(132a) Single-Cell Level Model of the Mammalian Circadian Clock

The circadian clock produces diverse behaviors in numerous organisms, leading, for example, to sleep/wake cycles in animals [1] and leaf movement in plants [2], all exhibiting an approximate 24-hour period. In mammals, the postulated ?master? clock is located in the suprachiasmatic nucleus (SCN) of the anterior hypothalmus [3]. This clock then directs putative ?slave? clocks throughout the body in miscellaneous organs such as liver and kidney [3].

The nature of the clock in mammals was first unraveled through carefully controlled experiments performed with whole animals. Typically, rodents were placed in hermetic conditions and subjected to an array of light/dark regimes while the researcher recorded their wheel-running activity. The models constructed with these data were then based upon the observable phase shifts induced by application of a light pulse at particular times during the animals' subjective day [4].

While whole-animal experiments continue to be useful, they have been supplemented by application of biochemical techniques to cells in the SCN. These investigations have uncovered many facets of the clock's molecular operation. Specifically, the mammalian clock functions as an oscillator because the principal clock components (Per and Cry) negatively regulate their own production. Beyond Per and Cry, various other elements feed into the clock as activators and repressors, adding subsidiary feedback loops to the circadian system and increasing its complexity [1,3]. This advancing appreciation of the clock's operation has led to the development of several mathematical models at the molecular level. To date, the most sophisticated of these are the deterministic model produced by Leloup and Goldbeter [5] and the deterministic and stochastic models produced by Forger and Peskin [6,7].

Though these representations produce sustained oscillations of clock components with correct periodicity, the data used to construct these models is a meld taken from cellular, tissular, and organismal levels of organization. It has been argued, however, that the correct phenotypes driven by intracellular (i.e. core) clock networks can only be observed when individual neurons are decoupled from one another [8]. Indeed, specific manifestations of level-specific clock behavior can be seen in both the broader spread of circadian period and the greater cycle-to-cycle variation in circadian period evident in decoupled neurons when compared to SCN explants [8]. Furthermore, a recent work shows that dispersed neurons with Per1 and Cry1 knockouts exhibit arrhythmic behavior, in contrast to the previously-reported results, developed from experiments involving interacting cells, which indicated merely altered rhythms [9].

Here, we take the phenotypes of the true, uncoupled oscillator and develop a mathematical model of the single-cell circadian clock. Two versions of the period gene (Per1 and Per2), both versions of the cryptochrome gene (Cry1 and Cry2), and also the Bmal1, Rev-ErbA, and RorC genes are included. These genes and their products are linked in a network of interactions with numerous positive- and negative-feedback loops. We show that the model correctly predicts a 24-hour period and also generally maintains accurate phase relationships among the components (i.e. a four-hour lead of Rev-ErbA over Per1 and Per2, four-hour leads of Per1 and Per2 over Cry1, Cry2, and RorC, four-hour leads of Cry1, Cry2, and RorC over Bmal1, and a twelve-hour lead of Bmal1 over Rev-ErbA). Additionally, the model accurately exhibits a lead of mRNAs over proteins of approximately four to six hours for most model components. Furthermore, the model correctly predicts the phenotypes and expression levels exhibited by numerous single- and double-knockout mutants.

Project supported by the Institute for Collaborative Biotechnologies through Grant DAAD19-03-D-0004 from the U. S. Army Research Office.

References

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6. Forger DB, Peskin CS (2003) Proc Natl Acad Sci USA 100:14806-14811.

7. Forger DB, Peskin CS (2005) Proc Natl Acad Sci USA 102:321-324.

8. Herzog ED, Aton SJ, Numano R, Sakaki Y, Tei H (2004) J Biol Rhythms 19:35-46.

9. Liu AC, Welsh DK, Ko CH, Tran HG, Zhang EE, Priest AA, Buhr ED, Singer O, Meeker K, Verma IM, et al. (2007) Cell 129:605-616.