An elasto-plastic model of avian gastrulation

A biaxial tensional model for early vertebrate morphogenesis

We propose a simple biaxial tensional model which is able to reproduce at a qualitative level several aspects of early stages of vertebrate morphogenesis. The model is based on subsequent excitable contractions of an orthoradial and periclinal (radial) set of contracting lines, which generate first the basic embryonic pattern (a motile tube), and second the lateral orifices such as ears, eyes, mouth, gills, etc. An important aspect of the model is the self-arresting character of the process, akin to wound healing. At later stages, the biaxial lines may also work in extension, and this generates a developmental feedback which is quadratic with respect to curvature.

Second-order division in sectors as a prepattern for sensory organs in vertebrate development

We present in vivo observations of chicken embryo development which show that the early chicken embryo presents a principal structure made out of concentric rings and a secondary structure composed of radial sectors. During development, physical forces deform the main rings into axially directed, antero-posterior tubes, while the sectors roll up to form cylinders that are perpendicular to the antero-posterior axis. As a consequence, the basic structure of the chicken embryo is a series of encased antero-posterior tubes (gut, neural tube, body envelope, amnion, chorion) decorated with smaller orifices (ear duct, eye stalk, nasal duct, gills, mouth) forming at right angles to the main body axis. We argue that the second-order divisions reflect the early pattern of cell cleavage, and that the transformation of radial and orthoradial lines into a body with sensory organs is a generic biophysical mechanism more general than the chicken embryo.

A tensile ring drives tissue flows to shape the gastrulating amniote embryo

Tissue morphogenesis is driven by local cellular deformations that are powered by contractile actomyosin networks. How localized forces are transmitted across tissues to shape them at a mesoscopic scale is still unclear. Analyzing gastrulation in entire avian embryos, we show that it is driven by the graded contraction of a large-scale supracellular actomyosin ring at the margin between the embryonic and extraembryonic territories. The propagation of these forces is enabled by a fluid-like response of the epithelial embryonic disk, which depends on cell division. A simple model of fluid motion entrained by a tensile ring quantitatively captures the vortex-like "polonaise" movements that accompany the formation of the primitive streak. The geometry of the early embryo thus arises from the transmission of active forces generated along its boundary.

Electrical stimulation of developmental forces reveals the mechanism of limb formation in vertebrate embryos

Current knowledge on limbs development lacks a physical description of the forces leading to formation of the limbs precursors or "buds". Earlier stages of development are driven by large scale morphogenetic movements, such as dipolar vortical flows and mechanical buckling, pulled by rings of cells. It is a natural hypothesis that similar phenomena occur during limb formation. However it is difficult to experiment on the developmental forces, in such a complex dynamic system. Here, we report a physical study of hindlimb bud formation in the chicken embryo. We use electrical stimulation to enhance the physical forces present in the tissue, prior to limb bud formation. By triggering the physical forces in a rapid and amplified pattern, we reveal the mechanism of formation of the hindlimbs: the early presumptive embryonic territory is composed of a set of rings encased like Russian dolls. Each ring constricts in an excitable pattern of force, and the limb buds are generated by folding at a pre-existing boundary between two rings, forming the dorsal and ventral ectoderms. The amniotic sac buckles at another boundary. Physiologically, the actuator of the excitable force is the tail bud pushing posteriorly along the median axis. The developmental dynamics suggests how animals may evolve by modification of the magnitude of these forces, within a common broken symmetry. On a practical level, localized electrical stimulation of morphogenetic forces opens the way to in vivo electrical engineering of tissues.

Physics of amniote formation

We present a detailed study of the formation of the amniotic sac in the avian embryo, and a comparison with the crocodile amniotic sac. We show that the amniotic sac forms at a circular line of stiffness contrast, separating rings of cell domains. Cells align at this boundary, and this in turn orients and concentrates the tension forces. The tissue fold which forms the amniotic sac is locked exactly along this line due to the colocalization of the stiffness contrast and of the tensile force. In addition, the tensile force plays a regenerative role when the amniotic sac is cut. The fold forming the ventral side of the embryo displays the same characteristics. This work shows that amniote embryogenesis consists of a cascade of buckling events taking place at the boundaries between regions of differing mechanical properties. Hence, amniote embryogenesis relies on a simple and robust biomechanical scheme used repeatedly, and selected ancestrally.

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.

Can physics help to explain embryonic development? An overview

Recent technical advances including digital imaging and particle image velocimetry can be used to extract the full range of embryonic movements that constitute the instantaneous 'morphogenetic fields' of a developing animal. The final shape of the animal results from the sum over time (integral) of the movements that make up the velocity fields of all the tissue constituents. In vivo microscopy can be used to capture the details of vertebrate development at the earliest embryonic stages. The movements thus observed can be quantitatively compared to physical models that provide velocity fields based on simple hypotheses about the nature of living matter (a visco-elastic gel). This approach has cast new light on the interpretation of embryonic movement, folding, and organisation. It has established that several major discontinuities in development are simple physical changes in boundary conditions. In other words, with no change in biology, the physical consequences of collisions between folds largely explain the morphogenesis of the major structures (such as the head). Other discontinuities result from changes in physical conditions, such as bifurcations (changes in physical behaviour beyond specific yield points). For instance, beyond a certain level of stress, a tissue folds, without any new gene being involved. An understanding of the physical features of movement provides insights into the levers that drive evolution; the origin of animals is seen more clearly when viewed under the light of the fundamental physical laws (Newton's principle, action-reaction law, changes in symmetry breaking scale). This article describes the genesis of a vertebrate embryo from the shapeless stage (round mass of tissue) to the development of a small, elongated, bilaterally symmetric structure containing vertebral precursors, hip and shoulder enlarges, and a head.

Development, triploblastism, physics of wetting and the Cambrian explosion

The Cambrian explosion is characterized by the sudden outburst of organized animal plans, which occurred circa 530 M years ago. Around that time, many forms of animal life appeared, including several which have since disappeared. There is no general consensus about "why" this happened, and why it had any form of suddenness. However, all organized animal plans share a common feature: they are triploblastic, i.e., composed of 3 layers of tissue, endoderm, ectoderm and mesoderm. I show here that, within simple hypotheses, the formation of the mesoderm has intrinsically a physical exponential dynamics, leading rapidly to triploblastism, and eventually, to animal formation. A novel physico-mathematical framework including epithelium-mesenchyme transition, visco-elastic constitutive equations, and conservation laws, is presented which allows one to describe gastrulation as a self-wetting phenomenon of a soft solid onto itself. This phenomenon couples differentiation and migration during gastrulation, and leads in a closed form to an exponential scaling law for the formation of the mesoderm. Therefore, the Cambrian explosion might have started, actually, by a true viscoelastic "explosion": the exponential run-away of mesenchymal cells.

The Textural Aspects of Vessel Formation during Embryo Development and Their Relation to Gastrulation Movements

We have investigated the microscopic physical inhomogeneity ("texture") of the avian embryo in vivo by shadowgraph. This noninvasive technique allows one to correlate the shape of blood vessels to the physical, micro-structural, pattern that exists in the embryo prior to vessel appearance. Before any vessel forms, vascular paths are present and are prepatterned, by fields of cellular orientations and lumen anisotropies. We find the origin of this prepattern in the movements of the embryo during gastrulation, and the related deformation and force field, which establish both the animal and vascular pattern.

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.

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

The morphogenesis of vertebrate body parts remains an open question. It is not clear whether the existence of different structures, such as a head, can be addressed by fundamental laws of tissue movement and deformation, or whether they are only a sequence of stop-and-go genetic instructions. I have filmed by time-lapse microscopy the formation of the presumptive head territory in chicken embryos. I show that the early lateral evagination of the eye cups and of the mesencephalic plate is a consequence of a sudden change in boundary conditions of the initial cell flow occurring in these embryos. Due to tissue flow, and collision of the two halves of the embryo, the tissue sheet movement is first dipolar, and next quadrupolar. In vivo air puff tonometry reveals a simple visco-elastic behaviour of the living material. The jump from a dipolar to a quadrupolar flow changes the topology of the early morphogenetic field which is observed towards a complex vortex winding with a trail (the eye cups and brain folds). The hydrodynamical model accounts for the discontinuity of the vector field at the moment of collision of the left and right halves of the embryo, at a quantitative level. This suggests a possible mechanism for the morphogenesis of the head of amniotes, as compared to cephalochordates and anamniotes.

Introducing the scanning air puff tonometer for biological studies

It is getting increasingly evident that physical properties such as elastoviscoplastic properties of living materials are quite important for the process of tissue development, including regulation of genetic pathways. Measuring such properties in vivo is a complicated and challenging task. In this paper, we present an instrument, a scanning air puff tonometer, which is able to map point by point the viscoelastic properties of flat or gently curved soft materials. This instrument is an improved version of the air puff tonometer used by optometrists, with important modifications. The instrument allows one to obtain a direct insight into gradients of material properties in vivo. The instrument capabilities are demonstrated on substances with known elastoviscoplastic properties and several biological objects. On the basis of the results obtained, the role of the gradients of elastoviscoplastic properties is outlined for the process of angiogenesis, limb development, bacterial colonies expansion, etc. which is important for bridging the gaps in the theory of the tissue development and highlighting new possibilities for tissue engineering, based on a clarification of the role of physical features in developing biological material.

Who moves whom during primitive streak formation in the chick embryo

Gastrulation is a critical stage in the development of all vertebrates. During gastrulation mesendoderm cells move inside the embryo to form the gut, muscles, and skeleton. In amniotes the mesendoderm cells move inside the embryo through a structure known as the primitive streak, extending from the posterior pole anterior through the midline of the embryo. Primitive streak formation involves large scale cell flows of a layer of highly polarized epithelial epiblast cells. The epiblast is separated from a lower layer of hypoblast cells through a well developed basal lamina. Recent experiments in which in vivo extracellular matrix dynamics was followed via labeling with fibronectin specific fluorescent antibodies and time-lapse microscopy have suggested that extracellular matrix dynamics essentially coincides with the observed epiblast cell displacements (Zamir et al., 2008, PLoS Biol 6, e247). These observations raise the important question of who moves whom and where do cells derive traction. We discuss these matters and their implications for our understanding of the mechanisms underlying cell flows during primitive streak formation in the chick embryo.

During vertebrate development, arteries exert a morphological control over the venous pattern through physical factors

The adult vasculature is comprised of three distinct compartments: the arteries, which carry blood away from the heart and display a divergent flow pattern; the capillaries, where oxygen and nutrient delivery from blood to tissues, as well as metabolic waste removal, occurs; and the veins, which carry blood back to the heart and are characterized by a convergent flow pattern. These compartments are organized in series as regard to flow, which proceeds from the upstream arteries to the downstream veins through the capillaries. However, the spatial organization is more complex, as veins may often be found paralleling the arteries. The factors that control the morphogenesis of this hierarchically branched vascular network are not well characterized. Here, we explain how arteries exert a morphological control on the venous pattern. Indeed, during vertebrate development, the following transition may be observed in the spatial organization of the vascular system: veins first develop in series with the arteries, the arterial and venous territories being clearly distinct in space (cis-cis configuration). But after some time, new veins grow parallel to the existing arteries, and the arterial and venous territories become overlapped, with extensive and complex intercalation and interdigitation. Using physical arguments, backed up by experimental evidence (biological data from the literature and in situ optical and mechanical measurements of the chick embryo yolk-sac and midbrain developing vasculatures), we explain how such a transition is possible and why it may be expected with generality, as organisms grow. The origin of this transition lies in the remodeling of the capillary tissue in the vicinity of the growing arteries. This remodeling lays down a prepattern for further venous growth, parallel to the existing arterial pattern. Accounting for the influence of tissue growth, we show that this prepatterned path becomes favored as the body extends. As a consequence, a second flow route with veins paralleling the arteries (cis-trans configuration) emerges when the tissue extends. Between the cis-cis and cis-trans configurations, all configurations are in principle possible, and self-organization of the vessels contributes to determining their exact pattern. However, the global aspect depends on the size at which the growth stops and on the growth rate.

Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts ("dead ends"), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.