Coin
tossing for beginners and macromolecular assembly
So let's play the creationist game and look at forming a
peptide by random addition of amino acids. This certainly
is not the way peptides formed on the early Earth, but it
will be instructive.
I will use as an example the "self-replicating" peptide
from the Ghadiri group mentioned above [7]. I could use other examples, such as the
hexanucleotide self-replicator [10], the
SunY self-replicator [24] or the RNA
polymerase described by the Eckland group [12], but for historical continuity with
creationist claims a small peptide is ideal. This peptide
is 32 amino acids long with a sequence of
RMKQLEEKVYELLSKVACLEYEVARLKKVGE and is an enzyme, a peptide
ligase that makes a copy of itself from two 16 amino acid
long subunits. It is also of a size and composition that is
ideally suited to be formed by abiotic peptide synthesis.
The fact that it is a self replicator is an added
irony.
The probability of generating this in successive random
trials is (1/20)^32 or 1 chance in 4.29 x
10^40. This is much, much more probable than the
1 in 2.04 x 10^390 of the standard creationist
"generating carboxypeptidase by chance" scenario, but still
seems absurdly low.
However, there is another side to these probability
estimates, and it hinges on the fact that most of us don't
have a feeling for statistics. When someone tells us that
some event has a one in a million chance of occuring, many
of us expect that one million trials must be undergone
before the said event turns up, but this is
wrong.
Here is a experiment you can do yourself: take a coin,
flip it four times, write down the results, and then do it
again. How many times would you think you had to repeat
this procedure (trial) before you get 4 heads in a row?
Now the probability of 4 heads in a row is is
(1/2)^4 or 1 chance in 16: do we have to do 16
trials to get 4 heads (HHHH)? No, in successive experiments
I got 11, 10, 6, 16, 1, 5, and 3 trials before HHHH turned
up. The figure 1 in 16 (or 1 in a million or 1 in
10^40) gives the likelihood of an event in a
given trial, but doesn't say where it will occur in
a series. You can flip HHHH on your very first trial
(I did). Even at 1 chance in 4.29 x 10^40, a
self-replicator could have turned up surprisingly early.
But there is more.
1 chance in 4.29 x 10^40 is still orgulously,
gobsmackingly unlikely; it's hard to cope with this number.
Even with the argument above (you could get it on your very
first trial) most people would say "surely it would still
take more time than the Earth existed to make this
replicator by random methods". Not really; in the above
examples we were examining sequential trials, as if there
was only one protein/DNA/proto-replicator being assembled
per trial. In fact there would be billions of
simultaneous trials as the billions of building
block molecules interacted in the oceans, or on the
thousands of kilometers of shorelines that could provide
catalytic surfaces or templates [2,15].
Let's go back to our example with the coins. Say it
takes a minute to toss the coins 4 times; to generate HHHH
would take on average 8 minutes. Now get 16 friends, each
with a coin, to all flip the coin simultaneously 4 times;
the average time to generate HHHH is now 1 minute. Now try
to flip 6 heads in a row; this has a probability of
(1/2)^6 or 1 in 64. This would take half an hour
on average, but go out and recruit 64 people, and you can
flip it in a minute. If you want to flip a sequence with a
chance of 1 in a billion, just recruit the population of
China to flip coins for you, you will have that sequence in
no time flat.
So, if on our prebiotic earth we have a billion peptides
growing simultaneously, that reduces the time taken to
generate our replicator significantly.
Okay, you are looking at that number again, 1 chance in
4.29 x 10^40, that's a big number, and
although a billion starting molecules is a lot of
molecules, could we ever get enough molecules to randomly
assemble our first replicator in under half a billion
years?
Yes, one kilogram of the amino acid arginine has
2.85 x 10^24 molecules in it (that's well
over a billion billion); a tonne of arginine has 2.85 x
10^27 molecules. If you took a semi-trailer load
of each amino acid and dumped it into a medium size lake,
you would have enough molecules to generate our particular
replicator in a few tens of years, given that you can make
55 amino acid long proteins in 1 to 2 weeks [14,16].
So how does this shape up with the prebiotic Earth? On
the early Earth it is likely that the ocean had a volume of
1 x 10^24 litres. Given an amino acid
concentration of 1 x 10^-6 M (a moderately dilute
soup, see Chyba and Sagan 1992 [23]),
then there are roughly 1 x 10^50 potential
starting chains, so that a fair number of efficent peptide
ligases (about 1 x 10^31) could be produced in a
under a year, let alone a million years. The
synthesis of primitive self-replicators could happen
relatively rapidly, even given a probability of 1 chance in
4.29 x 10^40 (and remember, our replicator could
be synthesized on the very first trial).
Assume that it takes a week to generate a sequence [14,16]. Then the Ghadiri
ligase could be generated in one week, and any cytochrome C
sequence could be generated in a bit over a million years
(along with about half of all possible 101 peptide
sequences, a large proportion of which will be functional
proteins of some sort).
Although I have used the Ghadiri ligase as an example,
as I mentioned above the same calculations can be performed
for the SunY self replicator, or the Ekland RNA polymerase.
I leave this as an exercise for the reader, but the general
conclusion (you can make scads of the things in a short
time) is the same for these oligonucleotides.