Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Abstract

Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of selfsustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms.

A Robust Model for Circadian Redox Oscillations

“…The results are shown in Figure A5. As expected [25,26], translocation and degradation rates d, e and q control the period most strongly, but interestingly also the reactivation kinetics represented by b has some effects on the period. Figure A5.…”

Modeling circadian clocks: From equations to oscillations

“…These predictions were consistent with the subsequent characterization of the dbt mutations that affect the stability and the period of the activity rhythm of Drosophila [84]. Note that the changes in the shape of the oscillations, as well as the variation of the period as a function of control parameters, depend not only the architecture but also on other parameter values and they are often difficult to predict intuitively [85][86][87].…”

The Goodwin model revisited: Hopf bifurcation, limit-cycle, and periodic entrainment

“…Since such mechanism is at the core of the circadian (and other) genetic network, it is of interest to study the dynamical properties of this model. Many circadian models are extensions and variants of the Goodwin model (Ruoff et al 1999, Gérard et al 2009.…”