JOURNALOF NEUROPHYSIOLOGY Vol. 41, No. I, January 1978. Prin?eJ
in U.S.A.
Synaptic Connectivity in a Crayfish Neuromuscular System. I. Gradient of Innervation and Synaptic Strength SAMUEL
J. VfiLEZ
Department
SUMMARY
of
Biology,
AND
ROBERT J. WYMAN
AND
Yale University,
New Haven,
CONCLUSIONS
2. The projection of six motoneuronsto a flat sheet of muscle fibers, the superficial flexor muscle of the crayfish Procambarus clarkii, was examined. Each of the motoneuronsis individually identifiable. Each of the muscle fibers can be homologized, with good accuracy, in successivepreparations. 2. Intracellular recording, while stimulating singleaxons at 10 Hz, yields the following data: a) When each animal is examined, the junction potentials (jp’s) produced by any given axon in neighboring musclefibers are of very dissimilar sizes, bordering on a random sequence. When homologous muscle fibers are examined in a series of animals, the jp’s received by these fibers are also very dissimilar.Yet when population averages are taken, it is found that: b) The minimumand maximum probabilities of innervation for each axon occur at the edgesof the muscle sheet. c) Between the minimum and maximum values, the probability of innervation increaseslinearly as a function of position in the muscle. d) The size of the jp’s producedby eachaxon is also a roughly linear function of position acrossthe muscle. 3. We propose a) that there is a process controlling the development of synapses, such that the strength of a synapse on any given fiber is not determined but is probabilistically controlled, i.e., a random process;b) that there is a single gradient across the muscle which controls the parametersof this random process. Thus, for any given axon the mean strength of synapsesincreases or decreasescontinuously from one end of the muscleto the other. There is no “recognition’ ’ between axon and muscle fiber. The probability that a fiber is innervated by an axon is simply the probability that the axon sendsout at least one ending in its region. Received
for publication
April
2, 1976.
Connecticut
06520
INTRODUCTION
The nerve cells of each animal speciesare interconnected in a manner appropriate for the behavioral needs of that species. Thus, each species is different. Nevertheless, neurophysiologists search for generalizations about connectivity that cross specieslines. Generalizations about the patterns of connectivity center aroundjust a few themes.One of these organizing themes is the possibility of random and specific connectivity. In the recent past there was much theoretical discussion of random neural circuitry (3) but, as more is known about real cases of neural connectivity, the pendulum has swung the other way and the emphasisin the literature is now on the specificity of neural connections(7, 8, 11). Invertebrate neurophysiologistsuse the term specificity to refer to the possibility that certain identified presynaptic cells always make connectionsto identified postsynapticcells in all individuals of the speciesexamined(12, 13, 27). In the ideal experimental situation one would have a group of presynaptic cells which could be individually identified in preparation after preparation and a group of postsynaptic cells which could be likewise identified. One would then test for the presence or absenceof connections between these two sets of cells in a series of animals. In a perfectly specific projection one would find that a connection between two particular cells would either always occur or never occur. To the extent that connections between two cells were sometimespresent and sometimesnot, the projection would be said to depart from specificity toward randomness. Recent experiments have produced evidence of very specific connections between populations of singly identifiable cells in invertebrates (2, 10, 12, 18, 24). As far as we know, the only empirical report of randomconnectivity is found in a study of the innervation of the slow flexor muscles of the crayfish abdomen 75
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76
S. J. Vl?LEZ
AND
(15). Here a set of six individually identifiable motoneurons innervate a sheet of about 40 muscle fibers which lie side by side and parallel to each other. It was found that different axons innervate different muscle regions with clear regularities. But even in the region where an axon innervated most densely, not all the fibers were innervated by the axon; the muscle fibers which did or did not get innervated by an axon seemed to be a random sample. In this original report, Kennedy and Takeda (15) determined if an axon had endings on a fiber by detecting unitary junction potentials (jp’s) caused by each axon’s firing during tactile stimulation of the animal. Some jp’s caused by these axons were very small and they could easily have been missed in the original experiments. For example, jp’s from the inhibitor axon were found on less than 50% of the muscle fibers. In 1972, Evoy and Beranek (6) found all the muscle fibers to be sensitive to the postulated inhibitory transmitter, GABA, and by stimulating the inhibitory axon they detected IPSPs in 111 of 116 muscle fibers tested. They concluded that all the fibers probably received synapses from the inhibitory axon. Thus, on more minute inspection, it turned out that what had appeared to be random connectivity of the inhibitor axon was, in fact, a form of very specific connectivity. Although randomness is a well-defined mathematical construct, in real situations the findings of randomness or order often depends on the minuteness of the inspection and on the types of nonrandomness that are searched for. As Kennedy et al. (14) warned: “Since we cannot distinguish formally between the alleged randomness of the connections and our own ignorance about them, the issue will have to await further experimental insights.” This paper is a reexamination of the connectivity of the neural projection to the crayfish slow flexor muscle in which we think we may have found such an insight. In nervous systems, one form of specific connectivity is repeatedly found to occur: the connections of a nerve cell depend on its positiorr in a manner that can be ascribed to a controlling gradient (1,9,22). The best examples of these are the topographic projections found in sensory and motor systems. In no case have the synaptic connections in a topographic projection been studied. Most claims of topographic connectivity are based on recording evoked potentials which represent arriving impulses in presynaptic axons. The postsynaptic cells have usually not been recorded from and so it is not known what synapses are actually activated by incoming axons. We believe that the motor connections to the
R. J. WYMAN
crayfish slow flexor muscle, although not topographic, is also controlled by some sort of gradient. This preparation has the advantage that the synaptic connections between preand postsynaptic cells can be individually studied. We have determined for each presynaptic cell the spatial range of its connections and the strength of the synapses it makes at each point. We believe this to be the first example of a gradient directed, nontopographic projection. The data has suggested to us a theory of how a gradient controls neuronal connectivity. MATERIALS
AND
METHODS
Dissection Crayfish Procatnbarus clarkii, obtained from Dahl Biological Co., Berkeley, California and kept in an aquarium at 22°C were used for this study. The abdomen was severed at the level of the first abdominal segment and pinned dorsal side up in a temperature-controlled bath filled with crayfish Ringer (25), which was changed several times during the dissection. The central portion of the carapace was then removed, leaving the edges intact. All the deep extensor and flexor muscles were removed so as to expose the superficial flexor muscles and the ventral nerve cord. In some preparations the specimen was also turned ventral side up and the cuticle on top of the superficial flexor muscles was removed, leaving the muscle accessible from both sides. If all the muscle fibers in the muscle were not in good condition, a new preparation was used. All studies were done on the superficial flexor muscles of the third segment, and in 95% of the experiments only the left side of the segment was used.
Recording The thin posterior branch of the third root was pulled into a suction pipette and the spontaneous activity of the six axons was recorded on film. With the recording suction pipette in place, the nerve was cut at its point of exit from the cord and the cut end was pulled into another suction pipette, which was used to stimulate the axons at a frequency of 10 Hz. Two glass microelectrodes with resistances from 10 to 30 Ma, tip sizes about 2 pm, were used in the experiments, one to record from the muscle fiber, the other to pass current. Both microelectrodes were filled with a solution of 4% fast green in distilled water. Fast green proved to be the best electrolyte for both electrical recording and marking the muscle fibers. Both microelectrodes could be used again and again without any changes in the current needed for dye injection and no appreciable changes in microelectrode resistances. The
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INNERVATION
GRADIENT
microelectrodes were connected to conventional recording equipment. The current microelectrode was used to measure input resistance and time constants of the muscle fibers in the conventional way (5). The recording electrode was used to determine the resting potential of the muscle fibers and the jp’s on stimulation of the axons. A series of intracellularly recorded jp’s were averaged using a Biomation 102 signal averager. The averager was triggered from the stimulator. Only jp’s greater than 100 PV were averaged during 64 sweeps, whereas jp’s lo-100 PV in size were detected by averaging 256 or 512 sweeps of the computer. In this muscle approximately the same size jp is recorded from any place along the fiber (1.5) because of multiterminal innervation and the long space constant of the fibers (26). The limit of resolution of our system was 10 pV. For these experiments, the absence of a jp at IO-Hz stimulation after 512 sweeps of the computer was taken to indicate the absence of a connection. The averaged signals were photographed on Kodak photographic paper (type 1732) using a Nihon-Kohden oscilloscope camera. The possibilities for artifact are large when detecting small signals by averaging; thus, the following controls were used (Fig. 1). After a jp was recorded on the averager both of the following measurements had to show a zero base line before the data was accepted: a) to control for signals synchronized with the stimulator but not due to jp’s, the averaging process was
AND SYNAPTIC
STRENGTH
77
repeated with stimuli just subthreshold for the axon under consideration; and b) to control for signals conducted passively from neighboring muscle fibers, the averaging process was repeated with suprathreshold stimulation, but with the recording microelectrode just out of the muscle cell. If no jp was recorded on the averager, the following criteria had to be met to ensure that both the axon and the muscle fiber were not damaged: a) the axon had to produce jp’s in nearby fibers, and b) the muscle fiber had to receive jp’s from other axons.
Zdentijication of axons and muscle fibers Axons were identified in each experiment, once before cutting the nerve by filming a portion of the spontaneous activity of the axons and again after cutting the nerve by selective stimulation of the axons at 10 Hz. If doubt existed about the identification of any of the axons, the data were not used. The axons were classified according to spike height, axon I being the smallest, axon 6 being the largest, and axon 5 being the inhibitor (15). In addition, the six nerve cells were distinguished by many other characteristics. Axons 2 through 6 have their cell bodies in the ganglion of the same segment as the muscle, but axon 1 has its cell body in the next most caudal ganglion. Axon 2 has the highest spontaneous frequency and the smallest excitatory jp sizes, axon 6 has the lowest spontaneous frequency, tends to fire in bursts, and has the largest (facili-
FIG. 1. Data and controls. A: large junction potential. 1, suction electrode recording stimulus artifact and spike of axon 6; 2, intracellular recording, stimulus below threshold for axon 6. Calibration pulse 20 pV, 10 ms; 3, intracellular recording; stimulus above threshold for axon 6. Calibration pulse 1 mV, 10 ms. B: small junction potential. 1, spike of axon 3; 2, averaged response, intracellular recording, stimulus above threshold for axon 3. Calibration pulse 20 pV, 10 ms; 3, stimulus above threshold for axon 3, but microelectrode moved to just outside the muscle fiber. Calibration pulse 20 pV, 10 ms.
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78
S. J. Vl?LEZ
AND
R. J. WYMAN
tated) jp sizes. The cells have different synapdetermined whether any intervening fiber had tic connections (15, 21, 23). Thus, each of the been missed. six presynaptic cells is unique and each can Previous reports (20) distinguished a medial be identified in preparation after preparation. and lateral head of the muscle, but this is misNot all six axons were mapped in a single leading. The muscle is divided anatomically into experiment. Usually three or four axons, those two layers, each one cell thick, differing in their that could be individually stimulated in that place of attachment to the sternum. The ventral preparation, were studied. layer extends the width of the muscle, while Even under the best optical conditions it the dorsal layer extends only over the lateral was not always possible to visualize the boundhalf of the muscle. ary between adjacent muscle fibers in the experiDifferent animals had a slightly different nummental chamber. In order to insure that no mus- ber of fibers in both dorsal and ventral layers. cle fibers were recorded from twice, and also that The total number of fibers is 42 ? 3 (unpubnone were missed, the following procedure lished data). Viewed from the ventral surface, was used. A recording electrode was placed the muscle is a continuous sheet of about 27 in one fiber and a current-passing electrode fibers. The fibers lie parallel to each other, side was placed in a neighboring fiber, as judged by side. The medial half of the muscle consists visually. If no current was detected in the first only of this sheet which is one fiber thick. fiber, then the two were considered electrically Viewed from the dorsal surface, a second row isolated, separate fibers. Electronic connections of about 15 fibers is seen to lie on top of the exist between some crayfish muscle fibers but first row from about the middle of the muscle not in the superficial extensor (19) nor the superto the lateral edge (Fig. 2). Fibers in this row ficial flexor (this paper). After the experican also be identified by their serial position. mental recordings were made, dye was in- Thus, in its lateral half the muscle is a sheet jected through the recording electrode. The two fibers thick (there is an occasional third boundaries of the fibers under study were clearly fiber sitting in between). marked within a few minutes and it could be In these experiments the muscle was ap-
FIG. 2. Scanning electron micrograph of the superficial flexor muscle of the third abdominal segment of the crayfish. Dorsal view, all the dorsal muscles have been removed. Rostra1 at top of picture, caudal at bottom. Ventral nerve cord runs down center of micrograph. Third and fourth abdominal ganglia are visible. First and second roots exit out of each ganglion. The third root of the third ganglion exists from the nerve cord between the two ganglia. The deep branch of the third root has been cut, leaving the superficial branch running onto the surface of the superficial flexor muscle. Scale: 1,000pm.
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INNERVATION
GRADIENT
proached from either the dorsal (usually) or the ventral surface. In both cases about 27 muscle fibers are visible on the surface. In order to combine data from different animals, the following scheme was used. The ventral fibers were numbered serially starting at the medial edge up to the point where the dorsal fibers started. Then the most lateral fiber was labeled27 and the remainingfibers were labeled in a medial direction with progressively lower numbers.If the preparation hadexactly 27 fibers, visible from the dissected surface, this scheme labels them l-27 from medial to lateral; if there were fewer than 27 fibers, some of the middle numbershad no fibers assignedto them; if there were more than 27 fibers, some of the middle numbers had two fibers assignedto them. In this way, each muscle fiber had a number that correspondedto its position on the surface of the muscle. The data were grouped by combining all fibers with the same number into the same bin. For graphical analysis, bins were further combined into groups of three, resulting in nine bins.
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Axons were individually stimulated at a frequency of 10 Hz, while an intracellular microelectrode measured the junction potential induced by that axon in each musclefiber. At this frequency, there is at least a 1,OOO-foldvariation in jp amplitudes, ranging from 10 PV to 12.5 mV. The jp sizes produced by a given axon in homologousmuscle fibers in different animals was very variable. The sizes of jp’s produced by a given axon in adjacent muscle fibers of each animal was also very variable. Several nonparametric statistics were used to test the hypothesis that in a given animal the jp’s delivered by one axon to successive fibers was a random series. When looked at across the whole muscle the series were not random since the jp’s either increased or decreased from one end of the muscleto the other. However, when each half of the muscle was tested separately, the variability was large compared to the amount of increase or decrease of jp size across half the muscle surface. Thus, the statistical tests came out nearly random for the half-muscles. In contrast to this near randomness,when innervation parameters are averaged for many animalsand displayed as a function of position in the muscle sheet, somevery straightforward patterns appear.
Positional dependence of presence and absence of innervation The crudest measureof innervation is whether or not a connection occurs between two ele-
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FIG. 3. Percentage of innervation of the slow flexor muscle by each axon. The muscle sheet was divided into nine regions of approximately three neighboring muscle fibers each. Each point pools data for that region for all animals. Percentage is number of fibers receiving a synapse/total number of fibers tested. Number of fibers tested for each axon was: I, 173; 2, 302; 3, 460; 4, 273; 5, 219; 6, 540.
ments, regardlessof the quantitative effectiveness of that synapse. Accordingly, we first tabulated the data in our sampleaccordingto the presenceor absenceof a synaptic connection. The percentage of fibers innervated by each of the axons is displayed for each location in the muscle sheetin Fig. 3. The simplest connectivity pattern was found for the inhibitor, axon 5. In all, we tested 219 muscle fibers to determine if they were innervated by the inhibitor axon. In only one fiber did we fail to record a jp. We conclude that axon 5 is programmedto innervate all the fibers in the muscle. This is in agreement with the finding of Evoy and Beranek (6). Axon 5 generally has very small inhibitory potentials, in the same range as axon 2, which has the smallest excitatory potentials. The fact that we were able to detect a jp produced by this axon in every muscle fiber encouraged us to believe that the lower limit of resolution of our experimental technique (10 pV) was sufficient to detect all jp’s present at lo-Hz stimulation.
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80
S. J. VkLEZ
AND
The connectivity pattern of the excitor axons was somewhat more complex. It can be seen from Fig. 3 that all the excitor axons show a maximum of innervation at one side of the muscle sheet and a minimum at the other side of the sheet. In fact, the probability of innervation is roughly proportional to position in the muscle, until the percentages reach 100 or 0%. The constant of proportionality is different for each fiber and has opposite sign for the three small excitors and the two large ones, such that the small ones increase their innervation from lateral to medial, while the larger fibers do the opposite.
Positional dependence of strength of synaptic interaction When the average jp caused by each axon on each muscle fiber is correlated with the position of the muscle fibers, a clear pattern also emerges. Figure 4 shows the average jp sizes for each axon at the different positions in the muscle. Each point is the average of the jp’s caused in three neighboring fibers by one axon in all the animals in which this axon was studied. For all the axons the average jp’s show a general increase from one edge of the muscle to the other in a direction paralleling the innervation probability of the axons. The increase in jp’s with position is roughly linear. The linear regression for each of these graphs was calculated and found to be significant at better than the 2% level (29); all had high correlation coefficients ranging from 0.77 to 0.95 in absolute magnitude, i.e., the linear regressions explained 60-90% of the variance of the data points. The simplest hypothesis one could make to describe these graphs is that, for all the axons, the average jpis increased linearly from zero at one edge of the sheet to a maximum at the other edge. Surprisingly, this simple hypothesis was statistically acceptable. The data points for each axon were normalized to the same amplitude scale by dividing the data points for each axon by twice the mean for that axon. This created a scaled amplitude axis on which the data points for all the axons had values ranging from 0 to approximately 1, with a mean of 0.5. The position axis was also scaled to have a length of one unit. The points for the six axons were then displayed on one graph with the points for axons 4 and 6 plotted in reverse direction from the others so that all axons had their lower amplitude points at the left of the graph (Fig. 5). The hypothesis predicts that the points lie along a line with a slope of 1 and an intercept of 0. The graph shows this theoretical regression line and the actual regression line. The actual regression slope was 1.03 with an intercept of -0.02. The correla-
R. J. WYMAN
tion coefficient was 0.83. The actual and the theoretical regression lines were not significantly different. Thus, the simple hypothesis that strength of innervation increases linearly from zero at one edge to a maximum at the other edge is statistically acceptable. Two possibilities for artifact arise in interpreting the position-dependent increase in jp. The physical size of the muscle fibers increases in a medial to lateral direction; correspondingly, the input resistances decrease laterally (26). If the same average amount of synaptic current was produced by an axon at all locations, then one should expect the jp’s to decrease laterally due to the decreased input resistance. This phenomenon could not explain the graphs for axons 4 and 6, which increase in the opposite direction. However, it could be part of the explanation of the graphs of axons I, 2,3, and 5. To check this we measured the input resistance of the fibers in about 75% of the experiments. The jp’s measured in each fiber were then divided by that fiber’s input resistance to yield a corrected jp. Graphs similar to Fig. 5 of these corrected jp’s as a function of position were then prepared in the same manner as outlined before. The general shape of the graphs were not changed. The same statistical procedures were performed on the corrected graphs as on the graph of Fig. 5. All the regressions were significant with, on the average, slightly higher correlation coefficients than for the uncorrected data. The graph for testing the hypothesis that the input resistance corrected jp increases linearly from zero to a maximum had a regression line slope of 1.09, an intercept of -0.05, and a correlation coefficient of 0.85. The hypothetical and actual regression lines were not significantly different. Thus, the measurements, after correction for fiber input resistance, are also in strong accord with the hypothesis. The second possibility for artifact is that the average jp is lower in regions of reduced percentage of innervation because the uninnervated fibers add zeros into the averages in these regions. To check this possibility we calculated the average jp’s excluding all zeros. This is the average jp size at each position for fibers which do receive a synapse from the axon in question. Using the statistical procedures described above, the graph was again similar to that of Fig. 5. In the composite graph, the correlation coefficient was 0.75 and the significance of the correlation was 0.001. Thus, calculated in a number of different ways, the correlation of junction potential size with position is always high, ranging from 0.75 to 0.85. Therefore, it can be concluded that although jp variations between individual fibers are great, the sizes of the jp have a direct
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relationship to the position of the musclefibers at 10 Hz. It remainsto be seen if the smooth over the entire musclesurface. position dependenceof innervation parameters It should be noted that the strength of a would also be obtained at other frequenciesof synaptic contact, as measuredby jp size, will stimulation. In addition to synaptic strength, appear to be very different at different fre- several other physiological variables of the quencies of stimulation because of facilitation muscleare a monotonicfunction of position (26). at the neuromuscularjunction (4, 16). All re- We suspect that the average facilitation propsults in this paper were obtained with stimuli per-tiesof the junctions might also be position
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S. J. Vl?LEZ AND R. J. WYMAN
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Synaptic Connectivity in a Crayfish Neuromuscular System. I. Gradient of Innervation and Synaptic Strength SAMUEL
J. VfiLEZ
Department
SUMMARY
of
Biology,
AND
ROBERT J. WYMAN
AND
Yale University,
New Haven,
CONCLUSIONS
2. The projection of six motoneuronsto a flat sheet of muscle fibers, the superficial flexor muscle of the crayfish Procambarus clarkii, was examined. Each of the motoneuronsis individually identifiable. Each of the muscle fibers can be homologized, with good accuracy, in successivepreparations. 2. Intracellular recording, while stimulating singleaxons at 10 Hz, yields the following data: a) When each animal is examined, the junction potentials (jp’s) produced by any given axon in neighboring musclefibers are of very dissimilar sizes, bordering on a random sequence. When homologous muscle fibers are examined in a series of animals, the jp’s received by these fibers are also very dissimilar.Yet when population averages are taken, it is found that: b) The minimumand maximum probabilities of innervation for each axon occur at the edgesof the muscle sheet. c) Between the minimum and maximum values, the probability of innervation increaseslinearly as a function of position in the muscle. d) The size of the jp’s producedby eachaxon is also a roughly linear function of position acrossthe muscle. 3. We propose a) that there is a process controlling the development of synapses, such that the strength of a synapse on any given fiber is not determined but is probabilistically controlled, i.e., a random process;b) that there is a single gradient across the muscle which controls the parametersof this random process. Thus, for any given axon the mean strength of synapsesincreases or decreasescontinuously from one end of the muscleto the other. There is no “recognition’ ’ between axon and muscle fiber. The probability that a fiber is innervated by an axon is simply the probability that the axon sendsout at least one ending in its region. Received
for publication
April
2, 1976.
Connecticut
06520
INTRODUCTION
The nerve cells of each animal speciesare interconnected in a manner appropriate for the behavioral needs of that species. Thus, each species is different. Nevertheless, neurophysiologists search for generalizations about connectivity that cross specieslines. Generalizations about the patterns of connectivity center aroundjust a few themes.One of these organizing themes is the possibility of random and specific connectivity. In the recent past there was much theoretical discussion of random neural circuitry (3) but, as more is known about real cases of neural connectivity, the pendulum has swung the other way and the emphasisin the literature is now on the specificity of neural connections(7, 8, 11). Invertebrate neurophysiologistsuse the term specificity to refer to the possibility that certain identified presynaptic cells always make connectionsto identified postsynapticcells in all individuals of the speciesexamined(12, 13, 27). In the ideal experimental situation one would have a group of presynaptic cells which could be individually identified in preparation after preparation and a group of postsynaptic cells which could be likewise identified. One would then test for the presence or absenceof connections between these two sets of cells in a series of animals. In a perfectly specific projection one would find that a connection between two particular cells would either always occur or never occur. To the extent that connections between two cells were sometimespresent and sometimesnot, the projection would be said to depart from specificity toward randomness. Recent experiments have produced evidence of very specific connections between populations of singly identifiable cells in invertebrates (2, 10, 12, 18, 24). As far as we know, the only empirical report of randomconnectivity is found in a study of the innervation of the slow flexor muscles of the crayfish abdomen 75
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76
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AND
(15). Here a set of six individually identifiable motoneurons innervate a sheet of about 40 muscle fibers which lie side by side and parallel to each other. It was found that different axons innervate different muscle regions with clear regularities. But even in the region where an axon innervated most densely, not all the fibers were innervated by the axon; the muscle fibers which did or did not get innervated by an axon seemed to be a random sample. In this original report, Kennedy and Takeda (15) determined if an axon had endings on a fiber by detecting unitary junction potentials (jp’s) caused by each axon’s firing during tactile stimulation of the animal. Some jp’s caused by these axons were very small and they could easily have been missed in the original experiments. For example, jp’s from the inhibitor axon were found on less than 50% of the muscle fibers. In 1972, Evoy and Beranek (6) found all the muscle fibers to be sensitive to the postulated inhibitory transmitter, GABA, and by stimulating the inhibitory axon they detected IPSPs in 111 of 116 muscle fibers tested. They concluded that all the fibers probably received synapses from the inhibitory axon. Thus, on more minute inspection, it turned out that what had appeared to be random connectivity of the inhibitor axon was, in fact, a form of very specific connectivity. Although randomness is a well-defined mathematical construct, in real situations the findings of randomness or order often depends on the minuteness of the inspection and on the types of nonrandomness that are searched for. As Kennedy et al. (14) warned: “Since we cannot distinguish formally between the alleged randomness of the connections and our own ignorance about them, the issue will have to await further experimental insights.” This paper is a reexamination of the connectivity of the neural projection to the crayfish slow flexor muscle in which we think we may have found such an insight. In nervous systems, one form of specific connectivity is repeatedly found to occur: the connections of a nerve cell depend on its positiorr in a manner that can be ascribed to a controlling gradient (1,9,22). The best examples of these are the topographic projections found in sensory and motor systems. In no case have the synaptic connections in a topographic projection been studied. Most claims of topographic connectivity are based on recording evoked potentials which represent arriving impulses in presynaptic axons. The postsynaptic cells have usually not been recorded from and so it is not known what synapses are actually activated by incoming axons. We believe that the motor connections to the
R. J. WYMAN
crayfish slow flexor muscle, although not topographic, is also controlled by some sort of gradient. This preparation has the advantage that the synaptic connections between preand postsynaptic cells can be individually studied. We have determined for each presynaptic cell the spatial range of its connections and the strength of the synapses it makes at each point. We believe this to be the first example of a gradient directed, nontopographic projection. The data has suggested to us a theory of how a gradient controls neuronal connectivity. MATERIALS
AND
METHODS
Dissection Crayfish Procatnbarus clarkii, obtained from Dahl Biological Co., Berkeley, California and kept in an aquarium at 22°C were used for this study. The abdomen was severed at the level of the first abdominal segment and pinned dorsal side up in a temperature-controlled bath filled with crayfish Ringer (25), which was changed several times during the dissection. The central portion of the carapace was then removed, leaving the edges intact. All the deep extensor and flexor muscles were removed so as to expose the superficial flexor muscles and the ventral nerve cord. In some preparations the specimen was also turned ventral side up and the cuticle on top of the superficial flexor muscles was removed, leaving the muscle accessible from both sides. If all the muscle fibers in the muscle were not in good condition, a new preparation was used. All studies were done on the superficial flexor muscles of the third segment, and in 95% of the experiments only the left side of the segment was used.
Recording The thin posterior branch of the third root was pulled into a suction pipette and the spontaneous activity of the six axons was recorded on film. With the recording suction pipette in place, the nerve was cut at its point of exit from the cord and the cut end was pulled into another suction pipette, which was used to stimulate the axons at a frequency of 10 Hz. Two glass microelectrodes with resistances from 10 to 30 Ma, tip sizes about 2 pm, were used in the experiments, one to record from the muscle fiber, the other to pass current. Both microelectrodes were filled with a solution of 4% fast green in distilled water. Fast green proved to be the best electrolyte for both electrical recording and marking the muscle fibers. Both microelectrodes could be used again and again without any changes in the current needed for dye injection and no appreciable changes in microelectrode resistances. The
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INNERVATION
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microelectrodes were connected to conventional recording equipment. The current microelectrode was used to measure input resistance and time constants of the muscle fibers in the conventional way (5). The recording electrode was used to determine the resting potential of the muscle fibers and the jp’s on stimulation of the axons. A series of intracellularly recorded jp’s were averaged using a Biomation 102 signal averager. The averager was triggered from the stimulator. Only jp’s greater than 100 PV were averaged during 64 sweeps, whereas jp’s lo-100 PV in size were detected by averaging 256 or 512 sweeps of the computer. In this muscle approximately the same size jp is recorded from any place along the fiber (1.5) because of multiterminal innervation and the long space constant of the fibers (26). The limit of resolution of our system was 10 pV. For these experiments, the absence of a jp at IO-Hz stimulation after 512 sweeps of the computer was taken to indicate the absence of a connection. The averaged signals were photographed on Kodak photographic paper (type 1732) using a Nihon-Kohden oscilloscope camera. The possibilities for artifact are large when detecting small signals by averaging; thus, the following controls were used (Fig. 1). After a jp was recorded on the averager both of the following measurements had to show a zero base line before the data was accepted: a) to control for signals synchronized with the stimulator but not due to jp’s, the averaging process was
AND SYNAPTIC
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repeated with stimuli just subthreshold for the axon under consideration; and b) to control for signals conducted passively from neighboring muscle fibers, the averaging process was repeated with suprathreshold stimulation, but with the recording microelectrode just out of the muscle cell. If no jp was recorded on the averager, the following criteria had to be met to ensure that both the axon and the muscle fiber were not damaged: a) the axon had to produce jp’s in nearby fibers, and b) the muscle fiber had to receive jp’s from other axons.
Zdentijication of axons and muscle fibers Axons were identified in each experiment, once before cutting the nerve by filming a portion of the spontaneous activity of the axons and again after cutting the nerve by selective stimulation of the axons at 10 Hz. If doubt existed about the identification of any of the axons, the data were not used. The axons were classified according to spike height, axon I being the smallest, axon 6 being the largest, and axon 5 being the inhibitor (15). In addition, the six nerve cells were distinguished by many other characteristics. Axons 2 through 6 have their cell bodies in the ganglion of the same segment as the muscle, but axon 1 has its cell body in the next most caudal ganglion. Axon 2 has the highest spontaneous frequency and the smallest excitatory jp sizes, axon 6 has the lowest spontaneous frequency, tends to fire in bursts, and has the largest (facili-
FIG. 1. Data and controls. A: large junction potential. 1, suction electrode recording stimulus artifact and spike of axon 6; 2, intracellular recording, stimulus below threshold for axon 6. Calibration pulse 20 pV, 10 ms; 3, intracellular recording; stimulus above threshold for axon 6. Calibration pulse 1 mV, 10 ms. B: small junction potential. 1, spike of axon 3; 2, averaged response, intracellular recording, stimulus above threshold for axon 3. Calibration pulse 20 pV, 10 ms; 3, stimulus above threshold for axon 3, but microelectrode moved to just outside the muscle fiber. Calibration pulse 20 pV, 10 ms.
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78
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R. J. WYMAN
tated) jp sizes. The cells have different synapdetermined whether any intervening fiber had tic connections (15, 21, 23). Thus, each of the been missed. six presynaptic cells is unique and each can Previous reports (20) distinguished a medial be identified in preparation after preparation. and lateral head of the muscle, but this is misNot all six axons were mapped in a single leading. The muscle is divided anatomically into experiment. Usually three or four axons, those two layers, each one cell thick, differing in their that could be individually stimulated in that place of attachment to the sternum. The ventral preparation, were studied. layer extends the width of the muscle, while Even under the best optical conditions it the dorsal layer extends only over the lateral was not always possible to visualize the boundhalf of the muscle. ary between adjacent muscle fibers in the experiDifferent animals had a slightly different nummental chamber. In order to insure that no mus- ber of fibers in both dorsal and ventral layers. cle fibers were recorded from twice, and also that The total number of fibers is 42 ? 3 (unpubnone were missed, the following procedure lished data). Viewed from the ventral surface, was used. A recording electrode was placed the muscle is a continuous sheet of about 27 in one fiber and a current-passing electrode fibers. The fibers lie parallel to each other, side was placed in a neighboring fiber, as judged by side. The medial half of the muscle consists visually. If no current was detected in the first only of this sheet which is one fiber thick. fiber, then the two were considered electrically Viewed from the dorsal surface, a second row isolated, separate fibers. Electronic connections of about 15 fibers is seen to lie on top of the exist between some crayfish muscle fibers but first row from about the middle of the muscle not in the superficial extensor (19) nor the superto the lateral edge (Fig. 2). Fibers in this row ficial flexor (this paper). After the experican also be identified by their serial position. mental recordings were made, dye was in- Thus, in its lateral half the muscle is a sheet jected through the recording electrode. The two fibers thick (there is an occasional third boundaries of the fibers under study were clearly fiber sitting in between). marked within a few minutes and it could be In these experiments the muscle was ap-
FIG. 2. Scanning electron micrograph of the superficial flexor muscle of the third abdominal segment of the crayfish. Dorsal view, all the dorsal muscles have been removed. Rostra1 at top of picture, caudal at bottom. Ventral nerve cord runs down center of micrograph. Third and fourth abdominal ganglia are visible. First and second roots exit out of each ganglion. The third root of the third ganglion exists from the nerve cord between the two ganglia. The deep branch of the third root has been cut, leaving the superficial branch running onto the surface of the superficial flexor muscle. Scale: 1,000pm.
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INNERVATION
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proached from either the dorsal (usually) or the ventral surface. In both cases about 27 muscle fibers are visible on the surface. In order to combine data from different animals, the following scheme was used. The ventral fibers were numbered serially starting at the medial edge up to the point where the dorsal fibers started. Then the most lateral fiber was labeled27 and the remainingfibers were labeled in a medial direction with progressively lower numbers.If the preparation hadexactly 27 fibers, visible from the dissected surface, this scheme labels them l-27 from medial to lateral; if there were fewer than 27 fibers, some of the middle numbershad no fibers assignedto them; if there were more than 27 fibers, some of the middle numbers had two fibers assignedto them. In this way, each muscle fiber had a number that correspondedto its position on the surface of the muscle. The data were grouped by combining all fibers with the same number into the same bin. For graphical analysis, bins were further combined into groups of three, resulting in nine bins.
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Axons were individually stimulated at a frequency of 10 Hz, while an intracellular microelectrode measured the junction potential induced by that axon in each musclefiber. At this frequency, there is at least a 1,OOO-foldvariation in jp amplitudes, ranging from 10 PV to 12.5 mV. The jp sizes produced by a given axon in homologousmuscle fibers in different animals was very variable. The sizes of jp’s produced by a given axon in adjacent muscle fibers of each animal was also very variable. Several nonparametric statistics were used to test the hypothesis that in a given animal the jp’s delivered by one axon to successive fibers was a random series. When looked at across the whole muscle the series were not random since the jp’s either increased or decreased from one end of the muscleto the other. However, when each half of the muscle was tested separately, the variability was large compared to the amount of increase or decrease of jp size across half the muscle surface. Thus, the statistical tests came out nearly random for the half-muscles. In contrast to this near randomness,when innervation parameters are averaged for many animalsand displayed as a function of position in the muscle sheet, somevery straightforward patterns appear.
Positional dependence of presence and absence of innervation The crudest measureof innervation is whether or not a connection occurs between two ele-
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ments, regardlessof the quantitative effectiveness of that synapse. Accordingly, we first tabulated the data in our sampleaccordingto the presenceor absenceof a synaptic connection. The percentage of fibers innervated by each of the axons is displayed for each location in the muscle sheetin Fig. 3. The simplest connectivity pattern was found for the inhibitor, axon 5. In all, we tested 219 muscle fibers to determine if they were innervated by the inhibitor axon. In only one fiber did we fail to record a jp. We conclude that axon 5 is programmedto innervate all the fibers in the muscle. This is in agreement with the finding of Evoy and Beranek (6). Axon 5 generally has very small inhibitory potentials, in the same range as axon 2, which has the smallest excitatory potentials. The fact that we were able to detect a jp produced by this axon in every muscle fiber encouraged us to believe that the lower limit of resolution of our experimental technique (10 pV) was sufficient to detect all jp’s present at lo-Hz stimulation.
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The connectivity pattern of the excitor axons was somewhat more complex. It can be seen from Fig. 3 that all the excitor axons show a maximum of innervation at one side of the muscle sheet and a minimum at the other side of the sheet. In fact, the probability of innervation is roughly proportional to position in the muscle, until the percentages reach 100 or 0%. The constant of proportionality is different for each fiber and has opposite sign for the three small excitors and the two large ones, such that the small ones increase their innervation from lateral to medial, while the larger fibers do the opposite.
Positional dependence of strength of synaptic interaction When the average jp caused by each axon on each muscle fiber is correlated with the position of the muscle fibers, a clear pattern also emerges. Figure 4 shows the average jp sizes for each axon at the different positions in the muscle. Each point is the average of the jp’s caused in three neighboring fibers by one axon in all the animals in which this axon was studied. For all the axons the average jp’s show a general increase from one edge of the muscle to the other in a direction paralleling the innervation probability of the axons. The increase in jp’s with position is roughly linear. The linear regression for each of these graphs was calculated and found to be significant at better than the 2% level (29); all had high correlation coefficients ranging from 0.77 to 0.95 in absolute magnitude, i.e., the linear regressions explained 60-90% of the variance of the data points. The simplest hypothesis one could make to describe these graphs is that, for all the axons, the average jpis increased linearly from zero at one edge of the sheet to a maximum at the other edge. Surprisingly, this simple hypothesis was statistically acceptable. The data points for each axon were normalized to the same amplitude scale by dividing the data points for each axon by twice the mean for that axon. This created a scaled amplitude axis on which the data points for all the axons had values ranging from 0 to approximately 1, with a mean of 0.5. The position axis was also scaled to have a length of one unit. The points for the six axons were then displayed on one graph with the points for axons 4 and 6 plotted in reverse direction from the others so that all axons had their lower amplitude points at the left of the graph (Fig. 5). The hypothesis predicts that the points lie along a line with a slope of 1 and an intercept of 0. The graph shows this theoretical regression line and the actual regression line. The actual regression slope was 1.03 with an intercept of -0.02. The correla-
R. J. WYMAN
tion coefficient was 0.83. The actual and the theoretical regression lines were not significantly different. Thus, the simple hypothesis that strength of innervation increases linearly from zero at one edge to a maximum at the other edge is statistically acceptable. Two possibilities for artifact arise in interpreting the position-dependent increase in jp. The physical size of the muscle fibers increases in a medial to lateral direction; correspondingly, the input resistances decrease laterally (26). If the same average amount of synaptic current was produced by an axon at all locations, then one should expect the jp’s to decrease laterally due to the decreased input resistance. This phenomenon could not explain the graphs for axons 4 and 6, which increase in the opposite direction. However, it could be part of the explanation of the graphs of axons I, 2,3, and 5. To check this we measured the input resistance of the fibers in about 75% of the experiments. The jp’s measured in each fiber were then divided by that fiber’s input resistance to yield a corrected jp. Graphs similar to Fig. 5 of these corrected jp’s as a function of position were then prepared in the same manner as outlined before. The general shape of the graphs were not changed. The same statistical procedures were performed on the corrected graphs as on the graph of Fig. 5. All the regressions were significant with, on the average, slightly higher correlation coefficients than for the uncorrected data. The graph for testing the hypothesis that the input resistance corrected jp increases linearly from zero to a maximum had a regression line slope of 1.09, an intercept of -0.05, and a correlation coefficient of 0.85. The hypothetical and actual regression lines were not significantly different. Thus, the measurements, after correction for fiber input resistance, are also in strong accord with the hypothesis. The second possibility for artifact is that the average jp is lower in regions of reduced percentage of innervation because the uninnervated fibers add zeros into the averages in these regions. To check this possibility we calculated the average jp’s excluding all zeros. This is the average jp size at each position for fibers which do receive a synapse from the axon in question. Using the statistical procedures described above, the graph was again similar to that of Fig. 5. In the composite graph, the correlation coefficient was 0.75 and the significance of the correlation was 0.001. Thus, calculated in a number of different ways, the correlation of junction potential size with position is always high, ranging from 0.75 to 0.85. Therefore, it can be concluded that although jp variations between individual fibers are great, the sizes of the jp have a direct
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INNERVATION
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relationship to the position of the musclefibers at 10 Hz. It remainsto be seen if the smooth over the entire musclesurface. position dependenceof innervation parameters It should be noted that the strength of a would also be obtained at other frequenciesof synaptic contact, as measuredby jp size, will stimulation. In addition to synaptic strength, appear to be very different at different fre- several other physiological variables of the quencies of stimulation because of facilitation muscleare a monotonicfunction of position (26). at the neuromuscularjunction (4, 16). All re- We suspect that the average facilitation propsults in this paper were obtained with stimuli per-tiesof the junctions might also be position
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S. J. Vl?LEZ AND R. J. WYMAN
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