6.3 Two-Phase Models
123
indicates its original position), a bleb is extruded. Bleb expansion is opposed by two
forces: extracellular osmotic pressure and membrane tension. The typical dynamics
of a protrusion is shown in Fig. 6.9d.
Apparently, the earliest simulations of a crawling cell based on the poroelastic
model were carried out by Taber et al (2011), where the same ubiquitous kerocytelike shape, seen on many pictures in this and the preceding sections, were produced.
Lewis et al (2014) applied this model to the dynamics of Physarum polycephalum
plasmodial slime mold (Sect. 5.8). The centerpiece of poroelastic models, the active
contractile force that drives deformation of the cell and the flow of cytosol, was
assumed in this work to be generated by a traveling wave of isotropic contractile
stress that corresponds to the peristaltic propagation mechanism, with waves of
contraction and flow traveling from posterior to anterior along the long axis of
the cell, as observed in the experiment (Matsumoto et al, 2008). The simulated
intracellular 2D flow and traction fields are shown in Fig. 6.10. The cell reshapes
and advances as the flow and traction oscillate.
Polymerization waves, mentioned among promising additional “modules” by
Ziebert and Aranson (2014), were later discussed in detail by Dreher et al (2014) and
Kruse (2016). They related waves of this kind to the dynamics of nucleators of actin
filaments, illustrated in Fig. 6.11a–c. The sequence of images shown in Fig. 6.11d has
been obtained by solving the dynamical equations of actin and nucleators together
with the equation of the phase, velocity, and polarization fields. The cell advances
here in an oscillatory fashion, similar to simulations by Lewis et al (2014), but
this is not the only way it can move. Under different conditions, simulations also
show oscillatory and erratic motion induced by different internal wavy patterns of
polarization and activity.
Fig. 6.11 Illustration of nucleator dynamics. (a) Nucleators (blue) exist in an active state or
are connected to the substrate (grey) by adhesion molecules (black). Inactive nucleators bind
cooperatively to the membrane and thus become activated. (b) Active nucleators generate new actin
filaments (red). (c) Actin filaments feed back on the nucleators and inactivate them. (d) Subsequent
snapshots of a moving cell, showing the polarization, indicated by arrows, and color-coded actin
density increasing from blue to red (Kruse, 2016)
123
indicates its original position), a bleb is extruded. Bleb expansion is opposed by two
forces: extracellular osmotic pressure and membrane tension. The typical dynamics
of a protrusion is shown in Fig. 6.9d.
Apparently, the earliest simulations of a crawling cell based on the poroelastic
model were carried out by Taber et al (2011), where the same ubiquitous kerocytelike shape, seen on many pictures in this and the preceding sections, were produced.
Lewis et al (2014) applied this model to the dynamics of Physarum polycephalum
plasmodial slime mold (Sect. 5.8). The centerpiece of poroelastic models, the active
contractile force that drives deformation of the cell and the flow of cytosol, was
assumed in this work to be generated by a traveling wave of isotropic contractile
stress that corresponds to the peristaltic propagation mechanism, with waves of
contraction and flow traveling from posterior to anterior along the long axis of
the cell, as observed in the experiment (Matsumoto et al, 2008). The simulated
intracellular 2D flow and traction fields are shown in Fig. 6.10. The cell reshapes
and advances as the flow and traction oscillate.
Polymerization waves, mentioned among promising additional “modules” by
Ziebert and Aranson (2014), were later discussed in detail by Dreher et al (2014) and
Kruse (2016). They related waves of this kind to the dynamics of nucleators of actin
filaments, illustrated in Fig. 6.11a–c. The sequence of images shown in Fig. 6.11d has
been obtained by solving the dynamical equations of actin and nucleators together
with the equation of the phase, velocity, and polarization fields. The cell advances
here in an oscillatory fashion, similar to simulations by Lewis et al (2014), but
this is not the only way it can move. Under different conditions, simulations also
show oscillatory and erratic motion induced by different internal wavy patterns of
polarization and activity.
Fig. 6.11 Illustration of nucleator dynamics. (a) Nucleators (blue) exist in an active state or
are connected to the substrate (grey) by adhesion molecules (black). Inactive nucleators bind
cooperatively to the membrane and thus become activated. (b) Active nucleators generate new actin
filaments (red). (c) Actin filaments feed back on the nucleators and inactivate them. (d) Subsequent
snapshots of a moving cell, showing the polarization, indicated by arrows, and color-coded actin
density increasing from blue to red (Kruse, 2016)