[…] In conclusion, much elegant work has been done starting from activated mono-nucleotides. However, the prebiotic synthesis of a specific macromolecular sequence does not seem to be at hand, giving us the same problem we have with polypeptide sequences. Since there is no ascertained prebiotic pathway to their synthesis, it may be useful to try to conceive some working hypothesis. In order to do that, I would first like to consider a preliminary question about the proteins we have on our Earth: “Why these proteins … and not other ones?”. Discussing this question can in fact give us some clue as to how orderly sequences might have originated. […] A grain of sand in the Sahara – This is indeed a central question in our world of proteins. How have they been selected out? There is a well-known arithmetic at the basis of this question, (see for example De Duve, 2002) which says that for a polypeptide chain with 100 residues, 20^100 different chains are in principle possible: a number so large that it does not convey any physical meaning. In order to grasp it somewhat, consider that the proteins existing on our planet are of the order of a few thousand billions, let us say around 10^13 (and with all isomers and mutations we may arrive at a few orders of magnitude more). This sounds like a large number. However, the ratio between the possible (say 20^100) and the actual chains (say 10^15) corresponds approximately to the ratio between the radius of the universe and the radius of a hydrogen atom! Or, to use another analogy, nearer to our experience, a ratio many orders of magnitude greater than the ratio between all the grains of sand in the vast Sahara and a single grain. The space outside “our atom”, or our grain of sand, is the space of the “never-born proteins”, the proteins that are not with us – either because they didn’t have the chance to be formed, or because they “came” and were then obliterated. This arithmetic, although trivial, bears an important message: in order to reproduce our proteins we would have to hit the target of that particular grain of sand in the whole Sahara. Christian De Duve, in order to avoid this “sequence paradox” (De Duve, 2002), assumes that all started with short polypeptides – and this is in fact reasonable. However, the theoretically possible total number of long chains does not change if you start with short peptides instead of amino acids. The only way to limit the final number of possible chains would be to assume, for example, that peptide synthesis started only under a particular set of conditions of composition and concentration, thus bringing contingency into the picture. As a corollary, then, this set of proteins born as a product of contingency would have been the one that happened to start life. Probably there is no way of eliminating contingency from the aetiology of our set of proteins. […]
Figure – The ratio between the theoretical number of possible proteins and their actual number is many orders of magnitude greater than the ratio between all sand of the vast Sahara and a single grain of sand (caption on page 69).
[…] The other objection to the numerical meaning suggested by Figure (above) is that the maximum number of proteins is much smaller because a great number of chain configurations are prohibited for energetic reasons. This is reasonable. Let us then assume that 99.9999% of theoretically possible protein chains cannot exist because of energy reasons. This would leave only one protein out of one million, reducing the number of never-born proteins from, say, 10^60 to 10^54. Not a big deal. Of course one could also assume that the total number of energetically allowed proteins is extremely small, no larger than, say, 10^10. This cannot be excluded a priori, but is tantamount to saying that there is something very special about “our” proteins, namely that they are energetically special. Whether or not this is so can be checked experimentally as will be seen later in a research project aimed at this target. The assumption that “our” proteins have something special from the energetic point of view, would correspond to a strict deterministic view that claims that the pathway leading to our proteins was determined, that there was no other possible route. Someone adhering strictly to a biochemical anthropic principle might even say that these proteins are the way they are in order to allow life and the development of mankind on Earth. The contingency view would recite instead the following: if our proteins or nucleic acids have no special properties from the point of view of thermodynamics, then run the tape again and a different “grain of sand” might be produced – one that perhaps would not have supported life. Some may say at this point that proteins derive in any case from nucleic-acid templates – perhaps through a primitive genetic code. However, this is really no argument – it merely shifts the problem of the etiology of peptide chains to etiology of oligonucleotide chains, all arithmetic problems remaining more or less the same. […] pp. 68-70, in Pier Luigi Luisi, “The Emergence of Life: From Chemical Origins to Synthetic Biology“, Cambridge University Press, US, 2006.