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Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting
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10.1063/1.3690092
/content/aip/journal/jcp/136/10/10.1063/1.3690092
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/10/10.1063/1.3690092
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Time-correlation functions Ct) for the sensitivity of the average protein number 〈Nss (top) and the average mRNA number 〈Mss (bottom) to the model parameters, for the constitutive gene expression model in Sec. IV A. Points with error bars are simulations using the ensemble-averaged correlation function method; error bars are estimated by block-averaging (100 blocks of 103 trajectories; total ≈1010 time steps). Open circles are simulations using the time-averaged correlation function method with time-step pre-averaging (plotted as a function of ); results are averages over 10 trajectories each of length 109 steps (in this case, the error bars are smaller than symbols). Solid lines are theoretical predictions from Eq. (22). Parameters are k = 2.76 min−1, λ = 0.12 min−1, ρ = 3.2 min−1, μ = 0.016 min−1, corresponding to the cro gene in a recent model of phage lambda.16 For these parameters, 〈Mss = 23 and 〈Nss = 4600.

Image of FIG. 2.
FIG. 2.

Steady-state absolute differential gain for the stochastic focusing model in Sec. IV B, where k s is varied to control 〈Sss, with other parameters as in Eq. (26). Open circles are Gillespie simulations using the time-averaged correlation function method with time-step pre-averaging; error bars are estimated by averaging over 10 trajectories of length 108 steps. The history array length was n = 2 × 104. The filled circle (blue) is from a Gibson-Bruck simulation in COPASI using the ensemble-averaged correlation function method; error bars are from block averaging (10 blocks of 103 samples). The thick solid line (red) is the numerical result from the FSP algorithm. The dashed line is the mean-field theory prediction.

Image of FIG. 3.
FIG. 3.

Representative time traces of U and V in the Gardner et al. genetic switch model (Sec. IV C). Parameters are α1 = 50, β = 2.5, α2 = 16, and γ = 1.

Image of FIG. 4.
FIG. 4.

Steady-state probability distribution for the order parameter qUV in the Gardner et al. switch, and the sensitivity to β. Points (with small error bars in the case of the sensitivity) are from Gillespie simulations using the time-averaged correlation function method with time-step pre-averaging; error bars are estimated by averaging over 10 trajectories of 109 steps. The history array length was n = 5 × 104. The solid lines (red) are the results of the FSP applied to this problem. Model parameters are as in Fig. 3.

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/content/aip/journal/jcp/136/10/10.1063/1.3690092
2012-03-12
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/10/10.1063/1.3690092
10.1063/1.3690092
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