Almost inevitably when talking about the possibility of extraterrestrial life you hear something along the lines of "there are billions of galaxies, billions of stars and billions of more planets, some of them at least must contain some sort of life". The argument–really more of an inclination–is intuitive in one sense but it misses something.
Biologists don't yet have a theory of abiogenesis (chemical evolution) but suppose we assume a purely chance-based explanation, what then is the (conditional) probability of forming the first living cell through random molecular interactions? Conditional on chance alone, that's now a very answerable question.
Even the simplest life is still very complex. The simplest extant cell, the mycoplasma genitalium a bacterium which inhabits the urinary tract in humans, contains 482 proteins and around 562,000 base pairs in its DNA. That's still a high number, as compared to what's suggested in knock out experiments which indicate a possible minimal complexity of around 250 proteins.
How complex is each protein? Some proteins are hundreds of amino acids long, let us assume then a modest average length of 150 amino acids. Each of these proteins must then meet three requirements: (a) every amino acid must form a peptide bond or the molecule will not form properly (b) every amino acid must be an L-form or the resulting polypeptide chain will not fold into a functioning protein and (c) the DNA bases must form a meaningful sequence, one that actually codes for a protein.
Peptide bonds form about as regularly as non-peptide bonds. So the probability is around half.
Likewise, the second of these conditions is about half. Amino acids (with one exception) come in two forms, L-form and D-form these are mirror images of each other known as "optical isomers" and only the left-hand form allows for a functional protein to be built.
The third of these conditions is more difficult to determine. What we need to know is the ratio of functional sequences of amino acids to non-functional sequences (i.e. those that fold into a protein to those that can't).
Amino acids have to meet up in a meaningful arrangement in order to produce a polypeptide chain, that folds into a functioning protein. There being exactly 20 different types of amino acid. The probability of a particular polypeptide chain is easy to calculate.
However, that isn’t the right probability for (c). We need to determine the probability for any functional protein, not just a specific protein. Enter Robert Sauer. Sauer performed experiments at MIT using a technique called "casette mutagenesis" to determine how tolerant proteins were to varying a given amino acid. Even taking variance into account, Sauer determined that the probability of getting a functional protein (100 amino acids long) is
Independently a Biologist named Douglas Axe formerly working at Cambridge university argued that Sauer underestimated the variance allowed by functional proteins. In a 150 amino acid long protein, estimated the probability to be
This estimation is based on his own mutagenesis experiments, published in a paper back in 2004. So now we have enough to determine the probability of a single protein forming by chance. We simply add each of the powers.
That may be the probability of obtaining a single functional protein but we want to know the probability of the first organism, of 250 proteins appearing by chance. We simply multiply the probability of one, by itself 250 times.
My calculation here is not far off Fred Hoyle's estimation (though his work was based on far more guesswork). The number which is so inconceivably small, that it can in effect be ruled out, no matter how many galaxies, stars or planets in our observable universe. That may just be our answer to the Fermi paradox.
When I began reading about the origin of life it didn't take me long to discover that no one really takes "chance only" explanations seriously anymore, not to my surprise, the oft-presented textbook picture of the first cell arising in a prebiotic soup, something like presented in the Miller-Urey experiment, is entirely outdated.
Not only are there other requirements for a functioning cell beyond proteins and DNA–ATP, phosphates, lipids, sugars, vitamins, metals, some kind of proto-cell membrane–but there probably wasn't a prebiotic soup, to begin with.
Famously James Brooks and Gordon Shaw discovered that the precambrian sedimentary layers of rock didn't contain enough nitrogen to suggest the existence of an ocean rich in amino acids. Its level is less than .015 per cent and the chemicals used in the experiment are also slightly off, in a reducing atmosphere forming amino acids isn't difficult (it's an exothermic reaction). But under early earth conditions which probably contained neutral gases, carbon dioxide, nitrogen, and water vapour and also much free oxygen, these present an environment which is hostile to the production of amino acids.
That might seem bad enough but it gets even worse, many destructive chemicals are also produced in simulations of this kind of model. Biochemically irrelevant compounds, a kind of black insoluble sludge which is normally removed by the researcher. As are the presence of medium to long wavelength ultraviolet light. These obviously further diminish the odds of producing the first life but I have no way of calculating those numbers. In any case, it's doesn't matter.
Now, of course, there are other alternatives to pure chance like biochemical predestination, external self-organisation or the RNA world hypothesis, which either doesn't rely on chance at all or it plays on far fewer odds. For example in the RNA world hypothesis now the currently favoured theory, chance may bring about a much smaller molecule that can self-replicate and then a kind of pre-biotic natural selection takes over.
I'm no expert on any of this but Origin of Life research is something I'm becoming incredibly interested it. We may just have to wait and see what happens.