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What is dynamic programming?

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Sequence alignment methods often use something called a 'dynamic programming' algorithm. What is dynamic programming and how does it work?

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Figure 1: The filled dynamic programming matrix for two DNA sequences, x = TTCATA and y = TGCTCGTA, for a scoring system of +5 for a match, −2 for a mismatch and −6 for each insertion or deletion.

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References

  1. Bellman, R.E. Eye of the Hurricane: An Autobiography (World Scientific, Singapore, 1984).

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Authors and Affiliations

  1. Howard Hughes Medical Institute & Department of Genetics, Washington University School of Medicine, 4444 Forest Park Blvd., Box 8510, Saint Louis, 63108, Missouri, USA

    Sean R Eddy

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  1. Sean R Eddy
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Supplementary information

Supplementary Note

An example of global sequence alignment by dynamic programming. (C 7 kb)

The program is ANSI C and should compile on any machine that has a C compiler, with a command line like: gcc -o global global.c

To run the program: ./global

To change the sequences or the scoring system, you have to edit the appropriate #define's at the top of the program, and recompile. This is meant to be a simple working example of the mechanics of dynamic programming sequence alignment. The details of reading FASTA files and such are left as an exercise to the reader. Any questions about this program should be addressed directly to the author.

Further study

Further study

To study a working example, you can download a small, bare-bones C implementation of this algorithm (see Supplementary Note). I used this C program to generate Figure 1.

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Eddy, S. What is dynamic programming?. Nat Biotechnol 22, 909–910 (2004). https://doi.org/10.1038/nbt0704-909

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  • DOI: https://doi.org/10.1038/nbt0704-909

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