We present an analytical model of the cell actin cytoskeleton as a finite droplet of polar active matter. Using hydrodynamic theory, we calculate the steady state flows that result from a splayed polarisation of the actin filaments. We relate this to a spherical cell embedded in a 3D environment by imposing a viscous friction at the fixed droplet boundary. We  show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, our model describes a simple mechanism for cell motility in a 3D environment  . Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation.
We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for the interaction with an arbitrary external medium by imposing a viscous friction at the fixed droplet boundary. We then show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, this calculation describes a simple mechanism for the motility of a droplet of active contractile fluid embedded in a 3D environment , which is relevant to cell migration in confinement (for example, embedded within a gel or tissue) . Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation.
R
an
a continuum level
R
the cell actin cytoskeleton as a finite droplet of polar active matter. Using hydrodynamic theory, we
a droplet of active contractile fluid consisting of filaments and motors. We
D
actin
R
relate this to a spherical cell embedded in a 3D environment
account for the interaction with an arbitrary external medium
A
then
R
our model
this calculation
R
cell motility
the motility of a droplet of active contractile fluid embedded
A
, which is relevant to cell migration in confinement (for example, embedded within a gel or tissue)