Abstract 

Spatially proximate amino acid positions in a protein tend to co-evolve, so a protein's 3D-structure leaves an echo of correlations in the evolutionary record. Reverse engineering 3D-structures from such correlations is an open problem in structural biology, pursued with increasing vigor as new protein sequences continue to fill the data banks. Within this task lies a statistical stumbling block, rooted in the following: correlation between two amino acid positions can arise from firsthand interaction, but also be network-propagated via intermediate positions; observed correlation is not enough to guarantee proximity. The remedy, and the focus of this thesis, is to mathematically untangle the crisscross of correlations and extract direct interactions, which enables a clean depiction of co-evolution among the positions.

Recently, analysts have used maximum-entropy modeling to recast this cause-and-effect puzzle as parameter learning in a Potts model (a kind of Markov random field). Unfortunately, a computationally expensive partition function puts this out of reach of straightforward maximum-likelihood estimation. Mean-field approximations have been used, but an arsenal of other approximate schemes exists. In this work, we re-implement an existing contact-detection procedure and replace its mean-field calculations with pseudo-likelihood maximization. We then feed both routines real protein data and highlight differences between their respective outputs. Our new program seems to offer a systematic boost in detection accuracy.