Model based conjectures on mammalian clock controversies

Forger, Daniel B.; Peskin, Charles S.

doi:10.1016/j.jtbi.2004.04.041

Cited by 25 publications

(15 citation statements)

References 22 publications

(31 reference statements)

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“…This finding is consistent with models of the mammalian clock for which simulated knockouts that are arrhythmic in ODE implementations can become rhythmic when stochasticity is incorporated [8]. (c) Individual stochastic runs.…”

Section: Investigating the Role Of Positive Feedbacksupporting

confidence: 83%

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Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Akman

Ciocchetta

Degasperi

et al. 2009

Computational Methods in Systems Biology

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Abstract. Circadian clocks are biochemical networks, present in nearly all living organisms, whose function is to regulate the expression of specific mRNAs and proteins to synchronise rhythms of metabolism, physiology and behaviour to the 24 hour day/night cycle. Because of their experimental tractability and biological significance, circadian clocks have been the subject of a number of computational modelling studies.In this study we focus on the simple circadian clock of the fungus Neurospora crassa. We use the Bio-PEPA process algebra to develop both a stochastic and a deterministic model of the system. The light on/off mechanism responsible for entrainment to the day/night cycle is expressed using discrete time-dependent events in Bio-PEPA.In order to validate our model, we compare it against the results of previous work which demonstrated that the deterministic model is in agreement with experimental data. Here we investigate the effect of stochasticity on the robustness of the clock's function in biological timing. In particular, we focus on the variations in the phase and amplitude of oscillations in circadian proteins with respect to different factors such as the presence/absence of a positive feedback loop, and the presence/absence of light. The time-dependent sensitivity of the model with respect to some key kinetic parameters is also investigated.

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Section: Investigating the Role Of Positive Feedbacksupporting

confidence: 83%

“…These include the fruit fly Drosophila melanogaster [3,4], the plant Arabidopsis thaliana [5,6] and the mouse Mus musculus [7,8]. Here we focus on the fungus Neurospora crassa, which possesses one of the most comprehensively studied circadian networks [9].…”

Section: Introductionmentioning

confidence: 99%

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Akman

Ciocchetta

Degasperi

et al. 2009

Computational Methods in Systems Biology

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“…CRY1 or CRY2 are transported by PER1 and PER2 into the nucleus of the cell, where they can bind to the control regions of the PER1, PER2, CRY1, and CRY2 genes to affect transcription. Rev-erb␣ is not included, because we previously found that its effect is negligible (10). Thus, our model consists of a biochemical feedback loop where PER1, PER2, CRY1, and CRY2 oscillate with an Ϸ24-h period.…”

Section: Simulation Methodsmentioning

confidence: 99%

Stochastic simulation of the mammalian circadian clock

Forger

Peskin

2004

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

156

136

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Circadian (nearly 24-h) clocks are remarkably accurate at timing biological events despite the randomness of their biochemical reactions. Here we examine the causes of their immunity to molecular noise in the context of a detailed stochastic mathematical model of the mammalian circadian clock. This stochastic model is a direct generalization of the deterministic mammalian circadian clock model previously developed. A feature of that model is that it completely specifies all molecular reactions, leaving no ambiguity in the formulation of a stochastic version of the model. With parameters based on experimental data concerning clock protein concentrations within a cell, we find accurate circadian rhythms in our model only when promoter interaction occurs on the time scale of seconds. As the model is scaled up by proportionally increasing the numbers of molecules of all species and the reaction rates with the promoter, the observed variability scales as 1͞n 0.5 , where n is the number of molecules of any species. Our results show that gene duplication increases robustness by providing more promoters with which the transcription factors of the model can interact. Although PER2 mutants were not rhythmic in the deterministic version of this model, they are rhythmic in the stochastic version. molecular noise ͉ Gillespie method ͉ mathematical models ͉ eukaryotic transcription regulation ͉ phosphorylation T he unicellular organism's timing of daily (circadian) biological events like luminescence (1) and O 2 consumption (2) can be attributed to an intracellular clock consisting of oscillating protein feedback loops. Higher organisms can time sleep, hormone release, and other biological processes by means of a population of cells, each of which seems to contain a biochemical clock similar in basic design to that found in unicellular organisms (3). Isolated cellular circadian clocks can time events with an error of less than Ϯ10% of the 24-h circadian day (2, 4) and might be able to time events with an error of Ͻ1% of the circadian day (1). Because chemical reactions in cells involve finite (and often low) numbers of molecules (5), individual molecular interactions can be important. One cause of circadian mistiming is molecular noise (the fact that interactions between individual molecules are stochastic). The accuracy of circadian clocks can be essential for survival, and there is likely a strong evolutionary selection to overcome molecular noise.This article is concerned with the mechanisms by which biochemical circadian clocks maintain high accuracy with low numbers of molecules despite the stochasticity of individual molecular interactions (molecular noise). Much recent attention has focused on model predictions of the accuracy of circadian rhythms in the presence of molecular noise, and the predictions of these models have been somewhat conflicting (6, 7). Although there is a widely accepted scheme for stochastic simulation of molecular processes, the Gillespie method (8), circadian clock models often are not detailed e...

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“…Th eir model contains 19 coupled equations with 53 parameters and accounts for physiological disorders and the existence of multiple sources of oscillatory behavior. Recently, Forger and Peskin [16,17] have developed a detailed, distinctly mammalian model by using the mass action kinetics with 73 diff erential equations. Th e parameters of their model, found by co-ordinate search method, accurately predicted the phase of the entrainment, amplitude of the oscillation and the time series of the mRNA and protein concentrations.…”

Section: Biological Circuit and Mathematical Model Description Of Earmentioning

confidence: 99%

Discrete Delay Model for the Mammalian Circadian Clock

2006

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A three-variable discrete delay model is proposed for the circadian rhythm of the mammals with BMAL1, PER-CRY complex and REV-ERBαprotein concentrations as the dynamical variables. The delay model is phenomenological in nature rather than the precise description of all the underlying complex processes. The goal of this paper is to study the effects of delay in the circadian rhythms of mammals that appears in both the positive and negative feedback loops of the model. The delay model exhibits 24-hour limit cycle oscillations, entrainment to light-dark (LD) cycles and phase response curves. The model is also found to exhibit quasiperiodic and chaotic oscillations under LD cycles when delay is varied. These are linked to non-24-hour sleep-wake syndrome and cancer incidence. The mutations in Bmal1^–/– , Per^Brdm¹, Rev-Erbα^–/–are explained in terms of delay, whereas the double mutations Per^Brdm¹/Cry2^–/–and Cry1^–/–/ Cry2^–/–are explained in terms of the strength of delayed positive and negative regulations. The delay model in essence captures the core mechanism of the mammalian circadian rhythms with a smaller number of variables and parameters.

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Model based conjectures on mammalian clock controversies

Cited by 25 publications

References 22 publications

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Stochastic simulation of the mammalian circadian clock

Discrete Delay Model for the Mammalian Circadian Clock

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