A new method for sensitivity analysis that elucidates the influence of model parameters on the period of oscillation is proposed. This method involves solving a Boundary Value Problem (the details haven't been carefully read). Using the solution of this BVP, the authors claims they can exactly calculate the sensitivities of state variables, amplitudes, and period of the oscillations.
They then apply this method to a detailed, mass-action-rate-law model of circadian clock in mammals. This model is probably the most detailed model to date published by Forger and Peskin (2003, PNAS) which consists of 73 species and 38 parameters. The mathematica file of the model is available. Sensitivity towards oscillatory period of parameters are ranked. It's found that most of the top ranked parametes involve the Per2 loop, suggesting its crucial importance in setting the period. In addition, CK1 Kinase activity was shown to be able to alter the period over a wide range.
This paer is useful for:
- Learn about sensivity analysis for oscillatory systems (need to study the method carefully though)
- Modelling of the mammalian circadian clock
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.