15 research outputs found
Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit
This letter is concerned with asymptotic analysis of a PDE model for motility
of a eukaryotic cell on a substrate. This model was introduced in [1], where it
was shown numerically that it successfully reproduces experimentally observed
phenomena of cell-motility such as a discontinuous onset of motion and shape
oscillations. The model consists of a parabolic PDE for a scalar phase-field
function coupled with a vectorial parabolic PDE for the actin filament network
(cytoskeleton). We formally derive the sharp interface limit (SIL), which
describes the motion of the cell membrane and show that it is a volume
preserving curvature driven motion with an additional nonlinear term due to
adhesion to the substrate and protrusion by the cytoskeleton. In a 1D model
problem we rigorously justify the SIL, and, using numerical simulations,
observe some surprising features such as discontinuity of interface velocities
and hysteresis. We show that nontrivial traveling wave solutions appear when
the key physical parameter exceeds a certain critical value and the potential
in the equation for phase field function possesses certain asymmetry.Comment: 7 pages, 3 figure
Effective Rheological Properties in Semidilute Bacterial Suspensions
Interactions between swimming bacteria have led to remarkable experimentally
observable macroscopic properties such as the reduction of the effective
viscosity, enhanced mixing, and diffusion. In this work, we study an individual
based model for a suspension of interacting point dipoles representing bacteria
in order to gain greater insight into the physical mechanisms responsible for
the drastic reduction in the effective viscosity. In particular, asymptotic
analysis is carried out on the corresponding kinetic equation governing the
distribution of bacteria orientations. This allows one to derive an explicit
asymptotic formula for the effective viscosity of the bacterial suspension in
the limit of bacterium non-sphericity. The results show good qualitative
agreement with numerical simulations and previous experimental observations.
Finally, we justify our approach by proving existence, uniqueness, and
regularity properties for this kinetic PDE model
Flagella bending affects macroscopic properties of bacterial suspensions
To survive in harsh conditions, motile bacteria swim in complex environment
and respond to the surrounding flow. Here we develop a PDE model describing how
the flagella bending affects macroscopic properties of bacterial suspensions.
First, we show how the flagella bending contributes to the decrease of the
effective viscosity observed in dilute suspension. Our results do not impose
tumbling (random re-orientation) as it was done previously to explain the
viscosity reduction. Second, we demonstrate a possibility of bacterium escape
from the wall entrapment due to the self-induced buckling of flagella. Our
results shed light on the role of flexible bacterial flagella in interactions
of bacteria with shear flow and walls or obstacles