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A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum

Abstract.

A mechano-chemical model for the spatiotemporal dynamics of free calcium and the thickness in protoplasmic droplets of the true slime mold Physarum polycephalum is derived starting from a physiologically detailed description of intracellular calcium oscillations proposed by Smith and Saldana (Biopys. J. 61, 368 (1992)). First, we have modified the Smith-Saldana model for the temporal calcium dynamics in order to reproduce the experimentally observed phase relation between calcium and mechanical tension oscillations. Then, we formulate a model for spatiotemporal dynamics by adding spatial coupling in the form of calcium diffusion and advection due to calcium-dependent mechanical contraction. In another step, the resulting reaction-diffusion model with mechanical coupling is simplified to a reaction-diffusion model with global coupling that approximates the mechanical part. We perform a bifurcation analysis of the local dynamics and observe a Hopf bifurcation upon increase of a biochemical activity parameter. The corresponding reaction-diffusion model with global coupling shows regular and chaotic spatiotemporal behaviour for parameters with oscillatory dynamics. In addition, we show that the global coupling leads to a long-wavelength instability even for parameters where the local dynamics possesses a stable spatially homogeneous steady state. This instability causes standing waves with a wavelength of twice the system size in one dimension. Simulations of the model in two dimensions are found to exhibit defect-mediated turbulence as well as various types of spiral wave patterns in qualitative agreement with earlier experimental observation by Takagi and Ueda (Physica D, 237, 420 (2008)).

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Correspondence to M. Radszuweit, H. Engel or M. Bär.

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Radszuweit, M., Engel, H. & Bär, M. A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum. Eur. Phys. J. Spec. Top. 191, 159–172 (2010). https://doi.org/10.1140/epjst/e2010-01348-2

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Keywords

  • European Physical Journal Special Topic
  • Linear Stability Analysis
  • Mechanical Part
  • Spatiotemporal Dynamic
  • Physarum Polycephalum