Just in order to provide, for protein-like substances, an illustrative image [and not more than that] of different patterns of bonding [different from that in a straight, single, unbranched polypeptide chain], one may, for instance, find out that amino acids,- in addition to both peptidic coupling "points" [points of possible peptide bonds, one on either side of the amino acid residue], - do possess three more possibilities of coupling ( H, R, CO) [not the H of the terminal NH2 group, but of another one, if present in the amino acid molecule, and, further, not the CO of the terminal COOH group (but that of another COOH group if there is any in the amino acid molecule, or some C=O in that molecule not being part of a COOH group in that same molecule)], [coupling possibilities] of which at least two may be realized. If one then goes one more step further (we here follow the ideas of a professional) and lets the amino acid residue with two chief and two subsidiary bondings transform into a valence-saturated complex, which formally about corresponds to a four-valence chemical element, then one can build with it spherical, cylindrical, and other polypeptides, which, as a result of the annex now of three more building blocks to each building block [amino acid] of the original aggregate, can satisfy the Bergmann-Niemann Rule exactly. To this consideration about possible branched polypeptide chains we do not allot a significance more than illustrating something, because it, according to our view, is tending already too much towards a crystalline order, and because today reference to the Bergmann-Niemann Rule is not recommended anymore.
Various special views, but referring rather more to genuine-protein matter (of the type of plasmatic globulines) and not to that what concerns us here most (vital 'proteins'), boil down to complement the open polypeptide sequence (to which we also still reckon the "simple" spiralization of it) by having it self-closed [i.e. by having it running into itself] according to a regular pattern of higher symmetry.
There are many "natural" ways leading to this end-point. One may, for instance, derive the sphero-proteins [the Globulines] -- which, as medium constituents, and thus as isolated [i.e. individual] [molecular] bodies, are physiologically truly important -- from an entangled polypeptide chain, whereby one, in the motion-statistical entanglement, it is true, must view only the mechanism first of all establishing that spatial nearness, which then leads to the chemically group-fixed and bond-saturatedly fixed high internal degree of symmetry, characterizing the sphero-proteins, and which then in turn prevents an even only partial motion-statistical re-entanglement [i.e., I presume, a further entanglement, or, perhaps, an unwinding] as long as no intense disturbance takes place having the nature of a gross denaturation effect.
As long as one, however, is not able to underpin a defined functional moment with these special symmetries and constitutional patterns, and in the end with it only establishes similarities with inorganic order, these considerations are of little value. Perhaps one should, for the time being, see all developed, and with many good arguments put forward, structural ideas, as representing a number of certain limiting possibilities among many others, in relation to which the vital proteins take some "mediate position" unequivocally determined by certain additional features.