Geometrical and probabilistic methods for determining association models and structures of protein complexes

Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of the complexes, it is important to know the manner in which they are assembled from the component subunits and their three dimensional structure. This thesis addresses both of these questions by developing geometrical and probabilistic methods for analyzing data from two complementary experiment types: Small Angle Scattering (SAS) and Nuclear Magnetic Resonance (NMR) spectroscopy. Data from an SAS experiment is a set of scattering intensities that can give the interatomic probability distributions. NMR experimental data used in this thesis is set of atom pairs and the maximum distance between them. From SAS data, this thesis determines the association model of the complex and intensities through an approach that is robust to noise and contaminants in solution. Using NMR data, this thesis computes the complex structure by using probabilistic inference and geometry of convex shapes. The structure determination methods are complete, that is they identify all consistent conformations and are data driven wherein the structures are evaluated separately for consistency to data and biophysical energy