A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM

Abstract

Many organisms display rhythms of physiology and behavior that are entrained to the 24-h cycle of light and darkness prevailing on Earth. Under constant conditions of illumination and temperature, these internal biological rhythms persist with a period close to 1 day ("circadian"), but it is usually not exactly 24h. Recent discoveries have uncovered stunning similarities among the molecular circuitries of circadian clocks in mice, fruit flies, and bread molds. A consensus picture is coming into focus around two proteins (called PER and TIM in fruit flies), which dimerize and then inhibit transcription of their own genes. Although this picture seems to confirm a venerable model of circadian rhythms based on time-delayed negative feedback, we suggest that just as crucial to the circadian oscillator is a positive feedback loop based on stabilization of PER upon dimerization. These ideas can be expressed in simple mathematical form (phase plane portraits), and the model accounts naturally for several hallmarks of circadian rhythms, including temperature compensation and the per(L) mutant phenotype. In addition, the model suggests how an endogenous circadian oscillator could have evolved from a more primitive, light-activated switch.

Discreteness-induced concentration inversion in mesoscopic chemical systems

“…As we show in the Supplementary Methods and Supplementary Discussion, discretenessinduced inversion effects also exist in the protein concentration output of a gene regulation network with negative feedback (Supplementary Figs S1 and S2). This motif is ubiquitous in biology, appearing in such diverse contexts as metabolism 38 , signalling 39 , somitogenesis 40 , and circadian clocks 41 . In biological systems, the gene network considered feeds into more complicated metabolic or signal-transduction networks, and it is plausible that the discreteness-induced concentration inversions at the level of the gene network are propagated into these downstream networks.…”

Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops

“…Hill coefficient of more than one was used to describe the activation of per expression by CLK or repression of per expression by PER to create oscillations, whereas in some models it was found that oscillations were preserved with a Hill coefficient of one if other parameters were properly chosen (Leloup and Goldbeter 1998;Tyson, Hong et al 1999;Kurosawa, Mochizuki et al 2002). Finally, we would like to make some comparisons with two previous models as the core mechanisms of these models are similar (Smolen, Hardin et al 2004;Ruoff, Christensen et al 2005).…”

“…In Drosophila, it has been shown experimentally that light enhances degradation of TIM, and consequently degradation of TIM in the light alters the level of other clock components and, thus, resets of phase of a oscillator (Zeng, Qian et al 1996). In terms of modelling, increase in TIM degradation rate has been used to model light response and entrainment to LD cycles in some previous models (Leloup and Goldbeter 1998;Tyson, Hong et al 1999). As TIM stabilises PER in the cytoplasm, the indirect effect of light is to regulate the localisation of PER and in turn to decrease the PER level in the nucleus.…”

“…(1) Single negative feedback model, where PER represses its own gene expression (Goldbeter 1995) or where PER/TIM dimers inhibit gene expression of per and tim (Leloup and Goldbeter 1998;Tyson, Hong et al 1999); (2) Two interlocking feedback loops model, where per and tim expressions are activated by CLK/CYC dimers and suppressed by PER/TIM dimers, and clk expression is repressed by CLK/CYC and derepressed by PER/TIM (Smolen, Baxter et al 2001;Ueda, Hirose et al 2002); (3) Most recent models involving clk expression activated by PDP1 and suppressed by VRI (Smolen, Hardin et al 2004;Ruoff, Christensen et al 2005). In this paper, we develop a mathematical model of gene expression for the five key components in the circadian clock in Drosophila.…”

A simple molecular mathematical model of mammalian hibernation

“…This is in striking contrast to research on circadian rhythms, which has a large and rapidly growing literature of models that span the metazoans (Forger and Peskin, 2003;Leise and Siegelmann, 2006;Nakajima et al, 2005;Tyson et al, 1999). The difference is largely due to the ubiquity of circadian rhythms, in particular their presence in several invertebrate and vertebrate model organisms including mammals (Dunlap and Loros, 2004;Hardin, 2005;K.…”