Reviewer’s report 1
Wentao Ma, College of Life Sciences, Wuhan University, China.
Reviewer comments 1.1:
This is an interesting effort to clarify the meaning of “self-sustaining”, which is no doubt significant for us to appreciate the concept of life, but the author should make more illustration on the relationship between the chemical systems he exemplified and real living systems.In this paper, Dr. Liu discussed, concerning the concept of life, an interesting issue: What is a self-sustaining chemical system? The analysis appears convincing and the conclusion is also interesting. However, I have some remarks on the paper. Since the topic is concerning the concept of life, first, a relevant clarification is necessary. As the author mentioned, NASA provided a relatively authoritative definition: “Life is a self-sustaining chemical capable of undergoing Darwinian evolution”. In a previous paper of my own (The essence of life, Biology Direct, 2016, 11:49), I noted that for the two aspects of life, self-sustaining and Darwinian evolution, the former is in respect of an individual (or entity), whereas the latter is in respect of a lineage (from the level of population to that of species and that above) - or rather, in respect of the form of the individual. Just image, how can an individual system undergoing Darwinian evolution? Therefore, I concluded, the definition of life should be split, as some expression like: “A life form is a matter form capable of undergoing Darwinian evolution; a living entity is a self-sustaining chemical system - in nature, it results from the Darwinian evolution and might engage into further Darwinian evolution”. But this splitting definition, as I also admitted, is somewhat complex to understand. For a compromise, here I would like to accept the definition: “Life is a sort of self-sustaining chemical systems capable of undergoing Darwinian evolution”. In this definition, by introducing the key phrase “a sort of”, we can appreciate “Darwinian evolution” is in regard of some kind of entities, whereas “self-sustaining remains” in regard of individual entities - i.e., just as we call it, living things. In fact, the new definition I propose here is to an extent just inspired by the analysis in the present paper. As the author concluded, there are many kinds of self-sustaining systems (“not uncommon”) - so life is just one sort of them. The point is: life is different from other self-sustaining systems by the other characteristic aspect - capable of undergoing Darwinian evolution. If so, I think this also offers an answer to the author’s question: How to distinguish life from self-sustaining fire (or other dissipative) systems?
Author’s response 1.1: I am grateful for the reviewer for his comments, appreciation and suggestions. I will try to give my thoughts. The definition of life is, of course, an essential question, but way beyond this paper to answer. Instead, I intend to give a formal and rigorous definition of self-sustainability that is explicitly included in the working definition of life from NASA and that serves as one of the two essential properties of life (the other is Darwin evolution as also pointed out by the reviewer). However, in the literature, there is no rigorous and satisfying definition of self-sustainability (some related concepts are discussed in this paper). This is the very motivation of this work, so I only touched the other aspect of life (the Darwinian /genetics /information side) by linking self-sustainability with preliminary heredity. As pointed out by the reviewer, life would be a self-sustaining system with extra criteria. If self-sustainability is now rigorously defined, the next steps to define life would be easier.
I am really happy that this paper can give some inspirations to the reviewer. I totally agree that self- sustainability and Darwinian evolution should be considered separately; and self-sustainability implies individuality while evolution implies interactions at the level of population. But I think adding “sort of” into the definition of life is still not satisfying, which makes the definition hand-waving and vague. But this kind of discussions or the definition of life certainly deserves a whole paper if not many more.
Reviewer comments 1.2:
About the capability of undergoing Darwinian evolution, we should appreciate the author’s effort to associate self-sustainability with heredity. As we know, heredity is one prerequisite of Darwinian evolution. The attempt to connect the trigger molecules to some preliminary heredity is attractive and somehow reasonable. But I think the author should make a more detailed annotation on the difference between this preliminary heredity (limited heredity) and real heredity in living things (unlimited heredity) - it is in fact just the unlimited heredity that makes Darwinian evolution possible, as highlighted by Szathmary and coworkers. Actually, in another paper of mine (What does “the RNA world” mean to “the origin of life”? Life, 2017,7:49), I stated that the ‘self-’ in the self-sustainment for life is just defined by its genetic information, carried on the genetic molecules (mainly DNA). Here, it seems that the information is just carried by the trigger molecules. That is, if the heredity mentioned by the author is comparable with the real heredity, it appears that the genetic molecules are just the trigger molecules in living things (but note that in the concrete scenario, some maternal mRNA are also necessary to trigger a new round ontogenesis). Similarly, when describing the self-sustainability in chemical systems (CRN), the author should make more efforts to connect real living things, especially considering that the author aimed for a clearer understanding on the concept of life. For example, for the situation in real living systems, the key components are enzymes (encoded by genetic information) instead of reactants—as mentioned by the author, for simplification, enzymes were neglected when exemplifying the metabolic cases (i.e., the glyoxylate cycle, the reverse citric acid cycle and the Calvin cycle), but I think that here is just a chance for the author to talk more about the situation in true living systems. As another example, in a living cell, genetic molecules (mainly DNA), the “trigger” of the self-sustaining system, are neither consumed nor produced (unless for cell division), which is apparently different from the CRN described by the author. So forth and so on. I think the author should comment on things like these.All in all, this is an interesting effort to clarify the meaning of “self-sustaining”, which is no doubt significant for us to appreciate the concept of life, but the author should make more illustration on the relationship between the chemical systems he exemplified and real living systems.
Author’s response 1.2: Thanks very much for appreciating the linking between self-sustainability and heredity. Yes, I do think the preliminary heredity that is carried by the trigger molecules corresponds to the limited heredity as Szathmary highlighted. Also, I do think the genetic molecules are just the trigger molecules in living things.
Nevertheless, the transition from limited to unlimited heredity deserves a close look, regarding the reviewer’s concern. In my opinion, the transition deeply relates to the number of possible configurations of the trigger molecules (or a group of trigger molecules). For example, (1) oxygen gas O2 is the trigger molecule in the exemplified system (atomic oxygen O combines into O2 in the upper atmosphere), but O2 only has one configuration and the heredity it carries is thus limited. (2) For larger molecules (imagine a crystal), if served as the trigger, they could have different configurations such as different isomers, left-handed or right-handed, the heredity they carry would be more but still finite and limited. (3) For DNA, RNA-like molecules, their length can be increased, their based pairs can be switched or replaced, so they basically have an infinite number of configurations which makes the heredity unlimited. The trigger molecules in (1) and (2) are constrained by their intrinsic physics which forbids extra configurations, but for RNA-like molecules, the physical constraint is just relaxed.
Another point to notice is that, we often consider all the possible RNAs for a bacterial species (for example) altogether, because no matter what particular RNA molecule, it can always trigger the similar chemical reactions in the body of the bacteria. This is also why RNA carries unlimited information, because we are basically talking about an infinite number of particular molecules. For oxygen or crystals as above, we simply cannot do that, as there is no such different oxygen gas or crystal. So, in my opinion, the limited and unlimited heredity is in principle the same in the sense of the underlying chemical system, but it appears different due to the different physics inside the molecules.
These discussions are interesting and important, but I thought they were beyond the point of defining self-sustainability. Nevertheless, in order to also give the credits to the reviewer for raising this issue, I added a sentence in “On Heredity” section to guide the reader here for more details.
For the last issue raised by the reviewer that “genetic molecules (mainly DNA) are neither consumed nor produced (unless for cell division)”, I actually have different opinions: DNA does “consumed” and “regenerated”. In the process of DNA being translated into mRNA under the help of enzyme RNA polymerase, this DNA segment and RNA polymerase (and part of the newly-formed mRNA) are first transformed into a different molecule, and transformed back when the process is done. In this process, the DNA segment and RNA polymerase basically both serve as catalysts. It is just very easy to neglect the transformation of DNA, because only a tiny segment of DNA is transformed and it does not even change positions after transforming back. For cell division, it is more obvious that DNA is consumed and regenerated.All in all, thanks again for the reviewer’s detailed comments and efforts.
Reviewer’s report 2
David Baum, Department of Botany, University of Wisconsin-Madison, USA; Wisconsin Institute for Discovery, University of Wisconsin-Madison, USA.
Reviewer comments 2.0:
This paper provides a formal treatment and definition of the property of self-sustenance, often articulated as a key property of life. Liu uses a mathematical abstraction of a chemical reaction network (CRN) in a CSTR and develops a 2-parted definition which basically states that a CRN is self-sustaining if reactions happen in the reactor (indicated by a steady state outflow that differs in composition from the inflow) and these reactions require seeding by chemicals that are not in the inflow (i.e., if the reactor is empty to start, the outflow converges to the inflow). The author provides some heuristics for evaluating whether a CRN has the potential to be self-sustaining and also lists a number of well-known networks that satisfy his criterion.There are several good aspects of this paper. I like the of idea of modeling CRNs in a CSTR and then identifying key signatures of self-sustenance, I agree that the need for a trigger chemical, what is more commonly called a “seed”, can be seen as a characteristic of self-sustaining systems, and I appreciate the point about self-sustenance entailing proto-heritability. That said, I see a number of major weaknesses in the paper. For example, the mathematical formalism is clunky and laborious to work through, the model invokes only unidirectional reactions when reversible reactions are the norm, and the framing in terms of existing “definitions” of self-sustenance seems contrived (neither Benner nor Luisi really “define” self-sustenance). The work also needs to compare/contrast self-sustenance with autocatalysis, the more common concept for evaluating the life-likeness of a CRN. I do not see clear value in the long list of example networks and the section of fire is pretty shallow.Overall, the core idea of diagnosing self-sustenance based on dynamic behavior in a CSTR is good, but the execution would be much improved.
Author’s response 2.0: Thanks the reviewer very much for the appreciation of this work, and the concerns/issues raised here. I will try to answer them one by one.
Please see Author’s reply 2.6 for the issue about uni-direction.
I framed this paper around self-sustainability is exactly because: NASA’s working definition of life (Benner 2010) explicitly said “life is a self-sustaining chemical system capable of undergoing Darwinian evolution”, but without mentioning what is “self-sustaining”; Luisi’s “autopoiesis” explicitly included the term “self-sustaining” but did not mention what is “self-sustaining” neither. It is not a straightforward and self-evident term. This issue also relates to the relation with “autocatalysis”. Please see Author’s reply 2.1 for more.
As for why I listed lots of examples and mentioned fire: The point of this paper is to (1) introduce the definition and the framework, (2) make the readers be aware of those self-sustaining systems which are not uncommon (this is why I introduced examples in various areas such as inorganic chemistry, biochemistry and metabolism), and (3) explain how the trigger molecule can be related to heredity. The third point is why I had a section to discuss fire, which I think is intriguing. As fire can grow, “replicate” and dynamically maintain its structure, then why should not it be considered as life? The classic answer to this question is that fire is a dissipative system but life should not be. This work provides a different angle: firstly, fires should be distinguished into non-self-sustaining fires and self-sustaining fires (the latter is more closely related to life); secondly, the trigger molecule for self-sustaining fire systems is easy to be produced (as the example mentioned, atom H for H2 combustion) but this is not the case for life (e.g., DNA molecules).
Reviewer comments 2.1:
The paper is framed around “self-sustenance”, but never clarifies how this relates to the much more common term (in chemistry if not astrobiology), “autocatalysis”. I believe that autocatalytic systems need not be self-sustaining (in your sense) because they can emerge without seeding. However, as far as I can tell, a self-sustaining CRN must be autocatalytic making self-sustenance a special case of autocatalysis that arises when one or more seed chemical is needed to trigger autocatalytic self-propagation. It would greatly strengthen the paper to explore this relation.
Author’s response 2.1: Thanks for the comments. Autocatalysis indeed appears quite often in the literature, but unfortunately it is often used with ambiguity. Let us first look at RAF theory (that the reviewer mentioned a few times) where autocatalysis is defined to be the case where every reaction is catalysed by some molecule produced by the system or present in the food set (ref 8 section 1 line 5, ref 18 section 1.1.1, ref 23 section 2.1). Note that in RAF theory, every reaction must be a catalytic reaction (while in our definition, there is no such requirement), i.e., A →B must be catalysed by another molecule C. Thus, a system is RAF requires that the catalysts are regenerated rather than the reactants. All the mathematical analysis is based on this formalisation, namely a chemical system is made of three rather than two parts: a set of molecules, a set of reactions, and a set of catalysts (e.g., ref 23 section 2.1). However, this requirement is too strong. Although most extant metabolic reactions are catalysed by enzymes, CRNs are generally not. Especially when we talk about the origin of life or the early stage of living systems, enzymes or catalysts should not be considered to be the default (they should emerge in the later stage of life). This is also the most criticised part of RAF theory. So in this sense, our definition is very different from the autocatalysis in RAF theory.
Nevertheless, I am guessing the reviewer concerned more about our definition with “the more general autocatalysis”, namely without the requirement of catalysed reactions. Note that besides the RAF theory (and its headstream: Kauffman’s autocatalytic set theory), there is no rigorous definition of “autocatalysis in the general sense”. The word “autocatalysis” was often used based on the intuition that reactants can also be produced by the system itself. That means, people can either (1) use “autocatalysis” in the sense of RAF theory (rigorous but requiring catalysts) or (2) use the word as a vague, intuitive and general term. If meaning (1) or (2) can be specified beforehand, the ambiguity will be gone, but unfortunately, it is often mixed-up and very confusing.
The reason I framed this paper around “self-sustaining” rather than “autocatalysis” is that: (1) I think “autocatalysis” is clear in principle (as meaning 1 and 2), as long as people can specify which they mean beforehand (but unfortunately not); and (2) the word “self-sustaining” appears in many important places even in NASA’s definition of life but it is not well-defined. There is one theory called Chemical Organisation Theory indeed defined “self-sustaining” rigorously, but I discussed the disadvantages in the Background section.
Now let us get back to the reviewer’s next comments “I believe that autocatalytic systems need not be self-sustaining...” If here “autocatalysis” refers to RAF theory, our definition of self-sustainability is definitely not a special case of autocatalysis, because no catalysed reaction is required. If here “autocatalysis” is used in a general sense, we could take it as a special case if we wish, but that should be OK, because the point is to define it rigorously, i.e., “autocatalysis” is vague and general, but “self-sustaining” is precise.
I added a paragraph in “On the definition” section to briefly explain how our definition relates to “autocatalysis”. The more details are referred here.
Reviewer comments 2.2:
After thinking about your model and “definition” can I suggest defining a self-sustaining set as a set of chemicals that, given a specified food influx, will constantly make more members of the set if and only if seeded by at least one member of the set. This makes much more sense to me. In particular, it would directly justify the trigger/seed criterion: a system cannot be seen to be SELF-sustaining if none of its parts are needed for it to emerge! This would imply two minor tweaks to your framing. 1: the formose self-sustaining CRN contains chemicals 2-4, but not chemical 1 (formaldehyde), which is the food needed for self-sustenance. 2: the zero initial condition should be redefined as the food-only initial condition - the is a reactor started with the designated food solution.
Author’s response 2.2: This suggested definition is in practical equivalent to our definition (except “a set of chemicals”, as it should be a set of reactions in my opinion, but that is minor). “Constantly make more members” and “requires seeds” are the natural consequences of our two conditions in the definition. It is indeed a very useful way to interpret the original definition. And I also totally agree with “a system cannot be seen to be SELF-sustaining if none of its parts are needed for it to emerge”. However, it seems strange if we impose the “trigger/seed” in the definition without explaining what a seed is beforehand. In the original definition on the other hand, the initial condition naturally serves as the seed and well-defined. But thanks very much for this comment and suggestion. I added a few sentences after the definition based on this suggestion, to help the reader interpret the definition.
Reviewer comments 2.3:
You talk about the state after a “transient” period. I think it would be better to say that the first criterion is about converging to a state (steady or fluctuating) that deviates from the influx but the second says that it will converge to a steady state that is the same as the influx.
Author’s response 2.3: Thanks very much for this. “Converging” is a nice word indeed. But “after a transient period” helps me keep the two nice equations in the definition which will be easily referred to later. An extra sentence is added below the definition based on this suggestion.
Reviewer comments 2.4:
The principles for determining if a network could be self-sustaining is a stronger part of the paper, which you might consider expanding. I wonder how many of these principles have already been discussed in the literature and how many mirror the formal analyses in RAF theory?
Author’s response 2.4: Thanks for the comments, interests and suggestion. The principles to determine if a CRN is self-sustaining definitely deserves further investigation (which is in the plan). There are indeed more principles discussed in the appendix. As mentioned, RAF theory explicitly requires catalysis, and its formal analysis also explicitly requires a catalyst set (ref 23 section 2.1). So the criteria I put forward are distinct from theirs. Nevertheless, we could see some similarities if we really force it. For example, the “self-driven” criterion in this paper requires that for each reaction, there is at least one reactant comes from the products of other reactions in the system. In RAF theory, the CATALYST for each reaction should either be produced by other reactions in the system or provided by the food set. If we force to exchange the word “reactant” and “catalysts”, they are quite similar, but normally we should not do that.
Reviewer comments 2.5:
(All minor issues below). You mention RAF theory and say: “self-sustaining was referred to that each molecule in a chemical network can be produced starting from the food source”. This sounds like a “constructively auto-catalytic and F-generated” set, which is a special case of a RAF set that does not require any seeding and would NOT, therefore, qualify as self-sustaining by your criterion.
Author’s response 2.5: In RAF theory, “self-sustaining” is used in a very vague and general sense indeed (please see ref 8 page 1 just under Introduction); while only “reflexively-autocatalytic” (either constructively or not) is precisely defined. Yes, a RAF set that does not require any seeding would not qualify as self-sustaining by my definition.
Reviewer comments 2.6:
You assume unidirectional reactions, but chemical reactions are generally reversible, even if the rate constants in the forward and reverse direction differ greatly. At the least, can you explain why you did this and how a deviation from this assumption would alter your conclusions?
Author’s response 2.6: For all the artificial chemistry examples I gave, I did only list one direction. But this is just for simplicity and for illustration purposes. The definition of self-sustainability will not be affected at all if we consider reversible reactions. This is also one advantage we can get from this definition because the only information we need to discern empirically whether a system is self-sustaining or not is the inflow and outflow, and what really happens inside the system (whether unidirectional, or reversible, or catalysed) can be analysed afterwards.
For the artificial chemistry model, namely those reactions written as \(\overline {1}+\overline {3} \rightarrow \overline {4}\), I borrowed from the previously published work (ref 35). In this model, every reaction is reversible indeed, but we only write down the spontaneous direction. When the forward and the backward reaction constants differ greatly, only the spontaneous direction matters. But in principle, in this model, there is no problem to include both directions: If solving it by ODE, just add the equations for the reverse direction; if solving it numerically by our program, both directions are automatically considered. I chose this model to illustrate the definition, just for the purpose of simplicity. We can choose any theoretical model or real chemistry, and the definition will work.
Reviewer comments 2.7:
The model feels overly cluttered with complex extra notation and often presents equations without putting them into words. I’ll be honest, but it took me very many hours to understand your approach. For example, it will help to provide a verbal descriptions of the criteria: “for a given inflow and starting condition, the steady state outflow differs from the inflow while it would have been the same as the inflow in the case that the reactor was initiated with just solvent.”
Author’s response 2.7: Thanks very much for this suggestion. I have added verbal explanations for some equations.
Reviewer comments 2.8:
If N is a count of molecules and you use ODEs, aren’t you implying that you can have a fractional number of molecules? Not a big deal, but worth stating the assumption that there are many molecules.
Author’s response 2.8: Yes, definitely we can have a fractional number of molecules as it is in the unit of mol. I choose N as the population rather than concentration is to keep the units of the reaction constant of the second-order reaction (synthesis reaction) and the first-order reaction (decomposition reaction) identical. It is easier to compare the effects of the reaction constants, although it does not matter for the definition.
Reviewer comments 2.9:You use the term “trigger” but I think “seed” is better. See for example Vasas et al. (2012) or Peng et al (2020, ArXiv)..
Author’s response 2.9: Thanks for this suggestion. I think “trigger” gives more “physical feelings” while “seed” gives some “vital feeling”. I do not want to impose any living-related feelings here, as self-sustainability does not imply life automatically. But I added “seed” here and there to make that link.
Reviewer comments 2.10:
Is “sequential” the best term? I understand the motivation: one can see steady changes over time in a system because there are sequences of reactions. But really the point is that these CRNs do not allow one to identify a food such that the system will only emerge if seeded. So maybe you don’t need a term, just say they are not-self-sustaining.
Author’s response 2.10: Thanks for the comment. I think it makes sense to distinguish “trivial” and “sequential” (refer to table 1), both of which should not be considered “self-sustaining” but have a bit different properties.
Reviewer comments 2.11:
In the “Hypothesis” section. You use the term “self-replicating.” Is that an error?
Author’s response 2.11: Thanks for pointing this out. It is not an error but a poor legacy from a previous paper. The term “self-replicating” was used in the previous paper (ref 35) to refer to a particular property of a CRN, i.e., at least one type of molecules in this CRN is produced more than consumed. I admit that it may not be a good term to use in that paper, but here it is just for a reference and used once.