The persistence exponent of DNA.
Using the complete genome of Thermoplasma volcanium, as an example, we have examined the distribution functions for the amount of C or G in consecutive, non-overlapping blocks of m bases in this system. We find that these distributions are very much broader (by many factors) than those expected for a random distribution of bases. If we plot the widths of the C-G distributions relative to the widths expected for random distributions, as a function of the block size used, we obtain a power law with a characteristic exponent. The broadening of the C-G distributions follows from the empirical finding that blocks containing a given C-G content tend to be followed by blocks of similar C-G content thus indicating a statistical persistence of composition. The exponent associated with the power law thus measures the strength of persistence in a given DNA. This behavior can be understood using Mandelbrot's model of a fractional Brownian walk. In this model there is a hierarchy of persistence (correlation between blocks) between all parts of the system. The model gives us a way to scale the C-G distributions such that all these functions are collapsed onto a master curve. For a fractional Brownian walk, the fractal dimension of the C-G distribution is simply related to the persistence exponent for the power law. The persistence exponent for T. volcanium is found to be gamma = 0.29 while for a 10 million base segment of the human genome we obtain gamma = 0.39, similar to but not identical with the value found for the microbe.
Poland
Douglas
D
Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA. poland@jhu.edu
D001482:Base Composition; D020029:Base Pairing; D001483:Base Sequence; D016386:Chromosome Walking; D003596:Cytosine / Q000737:chemistry*; D004247:DNA / Q000737:chemistry / Q000235:genetics*; D017709:Fractals; D016678:Genome; D006147:Guanine / Q000737:chemistry*; D006801:Humans; D013822:Thermoplasma / Q000235:genetics*
D006147:Guanine; D003596:Cytosine; D004247:DNA