Hypercycle (chemistry)

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pointed out by the authors, such packages are—contrary to hypercycles—vulnerable to deleterious mutations as well as a fluctuation abyss, resulting in packages that lack one of the essential RNA molecules. Eigen and colleagues 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 Eörs Szathmáry and László Demeter reconsidered whether packing hypercycles into compartments is a necessary intermediate stage of the evolution. They invented a stochastic corrector model 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, compartmentalization is sufficient to integrate information dispersed in competitive replicators without the need for hypercycle organization. Moreover, it was shown 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.

2170:. After that, the whole individualized and compartmentalized hypercycle can behave like a simple self-replicating entity. Compartmentalization provides some advantages for a system that has already established a linkage between units. Without compartments, genome integration would boost competition by limiting space and resources. Moreover, adaptive evolution requires the package of transmissible information for advantageous mutations in order not to aid less-efficient copies of the gene. The first advantage is that it maintains a high local concentration of molecules, which helps to locally increase the rate of synthesis. Secondly, it keeps the effect of mutations local, while at the same time affecting the whole compartment. This favours preservation of beneficial mutations, because it prevents them from spreading away. At the same time, harmful mutations cannot pollute the entire system if they are enclosed by the membrane. Instead, only the contaminated compartment is destroyed, without affecting other compartments. In that way, compartmentalization allows for selection for genotypic mutations. Thirdly, membranes protect against environmental factors because they constitute a barrier for high-weight molecules or 1825:

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 possible that a 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.

2199:. Nevertheless, it was able to catalyse 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 2013. While it has an ability to catalyse polymerization of longer sequences, even of its own length, it cannot replicate itself due to a lack of sequence generality and its inability to transverse secondary structures of long RNA templates. However, it was recently shown that those limitations could in principle be overcome by the assembly of active polymerase ribozymes from several short RNA strands. In 2014, a cross-chiral RNA polymerase ribozyme was demonstrated. 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 315:. Moreover, it was shown that the genome size of any organism is roughly equal to the inverse of mutation rate per site per replication. Therefore, a high mutation rate imposes a serious limitation on the length of the genome. To overcome this problem, a more specialized replication machinery that is able to copy genetic information with higher fidelity is needed. Manfred Eigen suggested that proteins are necessary to accomplish this task. However, to encode a system as complex as a protein, longer nucleotide sequences are needed, which increases the probability of a mutation even more and requires even more complex replication machinery. John Maynard Smith and Eörs Szathmáry named this vicious circle 2325:

increases, meaning that selection tends toward decreasing the amount of information stored in the hypercycle. Moreover, there is also a problem with adding new information into the system. In order to be preserved, the new information has to appear near to the core of the spiral wave. However, this would make the system vulnerable to parasites, and, as a consequence, the hypercycle would not be stable. Therefore, stable spiral waves are characterized by once-for-ever selection, which creates the restrictions that, on the one hand, once the information is added to the system, it cannot be easily abandoned; and on the other hand, new information cannot be added.

4803: 4730: 4529: 4350: 3841: 3329: 2268:, while other selfish genotypes were only able to self-assemble. In separation, the selfish subsystem grew faster than the cooperative one. After mixing selfish ribozymes with cooperative ones, the emergence of cooperative behaviour in a merged population was observed, outperforming the self-assembling subsystems. Moreover, the selfish ribozymes were integrated into the network of reactions, supporting its growth. These results were also explained analytically by the ODE model and its analysis. They differ substantially from results obtained in 2447: 2272:. According to evolutionary dynamics theory, selfish molecules should dominate the system even if the growth rate of the selfish subsystem in isolation is lower than the growth rate of the cooperative system. Moreover, Vaidya et al. proved that, when fragmented into more pieces, ribozymes that are capable of self-assembly can not only still form catalytic cycles but, indeed, favour them. Results obtained from experiments by Vaidya et al. gave a glimpse on how inefficient prebiotic polymerases, capable of synthesizing only short 1881:, and the selection based on it is very sharp. After one hypercycle wins the competition, it is very unlikely that another one could take its place, even if the new hypercycle would be more efficient than the winner. Usually, even large fluctuations in the numbers of internal species cannot weaken the hypercycle enough to destroy it. In the case of a hypercycle, we can speak of one-for-ever selection, which is responsible for the existence of a unique translation code and a particular 1807:

code were proposed by Crick and his collaborators. These were models stating that the first codons were constructed according to either an RRY or an RNY scheme, in which 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 utilization of ribozymes without the need for a hypercycle with translation, and there are many more theories about the

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only proved to be stable against moderately strong parasites, if the parasites' mutation rate is not too high, but the emergent pattern itself was generated as a result of interactions between parasites and replicase species. The same technique was used to model systems that include formation of complexes. Finally, hypercycle simulation extending to three dimensions showed the emergence of the three-dimensional analogue of a spiral wave, namely, the scroll wave.

20: 1955:. In theory, it is possible to incorporate into the hypercycle mutations that do not satisfy the second condition. They would form parasitic branches that use the system for their own replication but do not contribute to the system as a whole. However, it was noticed that such mutants do not pose a threat to the hypercycle, because other constituents of the hypercycle grow nonlinearly, which prevents the parasitic branches from growing. 275: 365: 2316:, and later Nobuto Takeuchi, studied the replicator equations with the use of partial differential equations and cellular automata models, methods that already proved to be successful in other applications. They demonstrated that spatial self-structuring of the system completely solves the problem of global extinction for large systems and, partially, the problem of parasites. The latter was also analysed by 2276:, could be sufficient at the pre-life stage to spark off life. This could happen because coupling the synthesis of short RNA fragments by the first ribozymal polymerases to a system capable of self-assembly not only enables building longer sequences but also allows exploiting the fitness space more efficiently with the use of the 1592: 1873:, but with the total concentration of all chains remaining constant. In this way, the system consisting of all chains can be expressed as a single, integrated entity. During the formation of hypercycles, several of them could be present in comparable concentrations, but very soon, a selection of the hypercycle with the highest 2259:

group I intron ribozyme that, when fragmented, has an ability to self-assemble by catalysing recombination reactions in an autocatalytic manner. They mutated the three-nucleotide-long sequences responsible for recognition of target sequences on the opposite end of the ribozyme (namely, Internal Guide

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Forty years after the publication of Manfred Eigen's primary work dedicated to hypercycles, Nilesh Vaidya and colleagues showed experimentally that ribozymes can form catalytic cycles and networks capable of expanding their sizes by incorporating new members. However, this is not a demonstration of a

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ribozyme 82 nucleotides long was sufficient to perform an acyltransfer reaction. Altogether, the results concerning the RNA ligase's catalytic domain and the acyltransferase ribozyme are in agreement with the estimated upper limit of 100 nucleotides set by the error threshold problem. However, it was

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and coworkers 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 that contain a special recognition motif. However, as

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formulations of Eigen's problem. Despite many advantages that the concept of hypercycles presents, there were also some problems regarding the traditional model formulation using ODEs: a vulnerability to parasites and a limited size of stable hypercycles. In 2012, the first experimental proof for the

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Another model based on cellular automata, taking into account a simpler replicating network of continuously mutating parasites and their interactions with one replicase species, was proposed by Takeuchi and Hogeweg and exhibited an emergent travelling wave pattern. Surprisingly, travelling waves not

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Several researchers proposed a solution to these problems by introducing space into the initial model either explicitly or in the form of a spatial segregation within compartments. Bresch et al. proposed a package model as a solution for the parasite problem. Later on, Szathmáry and Demeter proposed

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and Irina Gladkih showed that an unconditional coexistence can be obtained even in the case of a non-enzymatic template replication that leads to a subexponential or a parabolic growth. This could be observed during the stages preceding a catalytic replication that are necessary for the formation of

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process. Another experiment performed by Hannes 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

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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

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According to the definition of a hypercycle, it is a nonlinear, dynamic system, and, in the simplest case, it can be assumed that it grows at a rate determined by a system of quadratic differential equations. Then, the competition between evolving hypercycles can be modelled using the differential

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might have been crucial to inventing translation. An RNA ligase, in turn, could link various components of quasispecies into one chain, beginning the process of a genome integration. An RNA with a synthase or a synthetase activity could be critical for building compartments and providing building

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Despite the above-mentioned advantages, there are also potential problems connected to compartmentalized hypercycles. These problems include difficulty in the transport of ingredients in and out, synchronizing the synthesis of new copies of the hypercycle constituents, and division of the growing

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Eigen made several assumptions about conditions that led to the formation of the first hypercycles. Some of them were the consequence of the lack of knowledge about ribozymes, which were discovered a few years after the introduction of the hypercycle concept and negated Eigen's assumptions in the

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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

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pattern, which was observed during computational simulations performed on cellular automata, proved to be stable and able to survive the invasion of parasites if they appear at some distance from the wave core. Unfortunately, in this case, rotation decelerates as the number of hypercycle members

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actions. This kind of closed network consisting of self-replicating entities connected by a catalytic positive-feedback loop was named an elementary hypercycle. Such a concept, apart from an increased information capacity, has another advantage. Linking self-replication with mutual catalysis can

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reaction and makes it the smallest ribozyme that has been discovered. It supports a peptidyl-RNA synthesis that could be a precursor for the contemporary process of linking amino acids to tRNA molecules. An RNA ligase's catalytic domain, consisting of 93 nucleotides, proved to be sufficient to

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Another concept devised by Eigen and Schuster was a model in which each RNA template's replication was catalysed by its own translational product; at the same time, this RNA template performed a transport function for one amino acid type. Existence of more than one such RNA template could make

103:. In the hypercycle, all molecules are linked such that each of them catalyses the creation of its successor, with the last molecule catalysing the first one. In such a manner, the cycle reinforces itself. Furthermore, each molecule is additionally a subject for self-replication. The resultant 2194:

At the time of the hypercycle theory formulation, ribozymes were not known. After the breakthrough of discovering RNA's catalytic properties in 1982, it was realized that RNA had the ability to integrate protein and nucleotide-chain properties into one entity. Ribozymes potentially serving as

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Nevertheless, in both alternative concepts, the system will not survive due to the internal competition among its constituents. Even if none of the constituents of such a system is selectively favoured, which potentially allows coexistence of all of the coupled molecules, they are not able to

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coupled to a cycle that do not provide any advantage to the reproduction of a cycle, which, in turn, makes them useless and decreases the selective value of the system. Secondly, it reinforces the self-organization of molecules into the hypercycle, allowing the system to evolve without losing

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From the mathematical point of view, it is possible to find conditions required for cooperation of several hypercycles. However, in reality, the cooperation of hypercycles would be extremely difficult, because it requires the existence of a complicated multi-step biochemical mechanism or an

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raised an objection that the catalytic support for the replication given to other molecules is altruistic. Therefore, it cannot be selected and maintained in a system. He also underlined hypercycle vulnerability to parasites, as they are favoured by selection. Later on, Josef Hofbauer and

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It was suggested that the problem with building and maintaining larger, more complex, and more accurately replicated molecules can be circumvented if several information carriers, each of them storing a small piece of information, are connected such that they only control their own

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and break the positive feedback loop that sustains the hypercycle. The extinction of the hypercycle then follows. It was also emphasized that a hypercycle size of up to four is too small to maintain the amount of information sufficient to cross the information threshold.

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a stochastic corrector machine model. Both compartmentalized systems proved to be robust against parasites. However, package models do not solve the error threshold problem that originally motivated the idea of the hypercycle. A few years later, Maarten Boerlijst and

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During their research, Eigen and Schuster also considered types of protein and nucleotide coupling other than hypercycles. One such alternative was a model with one replicase that performed polymerase functionality and that was a translational product of one of the

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Analysis of potential molecules that could form the first hypercycles in nature prompted the idea of coupling an information carrier function with enzymatic properties. At the time of the hypercycle theory formulation, enzymatic properties were attributed only to

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hypothesized that even if the putative first RNA-dependent RNA-polymerases are estimated to be longer—the smallest reported up-to-date RNA-dependent polymerase ribozyme is 165 nucleotides long—they did not have to arise in one step. It is more plausible that

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Evolution of a hypercycle ensues from the creation of new components by the mutation of its internal species. Mutations can be incorporated into the hypercycle, enlarging it if, and only if, two requirements are satisfied. First, a new information carrier

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templates and catalysers of replication can be considered components of quasispecies that can self-organize into a hypercycle without the need to invent a translation process. In 2001, a partial RNA polymerase ribozyme was designed via

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and, therefore, may provide greater sequence generality. Various other experiments have shown that, besides bearing polymerase properties, ribozymes could have developed other kinds of evolutionarily useful catalytic activity such as

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Kruger, Kelly; Grabowski, Paula J.; Zaug, Arthur J.; Sands, Julie; Gottschling, Daniel E.; Cech, Thomas R. (1982). "Self-splicing RNA: Autoexcision and autocyclization of the ribosomal RNA intervening sequence of tetrahymena".

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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

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could not exceed a certain threshold length. This problem is known as the error threshold problem. It arises because replication is an imperfect process, and during each replication event, there is a risk of incorporating

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and prevent the creation of larger and fitter macromolecules. Moreover, it has been shown that hypercycles could originate naturally and that incorporating new molecules can extend them. Hypercycles are also subject to

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indicated that in reality, a hypercycle can maintain only fewer than five members. In agreement with Eigen and Schuster's principal analysis, they argued that systems with five or more species exhibit limited and

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is a dilution flux that guarantees that the total concentration is constant. According to the above model, in the initial phase, when several hypercycles exist, the selection of the hypercycle with the largest

83:. 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 4955:

Szabó, Péter; Scheuring, István; Czárán, Tamás; Szathmáry, Eörs (21 November 2002). "In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity".

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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.

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coevolve and optimize their properties. In consequence, the system loses its internal stability and cannot live on. The reason for inability to survive is the lack of mutual control of constituent

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Hypercycle theory proposed that hypercycles are not the final state of organization, and further development of more complicated systems is possible by enveloping the hypercycle in some kind of

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recognized by this replicase. The other RNA matrices, or just one of their strands, provided translational products which had specific anticodons and were responsible for unique assignment and

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Vaidya, Nilesh; Manapat, Michael L.; Chen, Irene A.; Xulvi-Brunet, Ramon; Hayden, Eric J.; Lehman, Niles (17 October 2012). "Spontaneous network formation among cooperative RNA replicators".

1587:{\displaystyle {\begin{aligned}{\dot {x}}_{i}^{0}&=f_{i}z_{i}-{\frac {x_{i}^{0}}{c_{I}}}\phi _{x},\\{\dot {y}}_{i}^{0}&=k_{i}x_{i}-{\frac {y_{i}^{0}}{c_{E}}}\phi _{y}\end{aligned}}} 2436:

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."

5712: 343:. Studies of the mathematical model describing replicating molecules revealed that to observe a cooperative behaviour among self-replicating molecules, they have to be connected by a 5707: 2346: 2146:

value takes place. When one hypercycle wins the selection and dominates the population, it is very difficult to replace it, even with a hypercycle with a much higher growth rate

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earlier. Apart from a substantial contribution of the above experiments to the research on the origin of life, they have not proven the existence of hypercycles experimentally.

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Guerrier-Takada, Cecilia; Gardiner, Katheleen; Marsh, Terry; Pace, Norman; Altman, Sidney (1983). "The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme".

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incorporation of more than two types of molecules. Both conditions seem very improbable; therefore, the existence of coupled hypercycles is assumed impossible in practice.

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that periodically reproduce themselves. Therefore, many cycles of the +/− nucleotide collectives are linked together by the second-order cycle of enzymatic properties of

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can be neglected, and, moreover, in the hypercycle, a template can be replicated only by itself and the previous member of the cycle, the equation can be simplified to:

908:; which guarantees that the total concentration is constant. Production and degradation rates are expressed in numbers of molecules per time unit at unit concentration ( 3744:

Hofbauer, J.; Schuster, P.; Sigmund, K.; Wolff, R. (April 1980). "Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree $ p = 2$ ".

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ZINTZARAS, ELIAS; SANTOS, MAURO; SZATHMÁRY, EÖRS (July 2002). ""Living" Under the Challenge of Information Decay: The Stochastic Corrector Model vs. Hypercycles".

714: 311:, mutations occur with a high probability. As a consequence, the information stored in a sequence can be lost due to the rapid accumulation of errors, a so-called 5095:

Takeuchi, Nobuto; Hogeweg, Paulien (23 October 2007). "The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems".

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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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was published, demonstrating their advantages over self-replicating cycles. However, even though this experiment proves the existence of cooperation among the

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chains would compete and select against each other instead of cooperating. The reproduction is possible thanks to translation and polymerization functions

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Over the years, the hypercycle theory has experienced many reformulations and methodological approaches. Among them, the most notable are applications of

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The hypercycle concept has been continuously studied since its origin. Shortly after Eigen and Schuster published their main work regarding hypercycles,

330:, which is assumed to be insufficient to encode replication machinery. This observation was the motivation for the formulation of the hypercycle theory. 2221:

blocks for growing RNA and protein chains as well as other types of molecules. Many examples of this kind of ribozyme are currently known, including a

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The above-described idea of a hypercycle's robustness results from an exponential growth of its constituents caused by the catalytic support. However,

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that incorporates both cooperation and selfishness. The coexistence of many genetically non-identical molecules makes it possible to maintain a high

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The dynamics of the hypercycle with translation can be described using a system of differential equations modelling the total number of molecules:

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McCaskill, J.S.; Füchslin, R.M.; Altmeyer, S. (30 January 2001). "The Stochastic Evolution of Catalysts in Spatially Resolved Molecular Systems".

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ribozyme subnetworks, this cooperative network does not form a hypercycle per se, so we still lack the experimental demonstration of hypercycles.

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Hogeweg, Paulien; Takeuchi, Nobuto (2003). "Multilevel Selection in Models of Prebiotic Evolution: Compartments and Spatial Self-organization".

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can be improved. From an evolutionary point of view, the hypercycle is an intermediate state of self-organization, but not the final solution.

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of smaller RNA chains performed by the first RNA ligases resulted in a longer chain with the desired catalytically active polymerase domain.

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Ekland, E.; Szostak, J.; Bartel, D. (21 July 1995). "Structurally complex and highly active RNA ligases derived from random RNA sequences".

1970: 5007:

Wasik, Szymon; Jackowiak, Paulina; Krawczyk, Jacek B.; Kedziora, Paweł; Formanowicz, Piotr; Figlerowicz, Marek; Błażewicz, Jacek (2010).

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Eigen, Manfred; Schuster, Peter (1977). "The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle".

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Suga, Hiroaki; Lee, Nick; Bessho, Yoshitaka; Wei, Kenneth; Szostak, Jack W. (1 January 2000). "Ribozyme-catalyzed tRNA aminoacylation".

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MC Boerlijst, P Hogeweg (1991) "Self-structuring and selection: Spiral Waves as a Substrate for Prebiotic Evolution". Conference Paper

2944:"Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization" 2846:

Boerlijst, M.C.; Hogeweg, P. (February 1991). "Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites".

500:. Later, he indicated that a general polymerase leads to the death of the system. Moreover, the whole cycle must be closed, so that 3905:

Szathmáry, Eörs; Gladkih, Irina (May 1989). "Sub-exponential growth and coexistence of non-enzymatically replicating templates".

2458: 2166:, a genome integration of the hypercycle can proceed by linking its members into a single chain, which forms a precursor of a 322:

According to current estimations, the maximum length of a replicated chain that can be correctly reproduced and maintained in

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Crick, F. H. C.; Brenner, S.; Klug, A.; Pieczenik, G. (December 1976). "A speculation on the origin of protein synthesis".

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In the initial works, the compartmentalization was stated as an evolutionary consequence of the hypercyclic organization.

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reaction scheme in which the concentration of complexes cannot be neglected. During replication, molecules form complexes

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were recognized only as carriers of information. This led to the formulation of a more complex model of a hypercycle with

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Johnston, W. K. (18 May 2001). "RNA-Catalyzed RNA Polymerization: Accurate and General RNA-Templated Primer Extension".

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problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (see:

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Hofbauer, J.; Schuster, P.; Sigmund, K. (February 1981). "Competition and cooperation in catalytic selfreplication".

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Boerlijst, Maarten C.; Hogeweg, Pauline (November 1995). "Spatial gradients enhance persistence of hypercycles".

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of the system. This, first, makes the system resistant to so-called parasitic branches. Parasitic branches are

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Rosen, R. (1958). "The representation of biological systems from the standpoint of the theory of categories".

1190: 144: 79:, which in theory were too short to store all essential information. The hypercycle is a special case of the 4256:

Cech, Thomas R.; Zhang, Biliang (6 November 1997). "Peptide bond formation by in vitro selected ribozymes".

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Eigen, Manfred (October 1971). "Selforganization of matter and the evolution of biological macromolecules".

1712:{\displaystyle {\begin{aligned}c_{I}&=\sum _{i}x_{i}^{0},\\c_{E}&=\sum _{i}y_{i}^{0}.\end{aligned}}} 2240: 1833:—which is relatively easy to achieve taking into account the quasispecies properties—is that the one chain 534: 304: 212:

Eigen and Schuster extend the hypercycle concept, propose a hypercycle theory and introduce the concept of

3808:"Dynamical systems under constant organization. III. Cooperative and competitive behavior of hypercycles" 1845:

originating from the same quasispecies population promotes the creation of the linkage between molecules

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Szathmáry, Eörs; Demeter, László (1987). "Group selection of early replicators and the origin of life".

2385:. All of these (including the hypercycle) found their original inspiration in Erwin Schrödinger's book 1363:{\displaystyle {\begin{aligned}x_{i}^{0}&=x_{i}+z_{i},\\y_{i}^{0}&=y_{i}+z_{i+1}.\end{aligned}}} 5732: 5349:

Cornish-Bowden, A. (2015). "Tibor Gánti and Robert Rosen: contrasting approaches to the same problem".

2477: 2304: 2063: 1866: 3008:"Evolutionary dynamics of RNA-like replicator systems: A bioinformatic approach to the origin of life" 119:. This can be a solution to the error threshold problem, which states that, in a system without ideal 2229:. A transaminoacylator described in 2013 has five nucleotides, which is sufficient for a trans-amino 1878: 457: 4802: 4729: 4528: 4349: 3840: 3328: 2251:. Earlier computer simulations showed that molecular networks can arise, evolve and be resistant to 5240:

Kauffman, S. A. (1969). "Metabolic stability and epigenesis in randomly constructed genetic nets".

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Eigen, M.; Schuster, P. (1982). "Stages of emerging life — Five principles of early organization".

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ancestor, which is much older: a large amount of evolution occurred before the appearance of LUCA.

5692: 5484:"Contrasting theories of life: historical context, current theories. In search of an ideal theory" 5145:

S Altmeyer, C Wilke, T Martinetz (2008) "How fast do structures emerge in hypercycle-systems?" in

4309:"Optimization and optimality of a short ribozyme ligase that joins non-Watson-Crick base pairings" 496:) of a more general polymerase acting in favour of formation of the successor of nucleotide chain 5727: 698:{\displaystyle {\dot {x_{i}}}=x_{i}\left(k_{i}+\sum _{j}k_{i,j}x_{j}-{\frac {1}{x}}\phi \right)} 3640: 3479: 2811: 4422:

Bartel, David P.; Unrau, Peter J. (17 September 1998). "RNA-catalysed nucleotide synthesis".

2277: 2269: 1882: 809:{\displaystyle {\begin{aligned}x&=\sum _{i}x_{i},\\k_{i}&=f_{i}-d_{i}.\end{aligned}}} 575: 386: 382: 296: 5654: 5607: 5552: 5495: 5448: 5405: 5358: 5292: 5249: 5104: 4965: 4829: 4551: 4489: 4431: 4376: 4265: 4212: 4155: 4095: 4048: 3962: 3914: 3863: 3819: 3702: 3536: 3471: 3245: 3182: 3081: 3019: 2955: 2897: 2855: 2803: 2765: 2714: 2570: 2468: 2261: 2222: 2163: 1877:

will take place. Here, the fitness value expresses the adaptation of the hypercycle to the

1862: 5541:"The Way forward for the Origin of Life: Prions and Prion-Like Molecules First Hypothesis" 5439:

Igamberdiev, A.U. (2014). "Time rescaling and pattern formation in biological evolution".

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have a limited chain length and carry the information necessary to build catalytic chains

8: 5048:

Wasik, Szymon; Jackowiak, Paulina; Figlerowicz, Marek; Blazewicz, Jacek (February 2014).

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STADLER, BÄRBEL M. R.; STADLER, PETER F. (March 2003). "Molecular Replicator Dynamics".

3540: 3475: 3249: 3186: 3085: 3023: 2959: 2901: 2859: 2807: 2769: 2718: 2574: 5672: 5575: 5540: 5521: 5316: 5128: 5077: 4989: 4937: 4892: 4855: 4713: 4688: 4664: 4637: 4618: 4575: 4512: 4477: 4455: 4333: 4308: 4289: 4233: 4200: 4176: 4143: 4116: 4083: 4004:

Eigen, M.; Gardiner, W.C.; Schuster, P. (August 1980). "Hypercycles and compartments".

3887: 3788: 3726: 3608: 3583: 3505: 3437: 3381: 3269: 3198: 3150: 3124: 3040: 3007: 2978: 2943: 2921: 2738: 2670: 2594: 2509: 2472: 2290: 2196: 300: 152: 148: 4875:

The theory of evolution and dynamical systems : mathematical aspects of selection

4399: 4364: 3926: 3093: 2417:

of all extant life. This is a serious error resulting from failure to recognize that

1142:{\displaystyle {\begin{aligned}k_{i,0}&=k_{i,n},\\x_{0}&=x_{n}.\end{aligned}}} 5623: 5580: 5525: 5513: 5508: 5483: 5464: 5460: 5421: 5374: 5308: 5265: 5261: 5212:

Life Itself: a comprehensive inquiry into the nature, origin, and fabrication of life

5163: 5120: 5069: 5030: 4981: 4929: 4878: 4847: 4791: 4748: 4718: 4669: 4610: 4567: 4517: 4473: 4447: 4404: 4338: 4281: 4238: 4181: 4121: 4064: 4021: 4017: 3986: 3978: 3974: 3953:

Bresch, C.; Niesert, U.; Harnasch, D. (1980). "Hypercycles, parasites and packages".

3930: 3879: 3832: 3807: 3792: 3718: 3673: 3613: 3564: 3559: 3524: 3497: 3429: 3421: 3417: 3373: 3365: 3361: 3261: 3142: 3097: 3045: 2983: 2913: 2867: 2825: 2777: 2730: 2656: 2586: 2514: 2496: 2374: 2366: 2260:

Sequences or IGSs) as well as these target sequences. Some genotypes could introduce

2248: 1910:

created by the mutation must be better recognized by one of the hypercycle's members

1874: 1186: 1035:{\displaystyle {\dot {x_{i}}}=x_{i}\left(k_{i,i-1}x_{i-1}-{\frac {1}{x}}\phi \right)} 905: 344: 312: 112: 108: 40: 5676: 5320: 5081: 4941: 4579: 3891: 3730: 3509: 3441: 3385: 2925: 2742: 2598: 2446: 464:, forming a catalytic hypercycle. Without the secondary loop provided by catalysis, 282:

When a model of replicating molecules was created, it was found that, for effective

5662: 5615: 5570: 5560: 5503: 5456: 5413: 5366: 5300: 5257: 5192: 5132: 5112: 5061: 5020: 4993: 4973: 4921: 4859: 4837: 4786: 4781: 4769: 4708: 4700: 4659: 4649: 4622: 4602: 4559: 4507: 4497: 4459: 4439: 4394: 4384: 4328: 4320: 4293: 4273: 4228: 4220: 4171: 4163: 4111: 4103: 4056: 4013: 3970: 3922: 3871: 3827: 3780: 3753: 3710: 3650: 3603: 3595: 3554: 3544: 3489: 3413: 3357: 3315: 3305: 3273: 3253: 3202: 3190: 3154: 3134: 3089: 3035: 3027: 2973: 2963: 2905: 2863: 2821: 2773: 2722: 2578: 2522: 2504: 2486: 2370: 571: 357: 353: 137: 84: 36: 3599: 2127:

is the total concentration of polynucleotide chains belonging to all hypercycles,

2116:

is the total concentration of all polynucleotide chains belonging to a hypercycle

1808: 263:

Experimental demonstration that ribozymes can form collectively autocatalytic sets

5065: 4502: 3294:"On the propagation of a conceptual error concerning hypercycles and cooperation" 2968: 2491: 2462: 2378: 2313: 2235: 287: 120: 64: 3031: 5619: 5417: 5370: 2453: 2247:

hypercycle in accordance with its definition, but an example of a collectively

2226: 2182: 538: 493: 60: 5667: 5642: 5116: 5025: 5008: 4476:; Zhao, Kun; Chen, Irene A.; Nowak, Martin A.; Doebeli, Michael (9 May 2013). 4324: 3654: 3138: 2909: 2342: 2337:

The hypercycle is just one of several current theories of life, including the

5701: 3982: 3425: 3369: 2500: 2382: 2265: 2252: 827: 340: 161: 100: 56: 44: 4654: 4563: 3493: 2216:

activities. Ribozymal aminoacylators and ribozymes with the ability to form

5627: 5584: 5517: 5468: 5425: 5378: 5124: 5073: 5034: 4985: 4933: 4795: 4770:"Self-Assembly of a Group I Intron from Inactive Oligonucleotide Fragments" 4722: 4704: 4673: 4614: 4521: 4408: 4389: 4342: 4242: 4185: 4125: 4068: 4060: 3549: 3501: 3265: 3146: 3049: 2987: 2917: 2518: 2295: 2217: 2213: 542: 469: 378: 213: 76: 5312: 5269: 4571: 4451: 4285: 4025: 3990: 3934: 3883: 3617: 3568: 3433: 3377: 3310: 3293: 3101: 2734: 2590: 2526: 424:

provides the matrix to reproduce itself and a matrix to build the protein

5565: 4851: 3722: 3115:

Musso, Fabio (16 March 2010). "A Stochastic Version of the Eigen Model".

2358: 2321: 2300: 1236:) will be the sum of free molecules and molecules involved in a complex: 168: 157: 124: 68: 4977: 4925: 4224: 3257: 2264:

by recognizing target sequences of the other ribozymes, promoting their

1936:

of the cycle has to better catalyse the formation of the polynucleotide

5304: 5196: 4636:

Costanzo, G.; Pino, S.; Ciciriello, F.; Di Mauro, E. (2 October 2009).

4167: 4107: 4082:

Attwater, James; Wochner, Aniela; Holliger, Philipp (20 October 2013).

3875: 3784: 3714: 3320: 2942:

Takeuchi, Nobuto; Hogeweg, Paulien; Stormo, Gary D. (16 October 2009).

2756:

Schuster, Peter; Sigmund, Karl (February 1983). "Replicator dynamics".

2726: 2582: 870: 485: 327: 308: 116: 88: 4693:

Philosophical Transactions of the Royal Society B: Biological Sciences

1736:

are total concentrations of all polypeptides and all polynucleotides,

4842: 4817: 3194: 2230: 2200: 2047:{\displaystyle {\dot {C_{l}}}=q_{l}C_{l}^{2}-C_{l}{\frac {\phi }{C}}} 442:

gives the catalytic support to build the next sequence in the cycle,

348: 129: 28: 5539:

Jheeta, S.; Chatzitheodoridis, E.; Devine, Kevin; Block, J. (2021).

4142:

Mutschler, Hannes; Wochner, Aniela; Holliger, Philipp (4 May 2015).

3757: 3582:

Drake, JW; Charlesworth, B; Charlesworth, D; Crow, JF (April 1998).

5049: 2338: 2273: 2256: 2205: 2159: 292: 164: 19: 5538: 5047: 4606: 4443: 4277: 3129: 2234:

catalyse a linking reaction between two RNA chains. Similarly, an

274: 247:

Partial RNA polymerase ribozyme is designed via directed evolution

136:. As a result, not only does the system gain information, but its 123:, an excess of mutation events would destroy the ability to carry 5643:"Origin of life: LUCA and extracellular membrane vesicles (EMVs)" 3581: 1045:

where according to the cyclic properties, it can be assumed that

574:

of the elementary hypercycle can be modelled using the following

397: 374: 3403: 3173:

May, Robert M. (17 October 1991). "Hypercycles spring to life".

2398:

Some authors equate models of the origin of life with LUCA, the

1946:

that was previously catalysed by the product of its predecessor

59:

in 1971 and subsequently further extended in collaboration with

2209: 2167: 1927:

that was previously recognized by it. Secondly, the new member

323: 104: 5723:

Knowledge articles published in peer-reviewed literature (J2W)

5392:

Letelier, J C; Cárdenas, M L; Cornish-Bowden, A (2011). "From

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The Hypercycle : a principle of natural self-organization

2153: 1958: 364: 5598:

Cornish-Bowden, A; Cárdenas, M L (2017). "Life before LUCA".

5158:

Gánti, Tibor (2003). Eörs Száthmary; James Griesemer (eds.).

4954: 4306: 4199:

Sczepanski, Jonathan T.; Joyce, Gerald F. (29 October 2014).

3235: 476:

chains. In his principal work, Manfred Eigen stated that the

72: 4745:

Evolutionary dynamics : exploring the equations of life

4307:

Robertson, MP; Hesselberth, JR; Ellington, AD (April 2001).

4144:"Freeze–thaw cycles as drivers of complex ribozyme assembly" 3743: 2432:

Gill and Forterre expressed the essential point as follows:

4747:. Cambridge, Mass. : Belknap Press of Harvard Univ. Press. 2451:

This article was adapted from the following source under a

5713:

Knowledge articles published in PLOS Computational Biology

2303:

cyclic behaviour, because some species can die out due to

1157:

A hypercycle with translation consists of polynucleotides

5396:

to metabolic closure: steps towards understanding life".

4911: 3853: 2332: 1861:

After formation, a hypercycle reaches either an internal

537:

catalysed the replication of sequences that had specific

530: 99:

The hypercycle is a cycle of connected, self-replicating

5708:

Knowledge articles published in peer-reviewed literature

5227:

Autopoiesis and cognition: the realisation of the living

4141: 4038: 3346: 2393: 2174:. Finally, the membrane surface can work as a catalyst. 862:

by self-replication of the template and its degradation

5283:

Dyson, F. J. (1982). "A model for the origin of life".

4081: 3770: 361:

information, which solves the error threshold problem.

5597: 5481: 4084:"In-ice evolution of RNA polymerase ribozyme activity" 3667: 2284: 2255:

branches. In their experiments, Vaidya et al. used an

4877:(Repr. ed.). Cambridge : Cambridge Univ. Press. 4472: 4003: 3952: 3399: 3397: 3395: 3006:

Takeuchi, Nobuto; Hogeweg, Paulien (September 2012).

2941: 2066: 1973: 1819: 1606: 1382: 1245: 1054: 935: 717: 587: 3805: 5693:

J. Padgett's Hypercycle model implemented in repast

4541: 1841:’. In this way, the existence of similar sequences 5050:"Multi-agent model of hepatitis C virus infection" 5013:Computational and Mathematical Methods in Medicine 3392: 2098: 2046: 1711: 1586: 1362: 1141: 1034: 808: 697: 3525:"Rates of spontaneous mutation among RNA viruses" 3216: 3214: 3212: 16:Cyclic sequence of self-reproducing single cycles 5699: 4592: 4137: 4135: 3904: 3287: 3285: 3283: 3071: 3067: 3065: 3063: 3061: 3059: 2845: 2841: 2839: 2837: 2835: 2793: 396:stands for intermediate) and the same number of 303:. In a system that is deprived of high-fidelity 5094: 4369:Proceedings of the National Academy of Sciences 4198: 3806:Schuster, P; Sigmund, K; Wolff, R (June 1979). 3529:Proceedings of the National Academy of Sciences 3457: 3455: 3453: 3451: 3005: 2887: 2789: 2787: 2755: 1218:). Thus, the total concentration of molecules ( 533:matrices existing among the quasispecies. This 5348: 5224: 5009:"Towards Prediction of HCV Therapy Efficiency" 4768:Hayden, Eric J.; Lehman, Niles (August 2006). 3630: 3209: 3001: 2999: 2997: 2937: 2935: 2890:Origins of Life and Evolution of the Biosphere 1152: 4905: 4680: 4300: 4132: 3948: 3946: 3944: 3898: 3692: 3342: 3340: 3338: 3280: 3231: 3229: 3056: 2883: 2881: 2879: 2877: 2832: 2704: 841:is the total concentration of all templates; 385:. The proposed model consists of a number of 278:A presentation of the error threshold problem 75:could have begun using only relatively short 5640: 5139: 5088: 4897:: CS1 maint: multiple names: authors list ( 4866: 4767: 4629: 4466: 4363:Paul, N.; Joyce, G. F. (18 September 2002). 4075: 3799: 3764: 3737: 3448: 2784: 2675:: CS1 maint: multiple names: authors list ( 2646: 2644: 2642: 2640: 2638: 2636: 2634: 2632: 2630: 2628: 1837:improves the synthesis of the similar chain 5438: 5333: 4689:"The origin of replicators and reproducers" 4421: 4192: 4032: 3624: 2994: 2932: 2749: 2700: 2698: 2696: 2694: 2692: 2690: 2688: 2686: 2626: 2624: 2622: 2620: 2618: 2616: 2614: 2612: 2610: 2608: 2556: 2554: 2552: 2550: 2548: 2546: 2544: 2542: 2540: 2538: 2154:Compartmentalization and genome integration 1959:Evolutionary dynamics: a mathematical model 5229:. Dordrecht: D. Reidel Publishing Company. 4761: 4535: 3941: 3335: 3226: 3168: 3166: 3164: 2874: 1803:(through replication and polymerization). 915:= 1). Assuming that at high concentration 855:, which is a difference between formation 848:is the excess production rate of template 269: 231:Discovery of ribozyme catalytic properties 5666: 5574: 5564: 5507: 5482:Cornish-Bowden, A; Cárdenas, M L (2020). 5151: 5041: 5024: 5000: 4948: 4841: 4809: 4785: 4736: 4712: 4686: 4663: 4653: 4511: 4501: 4415: 4398: 4388: 4362: 4332: 4255: 4249: 4232: 4175: 4115: 3847: 3831: 3686: 3668:Maynard Smith, J.; Szathmáry, E. (1995). 3644: 3607: 3575: 3558: 3548: 3516: 3483: 3319: 3309: 3291: 3128: 3108: 3039: 2977: 2967: 2815: 2655:(Reprint. ed.). Berlin : Springer. 2508: 2490: 2178:compartment linked to a packing problem. 1778:is the production rate of polynucleotide 5239: 5147:Third German Workshop on Artificial Life 4638:"Generation of Long RNA Chains in Water" 4478:"Selection for Replicases in Protocells" 4356: 4201:"A cross-chiral RNA polymerase ribozyme" 3461: 2683: 2650: 2605: 2535: 2320:, who noticed that an emergent rotating 1856: 565: 363: 273: 35:is an abstract model of organization of 18: 4872: 4586: 3161: 523: 196:Eigen introduces the hypercycle concept 63:. It was proposed as a solution to the 5700: 5214:. New York: Columbia University Press. 4873:Sigmund, Josef Hofbauer; Karl (1992). 2333:Comparison with other theories of life 1757:is the production rate of polypeptide 5282: 5209: 5182: 5157: 4816:Smith, John Maynard (9 August 1979). 4815: 4742: 3997: 3522: 3114: 2560: 2394:Last Universal Common Ancestor (LUCA) 1869:concentrations of each type of chain 560: 71:). As such, it explained how life on 5225:Maturana, H. R.; Varela, F. (1980). 4818:"Hypercycles and the origin of life" 4365:"A self-replicating ligase ribozyme" 2381:, similar to an earlier proposal by 174: 5054:Artificial Intelligence in Medicine 3746:SIAM Journal on Applied Mathematics 3172: 2285:Related problems and reformulations 1764:translated from the polynucleotide 886:is the production rate of template 13: 3670:The Major Transitions in Evolution 1820:Formation of the first hypercycles 1189:of nucleotide synthesis follows a 179: 14: 5744: 5718:Externally peer reviewed articles 5686: 4687:Szathmary, E. (29 October 2006). 3812:Journal of Differential Equations 2099:{\displaystyle C=\sum _{l}C_{l}.} 452:. The self-replicating sequences 5509:10.1016/j.biosystems.2019.104063 5461:10.1016/j.biosystems.2014.03.002 4801: 4728: 4527: 4348: 3839: 3327: 3117:Bulletin of Mathematical Biology 2445: 94: 47:manner. It was introduced in an 5641:Gill, S.; Forterre, P. (2016). 5634: 5591: 5532: 5475: 5432: 5385: 5342: 5327: 5276: 5233: 5218: 5203: 5176: 4642:Journal of Biological Chemistry 3773:Journal of Mathematical Biology 3661: 3584:"Rates of spontaneous mutation" 2651:Schuster, M. Eigen; P. (1979). 2467:Natalia Szostak; Szymon Wasik; 299:, leading to the creation of a 5097:Journal of Molecular Evolution 4787:10.1016/j.chembiol.2006.06.014 4041:Journal of Theoretical Biology 4006:Journal of Theoretical Biology 3955:Journal of Theoretical Biology 3907:Journal of Theoretical Biology 3074:Journal of Theoretical Biology 2848:Physica D: Nonlinear Phenomena 2796:Physica D: Nonlinear Phenomena 2758:Journal of Theoretical Biology 2707:Journal of Molecular Evolution 1211:(occurring with concentration 407:stands for enzyme). Sequences 368:A hypercycle with translation. 145:partial differential equations 49:ordinary differential equation 1: 5338:. Cambridge University Press. 3927:10.1016/S0022-5193(89)80177-8 3094:10.1016/S0022-5193(87)80191-1 2440: 458:positive and negative strands 5262:10.1016/0022-5193(69)90015-0 5066:10.1016/j.artmed.2013.11.001 4503:10.1371/journal.pcbi.1003051 4018:10.1016/0022-5193(80)90315-X 3975:10.1016/0022-5193(80)90314-8 3833:10.1016/0022-0396(79)90039-1 3418:10.1016/0092-8674(83)90117-4 3362:10.1016/0092-8674(82)90414-7 3298:Journal of Systems Chemistry 2969:10.1371/journal.pcbi.1000542 2868:10.1016/0167-2789(91)90049-F 2826:10.1016/0167-2789(95)00178-7 2778:10.1016/0022-5193(83)90445-9 2492:10.1371/JOURNAL.PCBI.1004853 2425:common ancestor, not to the 2189: 1814: 535:RNA-dependent RNA polymerase 132:and, as such, can undergo a 7: 5334:Schrödinger, Erwin (1944). 5162:. Oxford University Press. 3672:. Oxford University Press. 3633:Advances in Complex Systems 3600:10.1093/genetics/148.4.1667 3523:Drake, J. W. (1 May 1993). 3032:10.1016/j.plrev.2012.06.001 2134:is the rate of growth, and 1785:synthesised by the complex 1153:Hypercycle with translation 516:formation for some integer 456:form a cycle consisting of 326:-free systems is about 100 309:error-correction mechanisms 160:network among fragments of 10: 5749: 5620:10.1016/j.jtbi.2017.05.023 5418:10.1016/j.jtbi.2011.06.033 5371:10.1016/j.jtbi.2015.05.015 4482:PLOS Computational Biology 2948:PLOS Computational Biology 2478:PLOS Computational Biology 2225:ribozyme, a ligase, and a 1809:origin of the genetic code 1185:). It is assumed that the 5668:10.1017/S1473550415000282 5117:10.1007/s00239-007-9044-6 5026:10.1080/17486700903170712 4743:Nowak, Martin A. (2006). 4595:Nature Structural Biology 4325:10.1017/s1355838201002199 3655:10.1142/S0219525903000724 3139:10.1007/s11538-010-9525-4 333: 39:molecules connected in a 3292:Szathmáry, Eörs (2013). 1722:In the above equations, 484:chain can be a specific 87:, and selection against 53:Nobel Prize in Chemistry 4774:Chemistry & Biology 4655:10.1074/jbc.M109.041905 4564:10.1126/science.7618102 3494:10.1126/science.1060786 3012:Physics of Life Reviews 2910:10.1023/A:1025754907141 2563:Die Naturwissenschaften 819:In the equation above, 270:Error threshold problem 5160:The Principles of Life 4705:10.1098/rstb.2006.1912 4390:10.1073/pnas.202471099 4061:10.1006/jtbi.2002.3026 3550:10.1073/pnas.90.9.4171 2438: 2100: 2048: 1713: 1588: 1364: 1143: 1036: 810: 699: 549:translation possible. 369: 345:positive feedback loop 284:storage of information 279: 24: 3311:10.1186/1759-2208-4-1 2434: 2270:evolutionary dynamics 2227:nucleotide synthetase 2162:. After evolution of 2101: 2049: 1857:Evolutionary dynamics 1750:are dilution fluxes, 1714: 1589: 1365: 1191:Michaelis–Menten-type 1144: 1037: 811: 700: 576:differential equation 566:Elementary hypercycle 367: 277: 22: 5566:10.3390/life11090872 4914:Biological Chemistry 2223:peptidyl transferase 2201:Watson-Crick pairing 2064: 1971: 1604: 1380: 1243: 1178:(with concentration 1164:(with concentration 1052: 933: 715: 585: 524:Alternative concepts 387:nucleotide sequences 286:, macromolecules on 85:information capacity 5659:2016IJAsB..15....7G 5612:2017JThBi.434...68C 5557:2021Life...11..872J 5500:2020BiSys.18804063C 5453:2014BiSys.123...19I 5410:2011JThBi.286..100L 5363:2015JThBi.381....6C 5297:1982JMolE..18..344D 5254:1969JThBi..22..437K 5185:Bull. Math. Biophys 5109:2007JMolE..65..668T 4978:10.1038/nature01187 4970:2002Natur.420..340S 4926:10.1515/BC.2001.167 4834:1979Natur.280..445S 4699:(1474): 1761–1776. 4648:(48): 33206–33216. 4556:1995Sci...269..364E 4494:2013PLSCB...9E3051B 4436:1998Natur.395..260U 4381:2002PNAS...9912733P 4375:(20): 12733–12740. 4270:1997Natur.390...96Z 4225:10.1038/nature13900 4217:2014Natur.515..440S 4160:2015NatCh...7..502M 4100:2013NatCh...5.1011A 4053:2002JThBi.217..167Z 3967:1980JThBi..85..399B 3919:1989JThBi.138...55S 3868:1976OrLi....7..389C 3824:1979JDE....32..357S 3707:1977NW.....64..541E 3695:Naturwissenschaften 3541:1993PNAS...90.4171D 3476:2001Sci...292.1319J 3470:(5520): 1319–1325. 3258:10.1038/nature11549 3250:2012Natur.491...72V 3187:1991Natur.353..607M 3086:1987JThBi.128..463S 3024:2012PhLRv...9..219T 2960:2009PLSCB...5E0542T 2902:2003OLEB...33..375H 2860:1991PhyD...48...17B 2808:1995PhyD...88...29B 2770:1983JThBi.100..533S 2719:1982JMolE..19...47E 2575:1971NW.....58..465E 2020: 1701: 1652: 1557: 1510: 1457: 1410: 1316: 1264: 1171:) and polypeptides 138:information content 81:replicator equation 5305:10.1007/bf01733901 5210:Rosen, R. (1991). 5197:10.1007/BF02477890 4474:Bianconi, Ginestra 4168:10.1038/nchem.2251 4108:10.1038/nchem.1781 3876:10.1007/BF00927934 3785:10.1007/BF00275439 3715:10.1007/BF00450633 3222:Artificial Life II 2727:10.1007/BF02100223 2583:10.1007/BF00623322 2375:autocatalytic sets 2291:John Maynard Smith 2197:directed evolution 2096: 2082: 2044: 2006: 1709: 1707: 1687: 1686: 1638: 1637: 1584: 1582: 1543: 1487: 1443: 1387: 1360: 1358: 1302: 1250: 1139: 1137: 1032: 806: 804: 741: 695: 647: 561:Mathematical model 398:polypeptide chains 370: 280: 107:is a new level of 51:(ODE) form by the 25: 5733:Self-organization 5647:Int. J. Astrobiol 4964:(6913): 340–343. 4884:978-0-521-35838-5 4828:(5722): 445–446. 4550:(5222): 364–370. 4430:(6699): 260–263. 4211:(7527): 440–442. 4094:(12): 1011–1018. 3181:(6345): 607–608. 2367:Humberto Maturana 2305:stochastic events 2249:autocatalytic set 2073: 2042: 1990: 1677: 1628: 1568: 1497: 1468: 1397: 1022: 952: 732: 685: 638: 604: 313:error catastrophe 175:Model formulation 149:cellular automata 134:selection process 113:genetic diversity 109:self-organization 77:genetic sequences 5740: 5681: 5680: 5670: 5638: 5632: 5631: 5595: 5589: 5588: 5578: 5568: 5536: 5530: 5529: 5511: 5479: 5473: 5472: 5436: 5430: 5429: 5389: 5383: 5382: 5346: 5340: 5339: 5331: 5325: 5324: 5280: 5274: 5273: 5237: 5231: 5230: 5222: 5216: 5215: 5207: 5201: 5200: 5180: 5174: 5173: 5155: 5149: 5143: 5137: 5136: 5092: 5086: 5085: 5045: 5039: 5038: 5028: 5004: 4998: 4997: 4952: 4946: 4945: 4909: 4903: 4902: 4896: 4888: 4870: 4864: 4863: 4845: 4843:10.1038/280445a0 4813: 4807: 4806: 4805: 4799: 4789: 4765: 4759: 4758: 4740: 4734: 4733: 4732: 4726: 4716: 4684: 4678: 4677: 4667: 4657: 4633: 4627: 4626: 4590: 4584: 4583: 4539: 4533: 4532: 4531: 4525: 4515: 4505: 4470: 4464: 4463: 4419: 4413: 4412: 4402: 4392: 4360: 4354: 4353: 4352: 4346: 4336: 4304: 4298: 4297: 4264:(6655): 96–100. 4253: 4247: 4246: 4236: 4196: 4190: 4189: 4179: 4148:Nature Chemistry 4139: 4130: 4129: 4119: 4088:Nature Chemistry 4079: 4073: 4072: 4036: 4030: 4029: 4001: 3995: 3994: 3950: 3939: 3938: 3902: 3896: 3895: 3851: 3845: 3844: 3843: 3837: 3835: 3803: 3797: 3796: 3768: 3762: 3761: 3741: 3735: 3734: 3690: 3684: 3683: 3665: 3659: 3658: 3648: 3628: 3622: 3621: 3611: 3579: 3573: 3572: 3562: 3552: 3535:(9): 4171–4175. 3520: 3514: 3513: 3487: 3459: 3446: 3445: 3401: 3390: 3389: 3344: 3333: 3332: 3331: 3325: 3323: 3313: 3289: 3278: 3277: 3233: 3224: 3218: 3207: 3206: 3195:10.1038/353607a0 3170: 3159: 3158: 3132: 3112: 3106: 3105: 3069: 3054: 3053: 3043: 3003: 2992: 2991: 2981: 2971: 2954:(10): e1000542. 2939: 2930: 2929: 2896:(4/5): 375–403. 2885: 2872: 2871: 2843: 2830: 2829: 2819: 2791: 2782: 2781: 2753: 2747: 2746: 2702: 2681: 2680: 2674: 2666: 2648: 2603: 2602: 2558: 2531: 2530: 2512: 2494: 2471:(7 April 2016). 2463:reviewer reports 2456: 2449: 2371:Francisco Varela 2266:covalent binding 2105: 2103: 2102: 2097: 2092: 2091: 2081: 2053: 2051: 2050: 2045: 2043: 2035: 2033: 2032: 2019: 2014: 2005: 2004: 1992: 1991: 1986: 1985: 1976: 1865:or a state with 1718: 1716: 1715: 1710: 1708: 1700: 1695: 1685: 1669: 1668: 1651: 1646: 1636: 1620: 1619: 1593: 1591: 1590: 1585: 1583: 1579: 1578: 1569: 1567: 1566: 1556: 1551: 1542: 1537: 1536: 1527: 1526: 1509: 1504: 1499: 1498: 1490: 1479: 1478: 1469: 1467: 1466: 1456: 1451: 1442: 1437: 1436: 1427: 1426: 1409: 1404: 1399: 1398: 1390: 1369: 1367: 1366: 1361: 1359: 1352: 1351: 1333: 1332: 1315: 1310: 1294: 1293: 1281: 1280: 1263: 1258: 1148: 1146: 1145: 1140: 1138: 1131: 1130: 1114: 1113: 1097: 1096: 1074: 1073: 1041: 1039: 1038: 1033: 1031: 1027: 1023: 1015: 1010: 1009: 994: 993: 967: 966: 954: 953: 948: 947: 938: 815: 813: 812: 807: 805: 798: 797: 785: 784: 768: 767: 751: 750: 740: 704: 702: 701: 696: 694: 690: 686: 678: 673: 672: 663: 662: 646: 634: 633: 619: 618: 606: 605: 600: 599: 590: 545:of amino acids. 354:nonlinear growth 265: 264: 260: 258: 249: 248: 244: 242: 233: 232: 228: 226: 217: 216: 209: 207: 198: 197: 193: 191: 37:self-replicating 5748: 5747: 5743: 5742: 5741: 5739: 5738: 5737: 5698: 5697: 5689: 5684: 5639: 5635: 5596: 5592: 5537: 5533: 5480: 5476: 5437: 5433: 5394:L'Homme Machine 5390: 5386: 5347: 5343: 5332: 5328: 5281: 5277: 5238: 5234: 5223: 5219: 5208: 5204: 5181: 5177: 5170: 5156: 5152: 5144: 5140: 5093: 5089: 5046: 5042: 5005: 5001: 4953: 4949: 4910: 4906: 4890: 4889: 4885: 4871: 4867: 4814: 4810: 4800: 4766: 4762: 4755: 4741: 4737: 4727: 4685: 4681: 4634: 4630: 4591: 4587: 4540: 4536: 4526: 4488:(5): e1003051. 4471: 4467: 4420: 4416: 4361: 4357: 4347: 4305: 4301: 4254: 4250: 4197: 4193: 4140: 4133: 4080: 4076: 4037: 4033: 4002: 3998: 3951: 3942: 3903: 3899: 3856:Origins of Life 3852: 3848: 3838: 3804: 3800: 3769: 3765: 3758:10.1137/0138025 3742: 3738: 3701:(11): 541–565. 3691: 3687: 3680: 3666: 3662: 3629: 3625: 3580: 3576: 3521: 3517: 3460: 3449: 3402: 3393: 3345: 3336: 3326: 3290: 3281: 3244:(7422): 72–77. 3234: 3227: 3219: 3210: 3171: 3162: 3113: 3109: 3070: 3057: 3004: 2995: 2940: 2933: 2886: 2875: 2844: 2833: 2792: 2785: 2754: 2750: 2703: 2684: 2668: 2667: 2663: 2649: 2606: 2569:(10): 465–523. 2559: 2536: 2485:(4): e1004853. 2469:Jacek Blazewicz 2466: 2452: 2450: 2443: 2396: 2379:Stuart Kauffman 2335: 2314:Paulien Hogeweg 2287: 2236:acyltransferase 2192: 2156: 2144: 2132: 2121: 2114: 2087: 2083: 2077: 2065: 2062: 2061: 2034: 2028: 2024: 2015: 2010: 2000: 1996: 1981: 1977: 1975: 1974: 1972: 1969: 1968: 1961: 1954: 1945: 1935: 1926: 1917:than the chain 1915: 1909: 1859: 1822: 1817: 1802: 1793: 1783: 1776: 1769: 1762: 1755: 1748: 1741: 1734: 1727: 1706: 1705: 1696: 1691: 1681: 1670: 1664: 1660: 1657: 1656: 1647: 1642: 1632: 1621: 1615: 1611: 1607: 1605: 1602: 1601: 1581: 1580: 1574: 1570: 1562: 1558: 1552: 1547: 1541: 1532: 1528: 1522: 1518: 1511: 1505: 1500: 1489: 1488: 1484: 1483: 1474: 1470: 1462: 1458: 1452: 1447: 1441: 1432: 1428: 1422: 1418: 1411: 1405: 1400: 1389: 1388: 1383: 1381: 1378: 1377: 1357: 1356: 1341: 1337: 1328: 1324: 1317: 1311: 1306: 1299: 1298: 1289: 1285: 1276: 1272: 1265: 1259: 1254: 1246: 1244: 1241: 1240: 1235: 1226: 1216: 1210: 1201: 1183: 1176: 1169: 1162: 1155: 1136: 1135: 1126: 1122: 1115: 1109: 1105: 1102: 1101: 1086: 1082: 1075: 1063: 1059: 1055: 1053: 1050: 1049: 1014: 999: 995: 977: 973: 972: 968: 962: 958: 943: 939: 937: 936: 934: 931: 930: 924: 913: 898: 891: 885: 867: 860: 853: 846: 835: 824: 803: 802: 793: 789: 780: 776: 769: 763: 759: 756: 755: 746: 742: 736: 725: 718: 716: 713: 712: 677: 668: 664: 652: 648: 642: 629: 625: 624: 620: 614: 610: 595: 591: 589: 588: 586: 583: 582: 568: 563: 526: 515: 508: 451: 441: 432: 423: 415:. The sequence 336: 317:Eigen's Paradox 288:prebiotic Earth 272: 262: 256: 254: 252: 246: 240: 238: 236: 230: 224: 222: 220: 211: 205: 203: 201: 195: 189: 187: 185: 182: 180:Model evolution 177: 162:self-assembling 156:emergence of a 97: 65:error threshold 17: 12: 11: 5: 5746: 5736: 5735: 5730: 5728:Origin of life 5725: 5720: 5715: 5710: 5696: 5695: 5688: 5687:External links 5685: 5683: 5682: 5633: 5600:J. Theor. Biol 5590: 5531: 5474: 5431: 5404:(1): 100–113. 5398:J. Theor. Biol 5384: 5351:J. Theor. Biol 5341: 5326: 5291:(5): 344–350. 5275: 5248:(3): 437–467. 5242:J. Theor. Biol 5232: 5217: 5202: 5191:(4): 317–341. 5175: 5168: 5150: 5138: 5103:(6): 668–686. 5087: 5060:(2): 123–131. 5040: 5019:(2): 185–199. 4999: 4947: 4920:(9): 1343–63. 4904: 4883: 4865: 4808: 4780:(8): 909–918. 4760: 4753: 4735: 4679: 4628: 4585: 4534: 4465: 4414: 4355: 4299: 4248: 4191: 4154:(6): 502–508. 4131: 4074: 4047:(2): 167–181. 4031: 4012:(3): 407–411. 3996: 3961:(3): 399–405. 3940: 3897: 3862:(4): 389–397. 3846: 3818:(3): 357–368. 3798: 3779:(2): 155–168. 3763: 3752:(2): 282–304. 3736: 3685: 3679:978-0198502944 3678: 3660: 3646:10.1.1.71.7635 3623: 3594:(4): 1667–86. 3574: 3515: 3485:10.1.1.70.5439 3447: 3412:(3): 849–857. 3391: 3356:(1): 147–157. 3334: 3279: 3225: 3208: 3160: 3123:(1): 151–180. 3107: 3080:(4): 463–486. 3055: 3018:(3): 219–263. 2993: 2931: 2873: 2831: 2817:10.1.1.15.6408 2783: 2764:(3): 533–538. 2748: 2682: 2661: 2604: 2533: 2442: 2439: 2421:refers to the 2395: 2392: 2334: 2331: 2286: 2283: 2191: 2188: 2183:Carsten Bresch 2172:UV irradiation 2155: 2152: 2142: 2130: 2119: 2112: 2107: 2106: 2095: 2090: 2086: 2080: 2076: 2072: 2069: 2055: 2054: 2041: 2038: 2031: 2027: 2023: 2018: 2013: 2009: 2003: 1999: 1995: 1989: 1984: 1980: 1960: 1957: 1950: 1940: 1931: 1921: 1913: 1905: 1890:Eörs Szathmáry 1858: 1855: 1821: 1818: 1816: 1813: 1797: 1789: 1781: 1774: 1767: 1760: 1753: 1746: 1739: 1732: 1725: 1720: 1719: 1704: 1699: 1694: 1690: 1684: 1680: 1676: 1673: 1671: 1667: 1663: 1659: 1658: 1655: 1650: 1645: 1641: 1635: 1631: 1627: 1624: 1622: 1618: 1614: 1610: 1609: 1595: 1594: 1577: 1573: 1565: 1561: 1555: 1550: 1546: 1540: 1535: 1531: 1525: 1521: 1517: 1514: 1512: 1508: 1503: 1496: 1493: 1486: 1485: 1482: 1477: 1473: 1465: 1461: 1455: 1450: 1446: 1440: 1435: 1431: 1425: 1421: 1417: 1414: 1412: 1408: 1403: 1396: 1393: 1386: 1385: 1371: 1370: 1355: 1350: 1347: 1344: 1340: 1336: 1331: 1327: 1323: 1320: 1318: 1314: 1309: 1305: 1301: 1300: 1297: 1292: 1288: 1284: 1279: 1275: 1271: 1268: 1266: 1262: 1257: 1253: 1249: 1248: 1231: 1222: 1214: 1205: 1197: 1181: 1174: 1167: 1160: 1154: 1151: 1150: 1149: 1134: 1129: 1125: 1121: 1118: 1116: 1112: 1108: 1104: 1103: 1100: 1095: 1092: 1089: 1085: 1081: 1078: 1076: 1072: 1069: 1066: 1062: 1058: 1057: 1043: 1042: 1030: 1026: 1021: 1018: 1013: 1008: 1005: 1002: 998: 992: 989: 986: 983: 980: 976: 971: 965: 961: 957: 951: 946: 942: 922: 911: 904:is a dilution 896: 889: 877: 865: 858: 851: 844: 833: 822: 817: 816: 801: 796: 792: 788: 783: 779: 775: 772: 770: 766: 762: 758: 757: 754: 749: 745: 739: 735: 731: 728: 726: 724: 721: 720: 706: 705: 693: 689: 684: 681: 676: 671: 667: 661: 658: 655: 651: 645: 641: 637: 632: 628: 623: 617: 613: 609: 603: 598: 594: 567: 564: 562: 559: 543:transportation 525: 522: 513: 509:must catalyse 504: 446: 437: 433:. The protein 428: 419: 335: 332: 271: 268: 267: 266: 250: 234: 218: 199: 181: 178: 176: 173: 101:macromolecules 96: 93: 61:Peter Schuster 15: 9: 6: 4: 3: 2: 5745: 5734: 5731: 5729: 5726: 5724: 5721: 5719: 5716: 5714: 5711: 5709: 5706: 5705: 5703: 5694: 5691: 5690: 5678: 5674: 5669: 5664: 5660: 5656: 5652: 5648: 5644: 5637: 5629: 5625: 5621: 5617: 5613: 5609: 5605: 5601: 5594: 5586: 5582: 5577: 5572: 5567: 5562: 5558: 5554: 5550: 5546: 5542: 5535: 5527: 5523: 5519: 5515: 5510: 5505: 5501: 5497: 5493: 5489: 5485: 5478: 5470: 5466: 5462: 5458: 5454: 5450: 5446: 5442: 5435: 5427: 5423: 5419: 5415: 5411: 5407: 5403: 5399: 5395: 5388: 5380: 5376: 5372: 5368: 5364: 5360: 5356: 5352: 5345: 5337: 5336:What is Life? 5330: 5322: 5318: 5314: 5310: 5306: 5302: 5298: 5294: 5290: 5286: 5279: 5271: 5267: 5263: 5259: 5255: 5251: 5247: 5243: 5236: 5228: 5221: 5213: 5206: 5198: 5194: 5190: 5186: 5179: 5171: 5169:9780198507260 5165: 5161: 5154: 5148: 5142: 5134: 5130: 5126: 5122: 5118: 5114: 5110: 5106: 5102: 5098: 5091: 5083: 5079: 5075: 5071: 5067: 5063: 5059: 5055: 5051: 5044: 5036: 5032: 5027: 5022: 5018: 5014: 5010: 5003: 4995: 4991: 4987: 4983: 4979: 4975: 4971: 4967: 4963: 4959: 4951: 4943: 4939: 4935: 4931: 4927: 4923: 4919: 4915: 4908: 4900: 4894: 4886: 4880: 4876: 4869: 4861: 4857: 4853: 4849: 4844: 4839: 4835: 4831: 4827: 4823: 4819: 4812: 4804: 4797: 4793: 4788: 4783: 4779: 4775: 4771: 4764: 4756: 4754:9780674023383 4750: 4746: 4739: 4731: 4724: 4720: 4715: 4710: 4706: 4702: 4698: 4694: 4690: 4683: 4675: 4671: 4666: 4661: 4656: 4651: 4647: 4643: 4639: 4632: 4624: 4620: 4616: 4612: 4608: 4607:10.1038/71225 4604: 4600: 4596: 4589: 4581: 4577: 4573: 4569: 4565: 4561: 4557: 4553: 4549: 4545: 4538: 4530: 4523: 4519: 4514: 4509: 4504: 4499: 4495: 4491: 4487: 4483: 4479: 4475: 4469: 4461: 4457: 4453: 4449: 4445: 4444:10.1038/26193 4441: 4437: 4433: 4429: 4425: 4418: 4410: 4406: 4401: 4396: 4391: 4386: 4382: 4378: 4374: 4370: 4366: 4359: 4351: 4344: 4340: 4335: 4330: 4326: 4322: 4319:(4): 513–23. 4318: 4314: 4310: 4303: 4295: 4291: 4287: 4283: 4279: 4278:10.1038/36375 4275: 4271: 4267: 4263: 4259: 4252: 4244: 4240: 4235: 4230: 4226: 4222: 4218: 4214: 4210: 4206: 4202: 4195: 4187: 4183: 4178: 4173: 4169: 4165: 4161: 4157: 4153: 4149: 4145: 4138: 4136: 4127: 4123: 4118: 4113: 4109: 4105: 4101: 4097: 4093: 4089: 4085: 4078: 4070: 4066: 4062: 4058: 4054: 4050: 4046: 4042: 4035: 4027: 4023: 4019: 4015: 4011: 4007: 4000: 3992: 3988: 3984: 3980: 3976: 3972: 3968: 3964: 3960: 3956: 3949: 3947: 3945: 3936: 3932: 3928: 3924: 3920: 3916: 3912: 3908: 3901: 3893: 3889: 3885: 3881: 3877: 3873: 3869: 3865: 3861: 3857: 3850: 3842: 3834: 3829: 3825: 3821: 3817: 3813: 3809: 3802: 3794: 3790: 3786: 3782: 3778: 3774: 3767: 3759: 3755: 3751: 3747: 3740: 3732: 3728: 3724: 3720: 3716: 3712: 3708: 3704: 3700: 3696: 3689: 3681: 3675: 3671: 3664: 3656: 3652: 3647: 3642: 3638: 3634: 3627: 3619: 3615: 3610: 3605: 3601: 3597: 3593: 3589: 3585: 3578: 3570: 3566: 3561: 3556: 3551: 3546: 3542: 3538: 3534: 3530: 3526: 3519: 3511: 3507: 3503: 3499: 3495: 3491: 3486: 3481: 3477: 3473: 3469: 3465: 3458: 3456: 3454: 3452: 3443: 3439: 3435: 3431: 3427: 3423: 3419: 3415: 3411: 3407: 3400: 3398: 3396: 3387: 3383: 3379: 3375: 3371: 3367: 3363: 3359: 3355: 3351: 3343: 3341: 3339: 3330: 3322: 3317: 3312: 3307: 3303: 3299: 3295: 3288: 3286: 3284: 3275: 3271: 3267: 3263: 3259: 3255: 3251: 3247: 3243: 3239: 3232: 3230: 3223: 3217: 3215: 3213: 3204: 3200: 3196: 3192: 3188: 3184: 3180: 3176: 3169: 3167: 3165: 3156: 3152: 3148: 3144: 3140: 3136: 3131: 3126: 3122: 3118: 3111: 3103: 3099: 3095: 3091: 3087: 3083: 3079: 3075: 3068: 3066: 3064: 3062: 3060: 3051: 3047: 3042: 3037: 3033: 3029: 3025: 3021: 3017: 3013: 3009: 3002: 3000: 2998: 2989: 2985: 2980: 2975: 2970: 2965: 2961: 2957: 2953: 2949: 2945: 2938: 2936: 2927: 2923: 2919: 2915: 2911: 2907: 2903: 2899: 2895: 2891: 2884: 2882: 2880: 2878: 2869: 2865: 2861: 2857: 2853: 2849: 2842: 2840: 2838: 2836: 2827: 2823: 2818: 2813: 2809: 2805: 2801: 2797: 2790: 2788: 2779: 2775: 2771: 2767: 2763: 2759: 2752: 2744: 2740: 2736: 2732: 2728: 2724: 2720: 2716: 2712: 2708: 2701: 2699: 2697: 2695: 2693: 2691: 2689: 2687: 2678: 2672: 2664: 2662:9783540092933 2658: 2654: 2647: 2645: 2643: 2641: 2639: 2637: 2635: 2633: 2631: 2629: 2627: 2625: 2623: 2621: 2619: 2617: 2615: 2613: 2611: 2609: 2600: 2596: 2592: 2588: 2584: 2580: 2576: 2572: 2568: 2564: 2557: 2555: 2553: 2551: 2549: 2547: 2545: 2543: 2541: 2539: 2534: 2532: 2528: 2524: 2520: 2516: 2511: 2506: 2502: 2498: 2493: 2488: 2484: 2480: 2479: 2474: 2470: 2464: 2460: 2455: 2448: 2437: 2433: 2430: 2428: 2424: 2420: 2416: 2414: 2410: 2406: 2402: 2391: 2388: 2387:What is Life? 2384: 2383:Freeman Dyson 2380: 2376: 2372: 2368: 2364: 2363:self-building 2360: 2356: 2352: 2350: 2344: 2340: 2330: 2326: 2323: 2319: 2315: 2309: 2306: 2302: 2297: 2292: 2282: 2279: 2278:recombination 2275: 2271: 2267: 2263: 2258: 2254: 2253:parasitic RNA 2250: 2244: 2242: 2237: 2232: 2228: 2224: 2219: 2218:peptide bonds 2215: 2211: 2207: 2202: 2198: 2187: 2184: 2179: 2175: 2173: 2169: 2165: 2161: 2151: 2149: 2145: 2137: 2133: 2126: 2122: 2115: 2093: 2088: 2084: 2078: 2074: 2070: 2067: 2060: 2059: 2058: 2039: 2036: 2029: 2025: 2021: 2016: 2011: 2007: 2001: 1997: 1993: 1987: 1982: 1978: 1967: 1966: 1965: 1956: 1953: 1949: 1943: 1939: 1934: 1930: 1924: 1920: 1916: 1908: 1904: 1898: 1894: 1891: 1886: 1884: 1880: 1876: 1875:fitness value 1872: 1868: 1864: 1854: 1852: 1848: 1844: 1840: 1836: 1832: 1826: 1812: 1810: 1804: 1800: 1796: 1792: 1788: 1784: 1777: 1770: 1763: 1756: 1749: 1742: 1735: 1728: 1702: 1697: 1692: 1688: 1682: 1678: 1674: 1672: 1665: 1661: 1653: 1648: 1643: 1639: 1633: 1629: 1625: 1623: 1616: 1612: 1600: 1599: 1598: 1575: 1571: 1563: 1559: 1553: 1548: 1544: 1538: 1533: 1529: 1523: 1519: 1515: 1513: 1506: 1501: 1494: 1491: 1480: 1475: 1471: 1463: 1459: 1453: 1448: 1444: 1438: 1433: 1429: 1423: 1419: 1415: 1413: 1406: 1401: 1394: 1391: 1376: 1375: 1374: 1353: 1348: 1345: 1342: 1338: 1334: 1329: 1325: 1321: 1319: 1312: 1307: 1303: 1295: 1290: 1286: 1282: 1277: 1273: 1269: 1267: 1260: 1255: 1251: 1239: 1238: 1237: 1234: 1230: 1225: 1221: 1217: 1208: 1204: 1200: 1196: 1192: 1188: 1184: 1177: 1170: 1163: 1132: 1127: 1123: 1119: 1117: 1110: 1106: 1098: 1093: 1090: 1087: 1083: 1079: 1077: 1070: 1067: 1064: 1060: 1048: 1047: 1046: 1028: 1024: 1019: 1016: 1011: 1006: 1003: 1000: 996: 990: 987: 984: 981: 978: 974: 969: 963: 959: 955: 949: 944: 940: 929: 928: 927: 925: 918: 914: 907: 903: 899: 893:catalysed by 892: 884: 880: 876: 872: 869:, usually by 868: 861: 854: 847: 840: 836: 829: 828:concentration 825: 799: 794: 790: 786: 781: 777: 773: 771: 764: 760: 752: 747: 743: 737: 733: 729: 727: 722: 711: 710: 709: 691: 687: 682: 679: 674: 669: 665: 659: 656: 653: 649: 643: 639: 635: 630: 626: 621: 615: 611: 607: 601: 596: 592: 581: 580: 579: 577: 573: 558: 556: 550: 546: 544: 540: 536: 532: 521: 519: 512: 507: 503: 499: 495: 491: 487: 483: 480:coded by the 479: 475: 471: 467: 463: 459: 455: 449: 445: 440: 436: 431: 427: 422: 418: 414: 410: 406: 402: 399: 395: 391: 388: 384: 380: 379:nucleic acids 376: 366: 362: 359: 355: 350: 346: 342: 341:concentration 331: 329: 325: 320: 318: 314: 310: 306: 302: 298: 294: 289: 285: 276: 251: 235: 219: 215: 200: 184: 183: 172: 170: 166: 163: 159: 154: 150: 146: 141: 139: 135: 131: 126: 122: 118: 114: 110: 106: 102: 95:Central ideas 92: 90: 86: 82: 78: 74: 70: 66: 62: 58: 57:Manfred Eigen 54: 50: 46: 45:autocatalytic 42: 38: 34: 30: 21: 5650: 5646: 5636: 5603: 5599: 5593: 5548: 5544: 5534: 5491: 5487: 5477: 5444: 5440: 5434: 5401: 5397: 5393: 5387: 5354: 5350: 5344: 5335: 5329: 5288: 5285:J. Mol. 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