Synchronization in reaction–diffusion systems with multiple pacemakers

Abstract

Spatially extended oscillatory systems can be entrained by pacemakers, regions which oscillate with a higher frequency than the rest of the medium. Entrainment happens through waves originating at a pacemaker. Typically, biological and chemical media can contain multiple pacemaker regions which compete with each other. In this paper we perform a detailed numerical analysis of how wave propagation and synchronization of the medium depend on the properties of these pacemakers. We discuss the influence of the size and intrinsic frequency of pacemakers on the synchronization properties. We also study a system in which the pacemakers are embedded in a medium without any local dynamics. In this case, synchronization occurs if the coupling determined by distance and diffusion is strong enough. The transition to synchronization is reminiscent of systems of discrete coupled oscillators.

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm

“…In the latter case, the wave direction reverses, as the local concentration in the center is increased, leading to a higher cell cycle frequency. These observations are in agreement with an earlier theoretical analysis of competing pacemakers [37].…”

“…Moreover, in 2d, there is much more freedom to explore different sizes and geometries of pacemakers (e.g. nuclei), which in 1d has shown to be of importance for the dynamics of the system [37].…”

Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm

“…In the latter case, the wave direction reverses, as the local concentration in the center is increased, leading to a higher cell cycle frequency. These observations are in agreement with an earlier theoretical analysis of competing pacemakers [25].…”

Synchronizing an oscillatory medium: The speed of pacemaker-generated waves

“…When this is the case, they compete with each other until one takes over the whole medium. We recently investigated such systems of multiple pacemakers [52] and showed that both size and frequency matter in the determination of which pacemaker dominates the whole medium.…”