Correlated rigid modes in protein families.

A great deal of evolutionarily conserved information is contained in genomes and proteins. Enormous effort has been put into understanding protein structure and developing computational tools for protein folding, and many sophisticated approaches take structure and sequence homology into account. Several groups have applied statistical physics approaches to extracting information about proteins from sequences alone. Here, we develop a new method for sequence analysis based on first principles, in information theory, in statistical physics and in Bayesian analysis. We provide a complete derivation of our approach and we apply it to a variety of systems, to demonstrate its utility and its limitations. We show in some examples that phylogenetic alignments of amino-acid sequences of families of proteins imply the existence of a small number of modes that appear to be associated with correlated global variation. These modes are uncovered efficiently in our approach by computing a non-perturbative effective potential directly from the alignment. We show that this effective potential approaches a limiting form inversely with the logarithm of the number of sequences. Mapping symbol entropy flows along modes to underlying physical structures shows that these modes arise due to correlated compensatory adjustments. In the protein examples, these occur around functional binding pockets.

Analysis of F9 point mutations and their correlation to severity of haemophilia B disease.

Haemophilia B is an X-linked recessive disorder caused by deficiency of functional coagulation factor IX, which results almost exclusively from mutations in the F9 gene. We sought to determine features, which could distinguish between mutations that cause severe disease symptoms from those that cause non-severe disease symptoms. Towards this objective, we have performed a statistical analysis of reported point mutations in F9. These include: potential local changes in mRNA free energy, codon usage, charge and type of mutated amino acid, location of the mutation with regard to protein secondary structure and functional domain and amino acids' evolutionary conservation scores. Wilcoxon signed-rank tests showed highly significant differences between severe and non-severe disease causing mutations in their effect on free energy of small mRNA fragments and evolutionarily conserved amino acids. Our results suggest that information at the mRNA level as well as conservation of the amino acid correlate well with disease severity. This study demonstrates that computational tools may be used to characterize the severity of haemophilia B associated with point mutations and suggests their utility in predicting the outcome of sequence changes in recombinant proteins.

Transforming rooted agreement into unrooted agreement.

We give a simple technique that allows to transform dynamic programming type algorithms for the Maximum Agreement Subtree problem (MAST) for rooted trees into algorithms for the Maximum Agreement Subtree problem for unrooted trees (UMAST). Using this technique we obtain an O (n log n)-time algorithm for the UMAST problem for binary trees. This matches the complexity of the best known algorithm for the rooted case.