Asimov quote about "eight million trillion" arrangements of amino acids

Question

A friend of mine is subediting a book whose author died in 1999. The author, at some point, uses the word "trillion" which is, unfortunately, an ambiguous word in the UK: when I was at school it used to mean $10^{18}$ but nowadays it means $10^{12}$. My friend is faced with the following paragraph:

According to Asimov, the amino acids of the proteins behave in a much freer way than our words do: they can be rearranged in any manner and always retain some meaning. A simple protein is made up of eight amino acids, which can be classified putting the numbers one to eight in a series, changing the order of sequence by one digit each time. Out of the same number of "words" we can construct a little over 40,000 organised "biological phrases" from the same genetic code, each one with its own meaning, which is the mission of every protein. But if the chains become longer, as in the case of more complicated molecules such as insulin, which consists of 30 amino acids, the tally rises to a staggering eight million trillion possibilities.

The editor doesn't like "eight million trillion" and wants to replace it with "800000..000". The question, of course, is "how many zeros"? More precisely, the question is: is someone with a better understanding of chemistry than me able to reconstruct Asimov's calculation and see whether the answer is approximately $8 \times 10^{24}$ or $8 \times 10^{18}$?

Answer 1

What I think the author intends in the first part is that some piece of genetic code gives you $8$ distinct amino acids and you want to count the number of ways to rearrange them to get a protein, which is where the $8! \approx 40000$ number comes from. Since there are $20$ amino acids, the best you can do for $30$ amino acids is to use each of them once and ten of them twice, giving an answer of $\frac{30!}{2^{10}} \approx 2.59 \times 10^{29}$.

I am unable to find the actual list of amino acids in insulin (which is ridiculous to me; why isn't this information on a wiki somewhere?), but the above calculation suggests that the $10^{24}$ number is closer. If anyone wants to help me out, the actual polypeptide chain in question is the B chain.

Edit: According to this citation, Asimov's actual estimate is $8 \times 10^{27}$. So it looks like the author misquoted him.

Answer 2

The second sentence of that paragraph is meaningless, I think. The number of eight-amino-acid polypeptides (those are chains of amino acids) is 20^8, which is much larger than 40,000. And insulin isn't really big enough to be a good example of a typical protein; typical proteins have hundreds of amino acids.

That being said, Qiaochu's interpretation seems correct. I was able to track down the structure of human insulin -- note that the image is for bovine insulin, and human insulin differs by substituting Thr for Ala in the final position.

So the B-chain of human insulin has the sequence

Phe Val Asn Gln His Leu Cys Gly Ser His Leu Val Glu Ala Leu Tyr Leu Val Cys Gly Glu Arg Gly Phe Phe Tyr Thr Pro Lys Ala

which contains

4 Leu

3 each Phe, Val, Gly,

2 each His, Cys, Glu, Ala, Tyr,

1 each Asn, Gln, Ser, Arg, Thr, Pro , Lys

and the number of ways that all of these can be rearranged is

$$ \frac{30!}{4! 3!^3 2!^5} \approx 1.6 \times 10^{27} $$

which is not all that close to either of the proposed replacements. Then again, it's possible that whoever did the calculation was working from the sequence of some insulin other than human, or just made a mistake.