It is clear that the notion of an autocatalytic set is closely related to the first element of the definition of autopoiesis. Both involve the idea of a ``closed'' reaction network which may therefore be able to dynamically sustain itself indefinitely--subject to the availability of some basic ``substrate'' materials and the overall reaction kinetics etc. The definition of autopoiesis is, admittedly, somewhat ambiguous about the role of catalytic activity as such; but the computer model certainly explicitly involves at least one catalysed reaction, without which the putative reaction network could not be closed. Conversely, while the reaction networks posited for collective autocatalysis seem to be technically limited to include only catalysed reactions, there doesn't seem to be any particular difficulty about allowing some uncatalysed reactions to participate also; if anything, this possibility should slightly improve the prospects for the spontaneous emergence of such sets.
In trying to isolate more precisely what it is that both the notions of autopoiesis and collectively autocatalytic sets seem to share, I suggest it may be useful to think about the following more concrete scenario. Suppose we have a flow reactor, with a flow of some specified ``substrate'' or ``food set'' materials through it. There may be some reactions which occur spontaneously, at significant rates, among these, but we essentially discount such reactions (or assume they run to equilibrium etc.). Now suppose it is the case that this reactor can be seeded with some set of further molecular species, such that a reaction network is then established which sustains the presence of these same molecular species under flow conditions. This new network may involve some uncatalysed reactions (which did not previously occur because the relevant reactants did not arise); but it must necessarily involve at least one reaction which must be catalysed, and such that the catalyst species itself gets produced (directly or indirectly) only if this catalysed reaction takes place.
Let me call any reaction network with this property ``collectively self-sustaining''.
I suggest that this notion is at once both somewhat stronger and somewhat weaker that Kauffman's ``collectively autocatalytic set''. It is weaker because it allows the inclusion of some uncatalysed reactions. If anything, this relaxation should make it easier for such networks to arise, and would thus strengthen Kauffman's claims for the spontaneous emergence of such networks. However, it is stronger than Kauffman's notion in that it explicitly asks for the reaction network to be self-sustaining in practice--under some specific reaction conditions, and associated reaction kinetics; the collectively autocatalytic property, on the other hand, is a purely topological characteristic of a reaction network graph--indicating only the possibility of a self-sustaining network under some otherwise unspecified conditions. Of course, as a practical matter in the origin of life, only reaction networks which are actually self-sustaining under some reasonably feasible conditions can play any significant role.
The relationship between the idea of a self-sustaining network and autopoiesis is somewhat more obscure. Certainly, autopoiesis shares the requirement for actual (as opposed to ``potential'') self-maintenance, and would seem to have a similar requirement for some sort of (catalytic?) ``closure''. Yet, it also seems that autopoiesis does not promise a reaction network that would sustain itself under ``open'' flow conditions. In particular, as already mentioned, in the simplified computer model the molecular species termed ``catalyst'' does not get produced by any reaction in the network. Under flow conditions either catalyst would flow out without replacement and the reaction network would break down, or catalyst would have to be continuously supplied as a component of the ``food set''; but in the latter case the ``autopoietic'' reaction network would be immediately and unconditionally instantiated, rather than being contingent on seeding. On the face of it this suggests that autopoiesis is a significantly weaker notion than that of self-sustaining network, even to the point of being too weak to be of any interest.
But of course, autopoiesis was not intended to deal with an ``open'' flow reaction condition; instead it is concerned with very special flow conditions. Special firstly in that they can be (or must be?) selective--in the sense of something like a semi-permeable membrane; but special secondly in the requirement that the constraints on flow should themselves be a result or consequence of the autopoietic reaction network. It is this requirement for the reaction network to exhibit these two different kinds of closure--closure of the reaction network together with spatial closure--that critically demarcates autopoiesis per se, and makes it a significantly stronger and more interesting idea than a self-sustaining reaction network alone.
Maturana and Varela themselves have been clear from their earliest descriptions of autopoiesis that this spatial or topological separation is a critical distinction between their concept and autocatalysis per se:
Autocatalytic processes do not constitute autopoietic systems because among other things, they do not determine their topology. Their topology is determined by a container that is part of the specification of the system, but which is independent of the operation of the autocatalysis. Processes of this or similar kind are abundant in the physical space.
Maturana & Varela
(1973, p. 94, emphasis added)
I suggest that we might interpret Kauffman's work on the emergence of collective autocatalysis as, in significant part, a more formal and rigorous demonstration of the rather bold assertion at the end of this quotation. It should be noted that Kauffman is certainly well aware that spatial enclosure is a significant issue in this area. For example, he stipulates explicitly that, for the reactions of a putatively autocatalytic set to occur ``effectively'' then the reactants ``must be confined to a sufficiently small volume'' (Kauffman, 1993, p. 298). However, while he goes on to consider some candidate mechanisms for providing such confinement (e.g., coascervates, proteinoid microspheres, liposomes) it is not clear to me whether he attaches any particular importance to the idea that these containment devices should themselves be produced and maintained as products of the contained reaction network--which seems to be the decisive extra constraint involved in autopoiesis.
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