Annals of Applied Statistics

Estimating the occurrence rate of DNA palindromes

I-Ping Tu, Shao-Hsuan Wang, and Yuan-Fu Huang

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A DNA palindrome is a segment of letters along a DNA sequence with inversion symmetry that one strand is identical to its complementary one running in the opposite direction. Searching nonrandom clusters of DNA palindromes, an interesting bioinformatic problem, relies on the estimation of the null palindrome occurrence rate. The most commonly used approach for estimating this number is the average rate method. However, we observed that the average rate could exceed the actual rate by 50% when inserting 5000 bp hot-spot regions with 15-fold rate in a simulated 150,000 bp genome sequence. Here, we propose a Markov based estimator to avoid counting the number of palindromes directly, and thus to reduce the impact from the hot-spots. Our simulation shows that this method is more robust against the hot-spot effect than the average rate method. Furthermore, this method can be generalized to either a higher order Markov model or a segmented Markov model, and extended to calculate the occurrence rate for palindromes with gaps. We also provide a $p$-value approximation for various scan statistics to test nonrandom palindrome clusters under a Markov model.

Article information

Ann. Appl. Stat., Volume 7, Number 2 (2013), 1095-1110.

First available in Project Euclid: 27 June 2013

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DNA palindrome genome sequence hairpin structure higher order Markov model hot-spot Markov model occurrence rate Poisson process power $p$-value segmented Markov model


Tu, I-Ping; Wang, Shao-Hsuan; Huang, Yuan-Fu. Estimating the occurrence rate of DNA palindromes. Ann. Appl. Stat. 7 (2013), no. 2, 1095--1110. doi:10.1214/12-AOAS622.

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Supplemental materials

  • Supplementary material A: Appendix for the paper “Estimating the occurrence rate of DNA palindromes”. The technical proofs for the theorems and corollaries in this paper are put in Supplement A as the appendix.
  • Supplementary material B: Matlab scripts for the paper “Estimating the occurrence rate of DNA palindromes”. The matlab scripts to calculate the thresholds derived in Theorem 4 are provided. The instruction is in the file “README.txt.”.