Talk:PLOS/Hypercycle

Reviews[edit source]

We would like to thank the Referees for thorough reading of our Hypercycle article and very detailed suggestions regarding its improvement. We have considered all the remarks and we address them below, point-by-point.

Review by Niles Lehman[edit source]

This Topic Page is a good overview of the hypercycle concept and is a welcome addition to the Wiki compilation. In fact I searched for a Wiki page on hypercycles almost five years ago and was surprised that one did not exist. It is commendable that the authors have finally added one to our repertoire.

Overall I feel that this is a nice coverage of the history and features of the hypercycle idea. I only have a few concrete suggestions for improvement.

1. In the first paragraph of the introduction, it might be good to note that the hypercycle conditions are a special case of the replicator equation, an important general idea in molecular evolutionary biology. The authors can then refer to their mathematical treatment below.

We agree that we should point out that hypercycles are a special case of the replicator equation. Therefore, according to the suggestion, we added in the first paragraph an appropriate sentence:

The hypercycle is a special case of the replicator equation followed by the reference to the article P Schuster, K Sigmund (1983) Replicator dynamics. J. Theor. Biol. 100:553-538.

Words "replicator equation" leads to the replicator equation page on Wikipedia.

2. In the second paragraph of the introduction, I would say, “The coexistence of many genetically non-identical molecules makes it possible to maintain a high [not “higher”] genetic diversity of the population.”

According to suggestion, we changed the word "higher" to "high".

3. In the third paragraph of the introduction, the authors bring up our experiments with a cooperative network of ribozymes (Vaidya et al., 2012). This is great, but it should be made explicit (either here, or in the more detailed description in the “Hypercycles and Ribozymes” section below) that this is not a demonstration of a hypercycle per se. This is because, while we have clear cooperation among recombinase ribozyme sub-networks, we did not see hyperbolic growth. See, and perhaps reference, the commentary by Szathmary (2013; Journal of Systems Chemistry 4:1) on this point.

Thank you for pointing out this important issue. We made several changes concerning this remark to make the meaning of the experiment more clear and explicit in a context of the hypercycles. Firstly, at the end of the third paragraph of the introduction, we added a sentence:

However, even though this experiment proves the existence of cooperation among the recombinase ribozyme sub-networks, this cooperative network does not form a hypercycle per se, so we still lack the experimental demonstration of hypercycles..

It is followed by the reference to the commentary by Szathmary (2013; Journal of Systems Chemistry 4:1).

Secondly, in the second paragraph of the Hypercycles and ribozymes section, after Forty years after the publication of Manfred Eigen’s primary work dedicated to hypercycles, Vaidya et al. proved experimentally that ribozymes can form catalytic cycles and networks capable of expanding their sizes by incorporating new members. we added a sentence:

However, it is important to notice that this is not a demonstration of a hypercycle in accordance with its definition, but an example of a collectively autocatalytic set.

Words "autocatalytic set" lead to the appropriate Wikipedia article about autocatalytic sets.

Thirdly, at the end of the section Hypercycles and Ribozymes we expanded the issue and added sentences:

Another experiment performed by Mutschler et al. showed that the RNA polymerase ribozyme, which they described, can be synthesized in situ from the ligation of four smaller fragments, akin to a recombination of Azoarcus ribozyme from four inactive oligonucleotide fragments described by Hayden and Lehman. Apart from a substantial contribution of the above experiments to the research on the origin of life, it has not proved the existence of hypercycles experimentally.

with appropriate citations of H Mutschler, A Wochner, P Holliger (2015) Freeze-thaw cycles as drivers of complex ribozyme assembly. Nat. Chem. 7:502-8 and EJ Hayden, N Lehman (2006) Self-assembly of a group I intron from inactive oligonucleotide fragments. Chem. Biol. 13:909-18.

Finally, at the timeline at the beginning we changed 2012 – Vaidya et al. experimentally prove that ribozymes can form catalytic cycles into:

2012 – Vaidya et al. show experimentally that ribozymes can form collectively autocatalytic sets

to make the meaning of the experiment more explicit at the first glimpse.

4. In the “Formation of the First Hypercycles” section, the discussion mentions a couple of times that the original postulate by Eigen and Schuster (1979) was that both nucleic acids and proteins were required to establish a hypercycle. A few years later of course (1982) ribozymes were discovered, negating this requirement in a strict sense. While the authors do bring this up later, this present section seems a bit too elaborately focused on this idea, which then is obviated.

According to suggestions, we changed the Formation of the First Hypercycles section as follows:

Eigen made several assumptions about conditions that led to the formation of the first hypercycles.[2] Some of them were the consequence of the lack of knowledge about ribozymes which were discovered few years after the introduction of the hypercycle concept[24][25] and negated Eigen’s assumptions in the strict sense. The primary of them was that the formation of hypercycles had required the availability of both types of chains – nucleic acids forming a quasispecies population and proteins with enzymatic functions. Nowadays, taking into account the knowledge about ribozymes, it may be assumed that hypercycle’s members were selected from the quasispecies population and the enzymatic function was performed by RNA. According to the hypercycle theory, the first primitive polymerase emerged precisely from this population. As a consequence, the catalysed replication could exceed the uncatalysed reactions, and the system could grow faster. However, this rapid growth was a threat to the emerging system as the whole system could lose control over the relative amount of the RNAs with enzymatic function. The system required more reliable control of its constituents, for example by incorporating the coupling of essential RNAs into a positive feedback loop. Without this feedback loop, the replicating system would be lost. These positive feedback loops formed the first hypercycles.

In the process described above, the fact that the first hypercycles originated from the quasispecies population (a population of similar sequences) created a significant advantage. One possibility of linking different chains I, which is relatively easy to achieve taking into account the quasispecies properties, is that the one chain I improves the synthesis of the similar chain I’. In this way, the existence of similar sequences I originating from the same quasispecies population promotes the creation of the linkage between molecules I and I’.

5. The “Origin of the Translation Code” section is far too in depth and focused on outdated ideas. I would suggest eliminating this as a stand-alone section, and just mention one or two points about the genetic code elsewhere. The code evolution theories mentioned here were those favored by Eigen in the 1970s (e.g., the RNY code), but there are now hundreds of newer theories of how the code was established and later evolved.

We removed the Origin of the Translation Code section. And put few sentences about the RNY and RRY codes at the end of Hypercycle with translation section. These are:

Coupling nucleic acids with proteins in such a model of hypercycle with translation demanded the proper model for the origin of translation code as a necessary condition for the origin of hypercycle organization. At the time of hypercycle theory formulation, two models for the origin of translation code were proposed by Crick and his collaborators (Crick et al., 1976). These were models stating that the first codons were constructed according to either an RRY or an RNY scheme, where R stands for the purine base, Y for pyrimidine and N for any base, with the latter assumed to be more reliable. Nowadays, it is assumed that the hypercycle model could be realized by a utilization of ribozymes without the need of a hypercycle with translation, and there are much more theories about the origin of the genetic code.

The words "origin of the genetic code" link to the proper article at Wikipedia.

6. In the “Hypercycles and Ribozymes” section, I would say, “In 2001 a partial RNA polymerase ribozyme was designed via …” (note the “a” and the word “partial”). The 2001 version could only catalyze the polymerization of about 14 nucleotides, even though it was a ribozyme that was about 200 nucleotides long. Similarly, the most “up-to-date” version of this catalyst is described in Mutschler et al. (2015; Nature Chemistry 7:502-508), and this should be referenced. This molecule is still a “partial” RNA replicase ribozyme because, while it can catalyze polymerization of a template of its own length, it cannot replicate its own sequence. Thus we still don’t have a true replicase ribozyme in hand yet. This molecule is about 200 nt long. {Notably though, Mutschler et al. (2015) showed that it could be synthesized in situ from the ligation of four smaller fragments, akin to our recombination of the Azoarcus ribozyme from four fragments (e.g., Hayden & Lehman 2006; Chemistry & Biology 13:909-918). Thus there is a further similarity to – but not demonstration of – a hypercyclic system.}

We changed the Hypercycles and Ribozymes section according to the suggestions. We added the word "a partial" into the sentence:

In 2001 a partial RNA polymerase ribozyme was designed via …

Furthermore, we expanded this section by adding information about the pointed version of this ribozyme with the appropriate reference to Mutschler et al. (2015); Nature Chemistry 7:502-508. We also added the information about a cross-chiral RNA polymerase ribozyme (Szczepanski and Joyce, 2014). The modified paragraph looks as follows:

In 2001, a partial RNA polymerase ribozyme was designed via a directed evolution (Johnston et al., 2001). Nevertheless, it was able to catalyze only a polymerization of a chain having the size of about 14 nucleotides, even though, it was 200 nucleotides long. The most up-to-date version of this polymerase was shown in 2015 (Mutschler et al., 2015). While it has an ability to catalyze polymerization of longer sequences, even of its own length, it cannot replicate itself. In 2014, a cross-chiral RNA polymerase ribozyme was demonstrated (Szczepanski and Joyce, 2014). It was hypothesized that it offers a new mode of recognition between an enzyme and substrates, which is based on the shape of the substrate, and allows avoiding the Watson-Crick pairing and, therefore, may provide greater sequences generality.

We also pointed out that Mutschler et al. (2015) showed that their polymerase ribozyme could be synthesized in situ from the ligation of four smaller fragments, akin to the recombination of the Azoarcus ribozyme from four fragments (e.g., Hayden & Lehman 2006; Chemistry & Biology 13:909-918). Moreover, we underlined that, again, this is not a demonstration of a hypercyclic system:

Another experiment performed by Mutschler et al. (Mutschler et al., 2015) showed that the RNA polymerase ribozyme, which they described, can be synthesized in situ from the ligation of four smaller fragments, akin to a recombination of Azoarcus ribozyme from four inactive oligonucleotide fragments described by Hayden and Lehman (Hayden and Lehman, 2006). Apart from a substantial contribution of the above experiments to the research on the origin of life, it has not proved existence of hypercycles experimentally.

7. In describing our Azoarcus system, the word “mutant” should be replaced by “genotype” as there is no mutation per se in this system, at least as the term is normally understood.

According to the suggestion, we change the word "mutant" to "genotype".

8. In the “Hypercycles and Ribozymes” section, there are several missing articles (“a” or “the”); for example it should read, “An RNA ligase in turn could link…”

Thank you for this remark, we did our best to fix this problem.

Review by Mauro Santos[edit source]

To have an easy reading and comprehensible review of what hypercycles are or are not is a welcome and much needed contribution. Overall, I think this is a nice input but in my view it needs to elaborate and expand a little bit on some issues.

“Error threshold problem”

Because this important problem motivated the hypercycle, it would be probably fine to remind that the genome size n of any organism is roughly the inverse of the mutation rate per site and replication [Drake J.W. Rates of spontaneous mutation among RNA viruses. Proc. Natl. Acad. Sci. USA, 90, 4171–4175 (1993). Drake J.W., Charlesworth B., Charlesworth D., and Crow J.F. Rates of spontaneous mutations. Genetics, 148, 1667–1686 (1998)]. This can be visually appreciated by plotting the data in Drake et al. with genome size in the x-axis and log p (p is the per-digit error rate) in the y-axis. This plot can be seen in Stadler BMR, Stadler PF. 2003. Molecular replicator dynamics. Adv Complex Syst 6:47–77.

Thank you for pointing this out, we added an appropriate information in the mentioned section:

Moreover, it was shown that the genome size of any organism is roughly equal to the inverse of mutation rate per site per replication (Drake, 1993; Drake et al., 1998, Stadler and Stadler, 2003), therefore, high mutation rate imposes a serious limitation on the length of the genome.

“Evolutionary dynamics”

I agree that it might be good to note that the hypercycle conditions are a special case of the replicator equation.

We added the information that hypercycles are the special case of the replicator equation in the first paragraph of the introduction.

In the hypercycle theory Eigen and Schuster distinguished between subexponential, exponential and hyperbolic growth. The idea that ‘when one hypercycle wins the selection and dominates the population is very difficult to replace it’ is based on exponential growth. However, Szathmáry (Szathmáry E. and Gladkih I. 1989. Sub-exponential growth and coexistence of nonenzymatically replicating templates. J. theor. Biol., 138, 55–58) pointed out that unconditional coexistence can be obtained with subexponential or parabolic growth. Because a common problem of non-enzymatic artificial replicator systems is product inhibition leading to parabolic instead of exponential or Malthusian growth, a word of caution would be needed.

According to suggestions, we expanded the section "Evolutionary dynamics" by adding a paragraph:

The idea of hypercycle’s robustness described above results from an exponential growth of its constituents caused by the catalytic support. However, Szathmary and Gladkih showed that an unconditional coexistence can be obtained even in the case of a non-enzymatic template replication which leads to a subexponential or a parabolic growth (Szathmary and Gladkih, 1989). This could be observed during stages preceding a catalytic replication that are necessary for the formation of hypercycles. The coexistence of various non-enzymatically replicating sequences could help to maintain a sufficient diversity of RNA modules used later to build molecules with catalytic functions.

“Compartmentalization and genome integration”

The first to discuss so-called package models where Bresch et al. (Bresch, C., Niesert, U. & Harnasch, D. 1980. Hypercycles, parasites and packages. J. theor. Biol. 85, 399–405). They proposed the package model because problems with hypercycles arise when mutations are taken into account (i.e., parasites or short-cuts). In particular, they worried about the parasite problem originally introduced by Maynard Smith. Another important point is that adaptive evolution requires the package of transmissible information for advantageous mutations in order not to aid less-efficient copies of the gene. I don’t agree with the claim that “Such compartmentalization is an evolutionary consequence of hypercyclic organization”. Actually, the point of the stochastic corrector model initially developed by Szathmáry and Demeter was to ask whether or not the package of a truly hypercyclic system into compartments is a necessary intermediate stage of evolution. In essence, one of the main aims of the stochastic corrector model was to solve the parasite problem. Remember that this model was initially published in 1987, some years after Maynard Smith called attention to the parasite problem and a few years before this problem was tackled by Boerlijst and Hogeweg using an explicit spatial model. Actually, Zintzaras et al. (Zintzaras, E., M. Santos and E. Szathmáry. 2002. "Living" under the challenge of information decay: the stochastic corrector model vs. hypercycles. J. theor. Biol. 217: 167-181) showed that compartmentalized hypercycles are more sensitive to the input of deleterious mutations than a simple package of competing genes. However, it should be acknowledged that package models do not solve the error threshold problem that originally motivated the hypercycle.

Thank you for raising this importaint issue. We revised the problem with a compartmentalzation in the context of hypercycles. Firsly, we removed the sentence:

Such compartmentalization is an evolutionary consequence of hypercyclic organization.

Secondly, we expanded the section by adding new paragraph:

In the initial works the compartmentation was stated as an evolutionary consequence of the hypercyclic organization. Bresch et al.(Bresch et al., 1980) raised an objection that hypercyclic organization is not necessary if compartments are taken into account. They proposed the so-called package model in which one type of a polymerase is sufficient and copies all polynucleotide chains which contain a special recognition motif. However, as pointed by authors, contrary to hypercycles, such packages are vulnerable to deleterious mutations, as well as a fluctuation abyss, resulting in packages that lack one of the essential RNA molecules. Eigen et al. (Eigen et al., 1980) argued that simple package of genes cannot solve the information integration problem and hypercycles cannot be simply replaced by compartments, but compartments may assist hypercycles. This problem however raised more objections and Szathmary and Demeter reconsidered whether packing hypercycles into compartments is a necessary intermediate stage of the evolution. They invented a stochastic corrector model (Szathmary and Demeter, 1987) that assumed that replicative templates compete within compartments and selective values of these compartments depend on the internal composition of templates. Numerical simulations showed that when stochastic effects are taken into account, compartmentation is sufficient to integrate information dispersed in competitive replicators without the need of hypercycle organization. Moreover, Zintras et al. (Zintras et al., 2002) showed that compartmentalized hypercycles are more sensitive to the input of deleterious mutations than a simple package of competing genes. Nevertheless, package models do not solve the error threshold problem that originally motivated the hypercycle.

Another issue that I want to raise is whether or not hypercycles have been experimentally realized. The authors write that “In 2012, Vaidya et al. published the first experimental proof for the emergence of a cooperative network among fragments of ribozymes which have the ability to self-assemble, and demonstrated their advantages over self-replicating cycles.” Eörs Szathmáry (2013. On the propagation of a conceptual error concerning hypercycles and cooperation. Journal of Systems Chemistry 4:1) has published a critical appraisal on conceptual errors in the literature concerning hypercycles and molecular cooperation. The authors should read this paper to avoid making the same mistake.

Indeed, we agree that it should be underlined that Vaidya et al. experiment is not the demonstration of hypercycles, but an example of collectivey autocatalytic set. We made several changes to highlight this.

Firstly, at the end of the third paragraph of the introduction, we added a sentence: