ncts

To understand biological rhythms through mathematical modeling, these models, in the form of ODEs or delay equations, are known as coupled-cell systems. Many biological rhythms are composed of oscillators in single cells, coupled through intercellular connections. For instance, circadian rhythm has been studied through coupled-cell systems. A population of oscillators with different autonomous frequencies can generally attain frequency synchronization through coupling. Thus, understanding how to establish the frequency of a collective oscillation is a key issue in understanding biological rhythms. We consider two different types of gene regulation for circadian clock models: Hill-function-type and protein-sequestration-based repression. Based on Hopf bifurcation analysis and numerical computations extended from the analysis, we explore how the collective frequency in the coupled-cell systems varies with respect to the coupling strength. Moreover, we investigate the relationship between the collective frequency of oscillation in coupled-cell systems and the frequencies of isolated individual cells.