Of the 20 standard amino acids, cysteines are the only amino acids that have a reactive sulphur atom, thus enabling two cysteines to form strong covalent bonds known as disulfide bonds. Even though almost all proteins have cysteines, not all of them have disulfide bonds. Disulfide bonds provide structural stability to proteins and hence are an important constraint in determining the structure of a protein. As a result, disulfide bonds are used to study various protein properties, one of them being protein folding. Protein structure prediction is the problem of predicting the three-dimensional structure of a protein from its one-dimensional amino acid sequence. Ab initio methods are a group of methods that attempt to solve this problem from first principles, using only basic physico-chemical properties of proteins. These methods use structure libraries of short amino acid fragments in the process of predicting the structure of a protein. The protein structures from which these structure libraries are created are not classified in any other way apart from being non-redundant. In this thesis, we investigate the structural dissimilarities of short amino acid fragments when occurring in proteins with disulfide bonds and when occurring in those proteins without disulfide bonds. We are interested in this because, as mentioned earlier, the protein structures from which the structure libraries of ab initio methods are created, are not classified in any form. This means that any significant structural difference in amino acids and short fragments when occurring in proteins with and without disulfide bonds would remain unnoticed as these structure libraries have both fragments from proteins with disulfide bonds and without disulfide bonds together. Our investigation of structural dissimilarities of amino acids and short fragments is done in four phases. In phase one, by statistically analysing the phi and psi backbone dihedral angle distributions we show that these fragments have significantly different structures in terms of dihedral angles when occurring in proteins with and without disulfide bonds. In phase two, using directional statistics we investigate how structurally different are the 20 different amino acids and the short fragments when occurring in proteins with and without disulfide bonds. In phase three of our work, we investigate the differences in secondary structure preference of the 20 amino acids in proteins with and without disulfide bonds. In phase four, we further investigate and show that there are significant differences within the same secondary structure region of amino acids when they occur in proteins with and without disulfide bonds. Finally, we present the design and implementation details of a dihedral angle and secondary structure database of short amino acid fragments (DASSD) that is publicly available. Thus, in this thesis we show previously unknown significant structure differences in terms of backbone dihedral angles and secondary structures in amino acids and short fragments when they occur in proteins with and without disulfide bonds.