Extracting Dynamics from Static Cancer Expression Data

Static expression experiments analyze samples from many individuals. These samples are often snapshots of the progression of a certain disease such as cancer. This raises an intriguing question: Can we determine a temporal order for these samples? Such an ordering can lead to better understanding of the dynamics of the disease and to the identification of genes associated with its progression. In this paper, we formally prove, for the first time, that under a model for the dynamics of the expression levels of a single gene, it is indeed possible to recover the correct ordering of the static expression data sets by solving an instance of the traveling salesman problem (TSP). In addition, we devise an algorithm that combines a TSP heuristic and probabilistic modeling for inferring the underlying temporal order of the microarray experiments. This algorithm constructs probabilistic continuous curves to represent expression profiles and can thus account for noise and for individual background expression differences leading to accurate temporal reconstruction for human data. Applying our method to cancer expression data, we show that the ordering derived agrees well with survival duration. A classifier that utilizes this ordering improves upon other classifiers suggested for this task. The set of genes displaying consistent behavior for the determined ordering is enriched for genes associated with cancer progression.