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

Abstract

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.

Numerical modeling of cell differentiation and proliferation in force-induced substrates via encapsulated magnetic nanoparticles

“…Cells may respond to the mechanical properties of their ECM, such as substrate stiffness, by differentiation, proliferation and/or apoptosis [22,23,31,67]. Experiments demonstrate that a specific deformation range sensed by a cell leads to a specific differentiation [10,34,69].…”

“…To avoid such abnormal conditions, cells have to be particularized in such a way as to differentiate or proliferate in response to appropriate biological stimuli. Experiments have shown that, besides other factors [58,59], the mechanical structure of cellular micro-environments plays an important role in cell differentiation and proliferation [22,23,31,67]. For instance, Mesenchymal Stem Cells (MSCs) differentiate into specific phenotypes with high sensitivity to the tissue rigidity where they reside in.…”

Computational Modeling of Stem Cell Migration: A Mini Review

“…The FGF-8-induced chemotaxis that characterizes caudal undifferentiated cells was predicted using an equation for chemotactic energy (hybrid model) or a diffusive gradient. 25 This model has the potential to be extended to understand other developmental processes displaying a similar mode of axis extension coupled to cell differentiation. Another example of a model taking into account differentiation quantifies diverse aspects involved in the progression of bone healing for moderate fracture gap sizes and fracture stability.…”

Mathematical modelling in developmental biology

“…A number of mathematical studies have addressed the formation of gradients in the absence of morphogen diffusion, for example due to proliferation (Ibanes et al 2006, Chisholm et al 2010 or migration (Harrison et al 2011) of cells. Non-diffusive patterning mechanisms can be provided by direct contacts between cells, of which the classical example is Delta-Notch signalling associated with the binding of non-diffusive Delta to the Notch receptor of neighbouring cells (Collier et al 1996).…”

“…Furthermore, the movement of cells can, in turn, be affected by morphogen concentrations, for example if the movement is chemotactic and morphogens act as chemotactic agents. These possibilities have recently been explored in studies combining mathematical modelling and experiments (Vasiev et al 2010, Harrison et al 2011.…”