  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.
