On the Precision of Circadian Oscillators

Precision is a crucial property of noisy circadian oscillators that can be quantified by the quality factor (Q). Until now, deterministic properties of circadian oscillations like the period or amplitude attracted most of the attention while relatively few studies addressed the problem of assessing Q. One reason is that Q is more difficult to access experimentally and even theoretically. The main objective of this thesis is to provide methods to efficiently estimate Q both in experimental data of cell-autonomous circadian oscillations and stochastic models. First a theoretical study, in an effort to unify existing low noise approximations of Q with different domains of validity near or away of Hopf bifurcations (HBs), shows that the link between the two cases lies in the projection of the Langevin Equation onto the phase gradient vector. Furthermore we formulate both approximations in a way that permits application to generic oscillator models undergoing HBs and applied them to a 16-dimensional circadian model. We find that as the noise increases, the precision of oscillations of individual chemical species and agreement with the global precision predicted by the low noise approximations, become species dependent. In a second part we first discuss in detail which methods, based on our theoretic study, are best suited to reliably estimate Q for different types of experimental data. Comparing the simple brownian phase model with single cell resolution bioluminescence data, we then support the assumption, that it is reasonable to consider different cells as identical oscillators. This allows to compensate the relatively short time scales available in experimental data by sampling many different cells. Then we extend existing software to accurately track bioluminescence emitting mammalian cells, subjected to different conditions of reduced transcription rates, and, taking advantage of the methods that we elaborated, estimate Q. Comparing this additional information to the prediction of the minimal Normal Form model we arrive at the conclusion that these noisy oscillators are operating in a self-sustained rather than damped regime. This work yields a better understanding of how molecular noise affects the precision of biochemical oscillators and has important implications for the interpretation and design of experiments aimed at measuring the precision of molecular oscillators

Analysis of precision in chemical oscillators: implications for circadian clocks

Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms.</p

Circadian gene expression is resilient to large fluctuations in overall transcription rates

Mammalian circadian oscillators are considered to rely on transcription/translation feedback loops in clock gene expression. The major and essential loop involves the autorepression of cryptochrome (Cry1, Cry2) and period (Per1, Per2) genes. The rhythm-generating circuitry is functional in most cell types, including cultured fibroblasts. Using this system, we show that significant reduction in RNA polymerase II-dependent transcription did not abolish circadian oscillations, but surprisingly accelerated them. A similar period shortening was observed at reduced incubation temperatures in wild-type mouse fibroblasts, but not in cells lacking Per1. Our data suggest that mammalian circadian oscillators are resilient to large fluctuations in general transcription rates and temperature, and that PER1 has an important function in transcription and temperature compensation