Stochastic simulation of the mammalian circadian clock.
Circadian (nearly 24-h) clocks are remarkably accurate at timing biological events despite the randomness of their biochemical reactions. Here we examine the causes of their immunity to molecular noise in the context of a detailed stochastic mathematical model of the mammalian circadian clock. This stochastic model is a direct generalization of the deterministic mammalian circadian clock model previously developed. A feature of that model is that it completely specifies all molecular reactions, leaving no ambiguity in the formulation of a stochastic version of the model. With parameters based on experimental data concerning clock protein concentrations within a cell, we find accurate circadian rhythms in our model only when promoter interaction occurs on the time scale of seconds. As the model is scaled up by proportionally increasing the numbers of molecules of all species and the reaction rates with the promoter, the observed variability scales as 1/n(0.5), where n is the number of molecules of any species. Our results show that gene duplication increases robustness by providing more promoters with which the transcription factors of the model can interact. Although PER2 mutants were not rhythmic in the deterministic version of this model, they are rhythmic in the stochastic version.
Forger
Daniel B
DB
Department of Biology, Courant Institute of Mathematical Sciences, and Center for Neural Science, New York University, New York, NY 10012, USA. forger@post.harvard.edu
Peskin
Charles S
CS
D000818:Animals; D001683:Biological Clocks; D018797:Cell Cycle Proteins; D002940:Circadian Rhythm; D056931:Cryptochromes; D005420:Flavoproteins / Q000235:genetics; D006801:Humans; D009687:Nuclear Proteins / Q000235:genetics; D056950:Period Circadian Proteins; D011401:Promoter Regions, Genetic; D013269:Stochastic Processes; D014157:Transcription Factors
D018797:Cell Cycle Proteins; D056931:Cryptochromes; D005420:Flavoproteins; D009687:Nuclear Proteins; C539022:PER1 protein, human; C421902:PER2 protein, human; C539023:Per1 protein, mouse; C513312:Per2 protein, mouse; D056950:Period Circadian Proteins; D014157:Transcription Factors