Nussinov algorithm to predict secondary RNA fold structures

The prediction of secondary RNA structures is an interesting and important problem in bioinformatics. It is by no means at the forefront of the area, but still cool to look at as an introduction to bio(informatics/computation). This post will introduce the Nussinov-Jacobson algorithm for predicting and building secondary fold structures of RNA sequences. It is a dynamic programming algorithm and was one of the first developed for the prediction of RNA structures as RNA combinatorics can be quite involved and expensive. For a recap on dynamic programming, check out this post!

RNA & Nussinov

RNA, DNAs less famous cousin, is in charge of carrying out and transferring the genetic messages set out by DNA to your body for tasks such as protein synthesis. DNA codes and acts as a blueprint for your genetic traits, while the various types of RNA convert that genetic information into useful proteins by transferring the DNA blueprints out of the nucleus and into the ribosome. Both DNA and RNA are pretty cool.

Formally now, we can define RNA as a sequence \(S\), made up of four (nucleotide) bases; \(S \in \{G, C, A, U\}\). These 4 bases come in pairs, known as Watson-Crick pairs, and couple as follow: \(G \leftrightarrow C, \; A \leftrightarrow U\). These pairs are the “strong/stable” base pairs, however, in reality, we also have the coupling of less stable pairs, known as canonical pairs, namely \(G \leftrightarrow U\).

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