Multiscale Fractal Characterization of Three-Dimensional Gene Expression Data

This article reports on the application of the recently introduced concept of multiscale fractal dimension (MFD) as a resource for quantifying three-dimensional gene expression patterns in embryonic development. While traditional fractal dimensions provide interesting possibilities for quantifying pattern complexity, as defined by the intensity in which the pattern interacts with its surrounding space, those approaches fail to take into account the important fact that natural objects are not perfectly self-similar. By expressing the fractal behavior explicitly in terms of the spatial scale, the MFD provides a more comprehensive and objective characterization of the complexity of natural data such as gene expression profiles. After presenting the MFD concept as well as a technique for its numerical estimation, the potential of this measure for objectively quantifying gene expression is discussed, and a complete example is provided regarding the three-dimensional expression of the myogenic marker gene Myf5 along successive somites in a mouse embryo. In this specific case, the adopted technique proved itself a useful means for identifying spatial variations of gene expression intensity.