Fractal dimension of exon and intron sequences

Sequence Complexity of Chromosome 3 in Caenorhabditis elegans

The nucleotide sequences complexity in chromosome 3 of Caenorhabditis elegans (C. elegans) is studied. The complexity of these sequences is compared with some random sequences. Moreover, by using some parameters related to complexity such as fractal dimension and frequency, indicator matrix is given a first classification of sequences of C. elegans. In particular, the sequences with highest and lowest fractal value are singled out. It is shown that the intrinsic nature of the low fractal dimension sequences has many common features with the random sequences.

Packaging effects on site-specific DNA-protein interactions

We show that the rate of site-specific association of a protein molecule of interest with the DNA chain can be approximately 10(2) times higher than that of the three-dimensional diffusion-controlled collision rate limit approximately 10(8) mol(-1) s(-1) only when the protein molecule of interest searches for its specific site on the DNA chain in a reduced dimensional space with a dimensionality dr of dr<1. Upon considering the concurrent dynamics of the linear DNA chain that is embedded in a d-dimensional space along with the one-dimensional diffusion dynamics of the nonspecifically bound protein molecule on the DNA chain, we derive the generalized scaling law epsilon approximately 2(3(2-d)+3), where epsilon is the number of times by which the rate of site-specific association of the protein molecule with the DNA chain can be enhanced over the three-dimensional diffusion-controlled collision rate limit and d is the dimensionality of the reduced search space. Using the analogy between the self-intersection loop length in the theory of random walks and the ring-closure events in the theory of site specific interactions of a protein molecule with the DNA chain, we further show that the extent of packaging and volume compression of the genomic DNA inside the living cell is designed in such a way that the efficiency of the protein molecule in the process of searching for its specific site on the genomic DNA is a maximum. Our simulation results suggest that the volume compression factor theta which is the ratio between the total volume of the living cell and the volume occupied by the DNA chain along with all the other bound protein molecules should be such that theta>or=100 for an efficient site specific interaction of a protein molecule of interest with the linear DNA chain that is embedded in a three-dimensional space. Our theoretical and simulation results agree well with the E. coli cellular system.

Nonlinear analysis of correlations in Alu repeat sequences in DNA

We report on a nonlinear analysis of deterministic structures in Alu repeats, one of the richest repetitive DNA sequences in the human genome. Alu repeats contain the recognition sites for the restriction endonuclease AluI, which is what gives them their name. Using the nonlinear prediction method developed in chaos theory, we find that all Alu repeats have novel deterministic structures and show strong nonlinear correlations that are absent from exon and intron sequences. Furthermore, the deterministic structures of Alus of younger subfamilies show panlike shapes. As young Alus can be seen as mutation free copies from the "master genes," it may be suggested that the deterministic structures of the older subfamilies are results of an evolution from a "panlike" structure to a more diffuse correlation pattern due to mutation.

Fractals in pathology

Many natural objects, including most objects studied in pathology, have complex structural characteristics and the complexity of their structures, for example the degree of branching of vessels or the irregularity of a tumour boundary, remains at a constant level over a wide range of magnifications. These structures also have patterns that repeat themselves at different magnifications, a property known as scaling self-similarity. This has important implications for measurement of parameters such as length and area, since Euclidean measurements of these may be invalid. The fractal system of geometry overcomes the limitations of the Euclidean geometry for such objects and measurement of the fractal dimension gives an index of their space-filling properties. The fractal dimension may be measured using image analysis systems and the box-counting, divider (perimeter-stepping) and pixel dilation methods have all been described in the published literature. Fractal analysis has found applications in the detection of coding of coding regions in DNA and measurement of the space-filling properties of tumours, blood vessels and neurones. Fractal concepts have also been usefully incorporated into models of biological processes, including epithelial cell growth, blood vessel growth, periodontal disease and viral infections.