Peptide bonds are proteolytically unstable, which is why there have been many attempts to come up with their mimetics. The corresponding surrogates may or may not look similar to what they are designed to mimic, but their constituent atoms almost always occupy a similar volume in space (the isosteric hypothesis). In all of these cases, however, the hydrolytic stability of the peptidomimetic is substantially higher than that of its peptide counterpart.
There is an interesting recent paper by Mike Shipman and colleagues in Chem. Comm. The work centers around oxetanes as replacements for carbonyl groups in amides. The core synthetic chemistry involves conjugate addition of amines to oxetane-containing nitroalkenes. There are many interesting features of peptide structure that can be probed with this oxetane concept. The four-membered ring brings about a somewhat longer C-O distance than the one seen in a typical amide. In addition, there is a completely different rotational preference compared to the amide linkage that features the nitrogen lone pair in conjugation with the C=O antibonding orbital. This is a lovely piece of molecular engineering that goes to show that there is still a lot of room for basic research. I appreciate the fact that chemists have the ability to make something with no immediate application in mind, just to test the waters and to see what happens. And, by the way, the enduring rabbit ears are still expected to be there in “oxetanated” amides (see my earlier post: https://amphoteros.com/2015/06/25/rabbit-ears/).