If they are, it will be for completely unrelated reasons. Protein folding has very little in common with paper folding beyond the name. In particular, proteins are basically 1-dimensional, whereas paper folding is inseparable from the 2d nature of paper.
protein are 1-dimensional only if you throw away large numbers of degrees of freedom, and every detail of their folding is determined by their three-dimensionality.
That's equally (almost vacuously) true of origami, but the inherent topology of the building blocks still has a huge effect on what those degrees of freedom actually are. Do you think they're similar between a peptide chain and a sheet of paper? If no, then what are you actually arguing?
