pro Thr Ala Tyr Stop His Gln Asn Lys Asp Glu Cys Stop Trp Arg Ser Arg Gly = 6 box = 4 box = 3 box = 2 box = 1 box T C A G T C A G T C A G T C A G Codon 3rd position

132 Cysteine Stop Tryptophan Threonine Tyrosine Stop Isoleucine Leucine A UC G U C A G G C U C A G C U A G Methionine Phenylalanine Asparagine A U C G C A U U A Lysine Serine Arginine A U C G G A U C G Glutamine A U C G C G U A A UC U G U C A C U C G G A A G U C A G A A U U G C C G A U G C U A G C U A G C Serine Arginine Alanine Valine Histidine Leucine Aspartic acid Proline Glycine Glutamic acid

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134 1st Position T C A G Genetic code F S Y C T F S Y C C L $ S $ $ Q Y $ W W W W W C W W W A L S $ Q Q L L W G L T P H R T L T P H R C L T P Q R A L T S P Q R G I T N S T I T N S C I M M M M M T K N N N R $ S S G S S A M T K R $ S S G S S G V A D G T V A D G C V A E G A V A E G G T C A G 2nd Position 2nd Position

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136 N N N H N NH 2 NH N N H N O NH 2 N N H NH 2 O NH N H O O S Strong M amino K Keto W Weak W Weak M amino K Keto S Strong Y pyrimidine C Cytosine T Thymine Y pyrimidine R purine A Adenine G Guanine R purine H not-g V not-t D not-c B not-a N any

137 Electricaly charged side chains Positive Negative Arginine Histidine Lysine Aspartic acid Glutamic acid Polar uncharged side chains Special cases Serine Threonine Asparagine Glutamine Cysteine Selenocysteine Glycine Proline Pyrrolysine Hydrophobic side chains Alanine Valine Leucine Isoleucine Methionine Phenylalanine Tyrosine Tryptophan

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141 TPI = L - R (L + R = 1) Probability L R Changes 4 Valine A A A R M R R A V C V V C V A R 4 Arginine 5 Alanine Count the number of changes Calculate the distribution of changes

142 A B C GFP1 GFP1GFP2 GFP2GFP2 GFP2GFP1 TPI construct 2GFP GFP Intensity (arbitrary units) GFP2GFP1 GFP2GFP2 Position on gel GFP GFP Velocity ratio correlated vs. anti-correlated GFP1 GFP1 GFP1 All GFP2 GFP2 GFP2 TPI construct

143 Amino acid sequence MGCANLVSRLENNSRLLNRDLIAVTIGAIVYKDPHAGALRS... Subsequence of consecutive synonymous codons GCA GCA GCT GCG GCC... Observable output sequence 1, 1, 4, 3, 2,... 1 Count matrix of consecutive codon 1 1 1

144 Alanine Arginine Glutamine trna gene copy number GCA R squared = p val= GCT trna gene copy number R squared = p val= CGT CGG AGG AGA trna gene copy number CAG R squared = p val= CAA Codon frequency Glutamic acid Codon frequency Glycine Codon frequency Isoleucine trna gene copy number GAG R squared = p val= GAA trna gene copy number R squared = p val= GGA GGG GGC trna gene copy number ATA R squared = 1 p val= ATT Codon frequency Leucine 0e+00 4e+04 8e+04 Codon frequency Lysine Codon frequency Proline trna gene copy number R squared = p val= CTA CTC TTG TTA trna gene copy number R squared = AAG p val= AAA trna gene copy number CCT R squared = p val= CCA Codon frequency Serine Codon frequency Threonine Codon frequency Valine trna gene copy number R squared = p val= TCA AGC TCG TCT trna gene copy number R squared = p val= ACA ACG ACT trna gene copy number R squared = p val= 7e 04 GTG GTA GTT Codon frequency 2e+04 6e+04 1e+05 Codon frequency 4e+04 6e+04 8e+04 1e+05 Codon frequency

145 GCT GCC GCA GCG Alanine Arginine GCT GCC GCA GCG CGT CGC CGA CGG AGA AGG CGT CGC CGA CGG AGA AGG GGT GGC GGA GGG Glycine GGT GGC GGA GGG CCT CCC CCA CCG Proline CCT CCC CCA CCG CTT CTC CTA CTG TTA TTG Leucine Serine CTT CTC CTA CTG TTA TTG TCT TCC TCA TCG AGT AGC TCT TCC TCA TCG AGT AGC ACT ACC ACA ACG Threonine Valine ACT ACC ACA ACG GTT GTC GTA GTG GTT GTC GTA GTG

146 Alanine Arginine Glutamine HMM REG CC HMM REG CC HMM REG CC Glutamic acid Glycine Isoleucine HMM REG CC HMM REG CC HMM REG CC Leucine Lysine Proline HMM REG CC HMM REG CC HMM REG CC Serine Threonine Valine HMM REG CC HMM REG CC HMM REG CC

147 ψ ψ ψ

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