The concept of "buffering" in systems and control theory: from metaphor to math.

The paradigm of "buffering" is used increasingly for the description of diverse "systemic" phenomena encountered in evolutionary genetics, ecology, integrative physiology, and other areas. However, in this new context, the paradigm has not yet matured into a truly quantitative concept inasmuch as it lacks a corresponding quantitative measure of "systems-level buffering strength". Here, I develop such measures on the basis of a formal and general approach to the quantitation of buffering action. "Systems-level buffering" is shown to be synonymous with "disturbance rejection" in feedback-control systems, and can be quantitated by means of dimensionless proportions between partial flows in two-partitioned systems. The units allow either the time-independent, "static" buffering properties or the time-dependent, "dynamic" ones to be measured. Analogous to this "resistance to change", one can define and measure the "conductance to change"; this quantity corresponds to "set-point tracking" in feedback-control systems. Together, these units provide a systematic framework for the quantitation of buffering action in systems biology, and reveal the common principle behind systems-level buffering, classical acid-base buffering, and multiple other manifestations of buffering.