188
Brain Research, 151 (1978)188-193 O Elsevier/North-Holland Biomedical Press
A single propagation velocity in large and small branches of the R2 neuron of
Aplysio colifornico PETER HARLEY Department of Psychology and Marine Sciences Research Laboratory, Memorial University of Newfoundland, St. John's, Nfld. A1C 5S7 (Canada) (Accepted February 9th, 1978)
It was at one time considered something of a paradox that certain nerve and muscle fibres conducted impulses at their normal rates, even when stretched so as to greatly reduce their diameters 2,6,1°. However, these observations were explained 9,1°, in terms of the unfolding of wrinkles from the surface membranes of the lengthened fibres. It was thought that there might be a constant volume to surface ratio during stretch, and this was plausible in view of the known convoluted surfaces of the elements examined. Mirolli and Talbott 11 provided definitive support for this notion in a morphological study of the giant axon of Anisodoris. They observed that the cross-sectional area-to-perimeter (A/P) ratio of the giant axon was unchanged by stretch, or, in other words, that the volume to surface ratio of the fibre was indeed constant. A general geometrical factor for the length constant of an axon was shown to be H ---- V'A/P (where H is the factor, and A and P are the cross-sectional area and perimeter respectively). This factor was found to remain constant not only during stretch, but also throughout the remarkable degree of beading which the fibre exhibited naturally along its length. Following the precedent of Mirolli and Talbott 11, Pinsker et al. t2 made measurements of the cross-sectional areas and perimeters of right connective giant axons, RI and R2 of Aplysia (see ref. 4 for nomenclature). The smaller axon, R1, had been known for some time to conduct faster than the larger, R24,6; and it was therefore of interest to make a quantitative comparison of the geometries. It was found that the H-factor for the smaller axon was indeed greater that the same factor in the large, and that, therefore, the smaller axon would have been expected to conduct faster, had the two cells been identical as regards membrane and axoplasmic constants. To summarize, there is at present good reason to expect at least a monotonic relationship between the general geometric factor, H, of Mirolli and Talbott ~, and conduction velocitylL For cylindrical fibres, this H-factor will remain H ~ ~/D, where D is fibre diameter 9. However, since large molluscan axons are highly irregular in their cross-sectional shapes1,3,7,12, it is probably not reasonable to expect that they generally conduct faster than small fibres in this phylum.
189 The right giant neuron, R2, of Aplysia californica has a large axon in the right pleuro-abdominal connective, and a smaller one in the branchial nerve 4. Results of a procion dye study of this element 5 indicate that the right connective axon is 75-200 /~m in its cross-sectional aspect, while the branchial axon is only 10-20 # m wide. The present report points out that impulse velocity is equivalent in these two processes. Aplysia californica purchased from Pacific Bio-Marine Supply Company (P.O. Box 536 Venice, Calif.) were housed in an A-frame, where circulating natural seawater was normally maintained at 14-15 °C. The specimens taken for experiments were judged to have been healthy by their posture and activity in the living tank. Upon dissection, the abdominal ganglion was pinned out in a seawater bath kept at 14 ~ I °C and the nerves were stretched slightly beyond the point where the axon bundles could be seen to uncoil and lie in a straight line. R2 was impaled with glass microelectrode (filled with 3 M KCI and usually 2-4 Mf~) through which both stimulation and recording could be accomplished by means of a bridge circuit in a WPI M4A electrometer amplifier. The ground wire and electrode wire were chloridized silver, making bridge balance quite reliable and easy to achieve. The preparation was viewed through a dissecting microscope containing a measuring eyepiece graduated in 100 # m steps. To compare velocities in the right connective and branchial axons, the distance between the point of impalement on the soma and the cathodal pole of a micromanipulated, stimulating electrode was determined for stimulating sites on each of the two nerves, and intracellular latencies were determined for these sites. The stimulating electrode consisted of a pair of Teflon-coated silver wires, each approximately 200 # m in diameter. The wires were twisted around one another, and the anodal member cut about 2 mm shorter than the cathode. Thus, only the cathode normally touched the nerve, and the stimulating geometry was relatively constant from one site to the next, varying only with the angle at which the stimulating electrode touched the nerve. This angle was kept close to 90°. Stimulus strength was normally manipulated by varying the duration of a 160 V square pulse, but it was also ascertained that no reported results were any different if, instead, the voltage of a brief (about 1 msec) square pulse was varied. Latencies were determined on responses repetitively evoked with slightly suprathreshold stimulus strengths (usually about 0.1 msec duration) at a frequency of 1 Hz or less. Latencies consisted of the time between the stimulus artifact and the onset of positive deflection of the trace associated with the responses examined. A Tektronix 5031 storage oscilloscope was used, and the data were recorded with a pencil, on a simultaneously ongoing penwriter record of the experiment. In the earlier work oscilloscope gain was normally 5-10 mV per major division. However, in more recent experiments, gain was increased to 500-200/~V/major division, and the same gain was used for all latency determinations directly compared. To compare the right connective and branchial action potential velocities, latency-distance co-ordinates, for each of the stimulation sites, on one nerve from one preparation, were examined through a least squares linear regression analysis. This analysis yielded slope, reciprocal slope, intercept and standard error terms for the resultant line. Most of the data presented for consideration in Table I were examined first during the experiments, by
190 TABLE I
Summary data for the 1975 and 1976 samples are shown, as well as the individual measurements from the 1977 sample. Standard errors for the 1977 estimates are shown in parentheses. Dates o f measurements
Number o f R2 neurons examined
Velocity in right connective (m/sec)
Velocity in branchial nerve (m/sec)
Feb. 14-May 15, 1975 May 17-June 14, 1976 April 22, 1977 April 26 April 27, A April 27, B May 2, A May 2, B
7 8
~ ,~ 0.59 0.57 0.59 0.54 0.56 0.57 =
,X -~ 0.50 0.50 0.58 0.60 0.58 0.54 X --
0.51 0.61 (0.02) (0.02) (0.02) (0.03) (0.04) (0.01) 0.57
0.51 0.62 (< 0.01) (< 0.01) (0.02) (0.02) (0.02) (0.02) 0.55
plotting the points on graph paper. A single point was entered as a latency measurement for each distance considered, and any repeated examination oflatencies concluded with but a single latency estimate, which was judged to be the correct one for that particular distance. The latency measurements on stored C R O traces examined during the experiments were easier to make than the same measurements on 35 m m photographs, and, hence, the latter were used only occasionally for checking purposes. Illustrative p h o t o g r a p h s were made both by a Tektronix C-12 camera on the 503l master oscilloscope, and also with a N i h o n K o h d e n camera, which faced a slaved 502A oscilloscope in a darkened c h a m b e r over the rest of the experimental apparatus. The antidromic spike from the branchial nerve. The R2 antidromic spike consequent to branchial nerve stimulation normally ranges in amplitude from 1 to 5 mV. While this evoked response is only occasionally the lowest-threshold excitatory event seen in the soma, it almost invariably has the shortest latency. A n d while the shortestlatency all-or-nothing event to follow branchial nerve stimulation may normally be taken to be the R2 action potential, there are yet additional criteria which ensure that the response is identifiable as a distinct event. First, the small antidromic spike can be prevented from appearing if it is preceded by an action potential started elsewhere in the R2 neuron. The inset of Fig. 1 shows the small branchial spike failing in an allor-nothing fashion when it is temporally too close to the soma spike elicited by an antidromic invasion f r o m the right connective axon. The same result was obtained by exciting R2 with intracellular pulses. These experiments are, in themselves, adequate evidence for the physiological continuity of the branchial axon with the R2 cell body. Beyond this, however, the branchial spike can be blocked by hyperpolarizing the R2 soma (not illustrated); Tauc and Hughes la have discussed the differences in behaviors o f EPSPs and A-spikes in response to membrane potential changes in Aplysia neurons. A n d finally, the Y-intercept o f the latency-distance plot o f the branchial A-spike is normally within a few msec o f the origin at 14 °C (Fig. 1). This is in contrast to the Y-intercepts of branchial synaptic inputs to the R2 neuron; these are normally at least 10 msec (unpublished work).
191
14 12 lO u8 (/1
E6 4 2 2
4
6
8
10
12
mm
Fig. 1. Inset: positive identification of a small response as the antidromic spike from the branchial axon of R2. The branchial A-spike is prevented from occurring on about half of the illustrated sweeps, because it follows too closely the soma spike elicited by an antidromic invasion from the right connective axon. Suprathreshold stimuli have been applied to each nerve, and the branchial nerve stimulus has been brought closer and closer in time to the right connective stimulus, until the small, branchial response is failing on a large proportion of the sweeps; 2 mV AC; 40 mV DC; 20 msec. Plot: the latencydistance functions from which velocities were inferred in the preparation of June 1, 1976. B refers to branchial, and R to right connective; each letter represents a data point.
The antidromic spike from the right connective. At 14 °C, the A-spike from the right connective is usually adequate to fire the soma (inset in Fig. 1). It is almost always the earliest intracellular response to right connective stimulation, and is easily distinguished from EPSPs by its amplitude, its rate o f rise, its response to hyperpolarization o f the cell body, its latency-distance intercept (Fig. 1), and its one-for-one association with the largest all-or-none extracellular response in right connective action potential. M o s t o f the above attributes are c o m m o n l y appreciated, and therefore are not illustrated. The equivalent velocities of the branchial and right connective antidromic action potentials. It was at first by casual observation that the velocities o f the two action potentials were noticed to be similar. Following this, a quantitative comparison was made on 7 preparations in 1975, and the means o f the impulse velocities for the two processes were found to be exactly equal at 0.51 m/see. In 1976, another 8 preparations were examined, and it was found that the mean for the right connective axon was 0.61 m/sec, while the mean for the branchial axon was 0.62 m/see. In 1977 another 6 ganglia were considered, and this time the mean for the right connective axon was 0.57 m/sec, while the branchial mean was 0.55 m/see. These results are shown in Table I, together with a standard error term for each o f the 1977 velocity determinations. D a t a from a single preparation are shown in Fig. 1. It was checked that neither temperature variations nor oscilloscope gain accounted for the differences a m o n g samples.
192 The responses recorded in this study had to traverse regions of the R2 neuron entirely within the abdominal ganglion. Since neither the branching geometry of the axons nor their exact course through the neuropil was precisely known, it is natural to wonder what effects these conditions might have upon velocity determinations by the present technique. In spite of the fact that the axons may take variously tortuous routes within the ganglion, and in spite of the fact that the branchial impulse fails to fire either the large axon or the soma, neither of these considerations introduce error into the velocity estimates given above. The method used here determines conduction velocity for lengths of axon between stimulation sites. Thus, non-homogeneous shape and tortuous travel within the neuropil can introduce only constants to each of the latency-distance determinations, thereby affecting the intercepts (Fig. 1) but not the slopes of the fitted lines. Hence, the velocity estimates are good, allowing only the assumptions: (1) that the axons were straight within the lengths of nerve stimulated, and (2) that excitation began at a constant distance from the cathode at each of the stimulation sites. The correctness of the first assumption is assured by applying sufficient stretch to the nerve6; and the correctness of the second assumption is quite probable in view of the relatively invariant stimulating geometry (see above). For both the branchial and right connective velocity determinations, stimuli were sufficiently suprathreshold that no latency variations occurred during measurements. Table I provides evidence for the equivalence of mean conduction velocities in the large and small axons in 3 samples of R2 neurons. If the 1977 experiments are looked at individually, several can be selected to make the point that the branchial and right connective propagation rates are not always exactly the same. Nevertheless, the similarity of mean conduction rates remains striking, and it does appear that impulse velocities in the large and small axons are always approximately the same. Differences among the sample means are striking, but are probably not explicable in terms of the aging hypothesis previously suggested 8 (and manuscript in preparation). It seems most likely that the single propagation rate for the large and small R2 axons is to be explained in terms of a single area-to-perimeter ratio for the two processes. Since the electrical, membrane and axoplasmic constants for the two processes are those of a single cell, it is unlikely that inhomogeneities of these factors would exist and yet be exactly balanced for the creation of a single propagation rate in the two processes. On the contrary, a better first guess would seem to be that the R2 membrane and axoplasm have uniform electrical properties, but that the cross-sectional shapes of the fibres are such as to give rise to a single length constant throughout. The latter condition would also seem more consistent with the observation of Mirolli and Talbott 11 that the H-factor of the Anisodoris giant axon did not change as that fibre expanded and constricted along its length. To conclude, it is perhaps not outrageous to speculate on an intriguing possibility. It may be that the propagation of an action potential occurs at essentially a constant velocity throughout all the processes of any unmedullated, molluscan neuron. Certainly, the present report deals only with two identified cellular processes, reputedly differing in size by a factor of ten 5. However, many invertebrate neurons have several axons, and it will be interesting to see whether impulse velocity is uniform in such cells.
193 S u p p o r t e d by the N a t i o n a l Research C o u n c i l of C a n a d a G r a n t s A-9792 and SPE-752. M.S.R.L. C o n t r i b u t i o n N u m b e r 258. I t h a n k Fred White, Roger West, R i c h a r d N e u m a n and D o n a l d Geduldig for c o m m e n t i n g o n various drafts of this paper.
1 Batham•E.J.••nf••dings•fnerve•bremembranesinthe•pisth•branchm•••usc•Aplysiacalif•rni•a• J. biophys, biochem. Cytol., 9 (1961) 490-492. 2 Bullock, T. H., Cohen, J. J. and Faulstick, D., Effect of stretch on conduction in single nerve fibers, Biol. Bull., 99 (1950) 320. 3 Coggeshall, R. E., A light and electron microscope study of the abdominal ganglion of Aplysia californica, J. Neurophysiol., 30 (1967) 1263-1288. 4 Frazier, W. T., Kandel, E. R., Kufermann, I., Waziri, R. and Coggeshall, R., Morphological and functional properties of identifed neurons in the abdominal ganglion of Aplysia californica, J. Neurophysiol., 30 (1967) 1288-1351. 5 Gillette, E. and Pomeranz, B., A study of neuron morphology in Aplysia californica using Procion Yellow dye, Comp. Biochem. Physiol., 44 A (1973) 1257-1259. 6 Goldman, L., The effect of stretch on the conduction velocity of single nerve fibers in Aplysia, J. cell. comp. Physiol., 57 (1961) 185-191. 7 Graubard, K., Voltage attenuation within Aplysia neurons: the effect of branching pattern, Brain Research, 88 (1975) 325-332. 8 Harley, P. R., A possible age-related decrement in the conduction velocity of Aplysia neuron R2, Experientia (Basel), 31 (1975) 901-902. 9 Hodgkin, A. L., A note on conduction velocity, J. Physiol. (Lond.), 125 0954) 221-224. l0 Martin, A. R., The effect of change in length on conduction velocity in muscle, J. Physiol. (Lond.), 125 0954) 215-220. 11 Mirolli, M. and Talbott, S. R., The geometrical factors determining the electronic properties of a molluscan neuron, J. Physiol. (Lond.), 227 (1972) 19-34. 12 Pinsker, H., Feinstein, R., Sawada, M. and Coggeshall, R., Anatomical basis for an apparent paradox concerningconduction velocities of two identified axons in Aplysia, J. Neurobiol., 3 (1976) 241-253. 13 Tauc, L. and Hughes, G. M., Modes of initiationand propagation of spikes in the branching axons of molluscan central neurons, J. gen. Physiol., 46 (1963) 533-549.
Brain Research, 151 (1978)188-193 O Elsevier/North-Holland Biomedical Press
A single propagation velocity in large and small branches of the R2 neuron of
Aplysio colifornico PETER HARLEY Department of Psychology and Marine Sciences Research Laboratory, Memorial University of Newfoundland, St. John's, Nfld. A1C 5S7 (Canada) (Accepted February 9th, 1978)
It was at one time considered something of a paradox that certain nerve and muscle fibres conducted impulses at their normal rates, even when stretched so as to greatly reduce their diameters 2,6,1°. However, these observations were explained 9,1°, in terms of the unfolding of wrinkles from the surface membranes of the lengthened fibres. It was thought that there might be a constant volume to surface ratio during stretch, and this was plausible in view of the known convoluted surfaces of the elements examined. Mirolli and Talbott 11 provided definitive support for this notion in a morphological study of the giant axon of Anisodoris. They observed that the cross-sectional area-to-perimeter (A/P) ratio of the giant axon was unchanged by stretch, or, in other words, that the volume to surface ratio of the fibre was indeed constant. A general geometrical factor for the length constant of an axon was shown to be H ---- V'A/P (where H is the factor, and A and P are the cross-sectional area and perimeter respectively). This factor was found to remain constant not only during stretch, but also throughout the remarkable degree of beading which the fibre exhibited naturally along its length. Following the precedent of Mirolli and Talbott 11, Pinsker et al. t2 made measurements of the cross-sectional areas and perimeters of right connective giant axons, RI and R2 of Aplysia (see ref. 4 for nomenclature). The smaller axon, R1, had been known for some time to conduct faster than the larger, R24,6; and it was therefore of interest to make a quantitative comparison of the geometries. It was found that the H-factor for the smaller axon was indeed greater that the same factor in the large, and that, therefore, the smaller axon would have been expected to conduct faster, had the two cells been identical as regards membrane and axoplasmic constants. To summarize, there is at present good reason to expect at least a monotonic relationship between the general geometric factor, H, of Mirolli and Talbott ~, and conduction velocitylL For cylindrical fibres, this H-factor will remain H ~ ~/D, where D is fibre diameter 9. However, since large molluscan axons are highly irregular in their cross-sectional shapes1,3,7,12, it is probably not reasonable to expect that they generally conduct faster than small fibres in this phylum.
189 The right giant neuron, R2, of Aplysia californica has a large axon in the right pleuro-abdominal connective, and a smaller one in the branchial nerve 4. Results of a procion dye study of this element 5 indicate that the right connective axon is 75-200 /~m in its cross-sectional aspect, while the branchial axon is only 10-20 # m wide. The present report points out that impulse velocity is equivalent in these two processes. Aplysia californica purchased from Pacific Bio-Marine Supply Company (P.O. Box 536 Venice, Calif.) were housed in an A-frame, where circulating natural seawater was normally maintained at 14-15 °C. The specimens taken for experiments were judged to have been healthy by their posture and activity in the living tank. Upon dissection, the abdominal ganglion was pinned out in a seawater bath kept at 14 ~ I °C and the nerves were stretched slightly beyond the point where the axon bundles could be seen to uncoil and lie in a straight line. R2 was impaled with glass microelectrode (filled with 3 M KCI and usually 2-4 Mf~) through which both stimulation and recording could be accomplished by means of a bridge circuit in a WPI M4A electrometer amplifier. The ground wire and electrode wire were chloridized silver, making bridge balance quite reliable and easy to achieve. The preparation was viewed through a dissecting microscope containing a measuring eyepiece graduated in 100 # m steps. To compare velocities in the right connective and branchial axons, the distance between the point of impalement on the soma and the cathodal pole of a micromanipulated, stimulating electrode was determined for stimulating sites on each of the two nerves, and intracellular latencies were determined for these sites. The stimulating electrode consisted of a pair of Teflon-coated silver wires, each approximately 200 # m in diameter. The wires were twisted around one another, and the anodal member cut about 2 mm shorter than the cathode. Thus, only the cathode normally touched the nerve, and the stimulating geometry was relatively constant from one site to the next, varying only with the angle at which the stimulating electrode touched the nerve. This angle was kept close to 90°. Stimulus strength was normally manipulated by varying the duration of a 160 V square pulse, but it was also ascertained that no reported results were any different if, instead, the voltage of a brief (about 1 msec) square pulse was varied. Latencies were determined on responses repetitively evoked with slightly suprathreshold stimulus strengths (usually about 0.1 msec duration) at a frequency of 1 Hz or less. Latencies consisted of the time between the stimulus artifact and the onset of positive deflection of the trace associated with the responses examined. A Tektronix 5031 storage oscilloscope was used, and the data were recorded with a pencil, on a simultaneously ongoing penwriter record of the experiment. In the earlier work oscilloscope gain was normally 5-10 mV per major division. However, in more recent experiments, gain was increased to 500-200/~V/major division, and the same gain was used for all latency determinations directly compared. To compare the right connective and branchial action potential velocities, latency-distance co-ordinates, for each of the stimulation sites, on one nerve from one preparation, were examined through a least squares linear regression analysis. This analysis yielded slope, reciprocal slope, intercept and standard error terms for the resultant line. Most of the data presented for consideration in Table I were examined first during the experiments, by
190 TABLE I
Summary data for the 1975 and 1976 samples are shown, as well as the individual measurements from the 1977 sample. Standard errors for the 1977 estimates are shown in parentheses. Dates o f measurements
Number o f R2 neurons examined
Velocity in right connective (m/sec)
Velocity in branchial nerve (m/sec)
Feb. 14-May 15, 1975 May 17-June 14, 1976 April 22, 1977 April 26 April 27, A April 27, B May 2, A May 2, B
7 8
~ ,~ 0.59 0.57 0.59 0.54 0.56 0.57 =
,X -~ 0.50 0.50 0.58 0.60 0.58 0.54 X --
0.51 0.61 (0.02) (0.02) (0.02) (0.03) (0.04) (0.01) 0.57
0.51 0.62 (< 0.01) (< 0.01) (0.02) (0.02) (0.02) (0.02) 0.55
plotting the points on graph paper. A single point was entered as a latency measurement for each distance considered, and any repeated examination oflatencies concluded with but a single latency estimate, which was judged to be the correct one for that particular distance. The latency measurements on stored C R O traces examined during the experiments were easier to make than the same measurements on 35 m m photographs, and, hence, the latter were used only occasionally for checking purposes. Illustrative p h o t o g r a p h s were made both by a Tektronix C-12 camera on the 503l master oscilloscope, and also with a N i h o n K o h d e n camera, which faced a slaved 502A oscilloscope in a darkened c h a m b e r over the rest of the experimental apparatus. The antidromic spike from the branchial nerve. The R2 antidromic spike consequent to branchial nerve stimulation normally ranges in amplitude from 1 to 5 mV. While this evoked response is only occasionally the lowest-threshold excitatory event seen in the soma, it almost invariably has the shortest latency. A n d while the shortestlatency all-or-nothing event to follow branchial nerve stimulation may normally be taken to be the R2 action potential, there are yet additional criteria which ensure that the response is identifiable as a distinct event. First, the small antidromic spike can be prevented from appearing if it is preceded by an action potential started elsewhere in the R2 neuron. The inset of Fig. 1 shows the small branchial spike failing in an allor-nothing fashion when it is temporally too close to the soma spike elicited by an antidromic invasion f r o m the right connective axon. The same result was obtained by exciting R2 with intracellular pulses. These experiments are, in themselves, adequate evidence for the physiological continuity of the branchial axon with the R2 cell body. Beyond this, however, the branchial spike can be blocked by hyperpolarizing the R2 soma (not illustrated); Tauc and Hughes la have discussed the differences in behaviors o f EPSPs and A-spikes in response to membrane potential changes in Aplysia neurons. A n d finally, the Y-intercept o f the latency-distance plot o f the branchial A-spike is normally within a few msec o f the origin at 14 °C (Fig. 1). This is in contrast to the Y-intercepts of branchial synaptic inputs to the R2 neuron; these are normally at least 10 msec (unpublished work).
191
14 12 lO u8 (/1
E6 4 2 2
4
6
8
10
12
mm
Fig. 1. Inset: positive identification of a small response as the antidromic spike from the branchial axon of R2. The branchial A-spike is prevented from occurring on about half of the illustrated sweeps, because it follows too closely the soma spike elicited by an antidromic invasion from the right connective axon. Suprathreshold stimuli have been applied to each nerve, and the branchial nerve stimulus has been brought closer and closer in time to the right connective stimulus, until the small, branchial response is failing on a large proportion of the sweeps; 2 mV AC; 40 mV DC; 20 msec. Plot: the latencydistance functions from which velocities were inferred in the preparation of June 1, 1976. B refers to branchial, and R to right connective; each letter represents a data point.
The antidromic spike from the right connective. At 14 °C, the A-spike from the right connective is usually adequate to fire the soma (inset in Fig. 1). It is almost always the earliest intracellular response to right connective stimulation, and is easily distinguished from EPSPs by its amplitude, its rate o f rise, its response to hyperpolarization o f the cell body, its latency-distance intercept (Fig. 1), and its one-for-one association with the largest all-or-none extracellular response in right connective action potential. M o s t o f the above attributes are c o m m o n l y appreciated, and therefore are not illustrated. The equivalent velocities of the branchial and right connective antidromic action potentials. It was at first by casual observation that the velocities o f the two action potentials were noticed to be similar. Following this, a quantitative comparison was made on 7 preparations in 1975, and the means o f the impulse velocities for the two processes were found to be exactly equal at 0.51 m/see. In 1976, another 8 preparations were examined, and it was found that the mean for the right connective axon was 0.61 m/sec, while the mean for the branchial axon was 0.62 m/see. In 1977 another 6 ganglia were considered, and this time the mean for the right connective axon was 0.57 m/sec, while the branchial mean was 0.55 m/see. These results are shown in Table I, together with a standard error term for each o f the 1977 velocity determinations. D a t a from a single preparation are shown in Fig. 1. It was checked that neither temperature variations nor oscilloscope gain accounted for the differences a m o n g samples.
192 The responses recorded in this study had to traverse regions of the R2 neuron entirely within the abdominal ganglion. Since neither the branching geometry of the axons nor their exact course through the neuropil was precisely known, it is natural to wonder what effects these conditions might have upon velocity determinations by the present technique. In spite of the fact that the axons may take variously tortuous routes within the ganglion, and in spite of the fact that the branchial impulse fails to fire either the large axon or the soma, neither of these considerations introduce error into the velocity estimates given above. The method used here determines conduction velocity for lengths of axon between stimulation sites. Thus, non-homogeneous shape and tortuous travel within the neuropil can introduce only constants to each of the latency-distance determinations, thereby affecting the intercepts (Fig. 1) but not the slopes of the fitted lines. Hence, the velocity estimates are good, allowing only the assumptions: (1) that the axons were straight within the lengths of nerve stimulated, and (2) that excitation began at a constant distance from the cathode at each of the stimulation sites. The correctness of the first assumption is assured by applying sufficient stretch to the nerve6; and the correctness of the second assumption is quite probable in view of the relatively invariant stimulating geometry (see above). For both the branchial and right connective velocity determinations, stimuli were sufficiently suprathreshold that no latency variations occurred during measurements. Table I provides evidence for the equivalence of mean conduction velocities in the large and small axons in 3 samples of R2 neurons. If the 1977 experiments are looked at individually, several can be selected to make the point that the branchial and right connective propagation rates are not always exactly the same. Nevertheless, the similarity of mean conduction rates remains striking, and it does appear that impulse velocities in the large and small axons are always approximately the same. Differences among the sample means are striking, but are probably not explicable in terms of the aging hypothesis previously suggested 8 (and manuscript in preparation). It seems most likely that the single propagation rate for the large and small R2 axons is to be explained in terms of a single area-to-perimeter ratio for the two processes. Since the electrical, membrane and axoplasmic constants for the two processes are those of a single cell, it is unlikely that inhomogeneities of these factors would exist and yet be exactly balanced for the creation of a single propagation rate in the two processes. On the contrary, a better first guess would seem to be that the R2 membrane and axoplasm have uniform electrical properties, but that the cross-sectional shapes of the fibres are such as to give rise to a single length constant throughout. The latter condition would also seem more consistent with the observation of Mirolli and Talbott 11 that the H-factor of the Anisodoris giant axon did not change as that fibre expanded and constricted along its length. To conclude, it is perhaps not outrageous to speculate on an intriguing possibility. It may be that the propagation of an action potential occurs at essentially a constant velocity throughout all the processes of any unmedullated, molluscan neuron. Certainly, the present report deals only with two identified cellular processes, reputedly differing in size by a factor of ten 5. However, many invertebrate neurons have several axons, and it will be interesting to see whether impulse velocity is uniform in such cells.
193 S u p p o r t e d by the N a t i o n a l Research C o u n c i l of C a n a d a G r a n t s A-9792 and SPE-752. M.S.R.L. C o n t r i b u t i o n N u m b e r 258. I t h a n k Fred White, Roger West, R i c h a r d N e u m a n and D o n a l d Geduldig for c o m m e n t i n g o n various drafts of this paper.
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