title: The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells.
abstract: Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue.
authors.affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Marko
authors.initials: M
authors.lastname: Gosak
authors.affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Andraž
authors.initials: A
authors.lastname: Stožer
authors.affiliation: Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Rene
authors.initials: R
authors.lastname: Markovič
authors.affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Jurij
authors.initials: J
authors.lastname: Dolenšek
authors.affiliation: Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Marko
authors.initials: M
authors.lastname: Marhl
authors.affiliation: Institute of Physiology, Faculty of Medicine, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Marjan Slak
authors.initials: MS
authors.lastname: Rupnik
authors.affiliation: Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia.
authors.forename: Matjaž
authors.initials: M
authors.lastname: Perc
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D020013:Calcium Signaling / Q000502:physiology*; D002450:Cell Communication / Q000502:physiology*; D002478:Cells, Cultured; D003198:Computer Simulation; D004058:Diffusion; D004735:Energy Transfer / Q000502:physiology; D050417:Insulin-Secreting Cells / Q000502:physiology*; D051379:Mice; D008954:Models, Biological; D017711:Nonlinear Dynamics