126
6 Active Gels
Fig. 6.14 Spontaneous emergence of deformation, polarization, and a signaling species in a minimal
interaction model. (a) Scheme of interactions. (b) Bifurcation diagram (see the text for explanations).
(c) Stationary pattern midway through a coarsening sequence (d). Two antiphase snapshots of the
oscillatory pattern (Köpf and Pismen, 2013a)
that causes deformation of the elastic medium. It appears in combination with the
parameter β that quantifies the production of signaling molecules due to deformation.
The parameter α defines the polarization strength. An additional dynamic parameter,
the ratio of characteristic times of the deformation and polarization dynamics, affects
only the domain of oscillatory states, which shrinks as it increases, as the oscillatory
instability locus retreats from the solid to dashed to dotted lines in the diagram.
The oscillatory instability sets in at a certain wavelength, increasing with α, but the
preferred wavelength of the stationary instability is infinite, so the pattern, starting
from an initial perturbation, coarsened with time.
6.5 Modeling Tissues
A tissue can also be viewed as an oriented active gel in the framework of a continuous
approach, abstracting from its cellular structure, upon which we shall concentrate in
the next chapter. This approach is most suitable in the application to epithelial layers,
the most commonly encountered 2D dense cellular assembly, sketched in Fig. 6.15.
6 Active Gels
Fig. 6.14 Spontaneous emergence of deformation, polarization, and a signaling species in a minimal
interaction model. (a) Scheme of interactions. (b) Bifurcation diagram (see the text for explanations).
(c) Stationary pattern midway through a coarsening sequence (d). Two antiphase snapshots of the
oscillatory pattern (Köpf and Pismen, 2013a)
that causes deformation of the elastic medium. It appears in combination with the
parameter β that quantifies the production of signaling molecules due to deformation.
The parameter α defines the polarization strength. An additional dynamic parameter,
the ratio of characteristic times of the deformation and polarization dynamics, affects
only the domain of oscillatory states, which shrinks as it increases, as the oscillatory
instability locus retreats from the solid to dashed to dotted lines in the diagram.
The oscillatory instability sets in at a certain wavelength, increasing with α, but the
preferred wavelength of the stationary instability is infinite, so the pattern, starting
from an initial perturbation, coarsened with time.
6.5 Modeling Tissues
A tissue can also be viewed as an oriented active gel in the framework of a continuous
approach, abstracting from its cellular structure, upon which we shall concentrate in
the next chapter. This approach is most suitable in the application to epithelial layers,
the most commonly encountered 2D dense cellular assembly, sketched in Fig. 6.15.