The ability of organisms to survive under a multitude of conditions is readily apparent. This robustness in performance is difficult to precisely characterize and quantify. At a biochemical level, it leads to physiological behavior when the parameters of the system remain within some neighborhood of their normal values. However, this behavior can change abruptly, often becoming pathological, as the boundary of the neighborhood is crossed. Currently, there is no generic approach to identifying and characterizing such boundaries. We address the problem by introducing a method that involves quantitative concepts for boundaries between regions and “global tolerance”. To illustrate the power of these concepts, we analyzed a large class of biological modules called moiety-transfer cycles and characterized the specific case of the NADPH redox cycle in human erythrocytes, which is involved in conferring resistance to malaria. Our results show that the wild-type system operates well within a region of “best” local performance that is surrounded by “poor” regions.