| Zugriffsnummer | 25920 |
| Dokumenttyp | Zeitschriftenartikel |
| Peer Review | unbekannt |
| Sprache | Englisch |
| Titel | A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum |
| Autor(in); Institution |
Radszuweit, Markus; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
Engel, H.; TU, Institute for Theoretical Physics, Berlin, GERMANY
Bär, Markus; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
|
| Quelle/Jahr | European Physical Journal: Special Topics: 191 (2010), 1, 159 - 172 |
| ISSN | 1951-6355 (PRINT) ; 1951-6401 (ONLINE) |
| DOI | |
| Verlag | Berlin [u.a.]: Springer |
| Freie Schlagworte | Biophysical modelling ; Pattern formation |
| Zusammenfassung | 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)). |
