A model of the cell-autonomous mammalian circadian clock

Abstract

Circadian timekeeping by intracellular molecular clocks is evident widely in prokaryotes and eukaryotes. The clockworks are driven by autoregulatory feedback loops that lead to oscillating levels of components whose maxima are in fixed phase relationships with one another. These phase relationships are the key metric characterizing the operation of the clocks. In this study, we built a mathematical model from the regulatory structure of the intracellular circadian clock in mice and identified its parameters using an iterative evolutionary strategy, with minimum cost achieved through conformance to phase separations seen in cell-autonomous oscillators. The model was evaluated against the experimentally observed cell-autonomous circadian phenotypes of gene knockouts, particularly retention of rhythmicity and changes in expression level of molecular clock components. These tests reveal excellent de novo predictive ability of the model. Furthermore, sensitivity analysis shows that these knockout phenotypes are robust to parameter perturbation.

Fig. 1.

Model structure. (A) Gene regulation scheme for the mouse circadian clock. Per1, Per2, and Rev-erbα are activated at E-Boxes by CLK/BMAL1 and deactivated when PER/CRY also binds. Clk and Bmal1 are activated by RORc and deactivated by REV-ERBα at RORE. Cry1, Cry2, and Rorc have both an E-Box and a RORE and are regulated accordingly. (B) Schematic of the mouse circadian clock model incorporating genetic regulation at Per1, Per2, Cry1, Cry2, Rev-erbα, Clk, Bmal1, and Rorc, the degradation of mRNAs, the translation of mRNAs to protein, the formation and dissociation of PER/CRY and CLK/BMAL1, and the degradation of PER1, PER2, CRY1, CRY2, REV-ERBα, CLK, BMAL1, and RORc. The loops involving Rev-erbα and Rorc are shown in red.

Fig. 2.

Time courses for the mouse circadian model. mRNA time courses are given in blue, and protein time courses are given in red. Blue dots indicate desired positions for mRNAs, relative to the position of Rev-erbα mRNA. Red dots indicate desired positions for proteins, relative to the corresponding mRNA.

Fig. 3.

Time courses for Per2 mRNA in wild-type (solid) and Cry2 knockout (dashed) mice. Note the increase in amplitude in the knockout.

Fig. 4.

Michaelis–Menten curves (blue) for CLK/BMAL1 activation of Per2 with Cry2 knockout (A); PER1/CRY1 inhibition of Per2 with Cry2 knockout (B); PER2/CRY1 inhibition of Per2 with Cry2 knockout (C); CLK/BMAL1 activation of Per2 with Cry1 knockout (D); PER1/CRY2 inhibition of Per2 with Cry1 knockout (E); and PER2/CRY2 inhibition of Per2 with Cry1 knockout (F). The portions of the curves highlighted in red are the regions traversed, given the model-predicted concentrations of CLK/BMAL1 or the relevant PER/CRY. Curves in A–C, which pertain to Cry2 knockout, when multiplied together can yield a variety of gene activity levels, while curves in D–F, which pertain to Cry1 knockout, when multiplied together lead to near-inactivation of transcription.