Approach for comparing protein structures and origami models

The research fields of proteins and origami have intersected in the study of folding and de-novo design of proteins. However, there is limited knowledge on the analogy between protein structures and origami models. We propose a general approach for comparing protein structures with origami models, and present a test case, comparing transmembrane beta-barrel and alpha-helical barrel with the Yoshimura and Kresling origami models. While both shapes and structures may look similar, we demonstrated that the beta-barrel and the alpha-helical barrel are in agreement only with the shape and structural characteristics of the Kresling model. Through the analogy, it is explained how the structural characteristic can help the beta-barrel and alpha-helical barrel to adjust length and diameter in response to changes in the membrane structure. However, such conformations only apply to the alpha-helical barrel, and the beta-barrel, in spite of resembles to the Kresling model, remains stiff due to hydrogen bonds between the beta-strands. Thus, our analysis suggests that there are similar patterns between protein structures and origami models and that the proposed approach may provide important insight on the role that the structure of a protein fulfils, and on the preferred structural design of novel proteins with unique characteristics.