Stochastic simulation of the mammalian circadian clock

Abstract

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...

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

“…Some authors have also investigated stochastic effects in coupled cellular systems [11,[15][16][17][18] and the role of internal noise in stochastic resonance effects [16,[19][20][21][22][23]. To emphasize the importance of the stochastic treatment versus deterministic modeling, several comparisons of stochastic and deterministic models have been performed [12,[24][25][26][27][28].…”

Intrinsic, nondeterministic circadian rhythm generation in identified mammalian neurons

“…The variable nature of daily rhythms in isolated SCN neurons has been predicted by models of the transcription-translation circadian feedback loop in which noise (sometimes associated with low numbers of molecules) was added within a cell (7,24,25). Under these conditions, small perturbations (extrinsic or intrinsic to the cell) could push the molecular oscillator on or off a limit cycle.…”

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