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The light-based minimum-time circadian entrainment problem for mammals,Neurospora, and Drosophila is studied based on the mathematical models of theircircadian gene regulation. These models contain high order nonlineardifferential equations. Two model simplification methods are applied to thesehigh-order models: the phase response curves (PRC) and the Principal OrthogonalDecomposition (POD). The variational calculus and a gradient descent algorithmare applied for solving the optimal light input in the high-order models. Asthe results of the gradient descent algorithm rely heavily on the initialguesses, we use the optimal control of the PRC and the simplified model toinitialize the gradient descent algorithm. In this paper, we present: (1) theapplication of PRC and direct shooting algorithm on high-order nonlinearmodels; (2) a general process for solving the minimum-time optimal controlproblem on high-order models; (3) the impacts of minimum-time optimal light oncircadian gene transcription and protein synthesis.

Rapid Circadian Entrainment in Models of Circadian Genes Regulation