Because of new sequencing technologies and high throughput automatic experimental methods, there has been an exponential growth in sequence and three-dimensional (3D) molecular data. Throughout evolution, the 3D structure of a protein has been more conserved than its sequences. Thus, structure-based methods and analyses are more informative and hence more significant in the functional annotation of unknown proteins. Structure comparison plays a vital role in the understanding of the structural and functional relationships between proteins. This is essential when estimating the evolutionary distance between proteins and protein families. There are many comparison methods that deal with the 3D atomic coordinates of proteins for structural and functional analysis. These methods (e.g. SSAP - a Sequential Structural Alignment of Proteins, COMPARER and STAMP) are computationally intensive compared to graph-based or vector-based protein structure comparisons. Both the graph-based and vector-based methods use an abstract representation of protein structure. One such method is TOPS (Topology of Protein Structure) based protein structure comparison, which uses a graph-based approach. However, in most cases the significant biological information has not been recognized efficiently due to the abstract nature of the protein models. Moreover, the functional annotation problem is made much more complex by the fact that the number of protein fold is limited while their range of functions is very diverse (e.g., TIM barrels proteins). In this research, we introduced 'enhanced TOPS' or 'TOPS+ models', which incorporate biochemical features (such as ligand interaction information) into topological models of protein structures. The topological information of the protein structure records the relationships between any two secondary structural elements (SSE) in the form of hydrogen-bonding (ladders) patterns between beta-strands and the handedness of the chirality connections between SSEs. The ligand interaction information of the protein is represented at an abstract level with additional ligand node(s) connected to their interacting SSEs. Additionally, we augmented the amino-acid residue length for each SSE with their protein data bank (PDB) amino-acid residue's starting and ending positions. In addition, we developed a 'TOPSStrings+ model', which is a reduced topological model of the TOPS+ graph model, represented as an enhanced sequence model. In this TOPSStrings+ model, each SSE is enriched with ligand interaction information and topological information in the form of incoming and outgoing arcs, which maintains the directions, and arc type properties. All relevant SSE nodes are enhanced with SSE-ligand interaction information that includes loop-ligand interaction. We are able to abstract away from the ligands themselves, to give a string model characterized by a regular grammar rather than the context sensitive grammar of existing TOPS model. Furthermore, this enables the use of string matching algorithms rather than graph-based techniques. Our TOPSStrings+ model is sufficient to obtain biologically meaningful results and has the advantage of permitting fast structure matching and comparison as well as avoiding issues of NP-completeness associated with certain graph problems, e.g. subgraph isomorphism.