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For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breakingbifurcations that can emerge when two bulk diffusing species are coupled totwo-component nonlinear intracellular reactions that are restricted to occuronly within a disjoint collection of small circular compartments, or "cells",of a common small radius that are confined in a bounded 2-D domain. Outside ofthe union of these cells, the two bulk species with comparable diffusivitiesand bulk degradation rates diffuse and globally couple the spatially segregatedintracellular reactions through Robin boundary conditions across the cellboundaries, which depend on certain membrane reaction rates. In the singularlimit of a small common cell radius, we construct steady-state solutions forthe bulk-cell model and formulate a nonlinear matrix eigenvalue problem thatdetermines the linear stability properties of the steady-states. For a certainspatial arrangement of cells for which the steady-state and linear stabilityanalysis become highly tractable, we construct a symmetric steady-statesolution where the steady-states of the intracellular species are the same foreach cell. As regulated by the ratio of the membrane reaction rates on the cellboundaries, we show for various specific prototypical intracellular reactions,and for a specific two-cell arrangement, that our 2-D coupled PDE-ODE modeladmits symmetry-breaking bifurcations from this symmetric steady-state, leadingto linearly stable asymmetric patterns, even when the bulk diffusing specieshave comparable or possibly equal diffusivities. Overall, our analysis showsthat symmetry-breaking bifurcations can occur without the large diffusivityratio requirement for the bulk diffusing species as is well-known from a Turingstability analysis applied to a spatially uniform steady-state for typicaltwo-component activator-inhibitor systems.

Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D