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Leveraging the "cause-and-effect" network models together with Network Perturbation Amplitude (NPA) algorithms ([ 29, 43]), the fold changes of gene expression were translated into differential network backbone value for each backbone node in the network.
Using the backward reasoning, we develop the network perturbation amplitude (NPA) algorithm that provides a quantification of the backbone nodes [ 23, 25, 29], which is called the "differential network backbone value" (illustrated in Figure 1, inset).
The "differential network backbone value" was the result of a fitting procedure between the network model and the gene expression fold changes, where the smoothest function (accounting for the sign of the causal edges) was derived by further imposing a boundary condition on the backbone nodes corresponding to the gene expression changes.
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Subsequently, correlations between the backbone values were computed.
The 95%-confidence intervals of the differential backbone values are shown for the two perturbations (axes).
Consistently, we observed the upregulated differential network backbone values for these aforementioned CYPs).
The differential network backbone values were in turn summarized into a quantitative measure of NPA score for the entire network.
Thus, the differential network backbone values in this specific network exemplify the activity of biological mechanisms pertaining to xenobiotic metabolism.
Thus, the quantification of the backbone nodes (i.e., the "differential network backbone values") in this model reflects the biological mechanisms pertaining to xenobiotic metabolism.
Statistical correlations were computed for the differential network backbone values and fold changes of gene expression, including R, Pearson correlation, and Spearman correlation, along with the P values.
The differential network backbone values continue to be correlated between the bronchial and nasal at the 4, 24, and 48 h after exposure time).
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