# Rapid Circadian Entrainment in Models of Circadian Genes Regulation

## TL;DR

This paper develops methods for rapid circadian entrainment in biological models by simplifying complex gene regulation equations and applying optimal control techniques, demonstrating effective light input strategies.

## Contribution

It introduces a combined approach using PRC, POD, and gradient descent for optimal light control in high-order circadian models, advancing circadian entrainment methods.

## Key findings

- Effective light input strategies for circadian entrainment
- Simplification of complex nonlinear models
- Impact on gene transcription and protein synthesis

## Abstract

The light-based minimum-time circadian entrainment problem for mammals, Neurospora, and Drosophila is studied based on the mathematical models of their circadian gene regulation. These models contain high order nonlinear differential equations. Two model simplification methods are applied to these high-order models: the phase response curves (PRC) and the Principal Orthogonal Decomposition (POD). The variational calculus and a gradient descent algorithm are applied for solving the optimal light input in the high-order models. As the results of the gradient descent algorithm rely heavily on the initial guesses, we use the optimal control of the PRC and the simplified model to initialize the gradient descent algorithm. In this paper, we present: (1) the application of PRC and direct shooting algorithm on high-order nonlinear models; (2) a general process for solving the minimum-time optimal control problem on high-order models; (3) the impacts of minimum-time optimal light on circadian gene transcription and protein synthesis.