Modeling the Drosophila melanogaster Circadian Oscillator via Phase Optimization

The circadian clock, which coordinates daily physiological behaviors of most organisms, maintains endogenous (approximately 24 h) cycles and simultaneously synchronizes to the 24-h environment due to its inherent robustness to environmental perturbations coupled with a sensitivity to specific environmental stimuli. In this study, the authors develop a detailed mathematical model that characterizes the Drosophila melanogaster circadian network. This model incorporates the transcriptional regulation of period, timeless, vrille, PAR-domain protein 1, and clock gene and protein counterparts. The interlocked positive and negative feedback loops that arise from these clock components are described primarily through mass-action kinetics (with the exception of regulated gene expression) and without the use of explicit time delays. System parameters are estimated via a genetic algorithm-based optimization of a cost function that relies specifically on circadian phase behavior since amplitude measurements are often noisy and do not account for the unique entrainment features that define circadian oscillations. Resulting simulations of this 29-state ordinary differential equation model comply with fitted wild-type experimental data, demonstrating accurate free-running (23.24-h periodic) and entrained (24-h periodic) circadian dynamics. This model also predicts unfitted mutant phenotype behavior by illustrating short and long periodicity, robust oscillations, and arrhythmicity. This mechanistic model also predicts light-induced circadian phase resetting (as described by the phase-response curve) that are in line with experimental observations.