Interactive visualisation of oligomer frequency in DNA

Since 1990, bioinformaticians have been exploring applications of the Chaos Game Representation (CGR) for visualisation, statistical characterisation and comparison of DNA sequences. We focus on the development of a new computational algorithm and description of new software tool that enables CGR visualisation of frequencies of K-mers (oligomers) in a flexible way such that it is possible to visualise the whole genome or any of its parts (like genes), and parallel comparison of several sequences, all in real time. User can interactively specify the size and position of visualised region of the DNA sequence, zoom in or out, and change parameters of visualisation. The tool has been written in JAVATM language and is freely available to public

Efficient Boolean implementation of universal sequence maps (bUSM)

BACKGROUND: Recently, Almeida and Vinga offered a new approach for the representation of arbitrary discrete sequences, referred to as Universal Sequence Maps (USM), and discussed its applicability to genomic sequence analysis. Their work generalizes and extends Chaos Game Representation (CGR) of DNA for arbitrary discrete sequences. RESULTS: We have considered issues associated with the practical implementation of USMs and offer a variation on the algorithm that: 1) eliminates the overestimation of similar segment lengths, 2) permits the identification of arbitrarily long similar segments in the context of finite word length coordinate representations, 3) uses more computationally efficient operations, and 4) provides a simple conversion for recovering the USM coordinates. Computational performance comparisons and examples are provided. CONCLUSIONS: We have shown that the desirable properties of the USM encoding of nucleotide sequences can be retained in a practical implementation of the algorithm. In addition, the proposed implementation enables determination of local sequence identity at increased speed

Universal sequence map (USM) of arbitrary discrete sequences

BACKGROUND: For over a decade the idea of representing biological sequences in a continuous coordinate space has maintained its appeal but not been fully realized. The basic idea is that any sequence of symbols may define trajectories in the continuous space conserving all its statistical properties. Ideally, such a representation would allow scale independent sequence analysis – without the context of fixed memory length. A simple example would consist on being able to infer the homology between two sequences solely by comparing the coordinates of any two homologous units. RESULTS: We have successfully identified such an iterative function for bijective mappingψ of discrete sequences into objects of continuous state space that enable scale-independent sequence analysis. The technique, named Universal Sequence Mapping (USM), is applicable to sequences with an arbitrary length and arbitrary number of unique units and generates a representation where map distance estimates sequence similarity. The novel USM procedure is based on earlier work by these and other authors on the properties of Chaos Game Representation (CGR). The latter enables the representation of 4 unit type sequences (like DNA) as an order free Markov Chain transition table. The properties of USM are illustrated with test data and can be verified for other data by using the accompanying web-based tool:http://bioinformatics.musc.edu/~jonas/usm/. CONCLUSIONS: USM is shown to enable a statistical mechanics approach to sequence analysis. The scale independent representation frees sequence analysis from the need to assume a memory length in the investigation of syntactic rules

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Spatial representation of symbolic sequences through iterative function systems

Jeffrey proposed a graphic representation of DNA sequences using Barnsley's iterative function systems. In spite of further developments in this direction (Oliver et. al, 1993), (Roman-Roldan et. al, 1994), (Li, 1997), the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Jeffrey's graphic representation to accommodate (possibly infinite) sequences over an arbitrary finite number of symbols, 2) establish a direct correspondence between the statistical characterization of symbolic sequences via Renyi entropy spectra and the multifractal characteristics (Renyi generalized dimensions) of the sequences' spatial representations, 3) show that for general symbolic dynamical systems, the multifractal fH-spectra in the sequence space coincide with the fH-spectra on spatial sequence representations. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science