Circadian Rhythms in Neurospora Exhibit Biologically Relevant Driven and Damped Harmonic Oscillations

Circadian rhythms are endogenous cycles of approximately 24 hours reinforced by external cues such as light. These cycles are typically modeled as harmonic oscillators with fixed amplitude peaks. Using experimental data measuring global gene transcription in Neurospora crassa over 48 hours in the dark (i.e. with external queues removed), we demonstrate that many circadian genes frequently exhibit either damped harmonic oscillations, in which the peak amplitudes decrease each day, or driven harmonic oscillations, in which the peak amplitudes increase each day. By fitting extended harmonic oscillator models which include a damping ratio coefficient, we detected additional circadian genes that were not identified by the current standard tools that use fixed amplitude waves as reference, e.g. JTK_CYCLE. Functional Catalogue analysis confirms that our identified damped or driven genes exhibit distinct biological functions. The application of extended damped/driven harmonic oscillator models thus can elucidate, not only previously unidentified circadian genes, but also characterize gene subsets with expression patterns of biological relevance. Thus, expanded harmonic oscillators provide a powerful new tool for circadian system biology.