It should come as no surprise, our finding that independent viable autocatalytic cores embedded in a large molecular network can be considered as units of evolution, since the basic ingredients of differential growth rates and division times among potentially competing entities are fulfilled. The reader might, however, query that we have not properly addressed the issue of evolvability because no mention of heredity has been made. To fully understand that this criticism does not apply here it is important to appreciate the implications of the core-periphery dichotomy in autocatalytic sets. This dichotomy can be translated into a kind of genotype-phenotype mapping in fully fledged biological systems and, interestingly, allows us to appropriately use the terms replication and reproduction despite the fact that we are dealing with an assembly of molecules [37
]. Thus, the viable cores could be considered the units that replicate and, once transmitted to the offspring compartments after the parental compartment splits (reproduces), they give raise to the same periphery; that is; there is a clear matching between a viable core ('genotype') and the periphery ('phenotype'). 'Mutation' happens either when uncatalyzed reactions result in the emergence of a novel core, or when molecular components of a viable core are stochastically lost after compartment splitting. Thus, our autocatalytic networks are capable of stably transmitting information across generations [17
However, a viable core constitutes one bit of heritable information and therefore the number of possible selectable attractors is relatively small, meaning that autocatalytic networks may not be able to sustain open-ended evolution. While we think this to be the case, the potential role of these autocatalytic networks as a route to nucleotide-based template self-replicating systems should not be underestimated. The chemical reaction networks show an intrinsic tendency to increase in complexity. Whenever novel spontaneous reactions occur, the number of possible uncatalyzed reactions also increases, opening up new possibilities for discovering viable cores (genotypes) and their corresponding peripheries (phenotypes). This 'cooptive evolution' [13
] involves stepwise expansions into (and retractions from) the adjacent possible of reaction space [38
It is important to note that we do not claim that the present work renders the RNA world obsolete. In fact several of the authors of the present paper have worked under the assumption that indeed there had once been an RNA world. But this does not mean two things: first, that the RNA world was "clean" (probably it was not; other molecules, large and small, are likely to have been around and to have served even key functions), second, that reflexively autocatalytic networks could not have preceded the RNA world (they may have been indispensable "scaffolds", sensu
] for its appearance). As suggested by Dyson [10
], RNA could have entered as a kind of waste/parasite, but already under the catalytic influence of evolved
(as we argue) autocatalytic networks. Genetic takeover does not in principle require reverse translation or any similar esoteric process; one just needs room for stepwise innovation and improvement.
Our results should be contrasted with the lipid world scenario [4
] that so far has failed to offer models that would demonstrate a capacity for evolvability. The problem is that the simplicity of the underlying chemistry in GARD (lipid molecules are either in the assembly or not) allows only as many reactions as there are different molecular species available in the environment. Moreover, the number of distinct lipid types cannot be too high, partly because of practical considerations, but also because increasing diversity implies increasing noise in compotype replication. The restricted diversity of molecules and reactions means that the system will always quickly converge to the state set in stone by the underlying dynamical equations [4
]. The only possibility left open for change is the addition or removal of lipid species. Pointing out that altering the food set of a reaction network modifies its dynamics, however, has no relevance for evolution. A combinatorial chemistry like the polymer chemistry described in this article, on the other hand, provides an unlimited diversity of theoretically possible reactions originating from the same food set and a reasonable probability that a reaction network can discover novel cores in its shadow. Also, the permanent incorporation of a new core will extend the shadow, opening up new possibilities. Therefore we argue that such a combinatorial chemistry (or one with similar complexity) is essential for even limited evolution. The complexity of a lipid world is overshadowed by the possibilities enabled by the outlined polymer chemistry, which itself is only a shadow of the world of template-replicating nucleic acids.
We stress that there is a crucial difference between small-molecule autocatalytic cycles (such as the reductive citric acid cycle) and reflexively autocatalytic sets of polymers. First, a family of polymers (such as proteins) can be synthesized by a small set of canonical chemical reactions, whereas the reductive citric acid cycle consists of chemical steps of various kinds (cf. Orgel [41
]), thus the former can more readily be catalyzed by environmental (i.e. unevolved) catalysts. Second, and more important, polymers can, due to their modular construction, show targeted and specific activity in catalytic task space. The increased efficiency of catalysis carries over to resistance against side reactions [41
] that constantly divert material from useful pathways. However, these facts merely change the probability of formation of viable cores in particular chemical systems, not the fact that Darwinian evolution is possible once they appear.
The remaining open issues are experimental and theoretical in nature. We need better models and, above all, relevant experiments. The systematic consideration of the experimental realization and evolvability of autocatalytic networks of small organics (such as those of intermediate metabolism [2
]) require further scrutiny in the light of the proposed selectability principles. It is not farfetched to claim that an empirical scientific program implementing the sort of simple chemistry used in these models is worth pursuing. The recent calculations of Amend and McCollom [42
] indicate that amino acid production in ancient hydrothermal vents could have been thermodynamically favoured, providing a continuous supply of monomers for the hypothesized peptide network. Autocatalytic networks of peptides already have been synthesized by Ghadiri and Ashkenazy [21
], although there a direct templating effect plays a crucial role. Protein networks that do not employ templating are more difficult to realize, but several recent advances hint they might be possible. There exists a dipeptide that does catalyze ligation of peptides [43
]. Random peptides of length about 32 and 74, biased to known ratios of amino acids in evolved proteins, fold into compact structures for 30% of such sequences [44
], and longer random polypeptides have shown to have catalytic activity [45
]. The folding and catalytic properties of "never before born" peptides is therefore an open experimental question that could be addressed with random peptide libraries - it is a project much to be sought, and we should make it clear that these experiments are now needed, and hopeful given the promising results cited above.
Not every aspect of a key proposal for the spontaneous emergence of dynamical chemical organizations can be scrutinized in a single paper. Here we restricted ourselves to three issues: (i) the probability of the nucleation of reflexively autocatalytic networks, as questioned e.g. by Lifson [26
], (ii) the side reaction problem, as raised by Orgel [41
] and Szathmáry [28
], and (iii) the question of Darwinian evolvability of autocatalytic polymer sets, as left open by the previous investigations by Bagley et al. [14
]. We think we have advanced promisingly with all three problems in the present work. Our work shows that autocatalytic sets as first devised by Dyson [9
] and Kauffman [1
] are theoretically possible despite previous criticisms and, perhaps more interesting, that chemical evolution in these systems can lead to the appearance of viable autocatalytic cores, thus opening the possibility for evolution by natural selection. We have used an abstract chemistry not to avoid real chemistry, but to seek general principles. For example, selection between autocatalytic cores may even be a possibility in combinatorial inorganic systems evolving in iCHELL compartments [46
]. Naturally, one cannot be satisfied with abstract toy chemistry for long. But there is always a first step, and the scenario outlined here should give us hope that it is worthwhile to explore the idea further. After all, the pre-template Darwinian dynamics of rare core production and selection described here - fundamentally different from the mechanism advocated by Kauffman [1
] and dismissed by Eigen [18
] - is the only viable proposal so far for how autocatalytic reaction networks could accumulate adaptations.