Frequency domain properties of buffer-feedback regulation in cellular biology

Abstract

Feedback regulation in biochemical systems is fundamental to cellular 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 modify the topology of the closed-loop system. Here, we propose a frequency-domain framework for studying the regulatory properties of bufferfeedback systems. We determine standard single-output closed-loop transfer functions, discuss loop-shaping properties, and show that buffering can reduce or remove fundamental limits on feedback regulation. We apply the framework to study the fundamental limits of regulation for glycolysis (anaerobic metabolism) with creatine phosphate buffering.