Mathematical characterization of three-dimensional gene expression patterns.

Abstract

The importance of a systematic methodology for the mathematical characterization of three-dimensional gene expression patterns in embryonic development. By combining lacunarity and multiscale fractal dimension analyses with computer-based methods of three-dimensional reconstruction, it becomes possible to extract new information from in situ hybridization studies. Lacunarity and fractality are appropriate measures for the cloud-like gene activation signals in embryonic tissues. The newly introduced multiscale method provides a natural extension of the fractal dimension concept, being capable of characterizing the fractality of geometrical patterns in terms of spatial scale. This tool can be systematically applied to three-dimensional patterns of gene expression. Applications are illustrated using the three-dimensional expression patterns of the myogenic marker gene Myf5 in a series of differentiating somites of a mouse embryo.