114
6 Active Gels
By writing down generic equations in the hydrodynamic limit, one has replaced a hundred
thousand variables by only a few in a field theory. From our experience in soft condensed
matter, one can infer that the space of solutions is still large enough to describe most
experimental situations within a unified framework.
As we shall see, the problem with this space of solutions might be the opposite: within
its range of applicability, it may be so large that the same experimental situation can
be described in different ways.
The unified framework of the active gel theory extends the theory of orientationally ordered active fluids (Sect. 2.5), retaining polarization equations derived, as
before, by varying the appropriate energy functional, and replacing the Stokes equation of a viscous fluid by viscoelastic transport equations. Numerous coefficients of
the theory, including mechanical and orientational elasticities, viscosity, and activity,
have to be obtained from experimental data. The effective mechanical elasticity of
living tissues is feeble; hence the term gel. The elasticity of a network including stiff
polymers may be highly anisotropic.
Fig. 6.1 Magnetic beads embedded in an actin network. Crosslinker proteins are shown by red dots
(Bausch and Kroy, 2006)
The actin network behaves as an
elastic solid on short timescales, and
as a liquid on longer time intervals; the
characteristic relaxation time may vary
in different cells from tenths to tens
of seconds (Mogilner and Manhart,
2018). Viscous and elastic response
can be distinguished, for example, by
the frequency dependence of the displacement of imbedded magnetic particles in microrheological measurements (Fig. 6.1). A fine example is the
extraction of the physical parameters
of the actomyosin cortical layer in vivo
from laser ablation experiments with
embryonic cells (Saha et al, 2016).
However, different methods and procedures, including whole-cell deformation, beadbased measurements, atomic force microscopy, and more, as reviewed by Wu et al
(2018), lead to different results, which may be more or less relevant in a particular
situation.
Since the medium is anisotropic, both mechanical and orientational elastic coefficients, as well as viscosity, are, generally, expressed by fourth-rank tensors, and their
full characterization is practically unavailable, as already mentioned in Sect. 2.5.
The momentum conservation equations include activity, which generally depends
on the underlying chemistry. The mechanical balance equations necessarily include
pressure, although, as mentioned in Sect. 1.3 and illustrated by Fig. 1.7, pressure is
not a well-defined variable in active systems (Solon, Fily, et al, 2015).
While keeping in mind these drawbacks, we have to be aware that no feasible
alternative exists, save for following all microscopic motions, which would not be
6 Active Gels
By writing down generic equations in the hydrodynamic limit, one has replaced a hundred
thousand variables by only a few in a field theory. From our experience in soft condensed
matter, one can infer that the space of solutions is still large enough to describe most
experimental situations within a unified framework.
As we shall see, the problem with this space of solutions might be the opposite: within
its range of applicability, it may be so large that the same experimental situation can
be described in different ways.
The unified framework of the active gel theory extends the theory of orientationally ordered active fluids (Sect. 2.5), retaining polarization equations derived, as
before, by varying the appropriate energy functional, and replacing the Stokes equation of a viscous fluid by viscoelastic transport equations. Numerous coefficients of
the theory, including mechanical and orientational elasticities, viscosity, and activity,
have to be obtained from experimental data. The effective mechanical elasticity of
living tissues is feeble; hence the term gel. The elasticity of a network including stiff
polymers may be highly anisotropic.
Fig. 6.1 Magnetic beads embedded in an actin network. Crosslinker proteins are shown by red dots
(Bausch and Kroy, 2006)
The actin network behaves as an
elastic solid on short timescales, and
as a liquid on longer time intervals; the
characteristic relaxation time may vary
in different cells from tenths to tens
of seconds (Mogilner and Manhart,
2018). Viscous and elastic response
can be distinguished, for example, by
the frequency dependence of the displacement of imbedded magnetic particles in microrheological measurements (Fig. 6.1). A fine example is the
extraction of the physical parameters
of the actomyosin cortical layer in vivo
from laser ablation experiments with
embryonic cells (Saha et al, 2016).
However, different methods and procedures, including whole-cell deformation, beadbased measurements, atomic force microscopy, and more, as reviewed by Wu et al
(2018), lead to different results, which may be more or less relevant in a particular
situation.
Since the medium is anisotropic, both mechanical and orientational elastic coefficients, as well as viscosity, are, generally, expressed by fourth-rank tensors, and their
full characterization is practically unavailable, as already mentioned in Sect. 2.5.
The momentum conservation equations include activity, which generally depends
on the underlying chemistry. The mechanical balance equations necessarily include
pressure, although, as mentioned in Sect. 1.3 and illustrated by Fig. 1.7, pressure is
not a well-defined variable in active systems (Solon, Fily, et al, 2015).
While keeping in mind these drawbacks, we have to be aware that no feasible
alternative exists, save for following all microscopic motions, which would not be