Spontaneous mechanical and energetic state transitions during Caenorhabditis elegans gastrulation

Gastrulation, namely cell internalization, is a significant milestone during the development of metazoans from worm to human, which generates multiple embryonic layers with distinct cell fates and spatial organizations. Although many molecular activities are known to facilitate this process, in this paper, we focus on gastrulation of the nematode Caenorhabditis elegans and theoretically demonstrate that even a group of cells with only isotropic repulsive and attractive interactions can experience such internalization behavior when dividing within a confined space. As the cell number increases and cell size decreases, the cells contacted to the eggshell become closer to each other along with harder lateral compression, and a cell that internalizes could effectively increase the cell neighbor distance and lower the potential energy of the system. The multicellular structure transits from singleto double-layer spontaneously with bistable states existing from 15to 44-cell stages, near the gastrulation timing in vivo. Specifically, the cells with a larger size or placed near a smaller-curvature boundary are easier to internalize. Actively regulating a few cells’ internalizations can make the morphogenesis noise-resistant. Our work successfully recaptures the key characteristics in C. elegans gastrulation and provides a rational interpretation of how this phenomenon emerges and is optimally programmed. INTRODUCTION Metazoan embryogenesis starts from a single fertilized zygote and ends in a vast number of cells with stereotypic spatial patterns and fate specifications (Dehaan and Ebert, 1964; Kumar et al., 2015; Farrell et al., 2018; Packer et al., 2019). Those cells constitute multiple types of tissues and organs in an animal, such as intestine, muscle, and skin, which need precise and robust control on both morphogenesis and differentiation. During the rapid cleavage of blastomere, a dynamic process called gastrulation is activated at a specific timing to rearrange the cells into different germ layers, usually including endoderm, mesoderm, and ectoderm (Stern, 2004; Solnica-Krezel and Sepich, 2012). From the view of geometry, all cells are initially located adjacent to the inner side of the boundary (e.g., eggshell), like a two-dimensional curved surface, then they partially internalize so that the inner and outer layers are formed. Although the underlying regulations and the proportion of cells that move inward vary from species to species, this morphological change is common among all kinds of multicellular animals, including but not limited to nematode, ascidian, fly, frog, fish, chick, mouse, and human (Houthoofd et al., 2006; Swalla, 1993; Lemke et al., 2015; Heasman, 2006; Rohde and Heisenberg, 2007; Chapman et al., 2002; Tam and Behringer, 1997; Ghimire et al., 2021). As the developmental biologist Lewis Wolpert said, “not birth, marriage or death, but gastrulation which is truly the most important time in your life” (Vicente, 2015; Illman, 2021). The eutelic nematode Caenorhabditis elegans is a type of tiny transparent worm, which is famous for its highly invariant developmental programs at the cellular level and eventually generates 558 non-identical cells in a hatched larva (Sulston et al., 1983). Thus, it’s one of the most popular model animals for developmental biology and many regulatory mechanisms of gastrulation have been unraveled using this system (Corsi et al., 2015; Nance et al., 2005; Goldstein and Nance, 2020). During C. elegans embryogenesis, the gastrulating movements last for a long period (from 26to ~300-cell stages) and the cells from different lineages internalize group by group (roughly following the order as E → P4 → MS → D→ C → AB) (Chisholm and Hardin, 2005; Nance and Priess, 2002). Figure 1A shows the C. elegans embryonic development from 4to 350-cell stages imaged by 3-dimensional (3D) time-lapse confocal microscopy, which provides quantitative information for each cell’s nucleus position (GFP-labeled) and membrane morphology (mCherry-labeled) (Cao et al., 2020). Prior to gastrulation onset, all cells are in contact with the shell (Nance and Priess, 2002). Around 26to 28-cell stages, gastrulation starts and the two gut precursor cells, Ea and Ep in E lineage (i.e., E2), together migrate inward coordinated by their intensive adhesion to lateral neighbors and apical contraction near the shell (Marston et al., 2016). At 44-cell stage (right before E2 divisions), those motions result in a layered multicellular structure consisting of the E2 cells inside and the others outside (Figure 1B). Using the segmented cell morphology of 17 C. elegans wild-type embryos (Cao et al., 2020), the total number of internal cells (without contact with the outer space) is estimated, showing that the first fully internalization occurs at 42to 46-cell stages and the internal cells occupy around 18 ± 1% of all cells in a ~350-cell embryo (Figure 1C-D and Table S1). Despite that gastrulation is well studied in morphological and molecular levels, a comprehensive mechanical and energetic interpretation of such a general phenomenon (hereafter referred to as cell internalization) is lacking. The evolutional origin, emergence principle, and program strategy of gastrulation are largely unclear (Nakanishi et al., 2014). Previous reports showed that for different nematode species, cell adhesion essentially affects the 4-cell arrangement, while the curvature of the eggshell seems to be associated with the gastrulation timing (Yamamoto and Kimura, 2017; Schierenberg, 2006). How the physical parameters play their roles in cell internalization, including its activation timing, and the number and identity of internalizing cells, remains to be answered. In this paper, we establish a computational pipeline to simulate C. elegans embryogenesis from 4to 330-cell stages, using a coarse-grained model that simplifies the proliferating cells as particles interacting with isotropic repulsion and attraction. We find that cell internalization occurs spontaneously in all conditions of physical parameter setting, during which the cells are rearranged more sparsely and the system’s potential energy becomes lower. Over the blastomere cleavage, the compressive pressure between cells is enhanced and a more stable state with cell internalized emerges when the total cell number exceeds a threshold. Surprisingly, with the physical parameters obtained from the real embryo, the predicted timing of cell internalization is close to the one observed experimentally. Moreover, we systematically explore how different factors affect cell internalization, including stiffness and adhesion of cells, cell size, cell position, etc. Theoretically, the larger cell is easier to internalize, and the first internalizing cells E2 in a living embryo are also the largest due to their genetically regulated cell cycle lengthening. The match between model prediction and experimental observation suggests that the regulatory programs of gastrulation are designed considering the fundamental mechanical and energetics laws. Last but not least, we investigate how cell internalization responds to motional noise and the stabilizing effect of the active force that drives specific cells’