A change in boundary conditions induces a discontinuity of tissue flow in chicken embryos and the formation of the cephalic fold

Prediction of Growth Factor-Dependent Cleft Formation During Branching Morphogenesis Using A Dynamic Graph-Based Growth Model

This study considers the problem of describing and predicting cleft formation during the early stages of branching morphogenesis in mouse submandibular salivary glands (SMG) under the influence of varied concentrations of epidermal growth factors (EGF). Given a time-lapse video of a growing SMG, first we build a descriptive model that captures the underlying biological process and quantifies the ground truth. Tissue-scale (global) and morphological features related to regions of interest (local features) are used to characterize the biological ground truth. Second, we devise a predictive growth model that simulates EGF-modulated branching morphogenesis using a dynamic graph algorithm, which is driven by biological parameters such as EGF concentration, mitosis rate, and cleft progression rate. Given the initial configuration of the SMG, the evolution of the dynamic graph predicts the cleft formation, while maintaining the local structural characteristics of the SMG. We determined that higher EGF concentrations cause the formation of higher number of buds and comparatively shallow cleft depths. Third, we compared the prediction accuracy of our model to the Glazier-Graner-Hogeweg (GGH) model, an on-lattice Monte-Carlo simulation model, under a specific energy function parameter set that allows new rounds of de novo cleft formation. The results demonstrate that the dynamic graph model yields comparable simulations of gland growth to that of the GGH model with a significantly lower computational complexity. Fourth, we enhanced this model to predict the SMG morphology for an EGF concentration without the assistance of a ground truth time-lapse biological video data; this is a substantial benefit of our model over other similar models that are guided and terminated by information regarding the final SMG morphology. Hence, our model is suitable for testing the impact of different biological parameters involved with the process of branching morphogenesis in silico, while reducing the requirement of in vivo experiments.

Large Scale Tissue Morphogenesis Simulation on Heterogenous Systems Based on a Flexible Biomechanical Cell Model

The complexity of biological tissue morphogenesis makes in silico simulations of such system very interesting in order to gain a better understanding of the underlying mechanisms ruling the development of multicellular tissues. This complexity is mainly due to two elements: firstly, biological tissues comprise a large amount of cells; secondly, these cells exhibit complex interactions and behaviors. To address these two issues, we propose two tools: the first one is a virtual cell model that comprise two main elements: firstly, a mechanical structure (membrane, cytoskeleton, and cortex) and secondly, the main behaviors exhibited by biological cells, i.e., mitosis, growth, differentiation, molecule consumption, and production as well as the consideration of the physical constraints issued from the environment. An artificial chemistry is also included in the model. This virtual cell model is coupled to an agent-based formalism. The second tool is a simulator that relies on the OpenCL framework. It allows efficient parallel simulations on heterogenous devices such as micro-processors or graphics processors. We present two case studies validating the implementation of our model in our simulator: cellular proliferation controlled by cell signalling and limb growth in a virtual organism.

Buckling along boundaries of elastic contrast as a mechanism for early vertebrate morphogenesis

We have investigated the mechanism of formation of the body of a typical vertebrate, the chicken. We find that the body forms initially by folding at boundaries of stiffness contrast. These boundaries are dynamic lines, separating domains of different cell sizes, that are advected in a deterministic thin-film visco-elastic flow. While initially roughly circular, the lines of elastic contrast form large "peanut" shapes evoking a slender figure-8 at the moment of formation of the animal body, due to deformation and flow in a quadrupolar stretch caused by mesoderm migration. Folding of these "peanut" or "figure-8" motives along the lines of stiffness contrast creates the global pattern of the animal, and segregates several important territories. The main result is that the pattern of cell texture in the embryo serves simultaneously two seemingly different purposes: it regionalizes territories that will differentiate to different cell types and it also locks the folds that physically segregate these territories. This explains how the different cellular types segregate in physically separated domains.

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.

Clarifying tetrapod embryogenesis by a dorso-ventral analysis of the tissue flows during early stages of chicken development

The formation of an animal body remains largely a mystery. It is still not clear whether anything like an organization plan or an "archetype" as coined by Darwin himself, actually exists, or whether animals are organized by a succession of stop-and-go genetic, non-linear, instructions with no global pattern. Nevertheless, it was recognized long ago that the early stages of amniote development consist of large scale rotatory movements over a discoidal blastula (Wetzel, 1924). Such rotatory movements reshuffle a mass inside a finite volume, and thus may have to bear physical conservation laws which contribute to establish the plan of animals in a global fashion. In this article I use dual dorso-ventral imaging of the chicken blastula, to show experimentally that the global movement of early vertebrate embryogenesis is organized with a very simple topology, around and away of a series of hyperbolic points in the vector flow of movement. At the first hyperbolic point, a layer of tissue (the mesoderm) ingresses and moves as a viscous sheet radially. It is found that the sheet flows away with a scaling law for the radius R(t)∼exp(t/τ). Also, the movement of this mesoderm changes the flow on the other layer (the ectoderm) by the principle of action and reaction. By mesoderm wetting the ectoderm, the first hyperbolic point migrates from the anal region, to the umbilical region. The final location of the hyperbolic point defines eventually the central part of the body (the umbilical region). Thus, the formation of the vertebrate body is fixed, as a global movement, by the dynamics of singular points in the visco-elastic flow, governed by mechanical forces within the tissue.