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 increasein 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 resultsshould help to understand the amplitude-period co-variation of oscillators in biomolecular as well as other contexts .
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 .
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cataloguing instances where an increasein period is accompanied by an increase or decrease in amplitude as well as more complex co-variations. To
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
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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
oscillations, finding largely similar trends
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period increases the amplitude increases or remains constant . These resultsshould help to understand the amplitude-period co-variation of oscillators in biomolecular
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
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other contexts
the difficulty in achieving an oscillation with large amplitude and small period