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. 2006 Sep 8;2(9):e117.
doi: 10.1371/journal.pcbi.0020117. Epub 2006 Jul 25.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Manuel Barrio  1 , Kevin Burrage, André Leier, Tianhai Tian
Affiliations

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Manuel Barrio et al. PLoS Comput Biol. .

Abstract

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

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Conflict of interest statement

Competing interests. The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. DDE Solution: Exploring the Effect of h on Protein
Figure 2
Figure 2. DDE Solution: Exploring the Effect of Delay on Protein
Figure 3
Figure 3. DDE Solution: Exploring the Effect of Large P 0
Figure 4
Figure 4. DSSA Simulations: Exploring the Effects of Delay
The horizontal dotted line marks P 0, mRNA is represented by the solid line, and protein by the dashed line.
Figure 5
Figure 5. DSSA Simulations: Exploring the Effects of h
The horizontal dotted line marks P 0, mRNA is represented by the solid line, and protein by the dashed line.
Figure 6
Figure 6. DSSA Simulations: Exploring the Effects of P 0
The horizontal dotted line marks P 0, mRNA is represented by the solid line, and protein by the dashed line.
Figure 7
Figure 7. DSSA Simulation: Calculating the Arithmetic Mean over 1,000 Simulations for Both Constant and Variable Delay
Figure 8
Figure 8. Mean Oscillation Frequencies for Different Delay Values (P 0, h, μm, μp Are Fixed)
Figure 9
Figure 9. DSSA Simulations for P 0 = 100, h = 3, τ = 10 (Top) and P 0 = 100, h = 4, τ = 15 (Bottom) over 12 h and 2 h
Left, more than 12 h. Right, more than 2 h. The dotted horizontal line corresponds to P 0. Solid lines represent mRNA, dashed lines protein populations.
Figure 10
Figure 10. Sensitivity Analysis: DSSA Simulations with Perturbed Rate Constants
(A) αm . (B) αp . (C) μm . (D) μp.
Figure 11
Figure 11. DSSA Simulation
(A) Mimicking blocking of Hes1 protein degradation by a proteasome inhibitor. (B) Mimicking inhibition of translation by cycloheximide treatment.
See this image and copyright information in PMC

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