One of the most important aspects of life is the rhythmic behavior that is rooted in the many regulatory mechanisms that control the dynamics of living systems. The most common biological rhythms are circadian rhythms, which occur with a period close to 24 h, allowing organisms to adapt to periodic changes in the terrestrial environment [1]. With the rapid accumulation of new data on gene, protein and cellular networks, it is becoming increasingly clear that genes are heavily involved in the cellular regulatory interactions underpinning circadian rhythms [4,23]. However, a detailed picture of the genetic architecture of circadian rhythms has not been obtained, although ongoing projects such as the Human Genome Project will assist in the characterization of circadian genetics.
Traditional strategies for identifying circadian clock genes in mammals have been based on the analysis of single gene mutations and the characterization of genes identified by cross-species homology, and have laid an essential groundwork for circadian genetics [6,23]. However, these strategies do not include a more thorough examination of the breadth and complexity of influences on circadian behavior throughout the entire genome. Genetic mapping relying upon genetic linkage maps has provided a powerful tool for identifying the quantitative trait loci (QTL) responsible for circadian rhythms. In a mapping study of 196 F2 hybrid mice, Shimomura et al. [24] detected 14 interacting QTL that contribute to the variation of rhythmic behavior in mice by analyzing different discrete aspects of circadian behavior: free-running circadian period, phase angle of entrainment, amplitude of the circadian rhythm, circadian activity level, and dissociation of rhythmicity.
The data of Shimomura et al. [24] point to promising approaches for genome-wide analysis of rhythmic phenotypes in mammals including humans. Their most significant drawback is the lack of robust statistical inferences about the dynamic genetic control of circadian rhythms. Typically, biological rhythms are dynamic traits, and the pattern of their genetic determination can change dramatically with time. In this article, we have incorporated mathematical models and concepts regarding the molecular and cellular mechanisms of circadian rhythms into a general framework for mapping dynamic traits, called functional mapping [11]. Based firmly on experiments, robust differential equations have been established to provide an essential tool for studying and comprehending the cellular networks for circadian rhythms [1,25-27]. As an attempt to integrate differential equations into functional mapping, the statistical model shows favorable properties in estimating the effects of a putative QTL and its association with polymorphic markers. The simulation study results suggest that the parameters determining the behavior and shape of circadian rhythmic curves can be estimated reasonably even if the QTL effect is small to moderate. As seen in general functional mapping [11], the model implemented with a system of differential equations also allows us to make a number of biologically meaningful hypothesis tests for understanding the genetic control of rhythmic responses in organisms.
As a first attempt of its kind, the model proposed in this article has only considered one QTL associated with circadian rhythms. A one-QTL model is definitely not sufficient to explain the complexity of the genetic control of this trait. A model incorporating multiple QTL and their interactive networks should be derived; this is technically straightforward. In addition, the system of circadian rhythms is characterized by two variables, and this may also be too simple to reflect the complexity of rhythmic behavior. A number of more sophisticated models, governed by systems of five [28], ten [29] or 16 kinetic equations [4,30,31], have been constructed to describe the detailed features of a rhythmic system in regard to responses to various internal and environmental factors. While the identification of circadian clock genes can elucidate the molecular mechanism of the clock, our model will certainly prove its value in elucidating the genetic architecture of circadian rhythms and will probably lead to the detection of the driving forces behind circadian genetics and its relationship to the organism as a whole.
Competing interests
The author(s) declare that they have no competing interests.
Top Authors' contributions
The entire theoretical concept of the work was envisaged by RLW. The mathematical and statistical modeling was carried out by TL with feedback from XLL and YMC.
Acknowledgements
The preparation of this manuscript was supported by NSF grant (0540745) to RLW.
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