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Poroelastic two-phase model for droplets of Physarum polycephalum with free boundaries


Motivated by recent experiments, we model the flow-driven amoeboid motility that is ex-
hibited by protoplasmic droplets of Physarum [1].  Here, a feedback loop between a chemical
regulator,  active mechanical deformations,  and induced flows give rise to spatio-temporal
contraction patterns that result in directed motion.  Our model describes the droplet’s cy-
toskeleton as an active viscoelastic solid phase that is permeated by a passive viscous fluid
representing the cytosol.  The active tension in the solid phase depends on the concentra-
tion of a regulating agent that is advected by the fluid phase.  Previously, it was shown that
under rigid boundary conditions that impose a fixed shape, this model reproduces a large
variety of mechano-chemical patterns such as antiphase oscillations and rotating spirals [2].
This in line with experimental observations of contraction patterns in these droplets.  Here,
we present an approach that includes free boundary conditions, nonlinear friction between
droplet and substrate and a nonlinear reaction kinetic for the regulator to model the move-
ment of these droplets.  We find deformations of the droplet boundary as well as oscillatory
changes in the droplets position with a net motion in each cycle.

[1]  Zhang, Shun and Guy, Robert and Lasheras, Juan Carlos and del Alamo, Juan C. (2017). Self-Organized Mechano-Chemical Dynamics in Amoeboid Locomotion of Physarum Fragments, Journal of Physics D: Applied Physics.
[2]  Radszuweit, Markus and Engel, Harald and B ̈ar, Markus (2014). An Active Poroelastic Model for Mechanochemical Patterns in Protoplasmic Droplets of Physarum Polycephalum, PLoS ONE 9.

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