RNA Secondary Structure Prediction Eran Barash CS Ben
RNA – Secondary Structure Prediction © Eran Barash, CS, Ben Gurion University
RNA role in organisms • The central dogma of biology: • RNA as a catalyst: – Discovered in the early 1980’s. – Examples:
RNA as a catalyst • Spliceosome: • RNA structure (especially in UTR’s) affects post -transcriptional genetic regulation (i. e. alternative splicing).
Terminology
Nested base pairs • Two base pairs (i, j) and (i’, j’) are called nested if and only if. • Most base pairs in nature are nested. • When non-nested base pairs occur, they are called pseudoknots.
Pseudoknots
Sequence constrained by structure • It is relatively common to find examples of homologous RNAs with a common structure but without significant similarity. • It would be advantageous to be able to search for conserved structure in addition to sequence when searching homologous RNAs.
Sequence constrained by structure • An example of a conserved structure:
Structure Prediction • Suppose you need to predict the “best” base pair structure of a 200 bases long RNA. How many possible structures are there? • Answer: Over possible structures. • How solve this problem without iterating over all possible structures? • Dynamic Programming.
Nussinov Jacobson Algorithm • In order to solve the problem, first we’ll define a scoring system : – If i and j are complementary – Otherwise. . • Hence, our goal is to find a structure which maximizes , over all base pairs. • Keep in mind, this is a simplistic approach!
Nussinov Jacobson Algorithm • We’ll also need to make some assumptions, in order to be able to treat this problem as a proper DP problem. • The assumptions: – No pseudoknots. – No “multiknots” (included in the first assumption).
Nussinov Jacobson Algorithm • When observing a sequence i to j, four options are possible:
Nussinov Jacobson Algorithm • Or, in other words: • This recursive approach is only possible due to the lack of pseudoknots.
Nussinov Jacobson Algorithm • More formally:
Nussinov Jacobson Algorithm • Running example:
Nussinov Jacobson Algorithm • Running example:
Nussinov Jacobson Algorithm • Running example:
Nussinov Jacobson Algorithm • Running example:
Nussinov Jacobson Algorithm • Tracing back, to find the best structure:
Nussinov Jacobson Algorithm • And back to our example:
Nussinov Jacobson Algorithm • What is the algorithm’s runtime and complexity? • Runtime: • Space complexity: • The trace back algorithm is linear in both space and time.
Nussinov Jacobson Algorithm • Possible improvements?
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