Frequency Domain Properties and Fundamental Limits of Buffer-Feedback Regulation in Biochemical Systems

TL;DR

This paper introduces a frequency-domain framework to analyze buffer-feedback regulation in biochemical systems, revealing how buffering influences stability, disturbance handling, and fundamental regulation limits, with applications to glycolysis.

Contribution

It presents a novel frequency-domain approach to study buffer-feedback systems and derives fundamental limits showing buffering can reduce regulation constraints.

Findings

Buffering acts as a low-pass filter and can alter disturbance locations.

Buffering and removal processes can lower fundamental regulation limits.

Application to glycolysis demonstrates practical relevance.

Abstract

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.