A mechanism for neuronal coincidence revealed in the crayfish antennule

DeForest Mellon, Jr.* and Kate Christison-Lagay

Department of Biology, University of Virginia, Charlottesville, VA 22903

Edited by John G. Hildebrand, University of Arizona, Tucson, AZ, and approved August 6, 2008 (received for review May 7, 2008) Startle reflexes employ specialized neuronal circuits and synaptic duction velocities. Similar conduction-velocity adjustment mech- features for rapid transmission of information from sense organs anisms for achieving interneuronal or effector synchrony are to responding muscles. Successful excitation of these pathways known from a few central and efferent pathways in vertebrates requires the coincidence of sensory input at central synaptic (13, 14) as well as in cephalopod molluscs (15). Our findings contacts with giant fiber targets. Here we describe a pathway could be of critical importance in other systems where synchro- feature in the crayfish tailflip reflex: A position-dependent linear nous arrival of spikes may be required from spatially dispersed gradation in sensory axonal conduction velocities that can ensure primary sensory neurons, such as afferents from cercal filiform the coincident arrival of impulses from near-field hydrodynamic hairs in cockroaches, or lateral line neuromasts or skeletal– sensilla along the crayfish antennules at their synaptic contacts muscle spindles in vertebrates. with central nervous elements that drive startle behavior. This The medial giant-fiber system in crayfish, which mediates provides a previously unexplored mechanism to ensure optimum backward tailflips in response to sudden stimulation of the responses to sudden threatening stimuli. Preliminary findings thorax, legs, or head, is not nearly as well-examined as the lateral indicate that axons supplying distally located sensilla increase their giants, although it is thought that the synaptic organization of diameters at least ten-fold along the antennular flagella and raise afferent inputs to the medial giants is similar to that of the lateral the possibility that more modest, graduated, diameter changes in giants, and suddenness of onset is also critical for axons originating from progressively more proximal sensilla along evoking medial giant spikes (9, 16, 17). It seems reasonable to the antennule underlie the observed modifications in axonal con- hypothesize, therefore, that coincident arrival of afferent spikes duction velocity. at their synapses with the medial giants is as important as it is for lateral giant activation. In fact, the situation is even more critical crustacean ͉ sensory receptor ͉ startle reflex ͉ giant axons ͉ for the medial giants than for the lateral giants, whose distributed hydrodynamic sensilla afferent inputs to their synaptic targets in the several abdominal segmental ganglia comprise relatively short pathways; the two n prey–predator interactions, speed of responses to threaten- medial giants, by contrast, have only a single input and spike- Iing stimuli can mean the difference between capture and generating region—in the —and they receive afferents escape; thus, across phyletic boundaries have evolved from widely differing distances along the thoracic and head startle for rapid responses to approaching threats. The appendages via several different neuronal pathways (16). We neurophysiological substrates of startle behaviors include inter- have identified a small population of highly sensitive, bidirec- neuron axons of very large diameters that conduct impulses tional hydrodynamic receptor sensilla on the antennules (first rapidly to excite relevant efferent pathways (1–5) and electrical antennae) in the crayfish P. clarkii that potentially drives the synapses in the sensory-afferent pathways that trigger the inter- medial giant fibers, and whose dramatically calibrated axonal neurons and, in some systems, the motor neurons involved in the conduction properties must assure simultaneity of arrival in behavior (6). One of the startle behaviors that has been most spikes generated in the sensillar array. This constitutes a neu- intensively studied is a tailflip initiated by one of the two ronal coincidence mechanism that should subserve precisely the sets of these high-speed —the lateral giant fi- sort of afferent synchrony requirement so critical for both the bers—in the ventral nerve cord of crayfish (7–12). Rectifying lateral giant and the medial giant pathways. electrical synapses between sensory-afferent terminals and the lateral giant fibers and between large tactile interneurons and Results the lateral giants, passes current directly into these paired axons Feathered sensilla are prominent near-field hydrodynamic sen- and, when several afferent terminals fire simultaneously, they sors on the crayfish abdomen (18, 19) and undoubtedly largely sum effectively to produce enhanced excitatory postsynaptic comprise the afferent limb of the lateral giant startle reflex. potentials in their targets (11). Furthermore, nonrectifying Morphologically similar standing feathered sensilla occur electrical interconnections among the afferent terminals exist sparsely distributed along the ventro-lateral aspects of the lateral whereby active terminals can directly recruit inactive terminals antennular flagellum and the ventro-medial aspects of the to provide additional depolarization to the lateral giants (12). medial flagellum (Fig. 1A). Their numbers range from 6–10 Coincidence of arrival of afferent input is crucial to these individual sensilla on each flagellum (mean ϭ 8, Ϯ0.6; n ϭ 11), processes and, thus, to initiate the startle response mediated by and they are most numerous along the basal 50% of the flagellar the lateral giants. What is not understood, however, is the neural axis (Fig. 1C). Like feathered sensilla described on the tailfan mechanism that explains the synchronous arrival at central (18) and earlier on the cephalothorax (20), each antennular synapses of sensory-afferent impulses from varying distances, a sensillum is supplied by two sensory neurons that have opposite problem that is especially critical for the other giant-fiber system in the crayfish, the medial giants, because of the long distances traversed by sensory spikes to their target synapses in the brain. Author contributions: D.M. designed research; D.M. and K.C.-L. performed research; D.M. Here we report that a population of hydrodynamic receptor and K.C.-L. analyzed data; and D.M. wrote the paper. sensilla on the antennules of the crayfish Procambarus clarkii The authors declare no conflict of interest. potentially drives the medial giant system to initiate startle This article is a PNAS Direct Submission. behavior and achieves simultaneity of impulse delivery through *To whom correspondence should be addressed. Email: [email protected]. graded, position-dependent variations in the sensory-axon con- © 2008 by The National Academy of Sciences of the USA

14626–14631 ͉ PNAS ͉ September 23, 2008 ͉ vol. 105 ͉ no. 38 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0804385105 Downloaded by guest on September 24, 2021 Fig. 1. Physical properties and response characteristics of standing feathered sensilla. (A) Head of Procambarus clarkii, indicating (arrows) both flagella of the right-hand antennule (Attribution: see ref. 30). (B) Scanning electron micrograph of a standing feathered sensillum on the lateral flagellum of P. clarkii. Other types of sensilla are in the background and foreground. (Scale bar, 100 ␮m.) (C) Distribution of standing feathered sensilla on 11 different lateral and medial flagella along their normalized lengths. (D) Upper and lower traces are extracellularly recorded electrical responses of neuronal pairs to sinusoidal mechanical stimulation of two feathered sensilla. Probe excursions were 200 ␮m peak-to-peak and generated differential responses to bidirectional movements parallel to the flagellar axis, with occasional electrical summations. (E) Polar plots of responses from a pair of neurons associated with one feathered sensillum to ramp deflections of the sensillum tip of 100 ␮m in extent. Response overlap near the least preferred stimulus direction is partially because of minute, unavoidable, mechanical vibrations of the probe and the high sensitivity of the associated neurons. (F) Relationship between spike frequency and stimulus-probe velocity of NEUROSCIENCE 42 sensory neurons associated with feathered sensilla on the lateral and medial flagella. Data points represent mean spiking frequency Ϯ1 SE. At higher velocities, response magnitude begins to saturate. The curve best fit by the data is a first-order exponential, y ϭ 112–107eϪx/832.

directional preferences in their respective sensitivity to displace- latency of the medial giant electrical response was 12.59 msec ments. Typical electrophysiological recordings from two stand- (range: 6.96–17.32 msec, n ϭ 18), well within the range of ing feathered sensilla are shown in Fig. 1B to sinusoidal tip latencies for medial giant activation measured previously (16) displacements of 200 ␮m at a frequency of 1 Hz. The polar plots following sudden taps to the second antennae or the head. To shown in Fig. 1E indicate the mean, normalized spiking response determine whether the difference in response latencies—2.73 of a pair of neurons associated with a feathered sensillum to msec—obtained by the two stimulus methods might be because unidirectional 100-␮m tip excursions applied parallel to the of conduction time of the afferents within the flagella, we flagellar axis and at 30° increments. Spiking response falls off as recorded response latencies, again at 19.5°C, from 11 axons the imposed movements of the sensillum deviate farther than associated with feathered sensilla on the antennular flagella Ϸ60° from the neurons’ preferred vector. These sensory neurons taken from the same crayfish and from another of the respond reliably to even very small near-field disturbances in the same size (50-mm carapace length). The mean response latency hydrodynamic environment. Data from 18 neurons have shown to 1-msec mechanical pulses to the sensilla, measured at the that at 10 Hz their mean threshold to sinusoidal oscillations of flagellar base, was 2.75 Ϯ 0.13 msec (range: 2.12–3.5 msec). the fluid surface above the associated sensillum was 0.02 ␮m Although these results do not specifically identify the feathered (SD ϭϮ0.009). Moreover, as do those displacements associated sensilla as those driving the medial giant reflex, their appropriate with the tailfan feathered sensilla (18), displacements of increas- response latencies make them the most likely candidates because ing velocity generate monotonic increases in mean impulse spikes from axons of all other types of sensilla on the antennular frequency up to saturation near 1,000 ␮m/sec (Fig. 1F). flagella were well below the noise level of our recording tech- In an adult, unrestrained crayfish from which the second niques, were therefore much smaller in diameter than the antennae had been excised, a single, brief (2 msec), electrical feathered sensillar axons and, accordingly, would have had much stimuli delivered simultaneously to the bases of all four anten- slower conduction velocities. With three additional unrestrained nular flagella were sufficient to generate spikes in the medial crayfish, attempts were made to determine a critical, maximum giant system with a mean latency of 9.86 msec (range: 11.16–7.4 time interval between sequential, just-subthreshold shocks de- msec, n ϭ 12), as measured in the second abdominal segment at livered separately to the right and left antennules that are 19.5°C (Fig. 2A1). We then recorded responses in the same required to evoke medial giant-fiber activated tailflips. In our animal to a stimulus generated by dropping a 35-mm plastic, most complete series of tests on one animal, simultaneous shocks wax-filled Petri dish onto the surface of the water just ahead of delivered to the two antennules generated tailflips 81% of the the antennules from a height of 10 cm (Fig. 2A2). The mean time (n ϭ 21 trials); shocks delivered sequentially to the anten-

Mellon and Christison-Lagay PNAS ͉ September 23, 2008 ͉ vol. 105 ͉ no. 38 ͉ 14627 Downloaded by guest on September 24, 2021 Fig. 2. Response of medial giant fibers to stimulation, and axonal conduction velocity/distance relationships of feathered sensilla neurons. Local field potential responses of the medial giant fiber (arrows) and the much larger ones generated by the abdominal fast flexor muscles of an unrestrained crayfish (A1) to a 2-msec shock to the bases of all four antennular flagella and (A2) to an object (*) dropped on the water surface above and ahead of the animal. The large baseline excursions at the end of the records are mechanical artifacts generated by the tailflip. The two modes of stimulation were tested several days apart with the same animal (time calibrations, 10 msec). (B) Variation in mean conduction velocity of neurons associated with feathered sensilla at different positions along 11 different lateral flagella at 16.5°C. Each data point is the mean of ten measurements Ϯ1 SE. The straight line is the best linear fit of the data and is described by the equation, y ϭ 0.17x ϩ 0.25, R2 ϭ 0.98. (C) Variation in conduction velocity with distance along 10 different medial flagella at 16.5°C (data are means Ϯ1 SE). The best fit of the data is described by the equation, y ϭ 0.14x ϩ 0.63, R2 ϭ 0.97. (D) Conduction velocity versus position data from pairs of neurons associated with nine different medial or lateral flagella on four different animals. Each neuron of the pair had either a proximal (F) or distal (■) preferred directional sensitivity. These data are included in the combined measurements of graphs B and C. The best linear fits for the two data sets are virtually indistinguishable (analysis of covariance, P Ͻ0.0001), and the mean values are fit by the equation, y ϭ 0.17 ϩ 0.26, R2 ϭ 0.96.

nules at a 50-msec interval generated tailflips in 47% of the trials flagella and those generated near the flagellar base differ only (n ϭ 17); shocks delivered at 100-msec intervals evoked tailflips by 1.0–1.5 msec recorded at the base. We therefore systemati- 33% of the time (n ϭ 18); whereas shocks delivered at 200-msec cally measured mean conduction velocities in axons from feath- intervals evoked tailflips 29% of the time (n ϭ 14). These ered sensilla at different points along 11 lateral flagella and 10 findings and, especially, tests with very small time intervals, were medial flagella at 16.5°C. The results (Fig. 2 B–D) convincingly confounded by frequent, unpredictable fluctuations in behav- demonstrate that there is a continual, position-dependent rela- ioral threshold; therefore, any conclusion that the requirements tionship between mean axonal conduction velocity and location for synchronous arrival of afferent inputs to the medial giant of a sensillum along the flagellum, with those axons subserving nerve fiber are substantially less stringent than those required for the most distal sensilla being faster by a factor of 6 than those the lateral giant nerve fiber reflex must be tentative at best. We associated with the most proximal sensilla. The relationship is suggest that this question will best be examined by using highly especially striking when conduction velocities of each neuron reduced preparations, as has been done so successfully for the from pairs associated with single standing feathered sensilla are lateral giant fibers. measured. Fig. 2D illustrates conduction velocity measurements Axons associated with standing feathered sensilla, ranging up obtained from neuron pairs associated with nine different to 22 ␮m in diameter at the flagellum base, are the largest and, standing feathered sensilla on four different lateral or medial hence, the fastest conducting in the antennular nerve branches flagella. Statistically, by using analysis of covariance, the linear within the flagella (Fig. 3D). In a typical adult crayfish antennule relationships between conduction velocity and distance from that is 2.5 cm long, and assuming a mean axonal conduction flagellar base in these paired observations are essentially iden- velocity of 3 m/sec, differences in spike arrival time at the brain tical (P Ͻ 0.0001, R2 ϭ 0.96). (an additional 1-cm long pathway proximal to the flagellar bases) In a preliminary attempt to determine whether axonal diam- from sensilla at the base of a flagellum and from those near the eter differences along the antennular flagella may provide an tip could be as large as 8.5 msec. This latency difference could anatomical basis for changes in impulse conduction velocity, we obviate coincident spike arrival and compromise the kind of obtained electron micrographs and toluidine-blue stained light electrical interactions between central afferent terminals that micrographs of transverse sections cut through a medial anten- are so important for activation of the lateral giant system (11, nular flagellum at different points along its length. Examples are 12). Interestingly, however, we found that response latencies of shown in Fig. 3 A–C of a pair of axons from a distally located -in different flagellar frag (ء) spikes generated from sensilla near the tip of the antennular sensillum tentatively identified

14628 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0804385105 Mellon and Christison-Lagay Downloaded by guest on September 24, 2021 Fig. 3. Changes in diameter and in circumference/area ratio of feathered sensilla axons along the antennular flagellum. Electron micrograph (A) and light micrographs (B–D) of transverse sections through a tentatively identified pair (*) of axons from a distally located sensillum. (E) Relationship between transverse sections through the axon pair and the distance from the flagellum base at which they were sectioned. (F) Ratio between circumference and cross-sectional area as area increases for circular (F) and elliptical (■) axons. The elliptical relationship was calculated for axon cross-sections having a major axis/minor axis ratio of 4:1. (Calibration bars: A,2␮m; B and C,10␮m; D,20␮m.)

ments from position and landmarks within the respective sec- conduction velocity occur in the vertebrate retina. There, despite tions. Dramatic changes in axonal cross-sectional area with wide variations in axonal conduction times within the retina, distance from the flagellar base were found. Near the flagellum differences in conduction velocity in the optic nerve apparently tip all of the axonal diameters are very small, but a few profiles reduce these discrepancies so that spatiotemporal events on the of axons in progressively more proximal sections show increasing retinal surface are preserved intact at central targets of the

proportions of larger profiles (Fig. 3E). Near the base of the retinal ganglion cell axons (22). NEUROSCIENCE flagellum (Fig. 3D) 12 profiles approach 20 ␮m in equivalent Our findings with sensillar axons in the crayfish suggest the circular diameters. It is difficult to escape the conclusion that the possibility that diameter changes account for a linear variation diameters of selected axons increase continuously at progres- in conduction velocity with distance along the antennule. In sively more proximal locations along the flagellar axis, perhaps nonmyelinated nerve fibers such as those found in most inver- reaching a maximized diameter near the base. Our preliminary tebrate systems, conduction velocity is directly proportional to anatomical observations will require confirmation by using the square root of axon diameter (23); as axonal size increases— techniques that stain and identify the origin of individual feath- even in axons having an elliptical cross-section in which the ered sensillar neurons along the entire flagellum length and may minor axis:major axis ratio is Ͼ0.25 (cf., Fig. 3F)—the ratio of offer an explanation for the regulated changes in mean conduc- axon circumference:axon area becomes progressively smaller, tion velocity along the flagellum. The linear adjustment of ensuring greater axial current densities, more rapid discharging axonal conduction velocity in antennular sensors suggests that of membrane capacitance by an approaching spike and, in near-field hydrodynamic stimuli, such as those generated by a consequence, greater axonal conduction velocities. Our mea- rapidly approaching predator, could initiate a volley (or volleys) surements with a tentatively identified, distally originating axon of spikes from the array of feathered sensilla on the antennules pair indicate a gradual diameter increase over the distance that would all arrive at the brain coincidently and potentially measured (15 mm) of about a factor of 10; however, we were not have maximum affect at firing the medial giants. able to measure the diameters at the axons’ junction with the cell bodies, so the actual increase could be significantly greater. The Discussion conduction velocity for any axon, measured as distance/latency Spike conduction velocity adjustments are known from other at the flagellum base, will be a mean value dependent on the vertebrate and invertebrate nervous systems. In the vertebrate extent and the rate of change of axon diameter along the auditory system, coincidence detection is believed to arise from flagellum. This may or may not be uniform in axons originating neuronal conduction pathways of continuously differing lengths at different points along the flagellum, and until more extensive and whose spike travel times reflect, and thereby map, interaural observations are made with positively identified neurons origi- time differences (21). In the rat brain, olivocerebellar axons that nating from proximal as well as distal sensilla, it will not be terminate at different distances within the cerebellar cortex possible to determine whether predicted relationships between exhibit isochronicity in their arrival at Purkinje cell targets axon size changes, position of origin, and conduction velocity are through differential conduction velocities, possibly brought justified. about by variations in fiber diameter (13). In electric How might such a graduated system arise developmentally? modifications of both electromotor impulse conduction velocity Crayfish and many other crustaceans grow continuously and conduction pathway length occur with both variations throughout their lifespan, adding antennular segments and nas- providing for synchronous discharge of the distributed compo- cent sensilla at the base of each flagellum although shedding a nent cells of the electric organs (14). Finally, adjustments in fewer number of old segments at the tip every time they molt (24,

Mellon and Christison-Lagay PNAS ͉ September 23, 2008 ͉ vol. 105 ͉ no. 38 ͉ 14629 Downloaded by guest on September 24, 2021 25). Thus, older sensilla are situated more distally. If all axons ature of 16.5°C. The latex tubing was slipped over a small glass capillary associated with standing feathered sensilla continue to grow attached through a Ag–AgCl bridge to an AC preamplifier, and saline was isometrically in diameter as well as length throughout the life of pulled through the fragment to clear the blood sinus of hemolymph. Spikes their host animal, it would explain why those associated with were recorded from the proximally transected axons of feathered sensilla, filtered at 1 Hz–3 kHz, digitized, and stored in computer files by using Pclamp sensilla farthest from the antennular base would have the largest software. Mechanical stimuli to sensilla were provided via a small probe diameter gradients and, other things being equal, could account connected to the cone of an audio speaker. Ramp movements of the probe at for the more rapid conduction of action potentials in those axons various frequencies were provided by a function generator driving the compared to that in the younger axons from sensory neurons speaker or, when measuring axonal conduction velocities, from an electronic found in a more proximal position. A precedent for this sort of stimulator generating brief (0.5 msec) rectangular mechanical excursions of developmental regulation is the critical adjustments in size and 100 ␮m to a sensillum. Feathered sensilla responding to mechanical distur- function at the crayfish neuromuscular junctions that necessarily bances were identified visually—and the stimulus probe was positioned—by attend life-long incremental growth of the crustacean nervous a dissecting microscope. Their position along the flagellum from the basal system and its efferent targets (26, 27). segment was measured following electrophysiological observations, which were also monitored audibly. Threshold measurements were obtained by Findings by Edwards et al. (11) have indicated that coincidence accurate positioning of a sensillum on a flagellar fragment beneath a 2-cm of neighboring afferent spikes at their central targets must occur plastic disk oscillated vertically by a speaker cone on the saline surface. within a time window of Ϸ100 ␮sec to be maximally effective in Measurements of threshold responses to water particle movement were triggering the lateral giant-evoked tailflip, whereas our data show obtained by using the following relationship (18): latency variations at the flagellar bases between proximal sensilla 2 Ϫky and distal sensilla of 1–1.5 msec. The anatomical point on the r ϭ 1/␭fAe antennule where it bifurcates into the flagellar bases is only Ϸ70% where r ϭ radius of circular water particle movements, ␭ ϭ wavelength of the of the total afferent pathway to the brain from the most distal capillary surface wave, A ϭ amplitude of the surface wave, k ϭ 2␲/␭,yϭ depth sensilla, however, and we have not yet measured latency differences of sensillum beneath water surface, and f ϭ frequency of the water-surface wave. at the brain itself. It is entirely conceivable that additional conduc- Recordings from medial giant fibers and abdominal flexor muscle were tion velocity adjustments may take place within the final 30% of the obtained from paired 50-␮m copper wires insulated except at their tips; the pathway and in the brain itself and further reduce any spread in wires were threaded through the lateral tergite on the second abdominal spike latencies. Be that as it may, our experiments with sequential segment and beneath the flexible cuticle of the ventral abdomen of intact electrical stimulation of paired antennules suggest the possibility freely moving crayfish with the uninsulated ends positioned near the dorsal that the submillisecond intervals required to generate spikes in the surface of the ventral nerve cord. The paired leads were led to an AC pream- lateral giant fibers may not obtain with the medial giants. Future plifier, and recorded electrical activity was digitized and stored in computer files for later analysis. work employing highly reduced preparations will probably be Electrical stimulation of the antennules was accomplished by harnessing an necessary to address this difference. otherwise unrestrained crayfish to a pair of silver wire electrodes encircling An additional and rather critical question is: Why does anten- the bases of all of the antennular flagella. A grass S88 stimulator was used to nular flicking fail to generate a medial giant tailflip? The rapid deliver suprathreshold, 2-msec rectangular pulses through a stimulus isolation downward movement of the lateral flagellum and the advancing unit. For experiments with sequential electrical stimulation of the two anten- wave front must surely stimulate the feathered sensilla on, respec- nules, separate pairs of sliver wire electrodes were harnessed to the paired tively, the lateral and medial flagella. During both the medial giant- flagella on each side and individually subthreshold, and 0.5-msec shocks were delivered to the right and left antennule at decreasing time intervals. Medial and lateral giant-mediated tailflips, widespread so-called com- Ϸ mand-derived inhibition is fed forward and backward via corollary giant responses to such stimulus pairs were obtained 80% of the time when the interval between them was reduced to zero, with increasing failures as the discharge neurons to numerous neuronal elements in the abdom- stimulus interval was made larger. inal escape circuitry, including the afferent terminals themselves Measurements of axonal diameters were obtained from sectioned material and the sensory interneurons that they target (28, 29). Among other examined either in the electron or light microscope. A fresh medial antennular consequences, this prevents reafference generated by powerful flagellum, 20 mm in length, was obtained from an adult crayfish (55-mm cara- hydrodynamic inputs associated with the initial reflex from trig- pace length) and transected into seven fragments that were fixed overnight at gering subsequent tailflips. Although speculative at this time, we 4°C in 2.5% glutaraldehyde made up in 0.1 M sodium cacodylate buffer. The suggest that the brain neural circuit generating antennular flicks fragments were then post-fixed in 2% osmium tetroxide in buffer, dehydrated through an alcohol series, and imbedded in Epon. For light microscopy, sections uses a corollary discharge neural pathway to feed-forward synaptic ␮ inhibition to the terminals of feathered sensillar axons, suppressing were cut at 0.5 m, stained with toluidine blue, and imaged in bright field at 1,020ϫ. For electron microscopy, thin sections were stained in uranyl acetate, their effect at the medial giant axons. mounted on slot grids, and examined at low power in a JEOL electron microscope. Images obtained from both the light and electron microscopes were digitized Materials and Methods and saved by using Photoshop software. Measured cross-sectional areas were Adult (45–50-mm carapace length) crayfish were obtained from a supplier in obtained from specific axonal outlines by using ImageJ software. Most axon Louisiana and housed in a circulating freshwater culture system at constant profiles were not circular; therefore, measured areas of outlined axons were temperature (18°C.) and a light/dark cycle of 12 h:12 h. Crayfish were chilled converted to equivalent circular profiles and their radii were calculated to deter- on ice for 15 min to anesthetize them before removing antennular flagella at mine flagellar position-equivalent circular axon diameter relationships. Graphs their basal segment. Short fragments or entire flagella were mounted in a of linear fits were obtained by using Origin8 software. short length of Latex tubing having an internal diameter slightly smaller than the diameter of the flagellum. The flagellum fragment was lowered into a ACKNOWLEDGMENTS. We thank D. Sandeman for comments on an early draft bath of crayfish saline (Composition, in mM/L: NaCl, 205; KCl, 5.4; CaCl2 2H2O, of this paper, J. Redick for technical help with microscopy, J. Humphrey for 13.6; MgCl2 7H2O, 2.7; NaHCO3, 2.4; pH adjusted to 7.4 with HCl) at a temper- calculations of capillary surface wave velocity, and H. Wilbur for statistical advice.

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