Many methods of analyzing both the physical and chemical behavior of proteins require information about its structure and stability. Also various other parameters such as energy function, solvation, hydrophobic/hydrophilic effects, surface area and volumes too play an important part in such analysis. The contribution of cavities to these parameters are very important. Existing methods to compute and measure cavities are limited by the inherent inaccuracies in the method of acquisition of data through x-ray crystallography and uncertainities in computation of radii of atoms. We present a topological framework that enables robust computation and visualization of these structures. Given a fixed set of atoms, voids and pockets are represented as subsets of the weighted Delaunay triangulation of atom centers. A novel notion of (ε,π)-stable voids helps identify voids that are stable even after perturbing the atom radii by a small value. An efficient method is described to compute these stable voids for a given input pair of values (ε,π ). We also provide an implementation to visualize, explore (ε.π)-stable voids and also calculate various properties such as volumes, surface areas of the proteins and also of the cavities.

The sequence of a polypeptide chain determines its structure which in turns determines its function. A protein is stabilized by multiple forces; hydrophobic interaction, electrostatic interactions and hydrogen bond formation between residues. While the above forces are non-covalent in nature the protein structure is also stabilized by disulfide bonds. Structural features such as naturally occurring cavities in proteins also affect its stability. Studying factors which affect a protein’s structural stability helps us understand complex sequence-structure-function relationships, the knowledge of which can be applied in areas such as protein engineering. The work presented in this thesis deals with various and diverse aspects of protein structure. Chapter 1 gives an overall introduction on the topics studied in this thesis. Chapter 2 focuses on a unique, non-regular, structural feature of proteins, viz. protein cavities. Cavities directly affect the packing density of the protein. It has been shown that large to small cavity creating mutations destabilize the protein with the extent of destabilization being proportional to the size of cavity created. On the other hand, small to large cavity filling mutations have been shown to increase protein stability. Tools which analyze protein cavities are thus important in studies pertaining to protein structure and stability. The chapter presents two methods which detect and calculate cavity volumes in proteins. The first method, DEPTH 2.0, focuses on accurate detection and volume calculation of cavities. The second method, ROBUSTCAVITIES, focuses on detection of biologically relevant cavities in proteins. We then study another aspect of protein structure – the disulfide bond. Disulfide bonds confer stability to the protein by decreasing the entropy of the unfolded state. Previous studies which attempted to engineer disulfides in proteins have shown mixed results. Previously, disulfide bonds in individual secondary structures were characterized. Analysis of disulfides in α-helices and antiparallel β-strands yielded important common features of such bonds. In Chapter 3 we present a review of these studies. We then use MODIP; a tool that identifies amino acid pairs which when mutated to cysteines will most likely form a disulfide bond, to analyze disulfide bonds in parallel β-strands. A direct way to analyze sequence-structure relationships is via mutating individual residues, evaluating the effect on stability and activity of the protein and inferring its effect on protein structure. Saturation mutagenesis libraries, where all possible mutations are made at every position in the protein contain a huge amount of information pertaining to the effect of mutations on structure. Making such libraries and screening them has been an extremely resource intensive process. We combine a fast inverse PCR based method to rapidly generate saturation mutagenesis libraries with the power of deep sequencing to derive phenotypes of individual mutants without any large scale screening. In Chapter 4 we present an Illumina data analysis pipeline which analyzes sequencing data from a saturation mutagenesis library, and derives individual mutant phenotypes with high confidence. In Chapter 5 we apply the insights derived from structure-function studies and apply it to the problem of protein engineering, specifically immunogen design. The Human Immunodeficiency Virus adopts various strategies to evade the host immune system. Being able to display the conserved epitopes which elicit a broadly neutralizing response is the first step towards an effective vaccine. Grafting such an epitope onto a foreign scaffold will mitigate some of the key HIV defenses. We develop a computational protocol which grafts the broadly neutralizing antibody b12 epitope on scaffolds selected from the PDB. This chapter also describes the only experimental work presented in this thesis viz. cloning, expressing and screening the epitope-scaffolds using Yeast Surface Display. Our epitope-scaffolds show modest but specific binding. In a bid to improve binding, we make random mutant libraries of the epitope-scaffolds and screen them for better binders using FACS. This work is on-going and we aim to purify our epitope-scaffolds, characterize them biophysically and eventually test their efficacy as immunogens.