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We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorumand diffusion sensing phenomena in microbial systems, that characterizecommunication between localized spatially segregated dynamically activesignaling compartments that have a permeable boundary. Each cell secretes asignaling chemical into the bulk region at a constant rate and receives afeedback of the bulk chemical from the entire collection of cells. This globalfeedback, which activates signaling pathways within the cells, modifies theintracellular dynamics according to the external environment. The cellsecretion and global feedback are regulated by permeability parameters acrossthe cell membrane. For arbitrary reaction-kinetics within each cell, the methodof matched asymptotic expansions is used in the limit of small cell radius toconstruct steady-state solutions of the PDE-ODE model, and to derive a globallycoupled nonlinear matrix eigenvalue problem (GCEP) that characterizes thelinear stability properties of the steady-states. In the limit of large bulkdiffusivity an asymptotic analysis of the PDE-ODE model leads to a limiting ODEsystem for the spatial average of the concentration in the bulk region that iscoupled to the intracellular dynamics within the cells. Results from the linearstability theory and ODE dynamics are illustrated for Sel'kovreaction-kinetics, where the kinetic parameters are chosen so that each cell isquiescent when uncoupled from the bulk medium. For various specific spatialconfigurations of cells, the linear stability theory is used to construct phasediagrams in parameter space characterizing where a switch-like emergence ofintracellular oscillations can occur through a Hopf bifurcation.

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments