Geometry Of Alpha And Beta Protein Structures

Abstract

Proteins have a wide array of essential functions: from serving as enzymatic catalysts to protecting the immune system as antibodies. Proteins spontaneously self-organize into specific, folded structures determined by their amino acid sequences and the interaction between molecular forces. Since the 3-dimensional structure into which they fold often relates to the specific function of the protein, much effort has been directed towards methods to predict the folded structure from a given sequence, with the hope of being able to understand protein functions from sequence information. The protein folding problem can be summarized as the attempt to understand the relationship between a protein sequence and a protein's geometric shape, or fold. Thus, there are two principal problems: given a sequence, what 3-dimensional form will the protein take (forward problem), and given a particular fold, what sequence or sequences code for that form (the inverse problem). In this work, models that represent folds as continuous structures are explored. Models of the two prevalent motifs in protein folds, α helices and β barrels, are developed using axially deformed tubes and surfaces of revolution. These models are then analyzed and used to develop coordinate models of known and unknown structures.