The RNA Tie Club was definitely the brainchild of George Gamow, an amazing character in the annals of science. Soviet defector, influential physicist, popularizer of science and ultimately an important catalyst of molecular biology thinking, Gamow was a wonder -- and sadly amazing is that he doesn't seem to have attracted an independent biographer.
The degree to which others were in on the creation of the RNA Tie Club appears to be in some dispute; Judson in Eighth Day claims that neither Watson nor Crick were in the original membership, whereas the Wikipedia entry (citing a book called Who Wrote the Book of Life?) claims the club was created by Gamow and Watson. If I were a proper historian, I'd lay my hands on that book and Watson's Girls, Genes and Gamow (which I did not like -- far too much focus on Watson's dating escapades) and perhaps the rest of the books that might cover the subject. But I'm a lazy amateur, so I'll leave that to someone else.
The Tie Club is generally presented as a whimsical, charming little establishment. Most books mention only a few of members. It had a serious social angle -- an early invitation (referenced in Crick) refers to a "whiskey, twisty RNA party", though Crick sadly suggests that Gamow had a serious drinking problem (and indeed, would die of liver failure). It also served a community in which members could circulate unfinished ideas in a rapid manner. Another bit of whimsy was a unique tie for each member, who had each been assigned an amino acid.
Reading about this period one can see the primordial predecessors to bioinformatics. For example, there was the question of how DNA encoded proteins (messenger RNA's discovery would be in the future). Crick and Brenner and Gamow (and others) thought that the code might largely be sleuthed out, with a key clue being the number of amino acids that could be encoded. Since Fred Sanger had recently succeeded in sequencing proteins, and there was compositional data for many others, lists of amino acids found in proteins could be compiled. It was Crick who apparently first thought to filter this set by which amino acids seemed to be found in most proteins versus those that seemed to have a very restricted scope -- and he arrived at 20. Of course, we know now that there are actually a few more due to some clever coding (and Crick admits his scheme did not include N-formyl methionine, found at the N-terminus of bacterial proteins) -- but if those had been known it might well have gummed up the process. Crick's simplifying assumption proved to be very powerful. Of course, getting there must have required a lot of library work -- Margaret Dayhoff's pioneering Atlas of Protein Sequence and Structure was far in the future.
An interesting counter-view to this vision of the Tie Club as a charming whimsy comes from a new biography of Marshall Nirenberg titled "The Least Likely Man: Marshall Nirenberg and the Discovery of the Genetic Code" by Franklin Portugal. Portugal paints the Tie Club as an exclusionary group (in contrast to the phage group) and one that was barely known outside its membership. Indeed, in the snippet I've read online Portugal suggests that Crick credited Nirenberg shabbily in later years, though another source shows how Crick took great efforts to give Nirenberg a large stage for presenting his early results.
The membership of the club is a bit curious and deserves scrutiny. Judson blames Gamow for the membership, which was a bit of an odd lot. In addition to Crick and Watson some who had or would make great contributions to genetics included Alexander Rich, Leslie Orgel, Sydney Brenner, Gunther Stent and Max Delbruck. A bunch of Manhattan project alumni were aboard as well -- Richard Feynman mentions getting tempted by molecular biology in his memoirs and there was also Edward Teller and the mathematician Nicholas Metropolis. It turns out that Paul Doty, a biochemist, was another Manhattan Project alumnus admitted to the club.
The club also included a number of individuals who are well known, but not for genetics or RNA. Alexander Dounce, who I now know did more than homogenize , and Melvin Calvin of photosynthesis fame. Then there are less known individuals. Martynas Ycas was a Lithuanian biologist who published a number of papers (many with Gamow) on statistics of proteins. Robley Williams a pioneering electron microscopist of biological samples. Robert Ledley was a biophysicist who was an early pioneer in applying computers to biological problems (including collaborating with Dayhoff on the Protein Atlas).
When I started this exploration, there were three members of the club missing Wikipedia entries. I created one for Ycas, and I hope any history of bioinformatics includes him (if anyone reads Lithuanian is game, there is clearly a lot more information in the Wikipedia page in that language than my little stub! -- though I do capture one datum missing there (his death date)). Two still lack pages -- Norman Simons and Harold Gordon - -I haven't been able to find unambiguous information on either of these individuals.
If you count up the above, you should get 19 -- I've left one member out, because to be honest I couldn't believe my eyes. Erwin Chargaff??? Certainly he merited inclusion in the club based on his work, but he always seemed so acidly unimpressed with Watson or Crick (his pithy sketches of them in Heraclitean Fire are quite nasty) that it is rather shocking he would join a club that would have them as a member. I certainly don't remember him mentioning it in the book.
The charge of exclusion would certainly stick in today's world: the members were all very pale and certainly male. Har Gobind Khorana was not in the club yet would be a major contributor to cracking the code. Rosalind Franklin apparently wasn't invited, nor Dorothy Hodgkin. It is even easier to think of missing names that wouldn't have helped on diversity. Despite a heavy dose of members based in southern California, Linus Pauling isn't there. Nor is Maurice Wilkins. No Jacob, no Monod. Boris Ephrussi isn't there. Nor Arthur Pardee. Seymour Benzer was clearly making huge inroads on how DNA coded - -but wasn't in the club. And so on - - I'm again too much of an amateur to properly list all the likely candidates who were left out.
Whatever the shortcomings of the membership, it did succeed in making a number of insights into the code -- Wikipedia credits the Tie Group with the number of nucleotides in a codon, the concept of a codon and the adaptor hypothesis (i.e. tRNAs). And clearly the group was not hermetically sealed; Crick describes his excitement on discussing the PaJaMo experiment with Jacob in his memoirs.
The Tie Club probably deserves its own book. Alas, nearly all of the members have hit their personal amber codon -- I believe that only Watson, Brenner and Rich are still alive -- if you are interested in writing such a book, don't delay!