Long-range interaction effects on calcium-wave propagation

Long-range paracrine coupling-induced Ca^{2+} patterns in two-dimensional cell networks under inositol 1,4,5-triphosphate-cytosolic Ca^{2+} interaction

A two-dimensional model is designed for intercellular calcium (Ca^{2+}) waves in the presence of long-range (LR) paracrine coupling due to the action of extracellular messengers and Ca^{2+}-activated degradation of inositol 1,4,5-triphosphate (IP_{3}) by a 3-kinase. Using mean-field theory, a statistical variable is defined to detect the emergence of intercellular spiral waves of Ca^{2+}. The latter are generated by the local heterogeneity caused by asymmetrical stimulation of the network. It is confirmed that spiral waves may develop when the synchronization degree is low. It is found that balanced LR coupling and IP_{3} degradation, under appropriate external hormonal stimulation, can effectively control the creation and propagation of spiral waves. A higher LR degree disrupts network synchronization, and only specific ranges of stimulation factor support spiral waves. Weak IP_{3} degradation and stronger LR degree disintegrate spiral symmetry with increased hormonal stimulation. Strong IP_{3} degradation has the opposite effect.

Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state

In this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemichannels activity at the connexins level, which provides links between pre-synaptic and post-synaptic neurons. Results show that the long-range coupling enhances the range of the threshold parameter. We also investigate the long-range effects on the network dynamics, which induces enlargement of the oscillatory zone before the excitable regime. When considering bidirectional coupling, the long-range interaction induces traveling patterns such as traveling waves, while when considering unidirectional coupling, the long-range interaction induces multi-chimera states. We also studied the difference between the dynamics of coupled oscillators and coupled excitable neurons. We found that, for the coupled system, the oscillation period decreases with the increasing of the coupling parameter. For the same values of the coupling parameter, the oscillation period of the Oscillatory dynamics is greater than the oscillation period of the excitable dynamics. The analytical approximation shows good agreement with the numerical results.

Inferring local dynamics and connectivity of spatially extended systems with long-range links based on steady-state stabilization

A method is presented for system identification of spatially extended systems with structural inhomogeneities of local dynamics and additional long-range links. The proposed identification procedure is based on steady-state stabilization and is illustrated with an inhomogeneous two-dimensional grid of coupled FitzHugh-Nagumo models.