Statistical modelling and alignment of protein sequences

Transkript

1 Statistical modelling and alignment of protein sequences Martin Weigt Laboratoire de Biologie Computationnelle et Quantitative Université Pierre et Marie Curie Paris ENS Paris 11 July 2016

2 What is the information in -LNQFADDLAHELRTPVNILLGKNQVMLS-QERSAEEYQQALVDNIEELEGLSRLTENILFLARAEH- ALGELTAGIAHEINNPTAVILGNTELIRFLGADASRV-EEEIDAILLQIERIRNITRSLLQYSRQG-- SQRQFVTNASHELKTPIAIISANTEVLEI----TMGK-NQWTETILKQVKRLSGLVNDMVALAKLEE- ---AFVSNASHELRTPVTSIKGFAETIKG-MSAEEEAKDDFLDIIYKESLRLEHIVEHLLTLSKAQ-- -VGQLTGGIAHDFNNMLTGVIGSLDLIKLS----GRLVERFMDAALISAQRAASLTDRLLAFSRRQS- ---RMTHQVSHEVGNMIGIITGSLGLLERETGFNDRQ-KRHIARIRKAADRGRSLASSMLTIGS---- ALGEMLDHIAHQWKQPINSISLIAQDMADYGELTDGDVQTTIDKIMSLLEHMSQTVDVFRGFYR---- -VGRLAGGVAHDFNNLLSVINGYCEMLAA-QVSDRPQALREVSEIHRAGLRAAGLTRQLLAFGRRQ-- SLGELAAGVAHEINNPNAVILLNVDLVKKWSEMSEEL-PLLLTEMEEGAGRIKRIVDDLKDFARGD-- -MGEFAAYIAHEINQPLSAIMTNANAGTRNEPSNIPEAKEALARIIRDSDRAAEIIRMVRSFLKRQ-- --GQLAGGIAHDFNNILQIISGNTQILQYQTNPDPP----QLLEILKAVERGTALTRSMLAFSRKQT- --GQLTGGIAHDFNNLLQVILGNLEFVRAKLDGDAK-LQTRIERAAWAAQRGATLTGQLLAFARKQ-- AKTDFLSNMSHEIRTPLNAILGFIQVLKD-AEMKPKD-REYLELMDESSKNLLSLVNDIIEIDLIESG --GREVLHLVHDLKTPLATIEGLVSLMET-RWPDPKM-QEYCQTIYGSITSMSKMVSEILY RARLLADVAHELRTPVATLTGYLEAVEDVRPLDAST----IAVLRDQAVRLTRLAQDLADVTHAEGG SMKRMLTNMSHDLKTPLTVILGYIETIQSDPNMPDEERERLLGKLRQKTNELIQMINSFFDLAKLES- AKSEFLANMSHELRTPLNAIIGFSEMIQAFGPLGSDRYEEYINDIHTSGNFLLNVINDILDMSKIEAG -MQRFIADATHQLRTPLAAIDAEVELLTD-QTRDPKA----LDKLRGRIADLARLASQLLDHAM---- -RKKAVHTITHELRTPLTAITGYAGLIRK-EQCEDKS-GQYIQNILQSSDRMRDMLNTLLDFFRLDNG -REEFMNMTSHELMNPLSAAVQAAHTMISLHDDNSKSNIEIAKIILACGEHQQKLVEDARMMSKLD-- -KSRYVVGLSHELRSPLNAISGYAQLLEQDTSLAPKP-RDQVRVVRRSADHLSGLIDGILDISKIEAG ----AFSYMRHAINNPLSGMLYSRKALKN-TDLNEEQ-MRQIHVSDNCHHQLNKILADL QENFIDMTSHEMRNPLSAILQCSDEITST------LCLEAANTIALCASHQKRIVDDILTFSKLDS- SQRTLTNAIAHDLRQPLYRIRFALEMFND-SLLSIEQRQQYRQSIENSLRDLDHLINQSLQLSRYT-- --KLLLLSLSHDIKTPLSAIKLNAKALSRLYKDAEKQ-REAAEHINARADEIENFVSRITKASSE--- --HAFIADAAHELRTPLTALKLQLQLTER---ATSDVREVGFVKLNERLDRSIHLVKQLLTLARSES- -QKNFISNASHELNTPLTSIIVTADLALS-KQRTDEEYRTALSRIMDAAGHLE RGALLTSISHDLRTPLASILGATSSLESGEELDENARKELLSTIHDEADRLNRFVANLLDMTRLEAG -KSEFLANMSHELRTPLNGVIGFTRLTLK-TELTPTQ-RDHLNTIERSANNLLAIINDVLDFSKLEAG AKSEFLANMSHDIRTPMNAITGMTAIATA-HIDDPKQVKNCLRKIALSSRHLLGLINDVLDMSKIESG -LSQFSADLAHDFRTPLANLIGQTEVTLA-HPRSAEEYRAVLESSLEEYARLSRMIEDMLFLARADH- SKSMFLATVSHELRTPLYGIIGNLDLLQT-KELPKGV-DRLVTAMNNSSSLLLKIISDILDFSKIES- AKTAFLATLSHEIRTPMNGVLGTAQILLK-TPLSTEQ-EKHLKSLYDSGDHMMTLLNEILDFSKIEQG SKKQLIDGIAHELRTPLVRLRYRLEMSEN---LTPPE----SQALNRDIGQLEALIEELLTYARLDR- -KTQFFINTAHDIRTPLTLIKAPLEELLEEETLTDNG-ITRTNIALRNVEVLLRLVSNLINFERT---...?

3 Sequence data are accumulating 100 UniProt database millions of sequence entries 10 1 without manual annotation UniProtKB/TrEMBL UniProtKB/SwissProt with manual annotation

4 Protein can be classified into families

5 Protein can be classified into families Families of homologous proteins common evolutionary ancestry conserved structure and function diverged sequences (20-30% sequence identity) Questions: Can we identify and align homologous proteins? Can we extract family-specific signal from alignment? What are the underlying principles relating protein evolution and protein structure / function?

6 Protein can be classified into families Pfam 29.0 (2015) vs (2016): vs families (22 new, 11 deleted) 116 domains of unknown function (DUF) newly annotated (with >3750 remaining unknown) 11.9 million proteins vs million proteins families contain protein domains

7 Protein can be classified into families

8 Domains as modular building blocks domains = structural and functional modules [Casino et al. 09]

9 Pfam provides multiple-sequence alignments -LNQFADDLAHELRTPVNILLGKNQVMLS-QERSAEEYQQALVDNIEELEGLSRLTENILFLARAEH- ALGELTAGIAHEINNPTAVILGNTELIRFLGADASRV-EEEIDAILLQIERIRNITRSLLQYSRQG-- SQRQFVTNASHELKTPIAIISANTEVLEI----TMGK-NQWTETILKQVKRLSGLVNDMVALAKLEE- ---AFVSNASHELRTPVTSIKGFAETIKG-MSAEEEAKDDFLDIIYKESLRLEHIVEHLLTLSKAQ-- -VGQLTGGIAHDFNNMLTGVIGSLDLIKLS----GRLVERFMDAALISAQRAASLTDRLLAFSRRQS- ---RMTHQVSHEVGNMIGIITGSLGLLERETGFNDRQ-KRHIARIRKAADRGRSLASSMLTIGS---- ALGEMLDHIAHQWKQPINSISLIAQDMADYGELTDGDVQTTIDKIMSLLEHMSQTVDVFRGFYR---- -VGRLAGGVAHDFNNLLSVINGYCEMLAA-QVSDRPQALREVSEIHRAGLRAAGLTRQLLAFGRRQ-- SLGELAAGVAHEINNPNAVILLNVDLVKKWSEMSEEL-PLLLTEMEEGAGRIKRIVDDLKDFARGD-- -MGEFAAYIAHEINQPLSAIMTNANAGTRNEPSNIPEAKEALARIIRDSDRAAEIIRMVRSFLKRQ-- --GQLAGGIAHDFNNILQIISGNTQILQYQTNPDPP----QLLEILKAVERGTALTRSMLAFSRKQT- --GQLTGGIAHDFNNLLQVILGNLEFVRAKLDGDAK-LQTRIERAAWAAQRGATLTGQLLAFARKQ-- AKTDFLSNMSHEIRTPLNAILGFIQVLKD-AEMKPKD-REYLELMDESSKNLLSLVNDIIEIDLIESG --GREVLHLVHDLKTPLATIEGLVSLMET-RWPDPKM-QEYCQTIYGSITSMSKMVSEILY RARLLADVAHELRTPVATLTGYLEAVEDVRPLDAST----IAVLRDQAVRLTRLAQDLADVTHAEGG SMKRMLTNMSHDLKTPLTVILGYIETIQSDPNMPDEERERLLGKLRQKTNELIQMINSFFDLAKLES- AKSEFLANMSHELRTPLNAIIGFSEMIQAFGPLGSDRYEEYINDIHTSGNFLLNVINDILDMSKIEAG -MQRFIADATHQLRTPLAAIDAEVELLTD-QTRDPKA----LDKLRGRIADLARLASQLLDHAM---- -RKKAVHTITHELRTPLTAITGYAGLIRK-EQCEDKS-GQYIQNILQSSDRMRDMLNTLLDFFRLDNG -REEFMNMTSHELMNPLSAAVQAAHTMISLHDDNSKSNIEIAKIILACGEHQQKLVEDARMMSKLD-- -KSRYVVGLSHELRSPLNAISGYAQLLEQDTSLAPKP-RDQVRVVRRSADHLSGLIDGILDISKIEAG ----AFSYMRHAINNPLSGMLYSRKALKN-TDLNEEQ-MRQIHVSDNCHHQLNKILADL QENFIDMTSHEMRNPLSAILQCSDEITST------LCLEAANTIALCASHQKRIVDDILTFSKLDS- SQRTLTNAIAHDLRQPLYRIRFALEMFND-SLLSIEQRQQYRQSIENSLRDLDHLINQSLQLSRYT-- --KLLLLSLSHDIKTPLSAIKLNAKALSRLYKDAEKQ-REAAEHINARADEIENFVSRITKASSE--- --HAFIADAAHELRTPLTALKLQLQLTER---ATSDVREVGFVKLNERLDRSIHLVKQLLTLARSES- -QKNFISNASHELNTPLTSIIVTADLALS-KQRTDEEYRTALSRIMDAAGHLE RGALLTSISHDLRTPLASILGATSSLESGEELDENARKELLSTIHDEADRLNRFVANLLDMTRLEAG -KSEFLANMSHELRTPLNGVIGFTRLTLK-TELTPTQ-RDHLNTIERSANNLLAIINDVLDFSKLEAG AKSEFLANMSHDIRTPMNAITGMTAIATA-HIDDPKQVKNCLRKIALSSRHLLGLINDVLDMSKIESG -LSQFSADLAHDFRTPLANLIGQTEVTLA-HPRSAEEYRAVLESSLEEYARLSRMIEDMLFLARADH- SKSMFLATVSHELRTPLYGIIGNLDLLQT-KELPKGV-DRLVTAMNNSSSLLLKIISDILDFSKIES- AKTAFLATLSHEIRTPMNGVLGTAQILLK-TPLSTEQ-EKHLKSLYDSGDHMMTLLNEILDFSKIEQG SKKQLIDGIAHELRTPLVRLRYRLEMSEN---LTPPE----SQALNRDIGQLEALIEELLTYARLDR- -KTQFFINTAHDIRTPLTLIKAPLEELLEEETLTDNG-ITRTNIALRNVEVLLRLVSNLINFERT---...

10 Protein can be classified into homologous families If we assign a sequence to a family, we predict its structure and function

11 Aligning two sequences How to compare / align two amino-acid sequences (a 1,...,a La ), (b 1,...,b Lb )? take inspiration from evolution underlying evolutionary processes: mutation, insertion, deletion assume independent evolution of distinct positions for simplicity

12 Aligning two sequences How to compare / align two amino-acid sequences (a 1,...,a La ), (b 1,...,b Lb )? take inspiration from evolution underlying evolutionary processes: mutation, insertion, deletion assume independent evolution of distinct positions for simplicity two ingredients similarity between amino acids - based on physico-chemical properties - based on pre-existing sequence alignments: substitution matrix (e.g. BLOSUM) S(a, b) = log f(a, b) f(a)f(b) from frequency counts of aligned positions

13 Aligning two sequences How to compare / align two amino-acid sequences (a 1,...,a La ), (b 1,...,b Lb )? take inspiration from evolution underlying evolutionary processes: mutation, insertion, deletion assume independent evolution of distinct positions for simplicity two ingredients similarity between amino acids gap penalty for gap of length k... a i a i+1 a i+2... a i+k a i+k b j... b j+1... affine gap penalty d +(k 1)e, d > e > 0 (gap opening more costly than gap extension)

14 Aligning two sequences How to compare / align two amino-acid sequences (a 1,...,a La ), (b 1,...,b Lb )? take inspiration from evolution underlying evolutionary processes: mutation, insertion, deletion assume independent evolution of distinct positions for simplicity two ingredients similarity between amino acids gap penalty total alignment score = sum of substitution scores - gap penalties

15 Needleman-Wunsch algorithm (1970) global alignment maximise total alignment score by dynamic programming iterative construction of alignment score F (i, j) =Score(a 1,...,a i ; b 1,...,b j )

16 Needleman-Wunsch algorithm (1970) global alignment maximise total alignment score by dynamic programming iterative construction of alignment score initialisation F (0, 0) = 0 recursion by adding two aligned amino acids, or one amino acid, one gap until 8 >< F (i, j) = max >: F (i, j) =Score(a 1,...,a i ; b 1,...,b j ) F (L a,l b ) is reached F (i 1,j 1) + S(a i,b j ) adding a i b j F (i 1,j)+d adding a i F (i, j 1) + d adding bj

17 Needleman-Wunsch algorithm (1970) global alignment maximise total alignment score by dynamic programming iterative construction of alignment score initialisation F (0, 0) = 0 recursion by adding two aligned amino acids, or one amino acid, one gap 8 >< F (i, j) = max >: F (i, j) =Score(a 1,...,a i ; b 1,...,b j ) F (i 1,j 1) + S(a i,b j ) adding a i b j F (i 1,j)+d adding a i F (i, j 1) + d adding bj until F (L a,l b ) is reached traceback: follow backwards path leading from (0, 0)! (L a,l b )

18 Smith-Waterman algorithm (1981) local alignment: find similar sub-sequences (e.g. common domains) reset negative scores to zero 8 >< F (i, j) = max >: F (i 1,j 1) + S(a i,b j ) adding a i b j F (i 1,j)+d adding a i F (i, j 1) + d adding bj 0 restart local alignment traceback: start from maximal score traceback until zero score hit

19 BLAST (Altshul et al. 1990) Basic Local Alignment Search Tool dynamic programming too slow when searching one sequence against large sequence database (e.g. Uniprot) heuristic speedup: idea: alignments contain typically highly similar subsequences - construct all 3-letter subsequences from query sequence - construct list of similar 3-letter sequences - locate in search database - extend alignment around hits

20 Multiple-sequence alignments How to align M sequences: (a 1 1,a 1 2,...,a 1 L 1 ) (a 2 1,a 2 2,...,a 2 L 2 )... (a M 1,a M 2,...,a M L M ) dynamic programming: exact but time O(L 1 L 2... L M ) need heuristic methods for up to 10 6 sequences basic idea (Feng Dolittle 1987): organise data hierarchically align closest sequences first align alignments when proceeding into the tree possibly iteratively refined

21 Multiple-sequence alignments A 34 = align(a 3,a 4 ) A 12 = align(a 1,a 2 ) A 1234 = align(a 12,A 34 )

22 Multiple-sequence alignments A 34 = align(a 3,a 4 ) A 12 = align(a 1,a 2 ) A 1234 = align(a 12,A 34 ) need to align alignments e.g. and gives STAR STIR SKAT PIT PIG STAR STIR SKAT P-IT P-IG

23 Multiple-sequence alignments A 34 = align(a 3,a 4 ) A 12 = align(a 1,a 2 ) A 1234 = align(a 12,A 34 ) need to align alignments e.g. and gives STAR STIR SKAT PIT PIG STAR STIR SKAT P-IT P-IG insertion of column of gaps into input alignments substitution score for two columns = sum over pairwise substitution scores e.g. for last column S(R, T )+S(R, G)+S(R, T )+S(R, G)+S(T,T)+S(T,G) standard pairwise alignment algorithms can be used

24 What is the information in -LNQFADDLAHELRTPVNILLGKNQVMLS-QERSAEEYQQALVDNIEELEGLSRLTENILFLARAEH- ALGELTAGIAHEINNPTAVILGNTELIRFLGADASRV-EEEIDAILLQIERIRNITRSLLQYSRQG-- SQRQFVTNASHELKTPIAIISANTEVLEI----TMGK-NQWTETILKQVKRLSGLVNDMVALAKLEE- ---AFVSNASHELRTPVTSIKGFAETIKG-MSAEEEAKDDFLDIIYKESLRLEHIVEHLLTLSKAQ-- -VGQLTGGIAHDFNNMLTGVIGSLDLIKLS----GRLVERFMDAALISAQRAASLTDRLLAFSRRQS- ---RMTHQVSHEVGNMIGIITGSLGLLERETGFNDRQ-KRHIARIRKAADRGRSLASSMLTIGS---- ALGEMLDHIAHQWKQPINSISLIAQDMADYGELTDGDVQTTIDKIMSLLEHMSQTVDVFRGFYR---- -VGRLAGGVAHDFNNLLSVINGYCEMLAA-QVSDRPQALREVSEIHRAGLRAAGLTRQLLAFGRRQ-- SLGELAAGVAHEINNPNAVILLNVDLVKKWSEMSEEL-PLLLTEMEEGAGRIKRIVDDLKDFARGD-- -MGEFAAYIAHEINQPLSAIMTNANAGTRNEPSNIPEAKEALARIIRDSDRAAEIIRMVRSFLKRQ-- --GQLAGGIAHDFNNILQIISGNTQILQYQTNPDPP----QLLEILKAVERGTALTRSMLAFSRKQT- --GQLTGGIAHDFNNLLQVILGNLEFVRAKLDGDAK-LQTRIERAAWAAQRGATLTGQLLAFARKQ-- AKTDFLSNMSHEIRTPLNAILGFIQVLKD-AEMKPKD-REYLELMDESSKNLLSLVNDIIEIDLIESG --GREVLHLVHDLKTPLATIEGLVSLMET-RWPDPKM-QEYCQTIYGSITSMSKMVSEILY RARLLADVAHELRTPVATLTGYLEAVEDVRPLDAST----IAVLRDQAVRLTRLAQDLADVTHAEGG SMKRMLTNMSHDLKTPLTVILGYIETIQSDPNMPDEERERLLGKLRQKTNELIQMINSFFDLAKLES- AKSEFLANMSHELRTPLNAIIGFSEMIQAFGPLGSDRYEEYINDIHTSGNFLLNVINDILDMSKIEAG -MQRFIADATHQLRTPLAAIDAEVELLTD-QTRDPKA----LDKLRGRIADLARLASQLLDHAM---- -RKKAVHTITHELRTPLTAITGYAGLIRK-EQCEDKS-GQYIQNILQSSDRMRDMLNTLLDFFRLDNG -REEFMNMTSHELMNPLSAAVQAAHTMISLHDDNSKSNIEIAKIILACGEHQQKLVEDARMMSKLD-- -KSRYVVGLSHELRSPLNAISGYAQLLEQDTSLAPKP-RDQVRVVRRSADHLSGLIDGILDISKIEAG ----AFSYMRHAINNPLSGMLYSRKALKN-TDLNEEQ-MRQIHVSDNCHHQLNKILADL QENFIDMTSHEMRNPLSAILQCSDEITST------LCLEAANTIALCASHQKRIVDDILTFSKLDS- SQRTLTNAIAHDLRQPLYRIRFALEMFND-SLLSIEQRQQYRQSIENSLRDLDHLINQSLQLSRYT-- --KLLLLSLSHDIKTPLSAIKLNAKALSRLYKDAEKQ-REAAEHINARADEIENFVSRITKASSE--- --HAFIADAAHELRTPLTALKLQLQLTER---ATSDVREVGFVKLNERLDRSIHLVKQLLTLARSES- -QKNFISNASHELNTPLTSIIVTADLALS-KQRTDEEYRTALSRIMDAAGHLE RGALLTSISHDLRTPLASILGATSSLESGEELDENARKELLSTIHDEADRLNRFVANLLDMTRLEAG -KSEFLANMSHELRTPLNGVIGFTRLTLK-TELTPTQ-RDHLNTIERSANNLLAIINDVLDFSKLEAG AKSEFLANMSHDIRTPMNAITGMTAIATA-HIDDPKQVKNCLRKIALSSRHLLGLINDVLDMSKIESG -LSQFSADLAHDFRTPLANLIGQTEVTLA-HPRSAEEYRAVLESSLEEYARLSRMIEDMLFLARADH- SKSMFLATVSHELRTPLYGIIGNLDLLQT-KELPKGV-DRLVTAMNNSSSLLLKIISDILDFSKIES- AKTAFLATLSHEIRTPMNGVLGTAQILLK-TPLSTEQ-EKHLKSLYDSGDHMMTLLNEILDFSKIEQG SKKQLIDGIAHELRTPLVRLRYRLEMSEN---LTPPE----SQALNRDIGQLEALIEELLTYARLDR- -KTQFFINTAHDIRTPLTLIKAPLEELLEEETLTDNG-ITRTNIALRNVEVLLRLVSNLINFERT---...?

25 Profile models Sequence profiles assume independent residue positions LY P (A 1,...,A L )= f i (A i ) i=1 Information in a column = amino-acid conservation score I i = log 2 (21) + X A f i (A) log 2 f i (A)

26 Profile Hidden Markov Models (phmm) S. Eddy - HMMer D: amino-acid deletion M: amino-acid match I: amino-acid insertion parameters (transition & emission probs) inferred from seed alignment alignment of query sequence to phmm = path from START to END (e.g. seq. HMMPATH aligned as hmmpath)

27 Profile models Sequence profiles = one of the most frequently used tools in bioinformatics detection of conserved residue multiple-sequence alignments homology detection structural modelling and functional annotation BUT: treats residues independently intrinsically unable to provide structural information intrinsically unable to detect protein-protein interaction intrinsically unable to detect epistasis between mutations What can we learn from residue-residue correlations?

28 From sequence variability to phenotype Sequence alignment -LNQFADDLAHELRTPVNILLGKNQVMLS-QERSAEEYQQALVDNIEELEGLSRLTENILFLARAEH- ALGELTAGIAHEINNPTAVILGNTELIRFLGADASRV-EEEIDAILLQIERIRNITRSLLQYSRQG-- SQRQFVTNASHELKTPIAIISANTEVLEI----TMGK-NQWTETILKQVKRLSGLVNDMVALAKLEE- ---AFVSNASHELRTPVTSIKGFAETIKG-MSAEEEAKDDFLDIIYKESLRLEHIVEHLLTLSKAQ-- -VGQLTGGIAHDFNNMLTGVIGSLDLIKLS----GRLVERFMDAALISAQRAASLTDRLLAFSRRQS- ---RMTHQVSHEVGNMIGIITGSLGLLERETGFNDRQ-KRHIARIRKAADRGRSLASSMLTIGS---- ALGEMLDHIAHQWKQPINSISLIAQDMADYGELTDGDVQTTIDKIMSLLEHMSQTVDVFRGFYR---- -VGRLAGGVAHDFNNLLSVINGYCEMLAA-QVSDRPQALREVSEIHRAGLRAAGLTRQLLAFGRRQ-- SLGELAAGVAHEINNPNAVILLNVDLVKKWSEMSEEL-PLLLTEMEEGAGRIKRIVDDLKDFARGD-- -MGEFAAYIAHEINQPLSAIMTNANAGTRNEPSNIPEAKEALARIIRDSDRAAEIIRMVRSFLKRQ-- --GQLAGGIAHDFNNILQIISGNTQILQYQTNPDPP----QLLEILKAVERGTALTRSMLAFSRKQT- --GQLTGGIAHDFNNLLQVILGNLEFVRAKLDGDAK-LQTRIERAAWAAQRGATLTGQLLAFARKQ-- AKTDFLSNMSHEIRTPLNAILGFIQVLKD-AEMKPKD-REYLELMDESSKNLLSLVNDIIEIDLIESG --GREVLHLVHDLKTPLATIEGLVSLMET-RWPDPKM-QEYCQTIYGSITSMSKMVSEILY RARLLADVAHELRTPVATLTGYLEAVEDVRPLDAST----IAVLRDQAVRLTRLAQDLADVTHAEGG SMKRMLTNMSHDLKTPLTVILGYIETIQSDPNMPDEERERLLGKLRQKTNELIQMINSFFDLAKLES- AKSEFLANMSHELRTPLNAIIGFSEMIQAFGPLGSDRYEEYINDIHTSGNFLLNVINDILDMSKIEAG -MQRFIADATHQLRTPLAAIDAEVELLTD-QTRDPKA----LDKLRGRIADLARLASQLLDHAM---- -RKKAVHTITHELRTPLTAITGYAGLIRK-EQCEDKS-GQYIQNILQSSDRMRDMLNTLLDFFRLDNG -REEFMNMTSHELMNPLSAAVQAAHTMISLHDDNSKSNIEIAKIILACGEHQQKLVEDARMMSKLD-- -KSRYVVGLSHELRSPLNAISGYAQLLEQDTSLAPKP-RDQVRVVRRSADHLSGLIDGILDISKIEAG ----AFSYMRHAINNPLSGMLYSRKALKN-TDLNEEQ-MRQIHVSDNCHHQLNKILADL QENFIDMTSHEMRNPLSAILQCSDEITST------LCLEAANTIALCASHQKRIVDDILTFSKLDS- SQRTLTNAIAHDLRQPLYRIRFALEMFND-SLLSIEQRQQYRQSIENSLRDLDHLINQSLQLSRYT-- --KLLLLSLSHDIKTPLSAIKLNAKALSRLYKDAEKQ-REAAEHINARADEIENFVSRITKASSE--- --HAFIADAAHELRTPLTALKLQLQLTER---ATSDVREVGFVKLNERLDRSIHLVKQLLTLARSES- -QKNFISNASHELNTPLTSIIVTADLALS-KQRTDEEYRTALSRIMDAAGHLE RGALLTSISHDLRTPLASILGATSSLESGEELDENARKELLSTIHDEADRLNRFVANLLDMTRLEAG -KSEFLANMSHELRTPLNGVIGFTRLTLK-TELTPTQ-RDHLNTIERSANNLLAIINDVLDFSKLEAG AKSEFLANMSHDIRTPMNAITGMTAIATA-HIDDPKQVKNCLRKIALSSRHLLGLINDVLDMSKIESG -LSQFSADLAHDFRTPLANLIGQTEVTLA-HPRSAEEYRAVLESSLEEYARLSRMIEDMLFLARADH- SKSMFLATVSHELRTPLYGIIGNLDLLQT-KELPKGV-DRLVTAMNNSSSLLLKIISDILDFSKIES- AKTAFLATLSHEIRTPMNGVLGTAQILLK-TPLSTEQ-EKHLKSLYDSGDHMMTLLNEILDFSKIEQG SKKQLIDGIAHELRTPLVRLRYRLEMSEN---LTPPE----SQALNRDIGQLEALIEELLTYARLDR- -KTQFFINTAHDIRTPLTLIKAPLEELLEEETLTDNG-ITRTNIALRNVEVLLRLVSNLINFERT VFIDNMTHEMKTPLTSIIGFSDLLRS-ARLDDETVHDYAESIYKEGKYLKSISSKLMDL Phenotype protein structure protein function P RR HK P ATP ADP RR target gene [Casino et al. 09] mutational effects [Podgornia et al. 15] using ONLY sequence information

29 First observation: Residue contacts induce residue coevolution contact in 3D co-evolution statistical analysis R I D H R L K N T D H F L N G R L R D T D H H E R Q E T G E L K H K Y R T R L T D L D H R R A M E V G N L K H T Q K E E L A N L K H K Q Q S E V E N A K H R L N Q R A D D L D H correlation

30 First observation: Residue contacts induce residue coevolution contact in 3D co-evolution statistical analysis R I D H R L K N T D H F L N G R L R D T D H H E R Q E T G E L K H K Y R T R L T D L D H R R A M E V G N L K H T Q K E E L A N L K H K Q Q S E V E N A K H R L N Q R A D D L D H correlation Inverse question: Are sequence correlations indicative for residue-residue contacts? [Gobel et al. 94, Neher 94, Ranganathan et al. 99 ]

31 First observation: Residue contacts induce residue coevolution contact in 3D co-evolution statistical analysis Mutual information measures pair correlation MI ij = A,B f ij (A, B) ln f ij(a, B) f i (A) f j (B) R I D H R L K N T D H F L N G R L R D T D H H E R Q E T G E L K H K Y R T R L T D L D H R R A M E V G N L K H T Q K E E L A N L K H K Q Q S E V E N A K H R L N Q R A D D L D H correlation f i (A) f j (B) f ij (A, B)

32 Strong correlations residue contacts Trypsin inhibitor: i j > 4 30 strongest correlations - contact - no contact

33 Second observation: Correlation is not coupling i j i j i j direct-coupling analysis contact pair prediction: only direct coupling inter-protein correlation: direct + indirect coupling i j i j correlations are mediated by network of direct couplings disentangle direct and indirect couplings: P (A 1,..., A L )

34 Direct coupling analysis (DCA) Maximum-entropy modeling (I) coherence with data: model generates empirical correlations P ij (A i, A j ) = {A k k=i,j} P (A 1,...,A L ) P (A 1,..., A L ) = f ij (A i, A j )!

35 Direct coupling analysis (DCA) Maximum-entropy modeling (I) coherence with data: model generates empirical correlations P ij (A i, A j ) = (II) minimally constrained statistical model P (A 1,..., A L ) maximum entropy {A i } {A k k=i,j} P (A 1,...,A L ) P (A 1,..., A L ) = f ij (A i, A j ) P (A 1,..., A L ) ln P (A 1,..., A L ) max!

36 Direct coupling analysis (DCA) Maximum-entropy modeling (I) coherence with data: model generates empirical correlations P ij (A i, A j ) = {A k k=i,j} P (A 1,..., A L ) = f ij (A i, A j ) (II) minimally constrained statistical model P (A 1,..., A L ) maximum entropy {A i } P (A 1,...,A L ) P (A 1,..., A L ) ln P (A 1,..., A L ) max! Potts model / Markov random field P (A 1,..., A L ) exp + e ij (A i, A j ) + i<j i h i (A i ) direct coupling of residues i and j

37 Direct coupling analysis (DCA) determine correlations generated by model! P ij (A i, A j ) = P (A 1,..., A L ) = f ij (A i, A j ) {A k k=i,j} exponential time complexity ~ 21 L our approximations - the first: belief propagation - the fastest: naive mean-field - the most accurate: pseudo-likelihood max - less overfitting: dimensional reduction and approximations by others - MCMC sampling - Bayesian networks - pseudo-likelihood maximization - sparse inverse covariance (PSICOV) - meta classification [Weigt et al, PNAS 09] [Morcos et al, PNAS 11] [Ekeberg et al, Phys Rev E 13] [Cocco et al, PLoS CB 13] [Lapedes et al, LANL preprint 02] [Burger et al, PLoS Comp Biol 10] [Balakrishnan et al., Proteins 11] [Jones et al., Bioinformatics 12] [Skwark et al., Bioinformatics 13]

38 DCA strongly improves contact prediction Trypsin inhibitor: i j > 4 30 strongest correlations 30 strongest couplings - contact - no contact works across numerous protein families accurate prediction requires >1000 sufficiently diverged sequences

39 Not all contacts co-vary, but... Ras (correlation) Ras (DCA) DCA can guide complex assembly: protein structure prediction: [Schug, MW, Onuchic, Hwa, Szurmant, PNAS 09] [Dago, Schug, Procaccini, Hoch, MW, Szurmant, PNAS 12] [Ovchinnikov et al., elife 14] [Marks et al., PLoS ONE 11] [Sadowski et al., Comp Biol Chem 11] [Sulkowska, Morcos, MW, Hwa, Onuchic, PNAS 12] [Hopf et al., Cell 12] [Nugent, Jones, PNAS 12] [Ovchinnikov et al., elife 15] RNA structure prediction: [De Leonardis, Lutz, Cocco, Monasson, Schug, MW, NAR 15]

40 From contacts to 3D structure [Sulkowska, Morcos, MW, Hwa, Onuchic, PNAS 12]

41 ab initio protein folding simulations: molecular-dynamics simulations of structure-based models (Go-models): r V = V bond + V torsion + V contact with V bond = k b bonds From contacts to 3D structure (r r 0 ) 2 V torsion = k a angles ( 0) 2 + k d dihedral [1 cos( 0 )] [1 cos 3( 0)] V contact = c contacts ij r ij 12 2 ij r ij 6 use only DCA contacts

42 DCA for protein-protein interaction how to detect inter-protein residue contacts in protein complexes? DCA on joint multiple sequence alignment : each row contains a pair of interacting proteins protein family 1 protein family 2 cf. talk by AF Bitbol, poster by T. Gueudré

43 DCA for protein-protein interaction how to detect inter-protein residue contacts in protein complexes? DCA on joint multiple sequence alignment : each row contains a pair of interacting proteins consider the strongest inter-protein residue couplings response regulator histidine sensor kinase [Weigt et al. PNAS 09] [Schug et al. PNAS 09] [Ovchinnikov et al. elife 14] 29 known complexes, 36 predictions [Hopf et al. elife 14] 76 known complexes, 32 predictions [Uguzzoni et al., in preparation 16] ~750 homo-dimeric proteins

44 DCA for protein-protein interaction how to detect inter-protein residue contacts in protein complexes? DCA on joint multiple sequence alignment : each row contains a pair of interacting proteins consider the strongest inter-protein residue couplings response regulator histidine sensor kinase Question: Can we discriminate between interacting & non-interacting protein families?

45 Inference of protein-protein interaction networks Bacterial ribosomal proteins Small ribosomal subunit 20 proteins 21 interactions (11% of 190 pairs) 5.8% of contacts between proteins Large ribosomal subunit 29 proteins 29 interactions (7% of 406 pairs) 4.5% of contacts between proteins sparse interaction network modular contact map [Feinauer, Szurmant, MW, Pagnani, PLoS ONE 16]

46 Inference of protein-protein interaction networks Bacterial ribosomal proteins Pairwise alignments ( seqs.) Top 10 predictions for each subunit 16 true positive interactions (80% TP vs. 8% in random prediction) find most large interfaces fail to detect small interfaces false predictions appear in smaller alignments larger alignments needed [Feinauer, Szurmant, MW, Pagnani, PLoS ONE 16]

47 Predicting mutational effects in proteins Quantifying the fitness effect of mutations is crucial for understanding the determinants of genetic disease understanding the mechanism of evolution of drug resistance understanding the onset and proliferation of cancer helping to develop novel diagnostic and therapeutic tools cf. talks by M Kardar, M Lässig

48 Predicting mutational effects in proteins Quantifying the fitness effect of mutations is crucial for understanding the determinants of genetic disease understanding the mechanism of evolution of drug resistance understanding the onset and proliferation of cancer helping to develop novel diagnostic and therapeutic tools The most common approach supervised feature extraction using case/control studies (e.g. genome-wide association studies)

49 Predicting mutational effects in proteins Quantifying the fitness effect of mutations is crucial for understanding the determinants of genetic disease understanding the mechanism of evolution of drug resistance understanding the onset and proliferation of cancer helping to develop novel diagnostic and therapeutic tools The most common approach supervised feature extraction using case/control studies (e.g. genome-wide association studies) Our approach unsupervised modelling of evolutionary sequence data Bayesian integration of complementary knowledge (structure, mutagenesis)

50 Measuring mutational effects in proteins PNAS 110 (2013) Quantitative high-throughput mutagenesis TEM-1 protein causes antibiotic resistance generated ~10 4 random mutants 1,700 without mutation 990 distinct single AA changes measured resistance to amoxicillin minimum inhibitory concentration as proxy for fitness

51 Landscape inference by Direct-Coupling Analysis Beta-lactamase2 family (PF13354) TEM-1 Statistical landscape inference (DCA)... ~2,500 diverged sequences P (A 1 (a,...,a 1,...,a L L ) = X ) 8 ' i (a i )+ X 9 < LX ' ij (a LX i,a j ) = exp e : i ij (A i,a i,j j )+ h i (A i ) ; i,j=1 i=1? Score for mutant AA sequences = (mutant) P (mutant) (wildtype) = log P (wildtype) MIC changes of TEM-1 due to single-aa changes Evolutionary constraints across diverged homologs [Figliuzzi, Jacquier, Schug,Tenaillon, MW, Mol Biol Evol 16]

52 Landscape inference by Direct-Coupling Analysis Beta-lactamase2 family (PF13354) TEM-1 Statistical landscape inference (DCA)... ~2,500 diverged sequences P (A 1 (a,...,a 1,...,a L L ) = X ) 8 ' i (a i )+ X 9 < LX ' ij (a LX i,a j ) = exp e : i ij (A i,a i,j j )+ h i (A i ) ; i,j=1 i=1? Score for mutant AA sequences = (mutant) P (mutant) (wildtype) = log P (wildtype) MIC changes of TEM-1 due to single-aa changes Evolutionary constraints across diverged homologs [Figliuzzi, Jacquier, Schug,Tenaillon, MW, Mol Biol Evol 16]

53 Predicting mutational effects in proteins profile model DCA model SIFT PolyPhen2 Popmusic Imut+ MUpro Imut force fields solvent accessibility Blosum62 evolution based structural-stability based [Figliuzzi, Jacquier, Schug,Tenaillon, MW, Mol Biol Evol 16]

54 Capturing the context dependence of mutations A B i direct contacts all residue pairs i D structure MSA i R i 0.45 residue fraction 0.5 i i cutoff distance

55 Is there more information in ACSLPKVQGPCSGKHSYYYFNSANQQCETFVYGGCLGNTNRFATIEECNARC- VCLLPKSAGPCTGFTKKWYFDVDRNRCEEFQYGGCYGTNNRFDSLEQCQGTC- VCAMPPDAGVCTNYTPRWFFNSQTGQCEQFAYGSCGGNENNFFDRNTCERKCM TCSLSPSPGTCGPGVFKYHYNPQTQECESFEYLGCDGNSNTFASRAECENYCG -CHTEHSSGACPGAVTMFYHDPRTKKCTPFTFLGCGGNSNKFDTRPQCERFCK PCMLPSDKGNCQDILTRWYFDSQKHQCRAFLYSGCRGNANNFLTKTDCRNACM -----RLVGYCSPYLRRYFFNRTTEKCVLFIPERCEKDGNNFPNRKVCMKTCM PCSLKEDYGIGRAYYERWYFNTTTANCTRFIWGGNHKEWQQFR PCKQDLDQGHGKTLQARYYFNKYAKVCEQFDYRGIDGNRNNFESLQECQQQC- -CFLKPDEGVGRAILKAFYYNPKNRRCEEFEYGGLGGNENNFETMEKCEEECK -CSQPAASGHGEQYLSRYFYSPEYRQCLHFIYSGERGNLNNFESLTDCLETCV LCNLKYDSGVGGEKSDKYFWVPKYTTCMRFSFYGTLGNANNFPNYNSCMATCG RGADTIQRWYWDTNDLTCRTFKYHGQGGNFNNFGDKQGCLDFC- PCEQAIEEGIGNVLLRRWYFDPATRLCQPFYYKGFKGNQNNFMSFDTCNRACG PCGQPLDRGVGGSQLSRWYWNQQSQCCLPFSYCGQKGTQNNFLTKQDCDRTC- VCIQPLESGD-EPSVPRWWYNSATGTCVQFMWDPDTTNANNFRTAEHCESYCR TCVQPTATGP-NPTEPRWWYNSITGMCQQFLWDPTASGPNNFRTVEHCESFCR -CDQQLMLGVGGASMERFYYDTTDDACLVFNYSGVGGNENNFLTKAECQIAC- PCSVPLAPGTGNAGLARYYYNPDDRQCLPFQYNGKRGNQNNFENQADCERTC- ----PESEGVTGAPTSRWYYDQTDMQCKQFTYNGRRGNQNNFLTQEDCAATC- ACKMPLSVGIGGAPANRWYYDAAASTCKTFEYNGRKGNQNNFISEADCAATC- VCNLPMSTGEGNANLDRFYYDQQSKTCRPFVYNGLKGNQNNFISLRACQLSC- ICQQPMAVGTGGATLPRWYYNAQTMQCVQFNYAGRMGNQNNFQSQQACEQTC- PCSLPMFSGEGTGNLTRWYADSCSRQCKSFTYNGSKGNQNNFLTKQQCESKCK PCEEEMTQGEGSAALTRFYYDALQRKCLAFNYLGLKGNRNNFQSKEHCESTC- TCELPMTKGYGNSHLTRWHFDKNLNKCVKFIYSGEGGNQNMFLTQEDCLTVC- TCELTMTKGYGNSHLTRWHFDKNLNKCVKFIYSGEGGNQNMFLTQEDCLSVC- RCHLPPAVGYGKQRMRRFYFDWKTDACHELQYSGIGGNENIFMDYEQCERVCR -CMESLDRGSCEAMSNRYYFNKRARQCKGFHYTGCGKSGNNFLTKEECQTKC- PCQQPLQRGNCSQRIPLFYYNIHNHKCRKFMYRGCNGNENRFSNRRQCQAKCG?