Doctoral Dissertation Defense: Zainab Almutawa

Title:  Dynamics and Synchronization in Beta Cell Networks:  From Coupling Conditions to Genetic Optimization for Sensitivity to Individual Cells

Abstract 
Pancreatic beta cells secrete insulin to maintain glucose homeostasis and are organized in the islets of Langerhans as clusters of electrically coupled cells. Gap junctions connect neighboring cells, coordinating synchronized oscillations in voltage, intracellular calcium, and insulin secretion which is a process disrupted in diabetic islets. Recent experimental work suggests that optogenetic silencing of key beta cells, or ``hub cells", can impair this coordination, challenging the view that all beta cells contribute more or less equally to islet function. Furthermore, experiments that disconnect a cell from its neighbors illustrate how the loss of coordination may lead to network dysfunction. The identification of heterogeneous beta cell networks, characterized by variable metabolic activity and nonuniform gap junctions connectivity, further complicates our understanding of islet synchrony. To investigate these phenomena, we applied a mathematical model of the electrical dynamics of beta cells to a gap junction-coupled network. By combining computational simulations with rigorous theoretical frameworks such as Lyapunov analysis and the Master Stability Function, we derived both sufficient and necessary coupling conditions for a network that guarantees synchronization. These conditions depend on network connectivity (notably the second smallest eigenvalue of the network Laplacian) and cellular excitability parameters.

Our analysis shows that ablation of a single beta cell reduces network connectivity and disrupts synchronization, which is a hallmark of the switch cell phenomenon. Complementing these approaches, analysis of Hopf bifurcation curves allowed us to determine the parameter boundaries at which a small network transitions from an inactive state to a synchronized, oscillatory state. While traditional hub cell concepts rely on scale-free network properties and functional connectivity, our approach does not assume a scale-free architecture; instead, we identify a switch cell whose silencing disrupts network activity. Recognizing the challenge of arbitrarily assigning values in heterogeneous networks, we employed a Genetic Algorithm to optimize cell specific excitability (pump rate) and gap junctions parameters. Key findings indicate that precise variations in pump rates and gap junction properties define distinct active and inactive regimes, and where silencing a switch cell leads to a loss of synchronization in the network.