Amplitude bounds for biochemical oscillators

TL;DR

This paper introduces a practical method to determine amplitude bounds for biochemical oscillators with negative feedback, providing explicit analytical expressions and demonstrating their effectiveness through simulations.

Contribution

It offers a novel approach to bounding oscillation amplitudes in biochemical models, independent of feedback delays, with explicit formulas for certain systems.

Findings

Bounds depend on feedback nonlinearity

Explicit bounds match numerical simulations

Method applicable to large classes of models

Abstract

We present a practical method to obtain bounds for the oscillation minima and maxima of large classes of biochemical oscillator models that generate oscillations through a negative feedback. These bounds depend on the feedback nonlinearity and are independent of explicit or effective feedback delays. For specific systems, we obtain explicit analytical expressions for the bounds and demonstrate their effectiveness in comparison with numerical simulations.