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Location and Magnitude of Conductance Changes Produced by RenshawRecurrent Inhibition in Spinal Motoneurons

Mitchell G. Maltenfort, Martha L. McCurdy, Carrie A. Phillips, Vladimir V. Turkin, and Thomas M. HammDivision of Neurobiology, Barrow Neurological Institute, St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013

Submitted 8 September 2003; accepted in final form 13 April 2004

Maltenfort, Mitchell G., Martha L. McCurdy, Carrie A. Phillips,Vladimir V. Turkin, and Thomas M. Hamm. Location and mag-nitude of conductance changes produced by Renshaw recurrent inhi-bition in spinal motoneurons. J Neurophysiol 92: 1417–1432, 2004.First published April 21, 2004; 10.1152/jn.00874.2003. The meanlocation of Renshaw synapses on spinal motoneurons and their syn-aptic conductance were estimated from changes in impedance mag-nitude produced by sustained recurrent inhibition. Motoneuron im-pedance was determined by injecting quasi-white noise current intolumbosacral motoneurons of pentobarbital-anesthetized cats. Synapticlocation and conductance were estimated by comparing observedimpedance changes to simulation results obtained using standardmotoneuron models and compartmental models fit to each impedancefunction. Estimated synaptic locations ranged from 0.10 to 0.41�,with a mean of 0.19 or 0.24�, depending on the estimation method.Average dendritic path length was 262 �m. Average synaptic con-ductance was 23 to 27 nS (range: 6.7 to 57.9 nS), corresponding toconductance changes of 78 to 88% of resting membrane conductance.Estimated accuracy was supported by consistency using differentestimation methods, agreement with Fyffe’s 1991 morphological data,and comparisons of observed and simulated recurrent IPSP ampli-tudes. Synaptic location, but not synaptic conductance, was correlatedwith rheobase, a measure of motoneuron excitability. Synaptic con-ductance did not depend on synaptic location. A regression analysisdemonstrated that synaptic conductance and cell impedance were theprincipal factors determining recurrent IPSP amplitude. Simulationsusing the observed values and locations of Renshaw conductancedemonstrate that recurrent inhibition can require as much as anadditional 14 to 18% sustained excitatory synaptic conductance todepolarize motoneurons sufficiently to activate somatic or dendriticinward currents and recruit motoneurons or amplify excitatory syn-aptic currents.

I N T R O D U C T I O N

Recurrent inhibition by Renshaw interneurons is an appar-ently simple spinal circuit, and its anatomy and physiologyhave been extensively documented (Windhorst 1996). Despitethis, its specific function is still under debate. The recurrentinhibitory input to motoneurons is small, as assessed by eitherthe amplitude of postsynaptic potentials (e.g., Eccles et al.1961; Hamm 1990; Hultborn et al. 1971) or the magnitude ofsynaptic current reaching the soma (Lindsay and Binder 1991).However, these measures do not consider the potential ofrecurrent inhibition to inhibit by shunting excitatory synapticinputs originating in the dendrites. Morphological studies showthat Renshaw synapses on motoneurons are dendritic, averag-ing 0.25 electrotonic length constants from the motoneuronsoma (Fyffe 1991). This position would allow Renshaw syn-

apses to shunt excitatory synaptic inputs that are located moredistally on those dendrites.

Estimates of the conductance change produced by recurrentinhibition have shown negligibly small increases or paradoxi-cal results. Sustained recurrent inhibition produces only a smalldecrease in input resistance measured at the soma (Lindsay andBinder 1991), and measurements during transient recurrentinhibitory postsynaptic potentials (RIPSPs) have yielded insig-nificant changes in input resistance or increases in neuronimpedance (Friedman et al. 1981; Smith et al. 1967). However,in the companion paper (Maltenfort et al. 2004) we have shownthat relatively large synaptic conductances on the dendritic tree(e.g., a doubling of membrane conductance over a span of 0.15electrotonic length constants, applied equally to all dendrites)produce only small changes (�5%) in the input resistancemeasured at the soma.

Following the work of Fox (1985), Maltenfort et al. (2004)demonstrated that changes in motoneuron impedance can beused to estimate the electrotonic location and relative magni-tude of synaptic conductances. The measured impedance at themotoneuron soma is increased at higher frequencies by anactive synapse on the dendritic tree, and the frequency at whichthis takes place, the reversal frequency, is inversely propor-tional to the mean distance of the synaptic conductance fromthe soma. For a known electrotonic position, the relativechange in impedance below this frequency increases linearlywith the relative magnitude of the synaptic input.

In the current study, RIPSPs and resulting impedancechanges in motoneurons were measured. The goal was toestimate the location and magnitude of conductance changesproduced by recurrent inhibition, and to assess the ability ofrecurrent inhibition to shunt excitatory synaptic inputs to thedendritic tree of motoneurons. Our estimates of the location ofRenshaw synapses obtained using impedance measurementsare in good agreement with the estimates made by Fyffe (1991)from morphological data. The estimated conductance of recur-rent inhibition causes a modest shunting of somatic and den-dritic potentials produced by excitatory synaptic inputs. Pre-liminary accounts of the work were previously presented(Hamm and McCurdy 1992; Hamm et al. 1993).

M E T H O D S

Experimental preparation

Experiments were performed in 10 adult pentobarbital-anesthetizedcats of either sex. The first 6 animals were used in the development of

Address for reprint requests and other correspondence: T. M. Hamm, Divisionof Neurobiology, Barrow Neurological Institute, St. Joseph’s Hospital and MedicalCenter, 350 W. Thomas Rd., Phoenix, AZ 85013 (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Neurophysiol 92: 1417–1432, 2004.First published April 21, 2004; 10.1152/jn.00874.2003.

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the experimental techniques; the data presented in this paper wereobtained from the last 4 animals in this series. All experimentalprocedures were reviewed and approved by the Institutional AnimalCare and Use Committee at St. Joseph’s Hospital and complied withprinciples from the Guide for the Care and Use of LaboratoryAnimals (National Research Council 1996). Anesthesia was inducedin a chamber with 5% isoflurane mixed with nitrous oxide andoxygen. After induction, 3% isoflurane was delivered by a mask whilea tracheal cannula was inserted. After insertion of a tracheal cannula,isoflurane was maintained between 1.7 and 2.3% as needed. A cannulaplaced in one carotid artery was used to monitor blood pressure.

Pentobarbital was given gradually, intravenously, to replace theisofluorane and periodically supplemented throughout the experiment.The initial dosage was adjusted to effect a deep surgical anesthesiaafter complete removal of isoflurane (29–43 mg/kg). A neuromuscu-lar blocker (gallamine triethiodide) was given during recording toprovide mechanical stability. Paralysis was allowed to subside aftereach administration to permit assessment of reflex signs and muscletone in addition to heart rate and blood pressure for administration ofsupplemental anesthesia.

Expired CO2 was monitored and maintained at 3–4% throughoutthe experiment. Cats were infused with a slow drip infusion of a buffersolution (5% glucose, 0.85% NaHCO3) or lactated Ringer solutionthroughout the experiment. Flaps of skin were tied up to form poolsof mineral oil around the exposed spinal cord and dissected musclenerves in the hindlimb. Core temperature and temperatures of thespinal and hindlimb pools were maintained at 37°C with a heating padand radiant heat. The muscle nerves to anterior and middle bicepsfemoris (ABF), lateral gastrocnemius (LG), medial gastrocnemius(MG), and soleus (Sol) were sectioned and placed on bipolar hookelectrodes for stimulation. The dorsal roots (L4–S2) were sectioned sothat RIPSPs could be produced by stimulation of muscle nerves.

Recording procedures

Intracellular recordings and current injection were performed withglass micropipettes with beveled tips (3–7 M�) filled with 2 Mpotassium citrate. Recordings were made with an intracellular ampli-fier with a high-impedance probe (Axoclamp 2A or 2B) and asample-and-hold amplifier, which provided amplification without lossof low frequency components in the recording of motoneuron poten-tials. Electrode position was controlled by a stepping motor orpiezoelectric microdrive. After penetration of each motoneuron, thefollowing recordings were made: antidromic action potential, fordetermination of its amplitude and conduction velocity; heteronymousRIPSPs produced by stimulation at 3 times threshold for the motorvolley (and the homonymous RIPSP if the threshold for antidromicinvasion was high enough to allow recording of a near maximumRIPSP without antidromic invasion); responses to injection of currentpulses, for the determination of input resistance and rheobase; and thevoltage responses to injection of a mixture of sinusoidal currents, withand without concurrent stimulation of a muscle nerve at 200 Hz toproduce recurrent inhibition, for calculation of the impedance functionof the motoneuron. A stimulus frequency of 200 Hz was selected toproduce a Renshaw conductance as steady as possible. The respon-siveness (spikes/cycle) of Renshaw cells to vibratory orthodromic andrepetitive antidromic stimuli decreases at higher frequencies, but theaverage Renshaw cell should be responsive to each stimulus at 200 Hz(Pompeiano et al. 1975; cf. Lindsey and Binder 1991).

If the resting potential was stable throughout the recording, then asecond record was made of the same motoneuron receiving a heter-onymous RIPSP from a different muscle nerve. Of the 30 cellsexamined in this study, recording conditions in 14 cells were stableenough to allow more than one heteronymous nerve to be used forstimulation during separate impedance tests. The electrode was with-drawn from the cell at the end of the final record to determine the net

resting potential. Records were accepted for analysis only if the netresting potential was �50 mV.

Input resistance was determined from the responses to injection of4–6 rectangular current pulses of 50 ms each (range of �2 nA).Voltage responses were measured after adjustment of capacitancecompensation to minimize the initial capacitive transient, and adjust-ing the bridge balance to remove the offset produced by electroderesistance. Input resistance was estimated as the slope of the regres-sion line between the amplitudes of the current steps and the corre-sponding voltage responses. These values were similar to impedancemagnitude at 10 Hz (�Z(10)� � 0.270 � 0.968 � RN, r2 � 0.840),although the impedance values were larger on average (1.44 vs. 1.21M�, P � 0.0005, paired t-test). Differences between input resistanceand �Z(10)� may have arisen from the use of bridge mode versusdiscontinuous current clamp (see following text), respectively, for the2 measurements and small errors in the adjustments needed for eachrecording mode (e.g., bridge balance).

Recordings were made of RIPSPs produced by 1- to 2-Hz stimu-lation of each heteronymous nerve and the homonymous nerve (if thethreshold for antidromic activation was sufficiently high). The nerveproducing the largest average heteronymous RIPSP (16–32 samples)was selected for stimulation during the determination of impedance in26 of 44 records. In the remaining cases, the nerve producing thesmaller RIPSP was selected for use in this test to obtain a morerepresentative distribution of RIPSP amplitudes. RIPSP amplitudesproduced by 200-Hz stimulation during the impedance tests were alsomeasured. Mean amplitudes were determined for: the peak of theRIPSP; the sustained RIPSP just before the onset of white noise; andthe sustained RIPSP just after the end of white noise. The sustainedRIPSPs were determined from averages of 125 points (50 ms) in eachrecord.

Classification of motoneurons

Motoneurons were classified by type based on the ratio of rheobaseto input resistance (Zengel et al. 1985), with neurons classified as FFif this ratio was above 18, as S if the ratio was below 5.6, and as FRat intermediate values. For the 30 cells in this study, 5 were classifiedas S, 14 as FR, and 11 as FF. Rheobase was not measured in 3 cellswith blocked spikes; these were classified as FR on the basis of inputresistance and conduction velocity (0.86, 1.69, 1.30 M�; 102, 98.9,91.2 m/s).

Zengel et al. (1985) based their classification on MG motoneurons.Whether this classification is valid for all motor nuclei has not beenestablished, although Dum and Kennedy (1980) found that inputresistance increased in the order FF � FR � S for motoneuronsassociated with tibialis anterior and extensor digitorum longus. Thedistribution of rheobase and input resistance values for our mixed setof motoneurons was similar to that found by Zengel et al. (1985).

Estimates of impedance

A discontinuous current clamp was used to inject a quasi-whitecurrent into the motoneuron for impedance determinations. Eachcurrent waveform consisted of a sum of 300 equal-amplitude sinu-soids of 2.44–732, each an integer multiple of 2.44 Hz. Fifty uniquecurrent waveforms were used; the phase of each sinusoid in eachwaveform was determined by a pseudorandom number generator.Each waveform was used twice, once during synaptic activation, asshown in Fig. 1, and once without synaptic activation. The power inthe current waveforms was constant across trials, usually with anamplitude of 1 nA2.

Before each motoneuron was impaled, the voltage monitor of theamplifier was used to adjust capacitance compensation to optimize thesettling rate of the electrode and to choose a suitable sampling rate forthe discontinuous current clamp. Sampling rates ranged from 2.4 to7.2 kHz; for records accepted for complete analysis, rates ranged from

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2.9 to 7.2 kHz (mean of 5.4 kHz). In each trial, the noise waveform(lasting 820 ms) was injected 600 ms after reset of the sample-and-hold amplifier. In trials with recurrent inhibition, a muscle nerve wasstimulated for 1.5 s commencing within 10 ms after the sample-and-hold reset. With this timing inhibition approached a near-constantlevel before current injection. Voltage and current were low-passfiltered (800 Hz, fourth order Butterworth) and sampled at a rate of2.5 kHz.

The impedance functions, Zn(f), were estimated as the transferfunctions between voltage and current (Bendat and Piersol 1986).Coherence functions (squared magnitude of the cross spectral densitydivided by the product of the power spectral densities of current andvoltage) were used to determine whether noise or nonlinearitiesaffected the impedance estimates. If the estimated coherence function[�2(f), analogous to an r2 value in the time domain; see Bendat andPiersol 1986] between measured voltage and injected current did notreach 0.95 in the first 30 Hz of the power spectrum, the record wasexcluded from the study.

For each voltage or current record, the first 512 points (205 ms) ofwhite noise trials were discarded so that initial transients would notaffect the power spectra. The remaining 1,536 points were used toform 5 overlapping (by 50%) 512-point records. This procedureprovided effectively 4.1 segments per record for calculating imped-ance (Press et al. 1992). Each record was multiplied by a Welch(parabolic) window (chosen to minimize loss of spectral resolution;Press et al. 1992) to remove the “picket-fence” effect introduced bythe finite length of the time series (Bendat and Piersol 1986; Press etal. 1992).

The power of the voltage response to current injection was analyzedin each set of trials to ensure that the response was not affected byprogressive changes in electrode or cell impedance. A reverse ar-rangements test (Bendat and Piersol 1986) was used to identify astatistically stationary (P � 0.05) subset of trials, which was used tocalculate the impedance estimates.

Quantifying impedance changes

The change in impedance caused by an active synapse was quan-tified using a cumulative normalized, frequency-weighted measure ofthe change in impedance magnitude at frequencies less than thereversal frequency, Fr (Maltenfort et al. 2004)

cu�Z � 100 � ¥ �Zn�f/f/¥ �f/f (1)

where �Zn is the normalized change in impedance magnitude[�Z(f)� � �Zsyn(f)�]/ �Z(f0)�; f0 is the lowest nonzero frequency in thespectrum; �Z(f)� and �Zsyn(f)� are impedance magnitudes withoutand with Renshaw conductance, respectively; and �f/f is the fre-quency interval divided by the frequency at each point, the sum ofwhich is taken from f0 to Fr. The statistical errors in the impedancefunction estimates, although small relative to the impedance func-tions, were large compared with �Zn. The cumulative sum in Eq. 1was chosen to minimize the variance in the estimate of the impedancechange, but it is still sensitive to noise in �Zn at low frequencies,which contribute most to cu�Z. To reduce further the variance of thisestimate, �Zn was smoothed with a 5-point running average and thesummation of Eq. 1 was performed using the trapezoidal rule toapproximate integration.

The reversal frequency was estimated as the frequency f � Fr atwhich �Zsyn� exceeded �Z�. To determine Fr, �Zn was smoothed usingmedian filters (Hamalainen et al. 1994) of width 34–100 Hz (7–21spectral points). Each �Zn record was inspected using filters ofseveral widths, starting with a narrow filter and progressively increas-ing filter width. The filtered �Zn waveforms (Fig. 3) and apparentreversal frequencies were compared to determine the narrowest filterthat provided a clear and consistent reversal frequency. A medianfilter was preferable to weighted averaging windows for determiningreversal frequency. Although the median filter may distort the dynam-ics of a signal, for our purposes it was sufficient to identify thetransition across zero, that is, the frequency at which more than halfthe points in the window were positive.

The reliability of estimates of synaptic location and conductancedeteriorates as the SD of cu�Z (�cu�Z) increases in relation to cu�Z(Maltenfort et al. 2004). To assess the reliability of each estimate,�cu�Z was estimated for each set of recordings. The variance ofimpedance magnitude, �Z

2 was computed from the squared product ofimpedance magnitude and the normalized random error of the imped-ance magnitude EZ, where EZ is determined by the coherence betweenthe injected current and voltage response and the number of samplesused to calculate the impedance function (Maltenfort et al. 2004; Eq.4). The variances of the impedance records with and without synapticactivation were added to compute the variance of the change inimpedance magnitude ��Z

2 . The normalized change in impedance��Zn

2 was approximated by

��Zn2 � ��z

2 / �Zf0� 2 (2)

Equation 2 neglects the contribution of variability in Z(f0) to ��Zn2 .

However, these contributions are small and contributed no more than2–3% in the present data. ��Zn

2 was determined for each point of �Znfrom the lowest frequency to the reversal frequency. The variance ofcu�Z was then computed by summing these terms, weighting each bya factor based on the number of times each term was used in thesummation of Eq. 1 (determined by the use of the moving average andtrapezoidal rule) and the �f/f term. The square root of the variance�cu�Z and the ratio cu�Z/�cu�Z were used to qualify records foranalysis (Maltenfort et al. 2004; see RESULTS).

Estimation of synaptic locations andconductance magnitudes

Estimates of synaptic location and conductance magnitude weremade using Fr and cu�Z (Maltenfort et al. 2004). The absolute mean

FIG. 1. Examples of voltage and current records used to determine mo-toneuron impedance. These records were obtained from a Sol motoneuron. Inthis trial a recurrent inhibitory postsynaptic potential (RIPSP) was produced bystimulating the MG nerve at 200 Hz (immediately after a 1-mV calibrationpulse at the start of the voltage record). A noise current, consisting of a sum ofsinusoids, was injected 0.6 s after the start of muscle nerve stimulation. Trialswere alternated with and without nerve stimulation to provide impedanceestimates with and without recurrent inhibition. In this example, the power ofthe noise waveform was 1 nA2, with a bandwidth of 2.44–732 Hz. Peak RIPSP(based on an average of 30 trials) was 1.61 mV, and the sustained RIPSP was0.56 mV. Arrowheads under the voltage record indicate times at which peakRIPSP amplitude (“peak”) and sustained RIPSP amplitude (“RIPSP”) weremeasured. Dashed line shows the baseline for the RIPSP.

1419CONDUCTANCE AND LOCATION OF RENSHAW INHIBITION


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position of the set of Renshaw synapses on the equivalent dendriticcable or a compartmental model representing each motoneuron wasdetermined from the reversal frequency

Position along equivalent cable cm � 1.90 � Fr�0.62 (3)

This equation was derived from simulated data from step (somaticshunt) and sigmoidal representations of 6 motoneurons in the data ofFleshman et al. (1988).

Dendritic path lengths from the soma to mean synaptic location(Fig. 5) were based on the position estimates from Eq. 3, and on themeasurements by Cullheim et al. (1987; their Fig. 7) of mean dendriticdiameter as a function of path length from the soma for motoneurons.Noting that the electrotonic length (le) of each dendritic compartmentdepends on the length of each dendritic (ld) or cable compartment(leq), dendritic resistivity (Rmd), and the diameter of the dendrites (Dd)or equivalent cable (Deq)

le � leq/�Rmd � Deq/4Ri � ld/�Rmd � Dd/4Ri (4)

the length of each dendritic compartment can be determined from thecorresponding cable compartment length by rearranging Eq. 4

ld � leq�Dd/Deq (5)

Using a standard cable profile (Maltenfort et al. 2004) and theCullheim data, Eq. 5 was applied iteratively starting at the soma todetermine ld for small increments of leq until the sum of the leq equaledthe position on the equivalent cable indicated by Eq. 3. Thesecalculations used a proximal cable diameter of 34.5 �m (the approx-imate diameters of the equivalent cables of FF motoneuron 41/2 andS motoneuron 36/4, and close to the average for the motoneurons ofFleshman et al. 1988). The relations between average dendritic diam-eter and dendritic path length for S and F motoneurons described byCullheim et al. (1987) were applied to motoneurons classified in thisstudy as S and FR or FF, respectively.

Reversal frequency and cu�Z were used to determine electrotonicsynaptic location and conductance changes by 2 methods. In the first,values of Fr and cu�Z were normalized by the system time constant(�) and the dendritic-to-somatic conductance ratio (�); estimates ofnormalized (electrotonic) synaptic location (Xsyn) and relative con-ductance (expressed as a percentage, %�G) were determined fromnormalized grids using the following equations

Xsyn � 0.26 � �*Fr�0.54 (6)

%�G � k � cu�Z � �0.33/�0.46 (7)

k � 2.37 6.49 � Xsyn3.47 (8)

These equations were determined from curve fits to normalizedimpedance grids determined for 6 step (somatic shunt) models fromthe data of Fleshman et al. (1988), as described in Maltenfort et al.(2004).

Estimates of � and � for each neuron were made from the computedstep response to a hyperpolarizing current pulse. This response wascalculated for each neuron by multiplying each cell’s impedancefunction by the Fourier transform of a 25-ms current pulse. Theimpedance function was multiplied by a Welch window (in thefrequency domain) before multiplication to compensate for its limitedbandwidth and reduce the picket-fence effect. The inverse Fouriertransform of this product, equivalent to the convolution of the mo-toneuron’s impulse response and the current step, provided the esti-mate of the neuron’s step response. � and � were then determined forthe equivalent somatic shunt representation of the motoneuron usingthe method of Durand (1984) and Kawato (1984). The first 2 expo-nential components of the response derivative, with time constants �0

and �1, were determined by exponential peeling (Rall 1969). Aconstant was added to the derivative of the response as needed toreduce the effect of sag on the response (cf. Fleshman et al. 1988). �0

was taken as �. The values of Rmd (to determine �md) and L thatprovided the best fit between the measured values of C0 and C1, thecoefficients of the 2 exponential terms in the step response, and thevalues given by the Durand–Kawato equations were determined froma matrix of Rmd and L values. � and the ratio of somatic to dendriticresistivity were then determined from �0, �1, �md, and L, as summa-rized by Rose and Dagum (1988).

Values of � and � obtained in this manner were used to normalizeFr and cu�Z and calculate mean electrotonic synaptic location and therelative change in membrane resistivity produced by activated Ren-shaw synapses. Absolute synaptic conductance was also obtainedfrom �, L, and Z(10) (as an estimate of input resistance). Assumingthat Renshaw synapses in each motoneuron are distributed over 0.15length constants in the equivalent dendritic cable, synaptic area Asyn

is given by

Asyn � 0.15 � Ad/L (9)

where Ad is the area of the equivalent dendritic cable. Based on theequation for input conductance of a uniform-diameter dendritic cablewith sealed end (Rall 1977), Ad is given by

Ad � Rmd � Gd � L/tanh L � Rmd � �

� L/��Z10� � 1 � � tanh L (10)

where Gd is dendritic conductance. The absolute synaptic conductancegsyn is given by the product of Ad and relative change in membraneconductance

gsyn � Asyn � �G/Rmd � 0.15 � �G � �/��Z10� � 1 � � tanh L

(11)

The second method for determining %�G, gsyn, and synaptic locationused models whose parameters were fit to match the impedancefunctions (Maltenfort and Hamm 2004). Parameters were fit to stepmodels in which separate values were specified for somatic anddendritic resistivity. Most of these models included a linearizedvoltage-dependent conductance distributed uniformly through theneuron, or localized to the soma. The choice of model was determinedby the goodness of fit. � and � were computed for each model andinitial estimates of %�G and synaptic location were computed fromcu�Z and Fr using Eqs. 6–8. The user then determined cu�Z and Fr

for successive estimates of %�G and synaptic location in the best-fitmodel until a good match was found between model and experimentalvalues of cu�Z and Fr. The change in magnitude of Z produced by thesynaptic conductance in the model was also computed for comparisonto the measured function (see Fig. 3). Once %�G and location weredetermined, gsyn was computed as �G � Asyn/Rmd, where Asyn wasthe area spanning 0.15� of dendritic cable centered at the synapticlocation. These computations were repeated using sigmoidal models,in which resistivity increased smoothly from soma through the den-drites, for most neurons. These models had linearized voltage-depen-dent conductances distributed uniformly through each motoneuron.

Simulation of postsynaptic potentials in motoneurons

The time courses of transient and sustained excitatory postsynapticpotentials (EPSPs) were simulated to examine the effect on EPSPmagnitude of an inhibitory conductance with locations and magnitudeas observed in this study (Figs. 9 and 10). Using Simulink (v. 5,MathWorks 2002), compartmental models of cells from Fleshman etal. (1988) were constructed. These models incorporated the sametapering equivalent dendritic cables used for impedance calculations;the length of each compartment was 0.05 length constants. Thevoltage V at each compartment j (relative to resting potential) wasdefined by

Cm � dVj/dt � gj�1, j � Vj�1 gj, j�1 � Vj�1 gsyn � Esyn

gm gsyn gj�1, j gj, j�1 � Vj (12)



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where Cm and gm are the capacitance and resting conductance of themembrane in each compartment; gj�1,j is the axial conductancebetween the (j � 1)th and jth compartments; and gsyn and Esyn are theconductance and reversal potential associated with the synapse (ifany) active on the compartment (Segev et al. 1989). Esyn was �10 mVfor Renshaw synapses and �80 mV for excitatory synapses.

The amplitudes of sustained IPSPs (Fig. 8) were computed (MAT-LAB) using best-fit compartmental models from Maltenfort andHamm (2004) and estimates of synaptic location and gsyn from thepresent study. Compartmental lengths were 0.0125 or 0.025�. SettingdV/dt to zero in Eq. 12 and adding a voltage-dependent conductanceterm, gv, give the following equation for each compartment

gm gsyn gv gj�1,j gj, j�1 � Vj gj�1, j � Vj�1 gj, j�1 � Vj�1

� gsyn � Esyn (13)

This set of equations was represented by the following matrix equa-tion

G � V � Y (14)

where G is a matrix of the conductance terms on the left of Eq. 13, Vis a vector representing the potential in each compartment, and Y is avector of the terms on the right of Eq. 13. The elements of V weredetermined by left division of G by Y in MATLAB, equivalent to theoperation

V � G�1 � Y (15)

Esyn was set to the difference between the recorded resting potentialand �77 mV for the reversal potential for RIPSPs (Forsythe andRedman 1988; Lindsay and Binder 1991). The sustained recurrentPSP was given by the value of V in the somatic compartment.

Two sets of simulations were performed. One set assumed auniform resting potential. A second series of sustained potentials werecomputed in which resting potential varied through the neuron torepresent somatic depolarization associated with the somatic shunt. Inthese simulations, terms for reversal potential times conductance (forgm and gV) were added to the right side of Eq. 13 and to vector Y.Dendritic reversal potentials were �77, �75, and �70 mV for Esyn,Em, and Egv, respectively. Somatic reversal potentials were adjusted tomatch the observed resting potential. Equation 14 was solved with andwithout synaptic conductance terms, and the sustained RIPSP wasdetermined from the difference in the solutions.

R E S U L T S

The change in impedance produced by recurrent inhibitionwas determined in 44 records from 30 ABF, MG, LG, and Solmotoneurons by antidromic activation of one of the heterony-mous nerves in this group. A subset of these records wasaccepted for analysis of Renshaw synaptic location and con-ductance. The following criteria were used in this selection: 1)the estimated SD of cu�Z, �cu�Z, was �0.75% (approximately1/3 of the range of cu�Z); 2) the ratio cu�Z/�cu�Z was �1.0;3) records in which the control impedance (no synaptic acti-vation) changed progressively over time were excluded; 4)RIPSP amplitudes before and after noise injected differed byno more than 50%; 5) a compartmental model could be fitsatisfactorily to the impedance function of each motoneuron.These criteria were selected to limit the uncertainty in esti-mates of Fr and cu�Z, minimize nonstationarity in the records,and ensure that the analyzed records had been obtained inacceptable recording conditions. Based on these criteria, 19records from 15 motoneurons (4 ABF, 4 MG, 5 LG, and 2 Sol)were used to estimate the location and conductance change of

Renshaw synapses. Five of these motoneurons were classified(based on input resistance and rheobase) as FF, 8 as FR, and 2as S.

The RIPSP produced by 200-Hz stimulation increased rap-idly to a peak and then declined to approach a sustained levelwithin 250 ms from the beginning of stimulation (Fig. 1).RIPSP amplitudes measured after noise injection were oftenlower than those before noise injection, averaging 78% of theamplitude before noise injection in records accepted for fullanalysis. RIPSP amplitudes were assumed to move linearlyfrom pre- to postnoise values. This assumption has beensupported by observations of the profiles of RIPSPs producedby 200-Hz stimulation without noise injection (Maltenfort etal. 1999).

Figure 2A shows the relation between peak RIPSP andsustained RIPSP. In all cells, inhibition declined from a meanpeak of 0.66 � 0.35 mV to a sustained value of 0.21 � 0.14mV. Changes in the smaller set of 19 records were similar(peak of 0.80 � 0.38 mV, sustained value of 0.27 � 0.14 mV),although RIPSP amplitudes tended to be slightly larger in thisgroup. For comparison, the mean amplitude of RIPSPs pro-duced by applying single stimuli to the same muscle nerveswas 0.52 � 0.28 mV. Lindsay and Binder (1991) observed asimilar decrease in RIPSP amplitude from an initial peak. Theynoted a greater relative decrease in motoneurons putativelyclassified as type FR or FF than S. This difference was notevident in the few (5) S motoneurons in our total sample.

RIPSP amplitude was not significantly correlated with anyof the size-related parameters: conduction velocity, input re-sistance, or equivalent dendritic diameter (in neurons in whichacceptable model fits were obtained; Maltenfort and Hamm2004). However, RIPSP amplitude was correlated with rheo-base, such that larger RIPSPs were found in more excitablemotoneurons (Fig. 2B). A multiple regression was performedto determine whether this relation was dependent on restingpotential. The regression slope of RIPSP amplitude versusrheobase was significant in both the total and smaller samples(P � 0.001 and P � 0.021, respectively), whereas the relationbetween RIPSP amplitude and resting potential was not sig-nificant.

Overall, characteristics of the final sample of 19 recordswere similar to those of the total sample with respect to inputresistance, rheobase, and RIPSP characteristics, with the ex-ception that the selection criteria tended to favor records withslightly larger RIPSP amplitudes.

Changes in motoneuron impedance produced byrecurrent inhibition

The changes in impedance at the lowest frequencies pro-vided a measure of the change in input resistance produced byrecurrent inhibition. The average decrease in Z(10) was 1.9%for the total set of records in this study, and 2.7% for the finalset of 19. For comparison, Lindsay and Binder (1991) esti-mated a decrease in input resistance of 3.5%.

Figure 3 illustrates the impedance changes observed in thecurrent study. Figure 3A shows the unfiltered change in im-pedance, and Fig. 3B shows the result of applying the medianfilter to these data. There is a region of about 300 Hz (identifiedwith arrows) where the difference in impedance function is



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clearly positive [i.e., the synaptic input from recurrent inhibi-tion has increased impedance in accordance with model pre-dictions (Maltenfort et al. 2004)]. The thick, smooth curvesuperimposed on this plot is a simulated change in impedancemagnitude. This curve was generated using a best-fit model ofthe motoneuron represented in Fig. 3, A and B, in whichsynaptic location and relative conductance change were chosento match the observed values of cu�Z and Fr. The simulatedimpedance change matched the observed change reasonablywell in this record and in all but one of 13 records in which Frcould be determined. Matches between simulated and observedrecords were judged acceptable if the records had similarprofiles from intermediate (20 to 40 Hz) through higher fre-quencies.

Figure 3C shows one of 6 cases in which Fr could not bedetermined: the change in impedance produced by recurrentinhibition decreases with frequency but never becomes clearlypositive. The observed change in impedance could be matchedby selecting Fr greater than the highest frequency in theexperimental impedance function for the example in Fig. 3Cand in one other record. The change in impedance approachedzero more rapidly, and �Z was smaller than expected for asomatic conductance change (cf. Fig. 4 in Maltenfort et al.2004). These 2 records were judged to be produced by “jux-tasomatic” synapses, with mean electrotonic locations �0.15�from the soma. Synaptic locations were estimated in the 14records with acceptable matches between the simulated andobserved impedance records. Acceptable matches were notfound in the other 4 records in which Fr could not be deter-mined, nor in one of the 13 records in which Fr was evident.The observed change in impedance was flatter at intermediateand/or high frequencies than the simulated response in recordswithout acceptable matches, as shown by the example in Fig.3D. Estimated synaptic conductance values for records withpoor matches were computed based on an assumed proximallocation, given that conductance is relatively insensitive tolocation (cf. Fig. 6).

Estimates of Renshaw synaptic location andconductance change

Reversal frequencies were used to compute both absoluteand normalized distances between the motoneuron soma andRenshaw synapses. Figure 4A shows that reversal frequencies

FIG. 2. Distribution of RIPSP amplitudes. A: distribution of peak RIPSPamplitudes produced by 200-Hz stimulation plotted against the sustainedRIPSP amplitudes. B: sustained RIPSP amplitudes plotted against rheobase asa measure of motoneuron size. Data points are labeled as FF, FR, or Saccording to putative type established by input resistance and rheobase. Largersymbols represent cells that met all requirements for determination of synapticlocation and conductance.

FIG. 3. Changes in impedance magnitude produced by recurrent inhibition.A: difference between the magnitudes of the impedance functions[�Zwith inhibition(f)� � �Zwithout inhibition(f)�]. These differences were small andcorrespondingly noisy. B: difference between magnitude functions in A aftersmoothing with a median filter (in this example, 11-point width; �24 Hz); theapproximately 300 Hz in which the difference was clearly positive is identifiedby the vertical arrows. Smooth, thicker line is the change in impedancemagnitude produced in a best-fit model in which synaptic location andmagnitude were selected to yield the same reversal frequency and cu�Z valuesas observed in the recorded neuron. Differences between impedance magni-tudes in 2 neurons in which reversal frequency could not be determined areillustrated in C [7-point filter (�15 Hz) used to smooth] and D (11-point filter;�24 Hz). Agreement between the observed and modeled change in impedancemagnitude was satisfactory in C but not in D.



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tended to be greater in cells with lower rheobase values.Because Fr is a direct measure of synaptic location on a cablerepresenting the dendrites of a motoneuron, this finding sug-gested mean synaptic location is closer to the soma in moreexcitable motoneurons. Equivalent-cable locations were com-puted from the Fr values shown in Fig. 4A using Eq. 3 and areplotted against rheobase in Fig. 4B. Equivalent-cable locationwas correlated with rheobase (r2 � 0.50, P � 0.005), support-ing this suggestion.

Estimated dendritic path lengths from soma to mean synap-tic location in branching dendritic arbors were computed fromequivalent-cable locations using data on dendritic diametersand path lengths from Cullheim et al. (1987) as described inMETHODS. Dendritic path lengths were also directly correlatedwith rheobase (r2 � 0.53, P � 0.003). In Fig. 5, the distribution

of path lengths is plotted with the morphological data of Fyffe(1991). The 2 distributions are very similar. The mean den-dritic path length from soma to Renshaw synapses in thepresent data was 262 � 90 �m (range: 128 to 412 �m), incomparison to a mean of 255 � 171 �m reported by Fyffe.

The distributions of Fr and cu�Z values for the selected setof 19 motoneurons are shown in Fig. 6, plotted on cu�Z–Fr

grids determined for the 6 “step” model motoneurons used inMaltenfort et al. (2004). The cu�Z values of records in whichreversal frequency could not be determined are plotted on theright of each graph; cases in which the simulated impedancechange did not match the observed change are marked by �’s.The left side of each figure shows the observed values of Fr andcu�Z, whereas the right side shows Fr and cu�Z values afternormalization by � and � (Maltenfort et al. 2004). Comparisonof the data points to the grids in Fig. 6 shows that Renshawconductance ranged from roughly 25 to 150% of restingmembrane conductance and that most mean synaptic locationswere within 0.3� of the soma.

Values of � and � used for normalization in Fig. 6 weredetermined from a step response (computed from the controlimpedance function) using the method of Durand (1984) andKawato (1984) for estimating electrotonic parameters of neu-rons with somatic shunts (see METHODS). In 2 cases, thisestimation could not be made. In both cases, the derivative ofthe step response included an intermediate component thatprevented accurate determination of the coefficients of the first2 exponential terms of the response; the best-fit models of bothneurons (Maltenfort and Hamm 2004) included large somaticvoltage-dependent conductances with short time constants. Forthe normalization used in Fig. 6, values of � and � for these 2neurons were based on the passive electrotonic properties ofbest-fit compartmental models.

FIG. 4. Relation between synaptic location and rheobase. A shows thatreversal frequency (Fr) tended to be greater in more excitable motoneurons(i.e., those with lower rheobase values). Tendency for the location of Renshawsynapses to vary systematically with excitability is demonstrated in B, in whichFr values have been converted to location on the equivalent dendritic cable ofa somatic shunt model. Relation between cable location, lc, and rheobase, Ir, isdescribed by the regression lc � 310 � 30.7Ir (r2 � 0.495; P � 0.005).

FIG. 5. Distribution of estimated locations of Renshaw synapses on thedendritic tree. Filled bars in this histogram represent the dendritic pathdistances to individual Renshaw synapses on motoneuron dendrites identifiedby Fyffe (1991). Renshaw synapses were located 255 � 171 �m (mean � SD)from the soma. Shaded bars show the estimates of mean synaptic position inthe current study, based on mapping reversal frequency to absolute position onthe equivalent dendritic cable, and on the relationship between the equivalentcable and the actual path length of dendrites in a typical motoneuron. Averageof these estimates was 262 � 90 �m from the soma.



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Estimates of electrotonic synaptic location and conductancemagnitude were made by 2 methods. One method used Eqs.6–8 and normalized values of Fr and cu�Z. This method gavean estimated average electrotonic location of 0.24 � 0.10�(range 0.10–0.41�). The estimated relative conductancechange was 78 � 42% (range 19–158%), which correspondedto a synaptic conductance of 27.1 � 14.5 nS (range 7.0–57.9 nS).

The second set of estimates was made by choosing synapticlocation and conductance to obtain a match between observedand simulated values of Fr and cu�Z, using a compartmentalmodel of each neuron (Maltenfort and Hamm 2004). Electroniclocations determined from best-fit models were somewhatcloser to the soma, with a mean location of 0.19 � 0.09�(range 0.1–0.35�). The best-fit estimate of the relative conduc-



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tance change produced by Renshaw inhibition was 88 � 53%(range 30–193%). The estimated synaptic conductance was23.1 � 11.3 nS (range 6.7–45.3 nS). The 2 sets of estimateswere correlated (r2 � 0.58, P � 0.004, for synaptic location,Fig. 7A; r2 � 0.38, P � 0.008 for relative synaptic conduc-tance, not shown; and r2 � 0.87, P � 0.0001, for synapticconductance, Fig. 7B).

Comparisons were also made of synaptic location and con-ductance estimates obtained from step and sigmoidal models fitto each motoneuron (Maltenfort and Hamm 2004). Synapticlocations obtained using sigmoidal models, each with a uni-formly distributed voltage-dependent conductance, had a meanof 0.38 � 0.16� (range 0.15–0.71 �). The values obtained withsigmoidal models were well correlated with those obtainedusing step models (Xsig � 0.05 � 1.72 � Xstep, r2 � 0.84).Electrotonic synaptic locations were further from the soma inthe sigmoidal models, consistent with their different electro-tonic structure (Fleshman et al. 1988). Mean synaptic conduc-tance obtained with the sigmoidal model was 24.0 � 11.7 nS(range 6.9–46.3 nS). Synaptic conductance estimates obtainedwith sigmoidal and step models were also correlated (gsig �0.74 � 1.01 � gstep, r2 � 0.94, P � 0.0001).

We examined the distributions of both electrotonic synapticlocation and synaptic conductance with respect to cell proper-ties, using averages of the estimates provided by the normal-ized grids and best-fit models. Electrotonic synaptic locations,like dendritic path length and equivalent-cable location, weredirectly correlated with rheobase (Xsyn � 0.08 � 0.011 � IR,r2 � 0.58, P � 0.001). Location was not related to inputresistance or conduction velocity. Unlike synaptic location,synaptic conductance was not correlated with rheobase, norwith conduction velocity or input resistance. There was norelation between synaptic conductance and synaptic location(r2 � 0.09, P � 0.29).

Dependency of RIPSPs on synaptic parameters

RIPSP amplitudes were computed using the estimates ofsynaptic location and conductance magnitude just described,recorded resting potentials, and a compartmental model (stepmodel) based on the impedance function of each motoneuron(Maltenfort and Hamm 2004). Figure 8A shows these predictedvalues plotted against the recorded sustained RIPSP ampli-tudes. The simulated RIPSP amplitudes were correlated withthe observed values (r2 � 0.30, P � 0.02). Agreement betweenthe predicted and observed amplitudes was reasonably good inmost cases, although simulated amplitudes were substantiallygreater in a subset of these pairs. The mean simulated RIPSPamplitude was 0.36 � 0.21 mV compared to the observedmean of 0.27 � 0.14 mV.

A motoneuron with a somatic shunt could have a lowerresting potential if a nonspecific leakage conductance contrib-utes to the shunt. A second series of simulations were per-formed in which resting potential was nonuniform (Fig. 8B).The correlation between simulated and recorded amplitudes

FIG. 7. Comparison of synaptic location and conductance estimates. Thisfigure compares estimates of normalized synaptic location (A) and synapticconductance (B) obtained by separate methods. Normalized-grid estimatesobtained using values of Fr and cu�Z after normalization by � and � (Eqs. 6–8,METHODS) are plotted on the abscissa in each plot. Best-fit estimates plotted onthe ordinates were obtained by matching Fr and cu�Z values from simulatedimpedance changes of compartmental models to the observed experimentalvalues. Regression line in A is described by Xbf � 0.03 � 0.69Xng (r2 � 0.58).Regression line in B is described by gbf � 2.66 � 0.76gng (r2 � 0.87).

FIG. 6. Distribution of reversal frequencies and cu�Z values. Values of reversal frequency (Fr) and the cumulative, low-frequency impedance change (cu�Z) determined in motoneurons putatively typed as FF (top), FR (middle), and S (bottom) areplotted on grids of cu�Z and Fr produced by known conductance magnitudes and locations in 6 type-identified somatic-shunt (step)motoneuron models. Moving up from the bottom (increasing cu�Z), the horizontal lines in each grid describe the effect of relativeconductance changes of 10, 25, 50, 100, and 200%. Moving from left to right (increasing Fr), the vertical lines representconductance changes centered at 0.75, 0.60, 0.45, 0.30, and 0.15 electrotonic length constants (�) from the soma. Each conductancechange occurs over a span of 0.15�. Left column: original values of cu�Z and Fr plotted on model grids. Right column: values ofFr and cu�Z normalized by multiplication by � and by �0.33/�0.46, respectively. Grids in the right column have also been normalizedby these factors. Circles represent neurons in which the change in impedance magnitude determined in a model of that motoneuronprovided a reasonable fit to the change observed experimentally. � symbols represent neurons in which a reasonable fit was notobtained. Symbols on the extreme right of each grid represent data from neurons in which Fr values could not be determined.



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was similar to that found for simulations with a uniform restingpotential (r2 � 0.34, P � 0.009), but the difference betweensimulated and observed amplitudes was slightly smaller withnonuniform resting potentials (paired t � 2.72, P � 0.01). Themean simulated RIPSP amplitude with nonuniform restingpotential was 0.32 � 0.19 mV.

These simulations also provided estimates of the currentproduced by Renshaw synapses at the synaptic site. Using aheterogeneous resting potential, the mean synaptic current was0.32 � 0.20 nA (range 0.09–0.80 nA). Synaptic current wasnot correlated with cell properties.

Predictions of RIPSP amplitude using a sigmoidal compart-mental model (uniform resting potential) were quite similar tothose from step models, with a mean of 0.36 � 0.21 mV (range0.07–0.80 mV). The regression equation that described therelation between the 2 estimates was RIPSPsig � 0.001 �1.00 � RIPSPstep (r2 � 0.96).

These comparisons suggested that analysis of impedanceprovided reasonable estimates of synaptic location and con-ductance. We then investigated the dependency of observedRIPSP amplitude on synaptic location, synaptic conductance,motoneuron impedance magnitude, and resting potential usinga multiple regression analysis. We assumed that RIPSP ampli-tude was proportional to the product of 4 variables

VRIPSP � exp Xsyn � gsyn � �Z10� � �V

where VRIPSP is the sustained RIPSP amplitude, Xsyn is theelectrotonic synaptic location, gsyn is the synaptic conductance,�Z(10)� is the impedance magnitude at 10 Hz, and �V is thesynaptic drive potential (estimated as the difference betweenrecorded rest potential and �77 mV). The multiple regressionwas performed after taking the logarithm of both sides

ln VRIPSP � Xsyn ln gsyn ln �Z10� ln �V

The regression using this equation was significant, but only thedependency of VRIPSP on gsyn was significant (P � 0.004), andVRIPSP was unrelated to �V (P � 0.84). Repeating this analysiswithout the �V term provided the regression equation (r2 �0.66, P � 0.01)

ln VRIPSP � 3.50 2.06 � Xsyn 0.79 � ln gsyn

0.65 � ln �Z10�

The coefficients for ln (gsyn) and ln (�Z(10)�) were both signif-icant (r � 0.79, P � 0.002 and r � 0.63, P � 0.03, respec-tively); the coefficient of Xsyn was not (r � �0.52, P � 0.08).This analysis suggests that RIPSP amplitude in our sample wasdetermined primarily by synaptic conductance and neuronimpedance and perhaps to a lesser extent by synaptic location.

Estimated number of Renshaw cells per RIPSP

The number of Renshaw cells contributing to RIPSPs ineach motoneuron was estimated based on the estimated syn-aptic conductance. RIPSPs are mediated by both glycine andGABA (Cullheim and Kellerth 1981; Schneider and Fyffe1992). We assumed that both glycine and GABA are releasedfrom Renshaw cells based on evidence for corelease of thesetransmitters from unidentified ventral horn neurons to mo-toneurons (Jonas et al. 1998). The synaptic conductance pro-duced by individual Renshaw cells in motoneurons is un-known. The glycinergic IPSP produced by individual Ia recip-rocal interneurons in motoneurons has a peak transientconductance of 9.1 nS, with rise time and decay time constantsof 0.3 and 0.8 ms, respectively (Stuart and Redman 1990). Weassumed that the peak synaptic conductance produced by theaverage Renshaw cell had the same value, and that its glycin-ergic component had the same time course as that mediatingthe Ia reciprocal IPSP. The rise time and decay time constantfor the GABA-mediated component were set at 0.3 and 3 ms,respectively, based on the relative time course of glycine- andGABA-mediated synaptic currents observed by Jonas et al.(1998). The peak GABA conductance was set at values from15 to 33% of the total conductance (cf. Cullheim and Kellerth1981; Jonas et al. 1998; Schneider and Fyffe 1992). Theconductance time course for activation at 200 Hz was simu-lated in MATLAB using these values, and the time-averagedconductance was determined.

FIG. 8. Comparisons of simulated and recorded RIPSP amplitudes. Theamplitudes of simulated sustained RIPSPs are plotted vs. the observed values.Simulations used compartmental models fit to impedance functions (Malten-fort and Hamm 2004) with synaptic locations and conductances determinedwith these same models. A: simulations performed with uniform restingpotentials. Solid regression line is described by RIPSPsim � 0.13 � 0.853 �RIPSP. B: simulations performed with nonuniform resting potentials. Regres-sion in this case is RIPSPsim � 0.10 � 0.80 � RIPSP. Dashed lines are linesof identity.



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The average conductance per Renshaw cell ranged from 3.3nS (GABA contribution of 15%) to 4.1 nS (GABA contribu-tion of 33%). Based on these values and an average synapticconductance of 20–23 nS, we estimate that the average RIPSPin our study was produced by 5 to 7 Renshaw cells. Thesmallest conductance values we observed (7 nS) would beproduced by 1 or 2 Renshaw cells, whereas 11–16 Renshawcells would be required for the largest conductance values(45–58 nS).

Assessment of shunting produced by recurrent inhibition

An assessment was made of the extent to which recurrentinhibition would shunt an excitatory synaptic input located onthe dendritic tree using a Simulink model (see METHODS).Figure 9A illustrates an EPSP produced by a transient synapticconductance in a compartment spanning 0.3–0.45� (typical of

Ia EPSP synaptic locations; e.g., Burke and Glenn 1996). ThisEPSP was simulated with and without a Renshaw conductanceof 100% (34.6 nS) in the next most proximal compartment(from 0.15 to 0.3�). Figure 9B shows a sustained depolariza-tion produced at the same site, with and without activation ofRenshaw conductance in the adjacent compartment. Each plotshows the EPSP alone (solid line), combined EPSP and IPSP(dotted line), and the EPSP with inhibitory shunting (dashedline; the IPSP amplitude has been subtracted from this record).The diminution of the transient EPSP produced by the proxi-mal conductance change is negligible compared with the IPSPamplitude. The reduction in amplitude of the sustained depo-larization is more substantial: the decrease in EPSP amplitudeis 8.2%, compared with an IPSP amplitude that is 3.9% ofEPSP amplitude.

Simulations like those illustrated in Fig. 9B were performedusing excitatory conductances that produced depolarizationsover the subthreshold range to determine the effect of recurrentinhibition on somatic and dendritic potentials. The thresholdfor spike initiation was assumed to be 15 mV (Gustafsson andPinter 1984). Inhibitory conductances of 25 and 50 nS wereplaced 0.15 to 0.3� from the soma, whereas excitatory con-ductances spanning 0.15� were placed at various dendriticlocations (ranging from the 0.15� adjacent to the soma to0.6–0.75� from the soma). Figure 10, A and B show the effectof inhibitory conductance on somatic potentials. At excitatoryconductances sufficient to depolarize the soma by 15 mV fromeach of the dendritic sites, inhibitory conductances of 25 and50 nS reduced somatic potentials by 0.57–0.66 and by 1.11–1.28 mV, respectively. The reduction in depolarization wasslightly greater when the excitatory conductance was locatedjust distal (0.3–0.45�) to or at the site of the inhibitoryconductance. The inhibitory conductances alone yielded hy-perpolarizations of 0.28 and 0.54 mV. The additional excita-tory conductance required to depolarize the soma to 15 mV inthe presence of inhibition was noted as an approximate mea-sure of the effect of inhibition on motoneuron threshold. A50-nS inhibitory conductance increased the required conduc-tance by 18.7 to 43.2 nS (9.7–14.7%), depending on the site ofthe excitatory conductance. Simulations with the other 5 modelneurons gave similar results, with a 50-nS inhibition producingdepolarization decreases ranging from 0.85 to 1.40 mV andthreshold elevations of 8.4 to 18.2%.

The right panels in Fig. 10, C and D show the effect ofinhibition on the potentials at the dendritic sites of excitatoryconductance. These simulations were conducted over the con-ductance range needed to depolarize the dendritic compartmentto 15 mV, a depolarization sufficient to activate persistentinward currents (Lee and Heckman 2000; Powers and Binder2000). Inhibitory conductances reduced membrane potential(at an excitatory conductance that produced 15 mV of depo-larization) by 0.53 to 0.74 mV (25 nS) and by 1.03 to 1.43 mV(50 nS). A 50-nS inhibitory conductance increased the conduc-tance required for a 15-mV dendritic depolarization by 9.9 to19.1 nS (8.7–12.4%). Differences in the effect of recurrentinhibition on dendritic potentials at different sites were morepronounced than found for somatic potentials, being largest at0.15–0.3� and at 0.3–0.45�. In the 6 models, a 50-nS conduc-tance reduced depolarization produced by excitatory conduc-tance at 0.15 to 0.3� by 0.99 to 1.64 mV and raised the

FIG. 9. Effects of synaptic shunting on transient and sustained excitatorypostsynaptic potentials (EPSPs). In each figure, the solid line shows the EPSP,and the dotted line shows the EPSP plus a sustained recurrent inhibition(EPSP � IPSP). Effect of shunting on the EPSPs is shown by the dashed line,in which the EPSP � IPSP curve is shifted by the IPSP alone. EPSP wasproduced by a conductance spanning 0.30–0.45� in a step model based onmotoneuron 42/4 of Fleshman et al. (1988). An inhibitory conductance of100% of resting membrane conductance (34.6 nS) was placed from 0.15 to0.30�. A: a transient EPSP produced by a transient conductance with timecourse (t/�) � exp(�t/�); � � 0.1 ms. Peak EPSP conductance was 150 nS. B:a sustained EPSP produced by a conductance of 150 nS in the same motoneu-ron model.



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excitatory conductance needed for 15 mV of depolarization by8.4 to 14.3%.

D I S C U S S I O N

Results from this study provide estimated locations of Ren-shaw synapses on lumbosacral motoneurons that are in excel-lent agreement with previous studies. Our data also provideestimates of Renshaw synaptic conductance needed to assessthe potential of Renshaw cells to inhibit motoneurons throughshunting of excitatory synaptic inputs. In the following discus-sion, we consider how motoneuron and synaptic propertiesmay interact to determine the distribution of recurrent inhibi-tion, and how assumptions and experimental limitations mayaffect our estimates.

Reliability of estimated synaptic location andconductance magnitude

The primary limitation of the estimates of our synapticlocation and conductance magnitude is the reliance on valuesof cu�Z and Fr determined from small, noisy changes in

impedance magnitude. The greater the uncertainty in cu�Z, theless reliable the estimate of synaptic conductance; estimates ofFr are severely affected as well (Maltenfort et al. 2004). Forthese reasons, we estimated the SD of cu�Z and excludedrecords in which �cu�Z or the ratio of cu�Z to �cu�Z wasunacceptably large. This selection process should increaseestimate reliability. However, because the change in imped-ance (or input resistance) produced by a synaptic conductancedecreases with distance and is practically undetectable withdistal synapses (Rall 1967), rejection of records with smallvalues of cu�Z/�cu�Z could bias location estimates towardmore proximal locations. The excellent agreement between ourestimates and the data of Fyffe (1991) on locations of Renshawsynapses on motoneurons (Fig. 5) indicates that this bias, ifpresent, is negligible.

Our estimates were based on comparison of experimentaldata to the results of simulations performed with compartmen-tal motoneuron models. Estimates from normalized grids andequations fit to them were based on the 6 motoneurons de-scribed by Cullheim et al. (1987) and Fleshman et al. (1988).Although this model required simplifications, it accurately

FIG. 10. Reduction in somatic and dendritic depolarization produced by inhibitory conductances. This figure shows results fromsimulations performed with a compartmental motoneuron model based on cell 42/4 of Fleshman et al. (1988), as in Fig. 9.Simulations were run with total inhibitory conductances of 25 or 50 nS in dendritic compartments 0.15–0.3� from the soma.Excitatory conductance was placed in a dendritic segment of 0.15� at one of 5 sites (D1–D5), ranging from 0–0.15� to 0.6–0.75�from the soma. Left panels (A, B): effect of inhibitory conductances on somatic potentials. Right panels (C, D): effect of inhibitoryconductances on dendritic potentials. Dendritic potentials were taken from the middle compartment of the dendritic segment withthe excitatory conductance (e.g., from the compartment spanning 0.35–0.4� when the excitatory conductance was placed in D3,0.3–0.45�). Top panels: potentials without or with 25 or 50 nS of inhibitory conductance, as indicated in A. Dotted lines have beendrawn at 15 mV to indicate the approximate threshold for activating action potentials (A) or dendritic persistent inward currents(C). Bottom panels: potential changes produced by inhibitory conductances of 25 and 50 nS. Dendritic location of the excitatoryconductance is indicated at the end of each trace. With the exception of D, only 3 excitatory conductance sites are represented tomaintain clarity. Results for all 5 sites are included in D to illustrate the effect of the inhibitory conductance on dendritic potentialsproduced by excitatory conductances at different sites.



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replicated many of the properties of the 6 motoneurons. Modelcharacteristics were also consistent with the data of Clementsand Redman (1989). Compartmental models fit to each mo-toneuron (Maltenfort and Hamm 2004) relied on a standardcable profile based on the Fleshman data, but these individualmodels incorporated linearized voltage-dependent conduc-tances, which can affect the estimates of synaptic parameters(Maltenfort et al. 2004). In addition, normalized grid estimatesused values of � and � based on the expected response of aneuron with a somatic shunt. The normalized grid estimateswere independent in many respects of the assumptions of theindividual models. Comparing these 2 sets of estimates pro-vides a useful assessment of their reliability.

Agreement between estimates was generally good and wasexcellent with respect to the synaptic conductance estimates.Greater variability was found in estimates of synaptic location(normalized to �) and relative synaptic conductance. Thesedifferences may be attributed to limitations in the 2 methods ofidentifying motoneuron parameters. The least-reliable param-eter determined from fitting compartmental models to individ-ual impedance functions is the specific dendritic resistivityRmd, estimates of which were quite variable (Maltenfort andHamm 2004), ranging from 6.5 to 67.8 k�-cm2 in motoneu-rons with acceptable records. In contrast, estimates of mo-toneuron parameters from computed step responses yieldedlower Rmd estimates (5.7–18.7 k�-cm2). The determination ofmotoneuron parameters from step responses is complicated bythe presence of “sag” in the tail of the response, which shortensthe apparent time constant (Rose and Dagum 1988). This effectcan be only partly reduced by adding a constant to the response(Fleshman et al. 1988), as done in this study. Consequently,Rmd values may be underestimated by this method. Bothestimates of synaptic location (normalized to �) and relativesynaptic conductance are directly dependent on Rmd estimates.Considering the variability and biases in the 2 sets of Rmdestimates, the agreement between the 2 estimates of synapticlocation and relative conductance is rather good.

Reliability of the estimates was supported by agreementbetween the step and sigmoidal models. Although it is clearthat somatic resistivity is less than dendritic resistivity in spinalmotoneurons recorded with sharp electrodes (Clements andRedman 1989; Fleshman et al. 1988; Rose and Vanner 1988),it is unknown whether this difference in resistivity is repre-sented better by the step model (uniform Rmd), or the sigmoidalmodel (increasing Rmd from the soma). Despite the differencesin these models, agreement between synaptic conductanceestimates was excellent, and the differences between locationestimates were consistent with the different electrotonic pro-files of these representations (Fleshman et al. 1988). Consid-ering the overall agreement between these sets, our estimatesof synaptic location and conductance appear to be relativelyinsensitive to assumptions about motoneuron electrotonicstructure.

Some assumptions were common to all motoneuron repre-sentations. Our simulations used uniform synaptic distributionsover 0.15�. Actual synaptic distributions can be expected to benonuniform and have varying ranges, of course, as indicated bystudies of Ia and Renshaw synapses on motoneurons by Burkeand Glenn (1996) and Fyffe (1991), respectively. Estimationsof synaptic location based on Fr are relatively insensitive tochanges in the shape and width of the synaptic distribution

(Maltenfort et al. 2004). Estimated relative conductance mag-nitude would be affected by how both the width and the shapeof the actual distribution varied from that used in the model. If,for example, the actual synaptic distribution were uniform andtwice the width of the assumed distribution, then estimatedrelative conductance would have to be reduced by a factor of2. On the other hand, if most of the extra width in the realdistribution occurred in a “tail” of the distribution whereconductance is small, then the reduction in the estimate wouldbe slight. In either case, estimates of absolute synaptic con-ductance, determined by the product of relative conductanceand synaptic area, would be scarcely affected.

Our analysis assumes that antidromic activation of motoraxons affects heteronymous motoneurons only through theaction of Renshaw synapses. However, Renshaw cells inhibitboth Ia reciprocal inhibitory interneurons (Hultborn et al.1971) and other Renshaw cells (Ryall 1970). Either of theseeffects can produce a disinhibition. These effects, which can bereadily demonstrated in an unanesthetized spinal cord (e.g.,Turkin et al. 1998), would confound the estimates of synapticlocation and conductance magnitude. We do not think thatdisinhibition significantly affected our estimates. First stimu-lation was limited to nerves in a set in which activation ofRenshaw cells would inhibit Ia interneurons that project to theantagonists of these motor nuclei (Hultborn et al. 1971).Second, we used pentobarbital anesthesia, which tends tosuppress much of the spontaneous activity of interneuronsnecessary for disinhibition to be demonstrated. This effect isevident in the different results obtained by Eccles et al. (1961)and Wilson et al. (1960).

A critical assumption of the estimation method is that thesynaptic input does not activate or inactivate voltage-depen-dent currents. RIPSPs were generally small in this study, butwe did not test directly for activation of voltage-dependentcurrents. However, if the synaptic parameter estimates arereasonably accurate, then the amplitudes of simulated RIPSPsbased on these parameters should agree with recorded values.Simulated and actual RIPSP amplitudes (Fig. 8) agreed rea-sonably well. Simulated values were somewhat larger, andcorrelation between these values was weakened by severalsimulation values that were substantially higher than the re-corded values. One possible factor contributing to this mis-match is that Renshaw synapses were confined to part of thedendritic arbor. An assumption of the cable model is thatsynapses are distributed on all dendritic branches at the samedistance from the soma. However, Burke and Glenn (1996)found that the proportion of Ia synapses on motoneuron den-drites varied with dendritic orientation, and we consider itlikely that Renshaw synapses are not distributed uniformly onmotoneuron dendrites either. The effect of a nonuniform dis-tribution of Renshaw synapses would be that synaptic densityand relative synaptic conductance would be greater on den-dritic branches with Renshaw synapses than our estimateswould suggest, and hyperpolarization produced by Renshawcells at these sites would be correspondingly greater. RIPSPamplitudes would then be less than predicted because of adecrease in synaptic drive potential (cf. Rall and Rinzel 1973).Considering this possibility and the inherent uncertainty ineach of the parameters required to simulate RIPSPs, the resultspresented in Fig. 8 support the reliability of these estimates ofsynaptic location and conductance.



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RIPSP amplitudes, synaptic location, conductance changes,and motoneuron excitability

This study was not designed to examine the distribution ofrecurrent inhibition within a motoneuron pool, but we did findthe relation between RIPSP amplitude and rheobase (Fig. 2)that would be expected, based on the dependency of amplitudeon motoneuron type demonstrated in previous studies (Fried-man et al. 1981; Hultborn et al. 1988). These RIPSP ampli-tudes should be dependent on several factors, including syn-aptic conductance, resting potential (or synaptic drive poten-tial), distance of the Renshaw synapses from the (presumed)somatic recording site, and the impedance, or input resistance,of the motoneuron. The dependency of RIPSP amplitudes inthis study on these variables was examined in a multipleregression analysis. Significant relations were found betweenRIPSP amplitude and both synaptic conductance and imped-ance magnitude (measured at 10 Hz), but the regression coef-ficient for synaptic location was not quite significant, and norelation was found between RIPSP amplitude and the estimatedsynaptic drive potential. Although RIPSP amplitude is knownto vary with membrane potential within a cell, error in esti-mated synaptic drive potential may be introduced by difficultyin obtaining an accurate extracellular potential at the end of arecording and by uncertainty in the membrane potential at thesynaptic site. Such difficulties, in addition to the dependency ofRIPSP amplitude on several factors, can obscure the depen-dency of IPSP amplitude on resting potential (Hamm et al.1987; see also Lindsay and Binder 1991).

Both synaptic conductance and impedance influencedRIPSP amplitude in this analysis. Both �Z(10)� and inputresistance were inversely correlated with rheobase in our sam-ple (r2 � 0.19 and r2 � 0.21, respectively). Synaptic conduc-tance was not correlated with rheobase, nor was the synapticcurrent determined from simulations with compartmental mod-els. These results are consistent with those of Lindsay andBinder (1991), who found that effective synaptic current pro-duced by recurrent inhibition (i.e., the amount of injectedcurrent just sufficient to counteract the sustained RIPSP at thesoma) was distributed uniformly through medial gastrocne-mius motoneurons, and the well-known dependency of RIPSPamplitude on motoneuron properties was attributable to differ-ent input resistance values.

Both synaptic location and RIPSP amplitude were dependenton rheobase, yet the regression coefficient between locationand RIPSP amplitude was not statistically significant. A de-pendency of postsynaptic potential amplitude on synaptic lo-cation would be expected based on the well-known electrotonicproperties of dendrites. The dependency of postsynaptic poten-tial amplitude on synaptic location can be countered by adependency of synaptic conductance on location, as suggestedby the independence of individual Ia EPSP amplitudes fromestimated synaptic locations (Iansek and Redman 1973; Jack etal. 1981) and observations in other cell types (Magee and Cook2000). However, we found no relation between location andsynaptic conductance in our estimates, indicating that proper-ties of Renshaw synapses on motoneurons do not vary signif-icantly with location. The failure to demonstrate a statisticallysignificant dependency of RIPSP amplitude on synaptic loca-tion may be attributable to the small sample size and therelatively narrow range of synaptic locations. It is also possible

that active dendritic properties may have influenced RIPSPamplitude. Considering these several factors, we suspect thatsynaptic location contributes to RIPSP amplitude, but thisdependency remains to be demonstrated with a larger database.

Estimates of shunting by Renshaw synapses

Our simulations of interactions between recurrent inhibitionand excitatory synaptic inputs in a passive dendritic tree showthat the decrease in depolarization produced by Renshawconductance in the voltage region at which inward currents areactivated is approximately double the size of the RIPSP atresting membrane potential (Fig. 10). For the largest Renshawconductances observed in this study (�50 nS), these somaticeffects are small and indicate that recurrent inhibition shouldhave relatively weak effects on recruited motoneurons, witheffects on discharge consistent with those predicted frommeasurements of Renshaw effective synaptic current (Lindsayand Binder 1991). Recurrent inhibition also would reduce thenumber of motoneurons in the recruited pool. The additionalexcitatory conductance required to initiate discharge in thepresence of recurrent inhibition, approximated by the conduc-tance required to reach a 15 mV threshold, ranged from 8 to18% in our simulations.

Figure 10 shows that the effect of Renshaw conductance ondendritic potentials is similar to the effect on somatic poten-tials, although these actions of recurrent inhibition may bemore significant. Depolarizations sufficient to activate den-dritic persistent inward currents substantially amplify excita-tory synaptic currents in motoneurons (Bennett et al. 1998; Leeand Heckman 2000; Powers and Binder 2000; Prather et al.2001). Inhibitory currents that prevent activation of or inacti-vate persistent inward currents eliminate this amplification(Bennett et al. 1998; Kuo et al. 2003; Powers and Binder2000). This mechanism probably underlies the observation thatrecurrent inhibition is substantially more effective at reducingmotoneuron discharge produced by dendritic synaptic inputsthan by current injected at the soma (Hultborn et al. 2003). Ourresults (Fig. 10) indicate that a Renshaw conductance of 50 nSincreases the excitatory conductance needed to activate persis-tent inward currents in a dendritic compartment, as approxi-mated by the conductance required for a 15-mV depolarization,by 8 to 14%. This level of recurrent inhibition would modulateactivity in the motoneuron pool, in part, by reducing thefraction of the motoneuron pool in which synaptic amplifica-tion occurs.

Simulations that incorporate estimates of the magnitude andlocation of Renshaw conductance and those of excitatoryinputs, combined with information on persistent inward cur-rents, may provide a more complete assessment of the modu-lation of motoneuron discharge by recurrent inhibition duringphysiological patterns of motor activity. The largest values ofRenshaw conductance magnitude reported here probably areless than the maximum occurring during physiological activity,based on several considerations. The amplitudes of the RIPSPsproduced by our stimulus paradigm were small compared tothose of other studies (e.g., Eccles et al. 1961; Hultborn et al.1971; Lindsay and Binder 1991; Turkin et al. 1998). Estimatesof the number of Renshaw cells contributing to RIPSPs in thisstudy are also small compared with the size of the Renshaw



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cell pool (Carr et al. 1998). Also, motor activities like loco-motion involving the activation of multiple motoneuron poolsshould provide a stronger activation of the Renshaw cell pool,considering the extended pattern of recurrent inhibition and theconvergence on Renshaw cells from motoneuron pools (Eccleset al. 1961ab; Hultborn et al. 1971; Ryall 1981; see DISCUSSION

in McCurdy and Hamm 1994). The increase in motoneurondischarge observed during fictive locomotion following blockof cholinergic input to Renshaw cells (Noga et al. 1987) isconsistent with this argument. The values of conductance inthis study provide a starting point for simulations to assess therole of recurrent inhibition in dendritic integration and controlof motoneuron discharge.

A C K N O W L E D G M E N T S

We thank T. Fleming for technical assistance and Drs. R.E.W. Fyffe andP. K. Rose for comments on an early draft of this work. We also thank thejournal’s anonymous referees for constructive, helpful comments.

Present addresses: M. G. Maltenfort, Department of Neurobiology andAnatomy, Drexel University College of Medicine, 2900 Queen Lane, Phila-delphia, PA 19129; M. L. McCurdy, Department of Kinesiology, University ofWisconsin, 2146 Medical Science Center, 1300 University Ave., Madison, WI53706–1532; C. A. Phillips, Arizona Endocrinology, Diabetes, and Osteopo-rosis Center, 5130 W. Thunderbird Rd., #1, Glendale, AZ 85306.

G R A N T S

This work was supported by National Institute of Neurological Disordersand Stroke Grant NS-22454 to T. M. Hamm and NS-07309 to the Universityof Arizona—Barrow Neurological Institute Motor Control NeurobiologyTraining Program. M. G. Maltenfort received support from NS-10341 andC. A. Phillips received support from the Undergraduate Biology ResearchProgram at the University of Arizona.

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