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pathogenesis of diverse diseases, but it will also be exciting to discover how this novel toxin has exploited eukaryotic cell biology to accomplish its effects. Acknowledgements We thank Eric Hansen, James Kaper, Lawrence Dreyfus, Eric Oswald, Nancy Strockbine and Daniel Scott for stimulating discussions and the NIH for financial support (AI41477). References 1 Johnson, W.M. and Lior, H. (1987) FEMS Microbiol. Lett. 43, 19–23 2 Johnson, W.M. and Lior, H. (1987) FEMS Microbiol. Lett. 48, 235–238 3 Johnson, W.M. and Lior, H. (1988) Microb. Pathog. 4, 115–126 4 Johnson, W.M. and Lior, H. (1988) Microb. Pathog. 4, 103–111 5 Pérès, S.Y. et al. (1997) Mol. Microbiol. 24, 1095–1107 6 Comayras, C. et al. (1997) Infect. Immun. 65, 5088–5095 7 Whitehouse, C.A. et al. (1998) Infect. Immun. 66, 1934–1940 8 Sugai, M. et al. (1998) Infect. Immun. 66, 5008–5019 9 Cortes-Bratti, X. et al. (1999) J. Clin. Invest. 103, 107–115 10 Shenker, B. et al. (1999) J. Immunol. 162, 4773–4780
11 Aragon, V., Chao, K. and Dreyfus, L.A. (1997) Infect. Immun. 65, 3774–3780 12 Scott, D.A. and Kaper, J.B. (1994) Infect. Immun. 62, 244–251 13 Pickett, C.L. et al. (1994) Infect. Immun. 62, 1046–1051 14 Pickett, C.L. et al. (1996) Infect. Immun. 64, 2070–2078 15 Okuda, J., Kurazono, H. and Takeda, Y. (1995) Microb. Pathog. 18, 167–172 16 Cope, L.D. et al. (1997) Proc. Natl. Acad. Sci. U. S. A. 94, 4056–4061 17 Mayer, M.P.A. et al. (1999) Infect. Immun. 67, 1227–1237 18 Purven, M. et al. (1997) Infect. Immun. 65, 3496–3499 19 Okuda, J. et al. (1997) Infect. Immun. 65, 428–433 20 Bouzari, S. and Varghese, A. (1990) FEMS Microbiol. Lett. 71, 193–198 21 Guth, B.E.C. et al. (1994) Can. J. Microbiol. 40, 341–344 22 Albert, M.J. et al. (1996) J. Clin. Microbiol. 34, 717–719 23 Eyigor, A. et al. (1999) Appl. Environ. Microbiol. 65, 1646–1650 24 Ohya, T., Tominaga, K. and Nakazawa, M. (1993) J. Vet. Med. Sci. 55, 507–509 25 Purven, M., Falsen, E. and Lagergard, T. (1995) FEMS Microbiol. Lett. 129, 221–224 26 Bag, P., Ramamurthy, T. and Nair, U. (1993) FEMS Microbiol. Lett. 114, 285–292
Evolution of Wolbachia pipientis transmission dynamics in insects Elizabeth A. McGraw and Scott L. O’Neill
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olbachia are obligate, Wolbachia pipientis is an intracellular general way, Wolbachia and intracellular bacterial bacterial parasite of arthropods that its hosts are ideal candidates parasites that infect enhances its transmission by manipulating for the study of mechanisms of an extremely wide range of inhost reproduction, most commonly by host–parasite interaction and vertebrates, including 15–20% inducing cytoplasmic incompatibility. The the evolution of infectious disof insect species sampled1, discovery of isolates with modified eases, specifically host resistcytoplasmic incompatibility phenotypes crustaceans2, arachnids3 and ance, parasite virulence and even nematodes4. The appar- and others with novel virulence properties transmission dynamics. The ent ubiquity of these bacteria is an indication of the potential breadth of recent discovery of Wolbachia evolutionary strategies employed by and their diverse range of efvariants that are unique in fects on host reproduction, Wolbachia. their expression of virulence6 many of which lead to producand degree of host manipution of non-viable offspring E.A. McGraw and S.L. O’Neill* are in the Section of lation7 has expanded our view Vector Biology, Dept of Epidemiology and Public and skewing of sex ratios, have of the evolutionary strategies Health, Yale University School of Medicine, sparked intense research interemployed by these bacteria. 60 College St, New Haven, CT 06520, USA. est. A significant number of *tel: 11 203 785 3285, fax: 11 203 785 4782, the major insect pests of crops Effects on host reproduction e-mail:
[email protected] and livestock and insects reAlthough there is indirect evisponsible for the spread of dence of rare horizontal transhuman infectious diseases (such as African trypano- mission8,9, Wolbachia are primarily transmitted vertisomiasis and dengue fever) are also infected with cally from mother to offspring and have evolved to Wolbachia. It has been proposed that the changes in manipulate host reproduction. Wolbachia infection host reproduction induced by these bacteria could be produces various effects in hosts, including feminizused to control populations of insects that are im- ation, parthenogenesis and cytoplasmic incompatiportant for economic and health reasons5. In a more bility (CI) (Ref. 1). Feminization is seen in the crustacean, 0966-842X/99/$ - see front matter © 1999 Elsevier Science. All rights reserved. TRENDS
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Armadillidium vulgare (more commonly known as pillbugs), where genetic males develop as functional phenotypic females, resulting in female-biased broods and increased opportunity for maternal transmission of the parasite10. Wolbachia-induced parthenogenesis is commonly studied in wasps of the genus Trichogramma and occurs when unfertilized eggs (normally male in hymenopterans) develop into adult females11, again increasing opportunities for maternal transmission. In some hosts, including the fruitfly Drosophila, these parasites cause CI, which results in embryonic death. CI is expressed in certain crosses involving parents with different infection status and is most common between Wolbachia-infected males and uninfected females. The reciprocal cross, and crosses between flies that are infected with the same Wolbachia strain, lead to viable offspring. The cause of embryonic death is an incompatibility between sperm and egg. Although the biochemical basis of CI is not well understood, it is clear that infected males produce mature sperm that do not contain Wolbachia, but that have been modified by the bacteria that were present in the immature spermatids. Viability following fertilization by modified sperm requires rescue of the defect by interaction with Wolbachia-infected egg cytoplasm12. The eggs produced by infected females are compatible with unmodified sperm and with sperm produced by males infected with the same strain. As a result, the presence of infected males in a population serves to prevent reproduction by uninfected females. Infected females therefore make a greater contribution of offspring to the next generation and the proportion of infected hosts increases with each successive generation. In this way, Wolbachia can effectively and rapidly invade host populations. This is independent of the direct effects of infection on host fitness, which are predominantly mild and range from slightly deleterious to weakly positive13–16. The success of any particular mating is further complicated by the observation that CI also occurs between hosts that carry different Wolbachia strains (Fig. 1a). Depending on the particular parasite–host combination, the level of embryo lethality induced in an incompatible cross can range from complete egg mortality to a partial reduction in egg hatch. Multiple infections involving distinct strains, within a single host individual, have been identified and these create further diversity of CI crossing types (Fig. 1b). Double infections have been isolated from natural populations17–19 and double and triple infections have been created in the laboratory20,21. Factors that affect the rate of spread of Wolbachia infection The Wolbachia Riverside strain (wRi), which infects Drosophila simulans, clearly demonstrates the ability of this bacterium to sweep rapidly through host populations. Monitoring its distribution has revealed its natural spread through Drosophila populations in northern California at a rate of 100 km y–1 (Ref. 22). The study of Wolbachia population sweeps has led to
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the identification of several environmental and hostphysiological factors that could work to slow the spread of infections in natural populations. For Drosophila reared in the laboratory, conditions of crowding and nutritional stress lead to decreased vertical transmission23,24. It also appears that maternal transmission is imperfect in nature: females rarely pass on Wolbachia to all of their offspring25. Similarly, a reduction in the bacterial density carried by males26, a common result of aging that leads to a decline in sperm modification27, might lessen CI expression and, consequently, allow uninfected females to produce offspring. Lastly, exposure of hosts to naturally occurring antibiotics could mimic effects seen in the laboratory, where such treatment leads to clearing of the Wolbachia infection and loss of the associated phenotypes28,29. Modification and rescue variants Screening of Drosophila strains has identified males infected with Wolbachia that do not modify host sperm and hence do not induce CI. Many such variants have been characterized as mod2resc1 (Refs 7,30,31) because they lack only the modification phenotype associated with male infection.The majority of these non-inducers are able to rescue sperm modification when their female hosts are mated with males harbouring other, closely related mod1 Wolbachia strains (Fig. 1c). Their existence is at first counterintuitive. Without the ability to cause CI, how can these strains spread through populations? One possible scenario is that host populations are infected in waves with Wolbachia of various CI phenotypes30–32 (Fig. 2). A mod2resc1 mutant could arise in an infected population and spread by ‘parasitizing’ the modification effect of the resident mod1resc1 strain. As the mod2resc1 strain increases in frequency, the rescue phenotype would become superfluous, which would allow a mod2resc2 variant to invade successfully. A population dominated by mod2resc2 Wolbachia would be vulnerable to any new isolate possessing full CI capabilities (mod1resc1) (Refs 30,31). Theoretical work shows that this scenario hinges on the assumption of near-perfect maternal transmission of mod2resc1 isolates32 and a genetic cost for Wolbachia to maintain the mod1 and resc1 phenotypes33. In fact, several mod2resc1 strains do demonstrate near-perfect vertical transmission7,34, lending support to this model. One prediction of this evolutionary framework is that mod2resc1 isolates should be sampled from natural populations that also contain compatible mod1 isolates (Fig. 2). Few data exist except for a Wolbachia infection of D. simulans called Coffs Harbour (wAu), found in Australia, that is mod2resc1, but is unable to rescue the only mod1resc1 Wolbachia infection present in the same population, wRi (Ref. 7). The wRi infection is known to spread rapidly22 and Coffs Harbour might therefore be a remnant from a previous infection cycle, where it was able to rescue another D. simulans infection that has since been lost. However, more sampling might uncover compatible combinations of mod2resc1 and mod1resc1 Wolbachia strains in a given host population.
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Fig. 1. Cytoplasmic incompatibility (CI) for single, double and mod2resc1 Wolbachia infections of Drosophila spp. Strains are most commonly named for the geographic region of isolation: wAu, Coffs Harbour; wMel, Vienna, Austria; wHa, Hawaii; wKi, Mt Kilimanjaro; wMa, Mauritania; w No, Noumea; w Ri, Riverside, California. White flies are uninfected; red flies are infected, but not with a specific strain; blue flies are infected with w Ha; yellow flies are infected with wNo; green flies are infected with either wKi, wAu, or wMa. Names in black have been isolated from Drosophila simulans and those in blue are found in Drosophila melanogaster. Each strain is listed on the horizontal bars in a position that corresponds to the level of CI it induces. (a) Basic crosses involving common single infections 18,46. The third cross demonstrates unidirectional incompatibility, because there is no reduction in survival in the reciprocal cross. The fifth and sixth crosses illustrate bidirectional incompatibility between wHa- and wNo (Ref. 47)-infected D. simulans as both crosses are highly incompatible. (b) CI between D. simulans carrying either a single infection (wHa) or a double infection (wHa and wNo). (c) Crosses involving strains that lack the modification phenotype (i.e. are mod2), only one of which (wKi) has been shown to be resc1 (Ref. 31). The last cross shows the outcome of a mating between flies infected with a mod2resc1 and a mod1resc1 strain.
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In order to explain the presence of modification and rescue phenotypic variants in populations, we need to determine if they have other characteristics that would assure their presence in a population without an evolutionary cycling scenario. Are the variants dissimilar only in their ability to express components of CI, or are there other factors, such as transmission efficiencies and effects on hosts, that may be variable? Currently, we only have snapshots of their distributions in populations, which makes it difficult to find support for cyclical patterns and long-term evolutionary scenarios. Studies of flies in cages that test the fate of variants in mixed populations could reveal the dynamic stability of strain coexistence. These experiments could also address the question of whether there is a fitness cost to Wolbachia of maintaining both modification and rescue phenotypes.
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Virulent Wolbachia: the popcorn phenotype Recently, a new phenotype caused by Wolbachia infection was discovered in a laboratory strain of Drosophila melanogaster that was exhibiting premature death6. Examination revealed that the flies were infected with a Wolbachia strain that was multiplying rapidly in the adult host nervous tissue. This isolate has been descriptively named popcorn for its characteristic effect
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transmission efficiency. Within an individual arthropod host, there appears to be a threshold level of infection required for reliable vertical transmission of Wolbachia17,24,35 but there is no evidence of a correlation between continuously increasing bacterial density and elevated transmission.
Fig. 2. Proposed evolutionary scenario for the cycling of modification and rescue phenotypic variants in a population30–32. The colours represent Wolbachia infections with different modification and rescue capacities: white, uninfected; red, mod1resc1; yellow, mod2resc1; blue, mod2resc2.
on brain cells, which become distended and rupture in response to increasing numbers of bacteria. Preliminary experiments indicate that this strain does not induce CI. Whether popcorn is a mod2resc2 or a mod2resc1 strain has yet to be determined, but the striking effect on its host marks it as the most phenotypically divergent Wolbachia strain identified to date in insects. Because popcorn is unique, it is still unclear whether it is a product of laboratory rearing that would never spread in a natural population or whether similar mutants have gone undetected because the phenotypic effects occur late in life6. With little information known about the mutant’s prevalence, origin and fitness, we can only speculate about the forces that have shaped its evolution. According to the predicted evolutionary scenario for Wolbachia strains that do not induce CI (Fig. 2), a variant like popcorn would only be a temporary inhabitant of any population. However, its greater virulence is reminiscent of a more traditional pathogenic lifestyle, in which increases in bacterial replication rate could be coupled with greater infectious
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Horizontal transfer The incongruent phylogenies of Wolbachia and the hosts it infects have led to the hypothesis of horizontal transfer of Wolbachia between host lineages (Fig. 3)8,9. The most distantly related strains of Wolbachia pipientis are estimated to have diverged ~60–100 million years ago, which is well after the divergence of even closely related host lineages2,36. Although there is no evidence of natural horizontal transmission, laboratory experiments have demonstrated horizontal transfer of Wolbachia in the isopod Armadillidium vulgare37 following injury and exposure to hemolymph, or by microinjection of Wolbachia38–41. Evidence does exist for transmission between parasitic wasps and their host insects35, but such scenarios are unlikely to explain the diversity of all horizontal transmission events36. If transmission events occur by injury, high densities of Wolbachia and proliferation in multiple tissues would be advantageous for the horizontal spread of infection. Perhaps the popcorn phenotype has evolved from a mod2resc2 progenitor and now exploits a more traditional niche, in which horizontal transmission can be achieved and the inability to induce CI is no longer detrimental to its survival.
The novel host theory Alternatively, the popcorn phenotype could be the result of a recent transfer from a host dissimilar to D. melanogaster. One tenet of the host–parasite theory has been that novel host–parasite relationships are likely to be poorly adapted, whereas old associations should have evolved to stable equilibrium points, where a balance has been achieved between parasite virulence and transmission efficiency42. In general, natural horizontal transmission of Wolbachia into phylogenetically diverse hosts contradicts a scenario dependent on coevolution of highly specialized adaptations by both host and parasite. There is limited support for the novel host theory. For instance, a recent study involving isopods found a premature-death effect in males, similar to that of popcorn, following transinfection of Wolbachia from one species to another43. In addition, transinfection of Wolbachia from D. simulans into Drosophila serrata led to the retention of high levels of CI expression, but parasite transmission was comparatively lower and the new host suffered a fitness cost (decreased fecundity)41.
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wsp gene tree
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Drosophila simulans Drosophila melanogaster
Drosophila melanogaster
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Drosophila simulans Aedes albopictus
Fig. 3. The incongruence between a host phylogeny, including Drosophila spp. and Aedes albopictus (mosquito), and a wsp (Wolbachia surface protein) gene tree. Lineages A and B correspond to the two major subdivisions within Wolbachia pipientis48.
Maladaptation in natural populations is likely to be transient and might be difficult to detect. More often, it appears that the flexibility of Wolbachia is the rule, perhaps as a result of the use of highly conserved host pathways for interaction. Inter-strain competition Another explanation for the increased reproductive rate of popcorn is that it is the product of inter-strain competition that occurred during a double infection44,45. Competition is a result of resource limitation, however, and preliminary data contradict such a scenario because they suggest that, for laboratory constructed dual infections, both strains grow to densities similar to those of single infections21 (S.L. O’Neill, unpublished). Additionally, theoretical work suggests that increases in reproductive outputs can evolve even in the absence of competitive pressure from another Wolbachia strain32. Future directions Wolbachia evolution in most insects has led to the dominance of a single CI phenotype and a low to nonexistent level of virulence. This limited diversity is, in part, a result of the rapid spread of single infections28,43 and constraints on the host–parasite relationship that are yet to be understood. However, there is some degree of phenotypic diversity in CI expression and virulence, and by virtue of their differences, these variants are the most obvious candidates for future study. The excitement surrounding the discovery of popcorn must be tempered by its potential rarity. Although the mutant will provide much information about the genetic basis for control of reproductive rate, it might not represent a phenotype capable of surviving in a natural population. Laboratory maintenance of the infection has shown that it is not easily lost from the population and therefore might possess other characteristics that enhance its survival. The vertical
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transmission efficiency of popcorn and its capacity for horizontal transmission must be measured. Another valuable endeavour would be to include this mutant in mixed-population cage studies, similar to those suggested for the modification and rescue variants, to determine its relative fitness. In addition, the generality of the strain’s virulence needs to be confirmed by transinfection studies. Introducing this mutant into novel host backgrounds and assaying for virulence effects will reveal whether the early-death phenotype is unique to this specific parasite–host interaction. Alternatively, if further study reveals more virulence mutants, characterization of their transmission efficiencies, mode of transmission, host specificity and modification and rescue status could reveal exactly which factors have played a role in shaping the coevolutionary relationship of this unique parasite and its hosts. Acknowledgements This work was supported by grants from the National Institutes of Health (AI40620, T32 AI07404), the McKnight Foundation and the UNDP–World Bank–WHO Special Programme for Research and Training in Tropical Diseases.
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Outstanding questions • Are modification and rescue variants dominant in populations in a cyclical manner, meaning that the ability of any one phenotype to rise in frequency is dependent on the current strain composition of the population? • Are the variants selected for and maintained in a non-cyclical manner in populations because of other phenotypic characteristics that relate to host fitness and parasite-transmission efficiencies? • Do virulent Wolbachia demonstrate increased horizontal transmission, which would suggest they have evolved the lifestyle of a more traditional pathogen? • Are virulent Wolbachia the product of a recent shift in host range that has led to poor adaptation in a novel environment?
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References 1 Werren, J.H. and O’Neill, S.L. (1997) in Influential Passengers (O’Neill, S.L., Hoffmann, A.A. and Werren, J.H., eds), pp. 1–41, Oxford University Press 2 Rousset, F. et al. (1992) Proc. R. Soc. London B Biol. Sci. 250, 91–98 3 Breeuwer, J.A. and Jacobs, G. (1996) Exp. Appl. Acarol. 20, 421–434 4 Sironi, M. et al. (1995) Mol. Biochem. Parasitol. 74, 223–227 5 Sinkins, S.P., Curtis, C.F. and O’Neill, S.L. (1997) in Influential Passengers (O’Neill, S.L., Hoffmann, A.A. and Werren, J.H., eds), pp. 155–175, Oxford University Press 6 Min, K.T. and Benzer, S. (1997) Proc. Natl. Acad. Sci. U. S. A. 94, 10792–10796 7 Hoffmann, A.A., Clancy, D. and Duncan, J. (1996) Heredity 76, 1–8 8 Rousset, F., Vautrin, D. and Solignac, M. (1992) Proc. R. Soc. London B Biol. Sci. 247, 163–168 9 O’Neill, S.L. et al. (1992) Proc. Natl. Acad. Sci. U. S. A. 89, 2699–2702 10 Rigaud, T. (1997) in Influential Passengers (O’Neill, S.L., Hoffmann, A.A. and Werren, J.H., eds), pp. 81–101, Oxford University Press 11 Stouthamer, R. (1997) in Influential Passengers (O’Neill, S.L., Hoffmann, A.A. and Werren, J.H., eds), pp. 102–124, Oxford University Press 12 O’Neill, S.L. and Karr, T.L. (1990) Nature 348, 178–180 13 Hoffmann, A.A., Turelli, M. and Harshman, L.G. (1990) Genetics 126, 933–948 14 Poinsot, D. and Merçot, H. (1997) Evolution 51, 180–186 15 Schoenmaker, A., Van Den Bosch, F. and Stouthamer, R. (1998) Oikos 81, 587–597 16 Girin, C. and Bouletreau, M. (1995) Experientia 51, 398–401 17 Merçot, H. et al. (1995) Genetics 141, 1015–1023 18 Rousset, F. and Solignac, M. (1995) Proc. Natl. Acad. Sci. U. S. A. 92, 6389–6393 19 Perrot-Minnot, M.J., Guo, L.R. and Werren, J.H. (1996) Genetics 143, 961–972 20 Sinkins, S.P., Braig, H.R. and O’Neill, S.L. (1995) J. Cell. Biochem. (Suppl. 21a), 202 21 Rousset, F., Braig, H.R. and O’Neill, S.L. Heredity (in press) 22 Turelli, M. and Hoffmann, A.A. (1991) Nature 353, 440–442
23 Clancy, D.J. and Hoffmann, A.A. (1998) Entomol. Exp. Appl. 86, 13–24 24 Sinkins, S.P., Braig, H.R. and O’Neill, S.L. (1995) Proc. R. Soc. London B Biol. Sci. 261, 325–330 25 Hoffmann, A.A., Hercus, M. and Dagher, H. (1998) Genetics 148, 221–231 26 Binnington, K.C. and Hoffmann, A.A. (1989) J. Invert. Pathol. 54, 344–352 27 Hoffmann, A.A., Turelli, M. and Simmons, G.M. (1986) Evolution 40, 692–701 28 Stevens, L. and Wicklow, D.T. (1992) Am. Nat. 140, 642–653 29 Stouthamer, R., Luck, R.F. and Hamilton, W.D. (1990) Proc. Natl. Acad. Sci. U. S. A. 87, 2424–2427 30 Merçot, H. and Poinsot, D. (1998) Nature 391, 853 31 Bourtzis, K. et al. (1998) Nature 391, 852–853 32 Turelli, M. (1994) Evolution 48, 1500–1513 33 Hurst, L.D. and McVean, G.T. (1996) Proc. R. Soc. London B Biol. Sci. 263, 97–104 34 Giordano, R., O’Neill, S.L. and Robertson, H.M. (1995) Genetics 140, 1307–1317 35 Turelli, M., Hoffman, A.A. and McKechnie, S.W. (1992) Genetics 132, 713–723 36 Werren, J.H., Zhang, W. and Guo, L.R. (1995) Proc. R. Soc. London B Biol. Sci. 261, 55–63 37 Rigaud, T. and Juchault, P. (1995) J. Evol. Biol. 8, 249–255 38 Boyle, L. et al. (1993) Science 260, 1796–1799 39 Braig, H.R. et al. (1994) Nature 367, 453–455 40 Chang, N.W. and Wade, M.J. (1994) Can. J. Microbiol. 40, 978–981 41 Clancy, D.J. and Hoffmann, A.A. (1997) Am. Nat. 149, 975–988 42 Levin, B.R. (1996) Emerg. Infect. Dis. 2, 93–102 43 Bouchon, D., Rigaud, T. and Juchault, P. (1998) Proc. R. Soc. London B Biol. Sci. 265, 1081–1090 44 Levin, S. and Pimentel, D. (1981) Am. Nat. 117, 308–315 45 Nowak, M.A. and May, R.M. (1994) Proc. R. Soc. London B Biol. Sci. 255, 81–89 46 Poinsot, D. et al. (1998) Genetics 150, 227–237 47 Merçot, H. and Poinsot, D. (1998) Entomol. Exp. Appl. 86, 97–103 48 Zhou, W., Rousset, F. and O’Neill, S. (1998) Proc. R. Soc. London B Biol. Sci. 265, 509–515
Corrigendum
2D-PAGE database
In the March issue of TIM, a mistake
A new 2D-PAGE database is now available at http://www.mpiib-berlin.mpg.de/2D-PAGE/. This database contains proteomic data from different Mycobacterium tuberculosis and M. tuberculosis var. bovis strains. 2D gels can be compared against the 2D gel maps in the database, and links are provided to other tuberculosis and 2D-PAGE databases. In the future, it is hoped that the database will be extended to include proteomic information from other bacterial strains.
was present in the review article ‘Selection of drug-resistant HIV’ by P.R. Harrigan and C.S. Alexander. On p. 121, in Box 1 ‘Mutation-selection model – the simplest case’, the three dy , dy wt and equations should refer to –– ––– dt dt dy mut ––––– and not to x , y wt and y mut. The dt authors apologize to the readers for this error.
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