Multiplicity: an organizing principle for cancers and somatic mutations

Background: With the advent of whole-genome analysis for profiling tumor tissue, a pressing need has emerged for principled methods of organizing the large amounts of resulting genomic information. We propose the concept of multiplicity measures on cancer and gene networks to organize the information in a clinically meaningful manner. Multiplicity applied in this context extends Fearon and Vogelstein's multi-hit genetic model of colorectal carcinoma across multiple cancers. Methods: Using the Catalogue of Somatic Mutations in Cancer (COSMIC), we construct networks of interacting cancers and genes. Multiplicity is calculated by evaluating the number of cancers and genes linked by the measurement of a somatic mutation. The Kamada-Kawai algorithm is used to find a two-dimensional minimum energy solution with multiplicity as an input similarity measure. Cancers and genes are positioned in two dimensions according to this similarity. A third dimension is added to the network by assigning a maximal multiplicity to each cancer or gene. Hierarchical clustering within this three-dimensional network is used to identify similar clusters in somatic mutation patterns across cancer types. Results: The clustering of genes in a three-dimensional network reveals a similarity in acquired mutations across different cancer types. Surprisingly, the clusters separate known causal mutations. The multiplicity clustering technique identifies a set of causal genes with an area under the ROC curve of 0.84 versus 0.57 when clustering on gene mutation rate alone. The cluster multiplicity value and number of causal genes are positively correlated via Spearman's Rank Order correlation (r(s)(8) = 0.894, Spearman's t = 17.48, p < 0.05). A clustering analysis of cancer types segregates different types of cancer. All blood tumors cluster together, and the cluster multiplicity values differ significantly (Kruskal-Wallis, H = 16.98, df = 2, p < 0.05). Conclusion: We demonstrate the principle of multiplicity for organizing somatic mutations and cancers in clinically relevant clusters. These clusters of cancers and mutations provide representations that identify segregations of cancer and genes driving cancer progression.