A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

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.

Frequency-amplitude correlation inducing first-order phase transition in coupled oscillators

“…This finding have advanced the understanding of amplitude effects in coupled oscillators [56][57][58][59]. In addition, the amplitude modulation of biological or chemical oscillators around the bifurcation points was considered to be significant [27,60,61]. For the Brusselator model, a forcing term was added into each oscillator equation for their amplitudes and frequencies modulated in the periodic oscillation state [62][63][64].…”

“…In the human body, the vital movements are usually regulated by the single or multiple biological oscillators, with varied frequencies and amplitudes [27,28]. The different frequencies indicate different functional consequences, while the different amplitudes abstract the differences in the expression levels of proteins, hormones, etc.…”

Network design principle for robust oscillatory behaviors with respect to biological noise

“…Thus, a natural question is how the biological systems achieve accurate oscillation in the presence of noise. Previous studies revealed that many kinetic parameters can influence the robustness of the biological oscillators, such as the system size and degree of cooperativity of reactions ( Gonze et al, 2002a ), timescale of the promoter interaction ( Forger and Peskin, 2005 ), repressor degradation rate ( Potvin-Trottier et al, 2016 ), free energy cost measured by ATP/ADP ratios ( Cao et al, 2015 ; Fei et al, 2018 ; Qin et al, 2021 ), and kinetic parameter-determined oscillation mechanisms (i.e., limit cycle or force driving) ( Monti et al, 2018 ). Moreover, growing evidence suggests the existence of the relationship between network configurations and noise buffering capabilities for biochemical oscillators.…”