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Four-dimensional physical modeling and numerical simulation of the early mouse embryo morphogenesis.

Periodic Reporting for period 1 - MecaMorphEME (Four-dimensional physical modeling and numerical simulation of the early mouse embryo morphogenesis.)

Reporting period: 2015-09-01 to 2017-08-31

The quantitative understanding of preimplantation mammalian development is essential to the progress of reproductive medicine. Specifically, the process of embryo selection in vitro, which relies on the assessment of blastocyst morphology, is critical to the success of implantation. While important progress on mammalian embryology was made over the past decades from a molecular biology perspective, the mechanical and physical principles governing the morphogenesis of mammalian embryos have remained largely unexplored.
The project MecaMorphEME was intended to provide a first physical & numerical framework for understanding the morphogenesis of early mouse embryos, through a tight collaboration with Jean-Léon Maître, experimentalist at the time in the laboratory of Takashi Hiiragi.
The project led to the development of a new physical framework describing the shape of cells in the early mouse embryo and a powerful simulation tool for calculating its predictions. This framework allowed us to describe in physical and quantitative terms the two first morphogenetic events in mammalian embryo development: the compaction at 8-cell stage and the formation of the inner-cell mass at the next round of divisions.
During mouse embryo compaction at the 8-cell stage, cell-cell contacts increase their size, as the embryo rounds up (Wennekamp et al., 2013). To understand the process of compaction, I developed a minimal physical model based on surface tensions, which describes the configuration of a doublet of cells. The model predicts that the state of compaction is controlled by a single dimensionless parameter, the “compaction parameter” that is defined as the ratio of surface tensions at cell-cell contacts and at the cell-medium interface. The process of compaction corresponds to a decrease in the compaction parameter, comprised between 1 and 0, and. Tension measurements at the cell-medium interface with a micropipette, coupled with measurements of the external angle of contact between blastomeres allowed Jean-Léon Maître to determine that the compaction parameter varies from 0.75 to 0.25 from the beginning to the end of compaction. From these measurements, I could quantify, using the model, that 76% of the compaction process is driven by an increase of surface tension at the cell-medium (Maître et al., 2015). This physical framework proved that the shape of blastomeres in the mouse embryo is essentially determined by the tension at their interface. To study the formation of the inner-cell mass at the 8-to-16 cell stage transition, I generalized this approach to asymmetric doublets.

During the 8-to-16 cell stage transition, blastomeres are segregated into two layers: the inner-cell mass (ICM), composed variably of 1 to 7 cells, is surrounded by a forming epithelial layer, the trophectoderm (TE). In coordination with their spatial allocation, blastomeres start acquiring different cell fates, which will determine their future outcome: TE cells will form exclusively extra-embryonic structures such as the placenta, while ICM cells will give rise to the embryo proper and other extra-embryonic structures (Wennekamp et al., 2013). Following my previous model of compaction (Maître et al., 2015), I assumed that the shape of blastomeres is controlled by surface tension. I first examined a doublet of cells formed after division of one 8-cell stage blastomere. Generally, this doublet is the result, experimentally, of an asymmetric cell division, which segregates an apical domain formed at the 8-cell stage to only one of the daughter cells. The apical domain shows experimentally a reduced contractile tension. As a result, the doublet is asymmetric in shape, and, in 60% of the experiments, this asymmetry eventually leads to the full internalization of the non-apical cell into its sibling, which inherited an apical domain. By considering an asymmetric doublet as a physical system, I could show analytically that its shape is characterized by only three dimensionless parameters, a compaction parameter α, controlling the size of the contact between blastomeres, a tension asymmetry δ, and a volume asymmetry β. The model predicts full internalization only for a doublet displaying an asymmetry in tension larger than a well-defined threshold δ ≥ 1 + 2α. In physical terms, the internalization event corresponds to a wetting transition, and happens when the tension of one cell is strong enough to counteract the combined tensions of the other cell and of the contact. The model also predicts a minor effect of the volume asymmetry on the transient internalization process, without changing the threshold for full internalization.

To generalize these results to an embryo with 16 cells, I decided to develop a new simulation framework for multicellular interfaces, inspired by recent progress in computer graphics. Cells interface are described by a triangular mesh, which is evolved to minimize a surface energy under the constraint of cells volume conservation. By setting the tensions at interface, the numerical framework evolves cells shape from an initial configuration towards mechanical equilibrium. By varying the compaction and tension asymmetry parameters we could show that the compaction and internalization processes are equivalent for a doublet and a 16-cell embryo. In particular the threshold for internalization of one cell in the embryo does not depend on the number of its neighbors, but relies only the tension asymmetry between this cell and its neighbors. The simulation results were successfully compared to experiments performed by Jean-Léon Maître, which consisted in mixing blastomeres engineered genetically to have different contractilities (Maître, Turlier et al., 2016).

Maître, J.-L. Niwayama, R., Turlier, H., Nédélec, F., and Hiiragi, T. (2015). Pulsatile cell-autonomous contractility drives compaction in the mouse embryo. Nat Cell Biol 17, 849–855.
Maître, J.-L. Turlier, H., Illukkumbura, R., Eismann, B., Niwayama, R., Nédélec, F., and Hiiragi, T. (2016). Asymmetric division of contractile domains couple cell positioning and fate specification. Nature.
Wennekamp, S., Mesecke, S., Nédélec, F., and Hiiragi, T. (2013). A self-organization framework for symmetry breaking in the mammalian embryo. Nat Rev Mol Cell Biol 14, 454–461.
My theoretical model of internalization, together with experimental validations, provides a first quantitative understanding of the mechanism and mechanical conditions for the formation of the inner cell mass.

The new numerical framework I developed constitutes a unique tool for the simulation of multicellular systems and paves the way for more advanced models of early embryos, which will couple cell mechanics with genetic & signaling regulation to unravel the self-organization principles of embryo development.

These progresses pave the way for the development of automated quantitative methods to select preimplantation human embryos for assisted reproduction based on their morphological features.