Abstract
Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.
Highlights
Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect
Flexible biological oscillators have a wide range of benefits for healthy sustainability
We consider the cyclic dynamics in a gene-regulatory network involving a microRNA cluster and a protein module[58]
Summary
Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Neuron spiking, cell reproduction, hormone secretion, protein synthesis, and heartbeat are common periodic activities in the human body These processes are usually regulated by single or multiple biological oscillators exhibiting various frequencies and amplitudes (Fig. 1). The former ones would result in distinct functional consequences[6], while the latter ones abstract expression levels meeting body demands for protein, hormone, energy, to name a few[7]. Frequency and amplitude modulations of biological oscillators has attracted more and more attentions, among which coordinating amplitude or frequency independently (Fig. 1a, b) is significant
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