Phylogenetic approach to molecular structure prediction

Methods based on the mutual information statistic predict structure by looking for statistical correlations between sequence positions in a set of aligned sequences. Although mutual information methods are often quite effective, these methods ignore the underlying phylogenetic relationships of the sequences they analyze. Thus, they cannot distinguish between correlations due to structural interactions, and spurious correlations resulting from phylogenetic history. In this thesis, I introduce methods analogous to mutual information that incorporate phylogenetic information. I show that these methods accurately recover the structures of well-known RNA molecules, and also are superior in protein pair-wise interaction predictions. I demonstrate, with both real and simulated data, that these phylogenetically based methods outperform standard mutual information methods, and improve the ability to distinguish interacting from non-interacting positions in RNA and protein molecules. Because these methods incorporate phylogenetic data, they also have the potential to be improved with the addition of more accurate phylogenetic information, although I show that even approximate phylogenies are helpful.; In the theoretical part, I analyze the behavior of some of the statistics used in the applications. A strong convergence result is presented for a particular branching process. I also find the variance of the selected statistics, and present a limit distribution result for these statistics.