Generic Theoretical Models to Predict Division Patterns of Cleaving Embryos

Abstract

Summary Life for all animals starts with a precise 3D-choreography of reductive divisions of the fertilized egg, known as cleavage patterns. These patterns exhibit conserved geometrical features and striking inter-species invariance within certain animal classes. To identify the generic rules that may govern these morphogenetic events, we developed a 3D-modelling framework that iteratively infers blastomere division positions and orientations, and consequent multicellular arrangements. From a minimal set of parameters, our model predicts detailed features of cleavage patterns in the embryos of fishes, amphibians, echinoderms and ascidians, as well as the genetic and physical perturbations that alter these patterns. This framework demonstrates that a geometrical system based on length-dependent microtubule forces that probe blastomere shape and yolk gradients, biased by cortical polarity domains, may dictate division patterns and overall embryo morphogenesis. These studies thus unravel the default self-organization rules governing early embryogenesis, and how they are altered by deterministic regulatory layers.

Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data

“…The increasing use of 3D imaging in fluorescence microscopy applications, with confocal microscopy being now mainstream, has allowed for the acquisition of large amounts of 3D data in both biological and physical systems. Examples include biological studies of the morphological changes that occur during cell migration (Soll, ; Soll et al ., ), the microbial cell shape (Ursell et al ., ), the cellular packings during tissue morphogenesis (Hayashi & Carthew, ; Lecuit & Lenne, ) and early embryonic development (Pierre et al ., ) and even the geometry of the cell nucleus at the subcellular scale (Kim et al ., ; Wang et al ., ). Studies of the mechanics of emulsions in soft‐matter physics also rely on the ability to characterize the geometry of individual droplets (Brujić et al ., ; Zhou et al ., ).…”

Predicting division planes of three-dimensional cells by soap-film minimization

“…Cell shape changes during animal cell mitosis make it difficult to assess whether factors such as geometric cues before mitosis are used to orient the division or if the division plane is specified by other interactions as the cell is dividing (Minc and Piel, 2012). Surface area minimization (akin to soap bubbles) along with cell-cell contacts or adhesion have been used to describe patterning and division plane orientation of animal cells (Kafer et al, 2007;Hayashi and Carthew, 2004;Goldstein, 1995;Pierre et al, 2016;Gibson et al, 2011). Landmark cues including tricellular junctions during mitotic rounding and contacts with the extracellular matrix can be maintained to properly orient animal cell division planes (Bosveld et al, 2016;Théry et al, 2005).…”

Multiscale mechanical model for cell division orientation in developing biological systems

“…In both animal and plant tissues the orientation of a cell's division plane often aligns orthogonal to the long geometrical axis of the dividing cell (Hertwig's rule, or HR, in animals [17][18][19], Errera's rule in plants [20,21]). The emergence * Corresponding author: bruno.leggio@inria.fr of these rules in animal cells has been linked to the action of mechanical forces [19,22,23]. In all these cases the predicted rule is in very good agreement with the direction of the cell's longaxis.…”

“…To understand the cause of this phase transition we looked at the correlations between cells within the simulated tissue. It is known that the agreement to geometrical rules give rise to alternating orthogonal directions for division orientations within one clone [22]. For a set of initial cells S (0) c consider the parameter…”