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Hypercycle (chemistry)
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Hypercycle (chemistry)
In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a cyclic, autocatalytic manner. It was introduced in an ordinary differential equation (ODE) form by the Nobel Prize in Chemistry winner Manfred Eigen in 1967 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (see: abiogenesis). As such, it explained how life on Earth could have begun using only relatively short genetic sequences, which in theory were too short to store all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small selective advantage, rapid evolvability, increased information capacity, and selection against parasitic branches.
The hypercycle is a cycle of connected, self-replicating macromolecules. 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 system is a new level of self-organization that incorporates both cooperation and selfishness. The coexistence of many genetically non-identical molecules makes it possible to maintain a high genetic diversity of the population. This can be a solution to the error threshold problem, which states that, in a system without ideal replication, an excess of mutation events would destroy the ability to carry information 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[citation needed]. Hypercycles are also subject to evolution and, as such, can undergo a selection process. As a result, not only does the system gain information, but its information content can be improved. From an evolutionary point of view, the hypercycle is an intermediate state of self-organization, but not the final solution.
Over the years, the hypercycle theory has experienced many reformulations and methodological approaches. Among them, the most notable are applications of partial differential equations, cellular automata, and stochastic 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 emergence of a cooperative network among fragments of self-assembling ribozymes was published, demonstrating their advantages over self-replicating cycles. However, even though this experiment proves the existence of cooperation among the recombinase ribozyme subnetworks, this cooperative network does not form a hypercycle per se, so we still lack the experimental demonstration of hypercycles.
When a model of replicating molecules was created, it was found that, for effective storage of information, macromolecules on prebiotic Earth 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 errors into a new sequence, leading to the creation of a quasispecies. In a system that is deprived of high-fidelity replicases and error-correction mechanisms, 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 error catastrophe. 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 Eigen's Paradox.
According to current estimations, the maximum length of a replicated chain that can be correctly reproduced and maintained in enzyme-free systems is about 100 bases, which is assumed to be insufficient to encode replication machinery. This observation was the motivation for the formulation of the hypercycle theory.
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 concentration. 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 positive feedback loop of catalytic 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 produce nonlinear growth of the system. This, first, makes the system resistant to so-called parasitic branches. Parasitic branches are species 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 information, which solves the error threshold problem.
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 proteins, while nucleic acids were recognized only as carriers of information. This led to the formulation of a more complex model of a hypercycle with translation. The proposed model consists of a number of nucleotide sequences I (I stands for intermediate) and the same number of polypeptide chains E (E stands for enzyme). Sequences I have a limited chain length and carry the information necessary to build catalytic chains E. The sequence Ii provides the matrix to reproduce itself and a matrix to build the protein Ei. The protein Ei gives the catalytic support to build the next sequence in the cycle, Ii+1. The self-replicating sequences I form a cycle consisting of positive and negative strands that periodically reproduce themselves. Therefore, many cycles of the +/− nucleotide collectives are linked together by the second-order cycle of enzymatic properties of E, forming a catalytic hypercycle. Without the secondary loop provided by catalysis, I chains would compete and select against each other instead of cooperating. The reproduction is possible thanks to translation and polymerization functions encoded in I chains. In his principal work, Manfred Eigen stated that the E coded by the I chain can be a specific polymerase or an enhancer (or a silencer) of a more general polymerase acting in favour of formation of the successor of nucleotide chain I. Later, he indicated that a general polymerase leads to the death of the system. Moreover, the whole cycle must be closed, so that En must catalyse I1 formation for some integer n > 1.
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 RNA matrices existing among the quasispecies. This RNA-dependent RNA polymerase catalysed the replication of sequences that had specific motifs 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 transportation of amino acids.
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Hypercycle (chemistry)
In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a cyclic, autocatalytic manner. It was introduced in an ordinary differential equation (ODE) form by the Nobel Prize in Chemistry winner Manfred Eigen in 1967 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (see: abiogenesis). As such, it explained how life on Earth could have begun using only relatively short genetic sequences, which in theory were too short to store all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small selective advantage, rapid evolvability, increased information capacity, and selection against parasitic branches.
The hypercycle is a cycle of connected, self-replicating macromolecules. 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 system is a new level of self-organization that incorporates both cooperation and selfishness. The coexistence of many genetically non-identical molecules makes it possible to maintain a high genetic diversity of the population. This can be a solution to the error threshold problem, which states that, in a system without ideal replication, an excess of mutation events would destroy the ability to carry information 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[citation needed]. Hypercycles are also subject to evolution and, as such, can undergo a selection process. As a result, not only does the system gain information, but its information content can be improved. From an evolutionary point of view, the hypercycle is an intermediate state of self-organization, but not the final solution.
Over the years, the hypercycle theory has experienced many reformulations and methodological approaches. Among them, the most notable are applications of partial differential equations, cellular automata, and stochastic 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 emergence of a cooperative network among fragments of self-assembling ribozymes was published, demonstrating their advantages over self-replicating cycles. However, even though this experiment proves the existence of cooperation among the recombinase ribozyme subnetworks, this cooperative network does not form a hypercycle per se, so we still lack the experimental demonstration of hypercycles.
When a model of replicating molecules was created, it was found that, for effective storage of information, macromolecules on prebiotic Earth 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 errors into a new sequence, leading to the creation of a quasispecies. In a system that is deprived of high-fidelity replicases and error-correction mechanisms, 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 error catastrophe. 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 Eigen's Paradox.
According to current estimations, the maximum length of a replicated chain that can be correctly reproduced and maintained in enzyme-free systems is about 100 bases, which is assumed to be insufficient to encode replication machinery. This observation was the motivation for the formulation of the hypercycle theory.
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 concentration. 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 positive feedback loop of catalytic 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 produce nonlinear growth of the system. This, first, makes the system resistant to so-called parasitic branches. Parasitic branches are species 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 information, which solves the error threshold problem.
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 proteins, while nucleic acids were recognized only as carriers of information. This led to the formulation of a more complex model of a hypercycle with translation. The proposed model consists of a number of nucleotide sequences I (I stands for intermediate) and the same number of polypeptide chains E (E stands for enzyme). Sequences I have a limited chain length and carry the information necessary to build catalytic chains E. The sequence Ii provides the matrix to reproduce itself and a matrix to build the protein Ei. The protein Ei gives the catalytic support to build the next sequence in the cycle, Ii+1. The self-replicating sequences I form a cycle consisting of positive and negative strands that periodically reproduce themselves. Therefore, many cycles of the +/− nucleotide collectives are linked together by the second-order cycle of enzymatic properties of E, forming a catalytic hypercycle. Without the secondary loop provided by catalysis, I chains would compete and select against each other instead of cooperating. The reproduction is possible thanks to translation and polymerization functions encoded in I chains. In his principal work, Manfred Eigen stated that the E coded by the I chain can be a specific polymerase or an enhancer (or a silencer) of a more general polymerase acting in favour of formation of the successor of nucleotide chain I. Later, he indicated that a general polymerase leads to the death of the system. Moreover, the whole cycle must be closed, so that En must catalyse I1 formation for some integer n > 1.
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 RNA matrices existing among the quasispecies. This RNA-dependent RNA polymerase catalysed the replication of sequences that had specific motifs 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 transportation of amino acids.
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