Details of Insect Wing Design and Deformation

Details of Insect Wing Design and Deformation

(Parte 1 de 2)

DOI: 10.1126/science.1175928 , 1549 (2009); 325Science et al.John Young, Efficiency Enhance Aerodynamic Function and Flight Details of Insect Wing Design and Deformation w.sciencemag.org (this information is current as of October 2, 2009 ): The following resources related to this article are available online at http://www.sciencemag.org/cgi/content/full/325/5947/1549 version of this article at: including high-resolution figures, can be found in the onlineUpdated information and services, http://www.sciencemag.org/cgi/content/full/325/5947/1549/DC1 can be found at: Supporting Online Material found at: can berelated to this articleA list of selected additional articles on the Science Web sites http://www.sciencemag.org/cgi/content/full/325/5947/1549#related-content http://www.sciencemag.org/cgi/content/full/325/5947/1549#otherarticles , 13 of which can be accessed for free: cites 21 articlesThis article http://www.sciencemag.org/cgi/collection/biochem Biochemistry : subject collectionsThis article appears in the following http://www.sciencemag.org/about/permissions.dtl in whole or in part can be found at: this article permission to reproduce of this article or about obtaining reprintsInformation about obtaining registered trademark of AAAS. is aScience2009 by the American Association for the Advancement of Science; all rights reserved. The title CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theScience on October 2, 2009 w.sciencemag.org Downloaded from

1. K. E. Nelson et al., Nature 399, 323 (1999). 12. S. A. Lesley et al., Proc. Natl. Acad. Sci. U.S.A. 9, 11664 (2002). 13. S. B. Conners et al., FEMS Microbiol. Rev. 30, 872 (2006). 14. “Integrative Biology of Thermotoga maritima” Workshop,

San Diego, CA, 9 to 10 July 2007 (http://metagenomics. calit2.net/2007/thermotoga/). 15. S. Okuda et al., Nucleic Acids Res. 36, W423 (2008). 16. R. Overbeek et al., Nucleic Acids Res. 3, 5691 (2005). 17. C. H. Schilling et al., Biotechnol. Bioeng. 71, 286 (2000). 18. Materials and methods are available as supporting material on Science Online. 19. P. Kuhn et al., Proteins 49, 142 (2002). 20. TM0449 is a flavin adenine dinucleotide–dependent thymidylate synthase, and our structure has contributed to new developments in functional studies of this and related proteins [see (21, 2) and references therein]. 21. A. G. Murzin, Science 297, 61 (2002); published online 23 May 2002 (10.1126/science.1073910).

2. E. M. Koehn et al., Nature 458, 919 (2009). 23. Z. Yang et al., J. Biol. Chem. 278, 8804 (2003). 24. R. A. Jensen, Annu. Rev. Microbiol. 30, 409 (1976). 25. N. H. Horowitz, Proc. Natl. Acad. Sci. U.S.A. 31, 153 (1945). 26. G. L. Holliday et al., Nat. Prod. Rep. 24, 972 (2007). 27. S. C. Rison, J. M. Thornton, Curr. Opin. Struct. Biol. 12, 374 (2002). 28. E. V. Koonin, A. R. Mushegian, P. Bork, Trends Genet. 12, 334 (1996). 29. C. Pal et al., Nature 440, 667 (2006). 30. J. L. Hartman IV, B. Garvik, L. Hartwell, Science 291, 1001 (2001). 31. K. D. Pruitt, T. Tatusova, D. R. Maglott, Nucleic Acids Res. 35, D61 (2007). 32. C. Yang et al., J. Bacteriol. 190, 1773 (2008). 3. A. G. Murzin, S. E. Brenner, T. Hubbard, C. Chothia,

J. Mol. Biol. 247, 536 (1995). 34. We specifically acknowledge the invaluable work of individual crystallographers at the JCSG and other Protein Structure Initiative (PSI) centers, as well as individual research groups, who have solved structures analyzed here, either directly or that we used as modeling templates. The full list of these proteins is provided in the supporting online material. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of General Medical Sciences (NIGMS). This work was supported by the NIH PSI grants P20 GM076221 (JCCM) and U54 GM074898 (JCSG) from the NIGMS; grant DE-FG02-08ER64686 from the Office of Science (Biological and Environmental Research), U.S. Department of Energy; and the Gordon and Betty Moore Foundation CAMERA project.

Supporting Online Material w.sciencemag.org/cgi/content/full/325/5947/1544/DC1 Materials and Methods Figs. S1 to S9 Tables S1 to S13 References Metabolic reconstruction in SMBL and MATLAB formats

Details of Insect Wing Design and Deformation Enhance Aerodynamic

Function and Flight Efficiency John Young,1 Simon M. Walker,2 RichardJ. Bomphrey,2 Graham K. Taylor,2 Adrian L. R. Thomas2*

Insect wings are complex structures that deform dramatically in flight. We analyzed the aerodynamic consequences of wing deformation in locusts using a three-dimensional computational fluid dynamics simulation based on detailed wing kinematics. We validated the simulation against smoke visualizations and digital particle image velocimetry on real locusts. We then used the validated model to explore the effects of wing topography and deformation, first by removing camber while keeping the same time-varying twist distribution, and second by removing camber and spanwise twist. The full-fidelity model achieved greater power economy than the uncambered model, which performed better than the untwisted model, showing that the details of insect wing topography and deformation are important aerodynamically. Such details are likely to be important in engineering applications of flapping flight.

Insects achieve remarkable flight performance with a diverse range of complex wing designs (1, 2). Computationalfluid dynamics (CFD) offers an opportunity to identify the featuresunderpinningthe aerodynamicperformance of insect wings. By comparing numerical simulationsof different designs, it is possible to test the effects of modifications that may be outside the natural range of variation. Unfortunately, a lack of detailedmeasurementsof insect wing kinematics has limited previousnumerical studies of insect flight to two-dimensional(2D) models (3–6) or to 3D models in which the wings are modeled as rigid flat plates (7–1)o r as rigid sections with constantcamber and twist (12). Such simplifications can dramatically change the conclusionsdrawn about flow struc- ture (13), and no model has yet been validated experimentallyagainst flowvisualizationsfroma realinsect.We usedthemostdetailedsetofinsect wingkinematicspublishedto date(2) to develop the first 3D CFD model of an insect with deforming wings. We validated the results of our CFD simulations against qualitative and quantitativeflow visualizationsof reallocusts.We then used progressive simplifications of the wing kinematics to analyze the aerodynamic consequencesof the measured twistand camber.

We modeleda typicalwingbeatof the desert locust Schistocerca gregaria (14) by averaging the kinematics of four consecutive wingbeats from one of the individuals described in (2). These kinematics were obtained by using four high-speed digital video cameras to track more than 100 natural features and marked points on the wings, which were then used to reconstruct the deforming surface topography of the wings with a mean spatial error of 0.1 m (15). We fitted cubicsplinesto the wing outline and veins, and we interpolated these spatially to give the surface mesh forthe CFD simulations,whichwe theninterpolatedtemporallytogiveupto 800time steps per wingbeat (14). We gave the modeled wings a nominalconstantthickness of 0.05 m based on published cross-sections of the wing veinsand membrane (16). We did not attemptto model variations in thickness due to wing venation. Foldingof the hindwingagainst the thorax could not be modeled exactly, and we instead modeledthe hindwingas if it were joined to the thoraxalong its chord (14).

We solved the unsteady incompressible

Navier-Stokes equationsassuming laminar flow usinga commercialCFD package(14). We constructed the CFD grid for the locust kinematics in multiple parts by using commercialsoftware, and we incorporated the wing motions via a look-up table prescribing the kinematics (14). The wings and body were meshed with a triangular surface grid and surrounded with a thin boundary-layergrid to provide adequate resolution of velocity gradients normal to the surface. These were then surrounded with stationary outer regions representingthe wind tunnel, and a deforminginnerregionin whichthe wings and boundarylayer grids moved. A symmetryplane running through the sagittal plane of the insect was used.Aerodynamicforceson the wingsand body werecalculatedby integratingpressureand viscous shear stress over the surfaces. Starting transients in the calculated aerodynamic forces vanished rapidly within the first wingbeat, with very close agreement between wingbeats thereafter, so we allowed the simulation to run for four repeated wingbeats. Aerodynamic power requirements were calculatedby integrating the inner product of the local pressure and viscous forces with the local wing surface velocity in a coordinate system fixed to the insect’s body.

We validated our CFD method against an independent CFD algorithm (17) by using our methodtoreplicatepublishedforcecomputations for a simplemodel of a flappingdragonflywing in hover (1, 14). The predicted instantaneous vertical force coefficients from the two algorithmswere in excellent agreement,with a linear

1School of Engineering and Information Technology, University of New South Wales, Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia. 2Department of Zoology, University of Oxford,South Parks Road, Oxford OX1 3PS, UK.

*To whom correspondence should be addressed. E-mail: adrian.thomas@zoo.ox.ac.uk w.sciencemag.org SCIENCE VOL 325 18 SEPTEMBER 2009 1549 on October 2, 2009 w.sciencemag.org Downloaded from correlationcoefficientof 0.9 over the course of the wingbeat.To verifythe grid-independenceof the CFD simulations, we performed computations with several levels of grid and time-step refinement of the locust kinematics data (14). Thebaselinegrid consistedof 1.12× 106 volume cells and used 200 time steps per wingbeat. We comparedour baselineresultswith a refinedgrid consisting of 4.1 × 106 volume cells (14)a nd withthebaselinegridusing 400or800timesteps per wingbeat. We found no significantvariation in forceand powerresultsas the gridwas refined or the number of time steps was increased,and we therefore used the baselinegrid with200time steps per wingbeat for the remainder of our simulations.

We alsovalidatedtheresultsoftheCFDsimulation against flow visualizationdata from real locusts by comparingthe predictedflowstructures with qualitativesmoke visualizationsand quantitativedigital particle imagevelocimetry (DPIV) measurements at the same position mid-wing (14, 18). The CFD simulation capturesthe overall structure of the flow field with remarkably high fidelity throughout the wingbeat (Fig. 1). The CFD also shows a reasonably close quantitativefitto the DPIVdata,althoughbecauseeach of the three differenttechniqueswas appliedto a different individual, we do not expect to see an exact match. The main difference between the results of the three techniques is in the presence of smaller-scale flow features in the DPIV and smoke visualizations.In particular, the roll-up of theshearlayertrailing thewing is notparticularly well matched by the CFD: The shear layer is present in the simulation, but the grid is apparentlynot fine enough to capture the detail of wake instabilities behind the trailing edge. Further DPIV flow visualizations showing the consistency of the measured flowfield between different wingbeatsare shown in fig. S4.

DPIV also offers the opportunity for a detailed quantitative validation of the computed flow field.We compared a publisheddownwash distributionmeasured using DPIV (18)w ith the resultsof our CFD model at the same stagemiddownstroke(Fig.2).TheCFDmodelcloselycaptures the shape and magnitudeof the measured downwash distribution at the position shown, whichis approximatelyone chordlengthbehind the hindwings.Once again,we do not expect an exact match, because the DPIV measurements (18) were made on an individualdifferent from the one on which the kinematics measurementsthat we usedfor the CFD simulationwere made (2).

To investigate the effect of detailed wing shape and kinematics, we reran the CFD simulation with two progressively simplified sets of wing kinematics(Fig. 3). In the first simplified model, termed “uncambered,” we removed the corrugationand camber of the wings while retaining the same local instantaneous twist and angle of attack along the wing. We did this by replacingthe camberedchord with a straightline connecting the leading and trailing edge (rear wing) or a straight line at the same mean incidence (forewing). In this simplified model, the wings undergo the same torsional deformation along the span as the real wing does.

In the second simplified model, termed “untwisted,” we also removed torsional deformation along the span, by replacing the forewing with a flat plate of the same instantaneous projected area and same instantaneous angle of attack at the mid-wing position. The hindwing was replaced with two flat plates of the same totalinstantaneousprojectedarea,joined alonga line running from the axilla to a point midway between the fourth and fifth anal veins at the trailingedge. This allowedus to match the midwing angle of attack while avoiding unrealistic motions at the wing root. In this simplified model, the wings undergo the same wholesale rotation about their base as the real wing does, but the modeled wings undergo no torsional deformation.

Fig. 1. Validation of CFDsimulationusingfullfidelity wing kinematics (leftcolumn:3.3 m/s free stream, 9° body angle), against DPIV measurements (middle column: 3.5 m/s free stream, 7° body angle) and smoke visualizations(right column: 3.3m/s freestream, 9° body angle).Data are shownat four consecutive stages (A to D)o ft he wingbeat, beginning with thestart ofthe downstroke, for the verticalplanethat interceptsthehindwingat themid-wing positionwhen thewingis horizontal.The CFDand DPIVfiguresplot flow velocityvectorsin a body-fixedreferenceframe andare colored according to the vertical downwash speed.For clarity, only every fifth vectoris plotted in the DPIV figures.FurtherreplicatesoftheDPIV data are available in fig. S4.Overall,thenumerical simulationcapturestheempirical structureofthe flow fieldwith remarkablyhigh fidelity. Figure S5 shows the equivalent CFD simulationsfor the two simplifiedwing kinematics models,which do not capturethe empiricalstructure of the flow field with such fidelity.

Fig. 2. Computed downwash distribution (solid line) from the CFD simulationusing full-fidelity wing kinematics, validated against published DPIV measurements (crosses)ofthedownwash(18).Themeasurements are made approximatelyone mean chord lengthbehindthe trailing edgeof the hindwing. The datarepresent the stagemiddownstroke shown in Fig.1B, and the three differentdatapointsateachspanwisestation represent measurements made on different wingbeats from one individual. The simulation accurately captures the measured turningpointsin the downwashdistribution at about one-third and two-thirdsof wing length andalso the crossing to upwashnearthe wingtip.

do wnw ash speed (ms

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Both simplified kinematics models preserve the grosschanges in projectedand wettedwing area that result from corrugation and folding of the hindwing(2). Thewettedareaof the hindwing in thefull-fidelitymodelvariesby as muchas 14%, which reflects folding of the wing against the thorax. The wetted area of the hindwing in the untwistedmodelvariesby as much as 19%, and the 5% difference here reflects the fact that the untwistedwing does not corrugate,becauseit is modeled as a flat plate.

The computed surface pressure field for the full-fidelitymodelshowsno evidenceof leadingedge separation,with the locallyvaryingcamber ensuring that the leading edge is well aligned with the oncoming flow at all times (Fig. 3A). In contrast, the untwisted kinematic model shows massive separationon the hindwingmiddownstroke,when the downwardvelocityof the wingis maximal,as evidencedby a low-pressure regionextendingover much of the wing’s upper surface at this time (Fig. 3C). The uncambered model also shows evidence of separation, but with the low-pressure region confined to the basalpartofthehindwing(Fig.3B).The 2Dflow fields plottedin the bottomrow of Fig.3 confirm that flow separation is present in the two simplified models. Flow reversal is clearly visible overthe hindwingfor both the uncambered(Fig. 3B) and untwisted(Fig. 3C) models,but thereis no evidenceof flowreversal withthe full-fidelity kinematics (Fig. 3A). This difference is present despitethe hindwingangle of attackbeing identicalamongsimulationsinthe2Dplaneshownin Fig. 3, and it must therefore result from a combination of 3D effects and camber.

We compared the computed aerodynamic forces and aerodynamicpower requirementfor the full-fidelity, uncambered,and untwisted kinematicsmodels (Fig. 4). The aerodynamicforce is resolved into a lift component normal to the free stream and a thrust componentparallelto it. The uncambered wings generate less lift and thrust during the downstrokethanthefull-fidelity wings do, becauseof the absenceof the positive camber present on the real wings. The uncambered wings generate a similar amount of lift to the full-fidelity wings through most of the upstroke, however, which is presumably because the real wingsflattenand feather on the upstroke and are therefore betterapproximatedby the uncamberedmodel.The same featuresare reflected in the aerodynamic power requirement, with the uncambered wings requiring slightly less power than the full-fidelity wings on the downstroke but needing similar aerodynamic power on the upstroke. The pattern is more complicated for the untwistedwings, whichneverthelessproduce less lift and thrust than the full-fidelity model does and require greater aerodynamicpower to do so.

The aerodynamic advantages of the fullfidelity wing kinematicsare clearly revealed by comparing the total power economy of the different models, defined as the ratio of timeaveragedtotalforcetotime-averagedtotalpower. The total power economies in the uncambered (0.98 N W−1) and untwisted (0.84 N W−1) modelsare7% and 15% lower, respectively, than the totalpowereconomyof the full-fidelitymodel (1.06 N W−1). This lower efficiency of momentum transfer is attributable partly to the leading-edge separationthat occurs on the hindwings in the simplifiedmodels. In addition,the simplified wing kinematics cause the resultant force to havea less favorabledirection,as can be seen from the large decrementsin lift and thrust in Fig.4. Thisresultsin an evengreaterreduction in lift power economy, defined as the ratio of time-averaged lift to time-averaged total power: The lift power economy of the uncambered wings (0.78 N W−1) is 12% lower than that of the full-fidelity model (0.8 N W−1), whereas the lift power economy of the untwisted wings (0.51 N W−1) is 35% lower. In summary, wing deformation in locusts is important both in enhancing the efficiency of momentumtransferto the wake and in directingthe aerodynamic force vector appropriatelyfor flight.

Thehigh-liftaerodynamicsof insectflightare typicallyassociatedwithmassiveflowseparation and large leading-edge vortices (19–21). However, whenhighliftis notrequired,attached-flow aerodynamics can offer greater efficiency. The aerodynamicpowerefficiencyof locustsappears to derivefrom theirabilityto reduceflow separation and the associatedloss of energy as vortical motionin the wake. Simple heavingor flapping flat plates can generate high lift with stable leading-edge vortices (21, 2), but designing robust lightweight wings that can also support efficient attachedflow aerodynamics is likely to be much moredifficult.Ourresultsshowthatthe secret to doing so lies in building a wing that undergoes appropriate aeroelastic deformation through the course of the wingbeat. We have shown previouslythat the shape and structureof al ocust’s hindwing are tuned so that it twists appropriately to maintain a constant angle of attackacross the wingduringthedownstroke(2). Our CFD simulations demonstrate furthermore that time-varying wing twist and camber are essential to the maintenance of attached flow. Implementingsuch tailored deformations in an engineeredsystemis a difficultproblemand may demand an evolutionarilyoptimized solution in order evento approachthe eleganceof an insect.

Fig. 3. Computed surface pressuremaps from theCFDsimulationsusing full-fidelity kinematics (A),uncamberedkinematics(B), anduntwistedkinematics(C). Thesamefour consecutivestages of the wingbeat areshownas in Fig.1,beginningwiththe start of the downstroke. Thereis an extensive area of low pressure over the hindwinginthe untwisted model,indicativeofleadingedge separation.A more limitedseparationis visible near the root of the hindwing in the uncamberedmodel.Thereis no clearevidenceof separation with the full-fidelity kinematics. The plots at the bottom of the figure show the corresponding 2Dflowfieldsforthestage of the downstroke when the hindwing is horizontal, for the same vertical plane as in Fig. 1. The variation in flow separation between the three kinematicsmodelsisdemonstrated in these images by the reversed flow over the top surface of the uncambered and untwisted wings, even though the hindwingangleof attackis identical in all threesimulationsin thesesections.The reductionin the extent of flowseparationbetweentheuncamberedanduntwistedwingmustbe duetowing twistand associated 3D flow effects. The lack of reversed flows with the full-fidelity kinematics is presumably due to the curvature of the wing section and the reduced local angle of attack at the leading edge. Figure S5 shows the effects on the computed 2D flow field through the wingbeat.

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References and Notes 1. R. J. Wootton, Annu. Rev. Entomol. 37, 113 (1992). 2. S. M. Walker, A. L. R. Thomas, G. K. Taylor, J. R. Soc.

B. Balachandran, J. Exp. Biol. 212, 95 (2009). 7. H. Aono, F. Liang, H. Liu, J. Exp. Biol. 211, 239 (2008). 8. K. Isogai et al., AIAA J. 42, 2053 (2004). 9. H. Liu, C. P. Ellington, K. Kawachi, C. van den Berg,

J. Fluid Mech. 594, 341 (2008). 14. Materials and methods are available as supporting material on Science Online. 15. S. M. Walker, A. L. R. Thomas, G. K. Taylor, J. R. Soc.

Interface 6, 351 10.1098/rsif.2008.0245 (2009). 16. R. J. Wootton, K. E. Evans, R. Herbert, C. W. Smith,

J. R. Soc. Interface 3, 311 (2006). 19. C. P. Ellington, C. van den Berg, A. P. Willmott,

A. L. R. Thomas, Nature 384, 626 (1996). 20. W. Shyy, H. Liu, AIAA J. 45, 2817 (2007). 21. A. L. R. Thomas, G. K. Taylor, R. B. Srygley, R. L. Nudds,

R. J. Bomphrey, J. Exp. Biol. 207, 4299 (2004). 2. N. Vandenberghe, J. Zhang, S. Childress, J. Fluid Mech. 506, 147 (2004). 23. The research leading to these results has received funding from the Engineering and Physical Sciences Research Council (EPSRC) under grant GR/S23049/01 to A.L.R.T. and from the European Research Council (ERC) under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 204513 to G.K.T. J.Y. was supported by the Merit Allocation Scheme on the National Facility of the

Australian National Computing Infrastructure (NCI-NF) and gratefully acknowledges the Rector of the University of New South Wales at the Australian Defense Force Academy for the award of a sabbatical scholarship to perform this work. R.J.B. holds an EPSRC Career Acceleration Fellowship. G.K.T. is a Research Councils UK Academic Fellow and Royal Society University Research Fellow. We gratefully acknowledge the EPSRC Instrument Loan Pool and thank N. J. Lawson for advice and the loan of equipment for the DPIV measurements.

Supporting Online Material w.sciencemag.org/cgi/content/full/325/5947/1549/DC1 Materials and Methods SOM Text Figs. S1 to S5 References Movie S1

D-AminoAcidsGovernStationaryPhase

Cell Wall Remodeling in Bacteria

Hubert Lam,1* Dong-Chan Oh,2*† Felipe Cava,1* Constantin N. Takacs,1‡ Jon Clardy,2 Miguel A. de Pedro,3 Matthew K. Waldor1§

In all known organisms, amino acids are predominantly thought to be synthesized and used as their L-enantiomers. Here, we found that bacteria produce diverse D-amino acids as well, which accumulate at millimolar concentrations in supernatants of stationary phase cultures. In Vibrio cholerae, a dedicated racemase produced D-Met and D-Leu, whereas Bacillus subtilis generated D-Tyr and D-Phe. These unusual D-amino acids appear to modulate synthesis of peptidoglycan, a strong and elastic polymer that serves as the stress-bearing component of the bacterial cell wall. D-Amino acids influenced peptidoglycan composition, amount, and strength, both by means of their incorporation into the polymer and by regulating enzymes that synthesize and modify it. Thus, synthesis of D-amino acids may be a common strategy for bacteria to adapt to changing environmental conditions.

In all kingdoms of life, cells predominantly use L-aminoacids. In most bacteria,the only D-aminoacids produced in significantquantitiesare D-Alaand D-Glu,whichareincorporated into peptidoglycan(PG) (1). PG is a strong and elasticpolymerofthe bacterial cell wallthatissynthesized and modified by penicillin-binding proteins (PBPs). PG counteractsthe cell’s osmotic

Fig. 4. Instantaneous lift-generated, thrustgenerated, and aerodynamic powerrequired in theCFDsimulationsusing full-fidelity kinematics (A), uncambered kinematics(B),anduntwisted kinematics(C). Solidand dashedlines denote the liftor powercomponents forthehindwingandforewing, respectively. The wingbeat shown begins at the start of the hindwingdownstrokeandends at the point denotedby the verticalline. For the lift and thrust plots, the shadingshowsthedecrement (red) or increment (green)in instantaneous force for the simplified kinematicsas compared to the full-fidelitymodel. Fort he powerp lots,t he shadingshowstheequivalent increment(red)or decrement(green)in instantaneous powerrequired.

Lift (mN)

Power (mW)

Thrust (mN)

Lift (mN)

(Parte 1 de 2)

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