Multiple Alignment and Phylogenetic Trees Csc 487/687 Computing for Bioinformatics

Alignment problem Given a set of sequences, produce a multiple alignment which corresponds as well as possible to the biological relationships between the corresponding bio-molecules

For homologous proteins  Two residues should be aligned (on top of each other) if they are homologous (evolved from the same residue in a common ancestor protein) if they are structurally equivalent

Automatic approach  Need a way of scoring alignments fitness function which for an alignment quantifies its “goodness”  Need an algorithm for finding alignments with good scores  Not all methods provide a scoring function for the final alignment!

Analysis of fitness function  One can test whether the alignments optimal under a given fitness function correspond well to the biological relationships between the sequences  For example, if the structure of (some of) the proteins are known.

Scoring Alignments  In order to find an optimal alignment, we need to be able to measure how good an alignment is Sum of pairs (SP) method: in a column, score each pair of letters and total the scores. Pairs of gaps score 0. Total up scores for each column

SP Method Example  Using BLOSUM62 matrix, gap penalty -8  In column 1, we have pairs -,S S,S  k(k-1)/2 pairs per column -IK SIK SSE = -12

Align by use of dynamic programming  Dynamic programming finds best alignment of k sequences with given scoring scheme  For two sequences there are three different column types  For three sequences there are seven different column types x means an amino acid, - a blank Sequence1 x - x x - - x Sequence2 x x - x - x - Sequence3 x x x - x - x

Use of dynamic programming  Dynamic programming finds best alignment of k sequences given scoring scheme

Algorithm for dynamic programming

Analysis  O(n k ) entries to fill  Each entry combines O(2 k ) other entries  Costs O(k 2 ) to calculate each SP score  Overall cost is O(k 2 2 k n k ), or exponential in the number of sequences!  NP-complete

General progressive alignment Algorithm. General progressive alignment. Progressive alignment of the sequences {s 1, s 2,..., s m } Var C current set of alignments begin C := ∅ for i := 1 to m do C := C union {{s i }} end one alignment of each seq. for i := 1 to m − 1 do choose two alignments A p,A q from C; C := C − {A p,A q } A r := align(A p,A q );C := C union {A r } end C now contains the (single) final alignment end

The Clustal Algorithm  Three steps: 1 Compare all pairs of sequences to obtain a similarity matrix 2 Based on the similarity matrix, make a guide tree relating all the sequences 3 Perform progressive alignment where the order of the alignments is determined by the guide tree

(A) 1 pairwise comparison 2 clustering/making tree (B) 3 Align according to tree

Clustal - summary  Does not use a score for the final alignment  Each pairwise alignment is done using dynamic programming  Heuristics are used - tailored to globular proteins  Graphical version: ClustalX

Phylogeny  The basic principle is that the origin of similarity is common ancestry.  The field of phylogeny has the goals of working out the relationships among species, populations, individuals, or genes.  Usually expressed as a tree.

Phylogeny  The basic principle is that the origin of similarity is common ancestry.  The field of phylogeny has the goals of working out the relationships among species, populations, individuals, or genes.  Usually expressed as a tree.

Phylogeny  A statement of phylogeny among objects assumes homology and depends on classification.  Phylogeny states a topology of the relationships based on classification according to similarity of one or more sets of characters, or on a model of evolutionary processes.

Phylogeny  It is rare for species relationships and ancestry to be directly observable.  Evolutionary trees determined from genetic data are often based on inferences from the patterns of similarity, which are all that is observable among species living now.