Traveling chimeras and collective coordination in beta-cell networks

TL;DR

This work develops a hybrid network model for pancreatic $\beta$-cells by coupling slow metabolic oscillators $ (x_j,y_j) $ and fast electrical dynamics $ (u_j,v_j) $ on a nonlocal ring, with metabolic coupling $k_p$ and electrical coupling $k_r$. The model tracks the composite activity $c_j = x_j + b u_j$ and analyzes how coupling structure governs emergent spatiotemporal patterns, including phase synchronization, traveling waves, and traveling chimera states. Using a $N=100$ network and numerical integration (RK4 for slow dynamics, Euler for fast dynamics), the study shows that metabolic coupling predominantly controls global synchrony, while electrical coupling modulates the fine structure of partial synchrony, revealing a mechanism by which islets could sustain pulsatile insulin secretion under heterogeneous conditions. The findings offer theoretical insight into how intercellular communication shapes islet-wide coordination and may inform understanding of dysfunction in diabetes.

Abstract

Pancreatic $β$-cells play a central role in maintaining glucose homeostasis through the pulsatile secretion of insulin. This essential function relies not only on intracellular regulatory mechanisms but also on coordinated interactions among $β$-cells within the islets of Langerhans. Disruptions in this intercellular coordination are increasingly implicated in metabolic disorders such as type~I and type~II diabetes. In this work, we employ a computational framework to investigate the collective dynamics of a network of coupled $β$-cells interacting through a nonlocally coupled ring topology that incorporates both electrical and metabolic coupling pathways. This topology captures short- and long-range interactions known to shape islet communication. Numerical simulations reveal a variety of emergent behaviors, including synchronization, traveling waves, and traveling chimera states, in which coherent and incoherent domains coexist and propagate across the network. These findings provide new insight into the mechanisms governing coordinated $β$-cell activity and the regulation of pulsatile insulin secretion. By clarifying how coupling structure and intercellular communication shape islet-wide dynamics, this work contributes to a deeper understanding of the dysfunctions underlying diabetes.

Figures (9)

• Figure 1: Phase transition dynamics represented by the order parameter of the (a) metabolic, (b) electrical, and (c) composite signals as a function of the metabolic coupling strength $k_p$, for five values of the electrical coupling strength $k_r = \{-0.02, 0, 0.02, 0.1, 0.5\}$, with a fixed neighborhood size of $P = 20$.
• Figure 2: Synchronization dynamics of the (a,d) metabolic variable, (b,e) electrical activity, and (c,f) composite signal for the coupling parameters $k_p = 1$, $k_r = 0.1$, and $P = 20$. The first column illustrates the spatiotemporal evolution of the variables, while the second column shows the corresponding snapshots of the same variables.
• Figure 3: Phase transition dynamics represented by the order parameter of the (a) metabolic, (b) electrical, and (c) composite signals as a function of the metabolic coupling strength $k_p$, for four different neighborhood sizes $P = \{2, 5, 10, 20\}$, with the electrical coupling fixed at $k_r = 0.5$
• Figure 4: Order parameter of the (a) metabolic, (b) electrical, and (c) composite signals as a function of the metabolic and electrical coupling strengths $k_p$ and $k_r$, for a neighborhood size of $P = 20$ nodes.
• Figure 5: Spatio-temporal and snapshot diagrams illustrating: (a,d) the metabolic variable $x_i$, exhibiting a traveling wave; (b,e) the membrane potential $u_i$, displaying a traveling chimera state; and (c,f) the composite signal $c_i$, showing a weak traveling chimera very close to traveling wave pattern. The parameters used are $k_p = -2$, $k_r = -0.02$, and $P = 20$.