Differential network entropy reveals cancer system hallmarks

Abstract

The cellular phenotype is described by a complex network of molecular interactions. Elucidating network properties that distinguish disease from the healthy cellular state is therefore of critical importance for gaining systems-level insights into disease mechanisms and ultimately for developing improved therapies. By integrating gene expression data with a protein interaction network we here demonstrate that cancer cells are characterised by an increase in network entropy. In addition, we formally demonstrate that gene expression differences between normal and cancer tissue are anticorrelated with local network entropy changes, thus providing a systemic link between gene expression changes at the nodes and their local correlation patterns. In particular, we find that genes which drive cell-proliferation in cancer cells and which often encode oncogenes are associated with reductions in network entropy. These findings may have potential implications for identifying novel drug targets.

Figure 1

(A) Boxplots of the local network entropies (y-axis, S) (equation 1)in cancer (C) and normal (N) tissue for all nodes with degree ≥ 10 (~ 3500 nodes) and across the six different tissue types. P-values are from a one-tailed unpaired Wilcoxon rank sum test. Network entropies have been normalised so that the maximum attainable value is 1. See Fig. S2 for the corresponding plot using all nodes with degree ≥ 2. (B) Boxplots of the z-statistics of differential entropy between cancer and normal tissue. Positive z-statistics indicate higher entropy in cancer. P-values from a one-tailed Wilcoxon rank sum test are given.

Figure 2

(A) Scatterplots of absolute differential network entropy changes between normal and cancer (y-axis) against log₂(k) (x-axis) where k is the degree of the node, for each tissue type.(B) Scatterplots of the corresponding absolute differential entropy z-statistics (y-axis) against log₂(k) (x-axis). In both cases, we provide the Spearman rank correlation coefficient (SCC).

Figure 3. z-statistics of differential non-local network entropy (x-axis) for the six different tissues (y-axis).

The network entropy considered here is the measure (equation 2) which is defined for a stochastic diffusion matrix for maximum path lengths of order 2 (Methods). Positive z-statistics means higher entropy in cancer compared to normal. Green lines indicate the 95% confidence interval envelope and given P-values are from a normal null distribution centred at zero.