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Statistical scales of order in DNA.

Douglas Poland¹

¹Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA. poland@jhu.edu

Biophysical Chemistry

|March 4, 2009

Summary

This study reveals non-random patterns in DNA base pair composition across local, intermediate, and global scales. DNA sequences exhibit persistence in base composition, deviating from random models at larger scales.

Area of Science:

Genomics and Bioinformatics
Statistical Analysis of Biological Sequences

Background:

Previous research explored randomness and order in DNA sequences.
Local scale (10^0-10^1 bp) DNA composition follows binomial distribution, indicating randomness.
Larger scale composition analysis requires examining deviations from random models.

Purpose of the Study:

To investigate the statistical distribution of base pair composition (A-T, C-G) in DNA across various scales.
To identify and characterize non-random patterns and order in DNA sequences.
To extend previous findings on DNA sequence randomness and order.

Main Methods:

Analysis of net base composition in blocks of varying sizes for Bacillus anthracis and Escherichia coli genomes.
Fitting composition distributions using discrete binomial, standard normal, and modified normal distributions.

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Application of Mandelbrot's random walk model and maximum-entropy methods for distribution refinement.

Main Results:

Intermediate scale (10^2-10^4 bp) DNA composition deviates from standard normal distribution, fitting a modified normal distribution with power-law standard deviation.
This deviation suggests a 'persistence of composition' analogous to a biased random walk.
Bacillus anthracis distributions fit Mandelbrot-like models well, while Escherichia coli required a four-moment maximum-entropy distribution.

Conclusions:

DNA sequences exhibit order across local, intermediate, and global scales, not fully explained by simple random models.
A model incorporating Mandelbrot-type order at the intermediate scale can explain order across all scales.
The findings highlight inherent structural properties and non-random organization within DNA genomes.