6.4 Mechanics of Tissues
97
(lower, or inner) side (Fig. 6.12, top). Each cell contains a network of contractile microfilaments anchored to the plasma membrane (Sect. 5.4), and stressing them close
to the apical surface will produce the desired effect. Odell et al (1981) constructed a
mechanical model of this action – but of course, a chemical signal would be needed
to trigger it. A sheet of cells can also be folded by a programmed death (apoptosis) of cells at a certain location driving its neighbors down (Fig. 6.12, bottom). A
two-dimensional view in the right panel (Monier et al, 2015) shows the anisotropy
developing near the fold, with the cells elongating parallel to its direction.
The arrangement and motion of cells are correlated with their polarity. This term,
while having a definite meaning in physics, is loosely interpreted by biologists,
sometimes just relating to elongation in a certain direction. There are two kinds
of polarization: vector, visualized as an arrow pointing in a certain direction, and
nematic, lacking an arrowhead and therefore invariant under rotation by 180 rather
than 360 degrees (Sect. 3.3). Planar nematic polarisation can be associated with
anisotropy of tissues, and, indeed, disruption of a uniform planar polarization 5 produces kugel (German for “sphere” or “ball”) mutants instead of native elongated
forms (Gutzeit, 1990). Like everything else, polarity is driven genetically through
signaling (de la Loza and Thompson, 2017). In chimeric forms containing both polarizable and mutant cells, this has the character of a phase transition when the
fraction of mutant cells exceeds a certain limit (Viktorinova et al, 2011).
Fig. 6.12 Top: Invagination by apical constriction. Bottom: Folding of an epithelial shell due to
apoptosis: side view on the left and a view from above on the right. Shading indicates the anisotropy
of the cells
5 A uniform polarization of a closed shell is topologically impossible, as it must contain defects –
but a “meridional” alignment with two aster defects at the opposite ends can be viewed as perfectly
ordered for all practical purposes.
97
(lower, or inner) side (Fig. 6.12, top). Each cell contains a network of contractile microfilaments anchored to the plasma membrane (Sect. 5.4), and stressing them close
to the apical surface will produce the desired effect. Odell et al (1981) constructed a
mechanical model of this action – but of course, a chemical signal would be needed
to trigger it. A sheet of cells can also be folded by a programmed death (apoptosis) of cells at a certain location driving its neighbors down (Fig. 6.12, bottom). A
two-dimensional view in the right panel (Monier et al, 2015) shows the anisotropy
developing near the fold, with the cells elongating parallel to its direction.
The arrangement and motion of cells are correlated with their polarity. This term,
while having a definite meaning in physics, is loosely interpreted by biologists,
sometimes just relating to elongation in a certain direction. There are two kinds
of polarization: vector, visualized as an arrow pointing in a certain direction, and
nematic, lacking an arrowhead and therefore invariant under rotation by 180 rather
than 360 degrees (Sect. 3.3). Planar nematic polarisation can be associated with
anisotropy of tissues, and, indeed, disruption of a uniform planar polarization 5 produces kugel (German for “sphere” or “ball”) mutants instead of native elongated
forms (Gutzeit, 1990). Like everything else, polarity is driven genetically through
signaling (de la Loza and Thompson, 2017). In chimeric forms containing both polarizable and mutant cells, this has the character of a phase transition when the
fraction of mutant cells exceeds a certain limit (Viktorinova et al, 2011).
Fig. 6.12 Top: Invagination by apical constriction. Bottom: Folding of an epithelial shell due to
apoptosis: side view on the left and a view from above on the right. Shading indicates the anisotropy
of the cells
5 A uniform polarization of a closed shell is topologically impossible, as it must contain defects –
but a “meridional” alignment with two aster defects at the opposite ends can be viewed as perfectly
ordered for all practical purposes.