Analysing the robustness of cellular rhythms

Autonomous oscillations at the cellular level are important for various timing and signalling functions. The rhythms depend on environmental influences in a specific manner. In particular, the period of some rhythms has been shown to be very robust to certain environmental factors whereas other rhythms show a high sensitivity towards these factors. It is discussed that the robustness of the systems towards environmental changes results from underlying design principles. However, a comparison of robustness properties of different rhythms is lacking. Here we analyse the sensitivity of the oscillatory period with respect to parameter variations in models describing oscillations in calcium signalling, glycolysis and the circadian system. By comparing models for the same and different rhythms it is shown that the sensitivity depends on the oscillatory mechanism rather than the details of the model description. In particular, we find models of calcium oscillations to be very sensitive, those for glycolytic oscillations intermediately sensitive and models for circadian rhythms very robust. The results are discussed with respect to the temperature dependency of the rhythms. The question of what impact design principles have on the robustness of an oscillator, is addressed more explicitly by a direct comparison of systems with positive and negative feedback regulation for various reaction chain lengths. We find that the systems with negative feedback are more robust than corresponding systems with positive feedback. An increase in the length of the reaction chain under regulation leads to a decrease in sensitivity.