title: It is not the parts, but how they interact that determines the behaviour of circadian rhythms across scales and organisms.
abstract: Biological rhythms, generated by feedback loops containing interacting genes, proteins and/or cells, time physiological processes in many organisms. While many of the components of the systems that generate biological rhythms have been identified, much less is known about the details of their interactions. Using examples from the circadian (daily) clock in three organisms, Neurospora, Drosophila and mouse, we show, with mathematical models of varying complexity, how interactions among (i) promoter sites, (ii) proteins forming complexes, and (iii) cells can have a drastic effect on timekeeping. Inspired by the identification of many transcription factors, for example as involved in the Neurospora circadian clock, that can both activate and repress, we show how these multiple actions can cause complex oscillatory patterns in a transcription-translation feedback loop (TTFL). Inspired by the timekeeping complex formed by the NMO-PER-TIM-SGG complex that regulates the negative TTFL in the Drosophila circadian clock, we show how the mechanism of complex formation can determine the prevalence of oscillations in a TTFL. Finally, we note that most mathematical models of intracellular clocks model a single cell, but compare with experimental data from collections of cells. We find that refitting the most detailed model of the mammalian circadian clock, so that the coupling between cells matches experimental data, yields different dynamics and makes an interesting prediction that also matches experimental data: individual cells are bistable, and network coupling removes this bistability and causes the network to be more robust to external perturbations. Taken together, we propose that the interactions between components in biological timekeeping systems are carefully tuned towards proper function. We also show how timekeeping can be controlled by novel mechanisms at different levels of organization.
authors.affiliation: Department of Mathematics , University of Michigan , 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109 , USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: DeWoskin
authors.affiliation: Department of Mathematics , Southern Methodist University , 135 Clements Hall, Dallas, TX 75275 , USA.
authors.forename: Weihua
authors.initials: W
authors.lastname: Geng
authors.affiliation: Department of Mathematics , University of Michigan , 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109 , USA.
authors.forename: Adam R
authors.initials: AR
authors.lastname: Stinchcombe
authors.affiliation: Department of Mathematics , University of Michigan , 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109 , USA ; Center for Computational Medicine and Bioinformatics , University of Michigan , 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109 , USA.
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Forger
keywords: biological rhythms; circadian clocks; mathematical biology; systems biology