73.183.64.164: improve

2014-07-11T21:02:48Z

improve

en>Ted0673: Added examples, references, calculator

2014-02-04T06:09:34Z

Added examples, references, calculator

New page

[[Image:Luria-delbruck diagram.svg|thumb|The two possibilities tested by the Luria–Delbrück experiment. (A) If mutations are induced by the media, roughly the same number of mutants are expected to appear on each plate. (B) If mutations arise spontaneously during cell divisions prior to plating, each plate will have a highly variable number of mutants.]]

The '''Luria–Delbrück experiment''' (1943) (also called the '''Fluctuation Test''') demonstrates that in [[bacteria]], genetic [[mutation]]s arise in the absence of [[selection]], rather than being a response to selection. Therefore, [[Charles Darwin|Darwin]]'s theory of [[natural selection]] acting on random mutations applies to bacteria as well as to more complex organisms. [[Max Delbrück]] and [[Salvador Luria]] won the 1969 [[Nobel Prize in Physiology or Medicine]] in part for this work.

==History==

By the 1940s the ideas of inheritance and mutation were generally accepted, though the role of DNA as the hereditary material had not yet been established. It was thought that bacteria were somehow different and could develop heritable genetic mutations depending on the circumstances they found themselves: in short was mutation in bacteria pre-adaptive (random) or post-adaptive (directed adaption)? Luria ([[James Watson]]'s [[PhD]] advisor) in particular was obsessed with this idea and was determined to test it. He conceived the experiment at a faculty dance at [[Indiana University]] while watching a [[slot machine]].<ref name=Luria1984>Luria SE (1984) A slot machine, a broken test tube: An autobiography. Harper & Row</ref>

In their experiment, Luria and Delbrück inoculated a small number of bacteria (''[[Escherichia coli]]'') into separate [[microbiological culture|culture]] tubes. After a period of growth, they plated equal volumes of these separate cultures onto [[agar]] containing the T1 [[bacteriophage|phage]] (virus). If resistance to the virus in bacteria were caused by an induced activation in bacteria i.e. if resistance were not due to heritable genetic components, then each plate should contain roughly the same number of resistant colonies.
Assuming a constant rate of mutation, Luria hypothesized that if mutations occurred after and in response to exposure to the selective agent, the number of survivors would be distributed according to a [[Poisson distribution]] with the [[mean]] equal to the [[variance]]. This was not what Delbrück and Luria found: Instead the number of resistant colonies on each plate varied drastically: the variance was considerably greater than the mean.

Luria and Delbrück proposed that these results could be explained by the occurrence of a constant rate of random mutations in each generation of bacteria growing in the initial culture tubes. Based on these assumptions Delbrück derived a [[probability distribution]] (now called the [[Luria–Delbrück distribution]]<ref>{{cite doi|10.1016/S0025-5564(99)00045-0}}</ref><ref name=Sheng2010>{{cite journal | last1 = Zheng | first1 = Q. | year = 2010 | title = The Luria-Delbrück distribution: early statistical thinking about evolution | url = | journal = Chance | volume = 23 | issue = | pages = 15–18 }}</ref>) that gives a relationship between moments consistent with the experimentally obtained values. The distribution that follows from the directed adaptation hypothesis (the Poisson distribution) predicted moments inconsistent with the data. Therefore, the conclusion was that mutations in bacteria, as in other organisms, are [[random]] rather than directed.<ref name="Luria 1943 491–511">{{cite journal |last=Luria |first=S. E. |authorlink= |coauthors=Delbrück, M. |year=1943 |month= |title=Mutations of Bacteria from Virus Sensitivity to Virus Resistance |journal=[[Genetics (journal)|Genetics]] |volume=28 |issue=6 |pages=491–511 |id= |url=http://www.genetics.org/cgi/reprint/28/6/491 |accessdate= |quote= }}</ref>

The results of Luria and Delbrück were confirmed in more graphical, but less quantitative, way by Newcombe. Newcombe [[incubator (microbiology)|incubated]] bacteria in a [[Petri dish]] for a few hours, then [[replica plating|replica plated]] it onto two new Petri dishes treated with phage. The first plate was left unspread, and the second plate was then respread, that is, bacterial cells were moved around allowing single cells in some colony to form their own new colonies. If colonies contained resistant bacterial cells before entering into contact with the phage virus, one would expect that some of these cells would form new resistant colonies on the respread dish and so to find a higher number of surviving bacteria there. When both plates were incubated for growth, there were actually as much as 50 times greater number of bacterial colonies on the respread dish. This showed that bacterial mutations to virus resistance had randomly occurred during the first incubation. Once again, the mutations occurred before selection was applied.<ref>{{cite journal |last=Newcombe |first=H. B. |authorlink= |coauthors= |year=1949 |month= |title=Origin of Bacterial Variants |journal=[[Nature (journal)|Nature]] |volume=164 |issue= 4160|pages=150–151 |doi= 10.1038/164150a0|url= |accessdate= |quote= |bibcode = 1949Natur.164..150N }}</ref>

More recently, the results of Luria and Delbrück were questioned by Cairns and others, who studied mutations in sugar [[metabolism]] as a form of environmental stress.<ref>{{cite journal |last=Cairns |first=J. |authorlink= |coauthors=Overbaugh, J.; Miller, S. |year=1988 |month= |title=The Origin of Mutants |journal=Nature |pmid=3045565 |volume=335 |issue=6186 |pages=142–145 |doi=10.1038/335142a0 |url= |accessdate= |quote= |bibcode = 1988Natur.335..142C }}</ref> Some scientists suggest that this result may have been caused by selection for gene amplification and/or a higher [[mutation rate]] in cells unable to divide.<ref>{{cite journal |last=Slechta |first=E. S. |authorlink= |coauthors= Liu, J.; Andersson, D. I.; Roth, J. R. |year=2002 |month= |title=Evidence that selected amplification of a bacterial lac frameshift allele stimulates Lac(+) reversion (adaptive mutation) with or without general hypermutability |journal=[[Genetics (journal)|Genetics]] |pmid=12136002 |volume=161 |issue=3 |pmc=1462195 |pages=945–956 |id= |url=http://www.genetics.org/cgi/content/full/161/3/945 |accessdate= |quote= }}</ref> Others have defended the research and propose mechanisms which account for the observed phenomena consistent with adaptive mutagenesis.<ref>{{cite journal |last=Foster |first=Patricia L. |authorlink= |coauthors= |year=2004 |month= |title=Adaptive Mutation in Escherichia coli |journal=[[Journal of Bacteriology]] |pmid= |volume=186 |issue=15 |pmc= |pages=4846-4852 |id= |url=http://jb.asm.org/content/186/15/4846.full |accessdate= |quote= }}</ref>

This distribution appears to have been first determined by [[J. B. S. Haldane|Haldane]].<ref name=Sarkar1991>{{cite journal | last1 = Sarkar | first1 = S | year = 1991 | title = Haldane's solution of the Luria-Delbruck distribution | url = | journal = Genetics | volume = 127 | issue = 2| pages = 257–261 | pmc=1204353}}</ref> An unpublished manuscript was discovered in 1991 in at [[University College London]] describing this distribution. The derivation is different but the results are difficult to compute without the use of a computer.

==Description of the test==

A small number of cells are used to inoculate parallel cultures in a non-selective medium.<ref name=Hall2009>{{cite journal | last1 = Hall | first1 = BM | last2 = Ma | first2 = CX | last3 = Liang | first3 = P | last4 = Singh | first4 = KK | year = 2009 | title = Fluctuation analysis CalculatOR: a web tool for the determination of mutation rate using Luria-Delbruck fluctuation analysis | url = | journal = Bioinformatics | volume = 25 | issue = 12| pages = 1564–1565 }}</ref> The cultures are grown to saturation to obtain equal cell densities. The cells are plated onto selective media to obtain the number of mutants (''r''). Dilutions are plated onto rich medium to calculate the total number of viable cells ( ''N''t ). The number of mutants that appear in the saturated culture is a measure of both the mutation rate and when the mutants arise during the growth of the culture: mutants appearing early in the growth of the culture will propagate many more mutants than those that arise later during growth. These factors cause the frequency ( ''r'' / ''N''t ) to vary greatly, even if the number of mutational events ( ''m'' ) is the same. Frequency is not a sufficiently accurate measure of mutation and the mutation rate (''m'' / ''N''t) should always be calculated.

The estimation of the mutation rate (''m'') is complex. Luria and Delbruck estimated this parameter from the [[mean]] of the distribution but this estimator was subsequently shown to be biased. The method of the [[median]] was introduced in 1949.<ref name=Lea1949>{{cite journal | last1 = Lea | first1 = DE | last2 = Coulson | first2 = CA | year = 1949 | title = The distribution of the numbers of mutants in bacterial populations | url = | journal = J Genet | volume = 49 | issue = | pages = 264–285 }}</ref> This method is based on the equation

: <math> \frac{ r }{ m } - \ln( m ) - 1.24 = 0 .</math>

This method has since been improved on but these more accurate methods are complex. The Ma-Sandri-Sarkar [[maximum likelihood]] estimator is currently the best known [[estimator]].<ref name=Zheng2000>{{cite journal | last1 = Zheng | first1 = Q | year = 2000 | title = Statistical and algorithmic methods for fluctuation analysis with SALVADOR as an implementation | url = | journal = Math Biosci | volume = 176 | issue = 2| pages = 237–252 }}</ref> A number of additional methods and estimates from experimental data have been described.<ref name=Rosche2000>{{cite journal | last1 = Rosche | first1 = WA | last2 = Foster | first2 = PL | year = 2000 | title = Determining mutation rates in bacterial populations | url = | journal = Methods | volume = 20 | issue = 1| pages = 4–17 }}</ref>

A freely available programme for the calculation of the mutation rate (Falcor) has been published.<ref name="Hall2009"/>
A worked example is shown in this paper by Jones ''et al''.<ref name=Jones1994>Jones ME, Thomas SM, Rogers A (1994) Luria-Delbruk experiments: Design and analysis. Genetics 136: 1209-1216</ref>

==Distribution==

In all these models the mutation rate (''m'') and growth rates (''β'') are assumed to be constant. If these conditions are not applicable to the experiment the results may differ from the model. These rates are likely to differ in non experimental settings. The models also require that ''N''t ''m'' >> 0 where ''N''t is the total number of organisms. This assumption is likely to hold in most realistic or experimental settings.

Luria and Delbrück<ref name="Luria 1943 491–511"/> estimated the mutation rate from the equation

: <math> \mu = \frac{ \beta \log( \rho ) }{ 1 - \exp(- \beta t ) } </math>

where ''β'' is the cellular growth rate, ''t'' is the time and

: <math> \rho = \frac{ N_s }{ N } </math>

where ''N''s is the number of cultures without resistant bacteria and ''N'' is the total number of cultures.

Lea and Coulson's model<ref name="Lea1949"/> differed from the original in that the considered a collection of independent [[Birth–death process|Yule process]]es (a filtered [[Poisson process]]). Numerical comparisons of these two models with realistic values of the parameters has shown that they differ only slightly.<ref name=Zheng1999>Zheng Q (1999) Progress of a half century in the study of the Luria–Delbrück distribution. Mathematical Biosciences 162 (1–2) 1–32</ref> The [[generating function]] for the this model was found by Bartlett in 1978<ref name=Bartlett1978>Bartlett M. (1978) An introduction to stochastic processes. Cambridge University Press, Cambridge, 3rd edition</ref> and is

: <math> G( z, \mu, \phi) = \exp\left( \frac{ \mu }{ \phi }\left( \frac{ 1 }{ z } - 1 \right) \log\left( 1 - \phi z \right) \right)</math>

where ''μ'' is the mutation rate (assumed to be constant), ''φ'' = 1 - ''e''-βt with ''β'' as the cellular growth rate (also assumed to be constant) and ''t'' as the time.

The determination of ''μ'' from this equation has proved difficult but a solution was discovered in 2005{{Citation needed|date=December 2013}}. Differentiation of the generating function with respect to ''μ'' allows the application of the [[Newton-Raphson]] method which together with the use of a [[score function]] allows one to obtain [[confidence interval]]s for ''μ''.

==Molecular biology==

The mechanism of resistance to the phage T1 appears to have been due to mutations in the ''fhu''A gene - a membrane protein that acts as the T1 receptor.<ref name=Carvajal-Rodríguez2012>{{cite doi|10.1002/bmb.20615}}</ref> The ''ton''B gene product is also requited for infection by T1. The FhuA protein is actively involved in the transport of [[ferrichrome]], [[albomycin]] and [[rifamycin]].<ref name=Endriss2003>{{cite journal | last1 = Endriss | first1 = F | last2 = Braun | first2 = M | last3 = Killmann | first3 = H | last4 = Braun | first4 = V | year = 2003 | title = Mutant analysis of the Escherichia coli FhuA protein reveals sites of FhuA activity | url = | journal = J Bacteriol | volume = 185 | issue = 16| pages = 4683–4692 }}</ref> It also confers sensitivity to [[microcin J25]] and [[colicin M]] and acts as a receptor for the phages T5 and phi80 as well as T1.

The FhuA protein has a beta-barrel domain (residues 161 to 714) that is closed by a globular cork domain (residues 1 to 160).<ref name=Killmann2001>{{cite journal | last1 = Killmann | first1 = H | last2 = Braun | first2 = M | last3 = Herrmann | first3 = C | last4 = Braun | first4 = V | year = 2001 | title = FhuA barrel-cork hybrids are active transporters and receptors | url = | journal = J Bacteriol | volume = 183 | issue = 11| pages = 3476–3487 }}</ref> Within the cork domain is the TonB binding region (residues 7 to 11). The large membrane spanning monomeric β-barrel domains have 22 β-strands of variable length, several of which extend significantly beyond the membrane hydrophobic core into the extracellular space. There are 11 extracellular loops numbered L1 to L11. The L4 loop is where the T1 phage binds.

==References==
{{reflist|2}}

==External links==
*[http://virtuallaboratory.net/Biofundamentals/labs/OnMutation/OnMutation.html On Mutation lab]
* [http://profiles.nlm.nih.gov/ps/retrieve/Collection/CID/QL Profiles in Science: The Salvador E. Luria Papers] Information on Salvador Luria from the National Library of Medicine
{{History of biology}}

{{DEFAULTSORT:Luria-Delbruck experiment}}
[[Category:Biology experiments]]
[[Category:Genetics experiments]]
[[Category:Statistical genetics]]
[[Category:Bacteria]]
[[Category:1943 in science]]

Expected return - Revision history

73.183.64.164: improve

en>Ted0673: Added examples, references, calculator