Gibbs Clustering Massimo Andreatta Morten Nielsen CBS Department

Gibbs Clustering Massimo Andreatta, Morten Nielsen CBS, Department of Systems biology DTU, Denmark

Class II MHC binding • MHC class II binds peptides in the class II antigen presentation pathway • Binds peptides of length 9 -18 (even whole proteins can bind!) • Binding cleft is open • Binding core is 9 aa

Conventional Gibbs sampling MHC class II binding SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT. . . DFAAQVDYPSTGLY Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 9 AAs SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQ DV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT. . . DFAAQVDYPSTGLY 3

Gibbs sampling - sequence alignment 50 sequences 12 amino acids long try all possible combinations with a 9 -mer overlap 450 ~ 1030 possible combinations. . . computationally unfeasible Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Why sampling? SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT. . . DFAAQVDYPSTGLY 4

Gibbs sampling - sequence alignment SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS State transition move to state +1 5

Gibbs sampling - sequence alignment SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT move to state +1 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS State transition SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT Accept or reject the move? Department of Systems Biology Technical University of Denmark Note that the probability of going to the new state depends on the previous state only 6

Gibbs sampling - sequence alignment SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT move to state +1 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Numerical example - 1 SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT Accept move with Prob = 100% Department of Systems Biology Technical University of Denmark 7

Gibbs sampling - sequence alignment SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT move to state +1 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Numerical example - 2 SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT Accept move with Prob = 63. 8% Department of Systems Biology Technical University of Denmark 8

Gibbs sampling - sequence alignment CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS What is the MC temperature? it’s a scalar decreased during the simulation T iteration Department of Systems Biology Technical University of Denmark 9

Gibbs sampling - sequence alignment it’s a scalar decreased during the simulation T E. g. same d. E=-0. 3 but at different temperatures t 1=0. 4 t 2=0. 1 t 3=0. 02 iteration Department of Systems Biology Technical University of Denmark 10 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS What is the MC temperature?

CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS f(Z) Z Move freely around states when the system is “warm”, then cool it off to force it into a state of high fitness Department of Systems Biology Technical University of Denmark 11

Does it work? CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS HLA-DRB 3*01: 01 Department of Systems Biology Technical University of Denmark 12

It works Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS High Temperature Low Temperature 13

Gibbs sampler. Prediction accuracy CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 14

Next generation peptide-chip technology CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 15

Identification of receptor binding motifs CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 16

Data interpretation Signal LMLSLFEQSLSCQAQ 9 QGTDATKSIIFEAER -12 RLEEAQAYLAAGQHD 10 EISELRTKVQEQQKQ 44 FAGAKKIFGSLAFLP 70 VRASSRVSGSFPEDS -7 CKAFFKRSIQGHNDY 86 CEGCKAFFKRSIQGH 100 RLSEADIRGFVAAVV -7 Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Peptide 17

Or with multiple specificities? Signal LMLSLFEQSLSCQAQ 9 QGTDATKSIIFEAER -12 RLEEAQAYLAAGQHD 10 EISELRTKVQEQQKQ 44 FAGAKKIFGSLAFLP 70 VRASSRVSGSFPEDS -7 CKAFFKRSIQGHNDY 86 CEGCKAFFKRSIQGH 100 RLSEADIRGFVAAVV -7 Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Peptide 18

Gibbs clustering (multiple specificities) SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Multiple motifs! Cluster 1 ----SLFIGLKGDIRESTV---DGEEEVQLIAAVPGK-----VFRLKGGAPIKGVTF ---SFSCIAIGIITLYLG------IDQVTIAGAKLRSLN-WIQKETLVTFKNPHAKKQDV ------KMLLDNINTPEGIIP Cluster 2 --ELLEFHYYLSSKLNK-----LNKFISPKSVAGRFA ESLHNPYPDYHWLRT------NKVKSLRILNTRRKL------MMGMFNMLSTVLGVS---AKSSPAYPSVLGQTI-------RHLIFCHSKKKCDELAAK 19

The algorithm CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK Department of Systems Biology Technical University of Denmark 20

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK Department of Systems Biology Technical University of Denmark 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQD V --ELLEFHYYLSSKLNK----MMGMFNMLSTVLGVS-----AKSSPAYPSVLGQTI-- 3 Simple shift g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Remove peptide g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- Phase shift 21 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQDV --ELLEFHYYLSSKLNK----MMGMFNMLSTVLGVS-----AKSSPAYPSVLGQTI-- g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- 3. Finding 3 the optimal configuration (the MC moves) MMGMFNMLSTVLGVS Department of Systems Biology Technical University of Denmark 22

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQDV KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQDV --ELLEFHYYLSSKLNK-----AKSSPAYPSVLGQTI-- g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- 3. Finding the optimal configuration (the MC moves) MMGMFNMLSTVLGVS 5. Score new core to log-odds matrices 4. Random shift of the core MMGMFNMLSTVLGVS Department of Systems Biology Technical University of Denmark 6. Accept or reject move 23

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQD V --ELLEFHYYLSSKLNK----MMGMFNMLSTVLGVS-----AKSSPAYPSVLGQTI-- 3 Simple shift g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Remove peptide g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- Phase shift MMGMFNMLSTVLGVS Department of Systems Biology Technical University of Denmark 24 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQD V --ELLEFHYYLSSKLNK-----AKSSPAYPSVLGQTI-- 3 Simple shift g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Remove peptide g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- Phase shift MMGMFNMLSTVLGVS 4 b. Random shift of the core MMGMFNMLSTVLGVS Department of Systems Biology Technical University of Denmark 25 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQD V --ELLEFHYYLSSKLNK-----AKSSPAYPSVLGQTI-- 3 Simple shift g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Remove peptide g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK---- Phase shift MMGMFNMLSTVLGVS 5 b. Score new core to all log-odds matrices 4 b. Random shift of the core MMGMFNMLSTVLGVS E 1 E 2 Department of Systems Biology Technical University of Denmark E 3 26 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides

The algorithm SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK 2. create N random groups g 1 ----IDQVTIAGAKLRSLNWIQKETLVTFKNPHAKKQD V --ELLEFHYYLSSKLNK-----AKSSPAYPSVLGQTI-- 3 Simple shift g 2 -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Remove peptide g. N ---ESLHNPYPDYHWLRTRHLIFCHSKKKCDELAAK----VFRLKGGAPIKGVTF --LNKFISPKSVAGRFA-DGEEEVQLIAAVPGK----MMGMFNMLSTVLGVS--- Phase shift MMGMFNMLSTVLGVS 5 b. Score new core to all log-odds matrices 4 b. Random shift of the core MMGMFNMLSTVLGVS E 1 E 2 Department of Systems Biology Technical University of Denmark E 3 6 b. Accept or reject move 27 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 1. List of peptides

The scoring function CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS -SLFIGLKGDIRESTV----SFSCIAIGIITLYLG KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- -SLFIGLKGDIRESTV--SFSCIAIGIITLYLG-KMLLDNINTPEGIIP---LNKYVHGTWRSILP----NKVKSLRILNTRRKL- Avoid small specialized clusters (s = 10) Maximize intra cluster similarity whilst minimize inter cluster similarity P = Probability of accepting the move Department of Systems Biology Technical University of Denmark 28

A mixture of 500 9 mer peptides. How many motifs? CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS OR Department of Systems Biology Technical University of Denmark 29

A mixture of 500 9 mer peptides. How many motifs? CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 30

Two MHC class I alleles: HLA-A*0101 and HLA-B*4402 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Mixture of 100 binders for the two alleles ATDKAAAAY EVDQTKIQY AETGSQGVY ITDITKYLY AEMKTDAAT FEIKSAKKF LSEMLNKEY GELDRWEKI LTDSSTLLV FTIDFKLKY TTTIKPVSY EEKAFSPEV AENLWVPVY Department of Systems Biology Technical University of Denmark A*0101 B*4402 A*0101 B*4402 31

Two MHC class I alleles: HLA-A*0101 and HLA-B*4402 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Mixed A 0101 B 4402 G 1 G 2 Department of Systems Biology Technical University of Denmark 32

Two MHC class I alleles: HLA-A*0101 and HLA-B*4402 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Mixed A 0101 B 4402 G 1 97 3 G 2 3 97 Resolved Department of Systems Biology Technical University of Denmark 33

Five MHC class I alleles A 0201 A 0301 B 0702 B 4402 G 0 G 1 G 2 G 3 G 4 Department of Systems Biology Technical University of Denmark 34 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS A 0101

Five MHC class I alleles Department of Systems Biology Technical University of Denmark HLA-A 0101 80% HLA-A 0201 89% A 0201 A 0301 B 0702 B 4402 G 0 0 1 76 1 0 G 1 2 4 0 0 95 G 2 5 87 5 1 0 G 3 93 2 19 0 2 G 4 0 6 0 98 3 HLA-B 4402 94% HLA-B 0702 92% 35 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS HLA-A 0301 97% A 0101

The right number of specificities CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 36

How many motifs? CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS l=0 Department of Systems Biology Technical University of Denmark 37

How many motifs? CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS OR l>0 Department of Systems Biology Technical University of Denmark 38

Adding in alignment (MHC class II) CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS HLA-DRB 1*03: 01 HLA-DRB 1*04: 01 SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK Department of Systems Biology Technical University of Denmark 39

Dealing with noisy data CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS • Experimental data often contain false positives • Outliers do not match any recurrent motif • Introduce a garbage bin to collect outliers Department of Systems Biology Technical University of Denmark 40

Dealing with noisy data CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS • Introduce a garbage bin to collect outliers SLFIGLKGDIRESTV DGEEEVQLIAAVPGK VFRLKGGAPIKGVTF SFSCIAIGIITLYLG IDQVTIAGAKLRSLN WIQKETLVTFKNPHAKKQD V KMLLDNINTPEGIIP ELLEFHYYLSSKLNK LNKFISPKSVAGRFA ESLHNPYPDYHWLRT NKVKSLRILNTRRKL MMGMFNMLSTVLGVS AKSSPAYPSVLGQTI RHLIFCHSKKKCDELAAK g 1 Department of Systems Biology Technical University of Denmark g 2 Move to the trash cluster peptides that do not match any motif gn trash 41

Dealing with noisy data 3 alleles g 0 g 1 g 2 trash Department of Systems Biology Technical University of Denmark HLA-A 0101 0 199 0 1 200 HLA-B 0702 197 1 0 2 200 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 200 binders to 3 MHC class I alleles 50 random sequences are added to the data set HLA-B 4001 2 0 196 2 200 Random 6 2 5 37 50 205 202 201 42 42

Dealing with noisy data 3 alleles g 0 g 1 g 2 trash HLA-A 0101 0 199 0 1 200 HLA-B 0702 197 1 0 2 200 50 random sequences are added to the data set HLA-B 4001 2 0 196 2 200 DHHFTPQII NAFGWENAY SQTSYQYLI Department of Systems Biology Technical University of Denmark CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS 200 binders to 3 MHC class I alleles Random 6 2 5 37 50 205 202 201 42 ELPIVTPAL ADKNLIKCS 43

Dealing with noisy data CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 44

SH 3 domains CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS - SH 3 domains are small interaction modules abundantly found in eukaryotes - They preferentially bind prolinerich regions (minimum consensus sequence is Pxx. P) - Two main classes of ligands exist: class I +x Px P Department of Systems Biology Technical University of Denmark class II Px Px+ +: R or K : hydrophobic x: any amino acid Surface representation of the Hck SH 3 domain bound to an artificial highaffinity peptide ligand, in green. Schmidt et al. (2007) 45

SH 3 domains - Gibbs clustering WVTAPRSLPVLP GSWVVDISNVED NYSGNRPLPGIW RSPIVRQLPSLP RALPVMPTNGPM AKSRPLPMVGLV VRPLPSPEGFGQ YRGRMLPVIWGT RALPLPRAYEGI VPLLPIRNGAVN PVRVLPNIPLSV. . . Department of Systems Biology Technical University of Denmark *Kim, T. , et al. (2011) MUSI: an integrated system for identifying multiple specificity from large peptide or nucleic acid data sets, Nucleic Acids Res, 1 -8. 46 CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS - Large data set of 2, 457 unique peptide sequences* binding to Src SH 3 domain - 12 amino acids long peptides, unaligned with respect to the binding core

SH 3 domains CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Gibbs clustering - 1 cluster class I +x Px P 2, 350 sequences (107 to trash) Department of Systems Biology Technical University of Denmark class II Px Px+ 47

SH 3 domains CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Gibbs clustering - 2 clusters Class II class I +x Px P 1, 928 sequences Department of Systems Biology Technical University of Denmark (63 to trash) 466 sequences class II Px Px+ 48

SH 3 domains CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Gibbs clustering - 3 clusters 1, 404 sequences 445 sequences (48 to trash) Department of Systems Biology Technical University of Denmark 560 sequences class I +x Px P class II Px Px+ 49

SH 3 domains CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Optimal solution has two specificities Department of Systems Biology Technical University of Denmark class I +x Px P class II Px Px+ 50

http: //www. cbs. dtu. dk/services/Gibbs. Cluster CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS Department of Systems Biology Technical University of Denmark 51

Acknowledgements CENTER FOR BIOLOGICAL SEQUENCE ANALYSIS • Massimo Andreatta, Ph. D (for doing all the work) • • John Sidney (La Jolla Institute for Allergy and Immunology, California, USA) for the binding affinity validation of the predicted MHC class I outliers. The European Union 7 th Framework Program FP 7/2007 -2013 [grant number 222773] Department of Systems Biology Technical University of Denmark 52