An innovative combinatorial coordination ratio perturbation approach for decoupled period-amplitude modulation

Biological rhythms serve as essential timing mechanisms for regulating physiological processes, with period and amplitude being two key characteristics. Decoupled control of these characteristics is challenging due to their complex interdependencies. This study proposes a combinatorial coordination ratio perturbation approach for independently modulating the period and amplitude of biological rhythms. The approach integrates correlation analysis and Taylor expansion. Correlation analysis offers potential perturbation combinations, while Taylor expansion assists in determining the coordination perturbation ratio. We mathematically demonstrate the feasibility of independently adjusting the period and amplitudes through combinatorial perturbation and have developed an algorithm to identify optimal parameter combinations. When applied to the Per-Cry-Bmal1 circadian model, the method enables amplitude modulation while maintaining a constant period, and it also allows for period modulation while keeping the amplitude constant, thus demonstrating its practical effectiveness. This study advances circadian rhythm research by providing a simple and feasible method for decoupled period-amplitude control, with potential applications in the treatment of circadian-related disorders and chronomedicine. Moreover, this method exhibits excellent generality and is applicable to other oscillatory dynamics as well.