Multi layer network representation of membrane potential and cytosolic calcium concentration dynamics in beta cells

摘要

Modern theory of networks has been recognized as a very successful methodological concept for the description and analysis of complex systems. However, some complex systems are more complex than others. For instance, several real-life systems are constituted by interdependent subsystems and their elements are subjected to different types of interactions that can also change with time. Recently, the multilayer network formalism has been proposed as a general theoretical framework for the description and analysis of such multi-dimensional complex systems and is acquiring more and more prominence in terms of a new research direction. In the present study, we use this methodology for the description of functional connectivity patterns and signal propagation between pancreatic beta cells in an islet of Langerhans at the levels of membrane potential (MP) and cytosolic calcium concentration ([Ca2+](c)) dynamics to study the extent of overlap in the two networks and to clarify whether time lags between the two signals in individual cells are in any way dependent on the role these cells play in the functional networks. The two corresponding network layers are constructed on the basis of signal directions and pair-wise correlations, whereas the interlayer connections represent the time lag between both measured signals. Our results confirm our previous finding that both MP and [Ca2+](c), change spread across an islet in the form of a depolarization and a [Ca2+](c), wave, respectively. Both types of waves follow nearly the same path and the networks in both layers have a similar but not entirely the same structure. We show that the observed discrepancies are attributed to variability in delays between the depolarization and rise in [Ca2+](c). In particular, high-degree nodes in both layers are found to exhibit a larger time lag between the MP and the [Ca2+](c), signal than nodes with less connections. We speculate that this finding reflects a higher activity of endoplasmic reticulum calcium pumps in the most connected cells. Our findings indicate that visualizing and studying the temporal information flow and interaction patterns between beta cells as a multiplex network can provide valuable new insights into the physiology of the complex signaling processes in islets of Langerhans. (C) 2015 The Authors. Published by Elsevier Ltd.