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INTRODUCTION |
Motor neurons in many systems are not only the final common paths through which the products of central pattern-generating circuits are exported, but also contribute directly to the generation of motor patterns by synaptic interactions with other components of these circuits. In crayfish, some motor neurons that innervate the swimmerets
limbs that occur in pairs on several abdominal segments
perform both tasks (Heitler 1978
, 1983
; Sherff and Mulloney 1996
). When crustaceans swim forward by beating their swimmerets, each limb moves rhythmically through cycles of power strokes and return strokes that propel the animal forward. These movements are produced by alternating contractions of power-stroke (PS) and return-stroke (RS) muscles that are innervated by separate sets of PS and RS motor neurons. About half of the ~70 swimmeret motor neurons that control the movements of each swimmeret (Mulloney et al. 1990
; B. Mulloney and W. M. Hall, unpublished data) are PS motor neurons, and the other half are RS motor neurons. Within each of these sets, motor neurons can be further subdivided by their peripheral functions: glutamatergic excitors cause contraction, and GABAergic inhibitors prevent contraction (Atwood 1976
; Mulloney and Hall 1990
; Sherff and Mulloney 1996
). Thus we can distinguish four kinds of swimmeret motor neurons in the pool that innervates each swimmeret (Davis 1969
; Stein 1971
): PS excitors (PSEs), RS excitors (RSEs), PS inhibitors (PSIs), and RS inhibitors (RSIs). Given these four kinds of motor neurons, do differences in their passive properties play some role in producing the swimmeret motor pattern?
Because excitatory and inhibitory fast-flexor motor neurons that innervate the trunk musculature differ in their input resistances (Rins) and membrane time constants (
ms) (Edwards and Mulloney 1987
), and because these differences permit them to integrate synaptic currents in ways that affect their functions, we began with the hypothesis that the passive properties of excitatory swimmeret motor neurons would differ from those of inhibitory motor neurons, and that the passive properties of PS neurons might also differ from those of RS neurons.
In the crayfish Pacifastacus leniusculus, axons that innervate RS and PS muscles of each swimmeret are segregated into two branches of the swimmeret nerve, N1, that runs from the ganglion to the swimmeret. The anterior branch of N1 contains RS axons; the posterior branch contains PS axons (Mulloney et al. 1990
). We exploited this anatomic segregation to identify different kinds of swimmeret motor neurons by the N1 branch that contained their axons and by the phase of the motor pattern in which they fired (Stein 1971
). To visualize their cell bodies and processes within the ganglion, we backfilled neurons that had axons in these different branches. We also filled individual motor neurons by injecting a marker from a microelectrode. The cell bodies of PS and RS neurons were clustered on different sides of the base of each N1, but all four kinds had similar structures within the ganglion.
We measured membrane potentials (Vms), Rins, and
ms of neurons in each of the four kinds, and found little difference between them. To explore possible causes of the variability we observed in each of these parameters, we measured the relative sizes of different swimmeret motor neurons and noted whether they were firing in phase with the motor pattern or whether their Vm oscillated with the motor pattern. Preliminary descriptions of these passive properties have been published in abstract form (Sherff and Mulloney 1992
).
These similarities in passive properties contradict the idea that differences in the passive properties of these different neurons contribute to pattern generation. We propose that this similarity results from design constraints imposed by the motor neurons' task of exporting to their peripheral targetsa motor pattern that must vary smoothly in period andintensity.
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METHODS |
Crayfish (P. leniusculus) were obtained from local suppliers and kept in aerated freshwater aquaria. Animals were anesthetized by cooling on ice, then exsanguinated by removing the claws and perfusing the hemocoel with physiological saline (Sherff and Mulloney 1996
) through a hypodermic needle inserted into one of the wounds.
Backfills of swimmeret motor neurons
Selected N1s were backfilled according to the procedure of Leise et al. (1986)
. Abdominal nerve cords were pinned flat in Sylgard-lined (Dow-Corning) petri dishes. N1s were placed in a Vaseline well filled with 250 mM CoCl2. The CoCl2 was allowed to diffuse through the nerves overnight. The nerve cords were then washed in saline and incubated in 0.1 M sodium cacodylate. Cobalt sulfide was precipitated by adding ammonium sulfide. The nerve cords were washed in saline and then fixed in 2.7% glutaraldehyde overnight. Staining was intensified with the use of Timm's solution (Leise et al. 1986
). The nerve cords were dehydrated, cleared in methyl salicylate, and photographed as whole mounts.
Filling individual motor neurons
Neurobiotin (Vector Labs) was injected with the use of +3- to +5-nA current pulses 250 ms in duration at 2 Hz for ~30 min. Nerve cords were fixed overnight in 4% paraformaldehyde, rinsed in 0.1 M glycine in phosphate-buffered saline (PBS) (Sigma) and in straight PBS, dehydrated to 95% EtOH to increase their permeability, and rehydrated back to PBS. The tissue was washed in wash buffer [0.3% reduced Triton X-100 (Aldrich), 5% goat serum (BRL) in PBS] and in no-serum wash buffer (3 30-min washes in each buffer) and incubated in Texas-Red Streptavidin (Amersham), diluted 1:100 in no-serum wash buffer, for 18-20 h. Finally, the tissue was washed in PBS, dehydrated in ethanol, and cleared in methyl salicylate.
Preparations were viewed and photographed with a fluorescence microscope. Drawings of filled neurons in cleared ganglia were made with the use of a camera lucida, or from projections of slides of photographed ganglia.
Plastic sections
In preparation for sectioning, ganglia were stained with osmium-ethyl gallate, embedded in Spurr's plastic (Electron Microscopy Sciences), and sectioned (Leise and Mulloney 1986
; Mulloney and Hall 1991
). The diameters of axons were measured from2-µm cross sections of N1s from a different set of nerve cords.
Electrophysiology
Experiments were performed on isolated abdominal nerve cords. The N1s, which project bilaterally from each of the first five abdominal ganglia, were cut as far distally as possible to allow us to record from them with extracellular pin electrodes. In electrophysiology experiments, the last two thoracic ganglia were left attached to the abdominal cord to increase the stability of expression of the swimmeret motor pattern. Nerve cords were pinned in Sylgard-coated dishes. Recordings were made from 168 motor neurons in 83 nerve cords.
The swimmeret motor pattern was recorded extracellularly from the RS and PS branches of N1 with stainless steel pin electrodes (Mulloney and Selverston 1974
). Intracellular recordings were made from processes of motor neurons in the lateral neuropil LN (Skinner 1985
). Microelectrodes were filled either with 2.5 M KCl, or, if the motor neurons were to be filled for anatomic studies, with 10 mM KH2PO4 and 1 M KCl with 5% Neurobiotin in the tip. Microelectrode resistances were between 20 and 30 M
. Most measurements of Rin and
m were made in bridge mode with either a Getting M5 preamplifier or an Axoclamp-2A (Axon Instruments).
Both extracellular and microelectrode recordings were collected on video cassette recorded tape with the use of a Neuro-Corder 886 (Neurodata Instruments). Records were later transferred to computer for analysis with pClamp programs (Axon Instruments) or played back onto a Gould ES1000 electrostatic recorder. Recordings displayed in this paper were played onto a Gould 2400 pen recorder or were collected in Axotape files (Axon Instruments) and printed in SigmaPlot (Jandel Scientific).
Measuring Rin and
m
To measure Rin, responses to 50 200-ms pulses of
0.5-nA current were averaged with the use of the Clampfit program (Axon Instruments) and the averaged response was measured in theTableCurve program (Jandel Scientific). In a few cases, Rin was also measured as the slope of the current-voltage relation, measured in discontinuous current-clamp mode.
To calculate
m, responses to 50 2-ms pulses of
5.0-nA current were recorded and averaged. The recovery of the Vm to its rest level after the termination of the current, represented by the absolute values of the averaged data, was then fitted directly withone-, two-, and three-term exponential equations with the use of TableCurve (Jandel Scientific). The longest time constant in the equation that best fit the data was considered
m, whereas briefer time constants were considered equalizing constants (Rall 1969
; Rall et al. 1992
).
Statistical analysis
The SigmaStat program (Jandel Scientific) was used to calculate statistics of the different parameters we measured and to compare parameters from different types of neurons. Normally distributed data were summarized by mean ± SD; other data were described by median, 25th, and 75th percentiles. Deviations from normality were estimated with Kolmogorov-Smirnov tests. Student's t-tests were used to assess differences of normally distributed populations; Mann-Whitney rank sum tests were used to assess differences between populations that were not normally distributed. To compare parameters of more than two groups, we used one-way analysis of variance (ANOVA) if data were normally distributed or a Kruskal-Wallis one-way ANOVA on ranks if data were not normallydistributed.
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RESULTS |
Motor neuron morphology
The cell bodies of all the motor neurons that innervate a swimmeret are located in the same abdominal ganglion. Backfills of the RS and PS branches of the nerve, N1, that innervates each swimmeret, revealed that cell bodies of RS motor neurons were clustered together on the ventral surface of the ganglion, just anterior to the base of N1, whereas PS cell bodies formed their own ventral cluster just posterior to the base of N1. Regardless of whether they were RS or PS neurons, the shapes of most swimmeret motor neurons were similar (Fig. 1A). The primary neurite extended from the cell body toward LN (Skinner 1985
) and divided into two primary branches: one branch projected anteriorly and medially to the midline of the ganglion toward the contralateral LN, the other branch projected laterally to exit the ganglion as the axon in N1. Each of these primary branches had many fine secondary branches in the LN, where they synapse with other swimmeret motor neurons and with interneurons of the local swimmeret pattern-generating circuit (Murchison et al. 1993
; Paul and Mulloney 1985a
,b
).

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| FIG. 1.
A: whole mount of abdominal ganglion 3 that contained backfills of a few swimmeret motor neurons. Their cell bodies (cb) were clustered near the base of the swimmeret nerve (N1). Each motor neuron sent a process into the lateral neuropil (LN) and an axon out the ipsilateral N1. Within the LN, these neurons had many secondary branches. Large, lightly stained processes in posterior median region are parts of the segmental giant interneuron, not of a motor neuron (see RESULTS). This is a frontal view from the ventral side; anterior is at top. B: cross section of an N1 proximal to division into power-stroke (PS) and return-stroke (RS) branches. Diameters of axons were measured from 2-µm cross sections like this one. The 2 large axons (*) are those of nonspiking stretch receptors. Smallest axons ( ) are probably sensory afferents.
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Diameters of axons in N1 were measured from photographs of 2-µm cross sections of four N1s (Fig. 1B). In each N1, axons ranged from <2 to ~35 µm diam. Most of the axons in N1 are not axons of motor neurons. The numerous small axons are probably sensory hair afferents (Killian and Page 1992a
,b
; Nordlander and Singer 1973
); and the two largest axons belong to the nonspiking stretch-receptor neurons (NSSRs) (Heitler 1982
; McDonald 1981
). Thus most of the motor neuron axons are probably in the middle of the observed range, between 2 and 25 µm diam. These values may underestimate the actual sizes because of shrinkage that occurs during processing of the tissue. If our tissue shrank by 20%, as observed by Edwards et al. (1994)
, axon diameters would range from <3 to ~44 µm.
Physiological identification of swimmeret motor neurons
During spontaneous production of the swimmeret motor pattern, large bursts of excitatory RS action potentials alternate with bursts of excitatory PS action potentials (Fig. 2). Smaller bursts of impulses in axons of peripheral inhibitory motor neurons often occur between the larger, excitatory bursts. A cell was identified as a motor neuron if it had an axon in one of the N1 branches, which was determined by injecting current into the neuron to elicit orthodromic spikes in one of the N1 branches time-locked to intracellularly recorded action potentials, and by stimulating branches of N1 to elicit an antidromic action potential. RS motor neurons had axons in the anterior branch of N1; PS motor neurons had axons in the posterior branch. Neurons were classified as excitatory or inhibitory by the phases of their potentials' oscillations relative to the major bursts of impulses in the nerve that contained their axons (Fig. 3) (Stein 1971
).

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| FIG. 2.
Examples of activity in the swimmeret system from 3 preparations, including extracellular recordings of spikes in RS and PS branches of N1 and an intracellular recording from a swimmeret motor neuron. In active preparations, bursts of action potentials in RS excitor (RSE) axons alternate with bursts in PS excitor (PSE) axons. In RS record in B, bursts of impulses in an inhibitory motor neuron (RS inhibitor, RSI) alternate with RSEs. In active preparations, membrane potentials of most motor neurons oscillated in phase with the expressed motor pattern (A and B). Some motor neurons also fired action potentials (A). When preparation was quiescent (C), motor neurons did not oscillate; a few motor neurons fired action potentials tonically, but most were quiet.
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| FIG. 3.
The 4 functional types of swimmeret motor neurons (mn) were identified physiologically by phases of oscillations of their membrane potentials in the motor pattern and by the branch of N1 in which their axons occurred. One example of each type of swimmeret motor neuron is illustrated. Experimental depolarization caused action potentials in each motor neuron that were matched 1:1 with spikes recorded from 1 of the branches of N1. PSI, power-stroke inhibitor.
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The identifications of 18 neurons as PS or RS motor neurons with the use of these criteria were tested anatomically by filling the neurons with Neurobiotin. We observed no contradictions between the physiological identifications and the structures of the filled neurons. Motor neurons could be distinguished from those sensory neurons that also haveaxons in N1 by their central cell bodies; all known sensory neurons except the two NSSRs have peripheral cell bodies. One other neuron with an axon in N1, the segmental giant interneuron (Heitler and Darrig 1986
; Roberts et al. 1982
), also has a central cell body. Both this interneuron and the NSSRs could be identified by their characteristic electrical activity and by their shape (Fig. 1A).
Passive properties of swimmeret motor neurons
To ensure that errors in identification of motor neurons were not biasing these physiological results, we compared the cumulative frequency distributions of Vm, Rin, and
m measured in physiologically identified motor neurons with the distributions of these parameters measured in a separate set of 16 motor neurons whose identities we confirmed by filling them with Neurobiotin (Fig. 4). For each parameter, these distributions were not significantly different (Vm: P = 0.112; Rin: P = 0.360;
m: P = 0.715, Mann-Whitney rank sum test). We conclude that the observed distributions of these parameters from our larger set of physiologically identified motor neurons were not distorted by inclusion of neurons with properties different from those of anatomically identified swimmeret motor neurons, so in the rest of this paper we will focus on the larger set of results from physiologically identified neurons.

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| FIG. 4.
Cumulative frequency distributions of passive properties of all measured swimmeret motor neurons ( ) and of the subset whose identities were confirmed anatomically ( ; n = 16). Number of measurements of each parameter made from unfilled neurons is shown on left ordinate of each graph.
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Vm was measured during stable neuropil recordings. If the motor neuron's Vm was oscillating with the swimmeret motor pattern, Vm was recorded as the midpoint in the oscillation. Vms of the swimmeret motor neurons were not normally distributed, but skewed toward less polarized values (Fig. 4). Median Vm was
59.0 mV (n = 168), with 25th and 75th percentiles of
66.0 and
53.0 mV.
The Rins of five motor neurons were measured in two ways: as the slope of the current-voltage relation near resting potential (measured in discontinuous current-clamp mode), and as the steady-state response to a small hyperpolarizing current (measured in bridge mode). Within ~20 mV of resting potential, the measured current-voltage relations of these five neurons were linear (Fig. 5A). For each cell, the two methods yielded the same result, so we measured Rin in most cells by averaging steady-state voltage responses to 50
0.5-nA current pulses (Fig. 5). Measured Rins of swimmeret motor neurons were not normally distributed, but were skewed toward lower values (Fig. 4). The median Rin was 6.4 M
(n = 152), with 25th and 75th percentiles of 3.4 and 13.7 M
.

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| FIG. 5.
Ai: single response to a 0.5-nA pulse of current, and below, it averaged response to 50 such pulses. This neuron had an input resistance of 6.0 M . Aii: current-voltage relations of 1 RS motor neuron (Rin = 23.6 M ) and 1 PS motor neuron (Rin = 6.7 M ), plotted as deviations from resting potential. Bi: decay of a transient voltage response recorded in a swimmeret motor neuron ( ) plotted as absolute value of response vs. time, and graph of 3-exponential equation fitted to these data ( ). For clarity, only every 4th point is plotted. Time 0: time at which 5-nA current pulse stopped. Bii: residual differences between data points and fitted curve in Bi.
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To measure the
m of swimmeret motor neurons, we injected brief pulses of hyperpolarizing current through a bridge circuit and recorded the return of Vm to rest. The absolute values of the averaged transient response were fit with one-, two-, and three-exponential equations of the form
where C0 normalizes the steady-state Vm to 0 mV, Cx is a portion of the total voltage response,
x is time constant, and t is the time in milliseconds. The abilities of these different equations to fit the measured data were compared, and the equation that best fit the data was selected as the best description of the cell's properties. If two equations gave equally good fits but predicted different time constants, the cell was excluded from further analysis.
The longest of these
x recovered from the equation that best fit the measured response was taken to be
m (Rall 1969
). An example of a transient response recorded in one motor neuron is shown in Fig. 5B. This cell was fit with the three-exponential equation
yielding a
m value of 8.84 ms, and two equalizing constants of 0.33 ms and 1.96 ms. The graph of this equation is superimposed on the measured data in Fig. 5Bi, and the residual differences between this curve and the measured points are plotted in Fig. 5Bii; the coefficient of regression of these data to this equation was 0.9998.
The cumulative distribution of measured
ms of swimmeret motor neurons was not normally distributed, but skewed toward lower values (Fig. 4). The median
m was 9.2 ms (n = 49), with 25th and 75th percentiles at 5.7 ms and 14.5 ms. All cells were fit with equations that yielded regression coefficients between 0.997 and 1.00, with a median regression coefficient of 0.999.
Effects of recording site on these results
The cell body of a swimmeret motor neuron (Fig. 1) is at the end of a cable whose diameter is larger than that of many secondary processes, but smaller than that of the primary neurite in the neuropil, and smaller than the diameter of the axon. Because most of the synaptic contacts onto swimmeret motor neurons are located on their processes in the LN, we usually recorded intracellularly from their major processes in this neuropil. To see how the recording site influenced our measurements of passive properties, we compared the distributions of
m and Rin recorded from neuropil with those recorded from cell bodies (n = 17).
ms measured in the cell body were shorter than those measured in the neuropil (median: 5.2 vs. 10.2 ms, Mann-Whitney rank sum test, P = 0.05). This difference resembles those seen in other crayfish neurons (Czernasty et al. 1989; Takahashi et al. 1995
), and might be due to an elevated resting potassium current in the cell bodies (Chrachri 1995
).
Rin is determined not only by local membrane resistance but also by the axial resistances through which currents flow to other parts of the neuron (Edwards and Mulloney 1987
; Rall et al. 1992
), so we expect that Rin would change if we measured it at different locations in a cell with a complex branching structure. The median Rin measured in cell bodies was 16 M
, whereas the median measured in the neuropil was 6.4 M
(Mann-Whitney rank sum test, P = 0.14). This difference probably reflects the structure of these cells (Fig. 1A); although the diameter of the cell body is relatively large, only one process leaves it, so injected currents encounter fewer conductive pathways than they would in a major process in the neuropil.
Passive properties of different kinds of swimmeret motor neurons
To see whether different kinds of swimmeret motor neurons had different passive properties, we compared Vms, Rins, and
ms of excitors and inhibitors. These data were not normally distributed (cf. Fig. 4). Mann-Whitney rank sum tests of each parameter showed that excitors did not differ significantly from inhibitory motor neurons (P > 0.46).
Comparisons of the properties of PSE, RSE, PSI, and RSI motor neurons revealed that RSE motor neurons had a slightly lower average Vm than the others (Table 1). The mean Vm of RSE neurons was
52.1 mV; a one-wayANOVA indicated that the distributions of RSE potentials were not different from the others (P = 0.122). The Rins and
ms of these four kinds of neurons also differed twofold (Table 1). However, a Kruskal-Wallis ANOVA on ranks for Rin indicated that they were probably not different (P = 0.283), and a one-way ANOVA of
m indicated that they too were not different (P = 0.461). Thus differences in the resting membrane conductances of PSE and RSE neurons, which would cause differences in
m, can offer only a partial explanation of their observed differences in Vm.
Influence of cell size on integrative properties
In lobsters, the size of a swimmeret motor neuron's extracellularly recorded action potential is correlated with the order in which the neuron is recruited during each burst of impulses in synergist motor neurons (Davis 1971
). This observation suggested that some passive properties of swimmeret motor neurons might differ systematically with their size. To test this hypothesis, swimmeret motor neurons were classified as small, medium, or large on the basis of the size of their impulses (Figs. 3 and 6). Each neuron was stimulated by injecting current with a bridge circuit, and its impulses recorded by the microelectrode were matched with extracellular spikes in a branch of N1 (Figs. 3 and 6). The size of each neuron's extracellular spike was measured and normalized to the smallest unit recorded from that nerve in the same experiment. With the use of these measurements, we divided the data from motor neurons into three size categories: small motor neurons had spikes between 1 and 4 times larger than the smallest spike, medium neurons had spikes 7-20 times larger, and large motor neurons had spikes 25-80 times larger than the smallest unit (Fig. 6).

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| FIG. 6.
Sizes of impulses in motor neuron, measured relative to smallest active N1 unit, plotted as a histogram. Motor neurons between 1 and 4 times the size of the smallest unit were classified as small (S); those between 7 and 20 times smallest unit were medium (M); and those 25-80 times smallest unit were large (L). These ranges are marked by shaded boxes. Recordings from motor neurons in each of these categories, and their corresponding action potentials recorded from N1 when current pulses were injected into them, are shown below.
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Different sizes of motor neurons received qualitatively similar synaptic drive, but as a group, small swimmeret motor neurons were more likely to fire impulses than were larger ones (
2 test, P = 0.01). The Vms of between 75% and 89% of the small, medium, and large neurons oscillated in phase with the motor pattern. However, although 48% of these small motor neurons also fired impulses, only 8% of the medium motor neurons, and none of the large motor neurons, fired action potentials during the depolarizing phase of these spontaneous oscillations. The swimmeret motor patterns expressed spontaneously in our experiments did not cover the full range of periods and intensities of which the system is capable in the intact crayfish (Braun and Mulloney 1993
; Davis and Kennedy 1972
); this spontaneous activity was relatively weak and slow. When the system is producing stronger activity, it seems likely that these larger motor neurons would be systematically recruited (Davis 1971
).
Different sizes of motor neurons differed significantly in their Vms (Fig. 7). Small motor neurons had, on average, less polarized Vms than medium or large motor neurons(P < 0.05). Mean Vms for small, medium, and large motor neurons were
57,
63, and
69 mV. Eighty-three percent of the RS motor neurons from which we recorded were classified as small, whereas only 50% of the PS motor neurons were small; this size-related difference in Vm might explain why RSE neurons also had a lower average Vm (Table 1). The Rins and
ms of neurons in these different size categories were not significantly different (Fig. 7).

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| FIG. 7.
Box plots comparing passive properties of small, medium, and large motor neurons. Solid lines inside boxes: means. Dotted lines: medians. Top and bottom boundaries of boxes: 25th and 75th percentiles. Bars: 10th and 90th percentiles. Numbers: number of neurons in sample. Asterisks and daggers: distributions are significantly different (P < 0.05).
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Changes in passive properties of swimmeret motor neurons associated with changes in the state of the swimmeret system
Both in the intact crayfish and in vitro, the state of the swimmeret system can change from quiescent to active, a change marked by the expression of coordinated bursts of impulses in the nerves that innervate the swimmerets (Fig. 2). In a few isolated ventral nerve cords, these transitions occurred spontaneously and, in some preparations, frequently. When the state of the system changed from quiet to active, the Vms of most motor neurons began to oscillate in phase with the motor pattern expressed in their own ganglion. The oscillations of swimmeret motor neurons are not due to intrinsic cellular properties, but are caused by synaptic input from the local pattern-generating circuit (Murchison et al. 1993
). These oscillations ceased when the system stopped producing coordinated swimmeret activity (Fig. 2). From these observations it seemed possible that synaptic input from the local circuit might cause major changes in the passive properties of swimmeret motor neurons, changes that would alter the way they integrated synaptic information from sources other than the local pattern-generating circuit.
To examine the plausibility of this idea, we first compared the passive properties of motor neurons whose potentials oscillated when the system was active with those of neurons whose potentials did not oscillate. Neurons whose potentials oscillated were slightly more depolarized (+3 mV, P = 0.104) and had higher Rins (+2.5 M
, P = 0.146) and longer
ms (+4.0 ms, P = 0.020) than neurons whose potentials did not oscillate. The same trend occurred when we compared neurons measured in active preparations with those measured in quiet preparations. Motor neurons that fired during the depolarizing phase of their oscillations were also more depolarized (+7 mV, P = 0.006) and had higher mean Rins (+4.5 M
, P = 0.100) and longer mean
ms (+9.5 ms,P = 0.034) than neurons that did not fire.
The magnitudes of these mean difference were less than the ranges of values measured under these different conditions, so state changes do not explain all the observed variability of passive properties of swimmeret motor neurons (Fig. 4). When transitions from quiescence to active firing occurred during a continuous record from one neuron, we observed only small changes in the neuron's passive properties: Rin changed by an average of 3%,
m increased on average by 35%.
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DISCUSSION |
Passive properties and motor neuron function
Within each set of swimmeret motor neurons, we recognize four functional types (PSE, RSE, PSI, and RSI) that have different targets, different neurotransmitters, and different functions. Because excitor motor neurons and inhibitor motor neurons of the fast-flexor muscles differ in their passive properties in ways that contribute to the performance of the tail-flip escape circuit (Edwards and Mulloney 1987
), we thought that passive properties of these swimmeret neurons would differ in ways that might reveal something of the mechanisms that generate their normal patterned firing. Therefore it was surprising that these different types had similar passive properties (Table 1). In particular, the similarity of their
ms suggests that these neurons have similar membrane current densities, and integrate synaptic currents in similar ways. It follows that differences in the passive properties of these four types of motor neuron are unlikely to be important factors in generating the motor pattern that drives normal swimmeret movements.
The
ms we measured in these neurons were quite brief (Table 1) compared with those of some other crustacean motor neurons (e.g., Golowasch and Marder 1992
). Given these brief time constants, we conclude that their membrane resistances are low. The neurons' space constants are small, too, because the space constant is proportional to the square root of membrane resistance. This combination of small space constants and brief time constants implies that postsynaptic potentials and retrograde action potentials invading the central processes of swimmeret motor neurons would attenuate quickly as they spread passively through the neurite to the soma. It is characteristic of recordings from the cell bodies of these motor neurons, even when the system is vigorously producing coordinated activity in every ganglion, that action potentials are <5 mV high (Heitler 1983
; Stein 1977
).
Passive properties and motor neuron size
In preparations that spontaneously produced a weak motor pattern, small motor neurons oscillated and often fired action potentials, but larger motor neurons either oscillated with a very low amplitude or did not oscillate and were silent. In preparations with a stronger motor pattern, small, medium, and large cells oscillated and some of the small and medium motor neurons fired action potentials. Both in lobster swimmeret system (Davis 1971
; Davis and Kennedy 1972
) and in cat spinal cords (Henneman and Mendell 1977
), motor neurons that innervate the same muscle are recruited during spontaneous movements or graded nerve stimulation in order of increasing size. In the lobster, stimulation of certain axons in the nerve cord elicits firing from motor neurons with small extracellular spikes. Stronger stimulation recruits larger units in addition to the small ones. Similarly, in the cat, increasing muscle tension was associated with the recruitment first of small, then of larger
-motor neurons (Henneman et al. 1965
). In recordings of PS and RS activity driving a whole crayfish swimmeret, we also saw systematic recruitment of larger units when the level of excitation given to the system increased (Braun and Mulloney 1993
).
Although some small swimmeret motor neurons had higher Rins than did larger ones (Fig. 7), a feature of motor neurons in other systems (Burke 1968
; Burke et al. 1982
; Kernell and Zwaagstra 1981
; Zengel et al. 1985
; and Henneman et al. 1965
), Zucker (1973)
has shown that a strict scaling of Rin with the surface area of a neuron is not sufficient to account for a size principle, the orderly recruitment reviewed above, because a proportional change in Rin and surface area would preserve the densities of all kinds of channels; simply increasing the area of the cell's membrane would lower Rin but increase the absolute number of synaptic receptors, and so increase the synaptic currents. The simplest sort of scaling of neurons with similar time constants leads to bigger neurons with the same thresholds for both injected currents and synaptic excitation. However, given a case where small motor neurons receive a higher density of excitatory synapses, or have lower voltage thresholds for firing action potentials, or where large neurons have a disproportionately larger soma size than small motor neurons, a size principle could result (Zucker 1973
). In the swimmeret system, the small motor neurons had more depolarized resting Vms, which might act to keep them closer to firing threshold than the large motor neurons. In our experiments, large motor neurons never spontaneously fired action potentials even when the swimmeret system was active. We did observe that RSE motor neurons were normally less polarized than PSE motor neurons, a difference that might reflect differences in the synaptic drive to neurons of each type. However, all of our sample of RSE motor neurons consisted of small neurons, but half of our PSE neurons were either medium or large, so this difference in mean potential might be incidental to this difference in sizes of the PSE and RSE neurons we sampled (Fig. 7).
Synaptic influences on the integrative properties of swimmeret motor neurons
External influences like neuromodulators or synaptic input can alter passive membrane properties by gating ionic conductances (Golowasch and Marder 1992
; Moore and Buchanan 1993
). We saw little evidence that such factors had significant effects on the passive properties of swimmeret motor neurons. The distributions of Vm, Rin, and
m recorded from neurons in quiescent preparations were similar to those recorded from neurons in active preparations that were receiving phasic synaptic input from the pattern-generating circuit. There were some differences between motor neurons that were themselves in different activity states. Time constants of oscillating cells were longer than those in cells that were not oscillating. Cells that were firing action potentials had longer
ms and lower Vms than cells that were not firing. These trends indicate that synaptic drive from the active pattern-generating circuits is associated with a change in membrane conductance in these motor neurons. Quiet, nonoscillating motor neurons seem to be tonically inhibited by currents that hyperpolarize them, and when the swimmeret system changes to an active state, these tonic currents disappear. The magnitudes of these changes were smaller, however, than the differences between
m of flexor excitor and flexor inhibitor motor neurons that contribute to effective performance of the escape circuit (Edwards and Mulloney 1987
).
Changes on this scale might be functionally important because they are consistent with measured changes from swimmeret motor neurons exposed to
-aminobutyric acid (GABA) and glutamate (Sherff and Mulloney 1996
). Both of these neurotransmitters inhibit swimmeret motor neurons, often hyperpolarizing them and decreasing Rin by amounts similar to those seen during the transitions in state described here. It seems unlikely that changes this small would significantly alter the integrative characteristics of the motor neurons, but without modeling the neurons in detail, it is premature to conclude that these changes do not have a functional significance.
Why do different types of swimmeret motor neurons have such similar integrative properties?
Swimmeret motor neurons that are active in different phases of the motor pattern, and those that have different peripheral functions, nonetheless are similar in their Rins and
ms (Table 1). These similarities imply that they integrate synaptic currents in similar ways. Because measured values of
ms in other types of neurons range from <2 ms to >1,000 ms (Hille 1992
), and other motor neurons in these same ganglia have significantly different time constants that affect their performance (Edwards and Mulloney 1987
), the narrow ranges of these parameters observed in these swimmeret neurons suggest that some requirement of the system has selected for a narrow window of passive properties, despite difference in the neurons' peripheral targets and functions. The function common to all swimmeret motor neurons is to transform periodic synaptic currents from the premotor pattern-generating module into bursts of impulses that will trigger effective movements of the required period and power. Periods of these movements in intact animals range from <0.2 to ~2 s. The power produced also varies widely, although its range has not been quantitatively described. Unlike the extensor and flexor motor neurons of the tail-flip system (Wine and Krasne 1982
), which transform a brief synaptic input into a brief, relatively invariant synchronized discharge, swimmeret neurons fire periodic bursts that vary in intensity. These bursts last about half the period of the cycle (Fig. 2), and both the number and frequency of impulses in each burst can be regulated to control the force of the resulting movements (Braun and Mulloney 1993
; Davis 1969
).
On the basis of these considerations, we suggest that two features of the swimmeret system
brief
ms of motor neurons and graded synaptic transmission by the local interneurons that drive them (Paul and Mulloney 1985a
,b
)
are design constraints imposed by the system's need for periodic bursts of impulses that can be graded in intensity. The
ms of these local interneurons are >40 ms (D. H. Paul and B. Mulloney, unpublished data), 4 times longer than those of the motor neurons they drive. According to our hypothesis, the force of contraction in swimmeret muscles is regulated through a continuous range by continuous variation in firing frequency of the motor axon (Atwood 1976
). High impulse frequencies during each burst require high densities of sodium and potassium channels in the axons (cf. Hodgkin and Rushton 1946
), and the presence of these channels produces brief
ms because some minor fraction of these channels will be open, even at rest potential. However, in neurons with brief
ms, summation of transient synaptic currents triggered by presynaptic action potentials would produce rapidly fluctuating changes in Vm and impulse frequency, discontinuous transitions in force of the motor unit, and therefore a more restricted range of power for the system (cf. de Ruyter van Steveninck and Laughlin 1996
). Graded synaptic transmission by premotor interneurons avoids these fluctuations because it causes sustained changes in synaptic conductances and synaptic currents. These features of graded transmission permit these motor neurons to change their impulse frequency continuously through a wide range.