The acid-base two-timescale buffer

Blood pH is a loop quantity defended by two arms on different timescales: respiratory CO₂ (fast) and renal HCO₃ (slow). The Henderson-Hasselbalch relation plus the two timescales reproduce both the Winters respiratory-compensation slope and full pH restoration after a metabolic acid load.

Blood pH is held at 7.40 by a two-timescale buffer: fast respiratory CO₂ and slow renal HCO₃ regeneration. A metabolic acid load is partially compensated within minutes (respiratory) then fully corrected over hours (renal).

Henderson-Hasselbalch and the two timescales

pH = 6.1 + log₁₀(HCO₃ / (0.03·pCO₂)). An acid load (HCO₃ 24→14) drops pH to 7.167. The fast respiratory arm lowers pCO₂ (compensation slope dpCO₂/dHCO₃ = 1.10, matching the Winters rule ~1.2–1.5), partially restoring pH to 7.307. The slow renal arm regenerates HCO₃, returning pH to 7.401.

Failure of either arm is the metabolic/respiratory acid-base disorder axis; the cited pH 7.40 and the Winters slope are the literature anchors the simulation reproduces.