Period-Amplitude Co-variation in Biomolecular Oscillators

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 ten benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, cataloguing instances where an increase in period is accompanied by an increase or decrease in amplitude as well as more complex co-variations. To account for the amplitudes of the many biomolecular species that may be part of the oscillation circuit, we use a power norm-based amplitude metric, finding an increase of instances where an increase in period correlates with an increase in this amplitude metric. Finally, we calculate ”scaling laws” of period-amplitude co-variation for a subset of these benchmark oscillators, finding that as period increases the amplitude increases or remains constant. These results should help to understand the amplitude-period co-variation of oscillators in biomolecular as well as other contexts.