Distinguished words in data sequences: analysis and applications to neural coding and other fields

The modular structure of informational sequences

It is shown that DNA sequences can be decomposed into smaller units much the same as texts can be decomposed into syllables, words, or groups of words. Those smaller units (modules) are extracted from DNA sequences according to statistical criteria. Tests with sequences of known modular structure (two novels and a FORTRAN source code) were performed. The rate to which DNA sequences can be decomposed into modules (modularity) turns out to be a very sensitive measure to distinguish DNA sequences from random sequences.

The distribution of restriction fragment lengths for non-overlapping restriction sites in a random DNA sequence model

Overlapping subsequences in a DNA sequence are not independent even if independence is supposed for the single nucleotides. Therefore the often used geometric distribution for the length of restriction fragments is not exact. The exact distribution of this random variable is derived for non-overlapping restriction sites in a DNA sequence with an infinite (or very large) number of nucleotides. Correction to the finite case is easy. It is shown that the simple geometric distribution is a good approximation as long as the basic probability for the occurrence of the recognition sequence at a given site is small.

Linguistics of nucleotide sequences. I: The significance of deviations from mean statistical characteristics and prediction of the frequencies of occurrence of words

Mathematical models of the generation of genetic texts appeared simultaneously with the first sequencing DNA. They are used to establish functional and evolutionary relations between genetic texts, to predict the number and distribution of specific sites in a sequence and to identify "meaningful" words. The present paper deals with two problems: 1) The significance of deviations from the mean statistical characteristics in a genetic text. Anyone who has addressed himself to the statistical analysis of sequenced DNA is familiar with the question: what deviations from the expected frequencies of occurrence of particular words testify to the "biological" significance of those words? We propose a formula for the variance of the number of word's occurrences in the text, with allowance for word overlaps, making it possible to assess the significance of the deviations from the expected statistical characteristics. 2) A new method for predicting the frequencies of occurrence of particular words in a genetic text using the statistical characteristics of "spaced" L-grams. The method can be used for predicting the number of restriction sites in human DNA and in planning experiments on the physical mapping and sequencing of the human genome.

Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns

The findings presented here of work on the opisthobranch mollusc Pleurobranchaea californica indicate that some of the variability that has been observed in the activity of neurons during patterned motor activity may be attributable to low-dimensional chaos. We obtained long trains of action potentials (spikes) from these neurons, scanned them using adjacent temporal windows having equal widths, and converted the counts into frequency time series. These series were passed through a low-pass filter and detrended when necessary. The resulting time series gave a view of the envelopes of high-frequency bursts of spikes relating to the repetitive motor activity rather than of the intervals between spikes. Where applicable, we also compared analyses of smoothed data with the unprocessed spike intervals and found similar results for each type of time series. Autocorrelation functions of the processed data quickly decreased to zero, indicating that the long-term evolution of the time series could not be predicted from information at some given time. The first zero crossing of the autocorrelation function was used to define the lag for mapping the series into multidimensional phase space. These constructions were then used to examine the dynamics of the motor patterns directly from the state parameters of the time series: 1-D maps obtained from Poincaré slices of 2-D phase portraits, principal Lyapunov exponents, and correlation dimensions all indicated that the activity may be attributable to low-dimensional chaos. The present findings are similar to those of previous work in which equal-interval time series were obtained by interpolation of the unequal-interval spike trains. We discuss the implications of chaos and the difficulties in the application of extant dynamical tools to spike trains. An accompanying paper inquires into the ability of neural networks to read and transmit chaotic activity.

Linguistics of nucleotide sequences: morphology and comparison of vocabularies

The concept of "words" in continuous languages devoid of blanks is introduced and an operational definition of words given. With this novel concept nucleotide sequences become object for linguistic analysis. The typical word size of the nucleotide language is found to be 3 to 5 (tri- to pentamers). Different genomes have distinct vocabularies. Comparison of these vocabularies can serve as a basis for revealing functional and evolutionary relatedness of sequences.

TGTG, G clustering and other signals near non-mammalian vertebrate mRNA 3' termini: some implications

Analysis of non-mammalian vertebrate DNA sequences in the 500 nucleotides preceding and 200 nucleotides following mRNA 3' termini yields some distinct signals. In addition to the well known AATAAA sequence, TGTG recurs very frequently further downstream. GGGG, TGGG, GGAG and GAGG are frequent in this region too. It is suggested that unlike the AATAAA mRNA cleavage/processing signal, the other signals noted above are signals on the DNA, i.e. they are signals for mRNA termination. An asymmetric distribution of some complementary sequences, e.g. TGTG vs. CACA, GGGG vs. CCCC, on the same DNA strand is noted as well. A few other signals are also observed.