Searching protein databases is a difficult problem, partly because proteins cannot be sorted according to any objective criteria. A practical solution to this is similarity searching -- we can define a similarity function which determines the similarity between each pair of proteins. In 2018, a paper called The Case for Learned Index Structures has been published, arguing for a new paradigm for organizing and searching within complex data using machine learning. The goal of this thesis is to apply such an approach to the problem of similarity searching in protein data and evaluate the results. Firstly, the student will need to find a way to process data from the Protein Data Bank and represent it in a way that is suitable for machine learning. Secondly, the proteins will need to be indexed using an existing framework called Learned Metric Index (LMI) -- since the framework has never been used with this type of data, it will be necessary to identify the distinctive characteristics of protein data and modify the setup of LMI to appropriately represent similarity within this dataset. Finally, the searching efficiency of the resulting index will be evaluated.