Cell-based allometry: an approach for evaluation of complexity in morphogenesis

Morphogenesis is a complex process in a developing animal at the organ, cellular and molecular levels. In this investigation, allometry at the cellular level was evaluated.

Geometric information, including the time-lapse Cartesian coordinates of each cell's center, was used for calculating the allometric coefficients. A zero-centroaxial skew-symmetrical matrix ( CSSM), was generated and used for constructing another square matrix (basic square matrix: BSM), then the determinant of BSM was calculated ( d). The logarithms of absolute d (Lad) of cell group at different stages of development were plotted for all of the cells in a range of development stages; the slope of the regression line was estimated then used as the allometric coefficient. Moreover, the lineage growth rate (LGR) was also calculated by plotting the Lad against the logarithm of the time. The complexity index at each stage was calculated. The method was tested on a developing Caenorhabditis elegans embryo.

We explored two out of the four first generated blastomeres in C. elegans embryo. The ABp and EMS lineages show that the allometric coefficient of ABp was higher than that of EMS, which was consistent with the complexity index as well as LGR.

The conclusion of this study is that the complexity of the differentiating cells in a developing embryo can be evaluated by allometric scaling based on the data derived from the Cartesian coordinates of the cells at different stages of development.