Long-range intercellular Ca2+ wave patterns

摘要

Modulational instability is utilized to investigate intercellular Ca2+ wave propagation in an array of diffusively coupled cells. Cells are supposed to be connected via paracrine signaling, where long-range effects, due to the presence of extracellular messengers, are included. The multiple-scale expansion is used to show that the whole dynamics of Ca2+ waves, from the endoplasmic reticulum to the cytosol, can be reduced to a single differential-difference nonlinear equation whose solutions are assumed to be plane waves. Their linear stability analysis is studied, with emphasis on the impact of long-range coupling, via the range parameters. It is shown that s, as well as the number of interacting cells, importantly modifies the features of modulational instability, as small values of s imply a strong coupling, and increasing its value rather reduces the problem to a first-neighbor one. Our theoretical findings are numerically tested, as the generic equations are fully integrated, leading to the emergence of nonlinear patterns of Ca2+ waves. Strong long-range coupling is pictured by extended trains of breather-like structures whose frequency decreases with increasing s. We also show numerically that the number of interacting cells plays on the spatio-temporal formation of Ca2+ patterns, whilst the quasi-perfect intercellular communication depends on the paracrine coupling parameter. (C) 2015 Elsevier B.V. All rights reserved.