Local entropy changes in integrated PIN-mRNA networks. In the above hypothetical networks, an edge represents a documented interaction between the corresponding proteins in the PIN. The color of the edge codes for the pairwise correlation in mRNA expression in two different conditions, here non-metastatic and metastatic cancer. In this hypothetical example, gene-1 is positively correlated with maximal value (C = 1) to the first 6 genes, but negatively correlated (C = -1) to the remaining four in the non-metastatic PIN-mRNA network. These values translate to a stochastic positive flux vector p = 1/6 (1, 1, 1, 1, 1, 1, 0, 0, 0, 0) and to an entropy value of 0.78 (Methods). In this hypothetical example, gene-1 is lost/mutated in metastatic cancer, leading to a loss of mRNA expression correlation and anti-correlation with the nearest neighbors. This introduces more disorder/randomness in the local flux distribution, illustrated here by zero correlation values. The resulting local entropy takes on a maximum value of 1, and so for this node there is a large increase in the local entropy which is statistically significant. In contrast, a Wilcoxon rank sum test between the correlation values C = (1, 1, 1, 1, 1, 1, -1, -1, -1, -1) and C = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0) yields a non-significant P-value of 0.2.