A topological mechanism for robust and efficient global oscillations in biological networks

TL;DR

This paper introduces a topological model explaining how biological networks, like circadian rhythms, sustain robust and efficient oscillations by localizing dynamics at the system boundary, outperforming previous models.

Contribution

The study presents a novel topological mechanism for robust oscillations, demonstrating boundary localization, spectral gap analysis, and thermodynamic efficiency in biological networks.

Findings

Model localizes oscillatory currents on system boundary

Achieves high precision with low energetic cost

Saturates a global thermodynamic bound

Abstract

Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.