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Related Experiment Video

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Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

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Published on: May 8, 2015

Biological sequences as pictures: a generic two dimensional solution for iterated maps.

Jonas S Almeida¹, Susana Vinga

¹Dept Bioinformatics and Computational Biology, University of Texas MD Anderson Cancer Center, Houston, TX, USA. jalmeida@mathbiol.org

BMC Bioinformatics

|April 2, 2009

Summary

This summary is machine-generated.

This study presents an optimal graphical representation for any symbolic sequence using iterated maps. The new method ensures a unique mapping, generalizing existing methods like chaos game representation (CGR) for biological sequences.

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Area of Science:

Bioinformatics
Computational Biology
Data Visualization

Background:

Iterated maps offer a popular graphical method for representing symbolic sequences, known as chaos game representation (CGR).
CGR provides scale-independent representation and variable memory length, with potential for generalizing Markovian formalisms.
While initially for genomic data, CGR has been extended to protein sequences.

Purpose of the Study:

To develop a general, bijective graphical representation for any symbolic sequence using iterated maps.
To overcome limitations of previous methods in achieving a universally applicable transformation.

Main Methods:

Investigated the geometric challenge of creating regular fractal nesting of polygons for sequence mapping.
Evaluated Fiser's 1994 approach using non-overlapping circles and proposed an improved solution with overlapping circles.

Main Results:

Identified an optimal inscribed packing solution for iterated maps of biological and symbolic sequences.
The new solution preserves the bijective mapping property, ensuring a unique graphical representation.
Demonstrated that the Sierpinski triangle and CGR square are specific cases of this generalized formulation.

Conclusions:

A universally applicable, optimal inscribed packing solution for iterated maps of symbolic sequences has been identified.
This generalized method maintains bijective mapping and encompasses prior CGR variations.
The findings advance the graphical representation of symbolic sequences, with broad implications for bioinformatics.