A detailed predictive model of the mammalian circadian clock

Abstract

Experimental data on the circadian (approximately 24-h) clock in mammalian cells are vast, diverse, and detailed. Mathematical models are therefore needed to piece these data together and to study overall clock behavior. Previous models have focused on Neurospora or Drosophila or can be converted to a Drosophila model simply by renaming variables. Those models used Hill-type terms for transcription regulation and Michaelis-Menten type or delay terms for posttranslation regulation. Recent mammalian experimental data call into question some of the assumptions in these approaches. Moreover, gene duplication has led to more proteins in the mammalian system than in lower organisms. Here we develop a detailed distinctly mammalian model by using mass action kinetics. Parameters for our model are found from experimental data by using a coordinate search method. The model accurately predicts the phase of entrainment, amplitude of oscillation, and shape of time profiles of clock mRNAs and proteins and is also robust to parameter changes and mutations.

Fig. 1.

Model comparison with experimental data. Our model was first entrained to a 24-h day consisting of 12 h of light and 12 h of darkness at time 0, the expected onset of light; darkness for 24 h followed as we recorded the rhythms and compared their time profiles, peak, and trough with experimental data (4). Blue represents mRNA rhythms, whereas black represents protein rhythms. Curves are from the model, and filled circles are experimental data. See text for more details.

Fig. 2.

Fractions of PER1 and PER2 that are phosphorylated. Shown are the same simulations as in Fig. 1.

Fig. 3.

PER null mutants. Simulated time profile of promoter binding in the PER1 null mutant (solid) and the PER2 null mutant (dashed). See Fig. 5 for more detail. Note that the PER1 mutant is rhythmic and the PER2 mutant is not (the small-amplitude oscillation disappears with time).