  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.
