Circadian Simulation

Time Series	Phase Plot

Author: Shao-Ting Chiu (stevengogogo4321@gmail.com), 丁啟祐

---

Abstract

The circadian rhythm is a biological oscillator that behaves limit cycle and is synchronized with solar time. In this presentation, we simulates the circadian model(Goldbeter,1996) to describe the modulation of circadian clock by changing the degradation rate of PER protein.

Documentation

• PDF slides

Outline

Source: Ingalls, B. P. (2013).

Simulation

Circadian clock doesn't always oscillate under any degradation rate of PER

Time Series	Phase Plot

Negative Feedback between Nucleus PER and mRNA

Delay and Cascading Phosphorylation

Scripts

• Mathematical model of PER model
  • MODEL_PerGoldbeter1996.jl
• Plotting
  • plot_PERGoldbeter1996.jl
• Interactive Plotting
  • Interactive_Plotting.jl

Installation

The model is implemented in the Julia language v1.3.0.. Please install the following packages by Pkg module:

• ModelingTookkit
• DifferentialEquations
• Plots

References

1. Ingalls, B. P. (2013). Mathematical modeling in systems biology: an introduction. MIT press. (link)
2. Goldbeter, A. (1997). Biochemical oscillations and cellular rhythms: the molecular bases of periodic and chaotic behaviour. Cambridge university press. (link)