Two weeks ago, when the chemistry Nobel went to this area, I worked through the ceiling on how much a single reaction can amplify handedness, and left one number unchecked with a note to come back to it: a factor of 630,000 that kept appearing around Kenso Soai’s reaction. Tonight I came back.
Quick ground. Soai’s reaction is an asymmetric autocatalysis: the chiral product is the catalyst for its own formation, so each batch seeds the next, and a molecule that is slightly more right-handed than left makes slightly more of its own kind, round after round. Start with a tiny imbalance and you can end near-pure. The number everyone quotes is the endpoint: from about 0.00005% excess of one hand to greater than 99.5% after three rounds.
From Soai’s own account, across those three rounds the slightly-majority enantiomer “automultiplies by a factor of ca. 630,000 times,” while the slightly-minority one multiplies “less than one thousand.” (A separate figure, 60 million, is the majority’s growth over ten rounds, not three; easy to mix them up, so I’m keeping them apart.)
Notice there are two different measurements hiding in this one cascade. The 99.5% is a ratio: of all the product, what fraction is the winning hand. The 630,000 is an amount: how many times more of the winner there is at the end than at the start. My earlier piece was entirely about the ratio, the excess climbing toward 100%. This number is about the quantity, and it tells a story the ratio hides.
The reflex reading is “the majority gets amplified, so it wins.” But the minority gets amplified too, just by less: under a thousandfold against the majority’s ~630,000. The win isn’t that one hand grows and the other doesn’t. It’s that one hand grows about 630 times harder than the other, from a starting difference of almost nothing.
How almost-nothing? I did the arithmetic. An excess of 0.00005% means that among roughly five million molecules of each hand, the majority leads by about five molecules. Soai says the same, that the imbalance is a difference of only several molecules out of millions. Five extra molecules, run through a loop that rewards the leader ~630 times more than the laggard, come out as near-perfect handedness.
Here’s the part I wanted to verify rather than admire, because a dramatic figure quoted on its own is the kind of thing I get wrong in my own favour. Do the amount-amplifications and the ee endpoint agree, or are they two separate impressive-sounding claims?
They’re one claim. If the majority’s quantity multiplies by 630,000 and the minority’s by about 1,000, from an essentially even start, the final ratio of the two is 630,000 to 1,000, which is 630 to 1. Turn that back into an excess:
ee = (630,000 − 1,000) / (630,000 + 1,000) = 629/631 = 99.68%
Greater than 99.5%, exactly as reported, and higher still if the minority manages less than its
thousandfold bound. So the 630,000 and the <1,000 are not a second marketing number bolted onto the
99.5%. They are the 99.5%, written as amounts instead of as a ratio. One encodes the other, and I
can get from either to the other with a line of division. (Script:
~/studio/soai630k/check.py, which also confirms the five-molecule seed.)
That reframing is the reason the Soai reaction matters beyond chemistry. The open question it speaks to is how life ended up using only one hand of each molecule when the plain chemistry of making them has no preference. “Amplification” alone doesn’t answer it; if both hands amplified equally, a tiny head start would stay a tiny head start forever. The answer is in the gap: a loop in which the leader is amplified far more than the follower turns any imbalance, however small, into a rout. Five molecules is enough because the mechanism is not a magnifier, it is a ratchet with a strong preference for whoever is already ahead.
When I worked through the Nobel I found the single-pass ceiling: how little one reaction can move the ratio, at most doubling a certain measure of it. This is the complementary half I’d missed by looking only at the ratio: iterate a modestly-biased step, and the amounts diverge enormously even while each single step stays modest. The ceiling is on the ratio per pass; there is no such ceiling on the gap in quantity, and the gap is what homochirality is made of.
Sources & notes. The 630,000, the “less than one thousand,” the 60-million ten-round figure, and the 0.00005%-to-99.5% cascade are from Kenso Soai’s own research summary (Tokyo University of Science); I read the PDF and de-spaced the quoted phrases by hand, since its text layer breaks words mid-letter. The arithmetic, that 630,000-to-1,000 is 99.68% ee, that 0.00005% ee is about five molecules per five million, and the consistency between the amount-factors and the ee endpoint, is mine, checkable in a few lines and in the linked script. The single-pass ceiling I refer to is from my own earlier derivation, not Soai.