Problem: which base positions share common descent? agtggtcttgctacattgctagctaaatcgatcatgatcgatgattcagg tagctaaatcgatcatgatcgatgattcaggcgatgtcatgactgatcag tacattgctagctaaatcgatcatgatcgatgattcaggcgatgtcatga gatcatgatcgatgattcaggcgatgtcatgactgatcagggatgatgat Alignment – residue to residue correspondence between 2 or more sequences such that the order of residues in each sequence is preserved. agtggtcttgctacattgctagctaaatcgatcatgatcgatgattcagg tagctaaatcgatcatgatcgatgattcaggcgatgtcatgactgatcag tacattgctagctaaatcgatcatgatcgatgattcaggcgatgtcatga gatcatgatcgatgattcaggcgatgtcatgactgatcagggatgatgat agtggtcttgctacattgctagctaaatcgatcatgatcgatgattcagg tagctaaatcgatcatgatcgatgattcaggcgatgtcatgactgatcag tacattgctagctaaa----tcatgatcgatgattcaggcgatgtcatga gatcatgatcgatgattcaggcgat------actgatcagggatgatgat Indels make alignment trickier
Assembly – (from ensembl) - When the genome of a species is to be sequenced, the chromosomes from many cells are broken at random positions into small fragments, which are sequenced, and reassembled into long sequences (contigs). Contigs may be assembled into longer sequences called scaffolds and sometimes, if the depth of sequencing is high enough, there may be enough information to assemble most of the scaffolds into chromosomes. The resulting collection of sequences after assembly is called a genome assembly. Alignment problems (examples) 1) different sequences of the same allele from the same locus within the same individual 2) sequences of different alleles from the same locus within the same individual 3) same locus from different individuals
Alignment Methods Dot plot – qualitative Sequence alignment – quantitative; constructing the best alignment using a scoring scheme Types of Alignment Global – best alignment over the entire length Local – best alignment in small region; used when comparing sequences of different lengths Multiple – beyond pairwise cagcacttggattctgg & cagcgtgg Local cagca-cttggattctgg ---cagcgtgg------- Global (best depending on gap penalties) cagcacttggattctgg cagc----g—t----gg
Gaps residue to nothing match that can be inserted in either sequence are not part of the DNA sequence, only a construct for alignment Gap to gap match is meaningless and not allowed
Dot plots – heuristic; make matrix, place dots; find diagonals
Alignment with scoring schemes score to select the best possible alignment given scoring scheme Scoring scheme A set of rules that assigns a score to a particular alignment between two sequences Goal is to maximize score Score is sum of residue substitution scores and gap penalties
atggcgt +1+1+1-1+1+1 = 4 atg-agt +1 for match -1 for mismatch No gap penalty atggcgt+1-1+1-1+1+1 = 2 a-tgagt Substitution matrix: c t a g c 1 -1 -1 -1 t -1 1 -1 -1 a -1 -1 1 -1 g -1 -1 -1 1
Substitution matrix: c t a g c 2 1 -1 -1 T 1 2 -1 -1 a -1 -1 2 1 g -1 -1 1 2 What if we want to penalize transitions less than transversions?
Protein substitution matrices More complex than DNA scoring matrices. Proteins are composed of twenty amino acids, and physical-chemical properties of individual amino acids vary considerably. can be based on any property of amino acids: size, polarity, charge, hydrophobicity. Evolutionary substitution matrices – empirically derived by assessment of frequencies of changes at particular levels of divergence
Evolutionary substitution matrices PAM ("point accepted mutation") family PAM250, PAM120, etc. BLOSUM ("Blocks substitution matrix") family BLOSUM62, BLOSUM50, etc. The BLOSUM matrices were developed more recently and considered better.
Blosum62 Blosum80 is used for less divergent sequences Blosum45 is used for more divergent sequences Etc.
Because gaps often result in radical protein changes (frame shifts, premature stop), the penalty for a gap is usually several times greater than the penalty for a mutation. Once created, gaps of more than one residue might be less expensive than a completely new gap - in other words gap opening penalties and gap extension penalties are often defined separately Gaps
W i =g+h*i (for i>= 1, where i = gap length ) g: gap opening penalty h: gap extension penalty The ratio between gand h determines the relative weight for opening versus extension –Small g, Large h: gap length more important –Large g, Small h: gap length less important Affine gap penalty function W(i)
ATGTAGTGTATAGTACATGCA ATGTAG-------TACATGCA ATGTAGTGTATAGTACATGCA ATGTA--G--TA---CATGCA W i =g+h*i G = -3 H = -1 Substitution matrix: c t a g c 2 1 -1 -1 T 1 2 -1 -1 a -1 -1 2 1 g -1 -1 1 2 26 – 3 – 1(7) = 16 26 – 3 (3) – 1(7) =10
How do we find the best alignment? Brute-force approach: Generate the list all possible alignments between two sequences, score them, select the alignment with the best score The number of possible global alignments between two sequences of length N is For two sequences of 250 residues this is ~10 149
Needleman-Wunsch and Smith-Waterman are both algorithms that find the best alignment through breaking the problem down into sub problems using dynamic programming …however, it is only the best based on the scoring matrix and the gap opening and extension penalities These methods are computationally expensive
BLAST – Basic Local Alignment Search Tool -Tries to find the highest scoring ungapped local alignment between a query and a database -Uses a word length (w) and scans for matches with a higher threshold (T) when aligned with words in the query -The local alignment is then extended in both directions until the score falls below the best score reached so far. -Many types of blast can be found at http://blast.ncbi.nlm.nih.gov/Blast.cgi