In endocrine glands, vigorous and coordinated responses are often elicited by modest changes in the concentration of the agonist molecule. The mammalian parathyroid gland is a representative case. Small (5%) changes in serum calcium result in 10-fold (1,000%) changes in glandular parathyroid hormone (PTH) release. In vitro, single isolated cells are observed to secrete fewer hormones than cells residing within a connected group, suggesting that a network has emergent regulatory properties. In PTH-secreting tumors, however, the ability to respond quickly to changes in calcium is strongly damped. A unifying hypothesis that accounts for these phenomena is realized by extracellular modulation of calcium diffusivity. A theoretical model and computational experiments demonstrate qualitative agreement with published experimental results. Our results suggest that, in addition to the cellular mechanisms, endocrine glandular networks may have regulatory prowess at the level of interstitial transport.