翻訳と辞書 Words near each other ・ Error (disambiguation) ・ Error (Error EP) ・ Error (law) ・ Error (linguistics) ・ Error (song) ・ Error (VIXX EP) ・ Error 33 ・ Error account ・ Error amplifier (electronics) ・ Error analysis ・ Error analysis (linguistics) ・ Error analysis (mathematics) ・ Error analysis for the Global Positioning System ・ Error bar ・ Error card ・ Error catastrophe ・ Error code ・ Error concealment ・ Error correction mode ・ Error correction model ・ Error detection and correction ・ Error Detection and Handling ・ Error diffusion ・ Error exponent ・ Error floor ・ Error function ・ Error guessing ・ Error hiding ・ Error in Evolution ・ Error in the System Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Error catastrophe ： ウィキペディア英語版 Error catastrophe Error catastrophe is the extinction of an organism (often in the context of microorganisms such as viruses) as a result of excessive mutations. Error catastrophe is something predicted in mathematical models and has also been observed empirically.〔(Action of mutagenic agents and antiviral inhibitors on foot-and-mouth disease virus, Virus Res. 2005 )〕 Like every organism, viruses 'make mistakes' (or mutate) during replication. The resulting mutations increase biodiversity 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 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 ''2L'' distinct strains derived from the parent virus. Let ''xi'' denote the concentration of strain ''i''; let ''ai'' denote the rate at which strain ''i'' reproduces; and let ''Qij'' denote the probability of a virus of strain ''i'' mutating to strain ''j''. Then the rate of change of concentration ''xj'' is given by :$\backslash dot\_j\; =\; \backslash sum\_i\; a\_i\; Q\_\; x\_i$ At this point, we make a mathematical idealisation: we pick the fittest strain (the one with the greatest reproduction rate ''aj'') and assume that it is unique (i.e. that the chosen ''aj'' satisfies ''aj > ai'' 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: :$$ \begin \dot = & a(1-Q)x + bRy \\ \dot = & aQx + b(1-R)y \\ \end We are particularly interested in the case where ''L'' is very large, so we may safely neglect ''R'' and instead consider: :$$ \begin \dot = & a(1-Q)x \\ \dot = & aQx + by \\ \end Then setting ''z = x/y'' we have :$$ \begin \frac & = & \frac} \\ && \\ & = & \frac \\ && \\ & = & a(1-Q)z - (aQz^2 +bz) \\ && \\ & = & z(a(1-Q) -aQz -b) \\ \end . Assuming ''z'' achieves a steady concentration over time, ''z'' settles down to satisfy :$z(\backslash infty)\; =\; \backslash frac$ (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: :$z(\backslash infty)\; >\; 0\; \backslash iff\; a(1-Q)-b\; >0\; \backslash iff\; (1-Q)\; >\; b/a\; .$ 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 :$z(\backslash infty)\; >\; 0\; \backslash iff\; (1-Q)\; =\; (1-q)^L\; >\; 1-s$ Taking a logarithm on both sides and approximating for small ''q'' and ''s'' one gets :$L\; \backslash ln\; \backslash approx\; -Lq\; >\; \backslash ln\; \backslash approx\; -s$ reducing the condition to: : RNA viruses which replicate close to the error threshold have a genome size of order 104 base pairs. Human DNA is about ''3.3'' billion (109) base units long. This means that the replication mechanism for DNA must be orders of magnitude more accurate than for RNA. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Error catastrophe」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.