Emergence of catalytic function in prebiotic information-coding polymers

Reviewer #1 (Public Review):

Summary:
The emergence of catalytic self-replication of polymers is an important question in the context of the origin of life. Tkachenko and Maslov present a model in which such a catalytic polymer sequence emerges from a random pool of replicating polymers.

Strengths:
The model is part of a theme from many previous papers from the same authors and their colleagues. The model is interesting, technically correct, and demonstrates qualitatively new phenomena. It is good that the paper also makes a connection with possible experimental scenarios -- specifically, concrete proposals are made for testing the core ideas of the model. It would indeed be an exciting demonstration when such an experiment does indeed materialize.

Weaknesses:
Unlike the rest of the paper which is very tight in its arguments, I find that the discussion section is not so. Specifically, sentences such as " In fact, this can be seen as a special case of the classical error catastrophe" are a bit loose and not well substantiated -- although these are in the discussion section, I find this to be a weakness of an otherwise good paper. Tightening some of the arguments here will make it an excellent paper in my opinion.

Reviewer #2 (Public Review):

Summary:
The replication of information-coding polymers and the emergence of catalytic ribozymes pose significant challenges, both experimentally and theoretically, in the study of the RNA world hypothesis. In this context, Tkachenko et al. put forth a novel hypothesis regarding a replication oligomer system based on a cleavage ribozyme. They initially highlighted that the breakage of oligomers could contribute to self-replication, provided that these fragments function as primers for subsequent replications. Next, they proposed a self-replicating system of oligomers founded on a hammerhead structure that catalyzes cleavage. By a simple dynamical model, they demonstrated that such a system is self-sustainable in certain parameter regimes. Furthermore, they delved into discussions regarding the potential emergence of such a system and the evolution toward further optimized ribozymes.

Strengths:
Although the cleavage (hammerhead) ribozyme has been discussed in the context of the origins of life, the authors are the first to discuss how they could be selected using a mathematical model as far as I know. The idea is simple: ribozyme activity creates fragments by breakage of an oligomer, which works as a primer for the ribozyme itself, resulting in a positive feedback system (i.e., autocatalytic sets in a broader sense). This potentially enables us to resolve at the same time problems on the (i) supply of new primers (but note that there is a major concern on this as described in the 'weakness'), and (ii) the sustaining of the cleavage ribozyme.

Weaknesses:
The major weakness of their theory is that the ends of the new primers, formed through the breakage/cleavage of polymers, must be chemically active (as the authors have already emphasized in the last paragraph of their discussion) to enable further elongation. Reactivating the ends of preexisting oligomers without enzymes, to the best of our current knowledge, could be a challenging task. Although their model heavily relies on this aspect, the authors do not elaborate on it.

Another weakness is in the setup of their discussion on evolutionary dynamics. While they claim that their model is robust against replication errors, their approach to evolutionary dynamics appears unconventional, and it remains unclear under what conditions their assumptions are founded. They treat a whole set of oligos as a subject of evolution, rather than each individual oligo. This may necessitate more complex assumptions, such as the encapsulation of sets of oligos inside a protocell, to be adequately rationalized. Thus, it remains uncertain whether the system is indeed robust against replication errors in a more natural context. For example, if a mutant oligo, denoted as b', arises due to an error in the replication of oligo b, and if b' has lower catalytic activity but replicates more rapidly than b, it may ultimately come to dominate the system.

Reviewer #3 (Public Review):

Summary:
Non-enzymatic replication of RNA or a similar polymer is likely to be important for the origin of life. The authors present a model of how a functional catalytic sequence could emerge from a mixture of sequences undergoing non-enzymatic replication.

Strengths:
Interesting model describing details of the proposed replication mechanism.

Weaknesses:
A discussion of the virtual circular genome idea proposed in [33] is included in the discussion section together with the problem of sequence scrambling faced by this mechanism that was raised in [34]. However, the authors state that sequence scrambling is a special case of the classical error catastrophe. This should be reworded, because these phenomena are completely different. The error catastrophe occurs due to single-point mutational errors in a model that assumes that a complete template is being copied in one cycle. Sequence scrambling arises in models that assume cycles of melting and reannealing, in which case only part of a template is copied in one cycle. Scrambling is due to the many alternative ways in which pairs of sequences can reanneal. Many of these alternatives are incorrect and this leads to the disappearance of the original sequence. This problem exists even in the limit where there is zero mutational error rate. Therefore, it cannot be called a special case of the error catastrophe problem.

The authors seem to believe that their model avoids the scrambling problem. If this is the case, a clear explanation should be added about why this problem is avoided. Two possible points are mentioned.
(i) Replication is bidirectional in this model. This seems like a small detail to me. I don't think it makes any difference to whether scrambling occurs.
(ii) The functional activity is located in a short sequence region. I can imagine that if the length of a strand that is synthesized in a single cycle is long enough to cover the complete functional region, then sometimes the complete functional sequence can be copied in one cycle. Is this what is being argued? If so, it depends a lot on rates of primer extension and lengths of melting cycles etc, and some comment on this should be made.