Modeling temperature entrainment of circadian clocks using the Arrhenius equation and a reconstructed model from Chlamydomonas reinhardtii

Abstract

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.

Multiscale effects of heating and cooling on genes and gene networks

“…S1 B . Note that the Hill function constants have been considered temperature independent, as they are ratios of rate constants and are specific for a certain reaction ( 83 ). The Arrhenius scaling of reaction rates for the 12 and 38 °C temperature conditions is discussed in SI Appendix , section 1.2 .…”

Differential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

“…Moreover, the above system involves a negative feedback: G p is converted to G i , G i is converted to A and A promotes the degradation of G p (figure 1). In the Goodwin oscillator, which also consists of three variables, a negative feedback is the cause of oscillation [41,42]. Inspired by the observation in figure 5 that the oscillations vanish at high k 5 values, we apply the QSSA for G i .…”

Differential equation based minimal model describing metabolic oscillations inBacillus subtilisbiofilms

“…Moreover, the above system involves a negative feedback: G p is converted to G i , G i is converted to A and A promotes the degradation of G p (Figure 1). In the Goodwin oscillator, which also consists of three variables, a negative feedback is the cause of oscillation 32,33 . Inspired by the observation that the oscillations vanish at high k 5 values, we applied the quasi-steady-state approximation (QSSA) for G i .…”

“…Since this positive feedback is the driving force for oscillations, at low values of k 1 G E , we observe a steady state rather than oscillations. In glycolytic and calcium oscillations, the cause of oscillations is also a positive feedback 9,10,12,37 while in a Goodwin oscillator it is a negative feedback 32,33 .…”