Nussinov algorithm

Key takeaways

Nussinov algorithm belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Nussinov algorithm to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Nussinov algorithm from memory before moving on to harder problems.

Reference excerpt

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. The algorithm was developed by Ruth Nussinov in the late 1970s.

Background 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 that maximizes the total number of bonds between bases.

Motivation Consider an RNA sequence S {\displaystyle S} whose elements are taken from the set { A , U , C , G } {\displaystyle \{A,U,C,G\}} . Let us imagine we have an optimal solution to the subproblem of folding S i {\displaystyle S_{i}} to S j − 1 {\displaystyle S_{j-1}} , and an optimal solution for folding S u {\displaystyle S_{u}} to S v {\displaystyle S_{v}} i ≤ u ≤ v ≤ j − 1 {\displaystyle i\leq u\leq v\leq j-1} . Now, to align S i {\displaystyle S_{i}} to S j {\displaystyle S_{j}} , we have two options:

Leave S j {\displaystyle S_{j}} unpaired, and keep the structure of S i {\displaystyle S_{i}} to S j − 1 {\displaystyle S_{j-1}} . The score for this alignment will be equal to the score of the alignment of S i {\displaystyle S_{i}} to S j − 1 {\displaystyle S_{j-1}} , as no new base pairs were created. Pair S j {\displaystyle S_{j}} with S k {\displaystyle S_{k}} , where i ≤ k < j {\displaystyle i\leq k<j} . The score for this alignment will be the score of the base pairing, plus the score of the best alignment of S i {\displaystyle S_{i}} to S k − 1 {\displaystyle S_{k-1}} and S k + 1 {\displaystyle S_{k+1}} to S j − 1 {\displaystyle S_{j-1}} .

Algorithm Consider an RNA sequence S {\displaystyle S} of length n {\displaystyle n} such that S i ∈ { A , U , C , G } {\displaystyle S_{i}\in \{A,U,C,G\}} . Construct an n × n {\displaystyle n\times n} matrix M {\displaystyle M} . Initialize M {\displaystyle M} such that

M ( i , i ) = 0 {\displaystyle M(i,i)=0}

M ( i , i − 1 ) = 0 {\displaystyle M(i,i-1)=0}

for 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} .

M ( i , j ) {\displaystyle M(i,j)} will contain the maximum score for the subsequence S i . . . S j {\displaystyle S_{i}...S_{j}} . Now, fill in entries of M {\displaystyle M} up and to the right, so that

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Nussinov algorithm

Start with the simplest possible case. Write down what Nussinov algorithm claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nussinov algorithm before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nussinov algorithm ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nussinov algorithm

In research: Nussinov algorithm appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nussinov algorithm in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nussinov algorithm is common in secondary-school and first-year university syllabi. It links to neighbouring topics Bioinformatics algorithms, so understanding it makes those chapters shorter.
In everyday life: Look for Nussinov algorithm outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Nussinov algorithm in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Nussinov algorithm means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Nussinov algorithm out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nussinov algorithm in simple terms?

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. The algorithm was developed by Ruth Nussinov in the late 1970s.

Why does Nussinov algorithm matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nussinov algorithm?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nussinov algorithm.