An autocatalytic set is a collection of entities, each of which can be created catalytically by other entities within the set, such that as a whole, the set is able to catalyze its own production. In this way the set as a whole is said to be autocatalytic. Autocatalytic sets were originally and most concretely defined in terms of molecular entities, but have more recently been metaphorically extended to the study of systems in sociology, ecology, and economics.
Autocatalytic sets also have the ability to replicate themselves if they are split apart into two physically separated spaces. Computer models illustrate that split autocatalytic sets will reproduce all of the reactions of the original set in each half, much like cellular mitosis. In effect, using the principles of autocatalysis, a small metabolism can replicate itself with very little high level organization. This property is why autocatalysis is a contender as the foundational mechanism for complex evolution.
Prior to Watson and Crick, biologists considered autocatalytic sets the way metabolism functions in principle, i.e. one protein helps to synthesize another protein and so on. After the discovery of the double helix, the central dogma of molecular biology was formulated, which is that DNA is transcribed to RNA which is translated to protein. The molecular structure of DNA and RNA, as well as the metabolism that maintains their reproduction, are believed to be too complex to have arisen spontaneously in one step from a soup of chemistry.
Several models of the origin of life are based on the notion that life may have arisen through the development of an initial molecular autocatalytic set which evolved over time. Most of these models which have emerged from the studies of complex systems predict that life arose not from a molecule with any particular trait (such as self-replicating RNA) but from an autocatalytic set. The first empirical support came from Lincoln and Joyce, who obtained autocatalytic sets in which "two [RNA] enzymes catalyze each other’s synthesis from a total of four component substrates."[1] Furthermore, an evolutionary process that began with a population of these self-replicators yielded a population dominated by recombinant replicators.
Modern life has the traits of an autocatalytic set, since no particular molecule, nor any class of molecules, is able to replicate itself. There are several models based on autocatalytic sets, including those of Stuart Kauffman[2] and others.
Let R be the set of allowable reactions. A pair (M, R) is a reaction system (RS).
Let C be the set of molecule-reaction pairs specifying which molecules can catalyze which reactions:
C = {(m, r) | m ∈ M, r ∈ R}
Let F ⊆ M be a set of food (small numbers of molecules freely available from the environment) and R' ⊆ R be some subset of reactions. We define a closure of the food set relative to this subset of reactions ClR'(F) as the set of molecules that contains the food set plus all molecules that can be produced starting from the food set and using only reactions from this subset of reactions. Formally ClR'(F) is a minimal subset of M such that F ⊆ ClR'(F) and for each reaction r'(A, B) ⊆ R':
A ⊆ ClR'(F) ⇒ B ⊆ ClR'(F)
A reaction system (ClR'(F), R') is autocatalytic, if and only if for each reaction r'(A, B) ⊆ R':
there exists a molecule c ⊆ ClR'(F) such that (c, r') ⊆ C,
A ⊆ ClR'(F).
Example
Let M = {a, b, c, d, f, g} and F = {a, b}. Let the set R contain the following reactions:
a + b → c + d, catalyzed by g a + f → c + b, catalyzed by d c + b → g + a, catalyzed by d or f
From the F = {a, b} we can produce {c, d} and then from {c, b} we can produce {g, a} so the closure is equal to:
ClR'(F) = {a, b, c, d, g}
According to the definition the maximal autocatalytic subset R' will consist of two reactions:
a + b → c + d, catalyzed by g c + b → g + a, catalyzed by d
The reaction for (a + f) does not belong to R' because f does not belong to closure. Similarly the reaction for (c + b) in the autocatalytic set can only be catalyzed by d and not by f.
Probability that a random set is autocatalytic
Studies of the above model show that random RS can be autocatalytic with high probability under some assumptions. This comes from the fact that with a growing number of molecules, the number of possible reactions and catalysations grows even larger if the molecules grow in complexity, producing stochastically enough reactions and catalysations to make a part of the RS self-supported.[4] An autocatalytic set then extends very quickly with growing number of molecules for the same reason. These theoretical results make autocatalytic sets attractive for scientific explanation of the very early origin of life.
Formal limitations
Formally, it is difficult to treat molecules as anything but unstructured entities, since the set of possible reactions (and molecules) would become infinite. Therefore, a derivation of arbitrarily long polymers as needed to model DNA, RNA or proteins is not possible, yet. Studies of the RNA World suffer from the same problem.
Linguistic aspects
Contrary to the above definition, which applies to the field of Artificial chemistry, no agreed-upon notion of autocatalytic sets exists today.
While above, the notion of catalyst is secondary insofar that only the set as a whole has to catalyse its own production, it is primary in other definitions, giving the term "Autocatalytic Set" a different emphasis. There, every reaction (or function, transformation) has to be mediated by a catalyst. As a consequence, while mediating its respective reaction, every catalyst denotes its reaction, too, resulting in a self denoting system, which is interesting for two reasons. First, real metabolism is structured in this manner. Second, self denoting systems can be considered as an intermediate step towards self describing systems.
From both a structural and a natural historical point of view, one can identify the ACS as seized in the formal definition the more original concept, while in the second, the reflection of the system in itself is already brought to an explicit presentation, since catalysts represent the reaction induced by them. In ACS literature, both concept are present, but differently emphasised.
To complete the classification from the other side, generalised self reproducing systems move beyond self-denotation. There, no unstructured entities carry the transformations anymore, but structured, described ones. Formally, a generalised self reproducing system consists of two function, u and c, together with their descriptions Desc(u) and Desc(c) along following definition:
u : Desc(X) -> X c : Desc(X) -> Desc(X)
where the function 'u' is the "universal" constructor, that constructs everything in its domain from appropriate descriptions, while 'c' is a copy function for any description. Practically, 'u' and 'c' can fall apart into many subfunctions or catalysts.
Note that the (trivial) copy function 'c' is necessary because though the universal constructor 'u' would be able to construct any description, too, the description it would base on, would in general be longer than the result, rendering full self replication impossible.
This last concept can be attributed to von Neumann's work on self reproducing automata, where he holds a self description necessary for any nontrivial (generalised) self reproducing system to avoid interferences. Von Neumann planned to design such a system for a model chemistry, too.
Non-autonomous autocatalytic sets
Virtually all articles on autocatalytic sets leave open whether the sets are to be considered autonomous or not. Often, autonomy of the sets is silently assumed.
Likely, the above context has a strong emphasis on autonomous self replication and early origin of life. But the concept of autocatalytic sets is really more general and in practical use in various technical areas, e.g. where self-sustaining tool chains are handled. Clearly, such sets are not autonomous and are objects of human agency.
Examples of practical importance of non-autonomous autocatalytic sets can be found e.g. in the field of compiler construction and in operating systems, where the self-referential nature of the respective constructions is explicitly discussed, very often as bootstrapping.
Comparison with other theories of life
Autocatalytic sets constitute just one of several current theories of life, including the chemoton[5] of Tibor Gánti, the hypercycle of Manfred Eigen and Peter Schuster,[6][7][8] the (M,R) systems[9][10] of Robert Rosen, and the autopoiesis (or self-building)[11] of Humberto Maturana and Francisco Varela. All of these (including autocatalytic sets) found their original inspiration in Erwin Schrödinger's book What is Life?[12] but at first they appear to have little in common with one another, largely because the authors did not communicate with one another, and none of them made any reference in their principal publications to any of the other theories. Nonetheless, there are more similarities than may be obvious at first sight, for example between Gánti and Rosen.[13] Until recently[14][15][16] there have been almost no attempts to compare the different theories and discuss them together.
Last Universal Common Ancestor (LUCA)
Some authors equate models of the origin of life with LUCA, the Last Universal Common Ancestor of all extant life.[17] This is a serious error resulting from failure to recognize that L refers to the last common ancestor, not to the first ancestor, which is much older: a large amount of evolution occurred before the appearance of LUCA.[18]
Gill and Forterre expressed the essential point as follows:[19]
LUCA should not be confused with the first cell, but was the product of a long period of evolution. Being the "last" means that LUCA was preceded by a long succession of older "ancestors."
Related Research Articles
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The RNA world is a hypothetical stage in the evolutionary history of life on Earth, in which self-replicating RNA molecules proliferated before the evolution of DNA and proteins. The term also refers to the hypothesis that posits the existence of this stage.
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The term autopoiesis refers to a system capable of producing and maintaining itself by creating its own parts. The term was introduced in the 1972 publication Autopoiesis and Cognition: The Realization of the Living by Chilean biologists Humberto Maturana and Francisco Varela to define the self-maintaining chemistry of living cells.
Robert Rosen was an American theoretical biologist and Professor of Biophysics at Dalhousie University.
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The term chemoton refers to an abstract model for the fundamental unit of life introduced by Hungarian theoretical biologist Tibor Gánti. Gánti conceived the basic idea in 1952 and formulated the concept in 1971 in his book The Principles of Life. He suggested that the chemoton was the original ancestor of all organisms.
In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a cyclic, autocatalytic manner. It was introduced in an ordinary differential equation (ODE) form by the Nobel Prize in Chemistry winner Manfred Eigen in 1971 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth. As such, it explained how life on Earth could have begun using only relatively short genetic sequences, which in theory were too short to store all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small selective advantage, rapid evolvability, increased information capacity, and selection against parasitic branches.
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Woese's dogma is a principle of evolutionary biology first put forth by biophysicist Carl Woese in 1977. It states that the evolution of ribosomal RNA was a necessary precursor to the evolution of modern life forms. This led to the advancement of the phylogenetic tree of life consisting of three domains rather than the previously accepted two. While the existence of Eukarya and Prokarya were already accepted, Woese was responsible for the distinction between Bacteria and Archaea. Despite initial criticism and controversy surrounding his claims, Woese's three domain system, based on his work regarding the role of rRNA in the evolution of modern life, has become widely accepted.
Formamide-based prebiotic chemistry is a reconstruction of the beginnings of life on Earth, assuming that formamide could accumulate in sufficiently high amounts to serve as the building block and reaction medium for the synthesis of the first biogenic molecules.
A scenario is a set of related concepts pertinent to the origin of life (abiogenesis), such as the iron-sulfur world. Many alternative abiogenesis scenarios have been proposed by scientists in a variety of fields from the 1950s onwards in an attempt to explain how the complex mechanisms of life could have come into existence. These include hypothesized ancient environments that might have been favourable for the origin of life, and possible biochemical mechanisms.
A proto-metabolism is a series of linked chemical reactions in a prebiotic environment that preceded and eventually turned into modern metabolism. Combining ongoing research in astrobiology and prebiotic chemistry, work in this area focuses on reconstructing the connections between potential metabolic processes that may have occurred in early Earth conditions. Proto-metabolism is believed to be simpler than modern metabolism and the Last Universal Common Ancestor (LUCA), as simple organic molecules likely gave rise to more complex metabolic networks. Prebiotic chemists have demonstrated abiotic generation of many simple organic molecules including amino acids, fatty acids, simple sugars, and nucleobases. There are multiple scenarios bridging prebiotic chemistry to early metabolic networks that occurred before the origins of life, also known as abiogenesis. In addition, there are hypotheses made on the evolution of biochemical pathways including the metabolism-first hypothesis, which theorizes how reaction networks dissipate free energy from which genetic molecules and proto-cell membranes later emerge. To determine the composition of key early metabolic networks, scientists have also used top-down approaches to study LUCA and modern metabolism.
↑ Kauffman, Stuart A. (2008) Reinventing the Sacred: A New View of Science, Reason, and Religion. [Basic Books], ISBN0-465-00300-1, chapter 5, especially pp. 59–71
↑ Gánti, Tibor (2003). Eörs Száthmary; James Griesemer (eds.). The Principles of Life. Oxford University Press. ISBN9780198507260.
↑ Eigen, M; Schuster, P (1977). "The hypercycle: a principle of natural self-organization. A: emergence of the hypercycle". Naturwissenschaften. 64 (11): 541–565. doi:10.1007/bf00450633. PMID593400. S2CID42131267.
↑ Eigen, M; Schuster, P. "The hypercycle: a principle of natural self-organization. B: the abstract hypercycle". Naturwissenschaften. 65 (1): 7–41. doi:10.1007/bf00420631. S2CID1812273.
↑ Eigen, M; Schuster, P. "The hypercycle: a principle of natural self-organization. C: the realistic hypercycle". Naturwissenschaften. 65 (7): 41–369. doi:10.1007/bf00420631. S2CID1812273.
↑ Rosen, R. (1958). "The representation of biological systems from the standpoint of the theory of categories". Bull. Math. Biophys. 20 (4): 317–341. doi:10.1007/BF02477890.
↑ Rosen, R. (1991). Life Itself: a comprehensive inquiry into the nature, origin, and fabrication of life. New York: Columbia University Press.
↑ Maturana, H. R.; Varela, F. (1980). Autopoiesis and cognition: the realisation of the living. Dordrecht: D. Reidel Publishing Company.
↑ Schrödinger, Erwin (1944). What is Life?. Cambridge University Press.
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