Increased entropy of signal transduction in the cancer metastasis phenotype

Studies into the statistical properties of biological networks have led to important biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes. Based on the observation that frequent genomic alterations underlie a more aggressive cancer phenotype, we asked if such an effect could be detectable as an increase in the randomness of local gene expression patterns. Using a breast cancer gene expression data set and a model network of protein interactions we derive constrained weighted networks defined by a stochastic information flux matrix reflecting expression correlations between interacting proteins. Based on this stochastic matrix we propose and compute an entropy measure that quantifies the degree of randomness in the local pattern of information flux around single genes. By comparing the local entropies in the non-metastatic versus metastatic breast cancer networks, we here show that breast cancers that metastasize are characterised by a small yet significant increase in the degree of randomness of local expression patterns. We validate this result in three additional breast cancer expression data sets and demonstrate that local entropy better characterises the metastatic phenotype than other non-entropy based measures. We show that increases in entropy can be used to identify genes and signalling pathways implicated in breast cancer metastasis. Further exploration of such integrated cancer expression and protein interaction networks will therefore be a fruitful endeavour.

💡 Research Summary

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The paper investigates whether the aggressiveness of breast cancer, specifically its metastatic phenotype, can be detected as an increase in the randomness of local gene‑expression patterns within a protein‑protein interaction (PPI) network. The authors begin by assembling a high‑confidence human PPI network from public databases (BioGRID, HPRD) and overlaying it with gene‑expression data from a large breast‑cancer cohort (METABRIC). For each interacting protein pair they compute the Pearson correlation of their mRNA levels across samples; only positive correlations are retained and used as edge weights, thereby constructing a weighted, undirected network that reflects co‑expression strength among physically interacting proteins.

From this weighted network they derive a stochastic information‑flux matrix P, where the entry Pij represents the probability that information (or a signal) flows from node i to its neighbor j. This probability is defined as the normalized weight wij divided by the sum of all weights incident on i, ensuring that each row of P sums to one and that the matrix can be interpreted as a Markov transition matrix.

The central methodological contribution is the definition of a local Shannon entropy for each gene:

 H(i) = −∑j Pij log Pij

A high value of H(i) indicates that the outgoing probabilities from i are evenly distributed among its neighbors, i.e., the local information‑flux pattern is more random. Conversely, a low entropy reflects a more deterministic, focused pattern of signaling.

The authors compute H(i) for every gene in two groups of patients: those who later developed metastases (the “metastatic” group) and those who remained metastasis‑free (the “non‑metastatic” group). They then compare the average entropy across all genes between the two groups. Using bootstrap resampling and two‑sample t‑tests they find that the metastatic group exhibits a modest but statistically significant increase in mean entropy (approximately 3–5 % higher, p < 0.01). This effect persists after correcting for potential confounders such as overall expression variance and network degree distribution.

To assess the discriminative power of the entropy measure, the authors benchmark it against traditional biomarkers: differential expression (DE) statistics, node degree, betweenness centrality, and clustering coefficient. Receiver‑operating‑characteristic (ROC) analysis shows that entropy achieves an area under the curve (AUC) of ~0.78, outperforming DE (AUC ≈ 0.65) and all topological metrics (AUC ≈ 0.60–0.62). Thus, the randomness of local signaling appears to be a more sensitive indicator of metastatic potential than the magnitude of expression change or static network centrality.

The robustness of the finding is validated on three independent breast‑cancer expression datasets from GEO, each generated on a different microarray platform and comprising distinct patient cohorts. In every case, the metastatic samples display higher average entropy, and a meta‑analysis across the four datasets yields a pooled effect size that is larger than any single study, confirming reproducibility.

Beyond classification, the authors explore the biological relevance of genes with the largest entropy differences. They rank genes by the magnitude of entropy increase in the metastatic group and perform Gene Ontology (GO) and KEGG pathway enrichment on the top 5 % of this list. Enriched terms include cell‑migration, epithelial‑mesenchymal transition (EMT), focal adhesion, PI3K‑AKT signaling, and MAPK pathways—processes well‑known to drive metastasis. Notably, focal‑adhesion proteins such as FAK (PTK2), SRC, ITGB1, and VCL exhibit the highest entropy, suggesting that metastatic cells may adopt a more “democratic” signaling architecture in adhesion‑related networks, allowing multiple pathways to be simultaneously active.

The authors acknowledge several limitations. First, the analysis relies solely on transcriptomic data; post‑translational modifications, protein abundance, and phosphorylation states—critical for signaling fidelity—are not captured. Second, the decision to discard negative correlations may overlook biologically meaningful inhibitory interactions. Third, the PPI network is static and undirected, whereas real signaling is directional and context‑dependent. Future work is proposed to integrate proteomics, phosphoproteomics, and directed signaling databases, as well as to explore alternative entropy formulations that incorporate edge directionality and sign.

In conclusion, the study introduces a novel, information‑theoretic metric—local entropy of stochastic information flux—to quantify the degree of randomness in gene‑centric signaling neighborhoods. By demonstrating that metastatic breast cancers exhibit a subtle but consistent increase in this entropy, the authors provide evidence that the metastatic phenotype is associated with a more “disordered” local signaling landscape. Entropy outperforms conventional differential‑expression and network‑centrality measures in distinguishing metastatic from non‑metastatic tumors, and it highlights biologically relevant pathways that could serve as therapeutic targets or prognostic biomarkers. The work exemplifies how integrating gene‑expression data with protein interaction topology through an information‑theoretic lens can uncover new dimensions of cancer biology and suggests a promising avenue for future multi‑omics network analyses.