The Per2 Negative Feedback Loop Sets the Period in the Mammalian Circadian Clock Mechanism

Abstract

Processes that repeat in time, such as the cell cycle, the circadian rhythm, and seasonal variations, are prevalent in biology. Mathematical models can represent our knowledge of the underlying mechanisms, and numerical methods can then facilitate analysis, which forms the foundation for a more integrated understanding as well as for design and intervention. Here, the intracellular molecular network responsible for the mammalian circadian clock system was studied. A new formulation of detailed sensitivity analysis is introduced and applied to elucidate the influence of individual rate processes, represented through their parameters, on network functional characteristics. One of four negative feedback loops in the model, the Per2 loop, was uniquely identified as most responsible for setting the period of oscillation; none of the other feedback loops were found to play as substantial a role. The analysis further suggested that the activity of the kinases CK1δ and CK1ɛ were well placed within the network such that they could be instrumental in implementing short-term adjustments to the period in the circadian clock system. The numerical results reported here are supported by previously published experimental data.

Author Summary

Network models of biological systems are appearing at an increasing rate. By encapsulating mechanistic detail of chemical and physical processes, mathematical models can successfully simulate and predict emergent network properties. However, methods are needed for analyzing the role played by individual biochemical steps in producing context-dependent system behavior, thereby linking individual molecular knowledge with network properties. Here, we apply sensitivity analysis to analyze mammalian circadian rhythms and find that a contiguous series of reactions in one of the four negative feedback loops carries primary responsibility for determining the intrinsic length of day. The key reactions, all involving the gene per2 and its products, include Per2 mRNA export and degradation, and PER2 phosphorylation, transcription, and translation. Interestingly, mutations affecting PER2 phosphorylation have previously been linked to circadian disorders. The method may be generally applicable to probe structure–function relationships in biological networks.