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210:) but from an autocatalytic set. The first empirical support came from Lincoln and Joyce, who obtained autocatalytic sets in which "two enzymes catalyze each other’s synthesis from a total of four component substrates." Furthermore, an evolutionary process that began with a population of these self-replicators yielded a population dominated by
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stochastically enough reactions and catalysations to make a part of the RS self-supported. 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.
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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,
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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
431:
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
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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
473:
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
153:
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
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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.
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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.
158:. 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.
193:
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.
418:
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,
217:
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
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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.
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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
201:
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
446:, 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.
301:(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 Cl
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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."
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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.
518:
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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.
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first sight, for example between Gánti and Rosen. Until recently there have been almost no attempts to compare the different theories and discuss them together.
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reaction (or function, transformation) has to be mediated by a catalyst. As a consequence, while mediating its respective reaction, every catalyst
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58:
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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
526:
803:
Eigen, M; Schuster, P (1977). "The hypercycle: a principle of natural self-organization. A: emergence of the hypercycle".
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293:(small numbers of molecules freely available from the environment) and R' ⊆ R be some subset of reactions. We define a
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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:
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Eigen, M; Schuster, P. "The hypercycle: a principle of natural self-organization. C: the realistic hypercycle".
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Eigen, M; Schuster, P. "The hypercycle: a principle of natural self-organization. B: the abstract hypercycle".
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Mossel E, Steel M. (2005). "Random biochemical networks and the probability of self-sustaining autocatalysis".
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43:
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Rosen, R. (1958). "The representation of biological systems from the standpoint of the theory of categories".
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545:. All of these (including autocatalytic sets) found their original inspiration in Erwin Schrödinger's book
485:, where the self-referential nature of the respective constructions is explicitly discussed, very often as
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Examples of practical importance of non-autonomous autocatalytic sets can be found e.g. in the field of
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Cornish-Bowden, A. (2015). "Tibor Gánti and Robert Rosen: contrasting approaches to the same problem".
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a + b → c + d, catalyzed by g a + f → c + b, catalyzed by d c + b → g + a, catalyzed by d or f
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ancestor, which is much older: a large amount of evolution occurred before the appearance of LUCA.
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1123:"Contrasting theories of life: historical context, current theories. In search of an ideal theory"
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32:
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predict that life arose not from a molecule with any particular trait (such as self-replicating
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According to the definition the maximal autocatalytic subset R' will consist of two reactions:
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1180:"The Way forward for the Origin of Life: Prions and Prion-Like Molecules First Hypothesis"
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Igamberdiev, A.U. (2014). "Time rescaling and pattern formation in biological evolution".
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Autocatalytic sets constitute just one of several current theories of life, including the
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induced by them. In ACS literature, both concept are present, but differently emphasised.
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Let M = {a, b, c, d, f, g} and F = {a, b}. Let the set R contain the following reactions:
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of all extant life. This is a serious error resulting from failure to recognize that
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Life Itself: a comprehensive inquiry into the nature, origin, and fabrication of life
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together with their descriptions Desc(u) and Desc(c) along following definition:
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138:, but have more recently been metaphorically extended to the study of systems in
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134:. Autocatalytic sets were originally and most concretely defined in terms of
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as needed to model DNA, RNA or proteins is not possible, yet. Studies of the
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Let C be the set of molecule-reaction pairs specifying which molecules can
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helps to synthesize another protein and so on. After the discovery of the
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Jheeta, S.; Chatzitheodoridis, E.; Devine, Kevin; Block, J. (2021).
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Reinventing the Sacred: A New View of
Science, Reason, and Religion
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1282:"Origin of life: LUCA and extracellular membrane vesicles (EMVs)"
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Some authors equate models of the origin of life with LUCA, the
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Contrary to the above definition, which applies to the field of
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a + b → c + d, catalyzed by g c + b → g + a, catalyzed by d
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Letelier, J C; Cárdenas, M L; Cornish-Bowden, A (2011). "From
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can be roughly defined as pairs r = (A, B) of subsets from M:
1237:
Cornish-Bowden, A; Cárdenas, M L (2017). "Life before LUCA".
778:
Gánti, Tibor (2003). Eörs Száthmary; James
Griesemer (eds.).
694:"Autocatalytic Sets: From the Origin of Life to the Economy"
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Gill and
Forterre expressed the essential point as follows:
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u : Desc(X) -> X c : Desc(X) -> Desc(X)
415:, no agreed-upon notion of autocatalytic sets exists today.
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Let R be the set of allowable reactions. A pair (M, R) is a
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is a collection of entities, each of which can be created
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to metabolic closure: steps towards understanding life".
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Autopoiesis and cognition: the realisation of the living
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of the food set relative to this subset of reactions Cl
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169:, biologists considered autocatalytic sets the way
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331:, if and only if for each reaction r'(A, B) ⊆ R':
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381:Probability that a random set is autocatalytic
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616:"Self-sustained replication of an RNA enzyme"
305:(F) is a minimal subset of M such that F ⊆ Cl
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474:autonomous and are objects of human agency.
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962:. Dordrecht: D. Reidel Publishing Company.
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1121:Cornish-Bowden, A; Cárdenas, M L (2020).
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309:(F) and for each reaction r'(A, B) ⊆ R':
106:Learn how and when to remove this message
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453:This last concept can be attributed to
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947:. New York: Columbia University Press.
614:Lincoln TA, Joyce GF (February 2009).
493:Comparison with other theories of life
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554:Last Universal Common Ancestor (LUCA)
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958:Maturana, H. R.; Varela, F. (1980).
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44:adding citations to reliable sources
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183:central dogma of molecular biology
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682:, chapter 5, especially pp. 59–71
466:Non-autonomous autocatalytic sets
173:functions in principle, i.e. one
1148:10.1016/j.biosystems.2019.104063
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442:where the function 'u' is the
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335:there exists a molecule c ⊆ Cl
185:was formulated, which is that
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977:. Cambridge University Press.
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585:common ancestor, not to the
286:C = {(m, r) | m ∈ M, r ∈ R}
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973:Schrödinger, Erwin (1944).
782:. Oxford University Press.
670:Kauffman, Stuart A. (2008)
10:
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1010:10.1016/j.jtbi.2015.05.015
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339:(F) such that (c, r') ⊆ C,
1307:10.1017/S1473550415000282
711:10.1525/bio.2013.63.11.6
640:10.1126/science.1167856
444:"universal" constructor
780:The Principles of Life
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368:(F) = {a, b, c, d, g}
289:Let F ⊆ M be a set of
197:Several models of the
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479:compiler construction
323:A reaction system (Cl
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413:Artificial chemistry
40:improve this article
1298:2016IJAsB..15....7G
1251:2017JThBi.434...68C
1196:2021Life...11..872J
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918:Bull. Math. Biophys
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805:Naturwissenschaften
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55:"Autocatalytic set"
943:Rosen, R. (1991).
930:10.1007/BF02477890
895:10.1007/bf00420631
860:10.1007/bf00420631
817:10.1007/bf00450633
692:Hordijk W (2013).
407:Linguistic aspects
390:Formal limitations
241:chemical reactions
189:is transcribed to
136:molecular entities
1286:Int. J. Astrobiol
626:(5918): 1229–32.
539:Humberto Maturana
483:operating systems
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96:January 2011
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38:Please help
33:verification
30:
1292:(1): 7–15.
854:(1): 7–41.
531:autopoiesis
503:Tibor Gánti
457:'s work on
455:von Neumann
212:recombinant
1330:Categories
1190:(9): 872.
1133:: 104063.
1127:BioSystems
1080:BioSystems
698:BioScience
601:References
529:, and the
507:hypercycle
231:Definition
171:metabolism
128:as a whole
66:newspapers
1245:: 68–74.
1165:207946798
1086:: 19–26.
743:CiteSeerX
567:niversal
523:) systems
401:RNA World
266:+ ... + b
254:+ ... + a
237:molecules
161:Prior to
148:economics
140:sociology
1316:44428292
1267:28536033
1224:34575021
1157:31715221
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1065:21763318
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996:: 6–10.
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765:15652142
658:19131595
499:chemoton
397:polymers
281:catalyze
1294:Bibcode
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1215:8467930
1192:Bibcode
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998:Bibcode
903:1812273
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735:Bibcode
649:2652413
628:Bibcode
620:Science
575:ncestor
517:, the
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