What is "hypercycle"

n. 1 (context hyperbolic geometry English) A curve whose points have the same orthogonal distance from a given straight line. 2 (context chemistry English) A system of self-replicating molecules, as an explanation for the self organization of prebiotic systems.

In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis).

Given a straight line L and a point P not on L, one can construct a hypercycle by taking all points Q on the same side of L as P, with perpendicular distance to L equal to that of P.

The line L is called the axis, center, or base line of the hypercycle. The orthogonal segments from each point to L are called the radii. Their common length is called the distance or radius of the hypercycle.

The hypercycles through a given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity.

Hypercycle may refer to:

• Hypercycle (chemistry), a kind of reaction network prominent in a theory of the self-organization of matter
• Hypercycle (hyperbolic geometry),a curve whose points have the same orthogonal distance from a given straight line

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 winner Manfred Eigen in 1971 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (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. 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.