<i>PyCycleBio</i>: modelling non-sinusoidal-oscillator systems in temporal biology

<h4>Motivation</h4>Protein, mRNA, and metabolite abundances can exhibit rhythmic dynamics, such as during the day-night cycle. Leading bioinformatics platforms for identifying biological rhythms often utilize single-component models of the harmonic oscillator equation, or multi-component models based upon the Cosinor framework. These approaches offer distinct advantages: modelling either temporally resolved regulatory behaviour via the extended harmonic oscillator equation, or complex rhythmic patterns in the case of Cosinor.<h4>Results</h4>Here, we have developed a new platform to combine the advantages of these two approaches. <i>PyCycleBio</i> utilizes bounded-multi-component models and modulus operators alongside the harmonic oscillator equation, to model a diverse and interpretable array of rhythmic behaviours, including the regulation of temporal dynamics via amplitude coefficients. We demonstrate increased sensitivity and functionality of <i>PyCycleBio</i> compared to other analytical frameworks, and uncover new relationships between data modalities or sampling conditions with the qualities of rhythmic behaviours from biological datasets-including transcriptomics, proteomics, and metabolomics. We envision that this new approach for disentangling complicated temporal regulation of biomolecules will advance chronobiology and our understanding of physiology.<h4>Availability and implementation</h4><i>PyCycleBio</i> is available at: https://github.com/Glycocalex/PyCycleBio, and the Python package is available to install at: https://pypi.org/project/pycyclebio/. <i>PyCycleBio</i> can also be used at https://colab.research.google.com/github/Glycocalex/PyCycleBio/blob/main/PyCycleBio.ipynb with no installations necessary.