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.
Central ideas 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. 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.
Model formulation
Model evolution 1971 (1971): Eigen introduces the hypercycle concept 1977 (1977): Eigen and Schuster extend the hypercycle concept, propose a hypercycle theory and introduce the concept of quasispecies 1982 (1982): Discovery of ribozyme catalytic properties 2001 (2001): Partial RNA polymerase ribozyme is designed via directed evolution 2012 (2012): Experimental demonstration that ribozymes can form collectively autocatalytic sets
Error threshold problem
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.
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