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An effective method for computing the noise in biochemical networks
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10.1063/1.4792444
/content/aip/journal/jcp/138/8/10.1063/1.4792444
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/8/10.1063/1.4792444
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Figures

Image of FIG. 1.
FIG. 1.

Shown is that LNA gives approximate noise whereas our method gives exact noise. (a) The noise strength in two-species system (17) with is taken as a function of the parameter λ1. The other parameters are λ2 = 10, τ1 = 2, τ2 = 1. (b) The noise strength in the two-species system (17) with is taken as a function of the parameter λ2. The other parameters are λ1 = 1, τ1 = 2, τ2 = 1.

Image of FIG. 2.
FIG. 2.

Schematic of gene expression models considering promoter activity (active or inactive): (a) two-stage gene model and (b) three-stage gene model.

Image of FIG. 3.
FIG. 3.

Multi-state gene expression models and chromatin template-controlled noise in mRNA: (a) Schematic of a multi-inactive-state model of gene expression; (b) schematic of a multi-active-state model of gene expression; (c) the mean noise strength ratio as a function of two experimentally-measureable indices τ on and τ off , where both and are obtained from one of 1000 sets of randomly sampling τ1, …, τ K with the fixed τ on and τ off for the fixed KL = R = 10 (where L and R represent the number of OFF states and ON states, respectively). The other parameters are μ = 20, δ = 1, K = 10; (d), (e), and (f) shown is the histogram of (red) and (green), where (d), (e) and (f) correspond to points D, E and F labeled in (c), respectively.

Image of FIG. 4.
FIG. 4.

The effect of multi-state mechanism on the noise in gene expression. (a) Schematic of multi-inactive-active-state model of gene expression. (b)–(d) The noise strength as a function of the parameter k ≡ λ4 = λ 4 = λ5 = λ 5 = λ6 = λ 6. The other parameter values used in computation are λ1 = 2, λ2 = 1, λ3 = 1, γ2 = 1, γ3 = 1, μ = 5 and (b) γ1 = 1, (c) γ1 = 2, (d) γ1 = 1.7.

Image of FIG. 5.
FIG. 5.

The effect of feedback mechanisms on the noise in gene expression. (a) Schematic of auto-activation model of gene expression. (b) Schematic of auto-repression model of gene expression. (c) The noise strength as a function of the positive feedback strength (a) for system (62) , where the parameters are λ = γ = 1, μ = 5, δ = 0.1. (d) The noise strength as a function of the negative feedback strength (r) for system (71) , where the parameters are λ = γ = 1, μ = 5, δ = 0.1.

Image of FIG. 6.
FIG. 6.

(a) Schematic of the enzymatic futile cycle reaction mechanism. (b) The noise strength as a function of the total number N T , showing that there is an extreme, where the parameters are k 1 = 1, k −1 = 1, k 2 = 10, k −2 = 0.01.

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/content/aip/journal/jcp/138/8/10.1063/1.4792444
2013-02-26
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An effective method for computing the noise in biochemical networks
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/8/10.1063/1.4792444
10.1063/1.4792444
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