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The most widely used classification system describing enzyme-catalysed reactions is the Enzyme Commission (EC) number. Understanding enzyme function is important for both fundamental scientific and pharmaceutical reasons. The EC classification is essentially unrelated to the reaction mechanism. In this work we address two important questions related to enzyme function diversity. First, to investigate the relationship between the reaction mechanisms as described in the MACiE (Mechanism, Annotation, and Classification in Enzymes) database and the main top-level class of the EC classification. Second, how well these enzymes biocatalysis are adapted in nature. In this thesis, we have retrieved 335 enzyme reactions from the MACiE database. We consider two ways of encoding the reaction mechanism in descriptors, and three approaches that encode only the overall chemical reaction. To proceed through my work, we first develop a basic model to cluster the enzymatic reactions. Global study of enzyme reaction mechanism may provide important insights for better understanding of the diversity of chemical reactions of enzymes. Clustering analysis in such research is very common practice. Clustering algorithms suffer from various issues, such as requiring determination of the input parameters and stopping criteria, and very often a need to specify the number of clusters in advance. Using several well known metrics, we tried to optimize the clustering outputs for each of the algorithms, with equivocal results that suggested the existence of between two and over a hundred clusters. This motivated us to design and implement our algorithm, PFClust (Parameter-Free Clustering), where no prior information is required to determine the number of cluster. The analysis highlights the structure of the enzyme overall and mechanistic reaction. This suggests that mechanistic similarity can influence approaches for function prediction and automatic annotation of newly discovered protein and gene sequences. We then develop and evaluate the method for enzyme function prediction using machine learning methods. Our results suggest that pairs of similar enzyme reactions tend to proceed by different mechanisms. The machine learning method needs only chemoinformatics descriptors as an input and is applicable for regression analysis. The last phase of this work is to test the evolution of chemical mechanisms mapped onto ancestral enzymes. This domain occurrence and abundance in modern proteins has showed that the / architecture is probably the oldest fold design. These observations have important implications for the origins of biochemistry and for exploring structure-function relationships. Over half of the known mechanisms are introduced before architectural diversification over the evolutionary time. The other halves of the mechanisms are invented gradually over the evolutionary timeline just after organismal diversification. Moreover, many common mechanisms includes fundamental building blocks of enzyme chemistry were found to be associated with the ancestral fold.