Macroscopic Models for Networks of Coupled Biological Oscillators

TL;DR

This paper introduces a new macroscopic reduction method for networks of coupled biological oscillators, enabling simplified analysis of collective behaviors in complex systems like circadian rhythms and neural networks.

Contribution

The paper presents a novel macroscopic reduction technique based on an observed structure in experimental data and models, applicable to stochastic and heterogeneous oscillator networks.

Findings

The reduction captures collective dynamics effectively.

It applies to stochastic and heterogeneous systems.

Comparison shows good agreement with microscopic models.

Abstract

The study of synchronization in populations of coupled biological oscillators is fundamental to many areas of biology to include neuroscience, cardiac dynamics and circadian rhythms. Studying these systems may involve tracking the concentration of hundreds of variables in thousands of individual cells resulting in an extremely high-dimensional description of the system. However, for many of these systems the behaviors of interest occur on a collective or macroscopic scale. We define a new macroscopic reduction for networks of coupled oscillators motivated by an elegant structure we find in experimental measurements of circadian gene expression and several mathematical models for coupled biological oscillators. We characterize the emergence of this structure through a simple argument and demonstrate its applicability to stochastic and heterogeneous systems of coupled oscillators. Finally, we perform the macroscopic reduction for the heterogeneous stochastic Kuramoto equation and compare the low-dimensional macroscopic model with numerical results from the high-dimensional microscopic model.