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

Abstract

Background: 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.

Methods: 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.

Results: 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.

Conclusion: 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.

Author summary

This paper addresses evaluation of morphogenesis in Caenorhabditis elegans based on cellular strucuture of the organism, using allometry for studying of complexity. The x, y, z coordinates of a cell were considered in order to generate zero-centroaxial skew-symmetrical matrices (CSSMs) and used for constructing basic square matrices (BSMs). The complexity was determined using BSM determinant. The results were compared with complexity index based on calculation of the branching of the mitotic tree of developing embryos, and were found to be consistent with those of BSM. The lineage growth rate was also evaluated.

Graphical abstract

Keywords

embryogenesis / allometry / complexity / C. elegans / bioinformatics / skew matrix / morphogenesis

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ACKNOWLEDGEMENTS

We would like to express our profound gratitude to Prof. Dr. Ralf Schnabel (Institut fur Genetik, Technical University at Braunschweig, Germany), who provided the data of the embryo and SIMI-BioCell software in simi website, and The Wellcome Trust Sanger Institute at Cambridge. Our gratitude should be extended to other investigators involved in the development of softwares, and to Mrs. H. AliAkbar for editing the manuscript.

COMPLIANCE WITH ETHICS GUIDELINES

The authors Ali Tarihi, Mujtaba Tarihi and Taki Tiraihi declare that they have no conflict of interest or financial conflicts to disclose.

This article does not contain any studies with human or animal materials performed by any of the authors.

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