Cellular Fourier Transform: a new approach to analyse living tissues at multiple scales

Many questions in Biology concern the relation between different scales (i.e. sub-cellular, cellular or supra-cellular). For example, organ development often gives rise to robust sizes and shapes, in striking contrast with the variability observed at a cellular scale. In a classical physical context, many tools exist to investigate the relation between scales such as Fourier Transforms or wavelet decomposition but they are not well suited to biological tissues. In biological tissues, cells set a reference scale at which parameters and fields reflecting material properties and state are often assessed and space discretization based on standard coordinate systems is not commensurate with the natural discretization into geometrically disordered cells. We built a method, which we call Cellular Fourier Transform (CFT), to analyze cellular fields, which includes both discrete fields defined only at cell level and continuous fields smoothed out from their sub-cell variations. During my presentation, I will introduce the method and discuss its application to the growth of floral organs.