Nussinov algorithm

The Nussinov algorithm is a nucleic acid structure prediction algorithm used in computational biology to predict the folding of an RNA molecule that makes use of dynamic programming principles.[1] The algorithm was developed by Ruth Nussinov in the late 1970s.

ClassNucleic acid structure prediction
Worst-case performance
Worst-case space complexity

Backgound

RNA origami occurs when an RNA molecule "folds" and binds to itself. This folding often determines the function of the RNA molecule. RNA folds at different levels, this algorithm predicts the secondary structure of the RNA.

Algorithm

Scoring

We score a solution by counting the total number of paired bases. Thus, attempting to maximize the score maximizes the total number of bonds between bases.

Motivation

Consider an RNA sequence whose elements are taken from the set . Let us imagine we have an optimal solution to the subproblem of folding to , and an optimal solution for folding to . Now, to align to , we have two options:

  1. Leave unpaired, and keep the structure of to . The score for this alignment will be equal to the score of the aligmnent of to , as no new base pairs were created.
  2. Pair with , where . The score for this alignment will be the score of the base pairing, plus the score of the best alignment of to and to .

Algorithm

Consider an RNA sequence of length such that .

Construct an matrix . Initialize such that

for .

will contain the maximum score for the subsequence . Now, fill in entries of up and to the right, so that

where

After this step, we have a matrix where represents the optimal score of the folding of .

To determine the structure of by traceback, we first create an empty list of pairs . We initialize with . Then, we follow one of three scenarios.

  1. If , the procedure stops.
  2. If , then set and continue.
  3. Otherwise, for all , if and are complementary and , append to , then traceback both with and .

When the traceback finishes, contains all of the paired bases.

Limitations

The Nussinov algorithm does not account for the three-dimensional shape of RNA, nor predict RNA pseudoknots.[2] Furthermore, in its basic form, it does not account for a minimum stem loop size. However, it is still useful as a fast algorithm for basic prediction of secondary structure.

References

  1. Nussinov, R; Jacobson, A B (Nov 1980). "Fast algorithm for predicting the secondary structure of single-stranded RNA". Proceedings of the National Academy of Sciences of the United States of America. 77 (11): 6309–6313. ISSN 0027-8424. PMID 6161375.
  2. "RNA Structure and RNA Structure Prediction" (PDF).
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