Introduction to Bioinformatics Burkhard Morgenstern Institute of Microbiology and Genetics Department of Bioinformatics Goldschmidtstr. 1 Göttingen, March.
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Introduction to Bioinformatics
Burkhard Morgenstern
Institute of Microbiology and Genetics
Department of Bioinformatics
Goldschmidtstr. 1
Göttingen, March 2004
Introduction to Bioinformatics
Bioinformatics in Göttingen:
Dep. of Bioinformatics (UKG),
Edgar Wingender Dep. of Bioinformatics (IMG), BM Inst. Num. and Applied Mathematics,
Stephan Waack Dep. of Genetics (Hans Fritz, IMG),
Rainer Merkl
Introduction to Bioinformatics
Definition:
Bioinformatics
= development and application of software
tools for Molecular Biology
Bioinformatics:
Topics:
(a) Sequence Analysis (Gene finding …)
(b) Structure Analysis (RNA, Protein)
(c) Gene Expression Analysis
(d) Metabolic Pathways, Virtual Cell
Bioinformatics:
Areas of work:
(a) Application of software tools for data analysis in (Molecular) Biology
(b) Computing infrastructure, database development, support
(c) Development of algorithms and software tools
Information flow in the cell
Lots of data available at the sequence level
Fewer data at the structure and function level
Topics of lecture:
Data bases SwissProt, GenBank Pair-wise sequence comparison Data base searching Multiple sequence alignment Gene prediction
Protein data bases
Sanger and Tuppy: protein-sequencing methods (1951)
Margaret Dayhoff: Atlas of Protein Sequence and Structure (1972); later: Protein Identification Resource (PIR) as international collaboration
(a) Organize proteins into families;
(b) Amino acid substitution frequencies Amos Bairoch: SwissProt (1986)
DNA data bases
Maxam and Gilbert; Sanger: DNA sequencing methods (1977)
GenBank DNA data base (1979), now run by NCBI.
Collaboration with EMBL (1982), DDBJ (1984)
Translated DNA sequences stored in protein data bases (PIR, trEMBL)
The dot plot
Advantages:
1. Various types of similarity detectable (repeats, inversions)
2. Useful for large-scale analysis
Pair-wise sequence alignment
Evolutionary or structurally related sequences:
alignment possible
Sequence homologies represented by inserting gaps
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Global alignment: sequences aligned over the entire length
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Basic task:
Find best alignment of two sequences
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Basic task:
Find best alignment of two sequences
= alignment that reflects structural and evolutionary relations
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Questions:
1. What is a good alignment?
2. How to find the best alignment?
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Problem: Astronomical number of possible
alignments
Pair-wise sequence alignment
T Y I V A R E A Q Y E
C I - V M R E - Q Y –
Problem: Astronomical number of possible
alignments
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Problem: Astronomical number of possible
alignments
Stupid computer has to find out: which alignment is best ??
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
First (simplified) rules:
1. Minimize number of mismatches
2. Maximize number of matches
Pair-wise sequence alignment
T Y I V A R E A Q Y E
C I - V M R E - Q Y –
First (simplified) rules:
1. Minimize number of mismatches
2. Maximize number of matches
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
First (simplified) rules:
1. Minimize number of mismatches
2. Maximize number of matches
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
First (simplified) rules:
1. Minimize number of mismatches
2. Maximize number of matches
Pair-wise sequence alignment
T Y I V A R E A Q Y E
C I - V M R E - Q Y –
Second (simplified) rule:
Minimize number of gaps
Pair-wise sequence alignment
T Y I V - A R E A Q Y E
C I - V M - R E - Q Y –
Second (simplified) rule:
Minimize number of gaps
Pair-wise sequence alignment
For protein sequences: Different degrees of similarity among amino
acids. Counting matches/mismatches
oversimplistic
Pair-wise sequence alignment
T Y I V
T - L V
Use similarity scores for amino acids:
Define score s(a,b) for amino acids a and b
Pair-wise sequence alignment
T Y I V
T - L V
Given a similarity score for pairs of amino acids
Define score of alignment as
sum of similarity values s(a,b) of aligned
residues minus gap penalty g for each
residue aligned with a gap
Pair-wise sequence alignment
T Y I V
T - L V
Dynamic-programming algorithm finds
alignment with best score.
(Needleman and Wunsch, 1970)
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Alignment corresponds to path through comparison matrix
Pair-wise sequence alignment
T Y I V A R E A Q Y E
- C I V M R E - Q Y –
Alignment corresponds to path through comparison matrix
Pair-wise sequence alignment
Score of alignment: Sum of similarity values of aligned residues minus gap penatly
T W L V - R E A Q I - C I V M R E - H Y
Pair-wise sequence alignment
Example: S = - g + s(W,C) + s(L,L) + s(V,V) - g + s(R,R) …
T W L V - R E A Q I - C I V M R E - H Y
Pair-wise sequence alignment
T W L V R E A Q Y I X X C X Alignment corresponds I X to path through V X comparison matrix M X R X E X X H X Y X X
T W L V - R E A Q I - C I V M R E - H Y
Pair-wise sequence alignment
i T W L V R E A Q Y I X X Dynamic programming: C X Calculate scores S(i,j) I X of optimal alignment of V X prefixes up to positions M X i and j. j R X E H Y
T W L V - R - C I V M R
Pair-wise sequence alignment
i T W L V R E A Q Y I X X C X S(i,j) can be calculated from I X possible predecessors V X S(i-1,j-1), S(i,j-1), S(i-1,j). M X j R X E H Y
T W L V - R - C I V M R
Pair-wise sequence alignment
i T W L V R E A Q Y I X X C X Score of optimal path that I X comes from top left = V X M X S(i-1,j-1) + s(R,R) j R X E H Y
T W L V - R - C I V M R
Pair-wise sequence alignment
i T W L V R E A Q Y I X X C X Score of optimal path that I X comes from above = V X j-1M X S(i,j-1) – g j R X E H Y
T W L V R - - C I V M R
Pair-wise sequence alignment
i-1 i T W L V R E A Q Y I X X C X Score of optimal path that I X comes from left = V X M X S(i-1,j) – g j R X X E H Y
T W L - - V R - C I V M R -
Pair-wise sequence alignment
i-1 i T W L V R E A Q Y I X X C X Score of optimal path = I X V X Maximum of these three M X values j R X X E H Y
T W L - - V R - C I V M R -
Pair-wise sequence alignment
Recursion formula:
S(i,j) = max { S(i-1,j-i)+s(ai,bj) , S(i-1,j) – g , S(i,j-i) – g }
Pair-wise sequence alignment
T W L V R x x x C x x x I x x V x x M x x R x x E x x H x x Y x x Fill matrix from top left to bottom right:
Pair-wise sequence alignment
T W L V R x x x C x x x I x x x V x x M x x R x x E x x H x x Y x x Fill matrix from top left to bottom right:
Pair-wise sequence alignment
T W L V R x x x x x x C x x x x x x I x x x x x x V x x x x x x M x x x x x x R x x x x x x E x x x x x x H x x x x x x Y x x x x x x Fill matrix from top left to bottom right:
Pair-wise sequence alignment
T W L V R x x x x x x C x x x x x x I x x x x x x V x x x x x x M x x x x x x R x x x x x x E x x x x x x H x x x x x x Y x x x x x x Find optimal alignment by trace-back procedure
Pair-wise sequence alignment
T W L V R x x x x x x C x I x V x M x R x E x H x Y x Initial matrix entries?
Pair-wise sequence alignment
i
T W L V R
X X
C X Entries S(i,j) scores
I X of optimal alignment of
j V X prefixes up to positions
M i and j.
R
E
H
Y
T W L V
- C I V
Pair-wise sequence alignment
i T W L V R j X X X X X C Entries S(i,0) scores I of optimal alignment of V prefix up to positions M i and empty prefix. R E Score = - i* g H Y T W L V - - - -
Pair-wise sequence alignment
T W L V R 0 -2 -4 -6 -8 -10 C -2 I -4 V -6 M -8 R -10 E -12 H -14 Y -16 Initial matrix entries: Example, g = 2
Pair-wise global alignment
T W L V R E A Q Y I X X C X I X V X M X R X E X X F X Y X X
T W L V - R E A Q I - C I V M R E - F Y
Pair-wise global alignment
Complexity:
l1 and l2 length of sequences:
Computing time and memory proportional to
l1 * l2
Time and space complexity = O(l1 * l2)
Pair-wise local alignment
Sequences often share only
local sequence similarity
(conserved genes or domains)
Important for database searching
Pair-wise local alignment
T W L V R E A Q Y I X X C X I X V X M X R X E X X H X Y X X
T W L V - R E A Q I - C I V M R E - F Y
Pair-wise local alignment
T W L V R E A Q Y I X X C X I X V X M X R X E X X F X Y X X
T W L V - R E A Q I - C I V M R E - F Y
Pair-wise local alignment
Problem:
Find pair of segments with maximal
Alignment score
(not necessarily part of optimal global alignment!)
Pair-wise local alignment
T W L V R E A Q Y I X X C X I X V X M X R X E X X F X Y X X
T W L V - R E A Q I - C I V M R E - F Y
Pair-wise sequence alignment
Recursion formula for global alignment:
S(i,j) = max { S(i-1,j-i)+s(ai,bj) , S(i-1,j) – g , S(i,j-i) – g }
Pair-wise sequence alignment
Recursion formula for local alignment:
S(i,j) = max { 0 , S(i-1,j-i)+s(ai,bj) , S(i-1,j) – g , S(i,j-i) – g }
Pair-wise sequence alignment
T W L V R 0 0 0 0 0 0 C 0 I 0 V 0 M 0 R 0 E 0 H 0 Y 0 Initial matrix entries = 0
Pair-wise sequence alignment
Recursion formula for local alignment:
S(i,j) = max { 0 , S(i-1,j-i)+s(ai,bj) , S(i-1,j) – g , S(i,j-i) – g }
Store position with maximal value S(i,j) in matrix
Pair-wise local alignment
T W L V R E A Q Y I X X C X I X V X M X R X E X X F X Y X X
T W L V - R E A Q I - C I V M R E - F Y
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