Limits...
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.


Related in: MedlinePlus

Human melanocytic cells (primary tumour) were plated on 33 cm2 Petri dish with at the center a disk (32 mm2) at confluence.The day after, the disk was removed and cells were allowed to keep migrating and dividing, before they were fixed with 3.7% paraformaldeide and stained with hematoxillin/eosin solution, at different times. On top, typical experiment, at two different times, on bottom, details from the same images with X5 magnification, compared to the top (Leica MZFLIII mounted with a camera Leica DFC320). Observe the diffuse front and an increase of noise after 4 days. From publication12 with permission.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5037363&req=5

f1: Human melanocytic cells (primary tumour) were plated on 33 cm2 Petri dish with at the center a disk (32 mm2) at confluence.The day after, the disk was removed and cells were allowed to keep migrating and dividing, before they were fixed with 3.7% paraformaldeide and stained with hematoxillin/eosin solution, at different times. On top, typical experiment, at two different times, on bottom, details from the same images with X5 magnification, compared to the top (Leica MZFLIII mounted with a camera Leica DFC320). Observe the diffuse front and an increase of noise after 4 days. From publication12 with permission.

Mentions: Recently moving epithelium on a substrate has motivated many experimental12 and numerical works23 with the main aim to understand the collective migration of cell sheets occurring during development, inflammation, wound-healing4567 or tumour metastasis89. Consideration of the movement of several thousand cells in a tissue of constant thickness can explain the mechanism of cell communication and migration. Intercellular interactions and substrate adhesion10, i.e mechanical forces, together with sensitivity to biochemical signals11 are responsible for these phenomena. One may argue that the importance of these morphogenetic signals depends on the experimental context, some cells being more chemotactic than others. However, in physiological conditions, chemotaxis cannot be ignored, e.g. as in the wound-healing process: Just after injury4, a battery of morphogens originating from the immune system organizes the migration of several connected cell layers of the basal epithelium. In particular, it has been recognized that cells can produce their own chemoattractant, as melanocytic cells. For these cancerous cells, it is a way to escape the tumour and undergo metastasis9. As shown in Fig. 1, in the circular geometry12, in vitro advancing epithelium of melanocytic cells exhibits simultaneously a noisy front and a diffuse interface, which strongly suggests the local production of chemo-attractants.


Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia
Human melanocytic cells (primary tumour) were plated on 33 cm2 Petri dish with at the center a disk (32 mm2) at confluence.The day after, the disk was removed and cells were allowed to keep migrating and dividing, before they were fixed with 3.7% paraformaldeide and stained with hematoxillin/eosin solution, at different times. On top, typical experiment, at two different times, on bottom, details from the same images with X5 magnification, compared to the top (Leica MZFLIII mounted with a camera Leica DFC320). Observe the diffuse front and an increase of noise after 4 days. From publication12 with permission.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Human melanocytic cells (primary tumour) were plated on 33 cm2 Petri dish with at the center a disk (32 mm2) at confluence.The day after, the disk was removed and cells were allowed to keep migrating and dividing, before they were fixed with 3.7% paraformaldeide and stained with hematoxillin/eosin solution, at different times. On top, typical experiment, at two different times, on bottom, details from the same images with X5 magnification, compared to the top (Leica MZFLIII mounted with a camera Leica DFC320). Observe the diffuse front and an increase of noise after 4 days. From publication12 with permission.
Mentions: Recently moving epithelium on a substrate has motivated many experimental12 and numerical works23 with the main aim to understand the collective migration of cell sheets occurring during development, inflammation, wound-healing4567 or tumour metastasis89. Consideration of the movement of several thousand cells in a tissue of constant thickness can explain the mechanism of cell communication and migration. Intercellular interactions and substrate adhesion10, i.e mechanical forces, together with sensitivity to biochemical signals11 are responsible for these phenomena. One may argue that the importance of these morphogenetic signals depends on the experimental context, some cells being more chemotactic than others. However, in physiological conditions, chemotaxis cannot be ignored, e.g. as in the wound-healing process: Just after injury4, a battery of morphogens originating from the immune system organizes the migration of several connected cell layers of the basal epithelium. In particular, it has been recognized that cells can produce their own chemoattractant, as melanocytic cells. For these cancerous cells, it is a way to escape the tumour and undergo metastasis9. As shown in Fig. 1, in the circular geometry12, in vitro advancing epithelium of melanocytic cells exhibits simultaneously a noisy front and a diffuse interface, which strongly suggests the local production of chemo-attractants.

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.


Related in: MedlinePlus