Period-Amplitude Co-variation in Biomolecular Oscillators

TL;DR

This study analyzes how the period and amplitude of biomolecular oscillators co-vary using models, simulations, and analytical methods, revealing patterns and scaling laws that inform their tunability and design.

Contribution

It provides a systematic classification of period-amplitude co-variation patterns and derives scaling laws for biomolecular oscillators, advancing understanding of their parameter dependencies.

Findings

Amplitude and period co-variation patterns vary across models.

Similar trends are observed using different amplitude metrics.

Scaling laws relate period increase to amplitude bounds.

Abstract

The period and amplitude of biomolecular oscillators are functionally important properties in multiple contexts. For a biomolecular oscillator, the overall constraints in how tuning of amplitude affects period, and vice versa, are generally unclear. Here we investigate this co-variation of the period and amplitude in mathematical models of biomolecular oscillators using both simulations and analytical approximations. We computed the amplitude-period co-variation of eleven benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co-variation patterns such as a simultaneous increase/ decrease in period and amplitude. Next, we repeated the classification using a power norm-based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends. Finally, we calculate "scaling laws" of period-amplitude co-variation for a subset of these benchmark oscillators finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, we discuss the effect of different parameters on the type of period-amplitude co-variation as well as the difficulty in achieving an oscillation with large amplitude and small period.