A web server for interactive and zoomable Chaos Game Representation images

Genomic sequences exhibit characteristic nucleotide compositional bias, especially in the relative abundances of short oligonucleotides. While diverse dinucleotide frequencies are observed among various phyla, closely related species tend to display similar compositions [1]. Through these studies, the relative abundances of dinucleotides are considered to be the "genomic signature" [2,3]. Chaos Game Representation (CGR) was first proposed by Jeffrey as a scale-independent means to visualize this non-randomness of genomic sequences, by applying the concept of chaotic dynamical systems [4]. Further studies by Almeida et al. has shown that CGR is a generalized Markov chain probability table which can accommodate non-integer orders, and that CGR is advantageous over Markov transition tables for its computational efficiency and scale-independence [5-8].Several software tools, including a database of CGR images [9], a web server [5], and a tool in the EMBOSS package [10], are already available for CGR analysis; however, these tools produce static images, which limits the full utility of CGR as scale-independent Markov transition table. Zoomable User Interface (ZUI) is effective in representing such scalable information [11], as exemplified by the popularity of Google Maps [12] in representing the geographical data. Therefore, here we describe a web server for generating interactive and zoomable CGR images, using Google Maps API [13] and Web 2.0 technologies [14].In order to generate CGR for a given nucleotide sequence, a rectangular coordinate system is defined to be confined by four vertices representing the four nucleotides: A (-1, 1), C (-1, -1), G (1, 1), and T (1, -1). Then, starting from the origin (0, 0), a pointer is moved to the midpoint of current position and the vertex corresponding to the next nucleotide. For example, for a tetramer sequence "ACGT", the pointer is first moved to the midpoint between the origin (0, 0) and T (1, -1), which is (0.5, -0.5), and t