Not everyone was convinced that proteins were formed from Fischer's long chains of amino acids. Amino acids could also form rings. Diketopiperazine, for example, was a simple cyclic structure formed when two amino acids linked into a dipeptide, then fused their free ends through another peptide bond. Some investigators believed that other rings could be bigger, including more amino acids. Some were capable of making links from their side chains as well, opening the possibility of more complex structures. Theories began flying. A number of protein researchers thought that ringlike structures might explain the characteristics of proteins better than Pauling's and Astbury's long chains.

One of the most-talked-about approaches was called the "cyclol" theory of proteins, which supposed that rings of six amino acids could be linked into flat fabrics, or formed into cagelike structures. The major proponent of cyclols was the British theoretician Dorothy Wrinch. Wrinch, well versed in mathematics and physics, was intelligent - the first woman to receive a D.Sc. degree from Oxford – but rootless. She had become attracted to biology and held a series of apprentice positions in biological laboratories around Europe, raising a daughter as a single mother, and living the life of a scientific gypsy. She could be a fascinating conversationalist, unconventional, sharp-tongued, cigarette-smoking, and interested in everything from the ideas of Bertrand Russell to the question of two-career marriages.

But significant scientific discoveries eluded her. Warren Weaver thought her work on the application of mathematics to biological problems was promising, and gave her Rockefeller Foundation support for a generous five years during the Depression. The primary result was her cyclol approach to proteins. Her rings, she theorized, could form not only a flat fabric, but a closed polyhedron composed of, she estimated, 288 amino acids. Strikingly, her proposed cages were roughly the same size Svedberg had proposed as a possible basic size for protein subunits. Her ideas were intriguing enough to capture the attention of the American Nobel Prize winning chemist Irving Langmuir, who championed her ideas in print. Langmuir saw no reason that amino acids should only connect to each other end-to-end, using only "two arms," as he put it. Four-armed connections were also chemically possible. Cyclol cages were possible. The press started paying attention. One paper called Wrinch a "woman Einstein."

Linus Pauling thought her ideas were rubbish.