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Destructive interference may lead tocomplete cancellation when lightwaves travelling in different directions

cross, and in three-dimensional space thisoccurs along lines that are vortices ofelectromagnetic energy flow1. Here weconfirm theoretical predictions2,3 by experi-mentally creating combinations of opticallaser beams in which these dark threads formstable loops that are linked and knotted.

Since Kelvin proposed his vortex atomhypothesis4, temporally persistent vortexknots have been sought in fluid mechanics5,6,superfluid flow7, field theory8 and nonlinearexcitable media9.The optical vortices that wesynthesize here are embedded in light beamscreated by a single-frequency laser (Fig. 1a;

for methods, see supplementary informa-tion).A direct consequence ofthe linearity ofMaxwells equations for the electromagneticfield is that the intensity pattern in free spaceis static, so our optical vortices are stable inboth space and time.

The optical phase cannot be defined onthese dark threads: it is singular there (like theangle of longitude at the North Pole,for exam-ple). Consequently, there is a circulation ofelectromagnetic energy around the opticalvortex. Around such a singularity, the phasechanges by an integer multiple of 2; this inte-ger,m,is the strength of the singularity.

We combine Laguerregaussian beams10

,which have an optical vortex of integerstrength m along the beam axis and two fur-ther variable parameters:p, the discrete radi-al number (the number of nodal rings aboutthe beam axis), and w, the continuous waistwidth (which sets the transverse scale of thebeam). These additional degrees of freedomallow us to create the same basic structures asthose proposed in refs 2 and 3, but with thevortices more clearly defined by the sur-rounding intensity.

The loops, links and knot structures arisefrom the coaxial superposition of four

beams.Three of these beams have an on-axisvortex with the same strength m,but differentvalues ofp and w. The amplitudes are chosenso that both the field and its radial derivativeare zero at a specific radius in the focal plane.The resulting destructive interference formsa dark loop around the axial strength singu-larity. Adding a simple gaussian beam withsmall amplitude distorts this loop into an(m, 2) torus knot11, threaded by an m-stran-ded helix of strength-one vortices. Ifm2,the vortices form two linked loops (Fig.1b); ifm3,they form a trefoil knot (Fig.1c).

Our optical beams are produced by usinga single-frequency heliumneon laser beamilluminating a hologram. This forms the

intensity and phase structure of the desiredsuperposition of Laguerregaussian beams.As the fine structure of the singularities liesin regions of near darkness, it is necessary tooversaturate the camera to determine their

positions in the beam cross-section accu-rately. The resulting image contains pointsof darkness corresponding to the positions ofthe dark threads as they intersect the planeof the camera.

We have produced stable link and knotstructures formed from vortices in an opticalbeam. Our observations demonstrate theprecision control of light beams that isrequired to create complex regions of zerolight intensity. Such regions could be used,for example, to confine cold atoms and BoseEinstein condensates in complex topologies12.Jonathan Leach*,Mark R. Dennis,

Johannes Courtial*, Miles J. Padgett**Department of Physics and Astronomy,University of Glasgow, Glasgow G12 8QQ, UK

e-mail: j.leach@physics.gla.ac.uk

H. H. Wills Physics Laboratory, Tyndall Avenue,

Bristol BS8 1TL, UK

School of Mathematics, University of

Southampton, Highfield SO17 1BJ, UK

1. Nye,J. F. & Berry, M.V. Proc. R. Soc. Lond. A 336, 165190 (1974).

2. Berry, M.V. & Dennis, M.R. Proc. R. Soc. Lond. A 457,

22512263 (2001).

3. Berry, M.V. & Dennis, M.R. J. Phys. A 34, 88778888 (2001).

4. Thompson, W. Phil. Mag. 34, 1524 (1867).

5. Moffatt,H. K. J. Fluid Mech. 35, 117129 (1969).

6. Ricca,R. L.,Samuels, D.C. & Barenghi,C. F. J. Fluid Mech. 391,

2944 (1999).

7. Poole, D.R.,Scoffield,H.,Barenghi, C.F.& Samuels D. C.J. Low Temp. Phys. 132, 97117 (2003).

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8. Fadeev, L.& Niemi,A.J. Nature387, 5861 (1997).

9. Winfree,A. T. Nature371, 233236 (1994).

10.Allen, L.,Beijersbergen, M.W., Spreeuw,R. J.C. &

Woerdman, J. P. Phys. Rev. A 45, 81858189 (1992).

11.Adams, C.C. The Knot Book(Freeman, New York, 1994).

12.Ruostekoski,J. & Anglin,J. R. Phys. Rev. Lett. 86, 39343936

(2001).

Supplementary information accompanies this communication on

Natures website.

Competing financial interests: declared none.

Knotted threads of darknessDark lines within a laser beam can be manipulated to form stable vortex knots.

Plant genetics

Gene transfer fromparasitic to host plants

Plant mitochondrial genes are transmit-ted horizontally across mating barrierswith surprising frequency, but the

mechanism of transfer is unclear1,2. Here we

describe two new cases of horizontal genetransfer, from parasitic flowering plants totheir host flowering plants, and presentphylogenetic and biogeographic evidencethat this occurred as a result of direct physi-cal contact between the two. Our findingscomplement the discovery that genes can betransferred in the opposite direction, fromhost to parasite plant3.

Both cases of horizontal gene transferinvolve the mitochondrial gene atp1 andthe recipient Plantago, a large cosmopolitangenus comprising mostly weeds. We exam-ined 43 Plantago species, all containing anintact atp1 gene. Despite the exceptionaldivergence of these genes,their relationships

Figure 1 Knotted lines of darkness. a, Light from a hologram is passed through a spatial filter and a camera images the beam cross-

section in various planes.Thin black lines represent the threads of darkness that form the link or knot. Inset shows the observed over-

saturated beam cross-sections at the beam waist of the link; dark points indicate positions where the optical vortex threads cross the

observation plane. b,c, Three-dimensional representations of measured link (b) and trefoil knot (c) configurations. The link and knot are

threaded by further vortices (represented by the thinner tubes) that follow the axis of the light beam.

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to one another (Fig. 1, top) and their inclu-sion in Plantaginaceae agree with indepen-dent estimates4 of the phylogeny for thesetaxa. This clade of Plantago atp1 genes istherefore most likely to be the product ofstandard vertical transmission.

Each of three related Plantago speciescontains a second,full-length atp1 copy withseveral frameshift mutations. This clade of

pseudogenes is allied with the distantly relat-ed genus Cuscuta, as indicated by bootstrap(97%) and other analyses (Fig. 1, and seesupplementary information), implying thata species of Cuscutatransferred a copy ofatp1 to the common ancestor of these threePlantago species. Cuscutais a large genus offlowering plants (also known as dodders;Fig. 2) that parasitizes an unusually broadrange of hosts5, including Plantago6. Thethree Plantago species are native to Europeand north Africa, as are many dodders,includingC.europaea(Fig.1).

Two other species of Plantago (P. rigida

and P. tubulosa) also contain a second, full-length copy ofatp1. These too are pseudo-genes and are probably also derived byhorizontal gene transfer. Bartsia, a genus inthe parasitic family Orobanchaceae, is iden-tified as the likely gene donor by phylogeneticanalysis (81% bootstrap support; Fig. 1).Biogeography neatly supports this inference,because P. rigida, P. tubulosa and mostspecies of Bartsia are found exclusively athigh altitudes in the northern Andes7,8.

Both lineages of Plantago atp1 pseudo-genes were almost certainly acquired byhorizontal gene transfer, as indicated by evi-

dence against their inclusion in the Plantago-wide clade of vertically transmitted atp1genes and in favour of their phylogeneticallyanomalous inclusion with parasitic plants.(The possibility of DNA contamination canbe ruled out;see supplementary information.)Phylogenetic distribution of the transferredgenes and molecular clock analysis (see sup-plementary information) indicate that bothtransfers were recent (within the past fewmillion years).

Both transfers probably occurred bydirect plant-to-plant transmission of DNAfrom parasitic to host plants.This is indicated

by phylogenetic evidence that parasiticplants, which penetrate host plants intra-cellularly as part of their normal life cycle,served as donors in both transfers. It is alsosuggested by the striking biogeographic con-cordance of donors and recipients in the caseof the high-altitude,northern Andean Bart-sia, P. rigidaand P. tubulosa, as well as by thebroad host ranges of both groups of parasiticdonors. The well documented exchange inboth directions of macromolecules, virusesand phytoplasmas between parasitic plantsand their hosts911 is also consistent withplant-to-plant transmission.

We cannot altogether rule out the possi-bilitythat the involvement of parasitic plants

as donors is fortuitous for example, somebiological vector (such as pollen, fungus, abacterium or virus, or an insect) may havecaused indirect transfer. But our direct-transfer hypothesis is more parsimonious

and is supported by the evidence available.The parasitic lifestyle has evolved roughlya dozen times in flowering plants and thereare more than 4,000 species of parasiticplants12, providing plenty of opportunity forhorizontal gene transfer not only from para-site to host, but also from host to parasite3.Parasites with narrow host ranges mayexchange genes frequently with their hosts.Those with broad host ranges (dodders, forexample) may also act as vectors for genetransfer by directly bridging unrelated hostspecies. In addition to parasitism,other vec-tors, and non-vectored mechanisms suchas grafting, may promote horizontal genetransfer during plant evolution.

Jeffrey P. Mower, Sasa Stefanovic*,

Gregory J.Young, Jeffrey D. PalmerDepartment of Biology, Indiana University,

Bloomington, Indiana 47405, USA

e-mail: jpalmer@bio.indiana.edu

*Present address: Department of Biology,

University of Toronto at Mississauga,Mississauga, Ontario L5L 1C6, Canada

1. Bergthorsson, U., Adams, K.L., Thomason,B. & Palmer,J. D.

Nature424, 197201 (2003).

2. Won, H.& Renner, S.S. Proc. Natl Acad. Sci. USA 100,

1082410829 (2003).

3. Davis,C. C.& Wurdack, K.J. Science305, 676678

(2004).

4. Rnsted,N., Chase,M. W.,Albach,D.C. & Bello, M.A.

Bot. J. Linn. Soc. 139, 323338 (2002).

5. Yuncker, T. G. Mem. Torrey Bot. Club18, 111331 (1932).

6. Tessene, M.F. Mich. Bot. 8, 72104 (1969).

7. Molau,U.Opera Bot. 102, 199 (1990).

8. Luteyn, J.Pramos: A Checklist of Plant Diversity, Geographical

Distribution, and Botanical Literature(New York Botanical

Garden Press, Bronx, New York, 1999).

9. Hosford,R.M. Bot. Rev. 33, 387406 (1967).

10.Marcone, C., Hergenhahn, F., Ragozzino, A. & Seemller, E.

J. Phytopathol. 147, 187192 (1999).

11.Haupt, S.,Oparka,K. J.,Sauer,N. & Neumann,S. J. Exp. Bot. 52,

173177 (2001).

12.Nickrent,D. L. et al. in Molecular Systematics of Plants II

(eds Soltis, D.E., Soltis, P. S. & Doyle, J. J.) 211241 (Kluwer,

Boston, 1998).

Supplementary information accompanies this communication on

Natures website.

Competing financial interests: declared none.

brief communications arisingonline

www.nature.com/bca

Evolution: How do characters evolve?

A. Purvis (doi:10.1038/nature03092)

Reply: R. E. Ricklefs (doi:10.1038/nature03093)

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P. coronopus

P. macrorhizaP. subspathulata

P. crassifoliaP. rigidaP. tubulosaP. australisGlobularia

Digitalis

P. rigida ( )P. tubulosa ( )

Bartsia laticrenataBartsia inaequalis

ParentucelliaLindenbergia

LamourouxiaOrobanche

JusticiaStrobilanthes

SesamumCampsis

CatalpaVerbena

MenthaStachys

AlonsoaMyoporum

Paulownia

StreptocarpusJovellana

SyringaP. coronopus ( )

P. subspathulata ( )P. macrorhiza ( )Cuscuta europaea

Cuscuta sandwichianaConvolvulus

DinetusHumbertia

MontiniaNicotiana

Petunia

SchizanthusGelsemiumGentiana

Strychnos

0.01 substitutions per site0.05 substitutions per site

82

64

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9586

94

96

100

100

100

100100

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96

89

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Convolvulaceae}

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Figure 2A parasitic dodder (Cuscuta californica) in flower, with its

haustoria penetrating a host tomato plant.

Figure 1 Phylogenetic evidence for two horizontal transfer events of the gene atp1 into Plantago(blue). Seven Plantago atp1 genes at the

top of the maximum-likelihood tree are intact, vertically transmitted, and rapidly evolving (scale reduced by 80%). The other two sets of

Plantago atp1 genes are pseudogenes () acquired from parasitic plants in the Orobanchaceae (red) and Convolvulaceae (green). Boot-

strap values of over 50% are shown.For methods, see supplementary information.

B.

RICE

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