1,302 research outputs found
Confinement by biased velocity jumps: aggregation of Escherichia coli
We investigate a linear kinetic equation derived from a velocity jump process
modelling bacterial chemotaxis in the presence of an external chemical signal
centered at the origin. We prove the existence of a positive equilibrium
distribution with an exponential decay at infinity. We deduce a hypocoercivity
result, namely: the solution of the Cauchy problem converges exponentially fast
towards the stationary state. The strategy follows [J. Dolbeault, C. Mouhot,
and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass,
Trans. AMS 2014]. The novelty here is that the equilibrium does not belong to
the null spaces of the collision operator and of the transport operator. From a
modelling viewpoint it is related to the observation that exponential
confinement is generated by a spatially inhomogeneous bias in the velocity jump
process.Comment: 15 page
Mathematical Modeling of Myosin Induced Bistability of Lamellipodial Fragments
For various cell types and for lamellipodial fragments on flat surfaces,
externally induced and spontaneous transitions between symmetric nonmoving
states and polarized migration have been observed. This behavior is indicative
of bistability of the cytoskeleton dynamics. In this work, the Filament Based
Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum
model for the dynamics of the actin filament network in lamellipodia, is
extended by a new description of actin-myosin interaction. For appropriately
chosen parameter values, the resulting model has bistable dynamics with stable
states showing the qualitative features observed in experiments. This is
demonstrated by numerical simulations and by an analysis of a strongly
simplified version of the FBLM with rigid filaments and planar lamellipodia at
the cell front and rear
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