Error catastrophe refers to the cumulative loss of genetic information in a lineage of organisms due to high mutation rates. The mutation rate above which error catastrophe occurs is called the
error threshold. Both terms were coined by
Manfred Eigen
Manfred Eigen (; 9 May 1927 – 6 February 2019) was a German biophysical chemist who won the 1967 Nobel Prize in Chemistry for work on measuring fast chemical reactions.
Eigen's research helped solve major problems in physical chemistry and ...
in his mathematical evolutionary theory of the
quasispecies
The quasispecies model is a description of the process of the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry. A quasispecies is a large group or "cloud" of related genotypes that exist in an en ...
.
The term is most widely used to refer to mutation accumulation to the point of inviability of the organism or virus, where it cannot produce enough viable offspring to maintain a population. This use of Eigen's term was adopted by Lawrence Loeb and colleagues to describe the strategy of lethal mutagenesis to cure
HIV
The human immunodeficiency viruses (HIV) are two species of ''Lentivirus'' (a subgroup of retrovirus) that infect humans. Over time, they cause acquired immunodeficiency syndrome (AIDS), a condition in which progressive failure of the immune ...
by using mutagenic ribonucleoside analogs.
There was an earlier use of the term introduced in 1963 by
Leslie Orgel
Leslie Eleazer Orgel FRS (12 January 1927 – 27 October 2007) was a British chemist. He is known for his theories on the origin of life.
Biography
Leslie Orgel was born in London, England, on . He received his Bachelor of Arts degree in chemi ...
in a theory for cellular aging, in which errors in the translation of proteins involved in
protein translation would amplify the errors until the cell was inviable.
This theory has not received empirical support.
Error catastrophe is predicted in certain mathematical models of evolution and has also been observed empirically.
Like every organism, viruses 'make mistakes' (or
mutate
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitos ...
) during replication. The resulting mutations increase
biodiversity
Biodiversity or biological diversity is the variety and variability of life on Earth. Biodiversity is a measure of variation at the genetic (''genetic variability''), species (''species diversity''), and ecosystem (''ecosystem diversity'') l ...
among the population and help subvert the ability of a host's immune system to recognise it in a subsequent infection. The more mutations the virus makes during replication, the more likely it is to avoid recognition by the immune system and the more diverse its population will be (see the article on
biodiversity
Biodiversity or biological diversity is the variety and variability of life on Earth. Biodiversity is a measure of variation at the genetic (''genetic variability''), species (''species diversity''), and ecosystem (''ecosystem diversity'') l ...
for an explanation of the selective advantages of this). However, if it makes too many mutations, it may lose some of its biological features which have evolved to its advantage, including its ability to reproduce at all.
The question arises: ''how many mutations can be made during each replication before the population of viruses begins to lose self-identity?''
Basic mathematical model
Consider a virus which has a genetic identity modeled by a string of ones and zeros (e.g. 11010001011101....). Suppose that the string has fixed length ''L'' and that during replication the virus copies each digit one by one, making a mistake with probability ''q'' independently of all other digits.
Due to the mutations resulting from erroneous replication, there exist up to ''2
L'' distinct strains derived from the parent virus. Let ''x
i'' denote the concentration of strain ''i''; let ''a
i'' denote the rate at which strain ''i'' reproduces; and let ''Q
ij'' denote the probability of a virus of strain ''i'' mutating to strain ''j''.
Then the rate of change of concentration ''x
j'' is given by
:
At this point, we make a mathematical idealisation: we pick the fittest strain (the one with the greatest reproduction rate ''a
j'') and assume that it is unique (i.e. that the chosen ''a
j'' satisfies ''a
j > a
i'' for all ''i''); and we then group the remaining strains into a single group. Let the concentrations of the two groups be ''x , y'' with reproduction rates ''a>b'', respectively; let ''Q'' be the probability of a virus in the first group (''x'') mutating to a member of the second group (''y'') and let ''R'' be the probability of a member of the second group returning to the first (via an unlikely and very specific mutation). The equations governing the development of the populations are:
:
We are particularly interested in the case where ''L'' is very large, so we may safely neglect ''R'' and instead consider:
:
Then setting ''z = x/y'' we have
:
.
Assuming ''z'' achieves a steady concentration over time, ''z'' settles down to satisfy
:
(which is deduced by setting the derivative of ''z'' with respect to time to zero).
So the important question is ''under what parameter values does the original population persist (continue to exist)?'' The population persists if and only if the steady state value of ''z'' is strictly positive. i.e. if and only if:
:
This result is more popularly expressed in terms of the ratio of ''a:b'' and the error rate ''q'' of individual digits: set ''b/a = (1-s)'', then the condition becomes
:
Taking a logarithm on both sides and approximating for small ''q'' and ''s'' one gets
:
reducing the condition to:
:
RNA viruses which replicate close to the error threshold have a genome size of order 10
4 (10000)
base pairs. Human
DNA is about ''3.3'' billion (10
9) base units long. This means that the replication mechanism for human DNA must be
orders of magnitude
An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
more accurate than for the RNA of RNA viruses.
Information-theory based presentation
To avoid error catastrophe, the amount of information lost through mutation must be less than the amount gained through natural selection. This fact can be used to arrive at essentially the same equations as the more common differential presentation.
[M. Barbieri, ''The Organic Codes'', p. 140]
The information lost can be quantified as the genome length ''L'' times the replication error rate ''q''. The probability of survival, ''S'', determines the amount of information contributed by natural selection— and
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
is the negative log of probability. Therefore, a genome can only survive unchanged when
:
For example, the very simple genome where ''L = 1'' and ''q = 1'' is a genome with one bit which always mutates. Since ''Lq'' is then 1, it follows that S has to be ½ or less. This corresponds to half the offspring surviving; namely the half with the correct genome.
Applications
Some viruses such as
polio
Poliomyelitis, commonly shortened to polio, is an infectious disease caused by the poliovirus. Approximately 70% of cases are asymptomatic; mild symptoms which can occur include sore throat and fever; in a proportion of cases more severe s ...
or
hepatitis C operate very close to the critical mutation rate (i.e. the largest ''q'' that ''L'' will allow). Drugs have been created to increase the mutation rate of the viruses in order to push them over the critical boundary so that they lose self-identity. However, given the criticism of the basic assumption of the mathematical model, this approach is problematic.
The result introduces a
Catch-22
''Catch-22'' is a satirical war novel by American author Joseph Heller. He began writing it in 1953; the novel was first published in 1961. Often cited as one of the most significant novels of the twentieth century, it uses a distinctive non-ch ...
mystery for biologists,
Eigen's paradox: in general, large genomes are required for accurate replication (high replication rates are achieved by the help of
enzymes), but a large genome requires a high accuracy rate ''q'' to persist. Which comes first and how does it happen? An illustration of the difficulty involved is ''L'' can only be 100 if ''q is 0.99 - a very small string length in terms of genes.
See also
*
Error threshold
*
Extinction vortex
Extinction vortices are a class of models through which conservation biologists, geneticists and ecologists can understand the dynamics of and categorize extinctions in the context of their causes. This model shows the events that ultimately lead ...
*
Mutational meltdown
In evolutionary genetics, mutational meltdown is a sub class of extinction vortex in which the environment and genetic predisposition mutually reinforce each other. Mutational meltdown (not to be confused with the concept of an error catastrophe) ...
References
External links
Error catastrophe and antiviral strategyExamining the theory of error catastrophe
{{DEFAULTSORT:Error Catastrophe
Pathology
Population genetics