A mechanical model of early somite segmentation

Surrogate modeling of Cellular-Potts Agent-Based Models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 590 times compared to CPM code execution. Over multiple recursive evaluations, our model effectively captures the emergent behaviors demonstrated by the original Cellular-Potts model of such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM of biological processes at greater spatial and temporal scales.

Apical constriction requires patterned apical surface remodeling to synchronize cellular deformation

Apical constriction is a basic mechanism for epithelial morphogenesis, making columnar cells into wedge shape and bending a flat cell sheet. It has long been thought that an apically localized myosin generates a contractile force and drives the cell deformation. However, when we tested the increased apical surface contractility in a cellular Potts model simulation, the constriction increased pressure inside the cell and pushed its lateral surface outward, making the cells adopt a drop shape instead of the expected wedge shape. To keep the lateral surface straight, we considered an alternative model in which the cell shape was determined by cell membrane elasticity and endocytosis, and the increased pressure is balanced among the cells. The cellular Potts model simulation succeeded in reproducing the apical constriction, and it also suggested that a too strong apical surface tension might prevent the tissue invagination.

Engineering a computable epiblast for in silico modeling of developmental toxicity

Developmental hazard evaluation is an important part of assessing chemical risks during pregnancy. Toxicological outcomes from prenatal testing in pregnant animals result from complex chemical-biological interactions, and while New Approach Methods (NAMs) based on in vitro bioactivity profiles of human cells offer promising alternatives to animal testing, most of these assays lack cellular positional information, physical constraints, and regional organization of the intact embryo. Here, we engineered a fully computable model of the embryonic disc in the CompuCell3D.org modeling environment to simulate epithelial-mesenchymal transition (EMT) of epiblast cells and self-organization of mesodermal domains (chordamesoderm, paraxial, lateral plate, posterior/extraembryonic). Mesodermal fate is modeled by synthetic activity of the BMP4-NODAL-WNT signaling axis. Cell position in the epiblast determines timing with respect to EMT for 988 computational cells in the computer model. An autonomous homeobox (Hox) clock hidden in the epiblast is driven by WNT-FGF4-CDX signaling. Executing the model renders a quantitative cell-level computation of mesodermal fate and consequences of perturbation based on known biology. For example, synthetic perturbation of the control network rendered altered phenotypes (cybermorphs) mirroring some aspects of experimental mouse embryology, with electronic knockouts, under-activation (hypermorphs) or over-activation (hypermorphs) particularly affecting the size and specification of the posterior mesoderm. This foundational model is trained on embryology but capable of performing a wide variety of toxicological tasks conversing through anatomical simulation to integrate in vitro chemical bioactivity data with known embryology. It is amenable to quantitative simulation for probabilistic prediction of early developmental toxicity.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce a novel agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the respective contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism contributing to an increase in migratory speed of the tissue. Model outcomes are validated experimentally using mesendoderm tissue explants.

A human pluripotent stem cell-based somitogenesis model using microfluidics

Emerging human pluripotent stem cell (hPSC)-based embryo models are useful for studying human embryogenesis. Particularly, there are hPSC-based somitogenesis models using free-floating culture that recapitulate somite formation. Somitogenesis in vivo involves intricately orchestrated biochemical and biomechanical events. However, none of the current somitogenesis models controls biochemical gradients or biomechanical signals in the culture, limiting their applicability to untangle complex biochemical-biomechanical interactions that drive somitogenesis. Herein, we develop a human somitogenesis model by confining hPSC-derived presomitic mesoderm (PSM) tissues in microfabricated trenches. Exogenous microfluidic morphogen gradients imposed on the PSM tissues cause axial patterning and trigger spontaneous rostral-to-caudal somite formation. A mechanical theory is developed to explain the size dependency between somites and the PSM. The microfluidic somitogenesis model is further exploited to reveal regulatory roles of cellular and tissue biomechanics in somite formation. This study presents a useful microengineered, hPSC-based model for understanding the biochemical and biomechanical events that guide somite formation.

Cellular and molecular control of vertebrate somitogenesis

Segmentation is a fundamental feature of the vertebrate body plan. This metameric organization is first implemented by somitogenesis in the early embryo, when paired epithelial blocks called somites are rhythmically formed to flank the neural tube. Recent advances in in vitro models have offered new opportunities to elucidate the mechanisms that underlie somitogenesis. Notably, models derived from human pluripotent stem cells introduced an efficient proxy for studying this process during human development. In this Review, we summarize the current understanding of somitogenesis gained from both in vivo studies and in vitro studies. We deconstruct the spatiotemporal dynamics of somitogenesis into four distinct modules: dynamic events in the presomitic mesoderm, segmental determination, somite anteroposterior polarity patterning, and epithelial morphogenesis. We first focus on the segmentation clock, as well as signalling and metabolic gradients along the tissue, before discussing the clock and wavefront and other models that account for segmental determination. We then detail the molecular and cellular mechanisms of anteroposterior polarity patterning and somite epithelialization.

Sequential changes in cellular properties accompanying amniote somite formation

Somites are transient structures derived from the pre-somitic mesoderm (PSM), involving mesenchyme-to-epithelial transition (MET) where the cells change their shape and polarize. Using Scanning electron microscopy (SEM), immunocytochemistry and confocal microscopy, we study the progression of these events along the tail-to-head axis of the embryo, which mirrors the progression of somitogenesis (younger cells located more caudally). SEM revealed that PSM epithelialization is a gradual process, which begins much earlier than previously thought, starting with the dorsalmost cells, then the medial ones, and then, simultaneously, the ventral and lateral cells, before a somite fully separates from the PSM. The core (internal) cells of the PSM and somites never epithelialize, which suggests that the core cells could be 'trapped' within the somitocoele after cells at the surfaces of the PSM undergo MET. Three-dimensional imaging of the distribution of the cell polarity markers PKCζ, PAR3, ZO1, the Golgi marker GM130 and the apical marker N-cadherin reveal that the pattern of polarization is distinctive for each marker and for each surface of the PSM, but the order of these events is not the same as the progression of cell elongation. These observations challenge some assumptions underlying existing models of somite formation.

Phase separation dynamics in deformable droplets

Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types. Similarly, separation of different tissue types is also observed in stem cell aggregates, where the emergence of a polar organization can mimic early embryonic axis formation. Here, we describe such aggregates as deformable two-phase fluid droplets, which are suspended in a fluid environment (third phase). Using hybrid finite-volume Lattice-Boltzmann simulations, we numerically explore the out-of-equilibrium routes that can lead to the polar equilibrium state of such a droplet. We focus on the interplay between spinodal decomposition and advection with hydrodynamic flows driven by interface tensions, which we characterize by a Peclet number Pe. Consistent with previous work, for large Pe the coarsening process is generally accelerated. However, for intermediate Pe we observe long-lived, strongly elongated droplets, where both phases form an alternating stripe pattern. We show that these "croissant" states are close to mechanical equilibrium and coarsen only slowly through diffusive fluxes in an Ostwald-ripening-like process. Finally, we show that a surface tension asymmetry between both droplet phases leads to transient, rotationally symmetric states whose resolution leads to flows reminiscent of Marangoni flows. Our work highlights the importance of advection for the phase separation process in finite, deformable systems.

Molecular and Mechanical Cues for Somite Periodicity

Somitogenesis refers to the segmentation of the paraxial mesoderm, a tissue located on the back of the embryo, into regularly spaced and sized pieces, i.e., the somites. This periodicity is important to assure, for example, the formation of a functional vertebral column. Prevailing models of somitogenesis are based on the existence of a gene regulatory network capable of generating a striped pattern of gene expression, which is subsequently translated into periodic tissue boundaries. An alternative view is that the pre-pattern that guides somitogenesis is not chemical, but of a mechanical origin. A striped pattern of mechanical strain can be formed in physically connected tissues expanding at different rates, as it occurs in the embryo. Here we argue that both molecular and mechanical cues could drive somite periodicity and suggest how they could be integrated.

Morphogen-regulated contact-mediated signaling between cells can drive the transitions underlying body segmentation in vertebrates

We propose a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis, the process of body segmentation during embryonic development, that is invariant across all vertebrate species. This is achieved by combining inter-cellular interactions mediated via receptor-ligand coupling with global spatial heterogeneity introduced through a morphogen gradient known to occur along the anteroposterior axis. Our model reproduces synchronized oscillations in the gene expression in cells at the anterior of the presomitic mesoderm as it grows by adding new cells at its posterior, followed by travelling waves and subsequent arrest of activity, with the eventual appearance of somite-like patterns. This framework integrates a boundary-organized pattern formation mechanism, which uses positional information provided by a morphogen gradient, with the coupling-mediated self-organized emergence of collective dynamics, to explain the processes that lead to segmentation.