A Kuramoto phase model to explore the synchronisation of a network of circadian clocks
We propose a model of the circadian clock in a population of cells based on a network of oscillators, derived from the Kuramoto model. The coupling between oscillators is described by a global interaction term but we introduce a phase-dependent coupling mechanism, such that oscillators interact only within a specific interval of the cycle corresponding to a specific stage of the circadian cycle. We analytically demonstrate that this modified system achieves complete asymptotic phase synchronisation, provided specific conditions on the initial phase distribution and the coupling window length are met. To bridge this theoretical framework with experimental observations, we introduce a signal processing procedure based on wavelet decomposition to extract quantitative oscillatory features from Per2::luciferase reporter traces. We then calibrate the model against datasets from both wild type and Cry2 knockout hepatocyte spheroids using a two-step quasi-Monte Carlo filtering algorithm. The comparative analysis reveals significant phenotypic divergence, showing that the Cry2KO condition alters the identifiability landscape of the model's parameters and introduces new compensatory mechanisms that confound the initial population heterogeneity with long-term macroscopic signal decay.