A model of primitive streak initiation in the chick embryo

The mechanisms underlying primitive streak formation in the chick embryo

Formation of the primitive streak is one of the key events in the early development of amniote embryos. The streak is the site where during gastrulation the mesendoderm cells ingress to take up their correct topographical positions in the embryo. The process of streak formation can be conveniently observed in the chick embryo, where the streak forms as an accumulation of cells in the epiblast in the posterior pole of the embryo and extends subsequently in anterior direction until it covers 80% of the epiblast. A prerequisite for streak formation is the differentiation of mesoderm, which is induced in the epiblast at the interface between the posterior Area Opaca and Area Pellucida in a sickle shaped domain overlying Koller's sickle. Current views on the molecular mechanisms of mesoderm induction by inducing signals from the Area Opaca and inhibitory signals from the hypoblast are briefly discussed. During streak formation the sickle of mesoderm cells transforms into an elongated structure in the central midline of the embryo. We discuss possible cellular mechanisms underlying this process, such as oriented cell division, cell-cell intercalation, chemotactic cell movement in response to attractive and repulsive signals and a combination of chemotaxis and contact following. We review current experimental evidence in favor and against these different hypotheses and outline some the outstanding questions. Since many of the interactions between cells signaling and moving are dynamic and nonlinear in nature they will require detailed modeling and computer simulations to be understood in detail.

Speed of reaction diffusion in embryogenesis

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis.

Using cell potential energy to model the dynamics of adhesive biological cells

Developing a continuous mathematical model of a physical phenomenon which is based on a discrete model of the same system is not straightforward. Yet such a process is useful in illustrating the link between the individual behavior of the elements comprising a system and its macroscopic behavior. Collections of biological cells can exhibit phenomena such as pattern formation, aggregation, and invasion, and mathematics has proven useful in elucidating the underlying dynamics of these phenomena. The continuous models formulated are frequently of reaction-diffusion form, and central to their application is a knowledge of the diffusion coefficient of a collection of the elements comprising the system. Cohen and Murray [J. Math Biol. 12, 237 (1981)] developed a means of deriving this quantity which has since been largely neglected by model developers, and which is based on a knowledge of the potential energy associated with the mutual interaction between the cells. In this work, we begin by deriving the energy of interaction of biological cells modeled as adhesive, deformable spheres. In so doing, we are able to quantify the equilibrium density of a biological cell aggregate, and also obtain a quantitative estimate of the diffusion coefficient of a collection of cells modeled in this way. In so doing, we are able to use experimental data from single-cell studies of the adhesiveness and cell membrane elasticity of a biological cell to derive the diffusion coefficient of a cell mass composed of a collection of identical cells. This allows us to better inform the parameter values used in reaction-diffusion models of biological systems. We go on to apply this technique to a particular situation: modeling the dynamics of a collection of biological cells which experience strong cell-cell adhesion. In so doing, we derive a nonlinear fourth-order partial differential equation to model this system. We conclude by discussing the practical utility of this work in illuminating the link between the microscopic behavior of individual biological cells and the macroscopic behavior of the aggregate to which they give rise, and also by giving some insights into how the modeling of cell-cell adhesion may be treated mathematically.

The hypoblast of the chick embryo positions the primitive streak by antagonizing nodal signaling

The hypoblast (equivalent to the mouse anterior visceral endoderm) of the chick embryo plays a role in regulating embryonic polarity. Surprisingly, hypoblast removal causes multiple embryonic axes to form, suggesting that it emits an inhibitor of axis formation. We show that Cerberus (a multifunctional antagonist of Nodal, Wnt, and BMP signaling) is produced by the hypoblast and inhibits primitive streak formation. This activity is mimicked by Cerberus-Short (CerS), which only inhibits Nodal. Nodal misexpression can initiate an ectopic primitive streak, but only when the hypoblast is removed. We propose that, during normal development, the primitive streak forms only when the hypoblast is displaced away from the posterior margin by the endoblast, which lacks Cerberus.