A Note on D-brane - Anti-D-brane Interactions in Plane Wave Backgrounds

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Cellular/MolecularAdenosine Receptor Signaling Modulates Permeability of the Blood–Brain BarrierAaron J.Carman,Jeffrey ls,Antje Krenz,Do-Geun Kim,and Margaret S.BynoeDepartment of Microbiology and Immunology,Cornell University,College of Veterinary Medicine,Ithaca,New York14853The blood–brain barrier(BBB)is comprised of specialized endothelial cells that form the capillary microvasculature of the CNS and is essential for brain function.It also poses the greatest impediment in the treatment of many CNS diseases because it commonly blocks entry of therapeutic compounds.Here we report that adenosine receptor(AR)signaling modulates BBB permeability in vivo.A1and A2A AR activation facilitated the entry of intravenously administered macromolecules,including large dextrans and antibodies to␤-amyloid, into murine brains.Additionally,treatment with an FDA-approved selective A2A agonist,Lexiscan,also increased BBB permeability in murine models.These changes in BBB permeability are dose-dependent and temporally discrete.Transgenic mice lacking A1or A2A ARs showed diminished dextran entry into the brain after AR agonism.Following treatment with a broad-spectrum AR agonist,intravenously administered anti-␤-amyloid antibody was observed to enter the CNS and bind␤-amyloid plaques in a transgenic mouse model of Alzheimer’s disease(AD).Selective AR activation resulted in cellular changes in vitro including decreased transendothelial electrical resistance,increased actinomyosin stress fiber formation,and alterations in tight junction molecules.These results suggest that AR signaling can be used to modulate BBB permeability in vivo to facilitate the entry of potentially therapeutic compounds into the CNS.AR signaling at brain endothelial cells represents a novel endogenous mechanism of modulating BBB permeability.We anticipate these results will aid in drug design,drug delivery and treatment options for neurological diseases such as AD,Parkinson’s disease,multiple sclerosis and cancers of the CNS.IntroductionThe blood–brain barrier(BBB)is comprised of brain endothelial cells(BECs),which form the lumen of the brain microvascula-ture(Abbott et al.,2010).The barrier function is achieved through tight junctions between endothelial cells that regulate the extravasation of molecules and cells into and out of the CNS (Abbott et al.,2010).Although the BBB serves to restrict the entry of potentially toxic substances into the CNS,it poses a tremen-dous hurdle to the delivery of therapeutic drugs into the CNS.It has been estimated thatϾ98%of small-molecule drugsϽ500Da in size do not cross the BBB(Pardridge,2001,2005).Current approaches aimed at altering the BBB to permit the entry of ther-apeutics are either too invasive,too painful,can result in perma-nent brain damage or result in loss of drug efficacy(Hanig et al., 1972;Broadwell et al.,1982;Rapoport,2001;Bidros and Vogel-baum,2009;Hynynen,2010).There is a monumental need to modulate the BBB to facilitate the entry of therapeutic drugs into the CNS.Determining how to safely and effectively do this could greatly benefit a broad range of neurological diseases,such as Alzheimer’s disease(AD),Parkinson’s disease,multiple sclerosis, neurological manifestations of acquired immune deficiency syn-drome(AIDS),CNS cancers,and many more.Promising thera-pies are available to treat some of these disorders,but their potential cannot be fully realized due to the tremendous imped-iment posed by a functional BBB.Here,we provide novel data demonstrating that signaling through receptors for the purine nucleoside adenosine acts as a potent,endogenous modulator of BBB permeability.It is well established that adenosine has many diverse roles in mammalian physiology,including immunomodulatory roles regulating immune cell responses(Bours et al.,2006;Kobie et al., 2006;Deaglio et al.,2007)and roles in proper CNS functioning (Sebastia˜o and Ribeiro,2009;Stone et al.,2009).The first clues to adenosine’s involvement in CNS barrier permeability came from our recent findings demonstrating that extracellular adenosine, produced by the catalytic action of CD73(a5Ј-ectonucleotidase) from AMP,promotes lymphocyte entry into the CNS in experi-mental autoimmune encephalomyelitis(EAE)(Mills et al., 2008).These studies demonstrated that mice lacking CD73 (Thompson et al.,2004),which are unable to produce extracel-lular adenosine,are protected from EAE and that blockade of the A2A adenosine receptor(AR)inhibits T cell entry into the CNS (Mills et al.,2008).These observations led us to hypothesize that modulation of AR signaling at BECs might modulate BBB per-meability to facilitate the entry of molecules and cells into the CNS.Indeed,our results suggest that AR signaling represents a novel,endogenous modulator of BBB permeability.Received June30,2011;revised July26,2011;accepted July28,2011.Author contributions:A.J.C.,J.H.M.,M.S.B.,and A.K.designed research;A.J.C.,J.H.M.,M.S.B.,A.K.,and D.-G.K. performed research;A.J.C.,J.H.M.,M.S.B.,A.K.,and D.-G.K.analyzed data;A.J.C.,J.H.M.,M.S.B.,and A.K.wrote the paper.ThisworkwassupportedbyNationalInstitutesofHealthGrantsR01NS063011(toM.S.B.)andF32NS066682(to J.H.M.).WeacknowledgeDr.ChrisSchafferofCornellUniversityfortheADtransgenicmice,Dr.HelenMarquisforher critical reading of the manuscript,and Delbert Abi-Abdallah for help with Western blotting.We also acknowledge Adenios,Inc.for their kind gift of the anti-␤-amyloid antibody.The authors declare no competing financial interests.Correspondence should be addressed to Margaret S.Bynoe at the above address.E-mail:msb76@. DOI:10.1523/JNEUROSCI.3337-11.2011Copyright©2011the authors0270-6474/11/3113272-09$15.00/013272•The Journal of Neuroscience,September14,2011•31(37):13272–13280Materials and MethodsMouse and rat models.C57BL/6mice(Jackson Laboratories)were used as WT.A1Ϫ/ϪAR mice were a gift from Dr.Jurgen Schnermann (NIH/NIDDK,Bethesda,MD)(Sun et al.,2001).A2AϪ/ϪAR were a gift from Dr.Jiang-Fan Chen(Boston University School of Medicine, Boston,MA)(Chen et al.,1999).The transgenic AD mice[B6.Cg-Tg(APPswe,PSEN1dE9)85Dbo/J]were a gift from Dr.Chris Schaffer(Cor-nell University,Ithaca,NY)(Jankowsky et al.,2004).Typically,mice were aged7–9weeks and weighed between20and25g.Sprague Dawley rats (Charles River Laboratories)were female,aged8weeks and weighed200–220g.Animals were bred and housed under specific pathogen-free condi-tions at Cornell University,Ithaca,NY.All procedures were done in accordance with approved Institutional Animal Care and Use Committee protocols.Administration of drugs and tissue collection.NECA[1-(6-amino-9H-purin-9-yl)-1-deoxy-N-ethyl-␤-D-ribofuranuronamide],CCPA (2-chloro-N6-cyclopentyladenosine),CGS21680(4-[2-[[6-amino-9-(N-ethyl-b-D-ribofuranuronamidosyl)-9H-purin-2yl]amino]ethyl] benzenepropanoic acid),and SCH58261(5-amino-7(phenylethyl)-2-(2-furyl)-pyrazolo[4,3-e]-1,2,4-triazolo[1,5-c]-pyrimidine)(Tocris Biosci-ence)were each dissolved in DMSO then diluted in PBS to the desired concentration;in most cases final DMSO concentrations wereϽ0.5%(v/v). Lexiscan(regadenoson;Toronto Research Chemicals)was dissolved in PBS. For vehicle controls,DMSO was diluted in PBS to the same concentration. Dextrans labeled with either FITC or Texas Red(Invitrogen)were sus-pended in PBS to10mg/ml.Experiments involving dextran injection used 1.0mg of dextran in PBS.When drug and dextran were injected concomi-tantly,1.0mg of dextran was mixed with the drug to the desired concentra-tion in a final volume of200␮l.All injections except injections of SCH58261 were retro-orbital intravenous.Lexiscan was administered intravenously with3injections,5min apart,and tissues were collected at15min unless otherwiseindicated.Indose–responseexperiments,drugsanddextranswere injected concomitantly.SCH58261injections,1mg/kg,were intraperitoneal and mice were predosed with this concentration daily for4d before the day of the experiment.An additional injection was administered at the time of the experiment.At indicated times mice were anesthetized and perfused with cold PBS through the left ventricle of the heart.Brains were weighed and frozen for later analysis.Fluorimetric analysis.Tris-Cl,50m M,pH7.6,was added to brains(100␮l per100mg brain).Brains were homogenized with a Dounce homog-enizer and centrifuged at16.1ϫg for30min.Supernatants were trans-ferred to new tubes and an equal volume absolute methanol was added. Samples were centrifuged at16.1ϫg for30min.Supernatant(200␮l) was transferred to a Corning Costar96well black polystyrene assay plate (clear bottom).A series of standards containing0.001–10␮g/ml dextran in50%Tris-Cl/50%absolute methanol(v/v)was added to each plate. Absolute concentrations of dextrans were derived from these standard curves.Fluorimetric analysis was performed on a BioTek Synergy4. Primary brain endothelial cell isolation.This method has been adapted from previously described techniques(Song and Pachter,2003).Briefly, 12-week-old C57BL/6mice were killed and decapitated.Dissected brains were freed from the cerebellum and large surface vessels were removed by carefully rolling the brains on sterile Whatman paper.The tissue was then homogenized in a Dounce homogenizer in ice-cold DMEM-F12me-dium,supplemented with L-glutamine and Pen/Strep,and the resulting homogenate was centrifuged at3800ϫg,4°C for5min.After discarding the supernatant,the pellet was resuspended in18%(w/v)dextran in PBS solution,vigorously mixed,and centrifuged at10,000ϫg,4°C for10 min.The foamy myelin layer was carefully removed with the dextran supernatant by gentle aspiration.The pellet was resuspended in pre-warmed(37°C)digestion medium(DMEM supplemented with1mg/ml collagenase/dispase,40␮g/ml DNase I,and0.147␮g/ml of the protease inhibitor tosyllysine chloromethyl ketone)and incubated at37°C for75 min with occasional agitation.The suspension was centrifuged at3800ϫg. The supernatant was discarded;the pellet was resuspended in prewarmed (37°C)PBS and centrifuged at3800ϫg.The pellet was suspended in full medium(DMEM-F12medium containing10%plasma-derived serum, L-glutamine,1%antibiotic-antimycotic,100mg/ml heparin,and100mg/ml endothelial cell growth supplement).The resulting capillary fragments were plated onto tissue culture dishes coated with murine collagen IV(50␮g/ml) at a density corresponding to one brain per9.5cm2.Medium was exchanged after24and48h.Puromycin(8␮g/ml)wasadded tothemedium forthefirst 2d.Before analysis,the primary mouse brain endothelial cells were grown until the culture reached complete confluence after5–7d in vitro.Cell culture and quantitative reverse transcription PCR.Bend.3mouse BECs(ATCC)were grown in ATCC-formulated DMEM supplemented with10%ing TRIzol(Invitrogen),RNA was isolated.cDNA was synthesized using Multiscribe reverse transcriptase(Applied Biosys-tems).Primers(available upon request)for ARs and CD73were used to determine gene expression and standardized to TBP gene levels using Kapa Sybr Fast(Kapa Biosystems)run on a Bio-Rad CFX96real-time quantitative PCR(qPCR)system.Melt curve analyses were performed to measure the specificity for each qPCR product.Adenosine receptor Western blotting and immunofluorescent analysis. Primary mouse brain endothelial cells and Bend.3cell cultures were grown as described above.Cells were lysed with1ml of lysis buffer containing protease inhibitor and condensed with TCA solution up to 200␮l.Samples were run on a12%SDS-PAGE and transferred to nitro-cellulose paper.Membranes were blocked with1%polyvinyl pyrrolidone and incubated with anti-A1AR(AAR-006)and-A2A AR(AAR-002) primary antibodies(Alomone Labs)overnight.The membranes were washed and then incubated with goat anti-rabbit HRP.Membranes were washed thoroughly and developed with ECL solution and exposed to x-ray film.For adenosine receptor immunostaining,anesthetized mice were perfused with PBS and brains were isolated and snap frozen in Tissue Tek-OCT medium.Sections(5␮m;brains in a sagittal orienta-tion)were affixed to Superfrost/Plus slides(Fisher Scientific),fixed in acetone,and stored atϪ80°C.Slides were thawed,washed in PBS, blocked with casein(Vector Laboratories)in normal goat serum (Zymed),and then incubated with anti-CD31(MEC13.3,BD Biosci-ences)and anti-A1AR(A4104,Sigma)or anti-A2A AR(AAR-002,Alo-mone Labs).Slides were then incubated with goat anti-rat Ig Alexa Fluor 488(Invitrogen)and goat anti-rabbit Ig Texas Red-X(Invitrogen).Sec-tions were mounted with Vectashield mounting medium with DAPI (Vector Laboratories).Images were obtained on a Zeiss Axio Imager M1fluorescent microscope.Fluorescence in situ hybridization.For detection of adenosine receptor mRNA in brain endothelium,we performed fluorescence in situ hybrid-ization(FISH)using FITC-labeled CD31and either biotin-labeled A1or A2A DNA oligonucleotide probes(Integrated DNA Technologies,probe sequences available upon request).Anesthetized mice were perfused with PBS and brains were isolated and snap frozen in Tissue Tek-OCT me-dium.Twelve micrometer cryosections were mounted on Superfrost/ Plus slides(Fisher Scientific).After air drying on the slides for30min,the tissue was fixed in4%neutral buffered PFA for20min and rinsed for3 min in1ϫPBS.Next,the tissue was equilibrated briefly in0.1M trietha-nolamine and acetylated for10min in0.1M triethanolamine with0.25% acetic anhydride.Immediately following acetylation,the sections were dehydrated through an ascending ethanol series,and stored at room temperature.The tissue was rehydrated for2ϫ15min in PBS,and equilibrated for15min in5ϫSSC(0.75M NaCl,0.075M Na-citrate).The sections were then prehybridized for1h at42°C in hybridization buffer (50%deionized formamide,4ϫSSC,40␮g/ml salmon sperm DNA,20% (w/v)dextran sulfate,1ϫDenhardt’s solution).The probes(300ng/ml) were denatured for3min at80°C and added to the prewarmed(42°C) buffer(hybridization mix).The hybridization reaction was performed at 42°C for38h with250␮l of hybridization mix on each slide,covered with Parafilm.Prehybridization and hybridization were performed in a black box saturated with a4ϫSSC-50%formamide solution to avoid evapo-ration and photobleaching of FITC.After incubation,the sections were washed for30min in2ϫSSC(room temperature),15min in2ϫSSC (65°C),15min in0.2ϫSSC,0.1%SDS(65°C),and equilibrated for5min in PBS.For detection of the biotin-probes,sections were incubated for30 min at room temperature with Texas Red X-conjugated streptavidin (Invitrogen,S6370,1␮g/ml)in PBS containing1ϫcasein(Vector Lab-oratories).Excess streptavidin was removed by15min in PBS,followed by15min in0.2ϫSSC,0.1%SDS(65°C),and15min in PBS washes.Carman et al.•Adenosine Alters Blood–Brain Barrier Permeability J.Neurosci.,September14,2011•31(37):13272–13280•13273Sections were coverslipped with Vectashield mounting medium with DAPI(Vector Laboratories).Images were acquired using a Zeiss Axio Imager M1fluorescent microscope.Injection of anti-␤-amyloid antibodies and immunofluorescent micros-copy.WT and transgenic(AD)mice were given0.08mg/kg NECA(i.v.). After3h,400␮g of antibody to␤-amyloid(200␮l of2mg/ml;clone 6E10,Covance)was administered intravenously and the mice rested for 90min.Mice were anesthetized and perfused(as described above)and brains were placed in OTC and flash-frozen for sectioning.Sagittal sec-tions(6␮m)were fixed in acetone,washed in PBS,blocked with casein and incubated with goat anti-mouse Ig Cy5(Abcam),and then washed with PBS.Sections were mounted with Vectashield Hardset mounting medium with DAPI(Vector Laboratories).Images were obtained on a Zeiss Axio Imager M1fluorescent microscope.Transendothelial cell electrical resistance assays.Bend.3cells were grown in ATCC-formulated DMEM supplemented with10%FBS on24-well Transwell inserts,8␮m pore size(BD Falcon,BD Biosciences)until a monolayer was established.Transendothelial cell electrical resistance (TEER)was assessed using a Voltohmmeter(EVOMX,World Precision Instruments).Background resistance from unseeded Transwells was subtracted from recorded values to determine absolute TEER values. Change in absolute TEER from time0(t0)for each individual Transwell was expressed as percentage change and then averaged for each treatment group.F-actin staining of endothelial cells.Bend.3cells were grown(as de-scribed above)on circular coverslips in24-well plates.Cells were treated for3or30min with1␮M CCPA,1␮M Lexiscan,DMSO or media alone. Coverslips were washed with PBS,fixed in4%paraformaldehyde, washed again in PBS and then permeabilized with0.5%Triton X-100in PBS.After washing in PBS/1%BSA,coverslips were blocked with1% BSA then stained with phalloidin-Alexa Fluor568.Coverslips were washed and mounted on slides with ProlongGold containing DAPI(In-vitrogen).Images were obtained on an Olympus BX51fluorescent microscope.Albumin uptake assay.Bend.3cells grown on collagen-coated cover-slips were incubated with albumin-Alexa Fluor594(50mg/ml)(Invitro-gen)and either medium alone,DMSO vehicle,NECA(1␮M),or Lexiscan(1␮M)for30min.Albumin uptake was visualized(albuminϭred)using the Zeiss Axio Imager M1fluorescent microscope.Total albu-min fluorescence was recorded using Zeiss AxioVision software,and measured using ImageJ(NIH)software.Tight junction molecule staining.Bend.3cells grown on collagen-coated coverslips were incubated with DMSO vehicle,NECA(1␮M),or Lexiscan(1␮M)for1h.Cells were washed with PBS,fixed with4% paraformaldehyde,and permeabilized with0.5%Triton-X in PBS.Cells were blocked with PBS/BSA/goat serum and then stained with antibodies (Invitrogen)against either ZO-1(1A12),Claudin-5(34-1600),or Occlu-din(3F10).Following a wash step,cells were incubated with either goat anti-rabbit Ig Texas Red-X or goat anti-mouse Ig Cy5(Invitrogen).Cov-erslips were washed and mounted on slides with ProlongGold containing DAPI.Images were obtained on a Zeiss Axio Imager M1fluorescent microscope.Statistical analyses.Statistical differences,assessed using the Student’s t test,are indicated where pՅ0.05.ResultsThe broad-spectrum AR agonist NECA increases BBB permeability to macromoleculesWe established that intravenous administration of NECA,which activates all ARs(A1,A2A,A2B,A3),resulted in a dose-dependent increase in extravasation of intravenously administered fluores-cently labeled dextrans into the CNS of mice(Fig.1).Impor-tantly,varying the dose of NECA resulted in dose-dependent increases in CNS entry of both10kDa dextrans(Fig.1A)and70 kDa dextrans(Fig.1B)compared with treatment of vehicle alone. Maximum entry of dextrans into the CNS occurred with0.08 mg/kg NECA.Higher concentrations of NECA had no additional effect or show diminished efficacy,possibly due to receptor desensi-tization(Ferguson et al.,2000).These results demonstrate that AR activation increases BBB permeability.We next determined the duration and kinetics of increased BBB permeability after NECA administration.In time course ex-periments using the maximum effective dose of NECA deter-mined by our dose–response experiments(0.08mg/kg),we observed that increased barrier permeability following NECA treatment is temporally discrete(Fig.1C),with maximum entry of labeled dextran into the CNS between4and6h post-treatment.These data represent accumulation of FITC-dextran in the brain over time,since the dextran and NECA were admin-istered at t0.To determine how much dextran can enter the brain in a discrete period of time after NECA treatment,dextran was administered at different times after NECA administration(Fig. 1D).These data represent dextran entry into the brain90min after dextran injection.At8h post-NECA treatment,detectable levels of dextran in the brain decreased from the maximum and by18h post-treatment the levels returned to baseline,as dextrans administered18h after NECA treatment were not detectable in the brain at significant levels(Fig.1D).These results demonstrate that intravenous NECA administration results in a temporally discrete period of increased barrier permeability that returns to baseline by8–18h.A1and A2A AR activation increases BBB permeabilityAs AR activation increases BBB permeability to dextrans in mice, we next determined whether receptors for adenosine are ex-pressed by mouse BECs.Utilizing antibodies and probes against the A1and A2A ARs,we observed expression of both ARs on CD31 costained endothelial cells within the brains of mice by immuno-fluorescent staining(Fig.2A)and fluorescence in situ hybrid-ization(Fig.2B).Importantly,both A1and A2A AR protein Figure1.NECAtreatmentincreasesBBBpermeabilityinatemporallydiscreteandreversible manner.A,B,Dose-dependent increases in10kDa(A)and70kDa(B)dextrans into WT mouse brain3h after intravenous administration of NECA or vehicle as measured by fluorimetry (10–15animalspergroup).C,Extravasationtimecourseof10kDaFITC-dextranintoWTmouse brain when coadministered intravenously with NECA(0.08mg/kg)or vehicle,as measured by fluorimetry(10–15animals per group).D,Extravasation time course of10kDa Texas Red-dextran,administeredintravenously90minbeforeharvesttimes(asdisplayed),intoWTmouse brain tissue after intravenous pretreatment(timeϭ0)with NECA(0.08mg/kg)or vehicle,as measured by fluorimetry(3–5animals per group).Data are splined scatter plots with scaled time on the x-axis.Experiments were performed at least twice.*pՅ0.05,significant differ-ences(Student’s t test)from vehicle.Data are meanϮSEM.13274•J.Neurosci.,September14,2011•31(37):13272–13280Carman et al.•Adenosine Alters Blood–Brain Barrier Permeabilityexpression was detected by Western blot analysis on primary endothelial cells isolated from the brains of mice (Fig.2C ).Inter-estingly,the human brain endothelial cell line hCMEC/D3also expresses both the A 1and A 2A ARs (Mills et al.,2011).These data suggest that BECs are capable of directly responding to extracel-lular adenosine.To investigate the functional contribution of A 1and A 2A receptors in AR-mediated changes in BBB permeability,we stud-ied transgenic mice lacking these receptors.Importantly,there were no significant differences in the basal levels of BBB perme-ability to 10kDa dextrans between WT,A 1AR Ϫ/Ϫand A 2A AR Ϫ/Ϫmice (Fig.2D ).Following intravenous administration of NECA,both A 1AR Ϫ/Ϫand A 2A AR Ϫ/Ϫmice showed significantly lower levels of intravenously administered dextrans in their brains compared with WT mice.To examine the effect of NECA administra-tion on BBB permeability in mice when neither the A 1nor the A 2A AR is available for activation,A 1AR Ϫ/Ϫmice were treated with the selective A 2A antagonist SCH 58261before NECA administration.When A 2A AR signaling was blocked with this antagonist in mice lacking the A 1AR,no significant increase in BBB permeabil-ity was observed (Fig.2D ).These data suggest that modulation of BBB permea-bility is,at least in part,mediated by these two AR subtypes.To further confirm these results,we used commercially available AR agonists selective for either the A 1or the A 2A AR.We administered the selective A 1agonist CCPA and the selective A 2A agonist CGS 21680to WT mice.Both CGS 21680(Fig.2E )and CCPA (Fig.2F )treatment re-sulted in increased dextran entry into the CNS.While this increase was substantial compared with vehicle treatment,it was significantly lower than that observed af-ter NECA administration (Figs.2E ,F ).However,when used in combination,CCPA and CGS 21680recapitulated the magnitude of the effect of increased dex-tran entry into the CNS that was observed after NECA treatment (Fig.2G ).To-gether,these results suggest that while activation of either the A 1or A 2A AR on BECs can facilitate entry of molecules into the CNS,activation of both ARs has an additive effect.The selective A 2A AR agonist Lexiscan increases BBB permeabilityTo explore the possible therapeutic use of AR agonism to facilitate CNS entry of in-travenously administered compounds,we tested a commercially available,FDA-approved AR agonist in our experimental paradigm.The selective A 2A AR agonist Lexiscan,which has been successfully used in myocardial perfusion imaging inhumans (Iskandrian et al.,2007),did indeed increase BBB per-meability to 10kDa dextrans after intravenous administration in mice (Fig.3A ).Interestingly,dextran was detectable in the brain 5min following a single Lexiscan injection.Additionally,intra-venous administration of Lexiscan also increased BBB permea-bility in rats (Fig.3B ).In an injection paradigm intended to mimic continuous infusion of the drug,3injections of Lexiscan over 15min resulted in dramatically high levels of labeled-dextran detected in the brains of rats (Fig.3B ).To examine the duration of Lexiscan’s effects on BBB permeability,wedeter-Figure 2.Increased BBB permeability depends on selective agonism of A 1and A 2A ARs.A ,B ,Immunofluorescent staining (A )and fluorescence in situ hybridization (B )of CD31(endothelial cell marker;green),and A 1(left column;red)and A 2A (right column;red)ARs near the cortical area of the brain in naive mice.Scale bar,20␮m.C ,Western blot analysis of A 1(left)and A 2A (right)AR expression in isolated primary BECs from naive mice.␤-Actin expression is shown as a loading control.D ,Decreased levels of dextran in brains of A 1and A 2A AR knock-out mice 3h after intravenous administration of NECA (0.08mg/kg)or vehicle compared with WT mice,as measured by fluorimetry.No significant increase in dextran levels was detected in brains of A 1knock-out mice that were pretreated with the selective A 2A antagonist SCH 58261(5–8animals per group).E ,F ,Dose-dependent entry of 10kDa FITC-dextran into WT brain tissue 3h after intravenous coadministration of CGS 21860(selective A 2A AR agonist)(E )or CCPA (selective A 1AR agonist)(F ),as measured by fluorimetry.NECA (0.08mg/kg)was used as a positive control (10–13animals per group).G ,Levels of 10kDa FITC-dextran in WT mouse brain tissue 3h after intravenous administration of vehicle,NECA (0.08mg/kg),CGS 21680(0.54mg/kg),CCPA (0.37mg/kg),and in combination [left column,CGS 21680(0.54mg/kg)ϩCCPA (0.37mg/kg);right column CGS 21680(0.54mg/kg)ϩCCPA (0.037mg/kg)](3–4mice per group).Experiments were repeated at least twice.*p Յ0.05,significant differences (Student’s t test)from vehicle.Data are mean ϮSEM.Carman et al.•Adenosine Alters Blood–Brain Barrier Permeability J.Neurosci.,September 14,2011•31(37):13272–13280•13275mined CNS dextran entry over time in both mice and rats.Fol-lowing a single intravenous injection of Lexiscan,maximum increased BBB permeability was observed after 30min and re-turned to baseline by 180min post-treatment (Fig.3C ).Similar results were observed after Lexiscan treatment in rats (Fig.3D ).Importantly,the duration of the effects on BBB permeability after Lexiscan treatment is much shorter than after NECA treatment,probably due to the different half-lives of the compounds [NECA ϳ5h,Lexiscan ϳ3min (Astellas Pharma 2009,Lexiscan:U.S.Physicians Prescribing Information)].The Ͼ20-fold increase in labeled-dextran in Figure 3B (compared with single injections,Fig.3D )may be explained by a synergistic effect conferred on BBB opening as a result of multiple doses of Lexiscan.These results demonstrate that Lexiscan increases BBB permeability to macromolecules.Antibodies to ␤-amyloid enter the brain after NECA administrationAmong the most challenging therapeutic agents to get across the BBB are macromolecules,such as antibodies,due to their enormous size.We asked whether AR modulation with NECA can facilitate the entry of antibodies into the CNS.To test this,we used a double [amyloid precursor protein (APP)/presenilin (PSEN)]transgenic mouse model of AD [strain B6.Cg-Tg(APPswe,PSEN1dE9)85Dbo/J].These mice accumulate ␤-amyloid (A ␤)plaques that are a hallmark of AD (Jankowsky etal.,2004;Mineur et al.,2005).The monoclonal antibody 6E10has been shown to significantly reduce A ␤plaque burden in a mouse model of AD when administered by intracerebroventricular in-jection (Thakker et al.,2009).Binding of intravenously injected 6E10antibody to A ␤plaques was observed throughout the brains of NECA-treated AD mice (Fig.4A ),with a concentration of A ␤plaques in the hippocampal region.No binding of intravenously injected 6E10antibody was observed in AD mice treated with vehicle alone (Fig.4B )or in WT mice treated with NECA or vehicle (data not shown).Neither NECA nor vehicle treatment alone affected the ability of AD mice to form A ␤plaques (Fig.4C ,D ).These results demonstrate that intravenously adminis-tered antibody to A ␤can cross the BBB following AR agonism and bind CNS A ␤plaques (Fig.4E ),most of which are located near blood vessels within the brain (Fig.4F ,G).Figure 4.Anti-␤-amyloid antibody administered intravenously crosses the BBB and labels ␤-amyloid plaques in transgenic mouse brains after NECA administration.A–D ,Immunofluo-rescent microscopic images near the hippocampi of transgenic AD (APP/PSEN)mice.Mice were treatedwitheither(A ,C )NECA(0.08mg/kg)or(B ,D )vehicleandantibodyto ␤-amyloid(6E10)was administered intravenously (top;A ,B ).For mice that did not receive intravenous 6E10antibody (bottom;C ,D ),6E10was used as a primary antibody to control for the presence of plaquesandwasapplied exvivo duringimmunostaining.Blue,DAPI;red,Cy5-antibodylabeling 6E10-labeled ␤-amyloid plaques.Scale bar,50␮m.E ,Quantification of 6E10-labeled amyloid plaques per mouse brain section in transgenic AD mice treated with NECA or vehicle alone.F ,G ,Immunofluorescent microscopic images of the hippocampal and cortical regions from the brains of transgenic AD mice showing an overview (F )and close-up (G )of ␤-amyloid plaque locationsrelativetobloodvessels(endothelialcellsareCD31stained,green;␤-amyloidplaques are 6E10stained,red;nuclei are DAPI stained,blue).Scale bars,50␮m.Figure 3.The selective A 2A AR agonist Lexiscan increases BBB permeability in murine mod-els.A–D ,Lexiscan administration increases BBB permeability to 10kDa dextran in mice and rats.See Materials and Methods for experimental design.A ,Data bars before the line break represent groups that received 3Lexiscan injections.The bar after the line break represents a group that received a single Lexiscan injection.For the groups receiving 3injections,perfusion occurred 15min after the initial injection.The group that received a single injection was per-fused 5min after injection (10–15animals per group).Vehicle-treated mice (V)were perfused 15min after injection.B ,Lexiscan increases BBB permeability in rats.Animals received 3injec-tions of Lexiscan,5min apart,and were perfused 15min after the initial injection (3–4animals per group).As a control reference,animals received 1injection of NECA and were perfused 15min after injection.Vehicle-treated mice (V)were perfused 15min after injection.C ,Time courseofBBBpermeabilityafterLexiscantreatmentinmice.Lexiscan(0.05mg/kg)wasadmin-istered at time 0(10–14animals per group).D ,Time course of BBB permeability after Lexiscan treatment in rats.Lexiscan (0.0005mg/kg)was administered at time 0(3–4animals per group).All experiments were repeated at least twice.*p Յ0.05,significant differences (Stu-dent’s t test)from vehicle.Data are mean ϮSEM.13276•J.Neurosci.,September 14,2011•31(37):13272–13280Carman et al.•Adenosine Alters Blood–Brain Barrier Permeability。

Natural sesquiterpenoids1999-2

Natural sesquiterpenoidsBraulio M. FragaInstituto de Productos Naturales y Agrobiología, CSIC, 38206-La Laguna, Tenerife, Canary Islands, SpainReceived (in Cambridge, UK) 1st June 1999Covering: 1998Previous review: 1999, 16, 211Farnesane2Monocyclofarnesane 3Bicyclofarnesane4Bisabolane, sesquisabinane and parvifolane 5Sesquipinane6Trichothecane, cuparane, laurane, herbertane,italicane, barbatane and dunniane 7Chamigrane8Carotane, cedrane, allocedrane, prezizaane, zizaane,duprezianane and anisatin group9Cadinane, cubebane oplopanane, picrotoxane,helminthosporane, spiroaxane and tutin group 10Himachalane, longifolane and longipinane 11Caryophyllane, silphinane, presilphiperfolane,silphiperfolane, clovane, modhephane, isocomane,cameroonane, prenopsane, nopsane, quadrane and subergane12Humulane, pentalenane, tremulane, hirsutane,cucumane ceratopicane, lactarane, isolactarane,precapnellane, capnellane, protoilludane, illudane,africanane and asteriscane 13Germacrane 14Elemane15Eudesmane, cycloeudesmane, lindenane andiphionane 16Vetisperane17Eremophilane and bakkane18Guaiane, xanthane, pseudoguaiane, patchoulane andcarabrane19Aromadendrane, maaliane, bicyclogermacrane,ladaniferane, aristolane, nardosinane, ishwarane,gorgonane, prespatane and kelsoane 20Pinguisane21Miscellaneous sesquiterpenoids 22References 1Farnesane Three new sesquiterpene carbodiimide dichlorides 1–3have been obtained from a marine sponge of the genus Axinyssa .These substances showed potent antifouling activities against the larvae of the barnacle Balanus amphitriti .1Four novel sesquiterpenoid derivatives 4–7have been obtained from the roots of Ferula feruloides .2Six new furanosesquiterpenes of the dendrolasin type 8-13have been isolated from a cytotoxic extract of the deep ocean tunicate Ritterella rete ,3whilst known members of this sesquiterpene group have been found in the Patagonian nudibranch Tyrinna nobilis .4The biotransformation of (2Z ,6Z )-farnesol by the plant pathogenic fungus Glomerella cingulata has been studied.5The steric course of the methyl transfer from AdoMet to (S )-farnesyl-3-thiopropionate by G-protein methyltransferase has been determined.6The bio-synthesis of C 11and C 16homoterpenes in higher plants has been investigated.7Biosynthetic studies 8with Actinoplanes sp.A40644 have shown that the terpenoid BE-406441 149is mainly formed by the mevalonate pathway, while menaquinoneMK-9 15, a component of its mycelial membrane,10is produced by the non-mevalonate pathway. The isolation and bacterial expression of a sesquiterpene synthase cDNA clone from Mentha piperita , which produces the aphid alarm pheromone (E )-b -farnesene, has been reported.11The known sesquiterpene furan epingaione, which has been isolated from Bontia daphnoides , has been shown to be a bioactive metabolite against Cylas formicarius .12Two new putative juvenile hormones, 8A -hydroxy- and 12A -hydroxy-JH-III, have been identified in the corpora allata of the African locust, Locusta migratoria .13A review summarizing the total synthesis of acyclic and monocyclic sesquiterpenes during the period 1980–1994 hasThis journal is © The Royal Society of Chemistry 1999Nat. Prod. Rep., 1999, 16, 711–730711appeared.14A concise total synthesis of the marine sesqui-terpene dictyodendrillin B has been described.15Studies of the formation of sesquiterpene polyene hydroperoxides have been carried out.162MonocyclofarnesaneA new sesquiterpene 16has been found in the crude oil of Copaiba cearensis.17Three novel bioactive ionone derivatives 17–19have been isolated from Helianthus annuus.18Another compound of this type, 3-hydroxy-5,6-epoxy-b-ionone, has been obtained for the first time from a fungus, Athyrium yokoscense(Polypodiaceae). This compound showed inhibitory activity against lettuce seed germination.19A chemical study of an aqueous ethanol extract of the whole herb Wahlenbergia marginata afforded several new ionone glycosides.20The new striatane sesquiterpene 20has been isolated from the sponge Dysidea fragilis.21The biosynthesis of monocyclofarnesane sesquiterpenes of the blumenol C type has been shown to occur in mycorrhizal barley roots (Hordeum vulgare), via the glyceraldehyde 3-phosphate–pyruvate pathway.22A chiral and stereoselective synthesis,23starting from d-glucose, permitted the determination of the absolute configura-tion of the sesquiterpene FR65814 21, a potent immunosuppres-sant agent, which had been isolated from a Penicillium species.24An enzyme-mediated synthesis of (R)- and (S)-a-ionone has been accomplished.25The absolute configuration of a sesquiterpene, which had been isolated from Premna oligotricha26a and whose relative stereochemistry had been revised26b has been determined by the synthesis of its opposite enantiomer. In this work the synthesis of the (R)-enantiomer of another sesquiterpenoid ancistrodial, the defence sesquiterpene from Ancistrotermes cavithorax, has also been described.26The diterpene sclareol has been used as starting material for the preparation of (2)-caparrapi oxide 22and 8-epicaparrapi oxide 23,27which had been isolated from Nicotiana tabacum.28An enantiocontrolled route to the fungitoxic metabolite (2)-chokol G has been described,29whilst the furanosesquiterpene riccio-carpin has been synthesized as its racemate.30Total syntheses of sollasin A and sollasin D have been reported.31The role of farnesyltransferase in abscisic acid (ABA) regulation of the guard cells’ anion-channel and in the loss of plant water have been settled. These findings could lead to the development of drought-tolerant plants.32A comparative study of the rapid isocratic quantitation of ABA, using a fast liquid chromatography column and a standard column, has been carried out.333BicyclofarnesaneA new sesquiterpene hydrocarbon drim-8(12)-ene 24has been found in the essential oil of the rhizomes of Hedychium acuminatum.34Hodgsonal 25is a novel drimane sesquiterpene, which has been obtained from the mantle of the Antarctic nudibranch Bathydoris hodgsoni.35The new cytotoxic sesqui-terpene bolinaquinone 26has been isolated from a Philippine sponge of the genus Dysidea.36Another two compounds of this type, (2)-frondosin A 27and (2)-frondosin D 28, have been found in an extract of a marine sponge of an unidentified species of Euryspongia. Both compounds showed HIV-inhibitory properties.37An extract of the fungus Penicillium simplicissi-mum contains simplicissin 29, a new pollen growth inhibitor.38 Another fungus, LL-23G227, contains two novel antibacterial agents, hongoquercin A 30and hongoquercinB 31.39,40The structure of stachybotrin has been determined as 32. This compound has been isolated from Stachybotrys alternans,41 whilst kampanols A–C 33–35are novel Ras farnesyl-protein transferase inhibitors, which have been isolated from Stachy-botrys kampalensis.42Four new sesquiterpene nitrobenzoyl esters 36-39with cytotoxic properties have been obtained from the fungus Aspergillus versicolor, which grows on the surface of the Caribbean green alga Penicillus capitatus.43Several sesquiterpene derivatives of the type 40have been isolated from an Actinomycetes strain (MST-8651) and named drimentines. These compounds showed antitumor and antibacterial activ-ity.44The structure of 4A-methylaminoavarone has been deter-mined by X-ray analysis.45Dry powders of Cryptoporus volvatus were ingested and biotransformed by the beetle Tibolium castaneum to afford the sesquiterpenes 41and 42, the nor-sesquiterpenes 43and 44, and the bisnorsesquiterpenoid 45. These metabolites could be formed from cryptoporic acid. This712Nat. Prod. Rep., 1999, 16, 711–730work included a review of the biologically active substances, which have been isolated from inedible Japanese mushrooms.46 Eleven synthetic drimane derivatives have been tested for their deterrence to nymphs of Myzus persicae and Aphis gossypii.47 A novel sesquiterpenic coumarin, epi-samarcandin acetate, has been obtained from Ferula assa-foetida.48The labdane diterpene sclareol has been used as starting material for the synthesis of the drimane sesquiterpenes wiedendiol A and wiedendiol B.49Another two compounds of this latter type, pereniporin and 9-epi-warburganal, have been prepared starting from methyl zamoranate.50Syntheses of (+)-valdiviolide, (+)-12a-hydroxyisodrimenin, (+)-winterin,51 (-)-ambrox, (+)-zonarol52and (2)-ilimaquinone53have been described, whilst racemic syntheses of drim-8-en-7-one, albica-nol,54arenarol,55pallescensin A56and stachyflin57have been reported. The sesquiterpene polygodial has been used in the preparation of the (2)-enantiomer of polywood.58Several nucleophilic agents have been used in a study of the 1,6-con-jugate addition to the quinone-methide system of puupehe-none.594Bisabolane, sesquisabinane and parvifolaneTwo new sesquiterpenes, 46and 47, have been isolated from the heartwood of Pseudotsuga wilsoniana,60whilst bisaboangelone 48has been obtained from the roots of Angelica pubescens.61 The wood of Dysoxylum schiffneri contains the novel bisabo-lane sesquiterpenes schiffnerone A 49and schiffnerone B 50.62 Other bisabolane derivatives 51and 52and the sesquisabinene derivatives 53and 54have been identified as components of the essential oil obtained from the rhizomes of Hedychium gardnerianum(Kahili ginger).63Distillation of the heartwood oil of Oceanian sandalwood (Santalum austrocaledonicum) afforded the novel sesquiterpenes 6,12-dihydroxybisabola-2,10-diene and 7,13-dihydroxybisabola-2,10-diene.64The crys-tal and molecular structures of isoperezone, aminoperezone and isoaminoperezone have been reported.65The first member of a novel family of bioactive sesqui-terpenes, heliespirone A 55, has been found in an extract of Helianthus annuus.66The biosynthesis of the isoprene units of bisabololoxide, a sesquiterpene from Matricaria recutita(cha-Nat. Prod. Rep., 1999, 16, 711–730713momile), has been investigated. Two of the isoprene building blocks were predominantly formed via the triose–pyruvate pathway, whilst the third unit derived from both the mevalonic acid pathway and the triose–pyruvate pathway.67The isolation, characterization and bacterial expression of (E)-bisabolene synthase from grand fir (Abies grandis) has been reported.68 The antimicrobial activity of the sesquiterpene cernuol, which had been obtained from Bidens cernua, has been studied.69The bioactivity of the bisabolane sesquiterpenes from Curcuma longa70and Curcuma zedoaria71has been investigated.A stereoselective synthesis of (2S,3R,6S,7Z)- and (2R,3S,6S,7Z)-2,3-epoxybisabola-7,10-diene, the sex phero-mones of the southern green stink bug (Nezara viridula), has been reported.72(+)-Curcudiol,73(S)-(+)-curcumene,74and (S)-(+)-curcuphenol74,75have been synthesized using an enantio-selective route, whilst curcuphenol and b-sesquiphellandrene have been prepared as racemates.76Dehydrosesquicineole and dihydrosesquicineole have been synthesized with the aim of understanding the relationship between structure and odour properties.77In this latter context, the recent progress in fragrance chemistry, which also gives details of olfactory mechanisms and structure–odour relationships, has been re-viewed.78The first synthesis of radulanin A and helianane has been reported.79A total synthesis of the racemic sesquiterpene parvifoline has been achieved.805Sesquipinane(+)-cis-a-Bergamotene, (+)-trans-a-bergamotene and other sesquiterpene hydrocarbons have been identified as compo-nents of the Brazilian liverwort Dumortiera hirsuta.81The preparation and absolute configuration of (2)-(E)-a-trans-bergamotenone have been described.826Trichothecane, cuparane, laurane, herbertane, italicane, barbatane and dunnianeRacemic83and chiral84syntheses of trichodiene have been reported. A short preparation of an A-ring aromatic trichothe-cene analogue has been devised.85The total synthesis of (2)-verrucarol, the hydrolysis product of verrucarin A, has been carried out,86whilst a formal synthesis of (±)-verrucarol has been reported.87Two new cuparane sesquiterpenes, 56and 57, have been obtained from Jungermannia infusca.88A cyclocuparanol 58 has been obtained from Cryptothallus mirabilis.89Other compounds of this type, (2)-cyclocupar-9-en-2-one 59, (2)-a-microbiotene 60and (+)-b-microbiotene 61, have been isolated from the essential oil of the liverwort Mannia fragrans.90 Racemic syntheses of bromoether A, filiforminol,91tochuinyl acetate and dihydrotochuinyl acetate92have been devised. The first total synthesis of the sesquiterpene (2)-laurequinone has been accomplished,93whilst a synthesis of racemic herbertene has been reported.94On the other hand, a preparation of (±)-cuparene, and a formal synthesis of (±)-laurene and (±)-herbertene has been described.95(±)-Isoitalicene has been synthesized using electrolytic and photolytic methods in the main steps.96This sesquiterpene had been isolated from Helichrysum italicum.97The biosynthesis of (2)-b-barbatene in cultured cells of Heteroscyphus planus has been investigated.98Compound 62, which has been isolated from Illicium dunnianum, represents a new type of sesquiterpene. The name dunniane has been proposed for this skeleton and its biosynthesis may be related to that of the cuparanes.997ChamigraneThe known sesquiterpene 2,10-dibromo-3-chloro-a-chami-grene has been obtained from a novel red alga, Laurencia japonensis.100The structure of allo-obtusol has been revised to 63using X-ray data, confirming a previous suggestion by Italian authors, who had renamed it cartilagineol.101This compound had been isolated from Laurencia cartilaginea102and has now been found in another Laurencia species, collected in the Philippines.103In this last work the NMR data of ma’ilione have been reassigned. The first synthesis of (±)-laurencial has been achieved.104This compound, which possesses the absolute configuration shown in 64, had been isolated from Laurencia nipponica,105and it is probably formed by ring contraction of a chamigrane derivative.8Carotane, cedrane, allocedrane, prezizaane, zizaane, duprezianane and anisatin groupThe new sesquiterpene tinocordifolin 65has been found in an extract of the stem of Tinospora cordifolia.106Another compound of this type 66has been isolated from the rhizomes of Ferula communis,107whilst two isocarotane esters have been obtained from Ferula jaeschkeana.108The structures of the sesquiterpenes crispanone and crispane, which had been obtained from Petroselinum hortense, have been revised, showing them to be identical with those of siol angelate and lasidiol angelate, respectively.109The Japanese moss Plagiomnium acutum contains ent-b-cedrene 67, which represents the first isolation of this714Nat. Prod. Rep., 1999, 16, 711–730compound from the plant kingdom.110In the total synthesis of a-cedrene a new strategy, utilising N-aziridinylimine radical chemistry, has been used.111Syntheses of (±)-allo-cedrol (khusiol)112and (±)-isokhusimone113have been reported. Angustisepalin 68is a new prezizaane sesquiterpene, which has been obtained from the aerial parts of Illicium angustisepa-lum.114The structure of lacinan-8-ol has been determined as 69. This sesquiterpene, which possesses a duprezianane skeleton, has been found in an extract of the roots of Rudbeckia laciniata.115A chemical study of Illicium floridanum yielded three new lactones 70–72, which possess the anisatin type of framework. In this work, the structure of a sesquiterpene, previously described as debenzoyldunnianin, has been revised to 73.1169Cadinane, cubebane, oplopanane, picrotoxane, helminthosporane, spiroaxane and tutin groupThe novel isocyanosesquiterpene alcohol 74has been found in an extract of the nudibranch Phyllidia pustulosa.1 A new cadinane sesquiterpene 75has been isolated from Jasonia candicans.117Two trinorcadalane phytoalexins, hibiscanal 76 and o-hibiscanone 77, have been obtained from stem stele of Hibiscus cannabinus(kanaf), which had been inoculated with the fungus Verticillium dahliae.118Weyerstahl et al.119have isolated the new cadinane sesquiterpenes 78–80from Ageratina adenophora. This plant also contains the sesquiterpene 81, which was identical with a substance named chamomillol, to which the incorrect structure 82had been given.120a This latter structure had been correctly assigned to a compound obtained from Fabiana imbricata,120b but wrongly identified as chamomillol. The Weyerstahl group also pointed out that a compound previously isolated from Ageratina adenophora and named eupatorenone, to which a new skeleton was assigned (structure 511 in Ref. 120c), must also have an erroneous structure. The essential oils of Hedychium gardner-ianum63contain the novel cadinane derivatives 83–85. Other compounds of this type 86–88and the cubebane derivatives 89 and 90have been identified in commercial Labdanum oil.121 Two sesquiterpene glycosides 91and 92have been isolated from cotton oil cake (Gossypium hirsutum).122Another four new compounds of this type, named alagicadinosides F–I, have been obtained from Alangium premnifolium.123Known cadina-nolides and glaucolides have been identified in a phytochemical study of Lepidaploa remotiflora.124It has been shown that nerolidyl diphosphate is an intermediate in the enzymatic cyclization of the natural substrate (E,E)-farnesyl diphosphate to d-cadinane by soluble preparation of cotton stele tissue, infected with Verticillium dahliae, containing d-cadinene synthase.125 A new synthesis of (S)-gossypol, the yellow pigment of cotton seed, has been described.126Cadinane derivatives have been prepared starting from (R)-(2)- or S-(+)-carvone.127A review of the biologically active substances from the genus Artemisia has appeared.128An extract of the dried leaves of Artemisia annua afforded the new cadinane sesquiterpenes arteannuins H–N, 93–99,129the methyl ester of arteannuic acid and the unusual 7-hydroxy derivative 100.130X-Ray crystallo-Nat. Prod. Rep., 1999, 16, 711–730715graphic studies have confirmed the discovery of a new polymorphism of artemisinin.131This technique has also been used in a structural study of artemisinic acid.132The results of the biotransformation of this acid by cultured cells of Artemisia annua have been reported.133The studies of the mechanism of action of the antimalarial drug artemisinin have been re-viewed.134The alkylating properties of several antimalarial artemisinin derivatives by activation with a reduced heme model have been investigated.135Artemisinin and haemin react in vitro to afford d-meso hydroxy porphyrin.136A unified mechanistic framework for the Fe(ii)-induced cleavage of artemisinin (qinghaosu) and its analogues has been proposed. In this study an unstable epoxide, which had been postulated as being responsible for the antimalarial activity, has now been isolated. In addition, a secondary radical has also been trapped, thus providing the first direct evidence for the involvement of a radical species in the in vitro cleavage of artemisinin deriva-tives.137The stability of acetal and non-acetal type analogues of artemisinin in simulated stomach acid has been investigated.138 On the other hand, the C-glycoside formation of various artemisinin C-10 derivatives has been achieved with the aim of obtaining compounds that are more resistant towards hydrolysis than the corresponding ether or ester of dihydroartemisinin, which are used clinically as antimalarial drugs.139A simple HPLC method with electrochemical detection for the simultane-ous determination of artesunate and dihydroartemisin in biological fluids has been developed.140The cytotoxic action of artemisinin derivatives against bone marrow and tumour cells has been examined.141The enzymatic synthesis of artemisinin from natural and synthetic precursors has been reported.142 Artemisinin and deoxoartemisinin have been prepared from both arteannuin B and arteannuic acid.143The photochemistry of artemisinin derivatives has been studied.144Studies of the absolute configuration of (+)-heptelidic acid have been carried out.145The antimalarial activity of this acid and other fungal metabolites has been evaluated.146Bio-synthetic studies have shown that cubebane and ricciocarpin A are formed in Ricciocarpos natans and Conocephalum conicum via the mevalonic acid pathway, whilst the monoterpenes and the diterpene phytol are derived in these liverworts from the glyceraldehyde–pyruvate pathway.147A synthesis of racemic a-oplopenone has been carried out.148The total syntheses of picrotoxinin, picrotin and corianin have been reported.149,150 Biosynthetic studies have suggested that the precursor of sorokinianin is prehelminthosporol, another metabolite also obtained from Bipolaris sorokiana, together with a three-carbon fragment from the TCA pathway.151The synthesis of the sesquiterpene (2)-gleenol 101has been accomplished.152This spiro derivative had been isolated from Picea glehnii,153and has now been found, together with the ethers 102and 103, in commercial Brazilian Cabore oil.154The known sesquiterpenes tutin and coriamyrtin have been obtained from Coriaria ruscifolia.15510Himachalane, longifolane and longipinaneThe new sesquiterpene himachal-l-en-4b-ol 104has been isolated from an ether extract of the liverwort Pellia epi-phylla.156The regio- and stereoselective epoxidation of cis- and trans-himachalenes have been studied.157X-Ray analysis has been used in the structural determination of a compound produced by rearrangement of an a-cis-himachalene diep-oxide.158Longifolane has been used as the starting material in the preparation of 12-nor-allo isolongifolan-11-one, a com-pound with an amber-like odour.159Several longipinene diesters have been isolated from Stevia lucida.160The absolute configuration of two longipinene derivatives, which contain chiral epoxyangelates, has been determined.16111Caryophyllane, silphinane, presilphiperfolane, silphiperfolane, clovane, modhephane, isocomane, cameroonane, prenopsane, nopsane, quadrane and suberganeThe recent advances in the chemistry of caryophyllene have been reviewed.162The essential oil of the rhizomes of Echinops giganteus(Compositae) contains the new sesquiterpenes pre-silphiperfol-7-ene 105, prenopsan-8-ol 106, three diastereomers of silphiperfolan-6-ol 107–109, modheph-2-en-8-ol 110, silphi-perfola-4,7(14)-diene 111, cameroonan-7-ol 112, and nopsan-4-ol 113. Three of these compounds, 106, 112and 113, possess novel carbon skeleta, which have been named prenopsane, cameroonane and nopsane, respectively.163The solvolysis of a caryophyllen-8b-yl derivative led to caryophyllene as the main product, whilst solvolysis of a716Nat. Prod. Rep., 1999, 16, 711–73015-nor-caryophyllen-8b-yl tosylate afforded 12-nor-8a-pre-silphiperfolan-9b-ol.164On the other hand, the solvolysis of 1a-and 1ß-silphinyl mesylate led to a-terricyclene, silphinene and a bridgehead alcohol, as main products, and isocomene and modhephene, as traces.165The total synthesis of (2)-5-oxo-silphiperfol-6-ene 114has been achieved.166This compound had been obtained from Espeletiopsis guacharaca.167(+)-b-Cedrol has been used as starting material for the preparation of silphinane derivatives.168A total synthesis of (±)-modhephene and (±)-isocomene has been reported.169The rearrangement of theB andC rings in a clovane skeleton has been investigated using deuterium label-ling.170A chemical study of a methanolic extract of the Indian ocean gorgonian coral Subergorgia suberosa led to the isolation of the four novel sesquiterpenes 115-118.17112Humulane, pentalenane, tremulane, hirsutane, cucumane, ceratopicane, lactarane, isolactarane, precapnellane, capnellane, protoilludane, illudane, africanane and asteriscane1(10)-Epoxyhumula-4,7-diene, 1(10),4-diepoxyhumul-7-ene and other known sesquiterpenes have been isolated from the wood bark of Guarea guidonia.172The stereochemical struc-tures of natural sesquiterpenes of the humulene type have been reviewed.173An X-ray study of zerumbone has been carried out.174The complete epoxidation of humulene-9,10-epoxide has been studied.175Epolone A 119, epolone B 120and pycnidione 121are sesquiterpene-tropolones that induce ery-thropoietin production in human cells. These compounds have now been isolated from a fungus, OS-F69284.176Pycnidione had previously been obtained from a Phoma species.177The cDNA isolation, characterization and bacterial expression of humulene synthase and d-selinene synthase from Abies grandis have been reported. These encoded enzymes have been named in terms of the main compounds that are formed. However, each enzyme produces a remarkable number of sesquiterpenes.178 A formal and asymmetric synthesis of pentalenolactone E and pentalenolactone F has been achieved.179,180An efficient preparation of racemic pentalenene has been reported.181The total synthesis of (±)-tremulenolide A and (±)-tremulenediol A has been described.182The new sesquiterpenes hirsutanols A-C 122-124and ent-gloeosteretriol 125have been isolated from salt water cultures of an unidentified fungus separated from an Indo-Pacific sponge of the genus Haliclona, whilst hirsutanol D 126has been obtained from the terrestial fungus Coriolus consors, cultured under both sea water and deionized water.183 Cucumins A–D 127-130are novel hirsutane derivatives, whilst cucumins E–G 131-133represent a new type of linear triquinane, named cucumanes, and cucumin H 134is a novel member of the ceratopicane group. These metabolites, and the known hirsutane derivative anthrosporone 135, have been isolated from mycelial cultures of Macrocystidia cucumis. Inthis work the structure of 135has been confirmed by X-ray analysis.184Formal syntheses of (±)-ceratopicanol and (±)-hir-sutene have been reported.185A total synthesis of (±)-precapnelladiene has been re-ported.186Two novel cytotoxic capnellane sesquiterpenes, 136 and 137, have been isolated from the soft coral Capnella imbricata.187Acyclic ketones have been used as starting material in a formal synthesis of D9(12)-capnellene.188This hydrocarbon has also been prepared starting from p-cresol.189 The recent developments in general methodologies for the synthesis of linear triquinanes have been reviewed.190The four new compounds plorantinone D 138, epiplor-antinone B 139, deliquinone 140and 2,9-epoxydeliquinone 141 have been obtained from extracts of injured specimens of Russula delica. The illudane 142was also isolated, together with these substances. This last sesquiterpene had been found in submerged cultures of Agrocybe aegerita,191a and its structure assigned without stereochemistry. This has now been establish-ed.191b The novel protoilludane sesquiterpenes violascensol 143 and its 6-ketostearoyl ester have been found in an extract of the fruiting bodies of Lactarius violascens.192Three novel sesqui-terpenes of protoilludane origin, tsugicolines F–H 144–146and the norsesquiterpene tsugicoline I 147, have been isolated from solid cultures of Laurilia tsugicola. The furosesquiterpenes 144 and 145inhibited the germination of the water cress, Lepidium sativum.193Formal syntheses of (±)-D(6)-protoilludene194and (±)-sterpurene195have been reported. A novel and general approach for the preparation of protoilludane sesquiterpenes has been developed.196The total synthesis of the lactarane sesqui-terpene furanether B has been described.197Isodehydroilludin M, an oxidation product of the cytotoxic sesquiterpene illudin M, has been synthesized,198whilst several illudin S derivatives, labelled with tritium, have been prepared from the fermentation of the fungus Omphalotus illudens in the presence of [3H]-Nat. Prod. Rep., 1999, 16, 711–730717。

Introduction to Braid Theory

An Introduction to Braid TheoryMaurice ChiodoNovember4,2005AbstractIn this paper we present an introduction to the theory of braids.We lay down some clear deﬁnitions of a braid,and proceed to establish the braid group B n.We show that both the word and conjugacy problems are solvable on this group,and conclude with theorems by Alexander and Markov to develop a correspondence between braids and links.AcknowledgementsI would like to thank my supervisor Lawrence Reeves,whose guidance has proven extremely valuable over the course of this year.It has been a pleasure to work on such an interesting topic,alongside such an excellent mentor.Contents1Introduction5 2Deﬁnitions102.1Braids (10)2.2Braid equivalence (11)2.3Braid diagrams (16)3The braid group203.1Braids as a group (20)3.2A presentation of the braid group (27)4Properties of the braid group374.1Some results about the braid group (37)4.2Braid invariants (42)4.3Pure braids (44)4.4Quotients of B n (46)5The word and conjugacy problems on B n505.1The word problem (50)5.2The conjugacy problem (59)6Braids and links626.1Braid closure (62)36.2Alexander’s theorem (65)6.3Markov’s theorem (69)7Conclusion767.1Summary (76)7.2Further remarks (76)References7841IntroductionWe begin by giving an informal introduction,intended to give the reader an intuitive understanding of braids.The theory of braids has been studied since the early1920’s,founded by Emil Artin,a German mathematician(see[1],which is his original paper“Theorie der Zopfe”from1925).Though his studies were initially motivated by the geometric constructions of braids,it was not long before the powerful algebra behind braid theory became evident.Since then the theory has branched out into manyﬁelds of application,from encryption to solving polynomial equations.However,the study of braids in themselves is mathematically both rich and deep,being an extension of a concept that even a child can understand.We begin by giving an intuitive description of braids,to help motivate our deﬁnitions and ideas later on.So,what is a braid?Essentially,a braid is a geometric object that can,after some work,be viewed algebraically.We begin by taking a unit cube,and in it we place n strands of string,subject to the following conditions:1.No part of any strand lies outside the cube.2.Each strand begins on the top face of the cube,and ends on the bottomface.3.No two strands intersect.4.As we traverse any strand from the top face,we are always moving down-wards.This means that no strand has any horizontal segment,or any segment that‘loops up’.The resulting collection of strands is called an n-braid.Figure1shows some examples of3-braids,while Figure2shows some non-examples of3-braids.Now, given this loose deﬁnition of a braid,we can develop some sort of equivalence of braids.Given an n-braidβ(in the unit cube)we say it is equivalent to another n-braidβ′if the strands ofβcan be perturbed to the strands ofβ′without doing any of the following:1.Moving any part of any strand out of the cube.2.Cutting any strand.3.Moving any endpoint of any strand.5Figure1:Two3-braids.Figure2:Neither of these are braids,as they violate the conditions in the deﬁ-nition.6So imagine the strands in a box,with their ends glued to the top/bottom of the box.We are,in essence,only allowed to‘shake the box’.Figure3shows an example of such a move.It often becomes quite tedious and cumbersome to draw the cube around every braid,so for simplicity we omit it,and instead draw a projection of the braid onto the plane.Figure3:Perturbing the strands of a braid.We can also multiply two n-braidsβandβ′by joining the bottom ofβto the top ofβ′.By doing this we create a new n-braid which we shall denote byββ′. Figure4gives an example of this.It turns out that,for any given n∈N,the set of equivalence classes of n-braids form aﬁnitely-presented group,called the n-braid group B n,as we show in section3.Moreover,both the word and conjugacy problems are solvable for this group,and we show this in section5.Figure4:Two braids,and their product.Any given n-braidβcan be turned into an oriented link in a very intuitive manner.We simply draw a projection of the braid,and successively add arcs around the side ofβto‘close’the open ends of the braid.Each arc connects the start and end of a strand,so we use n arcs in total.This is called the closure of the braidβ,and is denoted by˜β.We give an example of a braid and its closure in Figure5.The orientation on˜βis given by orienting each strand of the original braidβwith an arrow from top to bottom,then continuing these arrows around.7Figure6shows the closure of a braid with orientation drawn in.Conversely,a theorem by Alexander shows us that given any oriented link L,we canﬁnd some braidβsuch that L is the closure ofβ.However,this reverse procedure is much more diﬃcult thanﬁnding the closure of a braid,as we shall see in section6.2. We give an example of an oriented link drawn as the closure of a braid in Figure 7.Figure5:A braid and its closure.Figure6:The induced orientation on the closure of a braid.8Figure7:An oriented link,drawn again as the closure of a braid.92DeﬁnitionsWe now make our our intuitive ideas of a braid more precise,by introducing formal deﬁnitions.This enables us to convey our ideas with no ambiguity,and thus prove some interesting and insightful results.2.1BraidsWe begin by giving a formal deﬁnition of a braid,as well as describing a conve-nient way to draw a braid.We are then in a position to go on to explore some direct consequences of our deﬁnition.Deﬁnition2.1.Deﬁne a level plane E s⊆R3byE s:={(x,y,z)∈R3|z=s}Thus E s is the inﬁnite horizontal plane that intersects the z-axis at z=s.Deﬁnition2.2.Let D be the unit cube in the positive octant of Euclidean3-space,with one vertex at the origin.So D={x,y,z∈R:0≤x,y,z≤1}.We deﬁne n points A1,...,A n on the top face of D byA i:= 12,i n+1,1 ,1≤i≤nSimilarly,we deﬁne n points B1,...,B n on the bottom face of D byB i:= 12,i n+1,0 ,1≤i≤nFigure8illustrates our set up of D.We now add n polygonal arcs d1,...,d n to D such that the following hold:1.The arcs d1,...,d n are mutually disjoint.2.Each d i begins at some A j and ends at some B k.3.For any0≤s≤1and any1≤i≤n,E s∩d i is exactly one point.4.Each d i in contained entirely in D.10Figure8:The unit cube D with vertex at the origin.Figure 9:Examples of 2,3and 4-braids.The resulting collection of n arcs d 1,...,d n is called an n -braid .For any given 1≤i ≤n ,d i is called the i th braid string (though we may refer to them as strands or arcs).For a given n ∈N ,the set of all n -braids is denoted B n .To clarify,condition 3of the above deﬁnition ensures that our braid strings are strictly decreasing.In Figure 9we give an example of 2,3and 4-braids.Note that,for simplicity,we will draw our braid strings as smooth arcs,but we must remember that we are actually dealing with polygonal arcs here.2.2Braid equivalenceWe now wish to give a concrete deﬁnition of what we mean by braid equivalence.Intuitively,two braids are the same if we can jiggle one to make it look like the other.With our new deﬁnition of a braid,we can clearly explain what we mean by this.So we begin by deﬁning a set of fundamental moves that we can perform on a braid,that equates to our intuitive idea of jiggling.11Figure10:The elementary moveΩ;replacing the existing edge AB with the edges AC∪BC.Deﬁnition2.3.Letβ∈B n be an n-braid,and let AB be an edge of some braid string d ofβ. Let C be another point in D such that the solid triangle ABC has the following properties:1.No other braid string ofβmeets ABC.2.ABC meets d only along AB.3.For any0≤s≤1,the level plane E s meets AC∪BC in at most one point. Then we shall deﬁne an operationΩas follows:Replace the edge AB in d by the two edges AC∪BC,as shown in Figure10.If instead edges AC and BC are in d,and the level planes E s each meet AB in at most one point,then we can also deﬁne an operationΩ−1in the reverse manner:Replace the edges AC∪BC in d by AB,as shown in Figure11.The movesΩandΩ−1are called elementary moves on the braidβ.Theorem2.4.Ifβis an n-braid and we perform an elementary move onβto obtain a collection of arcsβ′,thenβ′is also an n-braid.Proof.Any braid string inβaltered by an elementary move remains contained in D (Since A,B,C all lie in D),and condition3of Deﬁnition2.3ensures that ele-mentary moves do not create extra intersections of strings with level planes.At no point do we remove a string entirely,nor do we introduce any new strings.12Figure 11:The elementary move Ω−1;replacing the existing edges AC ∪BC with the edge AB .And the start/end points of the strings in βremain ﬁxed.Hence our resultant collection of strings β′is an n -braid.Deﬁnition 2.5.Let β,β′be n -braids.Suppose there exists a ﬁnite sequence of elementary moves that transform βto β′.Then βis said to be equivalent to β′,and is denoted by writing β∼β′.Note here that all elementary moves are,by deﬁnition,performed inside D .Theorem 2.6.The relation ∼is an equivalence relation on B n .Proof.1.Reﬂexivity.Let β∈B n .Then the ﬁnite sequence of no elementary moves transforms βto β,and so β∼β.2.Symmetry.Let β,β′∈B n such that β∼β′.Then there exists a ﬁnite sequence of elementary moves Ωǫ11,...,Ωǫm m that transforms βto β′.So we have βΩǫ11−→...Ωǫm m −→β′.Reversing the sequence gives β′Ω−ǫm m −→...Ω−ǫ11−→β.Thus the ﬁnite sequence of elementary moves Ω−ǫm m ,...,Ω−ǫ11transforms β′to β(i.e.,β′∼β′).3.Transitivity.Let β,β′,β′′∈B n such that β∼β′,β′∼β′′.Then there exists a ﬁnite sequence13of elementary movesΩǫ11,...,Ωǫm m that transformsβtoβ′,and aﬁnite sequenceof elementary moves¯Ω¯ǫ11,...,¯Ω¯ǫkk that transformsβ′toβ′′.So we haveβΩǫ11−→...Ωǫmm−→β′andβ′¯Ω¯ǫ11−→...¯Ω¯ǫkk−→β′′.This gives the sequenceβΩǫ11−→...Ωǫm m−→β′¯Ω¯ǫ11−→...¯Ω¯ǫkk−→β′′.Thus theﬁnite sequence of elementary movesΩǫ11,...,Ωǫm m,¯Ω¯ǫ11,...,¯Ω¯ǫkktransformsβtoβ′′(i.e.,β∼β′′).We now introduce three other equivalence relations on braids.Deﬁnition2.7.Letβ,β′be n-braids in D.Suppose there exists a homeomorphism H:D×[0,1]→D×[0,1]of the form H(x,t)=(h t(x),t)for x∈D and0≤t≤1. Also suppose that,for all t∈[0,1],the homeomorphism h t:D→D satisﬁes the following:1.h t|∂D=id:∂D→∂D2.h0=id:D→D3.h1(β)=β′Thenβis said to be ambient isotopic toβ′,denotedβ≈β′.Such a homeo-morphism H is called an ambient isotopy.The idea behind ambient isotopy is that,as well as deformingβto its homeomor-phic imageβ′,we also preserve the structure of the surrounding space.Given some n∈N,it is easy to show that any two n-braids are homeomorphic as topo-logical subspaces of R3.The way we distinguish them is to look at the structure of the remainder of D.Deﬁnition2.8.Letβ,β′and H be as in Deﬁnition2.7.Suppose that H also satisﬁes the following condition:4.For all t∈[0,1],h t(β)is an n-braid.Thenβis said to be strong isotopic toβ′,denoted byβ∼sβ′,and the homeomorphism H is called a strong isotopy,or just s-isotopy.14Strong isotopy is just a stronger form of ambient isotopy,where we impose the condition that the image ofβmust always be a braid throughout the deformation. We will see later that if two braids are ambient isotopic,then they are in fact strong isotopic.In other words,being able to deform one braid into another implies that there exists a‘better way’to do it,whereby at each step of the deformation we still have a braid.Deﬁnition2.9.Letβ,β′be n-braids in D.Suppose there exists a homeomorphism h:D→D such that the following conditions hold:1.h(β)=β′2.h|∂D=id:∂D→∂DThenβis said to be h-equivalent toβ′,denotedβ∼hβ′,and the homeomor-phism h is called an h-equivalence.All we really mean by h-equivalence is that we send D to itself via a homeomor-phism such thatβis sent toβ′,and the boundary of D is unchanged.It turns out that all the relations we have deﬁned so far tie in nicely with our idea of equivalence of braids,as the next theorem shows.Theorem2.10.Ambient isotopy,strong isotopy and h-equivalence are all equivalence relations. Proof.The proof of this is simple topology,giving us little insight into the bigger picture of braid theory.We leave it as an exercise.See[4],pp96-107.Intuition tells us that these deﬁnitions are all essentially saying the same thing. Namely,that two n-braidsβ,β′are the same if we can jiggle one in D to make it look like the other.The above equivalence relations are merely formalised ways of saying we can jiggle braids,and though they may appear diﬀerent,it turns out that they are not.That is,two braids equivalent under one of the above relations are equivalent under all others.The following theorem asserts this(though we omit the proof here and instead refer the reader to an appropriate reference).15Theorem2.11.Letβ,β′be n-braids in D.Then the following statements are equivalent:1.βis equivalent toβ′(i.e.,β∼β′).2.βis ambient isotopic toβ′(i.e.,β≈β′).3.βis h-isotopic toβ′(i.e.,β∼hβ′).4.βis strong-isotopic toβ′(i.e.,β∼sβ′).Proof.See[4],pp96-107for a full proof.2.3Braid diagramsNow that we have a more diverse(yet equivalent)set of equivalence relations on B n,we can be more relaxed in our interpretation of a braid.However,we have yet to formalise a simple visual presentation of a braid.Drawing D each time we wish to describe a braid can become cumbersome and confusing,especially when we have a braid on a large number of strings,or with a large number of crossings. So we deﬁne a simple way to project a braid onto the plane,that preserves enough information to allow us to recover the braid(up to equivalence).In the process, we uncover a way to generate braids from simple building blocks,which we shall see later.Deﬁnition2.12.Letβ∈B n be in D.We begin by retracting D to the yz plane via the projection map p:D→D,p(x,y,z)=(0,y,z).The eﬀect of this is to squash the braid strings d1,...,d n ofβonto the back face of D.For simplicity,we will treat our page as the yz plane,and denote p(β)byˆβ.See Figure12for an example of a braid and its projection.The projection p(β)gives a set of n curvesˆd1,...,ˆd n in the plane,eachˆd i being the image of d i under p.These curves may have many (or possibly inﬁnite)points of intersection,called intersection points.Any projectionˆβofβsatisfying the following three conditions is said to be a regular projection ofβ:1.p(β)has only aﬁnite number of intersection points.2.If Q is an intersection point ofˆβ,then the inverse image p−1(Q)∩βof Qinβhas exactly two points.That is,no more than two distinct points of16D1234Figure12:A braid and its projection.βare mapped on to any point inˆβ.Such a point Q is said to be a double point ofˆβ.3.No vertex ofβis mapped to any double point ofˆβ.We say that two regular projections are equivalent if they are the projections of two equivalent braids.Theorem2.13.Every braid has a regular projection.Proof.Say we are given a projectionˆβof our braidβ(whereˆβ=p(β)as above).Since we have aﬁnite number of polygonal arcs,then to ensure aﬁnite number of intersection points,all we need do is ensure that no two straight lines lie on top of each other.If this does occur,we can correct it by tilting one of the lines as shown in Figure13.Suppose an intersection point has a pre-image of more than two points.Then we can move subsequent arcs around the intersection point as shown in Figure14to ensure that only two arcs meet at the point.Suppose we have a vertex mapped to a double point.Then we merely truncate the vertex as shown in Figure15,so that the vertex no longer lies on the intersection point. Now,there can only be aﬁnite number of violations of conditions1-3.And each correctional move we have just deﬁned can be performed so that it does not introduce any more violations.Thus,after aﬁnite number of correctional moves, we have a regular projection.We now alter our regular projections to give us a more intuitive visual perception for our braid.We do this by indicating over/under crossings as in the following deﬁnition.17d d i j d d ijFigure 13:When two parallel lines in the projection intersect,we can tilt one slightly so that the intersection is now just one point.d i d jd k d i d j d kFigure 14:When more than two lines meet at a point,we can bend all but two of the lines around the point.d i d j d i d jFigure 15:When a vertex lies on an intersection point,we simply truncate the vertex.18Figure16:A double point,and the two possible modiﬁcations that can be made toˆβto indicate overstrands/understrands.1234Figure17:A regular diagram,re-drawn without any points labeled and with hor-izontal lines placed at the top and bottom.Deﬁnition2.14.Deﬁne the projection map onto the x-axis r:R3→R by r(x,y,z)=x.Let β∈B n,andˆβbe a regular projection ofβ.For each double point Q ofˆβ(say an intersection of d i,d j),decide which of d i,d j is‘in front’by seeing which of r(d i∩p−1(Q))or r(d j∩p−1(Q))is greater.This equates to seeing which of d i∩p−1(Q)or d j∩p−1(Q)lies closer to the front face of D.Without loss of generality,we can say d i is in front.Then remove a small section of p(d j) around Q inˆβ.This gives us an idea of which strandﬂows over and which ﬂows under.Figure16gives an example of a double point,and the two possible modiﬁcations that can be made toˆβ.This modiﬁed regular projection is called a regular diagram or just diagram for the braidβ.Two diagrams are said to be equivalent if they are the diagrams of equivalent braids.The idea behind a regular diagram is as follows:We take our braid and lay it out on a page,then draw what we see from above.Crossings are drawn as they appear to us from above,with the over/under strands marked accordingly.The rest is a simple tracing of the braid.From here on,we will draw our regular diagrams without the A i and B i labeled,and will place a horizontal line at the top and bottom of the diagram to indicate the top and bottom of the braid. Figure17gives an example of this.193The braid groupIn this section we develop a way to view braids as elements of a group,with a natural operation known as a braid product.We are then able toﬁnd aﬁnite presentation of this group.3.1Braids as a groupWe now move to deﬁning operations on the set of braids as a preliminary step to show that the set of n-braids can be viewed as a group,known as Artin’s n-braid group or just the n-braid group.We begin by introducing a way to multiply braids to give another braid.Deﬁnition3.1.Letβ1,β2∈B n.We shall deﬁne a new braid fromβ1,β2,called the braid product ofβ1withβ2and denotedβ1β2,as follows:Letβ1,β2lie in unit cubes D1,D2respectively.Identify(glue)the base(z=0)of D1to the top(z=1)of D2.Then scale the union D1∪D2by a factor of12and call this D.Clearlythe end points of arcs inβ1andβ2are matched up in this identiﬁcation.The resulting collection of n arcs in D is denotedβ1β2,the braid product ofβ1with β2.Figure18gives an example of two3-braids and their product.Theorem3.2.Letβ1,β2∈B n.Thenβ1β2∈B n.Proof.Letβ1lie in D1,with braid strings{d11,...,d1n},where each d1i begins at A1i and ends at B1j1(i).Letβ2lie in D2,with braid strings{d21,...,d2n},where each d2ibegins at A2i and ends at B2j2(i).Then,after we identify the bottom of D1with the top of D2,each B1i is identiﬁed with A2i.Thus,for each1≤i≤n,the endof d1i(i.e.,B2j1(i))connects to the start of d2j1(i).So{d1i∪d2j1(i)|1≤i≤n}is aset of n polygonal arcs in D,and we denote each d1i∪d1j1(i)by d i.In Figure18we illustrate this for the braid product of two3-braids.We now show that the d i form the braid strings of an n-braid,by direct veriﬁcation of the deﬁnition of an n-braid.•Sinceβ1(respectivelyβ2)is a braid,then all the d1i(respectively d2i)are disjoint.Thus the d i must be disjoint,each being the union of d1i and d2j1(i).•By deﬁnition,each d i begins at A1i and ends at B j2(j1(i)).201212Figure18:Two3-braids,re-drawn as one above the other,then re-scaled to give their product.•Sinceβ1(respectivelyβ2)is a braid,then each level plane in D1(respectively D2)intersects each d1i(respectively d2i)exactly once.Thus each level plane in D intersects each d i exactly once.•Each d1i(respectively d2i)is contained in D1(respectively D2).Thus eachd i is contained in D.Thus the collection of n arcs d1,...,d n satisfy the deﬁnition of an n-braid,soβ1β2 is in fact an n-braid.Before we can prove that B n forms a group,we require the following lemmas.21abbaFigure19:Two3-braids a and b,their product ab,and their product ba. Lemma3.3.Supposeβ,β′,β,β′∈B n withβ∼β′andβ∼β′.Thenββ∼β′β′Proof.We haveβ∼β′.Hence there exists the followingﬁnite sequence of elementary moves:β=β0Ω0−→β1...Ωm−1−→βm=β′This induces the following sequence:ββ=β0βΩ0−→β1β...Ωm−1−→βmβ=β′βAnd thusββ∼β′β.We also haveβ∼β′.Hence there exists aﬁnite sequence of elementary moves:β=β0¯Ω0−→β1...¯Ωk−1−→βk=β′This induces the following sequence:β′β=ββ0¯Ω0−→ββ1...¯Ωk−1−→ββk=β′β′And thusβ′β∼β′β′.So,sinceββ∼β′βandβ′β∼β′β′,then(by transitivity of∼),ββ∼β′β′.Lemma3.4.Letβ1,β2,β3∈B n.Then(β1β2)β3∼β1(β2β3).That is to say,taking braid products is associative.Note however that the product of braids is not(in general)commutative.That is,givenβ,β′∈B n,ββ′need not be equivalent toβ′β.Figure19shows a counter example,giving two3-braids a and b where ab and ba are not equivalent.Proof.Fix diagrams A,B,C forβ1,β2,β3respectively,as shown in Figure20.Then22Figure20:Diagrams A,B,C for braidsβ1,β2,β3respectively.Figure21:A diagram for(β1β2)β3,and a diagram forβ1(β2β3).Figure21a)gives a diagram for(β1β2)β3.Similarly,Figure21b)gives a diagram forβ1(β2β3).But these are identical diagrams.Thus they represent equivalent braids.Deﬁnition3.5.Let e be the n-braid deﬁned as follows:For each1≤i≤n,join A i to B i via a straight line segment d i.The braid e is called the identity or trivial braid, denoted1n.The trivial braid is just that;the simplest n-braid we canﬁnd.It is the only n-braid that has a diagram without any crossings.When we braid hair,the trivial braid is what we begin with,before we start adding twists to the strands. Lemma3.6.For anyβ∈B n we have thatβ1n∼βand1nβ∼β.Thus1n acts as an identity element for braid products.Proof.Fix a diagram forβas in Figure22a).Now,we know1n has a diagram as23Figure22:Diagrams forβ,1n,and their productβ1n.Figure23:Contracting the bottom of the vertical strands of a diagram forβ1n to obtain a diagram forβ.shown in Figure22b).Thusβ1n has(as one of its diagrams)that of Figure22 c).However,we can contract the vertical strands at the bottom of the diagram ofβ1n as shown in Figure23,and this is a braid equivalence.Henceβ1n∼β(And an almost identical argument shows that1nβ∼β).So attaching the trivial n-braid onto either end of an n-braidβdoes not change β.This makes sense since all we are eﬀectively doing is lengthening the top or bottom ends of the strands ofβ.Lemma3.7.Givenβ∈B n,there existsβ′∈B n such thatββ′∼1n andβ′β∼1n.Such a braidβ′is called the inverse ofβ,denoted byβ−1.Proof.Letβbe an n-braid in D.Create a new braidβ′by reﬂectingβin the bottom24Figure24:The crossing X and its mirror image over J.di d jJFigure25:Removing the two crossings X and its mirror image.face of D(i.e.,the plane z=0,which we shall call J).Then form the n-braid ββ′.We now perform elementary moves onββ′to transform it into the trivial braid as follows:We begin at the junction J ofβandβ′(i.e.,whereβends andβ′begins,which is the plane of reﬂection).We then traverse up the diagram forββ′(call this B)until we come to theﬁrst crossing(i.e.,the crossing closest to J).If there happen to be multiple such crossings,choose(any)one.So we have found ourﬁrst crossing X,say of strings d i and d j,and without loss of generality we can assume d i is the overstrand.Thus we have B looking locally like Figure24.This is because we know that B has mirror symmetry about J,and there are no other crossings between X and its image below J.Thus some simple elementary moves eliminate the crossing X and its mirror image,as shown in Figure25.However, we have managed to perform these moves without introducing any new crossings, and still keeping the mirror-symmetry in the diagram.So we now have a new diagram B′forββ′with two fewer crossings.We then iterate this process on the diagram B′and so forth,each time reducing the number of crossings by2,and yet preserving the symmetry.Eventually,we are left with an n-braid with no crossings,which is equivalent to the trivial braid.Soββ′∼1n.Now,placingβ′in D′and reﬂecting in the bottom face of D′gives usβagain,hence an almost identical argument showsβ′β∼1n.25So as we can see,it is extremely easy to construct the inverseβ−1of an n-braid β.The existence of such a braid means that we can undo any braid from below (or above).This is in contrast to knot theory,where it is known that the connect sum of any two non-trivial knots will give another non-trivial knot.See[8]for more details about the connect-sum of knots.Ourﬁnal step is to deﬁne a set in which two equivalent braids are considered the same.This quotient of B n will end up being our group of n-braids.Deﬁnition3.8.Letβ∈B n.We denote the∼-equivalence class ofβby[β].Denote by B n the set of all∼-equivalence classes of n-braids.That is,B n:=B n/∼Deﬁnition3.9.Let[β],[β′]∈B n.Deﬁne an operation on equivalence classes of braids as follows:[β]·[β′]:=[ββ′]whereββ′is the braid product ofβandβ′.Theorem3.10.The set B n forms a group,with operation·as deﬁned above.This group is called the n-braid group or Artin’s n-braid group.Proof.Let[β1],[β2],[β3],∈B n.1.[β1]·[β2]=[β1β2]∈B n by Theorem3.2.So B n is closed under the operation·2.([β1]·[β2])·[β3]=[β1β2]·[β3]=[(β1β2)β3]=[β1(β2β3)]by Lemma3.4=[β1]·[β2β3]=[β1]·([β2]·[β3])So·is an associative operation on B n.2612i i+1n-1n12i i+1n-1nFigure26:A diagram forσi,and forσ−1i.3.[1n]·[β1]=[1nβ1]=[β1]by Lemma3.6.[β1]·[1n]=[β11n]=[β1]by Lemma3.6.So[1n]is the identity element for B n.4.[β1]·[β−11]=[β1β−11]=[1n]by Lemma3.7[β−11]·[β1]=[β−11β1]=[1n]by Lemma3.7So[β−11]is the inverse to[β1],written[β1]−1,·)satisﬁes the deﬁnition of a group.Thus(BNote:To avoid awkward notation,we will denote an n-braidβ∈B n and its equivalence class[β]∈B n both byβ(since we intuitively hold all equivalent braids as being the same).It should be obvious in the context of what is being said which deﬁnition is being assumed.3.2A presentation of the braid groupWe now move on toﬁnding an explicit presentation for B n.As it turns out,B n isﬁnitely presented,and we shallﬁnd one suchﬁnite presentation.Deﬁnition3.11.For1≤i≤n−1,deﬁne the n-braidσi as the braid represented by the diagram in Figure26a).That is,σi is the braid with only one crossing,where the string from A i to B i+1crosses under the string from A i+1to B i.The inverse n-braid of σi(denotedσ−1i as usual)is thus given as the braid represented by the diagram in Figure26b).That is,σi is the braid with only one crossing,where the string from A i to B i+1crosses over the string from A i+1to B i.The set{σ1,...,σn−1}is know as the set of Artin generators for the braid group B n.Theσ′i s are the simplest n-braids(after the trivial braid),having diagrams with only one crossing(necessarily between two adjacent strands).It should not be27。

药物化学专业英语词汇

medicinal药品,药物, 药的,药用的 be split into 分成，分为pharmaceutical 药学的，制药的，药品 starting materialsynthetic, 合成的，人造的，；synthetics化学合成品, synthesis合成(法), semisynthetic, synthesize, synthesesalkaloid 生物硷lead structure 先导结构 intermediate 中间体isolation 分离 natural source 天然来源enzyme 酶 heart glycoside 强心苷steroid 甾体 precursor 前体organ/target organ 靶器官 peptidehormone 激素 insulinpancreas vaccinepolysaccharide serumcholesterol 胆固醇 amino acidgelatine hydrolysis水解/hydrolysate水解产物/hydrolyze水解hydroxylation antibiotic 抗生素，抗菌的antibody interferon 干扰素fermentation 发酵 dextran 葡聚糖ーlactam natural producttherapy/therapeutic治疗的/therapeutic margincaffeine咖啡因 yeastmicrobiological mutantmicroorganism geneticmould high performancebacterial proteinmucous membranemetabolism新陈代谢 metabolite代谢物plasma 血浆 molecule /molecular weightfood additive organiclactic acid乳酸 citric acid 柠檬酸penicillin penicilliumtetracycline derivative衍生物contamination污染 sterile无菌的aerobic oxygencarbon dioxide carbohydratestarch saccharide/ polysaccharideglucose葡萄糖 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extentpenetration spatial arrangement pharmacologic stereochemistrythree-dimensional structure lipidstructure-activity relationship stericcorrelation parameterpartition coefficient distribution fuction conformation extractionoptical isomerism/optical isomer enantiomorphic/ enantiomorph by no means tartaric acidManually magnificationdrug design polarized light dextrorotatory levorotatory Clokwise countclockwiseAntipode nonsuperimposable mirror imageCoincide with glyceraldehydeAbsolute literatureconfiguration crystallographyasymmetric center accessisomeric enantiomerdiastereoisomer atomic numberPrioritymagnification solubilityspatial sequencein vivo/in vitro receptorintravenous injection静脉注射 be susceptible to敏感的With respect to contractSubstrate epoxidationcarcinogen oxidation /oxidasepreparation predominantspecies complexdehydrase/dehydrogenase/decarboxylase/hydrolytic enzymes/isomerase/permease Choline one out of every ten 十分之一clinical 临床的 interactionexcrete/excretion inversionCoordination DelayEfficacy in place相称的，合适的entity drug developmentattrition toxicity/toxic/ toxicology/Anti-infectives Healthcarerepro-toxicology/genotoxicity drug candidateindication pharmacokinetics adverse profileformulary/formulation/formulor onsetdose/once a day dosing dosage/dosage form/overdosage regulatory interdependentsubacute亚急性的/chronic clinical/preclinicalvital optimum/ optimizeimpurity pilot plantcritical path criteriaupdate in paralleladequate stabilitypotency dermal cardiovascular 心血管的respiratory nervousconcurrently labelsynergies 协同作用 antagonizereversible/irreversible permissiblelifespan diseasetumour inhalercapsule rodentfoetal teratologyexposure patchset-up hazardOn a large scale shelf-lifetannin caffeineIn common vacuum fitrationhomogeneous gallic acidhydroxyl group esterifyphenolic precipitatenon-hydrolyzable carboxyl groupacidic calcium carbonatechloroform flavonoiddistillation sublimationsalicylic acid three neck round bottom flask separatory funnel steam 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acid直链淀粉amylose支链淀粉amylopectin糖原glycogen费林试验Fehling test苷glycoside糖杂体heteroside苷元aglycone苦杏仁酶emulsin氰苷cyanogenic glycoside, cyanogenetic glycoside 酚苷phenolic glycoside多酚polyphenol醛苷aldehyde glycoside醇苷alcoholic glycoside吲哚苷indole glycoside树脂醇苷resinol glycoside硫苷thioglycoside呫吨酮xanthone呫吨酮苷xanthonoid glycoside蒽醌anthraquinone蒽醌苷anthraquinone glycoside蒽酚anthranol氧化蒽酚oxanthranol蒽酮anthrone二蒽酮dianthrone羟基蒽醌hydroxyanthraquinone博恩特雷格反应Borntrager reaction 黄酮类flavonoid黄酮苷flavonoid glycoside黄酮flavone黄烷flavane黄酮醇flavonol黄烷酮flavanone黄烷酮醇flavanonol异黄酮isoflavone异黄烷酮isoflavanone新黄酮类neoflavonoid裂环烯醚萜苷secoiridoid glycoside 木脂体lignan木脂内酯lignanolide新木脂体neolignan木素lignin萜terpene萜类terpenoid半萜hemiterpene单萜monoterpene倍半萜sesquiterpene二萜diterpene三萜triterpene四萜tetraterpene多萜polyterpene齐墩果烷oleanane挥发油volatile oil精油essential oil鞣质tannin鞣酸tannic acid可水解鞣质hydrolysable tannin缩合鞣质condensed tannin鞣酐phlobaphene鞣花鞣质ellagitannin没食子鞣质gallotannin双缩脲反应biuret reaction脂肪fat脂肪油fatty oil去油de-fatting蜡wax环烯醚萜苷iridoid glycoside环烯醚萜iridoid裂环烯醚苷secoiridoid皂化saponification酸败rancidity饱和脂肪酸saturated fatty acid不饱和脂肪酸unsaturated fatty acid有机酸organic acid树脂resin油树脂oleoresin树胶树脂gum resin香树脂balsam香脂酸balsamic acid苷树脂glycosidal resin苦味素bitter principle色素pigment微量元素trace element生物碱alkaloid吖啶生物碱acridine alkaloid阿朴啡类生物碱aporphine alkaloid苄基异喹啉生物碱benzylisoquinoline alkaloid双苄基异喹啉生物碱bisbenzylisoquinoline alkaloid 双吲哚生物碱bisindole alkaloid咪唑生物碱imidazole alkaloid吲哚生物碱indole alkaloid吲哚联啶生物碱indolizidine alkaloid吲哚烷胺生物碱indolylalkylamine alkaloid异喹啉生物碱isoquinoline alkaloid大环生物碱macrocyclic alkaloid吗啡烷生物碱morphinane alkaloid羟吲哚生物碱oxindole alkaloid菲啶生物碱phenanthridine alkaloid苯烷胺生物碱phenylalkylamine alkaloid哌啶生物碱piperidine alkaloid嘌呤生物碱purine alkaloid吡啶生物碱pyridine alkaloid吡咯生物碱pyrrolidine alkaloid吡咯联啶生物碱pyrrolizidine alkaloid喹唑啉生物碱quinazoline alkaloid喹啉生物碱quinoline alkaloid喹啉联啶生物碱quinolizidine alkaloid甾体生物碱steroid alkaloid萜类生物碱terpenoid alkaloid四氢异喹啉生物碱tetrahydroisoquinoline alkaloid碘化汞钾试剂Mayer's reagent碘化铋钾试剂Dragendorff's reagent碘化钾碘试剂Wagner's reagent硅钨酸试剂Bertrand's reagent, silicotungstic acid reagent磷钼酸试剂Sonnenschein's reagent, phospho-molybdic acid reagent 苦味酸试剂Hager's reagent, picric acid reagent矾酸铵-浓硫酸试液Mandelin test solution钼酸铵-浓硫酸试液Frohde test solution甲醛-浓硫酸试液Marquis test solution莨菪烷tropane莨菪烷生物碱tropane alkaloid除虫菊素类pyrethroid-acetal 醛缩醇acetal- 乙酰acid 酸-al 醛alcohol 醇-aldehyde 醛alkali- 碱allyl 丙烯基alkoxy- 烷氧基-amide 酰胺amino- 氨基的-amidine 脒-amine 胺-ane 烷anhydride 酐anilino- 苯胺基aquo- 含水的-ase 酶-ate 含氧酸的盐、酯-atriyne 三炔azo- 偶氮benzene 苯bi- 在盐类前表示酸式盐bis- 双-borane 硼烷bromo- 溴butyl 丁基-carbinol 甲醇carbonyl 羰基-caboxylic acid 羧酸centi- 10-2chloro- 氯代cis- 顺式condensed 缩合的、冷凝的cyclo- 环deca- 十deci 10-1-dine 啶dodeca- 十二-ene 烯epi- 表epoxy- 环氧-ester 酯-ether 醚ethoxy- 乙氧基ethyl 乙基fluoro- 氟代-form 仿-glycol 二醇hemi- 半hendeca- 十一hepta- 七heptadeca- 十七hexa- 六hexadeca- 十六-hydrin 醇hydro- 氢或水hydroxyl 羟基hypo- 低级的，次-ic 酸的，高价金属-ide 无氧酸的盐，酰替…胺，酐-il 偶酰-imine 亚胺iodo- 碘代iso- 异，等，同-ite 亚酸盐keto- 酮ketone 酮-lactone 内酯mega- 106meta- 间，偏methoxy- 甲氧基methyl 甲基micro- 10-6milli- 10-3mono- ( mon-) 一，单nano- 10-9nitro- 硝基nitroso- 亚硝基nona- 九nonadeca- 十octa- 八octadeca- 十八-oic 酸的-ol 醇-one 酮ortho- 邻，正，原-ous 亚酸的，低价金属oxa- 氧杂-oxide 氧化合物-oxime 肟oxo- 酮oxy- 氧化-oyl 酰para- 对位，仲penta- 五pentadeca- 十五per- 高，过petro- 石油phenol 苯酚phenyl 苯基pico- 10-12poly- 聚，多quadri- 四quinque- 五semi- 半septi- 七sesqui 一个半sexi- 六sulfa- 磺胺sym- 对称syn- 顺式，同，共ter- 三tetra- 四tetradeca- 十四tetrakis- 四个thio- 硫代trans- 反式，超，跨-yl 基-ylene 撑(二价基，价在不同原子上）-yne 炔。

IEEE standard definitions of terms for antennas 145-1993

The Institute of Electrical and Electronics Engineers, Inc. 345 East 47th Street, New York, NY 10017-2394, USA Copyright © 1993 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Published 1993. Printed in the United States of America ISBN 1-55937-317-2
IEEE Std 145-1993
(Revision of IEEE Std 145-1983)
IEEE Standard Deﬁnitions of Terms for Antennas
Sponsor
Antenna Standards Committee of the IEEE Antennas and Propagation Society
Approved March 18, 1993
IEEE Standards Board
Abstract: Definitions of terms in the field of antennas are provided. Keywords: antennas, definitions, propagation, terminology
IEEE Standards documents are adopted by the Institute of Electrical and Electronics Engineers without regard to whether their adoption may involve patents on articles, materials, or processes. Such adoption does not assume any liability to any patent owner, nor does it assume any obligation whatever to parties adopting the standards documents.

专英词汇

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抗体效价的Elisa测定

戊二醛法，过碘酸氧化法将酶与Ab交联在一起
Ag-Ab-抗Ab-HRP
TMB+H2O2 产物（黄色，OD450)+H2O
图一直接型Elisa
图二间接型Elisa
图三双抗体夹心型ELISA
图四固相抗体竞争型ELISA 未知抗原量=A（1）-A（2）
每次反应后都要反复洗涤？ 1. 确保反应旳定量反应 2. 预防重叠反应，引起非特异现象。
HIV (human immunodeficiency virus) detection
Partially purified, inactivated HIV antigens
antigens pre-coated onto an ELISA plate
部分纯化，灭活病毒抗原抗原涂到酶标板
Patient serum which contains antibodies. If the patient is HIV+, then this serum will contain antibodies to HIV, and those antibodies will bind to the HIV antigens on the plate.病人血清中具有抗体。假如病人是艾滋病毒+，那么这个血清具有
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Protein protein interaction---ELISA
1.Remove the stacking gel from the gel.

2019年最新-Cosmic Strings and Superstrings宇宙字符串和超弦-精选文档

Witten (1985) discusses two instabilities that would prevent strings from reaching cosmic sizes. I. Some strings can break:
4-d picture: breakage of flux tube due to monopole-antimonopole pair production.
details of compactification.
• Strings with axion charge are confined.
• Strings with Aharonov-Bohm charges are absolutely stable.
Production of cosmic strings:
Example: gauge theory solitons. These solutions exist as topological defects in the Higgs field whenever a U(1) symmetry is broken:
our brane
Brane inflation:
An attractive model of inflation is that there were additional brane-antibrane pairs in the early universe. Their energy density induced inflation; subsequently they annihilated:
Instabilities of strings II
II. Some strings are ‘confined’ by a strong selfattraction:

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a r X i v :h e p -t h /0303255v 3 2 J u l 2003hep-th/0303255A Note on D–brane —Anti–D–brane Interactionsin Plane Wave BackgroundsCliﬀord V.Johnson,Harald G.Svendsen Centre for Particle Theory Department of Mathematical Sciences University of Durham Durham,DH13LE,U.K.c.v.johnson@,h.g.svendsen@ Abstract We study aspects of the interaction between a D–brane and an anti-D–brane in the maximally supersymmetric plane wave background of type IIB superstring theory,which is equipped with a mass parameter µ.An early such study in ﬂat spacetime (µ=0)served to sharpen intuition about D–brane interactions,showing in particular the key role of the “stringy halo”that surrounds a D–brane.The halo marks the edge of the region withinwhich tachyon condensation occurs,opening a gateway to new non–trivial vacua of the theory.It seems pertinent to study the fate of the halo for non–zero µ.We focus on the simplest cases of a Lorentzian brane with p =1and an Euclidean brane with p =−1,the D–instanton.For the Lorentzian brane,we observe that the halo is unaﬀected by the presence of non–zero µ.This most likely extends to other (Lorentzian)p .For the Euclidean brane,we ﬁnd that the halo is aﬀected by non–zero µ.As this is related to subtleties in deﬁning the exchange amplitude between Euclidean branes in the open string sector,we expect this to extend to all Euclidean branes in this background.1IntroductionA D–brane and its“anti–particle”,an anti–D–brane,upon approaching each other,will annihi-late.The generic product of this annihilation process is expected to be a state of closed strings, which carry no net R–R charge.This expectation is supported byﬁeld theory intuition and knowledge of which objects are the carriers of the available conserved charges in perturbative string theory.From experience withﬁeld theory one expects to be able to see the beginnings of the process of annihilation via the opening up of new decay channels at coincidence.These can be seen by studying the amplitude for exchange of quanta between the two branes,which gives a potential.At small separations,the behaviour of the interaction potential can signal new physics.Basically,a divergence in the amplitude as the objects are brought together can signal the opening up of a new channel(or new channels)not included in the computation of the amplitude away from the divergent regime.Inﬁeld theory,for a separation X of the two objects,the divergence follows simply from the fact that the amplitude for exchange is controlled by the position space propagator∆(X) which(for more than two transverse directions)is divergent at X=0.This is where the new channels can open up,which can include the processes for complete annihilation into a new sector,if permitted by the symmetries of the theory.For D–branes in superstring theory,such a divergence does indeed show up,but there is an important new feature[1].The divergence occurs when the D–branes areﬁnitely separated,by an amount set by X2H=2π2α′,whereα′is the characteristic length scale set by a fundamental string’s tension.This is interpreted as the fact that in addition to the many special features of D–branes,they have a“stringy halo”originating in the fact that the bulk of the open strings which(by deﬁnition)end on them can reach out in the transverse directions,forming a region of potential activity of size set by X H.This halo means that the D–branes can interact with each other before zero separation,as there is an enhancement of the physics of interaction by new light states formed by the entanglement of the halos,and the crossover into the annihilation channel begins before the branes are coincident.Recall that the amplitude of exchange can be thought of using two equivalent pictures: Either as tree level exchange of closed string quanta between the branes,or(after a modular transformation)as the one–loop vacuum diagram for open strings stretched between the two D–branes.In the open string description,at separation X H,the lightest open string becomes massless,and for any closer separation it becomes tachyonic,signalling that the entire vacuum conﬁguration is unstable and wishes to roll to another vacuum.It is this tachyon which produces the divergence in the amplitude,converting a decaying exponential into a growing one,spoiling the convergence of the amplitude in the infra–red(IR)region.The D–branes annihilate via conversion to closed strings in the generic situation,but thetachyon picture can be exploited in a beautiful way to produce more structure[2,3,4,5].For the G=U(N)×U(N)gauge theory on the(p+1)–dimensional world–volume on N D p–branes and N anti–D p–branes,the tachyonﬁeld,transforming as the(N,¯N),can be put into a conﬁguration endowed with non–trivial topological charge,and the tachyon potential need not yield a runaway to a sector containing only closed strings.Having such topological vacuum solutions in the tachyon sector allows for the possibility of a stable remnant—interpreted as a D–brane of lower dimension—of the annihilation process after the debris that is the closed string products has cleared.It turns out that the spectrum of hypermultiplets in the U(N)×U(N)world–volume theory supplies a set of variables which is isomorphic to those needed to perform a K–theoretic analysis of the topology of G–vector bundles over the world–volume,and so the classiﬁcation of all D–branes which can appear on a spacetime is apparently elegantly and economically by using the results of the appropriate K–theory of the spacetime which the D p–branes and anti–D p–branesﬁll[6,7,8].The case of p=9for Minkowski spacetime yields the entire classiﬁcation of D–branes in the most familiar symmetric vacuum of type IIB superstring theory.This is all well understood for the case ofﬂat ten dimensional spacetime.So when one en-counters another background which enjoys the same maximal supersymmetry asﬂat spacetime —a plane wave with R–Rﬂux[9]:ds2=2dx+dx−−µ2x2(dx+)2+4i=1dx i dx i+8 i=5dx i dx i,F+1234=F+5678=2µ,x2=8i=1x i x i,x±=12(x9±x0),(1)which also yields an exactly solvable string model[10](in light–cone gauge deﬁned by relat-ing worldsheet timeτto x+via x+=2πα′p+τ,where p+is the+component of spacetime momentum):L=12πα′(S a∂+S a+˜S a∂−˜S a−2MS aΠab˜S a),(2) with a mass parameter M=2πα′p+µ—it is inevitable that questions about the key lessons which were learned about D–branes will spring to mind1.Is the picture of D–branes as Dirichlet open string boundary conditions as powerful in this context as it has been inﬂat spacetime?In particular,do the dynamics hidden within a halo’s breadth of the branes bear any similarity to theﬂat spacetime case?Are all D–branes classiﬁed by K–theory,now of the new background?In this paper we note that the properties of the halo—the fact that it exists,and also its location and size—are unaﬀected by non–zeroµfor all branes that have a Lorentzian deﬁnition,i.e.,are at a deﬁnite position in space,but not time.So this particular (and important)property of D–branes in this non–trivial R–R background is very much like that in ﬂat space.This bodes well for an attempt to classify such D–branes in this background using tachyon condensation and K–theory.Howver,for branes with a Euclidean deﬁnition,such as the p =−1brane,we ﬁnd that the halo —or at least its analogue in this context—is deformed by non–zero µ.2The InteractionIt isconvenient[13,18]to label D–branes in the plane wave background given in equation (1)as (r,s ),if they are Euclidean,where r denotes the spatial extent in directions i =1,2,3,4and s denotes the spatial extent in directions i =5,6,7,8.A D p –brane would then have r +s =p +1.If the D–branes are Lorentzian,then their worldvolume extends in the x +and x −direction,and the notation is (+,−,r,s ).In that case,a D p –brane has r +s =p −1.The string theory diagram of interest is a cylinder,representing either the tree level exchange of closed string quanta between two D–branes,or the one–loop vacuum process involving the circulation of open strings with ends on either D–brane.See ﬁgure 1.2Figure 1:Cylinder diagram for computing the amplitude of interaction between two branes.The parameter t is open string propagation time,and is the modulus of the cylinder.We will focus on the results for the simplest branes in the Euclidean and Lorentzian classes.These are the D(−1)–branes (or (0,0)–branes),and the D1–branes (or (+,−,0,0)–branes),discussed in ref.[18].The former requires the time direction,in which the branes are also pointlike,to be Euclidean.The results are reasonably simple for these cases,compared to other (r,s )with r =s =0,and it would be interesting to explore those other cases in detail.We expect that the key observations made in this paper for these r =0=s cases will be quite generic,although there may be additional features to be deduced from studying other cases in detail.2.1The Amplitude and PotentialWe consider a D p–brane and its antiparticle for p=±1.If p=−1,it is an instanton,(a (0,0)–brane)and we consider it to be pointlike in Euclidean time.If p=+1it is a string,(a (+,−,0,0)–brane)and the theory is Lorentzian.So we place a D p–brane at position y i1in the x i directions(i=1,...,8),and a2t t−(p+12πα′ˆh0(t;y1,y2)ˆg(m)4(t)4 2∞n=1(1−qωn),ˆh(t;y1,y2)=exp −mt2l∈P−1−q|ωl| 1(2π)2∞p=1 ∞0ds e−p2s−π2m2(2π)2∞p=1(−1)p∞ r=0c p r m∂r m ∞0ds −s s,(4)and the parameter q and the deformed harmonic oscillator frequencies are deﬁned as:q=e−2πt,ωn=sign(n)√x−1 p+x−1The sets P−and P+are given as solutions of the equationsl∈P−:l−iml−im+e2πil=0.(7)The details of the derivation of these amplitudes can be found in ref.[18].We will not need them all here,and refer the reader there for more information.Some comments are in order however.For the case p=1,the computation was done directly in terms of the open string channel,with open string light cone gauge x+=2πα′p+τ,so we havet=X+2πα′p+,since light–cone gauge in the closed string sector is x+=2πα′p+τ,with mass parameterM=2πα′p+µ.(9) Open–closed string duality is then invoked to deﬁne the amplitude given in equation(3),where modular transformation gives the expression above,witht=1/˜t=2πα′p+2tt−(p+14π2α′sinh(mπ) cosh(mπ)(y21+y22)−2y1·y2 −4(ˆ∆m−2∆m)−i X+X−and the function G(t)is deﬁned as:G(t)= l∈P+(1−q|ωl|)2 l∈P−(1−q|ωl|)22in NS sector.For strings stretched between two D–branes,we have p m=x m/2πα′for transverse(to the branes)directions x m.So,splitting transverse(labelled m)and parallel(labelled i)directions we can writeL0=α′p i p i+N+z2α′ N+a R(NS)+z22)has mass squaredM20=12π2α′−1.(16)This is a tachyon if z2<2π2α′.In the usual case this ground state is eliminated by the GSO projection P=1+(−1)F2,since anti–branes come with a minus sign.This means that the NS ground state(N=0)will now survive,and the possible tachyon above is present in the spectrum.So for z2<2π2α′there is a tachyon,and so thereis a 1–1correspondence between the tachyon’s appearance and divergence of the integral.(For the case when all of the directions are transverse,as is the case for D–instantons,the tachyon interpretation follows from continuation and T–duality.)Let us write everything in terms z i ,the separation between the branes in the eight direc-tions x i ,deﬁned by y i 2=y i 1+z i .The expression for Z then becomesZ (m,y 1,z )=1tanh(mπ) (z +a )2−itanh(mπ)cosh(mπ)y 1,b =tanh(mπ) mπtanh(mπ).(18)For the Lorentzian p =1case,these parameters simplify further in the t →∞limit of interest.Since for ﬁxed X +the large t region corresponds to small p +(this follows from equation(8),orongeneral grounds from the operator deﬁnition of the amplitude),we see that m →0in all of these expressions,and so we obtain:Z −→1πµX +X +X −=2π2α′D (µX +)tanh(πµX +)2We thank Simon Ross for reminding us of the signiﬁcance of this for D–instantons.Recall thatˆ∆m and∆m tend to1/12and−1/48,respectively,when m=µX+tends to zero. The quantity D(µX+)decreases from unity and asymptotes to zero asµX+increases.Of course,whenµ(and hence m)vanishes,this gives the expected result:z2−iX+X−=2π2α′≡X2H.(22) Note here that the unusual factor of−i in this expression is as a result of the Wick rotation, which results in the(complexiﬁed)metricds2=−2idx+dx−+µ2x2(dx+)2+8i=1dx i dx i.(23)For non–zeroµit is hard to interpret the result cleanly,but there is certainly a non–trivial dependence of the location of the“halo”onµ,in contrast to the Lorentzian case.As a simple special case,one can place the branes at the same transverse position,and hence z i=0.Then we have the equation:−iX+X−=16π2α′ ˆ∆m−2∆m .(24) For orientation,let us consider theﬂat space caseµ=0.We can continue to a more familiar Lorentzian picture by choosing X−→iX−.This gives a hyperbola in the plane,with equationX+X−=2π2α′≡X2H.(25) Contrast this to the case ofﬁeld theory,where the right hand side would be zero,giving us the light–cone.This is as expected for point like behaviour.Theﬂat space string theory result gives us a hyperbola.This is the manifestation of the halo which broadens out the available region of contact by widening the light–cone into a sort of“light–funnel”.For theµ=0case, the hyperbola is deformed,since X−decreases more rapidly with increasing X+than before due to the behaviour of the function D(X+)discussed below equation(21).Seeﬁgure2.For the interpretation of the shape of the halo for non–zeroµonce the transverse positions of the branes are diﬀerent from each other,more work is needed.This is because the metric is no longerﬂat,and furthermore,one has to take seriously the matter of the Euclidean continuation of the metric implied in the computation of the amplitude.The choices made mean that the metric is no longer real(see equation(23)),and this presents diﬃculties of interpretation which must be explored further.3DiscussionWe have found that the structure of the halo for Lorentzian branes in the plane wave background is independent ofµ,giving the same physics as for D–branes inﬂat space.This is because theFigure2:The hyperbola(solid curve)represents the edge of the“halo”for D–instantons inﬂat space,µ=0.For theµ=0case,it is deformed to the dashed curve.Theﬁeld theory result is the pair of lines X+X−=0.mass parameter induced by non–zeroµin the eﬀective world–volume theory vanishes in the open string IR limit,the regime where the halo is to be found.We observed that this is not the case for the D–instanton(and presumably all Euclidean branes),since their being pointlike in the X±directions requires the relevant amplitudes to be deﬁned by starting with the closed string light cone gauge and then arriving at the open string physics by duality.The resulting open string physics sees a mass parameter which does not vanish in the IR limit, and hence the physics of the halo is not the same as inﬂat space.The signiﬁcance of this non–trivialµdependence of the structure of the halo of the D–instanton(and by extension, all Euclidean branes deﬁned by starting with the closed string amplitude)is not clear to us at present.However,it may have some signiﬁcance,since D–instantons contribute to type IIB string theory processes non–perturbatively(see e.g.,ref.[43]).Note on earlier version of this manuscriptIn an earlier version of this manuscript,we noted that there wereµ–dependent eﬀects for Lorentzian branes as well.That was a mistake,and we apologise for any confusion caused. 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