title: An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum.
abstract: Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.
authors.affiliation: Weierstraβ-Institut für Angewandte Analysis und Stochastik, Leibniz-Institut im Forschungsverbund Berlin e. V., Berlin, Germany; Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany; Physikalisch-Technische Bundesanstalt, Berlin, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Radszuweit
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.
authors.forename: Harald
authors.initials: H
authors.lastname: Engel
authors.affiliation: Physikalisch-Technische Bundesanstalt, Berlin, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Bär
mesh_terms: D001696:Biomechanical Phenomena; D002118:Calcium / Q000378:metabolism; D003593:Cytoplasm / Q000502:physiology*; D003599:Cytoskeleton / Q000502:physiology*; D004548:Elasticity; D008954:Models, Biological; D016839:Physarum polycephalum / Q000166:cytology* / Q000502:physiology*; D013314:Stress, Mechanical
chemical_list: D002118:Calcium