Long-range correlations in nucleotide sequences

DNA sequences have been analysed using models, such as an n-step Markov chain, that incorporate the possibility of short-range nucleotide correlations. We propose here a method for studying the stochastic properties of nucleotide sequences by constructing a 1:1 map of the nucleotide sequence onto a walk, which we term a 'DNA walk'. We then use the mapping to provide a quantitative measure of the correlation between nucleotides over long distances along the DNA chain. Thus we uncover in the nucleotide sequence a remarkably long-range power law correlation that implies a new scale-invariant property of DNA. We find such long-range correlations in intron-containing genes and in nontranscribed regulatory DNA sequences, but not in complementary DNA sequences or intron-less genes.

Effect of viscosity on neurite outgrowth and fractal dimension

The growth mechanism by which neurons achieve their characteristic ramified morphology has long been of interest, but determining whether physical parameters, such as viscosity, are important has been difficult due to a lack of useful hypotheses and standard reproducible techniques. We have recently shown that neurons exhibit fractal behavior and that their fractal dimension (df) is consistent with a physical process called diffusion-limited aggregation (DLA). We suggested that this DLA behavior might stem from viscosity differences, chemical gradients or electrical fields (Caserta et al., Phys. Rev. Lett., 64 (1990) 95-98). DLA is a model for a large family of growth processes. In order for a process to fit the DLA model, the growth rate must be proportional to the gradient of a field at a point on the growing structure (Feder, Plenum, New York, 1988, Ch. 4). Chemical, electrical, or fluid pressure fields can fit the model depending on the particular physical system under study. Here, we studied growth of retinal neurons from chick embryos in culture media of various fluid viscosities. Thus, we test whether DLA in this system was based on a fluid pressure field. As viscosity was increased from 1 to 4.3 cps, the number of neurite branches decreased 98%. However, there was no effect on df. Over this range of viscosities, total cellular protein synthesis decreased only 17%. The results indicate that, while differences in viscosity between the interior and exterior of the cell affect neurite outgrowth, they do not affect the fractal behavior of neurons. Thus, viscosity differences are not the basis for the DLA pattern of neuronal arborization.