Coordination of Cell Differentiation and Migration in Mathematical Models of Caudal Embryonic Axis Extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation

Vortex initiation in a heterogeneous excitable medium

We studied numerically the process of vortex initiation in the heterogeneous active medium which is described by a FitzHugh-Nagumo-type model. Vortex initiation results from interaction of two external stimuli with a stepwise inhomogeneity in refractoriness. The influence of distance between the place of stimulation and heterogeneity and geometrical sizes of the heterogeneity on the process of vortex initiation is examined. The drift and interaction of vortices is also studied

Simulation of Dictyostelium discoideum aggregation via reaction-diffusion model

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Large pulsating waves in a one-dimensional excitable medium

The term ''pulsating wave' has been introduced by Kerner and Osipov for an unmoving wave whose shape changes periodically. Such waves are known to occur in reaction-diffusion systems where stationary waves become unstable. The present paper investigates numerically the properties of pulsating waves in a modified FitzHugh-Nagumo model. In the range of the model parameters the pulsating waves have been shown to appear in the intermediate region between the ones where stationary and propagating waves occur. The mechanisms of the ''pulsations'' are discussed in terms of the wave front and the wave back dynamics