This dissertation concerns the study and prediction of loops in protein structures. Proteins perform crucial functions in living organisms. Despite their importance, we are currently unable to predict their three dimensional structure accurately. Loops are segments that connect regular secondary structures of proteins. They tend to be located on the surface of proteins and often interact with other biological agents. As loops are generally subject to more frequent mutations than the rest of the protein, their sequences and structural conformations can vary significantly even within the same protein family. Although homology modelling is the most accurate computational method for protein structure prediction, difficulties still arise in predicting protein loops. Protein loop structure prediction is therefore a bottleneck in solving the protein structure prediction problem. Reflecting on the success of homology modelling, I implement an improved version of a database search method, FREAD. I show how sequence similarity as quantified by environment specific substitution scores can be used to significantly improve loop prediction. FREAD performs appreciably better for an identifiable subset of loops (two thirds of shorter loops and half of the longer loops tested) than ab initio methods; FREAD's predictive ability is length independent. In general, it produces results within 2Å root mean square deviation (RMSD) from the native conformations, compared to an average of over 10Å for loop length 20 for any of the other tested ab initio methods. I then examine FREAD’s predictive ability on a specific type of loops called complementarity determining regions (CDRs) in antibodies. CDRs consist of six hypervariable loops and form the majority of the antigen binding site. I examine CDR loop structure prediction as a general case of loop structure prediction problem. FREAD achieves accuracy similar to specific CDR predictors. However, it fails to accurately predict CDR-H3, which is known to be the most challenging CDR. Various FREAD versions including FREAD with contact information (ConFREAD) are examined. The FREAD variants improve predictions for CDR-H3 on homology models and docked structures. Lastly, I focus on the local properties of protein loops and demonstrate that the protein loop structure prediction problem is a local protein folding problem. The end-to-end distance of loops (loop span) follows a distinctive frequency distribution, regardless of secondary structure elements connected or the number of residues in the loop. I show that the loop span distribution follows a Maxwell-Boltzmann distribution. Based on my research, I propose future directions in protein loop structure prediction including estimating experimentally undetermined local structures using FREAD, multiple loop structure prediction using contact information and a novel ab initio method which makes use of loop stretch.

<p>Nuclear magnetic resonance (NMR) spectroscopy is an established technique for macromolecular structure determination at atomic resolution. However, the majority of the current structure determination approaches require a large set of experiments and use large amount of data to elucidate the three dimensional protein structure. While current structure determination protocols may perform well in data-rich settings, protein structure determination still remains to be a difficult task in a sparse-data setting. Sparse data arises in high-throughput settings, for larger proteins, membrane proteins, and symmetric protein complexes; thereby requiring novel algorithms that can compute structures with provable guarantees on solution quality and running time.</p><p>In this dissertation project we made an effort to address the key computational bottlenecks in NMR structural biology. Specifically, we improved and extended the recently-developed techniques by our laboratory, and developed novel algorithms and computational tools that will enable protein structure determination from sparse NMR data. An underlying goal of our project was to minimize the number of NMR experiments, hence the amount of time and cost to perform them, and still be able to determine protein structures accurately from a limited set of experimental data. The algorithms developed in this dissertation use the global orientational restraints from residual dipolar coupling (RDC) and residual chemical shift anisotropy (RCSA) data from solution NMR, in addition to a sparse set of distance restraints from nuclear Overhauser effect (NOE) and paramagnetic relaxation enhancement (PRE) measurements. We have used tools from algebraic geometry to derive analytic expressions for the bond vector and peptide plane orientations, by exploiting the mathematical interplay between RDC- or RCSA-derived sphero-conics and protein kinematics, which in addition to improving our understanding of the geometry of the restraints from these experimental data, have been used by our algorithms to compute the protein structures provably accurately. Our algorithms, which determine protein backbone global fold from sparse NMR data, were used in the high-resolution structure determination protocol developed in our laboratory to solve the solution NMR structures of the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), which have been deposited into the Protein Data Bank. We have developed a novel, sparse data, RDC-based algorithm to compute ensembles of protein loop conformations in the presence of a moderate level of dynamics in the loop regions. All the algorithms developed in this dissertation have been tested on experimental NMR data. The promising results obtained by our algorithms suggest that our algorithms can be successfully applied to determine high-quality protein backbone structures from a limited amount of experimental NMR data, and hence will be useful in automated NOE assignments and high-resolution protein backbone structure determination from sparse NMR data. The algorithms and the software tools developed during this project are made available as free open-source to the scientific community.</p> / Dissertation