A detailed predictive model of the mammalian circadian clock

Abstract

Experimental data on the circadian (Ϸ24-h) clock in mammalian cells are vast, diverse, and detailed. Mathematical models are therefore needed to piece these data together and to study overall clock behavior. Previous models have focused on Neurospora or Drosophila or can be converted to a Drosophila model simply by renaming variables. Those models used Hill-type terms for transcription regulation and Michaelis-Menten type or delay terms for posttranslation regulation. Recent mammalian experimental data call into question some of the assumptions in these approaches. Moreover, gene duplication has led to more proteins in the mammalian system than in lower organisms. Here we develop a detailed distinctly mammalian model by using mass action kinetics. Parameters for our model are found from experimental data by using a coordinate search method. The model accurately predicts the phase of entrainment, amplitude of oscillation, and shape of time profiles of clock mRNAs and proteins and is also robust to parameter changes and mutations.mathematical models ͉ eukaryotic transcription regulation ͉ PER ͉ CRY ͉ CLOCK M en and women lead scheduled lives in which the time of day dictates when to eat, sleep, work, or relax. To live this way, our bodies must have internal clocks to know when to be prepared for eating, sleeping, working, or relaxing. Amazingly, many cells in our bodies have such a clock that is coordinated by the cellular clocks within the suprachiasmatic nucleus (SCN) cells of the brain. Each cell's clock is much more complex than some might naively imagine, because it involves many interacting genes and proteins. For this reason, mathematical models are needed for any hope of understanding cellular clocks in a detailed way.At its core, the circadian clock within a cell is a series of biochemical reactions that produce Ϸ24-h oscillations. As long as the details of these reactions were largely unknown, early modeling attempts made simplifying assumptions about the reactions within the clock to keep the number of equations at a minimum. For instance, some authors represented many biochemical processes as simply a delay (1). Most models also assumed low enzyme concentrations (summarized in ref.2). Both of these simplifying assumptions made it easier for a model to oscillate.Recent advances provide a more detailed picture of mammalian cellular circadian clocks than these earlier models represent and even challenge some assumptions made in previous models. There is no pure delay in the clock. Likewise, the key enzyme in the mammalian circadian clock, casein kinase I (CKI), is expressed at a higher concentration than its substrates, the PERIOD proteins, PER1 and PER2 (3). Moreover, with the recent advances in computational speed and software designed to simulate biochemical processes (e.g., BIOSPICE, www.biospice. org), the number of equations in a model does not need to be limited by computational resources. In short, we are now able to identify many of the specific reactions involved in the clock and directly simula...

Synchrony and entrainment properties of robust circadian oscillators

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“…In §4, we introduce stochasticity via multiplicative white noise and simulate the model as a system of stochastic differential equations (SDEs). By moving from a discrete stochastic to a continuous stochastic framework, the noise we consider is idealized 1 per3 is not taken into account because biological evidence shows that its disruption does not have a strong effect on clock performance ( Forger & Peskin 2003). 2 The study of phase synchrony via the coupling of a population of circadian oscillators is better understood in mammals than in flies.…”

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.…”

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

“…However, the models do not account for binding of transcription factors to promoters due to the description of transcriptional processes by Hill functions. A general model for the circadian clocks developed by Vilar (Vilar, Kueh et al 2002) and a mammalian circadian model proposed by Forger (Forger and Peskin 2003) include explicit descriptions of the binding and unbinding processes of transcription factors to promoters. We propose that such description needs to be incorporated into the Drosophila clock model to explore transcriptional behaviour more explicitly.…”