Two Mathematical Approaches to Inferring the Internal Structure of Proteins from their Shape

Abstract

sing a simple mathematical model, we propose two approaches to externally infer how the amino-acid sequence is folded in a protein. One is the previously proposed differential geometric approach. The other is a new category theoretical approach proposed in this paper. As an example, we consider detecting the presence of internal singularities from the outside. Knowledge of Category theory is not required. Proteins are represented as a loop of triangles. In both approaches, the outer contour of the loop is examined to detect the presence of singular triangles (such as isolated triangles) inside. By considering the interaction between loops, the new approach allows us to detect more singular triangles than the previous approach. We hope that this research will provide a new perspective on protein structure analysis and promote further collaboration between mathematics and biology.