Spliced Alignment Problem: Solution and Secondary Structure Prediction in RNA - Prof. Saur, Study notes of Computer Science

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Dynamic Programming

(cont’d)

CS 466

Saurabh Sinha

Spliced Alignment

• Begins by selecting either all putative exons between potential acceptor and donor sites or by finding all substrings similar to the target protein (as in the Exon Chaining Problem).
• This set is further filtered in a such a way that attempt to retain all true exons, with some false ones.
• Then find the chain of exons such that the sequence similarity to the target protein sequence is maximized

The DAG

• Vertices: One vertex for each block in B
• Directed edge connecting non-overlapping blocks
• Label of vertex = string of block it represents
• A path through the DAG spells out the string obtained by concatenating that particular chain of blocks
• Weight of a path is the score of the optimal alignment between the string it spells out and the target sequence

Dynamic programming

• Genomic sequence G = g 1 g 2 …g n
• Target sequence T = t 1 t 2 …t m
• As usual, we want to find the optimal alignment score of the i-prefix of G and the j-prefix of T
• Problem is, there are many i-prefixes possible (since multiple blocks may include position i)

If i is not the starting vertex of block B :

• S(i, j, B) = max { S(i – 1, j, B) – indel penalty S(i, j – 1, B) – indel penalty S(i – 1, j – 1, B) + δ(g i , t j ) } If i is the starting vertex of block B :
• S(i, j, B) = max { S(i, j – 1, B) – indel penalty max all blocks B’ preceding block B S(end(B’), j, B’) – indel penalty max all blocks B ’ preceding block B S(end(B’), j – 1, B’) + δ(g i , t j ) }

RNA secondary structure

prediction

RNA

• There’s more to RNA than mRNA
• RNA can adopt interesting non-linear structures, and catalyze reactions
• tRNAs (transfer RNAs) are the “adapters” that implement translation

Secondary structure

• Several interesting RNAs have a conserved secondary structure (resulting from base- pairing interactions)
• Sometimes, the sequence itself may not be conserved for the function to be retained
• It is important to tell what the secondary structure is going to be, for homology detection

Basics of secondary structure

• G-C pairing: three bonds (strong)
• A-U pairing: two bonds (weaker)
• Base pairs are approximately coplanar

Basics of secondary structure

Secondary structure elements

Loop: single stranded subsequences bounded by base pairs loop at the end of a stem stem loop single stranded bases within a stem … only on one side of stem … on both sides of stem

Non-canonical base pairs

• G-C and A-U are the canonical base pairs
• G-U is also possible, almost as stable

Pseudoknot

2 11 9 18 (9, 18) (2, 11) NOT NESTED

Pseudoknot problems

• Pseudoknots are not handled by the algorithms we shall see
• Pseudoknots do occur in many important RNAs
• But the total number of pseudoknotted base pairs is typically relatively small