Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way. The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili.     

Probing met repressor-operator recognition in solution.

The three-dimensional crystal structure of the Escherichia coli methionine repressor, MetJ, complexed with a DNA operator fragment is described in an accompanying article. The complex exhibits several novel features of DNA-protein interaction. DNA sequence recognition is achieved largely by hydrogen-bond contacts between the bases and amino-acid side chains located on a beta-ribbon, a mode of recognition previously hypothesized on the basis of modelling of idealized beta-strands and DNA, and mutagenesis of the Salmonella phage P22 repressors Arc and Mnt. The complex comprises a pair of MetJ repressor dimers which bind to adjacent met-box sites on the DNA, and contact each other by means of a pair of antiparallel alpha-helices. Here we assess the importance of these contacts, and also of contacts that would be made between the C-helices of the protein and DNA in a previous model of the complex, by studying mutations aimed at disrupting them. The role of the carboxy-terminal helix face in operator binding was unclear, but we demonstrate that recognition of operator sequences occurs through side chains in the beta-strand motif and that dimer-dimer interactions are required for effective repression.