Abstract
Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.
Highlights
Most living organisms present rhythmic phenomena whose periods range from few milliseconds to years
For the individual clock neurons we have adapted a model originally proposed by Goldbeter [6] that explicitly includes (i) transcription: the gene is transcribed into mRNA (Mp) in the absence of phosphorylated PER in the nucleus (PN ), assuming, that the repression is cooperative; (ii) translation: a portion of this mRNA is degraded, and another portion is translated into PER protein (P0) in the cytoplasm; (iii) phosphorylation: PER protein is phosphorylated in a reversible way twice; (iv) degradation: the fully phosphorylated PER (P2) is degraded by the default molecular machinery following a Michaelis-Menten rate expression; (v) transport: the entrance of PER into the nucleus is assumed to be a reversible first-order process
In the bottom-left panel (LD condition) we can see that vd must be smaller than 2.85 to obtain circadian oscillation; for higher values of vd the period is shorter than 24 hs
Summary
Most living organisms present rhythmic phenomena whose periods range from few milliseconds to years. The molecular mechanisms of these fundamental oscillators consist mainly of two interlocked transcriptional feedback loops involving per, tim, clk, vri and pdp genes [2,3]. The PER protein is phosphorylated at several residues This leads to a time delay between the rise of mRNAs and that of the PER acting as transcriptional repressor for the clk gene. A number of deterministic and stochastic models for the circadian clock have been proposed [6,7,8,9,10,11] They differ largely in the detail of the specific oscillator and, in their complexity
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