  Feedback regulation in biochemical systems is fundamental to homeostasis,
with failure causing disease or death. Recent work has found that cooperation
between feedback and buffering---the use of reservoirs of molecules to maintain
molecular concentrations---is often critical for biochemical regulation, and
that buffering can act as a derivative or lead controller. However, buffering
differs from derivative feedback in important ways: it is not typically limited
by stability constraints on the parallel feedback loop, for some signals it
acts instead as a low-pass filter, and it can change the location of
disturbances in the closed-loop system. Here, we propose a frequency-domain
framework for studying the regulatory properties of buffer-feedback systems. We
determine standard single-output closed-loop transfer functions and discuss
loop-shaping properties. We also derive novel fundamental limits for
buffer-feedback regulation, which show that buffering and removal processes can
reduce the fundamental limits on feedback regulation. We apply the framework to
study the regulation for glycolysis (anaerobic metabolism) with creatine
phosphate buffering.
