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Each the tympanal mem- and (8). tympanic the (ATM) anterior foretibia brane the as called the known (TMs), membranes in also tympanic located ear, is Different katydid organ, orientation. the which and of tetrapods, both perception (e.g., from (6–8), auditory communication detection mammals precise predator social in and require for (5) reported mate) hearing hearing a use finding of insects steps These basic also (5). three which the Tettigoniidae), Orthoptera, exhibit crickets; (bush katydids acuity. hearing directional enhancing source, relative compo- sound orientation potential asymmetrical the a an to create morphology of symmetrical ear outer in distribution The the of vary spatial (4). nents which abilities and hearing topology, (EC), species’ arrangement, canal a ear on involves the depending capture and sound instance, pinna (2, for birds the and mammals, and taxa terrestrial reptiles, In across mammals, 3). waves—vary in sound independently evolved the have of capture step— efficient first the the for Adaptations by (1). signals neurons electrochemical receptor auditory into the energy trans- mechanical the the by of duction followed decomposition frequency mechanical and T analysis element finite directional bioacoustics ear). avian human in the findings for one of discussed. are (only implication hearing ear and each paths for Research paths sound total four inputs each to internal for and velocities external sound Therefore, different membrane. tympanic imposing and inter- for paths narrow branch sound additional (one nal two level creating tympanal membrane), CO tympanic the each at excess that bifurcates when EC show further the also reduced Likewise, data is sound reducing numerical velocity factor sound and main the experimental is Both EC velocity. the of that radius demonstrate we narrowing EC, the (e.g., animal experimental EC each of three-dimensional the geometries precise on in analysis numerical composition and tomography, nar- gas the the CO should of velocity air, of sound consequence in independently a reduction a as persist true, arise If geometry. to EC suspected rowing was inputs. delay internal and The tempo- external causing between air, system. differences free pressure tracheal in and than ral respiratory slower travels the sound from nar- EC, a the derived Inside via (EC) internally canal and ear ear each row in membranes externally tympanic received two is via arthro- sound mammals, among Unlike to ear. analogous unique mammalian components, 2020) the are inner 14, and ears August middle, outer, review having katydid for in (received pods forelegs, 2021 24, the January in approved and Located MA, Cambridge, University, Harvard Weitz, A. David by Edited Austria Graz, 8010 Graz, Karl-Franzens-University colo ieSine,Jsp ak aoaois nvriyo icl,LnonL67S ntdKndm and Kingdom; United 7TS, LN6 Lincoln Lincoln, of University Laboratories, Banks Joseph Sciences, Life of School naaou ehns fhaighsbe eotdin reported been has hearing of mechanism analogue An rnfraino ibrevbain nofli vibrations, fluid capturing, into sound vibrations on airborne based of is transformation perception auditory etrapod 01Vl 1 o 0e2017281118 10 No. 118 Vol. 2021 2 .ItgaiglsrDplrvboer,microcomputed vibrometry, Doppler laser Integrating ). | ayi hearing katydid a,1 mn Celiker Emine , a n ennoMontealegre-Z Fernando and , | on propagation sound a,1,2 aa Aldridge Sarah , | 2 lsteEC. the fills a,2 a hita Pulver Christian , doi:10.1073/pnas.2017281118/-/DCSupplemental at online information supporting contains article This 2 1 ulse ac ,2021. 3, March Published BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is data; article analyzed This F.M.-Z. paper.y and the C.W., wrote T.J., F.M.-Z. and C.D.S., C.P., E.C., D.V., S.A., per- and E.C., C.P., F.M.-Z. D.V., D.V., data; tools; and reagents/analytic collected E.C., C.W. new D.V., contributed and F.M.-Z. research; and T.J., designed E.C., F.M.-Z. research; formed and C.D.S. contributions: Author down slowed and amplified 15). both (14, input is external EC, the through coming with the wave compared sound part, to the that internal) internal fact and the the (external via inputs and sound (7) TMs two the the katydids, by In formed membrane. is a across this pressure sound in gradient a internal ates the of convergence the inputs. by sound external caused and or TMs, difference pressure thorax, the a head, at form the inputs receiver acoustic on dual positioned The 2) were abdomen. they spatial if more than produces arrangement separation and This spaces (21). air displacement mechan- their to ical tracheal proprioceptors with sensitive 1) as regions, acting follows: organs foreleg chordotonal Nev- as in (6). located problem nature are this in ears sounds overcome relevant katydids in the ertheless, differences for interaural amplitude detect are to and insects ears time sound—the their for of small localization too the usually enable to it enough as not tapers gradually (14–20). that 1C) canal (Fig. organ a tympanal and the katydids approaches involves spiracle which of acoustic type, common species large a living a variation on focuses considerable 7,000 research has this circa and EC the (13), therefore The across will on. and morphology here EC in from an 1 EC of (Fig. role called forelegs the be the fulfills in trachea TMs acoustic the the of inside the reach owo orsodnemyb drse.Eal Clkrlnona.kor [email protected] Email: addressed. be may correspondence [email protected]. whom To work.y this to equally contributed E.C. and D.V. ol npr loihsfracrt cutctinuainin triangulation times, sensors. Findings acoustic detection accurate source. various for sound at algorithms the ears inspire pinpoint could the to reach chance various signal the Therefore, increasing same tympanum. the differ- each of impose for versions that asymmetrically, velocities paths bifurcates sound internal EC internal ent additional The the geometry. two causing EC Here, producing factor the hearing. major directional is the in delay in that role inputs demonstrate significant combined a two we exter- The play both (EC). arriving ear canal version sound each ear internal to gas-filled delayed the exposed a via with tympana internally, two and nally has mammals, ear ear Unlike inner each ears. and mammalian middle, to outer, analogous have components ears tympanal katydid The Significance sapesr ifrnercie,w en ytmta cre- that system a define we receiver, difference pressure a As is katydids in ear outer the of arrangement symmetrical The a alD Soulsbury D. 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BIOPHYSICS AND COMPUTATIONAL BIOLOGY of the EC and the location of recording on the ATM or PTM. The EC bifurcates near the TMs, so that ATM and PTM lie on two separate branches: the anterior and posterior branches, respectively. The cross-sectional area of the anterior branch is smaller than that of the posterior branch by 2.28% in males and 5.67% in females (SI Appendix, Table S3); hence, the branches are asymmetrical. We calculated the velocity of sound propagation through the EC by dividing the length of the EC with the time taken for a sound signal to transmit through it to the TM. To measure the time of sound transmission, the insect was mounted on a special platform that separates the internal and external sound inputs (Fig. 2). Sound was produced externally and passed into a probe loudspeaker, which delivered the signal into the EC, while the TMs were monitored with a microscanning laser Doppler vibrometer (LDV). The gas composition of the EC was manip- ulated by dispensing carbon dioxide gas (CO2) into the acoustic spiracle via a microcapillary needle (Materials and Methods; SI Appendix, section 1 has details). CO2 was used because the EC is derived from the respiratory system, and therefore, the gas could be present in naturally high concentrations; it is also known that sounds travel slower in CO2 (SI Appendix, section 2 has details). Experiments were also carried out with air-filled EC. For these experiments, the natural gas composition of the specimen was flushed out, and it was left to refill by itself, so that by air, we Fig. 1. Anatomy and 3D reconstruction of the katydid EC. (A) An image of refer to the gas composition inside the room (SI Appendix, sec- the katydid C. gorgonensis.(B) The µ-CT image of the katydid highlighting tion 3 has details). When compared with free-field sound velocity the acoustic tracheae. (C) The components of the acoustic trachea. (D) The in air, sound velocity within the EC across live, dead, and numer- finite element mesh formed in the tracheal tube. ically modeled data was significantly slower [F (2,45.16) = 68.19, P < 0.001] (Fig. 3 and Table 1). Both live and dead insects did not differ in their velocity reduction of 17.05% (live vs. dead: t ratio = 1.88, P = 0.158), but numerical data predicted a signif- The reduction in sound velocity was first reported and inferred icantly greater velocity reduction than was found in live or dead in Michelsen et al. (16) for crickets and Larsen (22) for crick- insects, in air (vs. live: t ratio = 10.76, P < 0.001; vs. dead: t ets and katydids. This was later experimentally quantified (15). ratio = 9.09, P < 0.001) (Fig. 3A and Table 1). EC length did However, the underlying assumptions of the interpretation of not affect the sound velocity reduction [F (1,8.13) = 1.60, P = results, such as the effect of the respiratory gases in the EC and 0.241], but the reduction of velocity was greater at the ATM propagation of sound in highly narrowing tubes being the cause [F (1,41.25) = 4.14, P = 0.048]. In live insects, with the EC filled of reduction of sound velocity (15, 23), have not been analyzed with air, sound propagated to the ATM and PTM at mean veloc- using experimental and numerical approaches. ities of 284 and 296 m/s, respectively. A numerical investigation Here, we experimentally determine the velocity of sound prop- on one specimen model showed sound propagation velocities of agation inside the EC of the katydid Copiphora gorgonensis 224.84 and 228.59 m/s at the ATM and PTM, respectively, of the (Tettigoniidae, Copiphorini) and test the hypothesis that the air-filled left EC; similar results were also obtained in the right gradually narrowing EC is the primary cause of any observed EC (Fig. 4B). changes in sound velocity. Furthermore, to corroborate results, Sound velocity data obtained at the TMs after the incident we investigate sound propagation velocity when the EC is filled wave traveled through the CO2-filled EC were significantly with different gases, under the expectation that sound velocity slower for all three insect statuses in comparison with free- will decrease in a narrow tube independently of the gas. Adding field CO2 sound velocity, but there was no significant difference to the experimental results, we applied finite element analysis among the different statuses [F (1,37.854) = 0.37, P = 0.696] to simulate the propagation of sound in the precise geometry (Fig. 3B and Table 1). More precisely, sound velocity of dead and of all experimental ECs (Fig. 1C), obtained through microcom- live insects was 31.56% slower than free-field CO2 sound veloc- puted tomography (µ-CT). Both the experimental and numerical ity. Neither EC length [F (1,6.43) = 2.61, P = 0.154] nor sound results demonstrate that EC geometry is the primary cause of velocity, at either tympanum, were significantly related to sound sound velocity reduction within the katydid middle ear. velocity with CO2 present [F (1,36.41) = 0.54, P = 0.467]. To explore the effect of the EC radius on the sound propaga- Results tion velocity inside of the ear in more detail, we also carried out We investigated factors leading to the reduction of sound veloc- numerical simulations after manipulating the EC geometry by ity in the EC of C. gorgonensis in comparison with sound velocity changing its radius. Considering the tube to be filled with air or in free air conditions (15), both experimentally and numerically. CO2, we obtained the sound velocity from ECs with median radii In particular, we considered the effect of the gas composition 75 to 600 µm. The results are presented in Fig. 4A, from which it within both the left and right ECs of the specimen on the velocity is evident that, regardless of the gas composition inside the tube, reduction in three different categories: live insects, dead insects, the ECs with a smaller radius display a greater reduction in sound and numerical models. The results from live and dead speci- velocity. In a separate simulation, we have also explored the mens were considered separately in order to observe the effect of effect of the asymmetric bifurcation of the EC on sound velocity. the metabolic CO2 reduction in the EC, which ensues after the The results are presented in Fig. 4B and complement the results specimen is dead. For each insect status, in addition to the gas in Fig. 4A since sound is distributed asymmetrically, with higher composition inside the EC, we also analyzed whether the reduc- velocity at the tympanum associated with the posterior branch of tion of sound propagation velocity was affected by the length the EC, which is the wider branch.

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(Fig. the at propagation tibia EC sound the affect of to base 150 enough the approximately starting of in EC, radius ending uniform the relatively and of Benade section femur in narrow the developed The in theory (25). Tijdeman tube a and narrow demonstrate (24) the with This which ECs. consistent narrower 4A, the is in Fig. the velocity the propagation from in to sound verified decreasing contributes presented further that is results factor that This numerical major suggests velocity. the in This is reduction EC. observed EC the 1), narrow in (Table very composition the conditions gas normal of under free- independent expected velocity the to propagation relation in field reduced always was velocity tion Findings. of Review gas Discussion the with along spiracle, the system. recording from laser and ears stimulation, acoustic the dispenser, replacement separate acoustically to 2. Fig. hog diinlivsiain thsbe bevdthat observed been has it investigation, additional Through source sound the of direction the determine insects These of that like Ears xeietlpeaain h lutainsostepafr used platform the shows illustration The preparation. Experimental LDV escmae ihta in that with compared less narad28.19% and air in u eut eosrt htsudpropaga- sound that demonstrate results Our .gorgonensis C. ◦ mltd differences amplitude gorgonensis, C. ciy 2)btrqie locomotion a requires but (26) acuity) membrane Tympanic r eivdt aea least at have to believed are in Customised platform CO CO 2 2 hncompared when , ebleethat believe We . Acoustic spiracle Fg ) small 5), (Fig. µm loudspeaker delivery system Gas Probe- eto 4 section Appendix, (SI velocity S1 sound Table and in reduction a projected Cfildwt CO with filled EC CO veloc- in (B) sound velocity m/s. free-field sound the free-field 343 represents air: line dashed in The specimens. ity air. dead with and filled live EC in (A) conducted were procedures Experimental cally. have velocity phase in the outlined calculating been for used variables (the kHz 150 23 of different radius three EC median for the and velocity He, propagation (air, density. the gases gas assumed on dependent have strongly thick- We boundary-layer are thermal and and respectively, viscous nesses, the to radius tube the and heats; cific where by defined velocity is phase theo- This the tube. the for narrow consider (24) a also in Benade we by developed ways, solution different retical in geometry EC with i.3. Fig. variation higher The approaches. multiple used (15) This pre- study the 25%. whereas vious consistent length, was and tracheal the precise reduction determine utilizing to velocity measurements study our where to (15), attributable al. is et Jonsson (16.24% in air in 17.60% obtained Further- and rate experimentally. reduction observed the we in more, what decrease than greater a velocity predicts sound model numerical the however, air; in model tubes. narrower ical in stronger are effects whose wall, formed layers EC boundary the composi- thermal near gas and viscous different the for from of EC result rates tions the differing in that in obtained concluded reduction on be which Based velocity can and properties. wall, it gas viscous results, the tube theoretical and the radius the the of tube the thickness near on the depend formed turn, by layers affected boundary also thermal is a tubes have in to ity assumed is and for- radius which uniform for tube a wall. the rigid has since (1) holds formula (1) of the mula use in the obtained with results numerical and the EC in difference expected an is 4.5% around was 7.3% reduction of reduction a hnteeprmna eut r oprdwt h numer- the with compared are results experimental the When veloc- sound of reduction the that demonstrates (1) Formula safrhrdmntainta ifrn ae ilinteract will gases different that demonstration further a As Sound Velocity (m/s) is there air in that show S1) Table Appendix , (SI results The 150 200 250 300 350 c on rpgto eoiymaue xeietlyadnumeri- and experimentally measured velocity propagation Sound stesedo on noe space; open in sound of speed the is A ieDa Model Dead Live nda net)i o slrea h eut obtained results the as large as not is insects) dead in ). 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BIOPHYSICS AND COMPUTATIONAL BIOLOGY Table 1. A summary of data across all treatments Free field Live Dead Numerical Air

Sample size NA nS = 8, nEC = 14 nS = 8, nEC = 15 nS = 7, nEC = 13 Mean sound velocity (m/s) ± SD 343 289.109 ± 16.245 280.172 ± 17.606 231.638 ± 16.763 % reduction from free-field sound velocity NA 15.712 18.317 32.467 Mean EC length (mm) ± SD NA 17.126 ± 0.998 17.067 ± 0.938 17.314 ± 0.935 Mean travel time (ms) ± SD NA 0.0595 ± 0.00545 0.0611 ± 0.00445 0.0750 ± 0.00485

CO2 Sample size NA nS = 8, nEC = 14 nS = 8, nEC = 14 nS = 7, nEC = 13 Mean sound velocity (m/s) ± SD 267 184.318 ± 42.546 181.13 ± 41.857 191.728 ± 12.046 % reduction from free-field sound velocity NA 30.968 32.161 28.192 Mean EC length (mm) ± SD NA 17.126 ± 0.998 17.095 ± 0.968 17.314 ± 0.935 Mean travel time (ms) ± SD NA 0.0972 ± 0.00205 0.0987 ± 0.00209 0.0905 ± 0.00524

Sample size shows both the number of specimens (nS) and number of ECs (nEC ). NA, not applicable.

displayed in the sound velocity measurements in CO2 likely the tympana and the crista acustica has never been investigated results from random error in gas dispensation. [Michelsen et al. (16) and Larsen et al. (22)]. Differences between the experimental and numerical results can also be attributed to some simplifying assumptions applied Dual-Input Ears in the Animal Kingdom. Other animals, including in the model. For instance, we assumed that the lumen of the EC some insects and tetrapods, utilize pressure difference receivers is smooth. Instead, the EC is derived from the respiratory trachea to localize sound. These include grasshoppers (30), lizards (31), built up of taenidia, which generally take the form of spiral thick- crocodilians (32), and birds. Unlike in katydids, the pressure dif- enings of the tracheal walls joined by soft material, forming an ference in these animals occurs between the membranes of two irregular sinuous surface. In the model, the gas is also assumed internally coupled ears. A signal transmitting internally from one to be quiescent; hence, it is at rest as the sound stimulus enters TM to another may suffer attenuation or depending on the inter- the trachea, which in reality, it is not since the tracheal tube is aural distance and frequency of the signal, a time delay. This part of the respiratory system of the insect. mechanism can present problems for smaller organisms such As follows from Table 1, the largest discrepancies between as the grasshopper (Acrididae). Grasshopper ears are located the experimental and numerical results are present in the data at lateral surfaces of the almost cylindrical body, on the first related to the sound velocity from the air-filled ECs, which sug- abdominal segment. The tympana are connected by a series gests some differences of the gas compositions inside the ECs of sound-guiding air sacs (30), permitting sound to internally during the experiments and the numerical simulations. The gas travel from one TM to the other. The vibration of the TMs, content inside the ECs for the experiments with air was ambient measured using LDV recordings, shows the occurrence of nulls atmospheric gas composition; hence, the EC might not be com- (i.e., frequencies where eardrum vibration is canceled because pletely free of CO2. However, for the numerical simulations the its two surfaces receive sounds with an identical amplitude and air filling the ECs is assumed to be under standard conditions and phase) (23). thus, does not contain any excess CO2. Nonetheless, both the The katydid outer ear reported here shows similarities with experimental and numerical results show that even though the some bird ears. Avian ears are located at the side of the head, and gas composition inside the EC plays a part in the rate of veloc- evidence suggests that some species utilize pressure difference ity reduction inside the tube, the key component causing it is the receivers to localize sound (33–35). Across taxa, the documented complex EC geometry. anatomy of the avian EC varies from the basic interaural canal of the barn owl (Tyto alba) (36) to the complex network of The Use of CO2 as a Potential Mechanism to Hone Sound Localization. tubes described in the zebra finch (Taeniopygia guttata) (37). The The purpose of filling the EC with CO2 was purely for testing zebra finch overcomes the size limitations of sound localization the mechanics of the EC, as the EC containing pure CO2 is through a delayed interaural signal (35). The mechanism behind an unrealistic situation in nature. However, since the results of this delay is unknown but could result from a series of narrow these mechanical experiments show that CO2 causes the sound tubes that internally connect each ear (37). The TMs of the zebra to propagate even slower than the normal (already reduced) finch are directly connected by an interaural canal but are also sound velocity in the EC, we would like to discuss a potential interconnected by several narrow canals [the figure in Larsen et effect of metabolic CO2 on binaural hearing. al. (37)]. Perhaps the most significant of the narrow pathways are In insects where the respiratory trachea are associated with the superolatero-orbital canals. These begin above the interaural active muscular-controlled spiracle openings, concentration of canal, at the sides of the head, arching upward to join together CO2 could be significantly higher when those spiracles are in a sinus on the forehead (superoantero-orbital sinus). The closed. When the spiracles are subsequently opened, the levels end result is a 27-mm-long canal with a cross-sectional area of 2 of CO2 and O2 equilibrate with those of air (17). During those 400 µm (radius = 11.3 µm). The superoantero-orbital sinus open and closed phases, sound propagation velocity would be also associates with other narrow canals, both of which run down affected, due to the varying CO2 concentration inside the EC. the longitudinal plane of the head. Resembling an exponential The degree of concentration change and the effect on propa- horn, the 5-mm-long hypomedial-orbital tube connects the sinus gation velocity are unknown, but we believe this idea should to the interaural canal. Near the sinus, at its most narrow be further investigated, especially in species that have control point, the cross-sectional area is 400 µm2. The narrowest tube is of spiracle valves and exhibit tracheal and acoustic connections 7-mm long and has a cross-sectional area of 100 µm2 (radius = between the left and the right ECs, like field crickets. To the best 5.6 µm). This extends from the sinus to a medium-sized tube of our knowledge, the effect of opened or closed EC spiracles on that runs parallel to the interaural canal. Proposed to be air sound propagation velocity and sound reception at the level of filled (37), these narrow tubes resemble the geometry of the

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h smerclrsos fteTscudas fetthe affect also could TMs the of response asymmetrical The filled is EC the when insects, live from data experimental The reduc- the and tubes narrowing of aspect relevant Another Sound Velocity (m/s) 150 200 250 300 Ear-canal medianradius(μm) AB iieeeetaayi fteefc fteE aisadasymmetric and radius EC the of effect the of analysis element Finite C 0 0 0 0 0 600 500 400 300 200 100 and D). C esrmnso h ECs. the of measurements µ-CT CO Air 2 ewe T n PTM. and ATM between µs 180 190 200 210 220 230 240 Left ◦ PTM branch ATM branch t2 H.Teactual The kHz. 23 at Ear-canal Right 2 fildlf and left -filled 2 Left sn finite using , Right e 05fo h ainlNtrlPr ogn,Clmi (lati- Colombia 22 Gorgona, (temperature Park vivaria Novem- Natural communal in in National collected tained the colony 2 from a tude 2015 of descendants ber eighth-generation were Animals. system Experimental delivery customized a of use veloc- the propagation 1 through section sound EC Appendix, the the (SI to on record added compositions We is gas Gas LDV. ity. different probe an of to of array and effect stimulus an external generators, the with sound the along function isolates the 15), that microphones, (5, takes utilized platform by loudspeakers, it is special calculated inputs time a be auditory the this, internal to achieve and by velocity To EC TM. sound the the enables reach of This length EC. determin- and the the katydid dividing a of of length EC the the through ing transmit to time acous- signal the measuring acoustic the involves an inside aspect for reduction experimental The velocity katydids. sound of of trachea tic cause the infer to approaches Design. Experimental Methods and Materials to exposed internally while air concentrated ambient to exposed externally are contain predominantly Do cavities investigation. the tympanal CO further from the at warrants conduction bifurcations asymmetrical hearing the the directional by in played TMs suggest role results our the nondirec- (9), that receiver the auditory as the of appreciated the component been and tional spiracle traditionally the have one though system only even with EC Therefore, (compared ear ear). inputs single human acoustic a the four TM, for of each total tak- at a inputs When face external ear. may two single the interference a it account in into destructive (41)], inputs, ing asymmetric source external is and an sound spiracle internal a the to between entering of lead energy position potentially sound the can if on and [depending 40), weak (9, response TMs directional both input highly of in a the enhance flaps to magnifying ear seem TMs The cantilever, Pseudophyllinae) (39). two force 1 output the type greater gorgonensis (9): a a asymmet- provide ear an as to the force produce concert around TMs in effect the work covering pressure interference, pinna sound destructive or example, rical flaps for the by, TMs as both of surface ieautidvdas(v ae n orfmls eeue nthis in used were females) four and males (five (n study individuals adult nine esrddsac ipae rmteaosi prcet h tympanal the ( C of to EC. females spiracle right and Female acoustic males in the area from organ displayed distance Measured 5. Fig. 2 ftu,hwaetemcaiso h M hnthey when TMs the of mechanics the are how true, If ? ◦ uniaierltosi ewe C(rce)rdu n length. and radius (trachea) EC between relationship Quantitative C AB 58 7ears). 17 = 0 7.4208 n ayohrktdd eg,Cncpaia and Conocephalinae (e.g., katydids other many and CO 00 aergtEC. right Male (D) EC. left Male ) ;lniue78 longitude N; 2 ? hsrsac obnseprmna n numerical and experimental combines research This hssuyue pcmn of specimens used study This a oedetails). more has ◦ eaelf C (B) EC. left Female (A) gorgonensis. C. https://doi.org/10.1073/pnas.2017281118 11 0 10.4964 D ◦ 00 o27 to C ) net eemain- were Insects W). .gorgonensis C. ◦ ) oa of total A C). PNAS | f8 of 5 that C.

BIOPHYSICS AND COMPUTATIONAL BIOLOGY Experimental Setup. To observe the effects of the internal pathway only, were conducted at ambient temperatures of 19.8 ◦C and 25.0 ◦C, with the we isolated the internal and external sound inputs. We did this by mount- body temperatures of the insects ranging from 23.6 ◦C to 28.1 ◦C. ing the insect on a customized platform (Fig. 2). The platform consists of two Perspex panels that fit together, the dorsal of which encompasses Anatomical Measurements of the EC. The anatomy of the EC was examined a central notch for the insect’s head along with two adjacent holes for using X-ray µ-CT and three-dimensional (3D) reconstruction, using stan- the forelegs. These panels are held together within a metal frame [addi- dard biomedical imaging software following the published protocols (15). tional details are in the work by Montealegre-Z et al. (5) and SI Appendix, All of the specimens were scanned with a Bruker SkyScan 1272 (Bruker section 5]. Micro-CT) at 50 kV and 200 mA, with a voxel size ranging from 3.12 to A 23-kHz pure tone is produced by a function generator (SDG1000 Series 10.99 µm. Reconstruction and automated measurements of EC were carried Function/Arbitrary Waveform Generator; Siglent Technologies Co. Ltd.) and out with AMIRA (version 6.7; VSG). The EC lengths of all individuals were emitted via an MF1-S 1 Multi Field Speaker (Tucker Davis Technologies) with measured from the 3D reconstructions using the Center Line Tree module a modified probe attachment (SI Appendix, section 6 and Fig. S1). in AMIRA. Prior to each experiment, a standardized reference point was recorded. The probe loudspeaker was mounted onto a micromanipulator (World Sound Analysis and Calculation of Velocity. The first local minimum of the Precision Instruments, Inc.). A calibrated 1/8-inch (3.2-mm) microphone sine wave chirp was used to obtain time measurements (SI Appendix, sec- (Bruel¨ & Kjær) was held in a clamp, and the loudspeaker probe was posi- tion 7 has more details on the reference signal). The time delay between the tioned 2 mm away from the microphone’s protective cap. The time taken reference signal and the amplitude signal of the tympanum was obtained for sound to travel from the loudspeaker probe to the microphone was using MatLab (R2014a; The Math-Works, Inc.). This delay was used to cal- recorded as the reference time. culate the velocity of sound propagation through each EC—dividing the EC The mounted insect was positioned in front of the LDV, and the laser lengths obtained from 3D segmentations by the respective mean time delay. point focused on a TM (Figs. 1 and 2). A gas delivery system (enabling the manipulation of the gas composition between experiments) was introduced Mathematical Model and Numerical Simulations. The numerical results are behind the prothoracic side keel, directed toward the acoustic spiracle (Fig. 1 based on the following system of equations. and SI Appendix, section 1). The probe loudspeaker was then placed 2 mm Let Ω denote the EC of C. gorgonensis, which is the domain of our math- away from the spiracle (matching the distance of the microphone reference ematical model formed by the union of two parts: Ωf is the inside of the EC signal), allowing sound to travel through the acoustic trachea and vibrate (the fluid domain) and Ωs is the EC wall (solid domain), which intersect at the tympanum (Fig. 1). For each ear, the LDV was used to record the time the interface γ = Ωs ∩ Ωf . The boundary of Ω consists of γ1, which denotes for the signal vibrations to arrive at the tympanum, measured as tympanal the acoustic spiracle; γ2, which denotes the TM; and γ3, which denotes the displacement. outer surface of the wall. Recordings were first taken without changes to the gas composition In the fluid domain Ωf , the propagation of the sound wave is modeled within the EC (normal conditions). The time taken for sound to travel from with the use of the scalar wave equation, which also takes into account the loudspeaker to the TM was noted and used as a benchmark throughout the viscosity of the quiescent fluid. This is represented with the following the experiment, to indicate when the gas composition in the EC was normal. equation and initial conditions: Then, over a period of 5 s, pure CO2 (Genuine Innovations) was introduced to the canal via the gas delivery system, and the time was recorded again 2   ∂ p 1 4 µ ∂∇p 2 (SI Appendix, section 1). The CO2 was left to diffuse out of the trachea until + + µB = c ∆p in Ω × (0, T], [2] ∂t2 ρ 3 ∂t f the signal reaching the tympanum returned to normal. This was replicated f ∂p three times, before being repeated on the opposite foreleg. Experiments p(x, 0) = 0, (x, 0) = 0 in Ω , [3] ∂t f

where T > 0 is a fixed positive time, c = speed of sound, µ = dynamic viscos- ∂ ∂ ∂ 2 ity, µB = bulk viscosity, ρf = fluid density, ∇ = ( ∂x , ∂y , ∂z ), and ∆ = ∇ . The dependent variable p = p(x, t) is the time-dependent sound pressure at the Head Thorax A (pronotum) B spatial point x = (x, y, z). A harmonic incident wave enters into the EC through the spiracle with a frequency of 23 kHz and an amplitude of 1 Pa, traveling at 343 m/s, represented by the boundary condition

Acoustic         spiracle 1 1 1 ∂p 1 1 1 ∂pi Left n · ∇p + = n · ∇pi + [4] ear ρf ρf c ∂t ρf ρf c ∂t 2 mm 20 µm EC on γ1, where EC    Dorsal wall (x − ek) C D (auditory receptors) pi = sin 2π × 23000 t − , Septum c|e | fold k Anterior Posterior EC EC and ek is the wave direction. branch branch ATM Taking into account the impedance of the TM, we request the boundary PTM condition (5) given below is satisfied on γ2:

Auditory Septum 1 1 ∂p receptors fold n · ∇p = , [5] Anterior ρf Zi ∂t Posterior EC branch EC branch Septum where Zi is the magnitude of the specific acoustic impedance of the TM. ATM PTM Next, we consider the displacement in the elastic wall due to the sound propagating inside the EC. This is represented by the elastic wave Eq. 6 given 20 µm below, which models the mechanical waves in the structure Ω assuming 200 µm s small deformations (42). We make the simplifying assumption that the EC wall is built of an isotropic, incompressible, and homogeneous material. Eq. Fig. 6. External and internal morphology of the EC showing the tracheal 6 also accounts for the damping properties of the EC wall: division at the tympanal organ location. (A) Lateral view of the body in transparency showing left and right ECs. (B) Internal view inside the EC. 2   ∂ us ∂us ∂σ (C) Close-up view of the ear section extracted from the dashed box in A. ρ + ρ α = ∇ · σ(u ) + β in Ω × (0, T], [6] s 2 s dM s dK s (D) Internal view inside the EC showing the branch division of the trachea ∂t ∂t ∂t at the tympanal organ location. Camera was placed inside the EC lumen ∂us us(x, 0) = 0, (x, 0) = 0 in Ωs, [7] approximately at the location of the yellow dashed line in C. ∂t

6 of 8 | PNAS Veitch et al. https://doi.org/10.1073/pnas.2017281118 A narrow ear canal reduces sound velocity to create additional acoustic inputs in a microscale insect ear Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 0 .Rjrmn .Mar,M an .Psls .Blkiha,D oet o-asfil- Low-pass Robert, D. Balakrishnan, T. Postles, M. Jain, M. Mhatre, N. Rajaraman, K. 10. 2 .Se,Aprpea ehns o uioydrcinlt ntebushcricket the in directionality auditory for mechanism peripheral A Shen, J. horn: exponential 12. an as Tettigoniids of trachea acoustic The Jatho, M. Hoffmann, E. 11. arwercnlrdcssudvlct ocet diinlaosi nusi irsaeinsect microscale a in inputs acoustic additional create to velocity sound ear reduces canal ear narrow A al. et Veitch structural fluid: the the and by structure experienced the on as load acceleration fluid the includes coupling The pled. wall. the on stress external no is there that so h imtro aheeeti esta h quantity the than less is element each in of mesh diameter the the forming elements tetrahedral The software commercial the (43). using 5.5 method version conditions, Multiphysics element boundary Comsol finite defined the the with with obtained along is equations, introduced the of where sound the of speed for formula the taken elementary calculate time the we the by this, obtain Using transmission TM. during to the able reach also to are stimulus sound we (2–12), system solving by structure. the by where respectively. coefficients, damping Rayleigh ratio damping the parameters damping variable tensor; strain the where with where σ .W .Bie,R .Sehn ietoaiyadadtr ltfnto:Ater of theory A function: slit auditory insects. and in Directionality organs Stephen, chordotonal O. R. auditory Bailey, of J. function W. and 9. structure The Yack, E. J. 8. in insects” in hearing “Directional Robert, D. R 7. H. Hartbauer, Convergent Robert, M. D. Postles, 6. M. Robson-Brown, A. K. Jonsson, T. Montealegre-Z, F. 5. .H .Hfnr .S efe,Teeouino amla on localization. sound mammalian of evolution The Heffner, reinterpreta- S. and R. analysis Heffner, An E. ear: H. tetrapod the 4. of Evolution Bolt, middle R. tympanic J. Lombard, The E. innovations: R. and 3. transitions evolutionary Major Tucker, S. A. 2. Gelfand, A. S. 1. (u ial,a h interface the at Finally, h nt lmn ehcntutdi h Ci eosrtdi i.1. Fig. in demonstrated is EC the in constructed mesh element finite The form variational the of solution numerical the discretization, spatial For (0, interval time the for EC the in distribution pressure the as well As On ern nbushcrickets. in hearing NY, York, Tech. Res. New Microsc. Springer, Research, Auditory of 6–35. pp. Handbook 25, (Springer vol. 2005), Eds. Fay, R. R. hearing. insect in computation audition. mammalian and insect between evolution cutctaha system. tracheal Acoustic gratiosa: socleis unusually an with call. bushcricket frequency paleotropical a low in tuning tympanal differential and ters Today tion. ear. 2005). Press, (CRC hoeia acltosadbocutclmeasurements. (1995). bioacoustical 1845–1851 and calculations Theoretical s are ) E γ hl rn.R o.B Soc. R. Trans. Phil. distance= n ρ α il .Ln.Sc Lond. Soc. Linn. J. Biol. 3 on’ modulus; Young’s = s eseiytebudr odto as condition boundary the specify we , 03 (2016). 20–35 12, dM stesraenra and normal surface the is u stedniyo h aladtecmoet ftesrs tensor stress the of components the and wall the of density the is s σ and stedslcmn etrin vector displacement the is ij = ern:A nrdcint scooia n hsooia Acoustics Physiological and Psychological to Introduction An Hearing: 1 β egho h EC. the of length + dK ξ E δ 1–3 (2004). 315–337 63, .Ep Biol. Exp. J. i ij ν n h aua frequencies natural the and r h aspootoa n tfns proportional stiffness and proportional mass the are mr rmmcoeod oscnsadminutes—time and seconds to microseconds From omer, steKoekrdlafnto;adtedependent the and function; Kronecker-delta the is α ¨  ij dM Science 0543(2017). 20150483 372, + n σ and (1 γ 97 (1979). 19–76 11, ij · ξ speed h endfli n oi ytm r cou- are systems solid and fluid defined the , · i + ρ rn.Physiol. Front. 7–8 (2012). 777–787 216, 1 ν = n 3–3 (1978). 633–634 201, f β j ν ∇p = oso’ ratio; Poisson’s = α dK F )(1 E 2ω A ν dM F = 0, = = A aif h olwn eainbetween relation following the satisfy i − distance stefreprui raexperienced area unit per force the is i + pn, −n , 2ν .Aos.Sc Am. Soc. Acoust. J. time j = ω .N Popper, N. A. Localization, Source Sound ) · i 3 (2014). 138 5, δ β 2 ,2 3, 2, 1, (u ij Ω dK X k s s ) =1 3 , utemr,teRayleigh the Furthermore, . tt , Ω Science , ω  f kk i aetersrcinthat restriction the have fa napdsystem: undamped an of ,  ij i , = 6–7 (2012). 968–971 338, .Aos.Sc Am. Soc. Acoust. J. j 2111 (1993). 1211–1217 94, = 2 1 ,2 3, 2, 1,  ∂ ∂ u x si j + ∂ ∂ u Acoust. x Gamp- sj i  [10] [12] [11] T [9] [8] 98, is ] , 4 .H eae ntepoaaino on ae naclnrclconduit. cylindrical a in waves sound of propagation the On Benade, ears. H. A. receiving difference 24. Pressure Larsen, N. O. Michelsen, A. ears. insect 23. some in resolution time Mechanical Larsen, insects. N. in O. systems auditory 22. of function and Evolution Helversen, Von to D. Stumpner, method A. biophysical new 21. A Stumpner, A. Heller, G. K. Rohrseitz, K. Michelsen, A. 20. tempera- of L Effect G. crickets: Wendler, G. in 19. singing of Energetics Walker, J. T. Prestwich, N. K. 18. Klowden, cricket J. the M. in hearing 17. directional of Physics Lewis, B. Popov, V. A. Michelsen, A. 16. Auditory Robert, D. Brown, Robson A. K. Soulsbury, D. C. Montealegre-Z, F. Jonsson, T. 15. 4 .Clkr .Jnsn .MnelgeZ h uioymcaiso h ue a of ear auter the of mechanics auditory The Montealegre-Z, F. Jonsson, T. Celiker, E. 14. in bushcricket” the of ear “The Bailey, J. W. 13. ..i upre hog h uoenCmiso i oio 00Marie 2020 Horizon (InWingSpeak). via 829208 Commission Fellowship European Skłodowska-Curie the Cochlea”). through Insect supported “The is project T.J. the for F.M.-Z. (to ERCCoG-2017-773067 Grant ACKNOWLEDGMENTS. (DOI: Dryad 2020). in November available 8 and deposited are format) files, .stl (in model files Comsol recordings), vibrometry Availability. Data out carried (46). was package emmeans testing the hoc from Post means assumptions. marginal estimated model using meet to (45). found heteroscedastic- 4.0.0 and and R normality ity in for checked (45) were lmerTest models using both run from same Residuals were models the effects of fac- random mixed a measures Linear as tor. individual repeated within nested for was (right/left) account EC To EC, and factors. individual fixed tracheal as with model) numer- variable, dead, ical (live, status dependent and (ATM/PTM) tympanum the and covariate a was as length Velocity models. effects 1. mixed Table sound in listed mean and The taken EC. were SD individual and each velocity for propagation along velocity values, propagation these remaining sound therefore, mean The from and obtained analysis. data dispensation, the length gas with from much removed too were CO to recordings using due was recordings replicates invalidated refer- three some was a of For against minimum recording. standardized a ence of were mean recordings using recorded the Postexperiment, was sample, calculated. TM EC the to each EC For the LDV. through propagate to sound for Analysis. taken Statistical and Comsol Processing of Data feature “scale” the using geom- by The (43). changed same. 5.5 was the version model Multiphysics kept EC been the have of above etry outlined conditions the radii, Eqs. in used parameters the S2 Table of Appendix, values (SI the (43) Multiphysics Comsol of module interaction kHz. 23 at cycles five aigit con httefeunyo h on tmlsi 3kz we kHz, 23 is stimulus sound the of of step frequency took time the that a account with into employed, Taking is Method Alpha alized variables. Quadratic dependent on the solu- based of is The all space for behaviors. in equations elements shell element Lagrange finite various (44), of capturing system type the for of Components used tion Tensorial type of mesh common Interpolation a Mixed of elements shell in mesh The on eoiyi cutctahawsaaye sn asinlinear Gaussian using analyzed was trachea acoustic in velocity Sound different with ECs on out carried been have that simulations the For Acoustic-Shell Transient 3D the using solved are equations outlined The ,teGener- the (2–12), system in derivatives time the of discretization the For o.Am. Soc. (2008). 011001 (1981). 297–304 Naturwissenschaften bushcrickets. in trachea acoustic (1994). the 145–151 of gain the determine cricket Gryllidae). (Orthoptera: species (1981). trilling three in ture pressure the in bimaculatus. inputs sound dual of evidence Direct receiver. difference bush-cricket: a in mechanics h uhcikt ueia approach. numerical Bathurst, A Press, cricket: bush House the (Crawford Eds. Rentz, F. C. D. 217–247. pp. Bailey, 1990), J. Australia, W. Evolution, and ics T = rlu bimaculatus. Gryllus 2 kHz) 5/(23 1–2 (1968). 616–623 44, Ω .Cm.Pyil A Physiol. Comp. J. f hsooia ytm nInsects in Systems Physiological scnetdt h ehon mesh the to connected is h,Terl ftemda etmi h cutctahao the of trachea acoustic the in septum medial the of role The ohe, ¨ ueia iuain,eprmna aa(ae Doppler (laser data experimental simulations, Numerical .R o.Interface Soc. R. J. = 5–7 (2001). 159–170 88, 7 ,s htw sue h on tmlshas stimulus sound the assumed we that so s, 2.174 hssuyi uddb uoenRsac Council Research European by funded is study This aeegho on wave sound of wavelength .Cm.Pyil A Physiol. Comp. J. 5–6 (1994). 153–164 175, C aa eete sdt aclt the calculate to used then were data, µ-CT 0650(2016). 20160560 13, 30 ipy.J. Biophys. https://doi.org/10.1073/pnas.2017281118 uigec xeiet h time the experiment, each During 2–12). h etgnia:Booy Systemat- Biology, Tettigoniidae: The Esve,e.2 2008). 2, ed. (Elsevier, 5–6 (1993). 557–564 173, 6–7 (2020). 464–475 118, 2 Ω 10.5061/dryad.2547d7wnn; .Cm.Physiol. Comp. J. a,terfrnesignal reference the gas, s hc sfre using formed is which , . C stereolithography µ-CT .Cm.Pyil A Physiol. Comp. J. .Cm.Pyil A Physiol. Comp. J. τ iisi.Biomim. Bioinspir. = 2.174 PNAS 199–212 143, × .Acoust. J. | 10 shows Gryllus f8 of 7 −8 143, 175, 3, s.

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