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Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

View Article: PubMed Central - PubMed

ABSTRACT

We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

No MeSH data available.


The three steps of leading edge evolution as the auto-chemotactif gradients increase.In grey, the cell sheet (Ωe), in colours, the bath of water and nutrients (Ωw). From left to right, a steady front with constant velocity, a wavy front at threshold of stability, then the spatio-dynamical pattern.
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f2: The three steps of leading edge evolution as the auto-chemotactif gradients increase.In grey, the cell sheet (Ωe), in colours, the bath of water and nutrients (Ωw). From left to right, a steady front with constant velocity, a wavy front at threshold of stability, then the spatio-dynamical pattern.

Mentions: A theoretical model is proposed to investigate the dynamics of a cellular sheet, controlled by auto-chemotactic gradients and cellular proliferation. A front separates the experimental cells into two domains Ωe (the epithelium) and Ωw (the water and nutrients), as shown in Fig. 2. Physical quantities characterizing the front, such as velocity, stress repartition, stochastic and spatio-temporal patterns, will be predicted with a minimal set of parameters according to the following strategy: steady leading edge dynamics, stochastic and wavy edge, spatio-temporal front, (see the three schemes of Fig. 2). Among the three scenarios, from left to right, there is an increase of the chemotactic gradients which controls the evolution: first an advancing linear epithelium edge with constant velocity, second a wavy edge, also advancing with constant velocity, then above the stability limit, a spatio-temporal pattern.


Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia
The three steps of leading edge evolution as the auto-chemotactif gradients increase.In grey, the cell sheet (Ωe), in colours, the bath of water and nutrients (Ωw). From left to right, a steady front with constant velocity, a wavy front at threshold of stability, then the spatio-dynamical pattern.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037363&req=5

f2: The three steps of leading edge evolution as the auto-chemotactif gradients increase.In grey, the cell sheet (Ωe), in colours, the bath of water and nutrients (Ωw). From left to right, a steady front with constant velocity, a wavy front at threshold of stability, then the spatio-dynamical pattern.
Mentions: A theoretical model is proposed to investigate the dynamics of a cellular sheet, controlled by auto-chemotactic gradients and cellular proliferation. A front separates the experimental cells into two domains Ωe (the epithelium) and Ωw (the water and nutrients), as shown in Fig. 2. Physical quantities characterizing the front, such as velocity, stress repartition, stochastic and spatio-temporal patterns, will be predicted with a minimal set of parameters according to the following strategy: steady leading edge dynamics, stochastic and wavy edge, spatio-temporal front, (see the three schemes of Fig. 2). Among the three scenarios, from left to right, there is an increase of the chemotactic gradients which controls the evolution: first an advancing linear epithelium edge with constant velocity, second a wavy edge, also advancing with constant velocity, then above the stability limit, a spatio-temporal pattern.

View Article: PubMed Central - PubMed

ABSTRACT

We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

No MeSH data available.