Modelling the effect of phosphorylation on the circadian clock of Drosophila

Translational thresholds in a core circadian clock model

Organisms have evolved in a daily cyclic environment, developing circadian cell-autonomous clocks that temporally organize a wide range of biological processes. Translation is a highly regulated process mainly associated with the activity of microRNAs (miRNAs) at the translation initiation step that impacts on the molecular circadian clock dynamics. Recently, a molecular titration mechanism was proposed to explain the interactions between some miRNAs and their target mRNAs; new evidence also indicates that regulation by miRNA is a nonlinear process such that there is a threshold level of target mRNA below which protein production is drastically repressed. These observations led us to use a theoretical model of the circadian molecular clock to study the effect of miRNA-mediated translational thresholds on the molecular clock dynamics. We model the translational threshold by introducing a phenomenological Hill equation for the kinetics of PER translation and show how the parameters associated with translation kinetics affect the period, amplitude, and time delays between clock mRNA and clock protein expression. We show that our results are useful for analyzing experiments related to the translational regulation of negative elements of transcriptional-translational feedback loops. We also provide new elements for thinking about the translational threshold as a mechanism that favors the emergence of circadian rhythmicity, the tuning of the period-delay relationship and the cell capacity to control the protein oscillation amplitude with almost negligible changes in the mRNA amplitudes.

Effects of different per translational kinetics on the dynamics of a core circadian clock model

Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.

Velocity response curves demonstrate the complexity of modeling entrainable clocks

Circadian clocks are biological oscillators that regulate daily behaviors in organisms across the kingdoms of life. Their rhythms are generated by complex systems, generally involving interlocked regulatory feedback loops. These rhythms are entrained by the daily light/dark cycle, ensuring that the internal clock time is coordinated with the environment. Mathematical models play an important role in understanding how the components work together to function as a clock which can be entrained by light. For a clock to entrain, it must be possible for it to be sped up or slowed down at appropriate times. To understand how biophysical processes affect the speed of the clock, one can compute velocity response curves (VRCs). Here, in a case study involving the fruit fly clock, we demonstrate that VRC analysis provides insight into a clock׳s response to light. We also show that biochemical mechanisms and parameters together determine a model׳s ability to respond realistically to light. The implication is that, if one is developing a model and its current form has an unrealistic response to light, then one must reexamine one׳s model structure, because searching for better parameter values is unlikely to lead to a realistic response to light.