Research

Coupling of Oscillators

M. Perc and M. Marhl

Local dissipation and coupling properties of cellular oscillators. A case study on calcium oscillations

Bioelectrochemistry
62 (2004) 1-10

Abstract: Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.

M. Perc and M. Marhl

Synchronisation of regular and chaotic oscillations: The role of local divergence and the slow passage effect. A case study on calcium oscillations

International Journal of Bifurcation and Chaos
14 (2004) 2735-2751

Abstract: In this paper, coupling properties of regular and chaotic calcium oscillations are examined. Synchronized calcium signals among coupled cells in tissue, where calcium ions were found to be one of the most important second messengers, have proven indispensable for proper and reliable functioning of living organisms. When modeling such systems, it is of particular interest to determine, which internal system properties guarantee best coupling abilities and herewith physiologically the most efficient signal transduction between cells. We found that local contractive properties of attractors in phase space, quantified by the local divergence, represent one of the crucial system properties that determine synchronization abilities of coupled regular and chaotic oscillators. In particular, parts of attractors with close to zero local divergence largely facilitate synchronization of initially unsynchronized oscillators. For bursting oscillations, this is fully in agreement with previous studies showing that synchronization abilities of bursters are closely related with the slow passage effect. We extended this concept with the help of local divergence and succeeded to apply our theory also to other oscillatory regimes, like regular spiking and complex chaotic oscillations.

Elsevier	*M. Perc and M. Marhl* Local dissipation and coupling properties of cellular oscillators. A case study on calcium oscillations Bioelectrochemistry 62 (2004) 1-10	Abstract: Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.

World Scientific	*M. Perc and M. Marhl* Synchronisation of regular and chaotic oscillations: The role of local divergence and the slow passage effect. A case study on calcium oscillations International Journal of Bifurcation and Chaos 14 (2004) 2735-2751	Abstract: In this paper, coupling properties of regular and chaotic calcium oscillations are examined. Synchronized calcium signals among coupled cells in tissue, where calcium ions were found to be one of the most important second messengers, have proven indispensable for proper and reliable functioning of living organisms. When modeling such systems, it is of particular interest to determine, which internal system properties guarantee best coupling abilities and herewith physiologically the most efficient signal transduction between cells. We found that local contractive properties of attractors in phase space, quantified by the local divergence, represent one of the crucial system properties that determine synchronization abilities of coupled regular and chaotic oscillators. In particular, parts of attractors with close to zero local divergence largely facilitate synchronization of initially unsynchronized oscillators. For bursting oscillations, this is fully in agreement with previous studies showing that synchronization abilities of bursters are closely related with the slow passage effect. We extended this concept with the help of local divergence and succeeded to apply our theory also to other oscillatory regimes, like regular spiking and complex chaotic oscillations.