Pattern discovery methods for protein topology diagrams

We are carrying out research into developing several approaches to pattern discovery in protein topology diagrams, and comparing them. The underlying motivation is to eeciently automatically generate patterns classifying sets of proteins and to apply this to characterising databases of protein structure. We are using TOPS protein topology diagrams, which we have formalised as a restricted kind of graph in 3]. In general pattern discovery in TOPS diagrams can be reduced to subgraph isomorphism/maximal common subgraph problems in oriented labelled graphs. We are using two diierent approaches (illustrated in an experiment software suite at Learning (pattern extension) is based on searching of common patterns constructed by pattern extension and on repeated pattern matching; in this sense it is similar to \pattern driven" approaches for strings 1]. In general this method is very simple: by starting with empty pattern we try to extend it in all possible ways and discard extensions that do not match a given set of examples, until we nd a largest pattern that cannot be extended further. Such an approach seems in general to be far too ineecient for graphs of size that is typical to TOPS diagrams; however a somewhat limited version of this method (that does not always guarantee the nding of best possible pattern) works surprisingly fast for most of the real examples from TOPS database. The good property of this approach is that algorithm complexity grows proportionally to the size of the set of examples in learning set. We are now working on improved versions on pattern matching and pattern learning algorithms and expect that we will be able to obtain practically eecient pattern discovery method that will guarantee the nding of maximal pattern(s). We have been experimenting with learning patterns for and domains at the H level in the CATH hierarchy. We are evaluating our results by determining how many false positives are returned by a search over the database using the discovered pattern; initial results are encouraging in many cases. Clique detection works by nding of common patterns via maximal clique detection in edge product graphs, using for example the Bron-Kerbosch algorithm 2]. We have implemented a modiied version for this approach that takes advantage of the ordering of graphs and reduces the number of edges in the edge product graph by the factor of 6. Unfortunately, this modiication also does not allow us to use Koch and Lengauer variant (algorithm …