To use all functions of this page, please activate cookies in your browser.

my.bionity.com

With an accout for my.bionity.com you can always see everything at a glance – and you can configure your own website and individual newsletter.

- My watch list
- My saved searches
- My saved topics
- My newsletter

## Quasispecies modelThe ## Additional recommended knowledge
## General descriptionThe model rests on four assumptions: - The self-replicating entities can be represented as sequences composed of a small number of building blocks--for example, sequences of RNA consisting of the four bases adenine, guanine, cytosine, and uracil.
- New sequences enter the system solely as the result of a copy process, either correct or erroneous, of other sequences that are already present.
- The substrates, or raw materials, necessary for ongoing replication are always present in sufficient quantity. Excess sequences are washed away in an outgoing flux.
- Sequences may decay into their building blocks. The probability of decay does not depend on the sequences' age; old sequences are just as likely to decay as young sequences.
In the quasispecies model, mutations occur through errors made in the process of copying already existing sequences. Further, selection arises because different types of sequences tend to replicate at different rates, which leads to the suppression of sequences that replicate more slowly in favor of sequences that replicate faster. However, the quasispecies model does not predict the ultimate extinction of all but the fastest replicating sequence. Although the sequences that replicate more slowly cannot sustain their abundance level by themselves, they are constantly replenished as sequences that replicate faster mutate into them. At equilibrium, removal of slowly replicating sequences due to decay or outflow is balanced by replenishing, so that even relatively slowly replicating sequences can remain present in finite abundance. Due to the ongoing production of mutant sequences, selection does not act on single sequences, but on mutational "clouds" of closely related sequences, referred to as The mutation rate and the general fitness of the molecular sequences and their neighbors is crucial to the formation of a quasispecies. If the mutation rate is zero, there is no exchange by mutation, and each sequence is its own species. If the mutation rate is too high, exceeding what is known as the error threshold, the quasispecies will break down and be dispersed over the entire range of available sequences. ## Mathematical descriptionA simple mathematical model for a quasispecies is as follows: let there be where . Sometimes a death rate term where δ This is just a system of linear equations. The usual way to solve such a system is to first diagonalize the ## Alternative formulationsThe quasispecies formulae may be expressed as a set of linear differential equations. Setting we can write: The quasispecies equations are usually expressed in terms of concentrations - .
- .
The above equations for the quasispecies then become for the discrete version: or, for the continuum version: ## A simple exampleThe quasispecies concept can be illustrated by a simple system consisting of 4 sequences. Sequence 1 is [0,0], and sequences [0,1], [1,0] and [1,1] are numbered 2,3 and 4 respectively. Lets say the [0,0] sequence never mutates and always produces a single offspring. Lets say the other 3 sequences all produce, on average, 1 − The diagonalized matrix is and the eigenvectors corresponding to these eigenvalues are: **Eigenvalue****Eigenvector**1-2k [0,-1,0,1] 1-2k [0,-1,1,0] 1 [1,0,0,0] 1+k [0,1,1,1]
Only the eigenvalue 1 + ## References- M. Eigen and P. Schuster,
*The Hypercycle: A Principle of Natural Self-Organization*(Berlin: Springer, 1979). - M. Eigen, "Selforganization of Matter and the Evolution of Biological Macromolecules,"
*Naturwissenschaften*58 (1971): 465-523. - P. Schuster and J. Swetina, "Stationary Mutant Distributions and Evolutionary Optimization,"
*Bulletin of Mathematical Biology*50 (1988): 636-660. - E. Domingo and J. J. Holland, "RNA Virus Mutations and Fitness for Survival,"
*Annual Review of Microbiology*51 (1997): 151-178; C. L. Burch and L. Chao, "Evolvability of an RNA Virus is Determined by its Mutational Neighbourhood,"*Nature*406 (2000): 625-628.
## Further reading- Eigen, M., J. McCaskill and P. Schuster. "The Molecular Quasi-species."
*Advances in Chemical Physics*75 (1989): 149-263. - Novak, M. A. "What is a Quasi-species?"
*Trends in Ecology and Evolution*7 (1992): 118-121.
Based on article from Nupedia (http://www.nupedia.com/article/600/) by Claus O. Wilke, posted 2001-10-12. Categories: Virology | Evolutionary biology | Microbial population biology | Evolutionary dynamics |
|||||||||||

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Quasispecies_model". A list of authors is available in Wikipedia. |