Posted on behalf of Retread

In the early days of quantum mechanics Einstein and Bohr threw thought experiments (gedanken experiments) at each other like teenagers throwing firecrackers. None were thought possible at the time, although thanks to Bell and Aspect, quantum nonlocality and entanglement now have a solid experimental basis.

Two Chemiotics posts ago there appeared the following: “I doubt that most strings of amino acids have a dominant shape (e.g., biological meaning), and even if they did, they couldn’t find it quickly enough (the Levinthal paradox again).”

How would you prove me wrong? The same way you’d prove a pair of dice was loaded. Just make (using solid-phase protein synthesis) a bunch of random strings of amino acids (say 41 amino acids long) and see how many have a dominant shape. If one crystallizes it does, if not, use NMR to look at them in solution. You can’t make all of them, because the earth doesn’t have enough mass to do so (see “How many proteins can we make?” a few posts back). That’s why this is a gedanken experiment — it can’t possibly be performed in toto.

Even so, the experiment is over (and I’m wrong) if even 1% of the proteins you make have a dominant shape.

However, choosing a random string of amino acids is far from trivial. Some amino acids appear more frequently than others depending on the protein. Proteins are definitely not a random collection of amino acids. Consider collagen. In its various forms (there are over 20, coded for by at least 30 distinct genes) collagen accounts for 25% of body protein. Statistically, each of the 20 amino acids should account for 5% of the protein, yet one amino acid (glycine) accounts for 30% and proline another 15%. Even knowing this, the statistical chance of producing 300 copies in a row of glycine–any amino acid–any amino acid by random distribution of the glycines are less than zilch. But one type of bovine collagen protein has >300 such copies in its 1042 amino acids.

One further example. If you were picking out a series of letters randomly hoping to form a word, you would not expect a series of 10 ‘a’s to show up. But we normally contain many such proteins, and for some reason too many copies of the repeated amino acid produce some of the neurological diseases I (ineffectually) battled as a physician. Normal people have 11 to 34 glutamines in a row in a huge (molecular mass 384 kiloDaltons — that’s over 3000 amino acids) protein known as huntingtin. In those unfortunate individuals with Huntington’s chorea, the number of repeats expands to over 40. One of Max Perutz’s last papers [Proc. Natl. Acad. Sci. USA 99, 5591–5595 (2002)] tried to figure out why this was so harmful.

On to the actual experiment. Suppose you had made 1,000,000 distinct random sequence proteins containing 41 amino acids and none of them had a dominant shape. This proves/disproves nothing. 10^6 is fewer than the possibilities inherent in a string of 5 amino acids, and you’ve only explored 10^6/(20^41) of the possibilities.

Would Karl Popper, philosopher of science, even allow the question of how commonly proteins have a dominant shape to be called scientific? Much of what I know about Popper comes from a fascinating book “Wittgenstein’s Poker” and it isn’t pleasant. Questions not resolvable by experiment fall outside Popper’s canon of questions scientific. The gedanken experiment described can resolve the question one way, but not the other. In this respect it’s like the halting problem in computer science (there is no general rule to tell if a program will terminate).

Would Ludwig Wittgenstein, uberphilosopher, think the question philosophical? Probably not. His major work “Tractatus Logico-Philosophicus” concludes with “What we cannot speak of we must pass over in silence”. While he’s the uberphilosopher he’s also the antiscientist. It’s exactly what we don’t know which leads to the juiciest speculation and most creative experiments in any field of science. That’s what I loved about organic chemistry years ago (and now). It is nearly always possible to design a molecule from scratch to test an idea. There was no reason to make ⁷paracyclophane, other than to get up close and personal with the ring current.

If the probability or improbability of our existence, to which the gedanken experiment speaks, isn’t a philosophical question, what is?