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Additivity of noise propagation in a protein cascade
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View: Figures


Image of FIG. 1.
FIG. 1.

Modeling genetic cascades, where the transcriptional rate of mRNA is assumed to be constant, and the transcriptional rates of mRNA are regulated only by protein for . The concentrations of proteins are denoted by for .

Image of FIG. 2.
FIG. 2.

The trajectories of difference [Eq. (21)] for four different cases are plotted, where (a) , (b) , (c) , and (d) .

Image of FIG. 3.
FIG. 3.

The sequence is plotted vs the cascade stage . It shows clearly how the expected output levels are dependent sensitively on the expected input levels, where (a) , , , and ; (b) , , , and ; (c) , , , and ; and (d) , , , and . For all the cases, we take .

Image of FIG. 4.
FIG. 4.

The Monte Carlo simulation results are plotted, where the cascade length is 10, and the parameters are taken as , , and in (a), and , , and in (b). The -axis denotes the noise and -axis the cascade stage . In both (a) and (b), all proteins have the same expectation, i.e., for for different values. The algorithm of Monte Carlo simulation is from Gillespie (Ref. 22). The stochastic simulation results match well with the theoretical predictions (dotted, solid dotted-broken, and broken lines).

Image of FIG. 5.
FIG. 5.

The noises vary as the function of input concentration and cascade length. The -axis denotes the cascade stage , -axis the input concentration , and -axis the noise. The parameters , , and are taken as , , and in (a), and , , and in (b).

Image of FIG. 6.
FIG. 6.

The normalized covariance measures the statistical correlation between proteins and . Here, the normalized covariance is plotted vs the input concentration and scade stage , where the parameters , , and are taken as , , and in (a), and , , and in (b).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Additivity of noise propagation in a protein cascade