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## Error threshold (evolution)The It was noted by Manfred Eigen in his 1971 paper (Eigen 1971) that this mutation process places a limit on the number of digits a molecule may have. If a molecule exceeds this critical size, the effect of the mutations become overwhelming and a runaway mutation process will destroy the information in subsequent generations of the molecule. The error threshold is also controlled by the fitness landscape for the molecules. Molecules which differ only by a few mutations may be thought of as "close" to each other, while those which differ by many mutations are distant from each other. Molecules which are very fit, and likely to reproduce, have a "high" fitness, those less fit have "low" fitness. These ideas of proximity and height form the intuitive concept of the "fitness landscape". If a particular sequence and its neighbors have a high fitness, they will form a quasispecies and will be able to support longer sequence lengths than a fit sequence with few fit neighbors, or a less fit neighborhood of sequences. Also, it was noted by Wilke (Wilke 2005) that the error threshold concept does not apply in portions of the landscape where there are lethal mutations, in which the induced mutation yields zero fitness and prohibits the molecule from reproducing. The concept of this critical mutation rate, or "error threshold" is crucial to understanding "Eigen's paradox" which is discussed in the next section. ## Additional recommended knowledge
## Eigen's Paradox
- Without error correction enzymes, the maximum size of a replicating molecule is about 100 base pairs.
- In order for a replicating molecule to encode error correction enzymes, it must be substantially larger than 100 bases.
This is a chicken-or-egg kind of a paradox, with an even more difficult solution. Which came first, the large genome or the error correction enzymes? A number of solutions to this paradox have been proposed: - Stochastic corrector model (Szathmáry & Smith, 1995). In this proposed solution, a number of primitive molecules of say, two different types, are associated with each other in some way, perhaps by a capsule or "cell wall". If their reproductive success is enhanced by having, say, equal numbers in each cell, and reproduction occurs by division in which each of various types of molecules are randomly distributed among the "children", the process of selection will promote such equal representation in the cells, even though one of the molecules may have a selective advantage over the other.
- Relaxed error threshold (Kun et al., 2005) - Studies of actual ribozymes indicate that the mutation rate can be substantially less than first expected - on the order of 0.001 per base pair per replication. This may allow sequence lengths of the order of 7-8 thousand base pairs, sufficient to incorporate rudimentary error correction enzymes.
## A simple mathematical model illustrating the error thresholdConsider a 3-digit molecule [A,B,C] where A, B, and C can take on the values 0 and 1. There are eight such sequences ([000], [001], [010], [011], [100], [101], [110], and [111]). Let's say that the [000] molecule is the most fit; upon each replication it produces an average of **Hamming** distance**Sequence(s)**0 [000] 1 [001] [010] [100]2 [110] [101] [011]3 [111]
Note that the number of sequences for distance where the fitness matrix where If we now go to the case where the number of base pairs is large, say L=100, we obtain behavior that resembles a phase transition. The plot below on the left shows a series of equilibrium concentrations divided by the binomial coefficient
It can be seen that there is a sharp transition at a value of In the limit as ## See also## References- Eigen, M. (1971). "Selforganization of matter and evolution of biological Macromolecules".
*Naturwissenschaften***58**(10): 465. - Quasispecies theory in the context of population genetics - Claus O. Wilke. Retrieved on October 12, 2005.
- Campos, P. R. A. and Fontanari, J. F. (1999). "Finite-size scaling of the error threshold transition in finite populations (PDF)".
*J. Phys. A: Math. Gen.***32**: L1–L7. - Holmes, Edward C. (2005). "On being the right size (PDF)".
*Nature Genetics***37**: 923 - 924. - Eörs Szathmáry & John Maynard Smith (1995). "The major evolutionary transitions".
*Nature***374**: 227-232. - Ádám Kun, Mauro Santos & Eörs Szathmáry (2005). "Real ribozymes suggest a relaxed error threshold (PDF)".
*Nature Genetics***37**: 1008-1011.
Categories: Virology | Evolutionary biology | Population genetics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Error_threshold_(evolution)". A list of authors is available in Wikipedia. |