As shown above, hierarchical currently graphs can be used in a formal manner to model cell signaling systems. In addition, they can be incorporated into executable mod els in place of regular graphs. As an example, we have developed a version of the popular Nauty code which can take as input hierarchical graphs. This is important because, as noted above, determining graph isomorph ism can take a significant amount of computation time in network generation. As detailed above, HNauty dif fers only slightly from the main outline of Nauty given by McKay. Indeed, the formalism distinguishing graphs and hierarchical graphs is also slight. Thus, we propose that the use of hierarchical graphs may, at little cost, allow for greater clarity of rule based models for biochemical systems.

Conclusions The graphs and algorithm introduced here lay the groundwork for rule based models that are easier to understand, because molecules with complicated sub structures can be more naturally represented. Esophageal cancer is one of the leading causes of death from cancers worldwide. The two major histotypes of esophageal cancer are esophageal squamous cell carci noma and Barretts adenocarcinoma. Several specific molecular alterations play crucial roles in the carcinogenesis of ESCC or BAC, with tumor cell aneuploidy and p53 mutations being major hallmarks of both ESCC and BAC. In fact, aneuploidy is found in 50% to 70% of ESCC and is associated with poor prognosis. In BAC, similar high rates of aneuploidy are seen for invasive carcinomas, and aneuploidy is an early event in the metaplasia dysplasia adenocarci noma sequence of BAC.

Moreover, p53 is mutated in 35% to 80% of ESCC and in about 50% to 90% of BAC. Together with deregulation of mitotic and post mito tic cell cycle control points, the presence of supernu merary centrosomes has been proposed as one likely mechanism for development and or maintenance of aneuploidy. Supernumerary centrosomes have been detected in several aneuploid human cancers or cell lines derived thereof by evaluation of centrosomal pro teins, such as g tubulin, pericentrin or Inhibitor of DNA binding protein 1. However, the associa tion of supernumerary centrosomes with multipolar mitoses in aneuploid ESCC and BAC cells has not been studied so far. The Aurora kinase family of serine threonine kinases regulates many processes during cell division and is cur rently discussed as therapeutic target in cancer.

Specifically, Aurora A is important for centrosome maturation, separation and spindle assembly. Amplification of the Aurora A locus and subsequent overexpression of Aurora A was observed for example in colorectal and pancreatic cancer, as well as in ESCCs and BACs. Overexpression Entinostat of Aurora A has been functionally asso ciated with supernumerary centrosomes and aneuploidy. In esophageal cancers, a polymorphism of Aur ora A was associated with increased esophageal cancer risk.