Computational Biology

Transcription

1 Compuaional Bioloy A.P. Gulyaev (Saha) Appliaion oriened view appliaion H.J. Hooeboom (Hendrik Jan) Theory oriened view

2 hemes problem model (e. raph) known alorihms haraerizaion unpreise daa omplexiy heurisis wha is he rih answer?

3 enral doma DNA RNA ransripion & spliin proein eiwi ranslaion ene expression

4 wo alphabes DNA bases 4 symbols a RNA a u proeins amino aids 2 symbols A R D N C E Q G H I L K M F P S T W Y V

5 reursion answer quesion

6 reursion: bad example a = a = a n+ = a n +a n (n ) (e.)

7 reursion: dynami prorammin a = a = a n+ = a n +a n (n ),,, 2, 3, 5, 8, 3, 2, dynami prorammin memoizaion sore resuls in able ( work boomup )

8 sruure of RNA sequene sruure funion 2D sruure 3D sruure hp://al.sie.nnu.edu.w/ourse/bioloy/slide_bioloy.pp

9 sequene alinmen TCAGACGATTG TCGGAGCTG inserion deleion subsiuion mah mismah ap TCAGACGATTG TCGGAGCTG TCAGACGATTG TCGGAGCTG TCAGACGATTG TCGGAGCTG

10 sequene alinmen TCAGACGATTG TCGGAGCTG TCAGACGATTG TCGGAGCTG TCAGACGATTG TCGGAGCTG 46=8 23=7 mah mismah ap +2 TCAGACGATTG TCGGAGCTG 44=9

11 basi alorihm alinmen reursive priniple dynami prorammin

12 alinmen: reursion a a a a a a σ(,x) = σ(x,) = σ(x,y) = σ(x,x) = 2 reward and punishmen a a

13 dynami prorammin a a a a * a a

14 dynami prorammin a a a a a a

15 iniializaion a a a

16 dynami prorammin i a[i,j] = max a j a a[i,j] + a[i,j] + σ( s[i],[j] ) a[i,j] + a a a a +2 a a a a

17 alinmen a a a a

18 raebak a a a a a a a a a a

19 /* Reursion: he hear of he DP alorihm.*/ /* Iniializaion. */ S[][] = ; for (i = ; i <= M; i++) S[i][] = i * INDEL; for (j = ; j <= N; j++) S[][j] = j * INDEL; Eddy S.R. (24a) /* Dynami prorammin, lobal alinmen (Needleman/Wunsh) reursion. */ for (i = ; i <= M; i++) for (j = ; j <= N; j++) { /* ase #: i,j are alined */ if (x[i x[i] == y[j]) S[i][j] ] = S[i][j ][j] + MATCH; else S[i][j] ] = S[i][j ][j] + MISMATCH; s = S[i][j] + INDEL; /* ase #2: i alined o */ if (s > S[i][j]) ]) S[i][j] ] = s; } s = S[i][j] + INDEL; /* ase #3: j alined o */ if (s > S[i][j]) ]) S[i][j] ] = s; /* The resul (opimal alinmen sore) is now in S[M][N]. */

20 sorin and parameer hoie A A A C AT TA vs. vs. vs. A C A C AT TA mah mismah ap M m A C G T A C 25 3 G 4 T 9 ap 4 + 3k ask your favourie moleular biolois!

21 PAM25 Marix deails noes APG biohemial properies muaion prob (evoluion)

22 alinmen CAGCACTTGGATTCTCGG CAGCGTGG CAGCACTTGGATTCTCGG CAGCGTGG

23 varians of alinmen > lobal Needleman & Wunsh loal Smih & Waerman semilobal end

24 loal alinmen a[i,j] = max a[i,j] + a[i,j] + σ( s[i],[j] ) a[i,j] + max soluion (raebak) from max o

25 loal alinmen max

26 end alinmen s iniial ap ssssssssssss max final ap iniializaion wih zero s max on border(s)

27 savin spae O(mn) boh spae & ime Hirshber: linear spae j [ i] [ j] [i m] [j n] i T(m,n) 2mn T(m,n) mn/2 + mn/2 + T(i,n/2)+T(ni,n/2) mn + in + (mi)n = 2mn

28 savin spae O(mn) boh spae & ime Hirshber: linear spae j [ i] [ j] [i m] [j n] i +/2+/4+ = 2

29 eneral ap penalies (k) = k (k) = +ke (k) ap penaly open ap, exend ap arbirary os sandard eneral affine ap lenh

30 a a dynami prorammin b wih hree maries a a a a a a a a a a a a a a a a a a b

31 affine ap penalies dynami prorammin wih hree maries (k) = +ke open ap, exend ap b[i,j]= max a[i,j] e b[i,j] e [i,j] e ap was already open j a a a a i a a b O(mn ) vs. O(mn 2 + m 2 n ) eneral ap penaly

32 omparin similar sequenes O(mn) quadrai boh spae & ime redue ime k depends on number of dashes k banded alinmen linear ime heurisi se k based on upper bound for alinmen exa while improvemen do k = 2k

33 alinin several sequenes aidi ribosomal proein P homolo (LE) enoded by he Rplp ene

34 omparin muliple sequenes how o sore? SP sumofpairs pairs of symbols pairs of srins deails noes APG A C T G G G A A T G C G A A C T C C C dynami prorammin possible bu oo muh spae & ime heurisi redue searh spae (banded alinmen) problem is NPomplee (# srins = dimension!) heurisi sar alinmen / proressive alinmen hidden Markov model

35 sar alinmen srin in ener (whih one?) ompue pairwise alinmens exend pairs ino muliple alinmen one a ap, always a ap O(k 2 m 2 ) k sequenes, m lenh heory: wihin faor 2 of opimal alinmen

36 sar alinmen ATTGCCATT 2 ATGGCCATT 3 ATCCAATTTT 4 ATCTTCTT 5 ACTGACC ATTGCCATT 2 ATGGCCATT ATTGCCATT 3 ATCCAATTTT ATTGCCATT 4 ATCTTCTT ATTGCCATT 5 ACTGACC ATTGCCATT 2 ATGGCCATT 3 ATCCAATTTT ATTGCCATT 2 ATGGCCATT 3 ATCCAATTTT 4 ATCTTCTT 5 ACTGACC

37 uide ree boomup sequenes in leaves proressive alinmen ree known evoluionary relaion build ree luserin alo s ClusalW inner nodes ombine alinmens (profiles varian basi alo)

38 probleem solved!? muh oo slow lon srins hue daabases heurisis FASTA alon diaonal BLAST minimal lose mah muliple alinmen (several srins) NP omplee exponenial

39 human enome saisis 23 pairs of hromosomes 3. 9 nuleoide bases avarae 3 bases / ene dysrophin 2.4 million 3, 4, enes proein varians million (spliin) 99.9% exaly he same in humans

40 Basi Loal Alinmen Searh Tools query query word (W=3) GSVEDTTGSQSLAALLNKCKTPQGQRLVNQWIKQPLMDKNRIEERLNL neihbourhood words hreshold PQG 8 PEG 5 PRG 4 PMG 3 PQA 2 PQN 2 SLAALLNKCKTPQGQRLVNQWIKQPLMDKNRIEERLNL TLASVLDCTVTPMGSRMLKRWLHMPVRDTRVLLERQQT subje hihsorin semen pair (HSP) parameers: W word size T hreshold S sore E expeed