Recently, ideas from graph theory have been applied to answer important questions in the study of protein dynamics. One unsolved problem that remains apt for sophisticated network analysis is the process of long range signalling in proteins known as protein allostery. Despite the fact that researchers first identified protein allostery over 50 years ago, a precise physicochemical description remains ever elusive. While a complete picture of allostery has yet to emerge, computationalists have achieved promising results by representing amino acid or atomic interactions in proteins as a network and applying various graph algorithms to interrogate properties of these network. Constructing these networks generally involves performing a molecular dynamics simulation of the protein and constructing an interaction graph based on the correlated motions or positions found in the simulation data. While the use of physical distance or correlated motions appear to be a good first-order approximation of residue coupling, there are some obvious limitations with this perspective. In this thesis, I propose a novel method of combining dynamic pairwise interaction energy values with information from Markov state models to illuminate signalling pathways in proteins. I then test this method on a model system and show that it indeed highlights regions of interaction that are known to be biologically important. Finally, I introduce and argue for a new method of cross-comparison of protein systems by studying the solution to the differential equation known as the heat kernel. I then introduce a measure known as embedding error which is generated by performing principal component analysis on the heat kernel and comparing the distributions of embedded points. Our hypothesis is that the energetic network perspective paired with our temporal heat kernel analysis can help tackle two large problems in computational signalling studies: the disregard of the importance of long-range interactions and failure to detect dynamic allostery.
"},{"label":"Degree","value":["Bachelor of Arts with Departmental Honors"]},{"label":"Author-supplied Keywords","value":["Spectral graph theory","Computational biology","Networks"]},{"label":"Administrative Note","value":"Drupal Node ID: 24256