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Medical Research Council Group in Sensory-Motor Neuroscience, Department of Physiology, Queen's University, Kingston, Ontario K7L 3N6, Canada
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Campbell, D. M. and P. K. Rose. Contribution of voltage-dependent potassium channels to the somatic shunt in neck motoneurons of the cat. J. Neurophysiol. 77: 1470-1486, 1997. The specific membrane resistivity of motoneurons at or near the soma (Rms) is much lower than the specific membrane resistivity of the dendritic tree (Rmd). The goal of the present experiments was to investigate the contribution of tonically active voltage-dependent potassium channels at or near the soma to the low Rms. These channels were blocked with the use of intracellular injections of cesium. Input resistance (RN), Rms/Rmd, a conductance representing voltage-dependent potassium channels on the soma, GK, and a conductance attributed to damage caused by electrode impalement, GDa, were estimated from voltage responses to a step of current. The effect of intracellular injections of cesium on electrotonic structure was determined with the use of two strategies: 1) a population analysis that compared data from two groups of motoneurons, those recorded with potassium acetate electrodes (control group) and those recorded with cesium acetate electrodes after the motoneurons were loaded with cesium; and 2) an analysis of changes in electrotonic structure that occurred over the course of multiple injections of cesium or during similar periods of time in control cells. RN of control and cesium-loaded motoneurons was similar. Over the course of the recordings, RN of control cells usually increased and this increase was associated with a hyperpolarization. In contrast, increases in RN after successive injections of cesium were closely linked to a depolarization. At corresponding membrane potentials, Rms/Rmd of cesium-loaded motoneurons was greater than Rms/Rmd of control motoneurons. Over the course of cesium injections, Rms/Rmd increased and the membrane potential depolarized. In contrast, increases in Rms/Rmd observed during the course of recordings from control cells were associated with a hyperpolarization. Compared with control cells at corresponding membrane potentials, GK was less in cesium-loaded cells. Increases in GK that occurred over the course of recordings in control cells were closely coupled to a depolarization. In cesium-loaded cells, GK usually decreased as the cell depolarized during the injections. In control cells, increases in GDa that occurred during the recording period were closely coupled to a depolarization. In contrast, changes in GDa that occurred during cesium injections were not related to the change in membrane potential and did not explain the corresponding changes in Rms/Rmd and membrane potential. The results of this study indicate that voltage-dependent potassium channels contribute to the somatic shunt (low Rms) in neck motoneurons and provide a voltage-dependent mechanism for the dynamic regulation of motoneuron electrotonic properties.
The spread of current within the dendritic tree is critically dependent on specific membrane resistivity (Rm). Traditionally, Rm was considered to be passive (i.e., voltage and time invariant) and uniform throughout the somatodendritic surface of a neuron (Rall 1959 Experimental preparation
Experiments were performed on 17 adult female cats weighing between 2.4 and 3.7 kg. Anesthesia was induced with pentobarbital sodium (35 mg/kg, ip) and was maintained with supplementary doses (2.5-5 mg/kg iv). Rectal temperatures were maintained at 37 ± 2.0°C (mean ± SE) with the use of a feedback-controlled heating pad. After a laminectomy exposing C1-C4, the animals were secured in a spinal frame. The spinal cord was bathed in a pool of silicone oil warmed to 37°C. The animals were paralyzed with gallamine triethiodide (2.5-5.0 mg·kg
Data collection
The voltage responses to 128 short (duration 50 ms, repeated every 150 ms) and 32 long (duration 150 ms, repeated every 500 ms) consecutive Subtraction of extracellular responses
Although the effect of electrode properties on the voltage response recorded intracellularly could be minimized by careful selection of low-resistance electrodes and capacitance neutralization, extracellular records of the voltage response to a current injection exhibited a fast "steplike" shift at the start of the current step followed by a slower voltage decay (Fig. 1Aii). The slower phase of the extracellular response (starting at 0.4-0.6 ms) followed an exponential time course (Fig. 1B) and could be fitted by the following equation
Data analysis
The voltage response to a hyperpolarizing step of current (I) decays in a multiexponential fashion as described by Rall (1969)
Calculation of somatic shunt conductances
According to the somatic shunt model of Durand (1984) Limitations of recording system
Recordings in which the DCC mode is used may fail to capture the rapid initial decay of the transient if the high-frequency components of the response are "filtered" by the digital sampling system. If the initial decay period is not captured, the faster equalizing time constants in Eq. 3 (i.e., The electrotonic structure of 42 motoneurons was determined. Thirty motoneurons received one or more injections of cesium. The other 12 motoneurons were recorded with potassium-acetate-filled electrodes. Both populations of cells contained a mixture of motoneurons supplying different neck muscles (control group: 6 biventer cervicis/complexus, 4 splenius, 2 trapezius; cesium group: 21 biventer cervicis/complexus, 9 splenius). Because previous studies (Rose and Vanner 1988 Action potential changes
The shape of the antidromic action potential was used as an index of the effectiveness of the block of voltage-dependent potassium channels by intracellular injections of cesium. After one or more injections of cesium the repolarization phase of the antidromic action potential became slower, largely because of the appearance of a prominent hump on the repolarization trajectory (Fig. 3). The increase in action potential duration was often associated with an increasein action potential amplitude. Compared with action potentials in control motoneurons at corresponding resting membrane potentials, action potentials in motoneurons injected with >40 nA*min cesium were 10-20 mV larger. These observations are consistent with a block of voltage-dependent potassium channels, particularly the delayed rectifier channel (Araki et al. 1962 Comparisons of control and cesium-injected motoneurons
Two strategies were used to determine the effect of intracellular injections of cesium on electrotonic structure. First, data obtained from motoneurons recorded with potassium acetate electrodes were compared with data obtained from motoneurons that had received one or more injections of cesium. For the purposes of this comparison, only one set of responses per motoneuron was used to determine the electrotonic parameters. For control cells, these data corresponded to observations collected when the membrane potential was most negative (i.e., healthiest, mean Effect of cesium on RN
RN of control motoneurons (1.48 ± 0.49 M
Effect of cesium on Rms/Rmd
Estimates of Rms/Rmd for control and cesium-loaded motoneurons are summarized in Fig. 5. The average Rms/Rmd of motoneurons injected with cesium, 0.25 ± 0.25, was not statistically different from that of motoneurons recorded with potassium acetate electrodes, 0.43 ± 0.38. However, a strong positive correlation (r2 = 0.81) was found between Rms/Rmd and the membrane potential of control motoneurons (Fig. 5A), and this relationship was altered by the injection of cesium. At corresponding membrane potentials, estimates of Rms/Rmd of cesium-loaded motoneurons were significantly higher than the values of Rms/Rmd of control motoneurons (analysis of covariance, F = 5.78, P = 0.021).
Effect of cesium on The first explanation predicts that Rms will increase because of a reduction in the conductance attributed to voltage-dependent potassium channels and decreased damage due to electrode impalement. Rmd will also increase because of a block of the voltage-dependent potassium channels on the dendritic tree. The combination of an increase in Rms and Rmd should result in an increase in Effects of cesium on Gk and Gda
The combination of effects of cesium on membrane potential, RN, Rms/Rmd, and
Other changes
The response to a long step (150 ms) of current consisted of an initial fast hyperpolarization followed by a slow late depolarization (Fig. 8A). This nonlinearity, often called "sag," is characteristic of most motoneurons (Chandler et al. 1994
The voltage responses of spinal motoneurons in vivo to short or long steps of current are consistent with the presence of a somatic shunt (Burke et al. 1994 Applicability of somatic shunt model
The somatic shunt model places several constraints on the electrical and morphological properties of the neuron (Durand 1984 Degree and specificity of channel block
The electrotonic properties of most motoneurons were altered after injection of cesium. However, the response of some motoneurons to hyperpolarizing steps of current appeared to be unaltered despite obvious changes in the width of the action potential, the index used to assess the degree of block of voltage-dependent potassium channels. For some motoneurons, this result is most likely attributed to the presence of a significant fraction of unblocked potassium channels (e.g., motoneurons receiving a single injection of cesium). However, the effect of multiple injections of cesium that likely caused a block of a significant fraction of voltage-dependent potassium channels was not the same for all motoneurons examined. Some motoneurons showed major changes in Rms/Rmd and GK, whereas other motoneurons had more modest changes. These results suggest that voltage-dependent potassium channels may not contribute to the somatic leak of all neck motoneurons. This variability may be related to other properties of the motoneurons, such as mechanical responses of the motor unit, membrane area, and recruitment thresholds, and may contribute to some of the intrinsic differences between motoneurons innervating type S and type F motor units (for a review, see Burke 1990 Conductances contributing to Gsh
The results of the present study demonstrate that GSh consists of at least two components, GDa and GK. Thus at least part of GSh is an inherent physiological property of spinal motoneurons. The decrease in Rms caused by tonic activation of voltage-dependent potassium channels will alter the input/output characteristics of motoneurons. In model neurons, a decrease in Rms has been shown to cause an attenuation of postsynaptic potentials generated by distal and proximal synapses (Poznanski 1987
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
, 1977). More recently, it has become apparent that Rm, even at subthreshold membrane potentials, is modulated by many voltage-dependent channels, as well as by tonic synaptic activity (Hille 1992; Rall et al. 1992). Furthermore, Rm is not uniform. Instead, the behavior of many neurons is consistent with the presenceof a somatic shunt (Durand 1984; Kawato 1984) in which Rm on the soma (Rms) is lower than Rm on the dendritictree (Rmd) (motoneurons: Burke et al. 1994; Clements andRedman 1989; Fleshman et al. 1988; Iansek and Redman 1973; Nitzan et al. 1990; Rose and Vanner 1988; see, however, Ulrich et al. 1994; hippocampal neurons: Durand et al. 1983; Spruston and Johnston 1992; Staley et al. 1992; see, however, Major et al. 1994; Thurbon et al. 1994; Purkinje cells: Rapp et al. 1994; Shelton 1985; ventral cochlear neurons: White et al. 1994; olfactory sensory neurons: Pongracz et al. 1991).
in a study of hindlimb motoneurons. More recent experiments have demonstrated that this property is common to many types of motoneurons (Nitzan et al. 1990; Rose and Vanner 1988), including both 
- and 
-motoneurons (Burke et al. 1994), and it has been estimated that Rmd exceeds Rms by a factor of 100-300 (Clements and Redman 1989; Fleshman et al. 1988). The exact cause of this regional difference in Rm is not known, but it has been suggested that three factors contribute to the low Rms. These include damage to the cell membrane due to intracellular impalement, differences in the activity of synapses on the soma and dendrites, and greater tonic activity of voltage-dependent channels on the soma than the dendritic membrane (Clements and Redman 1989; Fleshman et al. 1988; Rose and Vanner 1988). The purpose of the present study was to investigate the contribution of voltage-dependent potassium channels.
; Jack 1979). The finding that the membrane potentials of many motoneurons appear "healthy" suggests that either the damage caused by impalement is minimal or the resulting depolarization is partially offset by voltage-dependent currents that hyperpolarize the motoneuron. Voltage-dependent potassium channels, especially those responsible for the delayed rectifier current, are potential candidates for producing a postinjury hyperpolarization. Puil and Werman (1981) reported that intracellular injections of cesium, a potassium channel blocker, reduced the resting membrane conductance of motoneurons. Motoneuron input conductance is also reduced by extracellular application of tetraethylammonium (Yarom et al. 1985), and intracellular injections of this potassium channel blocker increased the amplitude and time course of single-fiber Ia excitatory postsynaptic potentials (Clements et al. 1986). These result are consistent with a tonic activation of voltage-dependent potassium channels at resting membrane potentials (for other types of neurons see Barrett et al. 1988; Connors et al. 1982; Reyes et al. 1994), although the increase in excitatory postsynaptic potentials can also be attributed to other factors, such as an increase in reversal potential (cf. Clements et al. 1986).
and modified by Durand (1984). The magnitude of the somatic shunt in a control population of motoneurons was compared with that in a second group of motoneurons whose voltage-dependent potassium channels were blocked with intracellular injections of cesium. The results indicate that voltage-dependent potassium channels contribute to the somatic shunt in neck motoneurons. A preliminary report of this study has appeared in abstract form (Campbell and Rose 1994).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
1·h1) and ventilated. After paralysis the pupillary reflex was used as an index of the anesthetic state. Additional doses of pentobarbital sodium (2.5 mg/kg iv) were administered if the pupils constricted in response to a bright light. Bilateral pneumothorax was performed to reduce large respiratory-related movements. End-tidal CO2 levels were monitored and maintained between 3.0% and 4.0% by adjustment of either the tidal volume or respiratory rate.
, when measured on the surface of the spinal cord. After the electrode was advanced into the ventral horn, electrode resistances were 4.4-7.6 M.
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FIG. 3.
Effect of intracellular cesium injections on action potential characteristics. A: progressive increase in the duration of an antidromic action potential following 0, 20, 38, and 60 nA*min cesium. B: calculation of action potential duration, defined by the interval between voltages at the 10% and 20% heights of the rising and falling phase of the action potential, respectively. C: cumulative frequency histograms of the duration of antidromic action potentials recorded before cesium injections ( 
), after 1 injection (
), and after multiple injections of cesium (
).
4-nA hyperpolarizing current steps were recorded with the use of an Axoclamp-2A amplifier in the discontinuous current-clamp (DCC) mode (sampling frequency 7.5-8.5 kHz). Capacitance neutralization and the antialiasing filter were adjusted to achieve optimal capacitance compensation and noise reduction. The DCC mode was chosen despite the increase in noise and decrease in signal recording bandwidth compared with bridge mode. In DCC mode the voltage responses were much less susceptible to large shifts in potential due to changes in electrode resistance associated with respiratory and cardiac related movements. Furthermore, problems caused by electrode rectification were reduced.
where m is the amplitude of the exponential; b is the rate constant(1/b = time constant of the extracellular response); and s is the magnitude of the steplike shift of the extracellular response.
![<IT>f</IT>(<IT>t</IT>) = <IT>m</IT>[1 − exp(−<IT>bt</IT>)] + <IT>s</IT>](/content/vol77/issue3/fulltext/1470/img001.gif)
(1)
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FIG. 1.
Minimization of artifacts caused by voltage transients due to nonideal electrode characteristics. A: voltage responses to a 4-nA current step (Ai) recorded extracellularly (Aii, average of 32 records) and intracellularly (Aiii, average of 128 records). B: high-gain record of the extracellular voltage response, 0.40-10.0 ms after the start of the current step (region enclosed in the box in Aii). Smooth thick line: regression line fit to the data with the use of Eq. 1. C: enlarged view of the intracellular voltage response enclosed in the box in Aiii. Data from 0 to 0.48 ms have been deleted. Slope A and slope B (defined in text) were compared to estimate the contribution of voltage responses due to nonideal electrode characteristics to the voltage response recorded intracellularly. For this example, slope A exceeded slope B by 43%.
; Major et al. 1994). The following subtraction procedure was therefore developed and represents a compromise between ignoring the electrode contribution to the voltage response (because it cannot be determined accurately) and a straightforward subtraction of the extracellular response (because it does not faithfully reproduce the electrode's contribution seen intracellularly). All dendritic neurons produce a smooth, multiexponential voltage decay in response to a step of current (Holmes et al. 1992). The initial slope of the response (in the absence of electrode contributions) will therefore be greater than the slope at later time points. The extracellular response subtraction procedure made use of two estimates of the slope of the voltage response at a time halfway between the start of the current step and the time at which the slower response usually began, near 0.5 ms (t1, see Fig. 1C). The first slope estimate, slope A, was determined by the voltage change from t0 to t1 and was largely due to the sum of steplike shift seen in the extracellular response and the response of the neuron. The second slope estimate, slope B, was a linear extrapolation of the slope (at time t1/2) and was based on measurements of the slope from t1 to t2 and from t2 to t3 (Fig. 1C). Slope B was largely due to the response of the neuron and a smaller component attributed to the slower phase of the extracellular response. A percentage of f(t) (e.g., 100%, 150%) was subtracted from the intracellular response until slope A exceeded slope B by 10-15%. This criterion is arbitrary, but it provides a standard for subtraction of all extracellular recordings and invariably resulted in a voltage response that followed a smooth multiexponential decay. Moreover, the application of this procedure to simulated responses of somatic shunt models to which were added typical extracellularly recorded responses usually led to estimates of electrotonic structure close to the theoretical parameters of the models (see APPENDIX). The percentage of the extracellular responses subtracted from the intracellular responses averaged 111% (range 15-375%).
where RN is the input resistance of the motoneuron and was calculated by dividing the maximum change in membrane potential (Vpeak, after subtraction of the extracellular response) by I (4 nA).
(2)
where an = Cn/
(3)
n. The coefficients and time constants of Eq. 3 are difficult to resolve accurately because of the "noise" in the voltage responses as a result of ongoing synaptic activity and respiratory- or cardiac-related movement. Even small errors in these coefficients and time constants can significantly alter estimates of electrotonic structure (Holmes et al. 1992; White et al. 1992). Therefore several procedures were adopted that were designed to minimize the effects of noise.
where V(tn) is the magnitude of membrane potential at tn. This average was calculated starting at 0.2 ms after the current step and was repeated six times.
(4)
1 was calculated were longer, 0.18-0.28 ms, but were sufficiently short to measure the smallest values of 1 that were encountered (0.9-1.1 ms). Time intervals during the late phase of the response were 1.0-2.5 ms. This selection procedure reduced errors in the calculation of the slope over the late phase of the response, where the slope is small and subject to large errors because of small voltage fluctuations.
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FIG. 2.
Estimation of electrotonic parameters. A: regression analysis of the slope of voltage response. Note increasing intervals between adjacent data points ( ) during the late phase of the response. Solid curve: results of a nonlinear regression analysis with the use of Eq. 7 for the last 28 data points with the sum of C0 and C1 fixed at 5.42. The results of this regression analysis were used to build a somatic shunt model whose response is shown in B. B: comparison of the averaged response of the motoneuron (fine line) and somatic shunt model (thick line). The comparison is restricted to the time period from 0.4 to 10.8 ms after the start of the current step. C: difference between experimental response (Ve) and model response (Vm), expressed as (Ve Vm)2, for data points starting at 0.4 ms and ending at 10.8 ms. D: determination of the "best match" between the experimental response and the response of 5 somatic shunt models. The electrotonic characteristic of the models were derived from a nonlinear regression analysis of the slope of the experimental response with C0 + C1 set at different values, e.g., 5.42.
where V(tn) and V(tn+3) represent the voltage values from the file described above, and tn and tn+3 represent their corresponding time values. Skipping two intervening data points resulted in a slope calculation that was less sensitive to spurious voltage transients.
(5)
The procedure was applied twice.
(6)
ignores the faster exponential components of Eq. 3 that contribute to the earliest phase of the slope of the voltage response. The regression analysis therefore excluded data points describing the earliest phase (0 to 1-2 ms) of the slope of the voltage response. To determine the most appropriate starting point for the regression analysis, parameter dependence for a0, a1,
(7)
0, and 1 was calculated. Dependencies near 1.0 indicate that the equation is too complicated and uses too many parameters. For example, fitting Eq. 7 to a response consisting of only one exponential component will lead to a dependency of 1.0. Because the late phase of the response is largely due to the slowest exponential component [a0 exp(t/0)], excluding too many early data points would be expected to give dependencies of 1.0. On the other hand, including earlier data points would reduce the dependencies, but could "contaminate" estimates of a0, a1, 0, and 1 by including the third fastest exponential component [a2 exp(t/2)]. To achieve a balance between these two extremes, the regression analysis was performed on several data sets. Early data points were successively removed until one or more dependencies exceeded 0.97. The coefficients and time constants of the preceding fit were selected as the "best fit" for the equation. To ensure that the coefficient and time constant of the slowest exponential component were measured accurately, a weighting function, w, where w = 1/(slope)2, was utilized in the regression analysis. The selection of this weighting function and the criterion that dependence 
0.97 were based on a regression analysis of the two slowest exponential components of a three-exponential-component equation with a range of coefficients and time constants similar to those encountered experimentally. Other weighting functions or different dependencies led to less accurate estimates of the coefficients and time constants of the two slowest exponential components.
0, and 1 from the regression analysis, together with RN, were used to calculate the electrotonic properties of two types of equivalent cylinder models. If the ratio, a1/a0, exceeded 2.0, it was assumed that the electrotonic properties of the motoneuron could be described by the somatic shunt model developed by Durand (1984). The cable properties (L, electrotonic length; 
, dendritic to somatic conductance ratio; md, time constant of the dendritic membrane; Rms/Rmd) of the model were estimated with the use of the equations derived by Durand (1984) and the procedures described by Rose and Dagum (1988). If the ratio, a1/a0, was <2.0, it was assumed that the response of the motoneuron could be described by an equivalent cylinder model with Rms = Rmd. The cable properties of this model were estimated with the use of the equations of Johnston (1981; see also Rose and Dagum 1988).
1 will be in error. Therefore a series of coefficients and time constants was generated for each experimental voltage response by constraining the sum of C0 and C1 to different values (Fig. 2). This procedure primarily affected a1 and 1. The electrotonic parameters of either the somatic shunt model or the equivalent cylinder model with Rms = Rmd were calculated with the use of each set of coefficients and time constants. Thus each experimental voltage response generated a family of somatic shunt or equivalent cylinder models. The response of these models to the same current injected experimentally was determined by numerical methods (Rose and Dagum 1988).
The relationship between GOF and the sum C0 + C1 was invariably parabolic (Fig. 2D). Thus a unique solution (i.e., model) was obtained for each voltage response. Tests of these methods with the use of simulated data (with and without noise) demonstrated that these methods gave estimates of electrotonic parameters that closely matched the characteristics of the models (see APPENDIX).
![GOF = <LIM><OP>∑</OP></LIM>[<IT>V</IT><SUB>n</SUB>(experimental) − <IT>V</IT><SUB>n</SUB>(model)]<SUP>2</SUP>](/content/vol77/issue3/fulltext/1470/img008.gif)
(8)
the shunt conductance at or near the cell body is
where GN = 1/RN.
(9)
attributed GSh to a "leak" conductance due to damage caused by microelectrode impalement of the neuron. If voltage-dependent potassium channels also contribute to the somatic shunt conductance, then GSh is composed of two conductances
where GK represents a potassium conductance and GDa represents the conductance due to impalement damage. At a constant membrane potential, the net current crossing the cell membrane is zero and is composed of three components: Ipas represents the current flow in the absence of a shunt, IK is the current due to activation of voltage-dependent potassium channels on the soma, and IDa is the current caused by damage due to electrode impalement. Thus
(10)
This is equivalent to
(11)
where E is recorded membrane potential; Epas is estimated membrane potential of a motoneuron with no damage or voltage-dependent activity (e.g.,
(12)
80 mV); EK is equilibrium potential for voltage-dependent potassium current; and EDa is equilibrium potential for leak current. Because GK is due solely to a potassium conductance (i.e., EK = 80 mV) and, if it is assumed that GDa shows no ionic selectivity (i.e., EDa = 0 mV), Eq. 10 and 12 can be rearranged and
(13)
1), may not be extracted correctly. To assess the ability of the recording system to capture the fast transients, the voltage responses of several resistor-capacitor circuits to steps of hyperpolarizing current were recorded with the use of the DCC mode and sampled at 8 kHz. A nonlinear regression analysis (single exponential) showed that the time constants of the voltage responses were 0.29, 0.55, 1.05, and 5.15 ms for resistor-capacitor circuits with theoretical time constants of 0.25, 0.50, 1.0, and 5.0 ms, respectively. Because the smallest 1 of the responses recorded from motoneurons was 0.66 ms, it is unlikely that limitations in the frequency response of the recording system influenced estimates of electrotonic parameters.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
) have not identified major differences in the electrotonic properties of motoneurons innervating different neck muscles, the motoneurons recorded with cesium acetate or potassium acetate electrodes were considered to belong to a homogeneous population of motoneurons.
; Clements et al. 1986; Connors et al. 1982; Hille 1992; Puil and Werman 1981; Schwindt and Crill 1980; Takahashi 1990).
as well as Puil and Werman (1981) observed that large injections of cesium (equivalent to 80 nA*min) abolished the AHP of antidromic action potentials in lumbosacral motoneurons. In the present experiments there was no effect on AHP amplitude or duration. The average AHP amplitude and duration in control motoneurons were 2.1 ± 0.7 mV and 56 ± 7 ms, respectively. Motoneurons receiving the largest cumulative injections of cesium, >40 nA*min, had an average AHP amplitude and duration of 2.2 ± 0.9 mV and 61 ± 5 ms, respectively.
64.7 ± 7.4 mV). The same criterion for data collection could not be applied to motoneurons injected with cesium, because these cells usually depolarized after each injection of cesium. Furthermore, the amplitude of the antidromic action potential, often used as another index of cell health, could not be used as a substitute for resting membrane potential, because cesium-loaded motoneurons typically had larger action potentials than control cells. Therefore, for motoneurons recorded with cesium acetate electrodes, the comparison was based on responses collected after the final cesium injection. The average membrane potential of these neurons was56.5 ± 6.2 mV. The difference between the membrane potentials of these two groups of motoneurons was statistically significant (t-test, P < 0.001). Although this difference is most likely due to the action of cesium, the possibility that the cesium-injected cells, as a group, were subjected to a greater degree of damage caused by electrode impalement cannot be discounted. The second strategy addressed this issue. For each cell, electrotonic parameters were determined several times over the course of the 10- to 40-min recordings. These estimates showed that changes were progressive (i.e., continued to increase or decrease) or reached a steady state. Thus comparisons of electrotonic parameters derived from the first and last data sets indicated the maximum changes observed over the impalement period. For cesium-injected cells this analysis was restricted to motoneurons with near-maximal voltage-dependent potassium channel block (i.e., cumulative cesium injection >40 nA*min) and the "control" parameters were measured before cesium injection or after one short injection of cesium (8-20 nA*min).
) was similar to RN of motoneurons recorded after the final injection of cesium (1.57 ± 0.36 M; t-test, not significant). An analysis of covariance of RN with respect to cesium and membrane potential did not find a statistically significant effect related to membrane potential (Fig. 4A). The absence of a correlation between RN and membrane potential for control and cesium-loaded motoneurons may be due to the dominance of other factors that determine RN (e.g., cell size, Rms, Rmd; Rall 1977). This suggestion was confirmed by comparing values of RN obtained from single cells over the course of the impalement. For control motoneurons, changes in RN and membrane potential followed one of three patterns (Fig. 4B). Most commonly (6 of 9 neurons), RN increased with time and this increase was associated with a hyperpolarization. One cell displayed the reverse relationship, and two cells showed little change in either RN or membrane potential. These results can be explained most simply by changes in the quality of electrode impalement
an improvement leading to an increase in RN and a hyperpolarization, a deterioration resulting in a decrease in RN along with a depolarization. In contrast, RN of motoneurons always increased over the period of cesium injections and, for 9 of 10 cells, this change was associated with a depolarization (Fig. 4C). There are three explanations for the latter results (assuming, for the moment, that voltage-dependent potassium channels are uniformly distributed on the soma and dendrites and cesium is equally effective in blocking somatic and dendritic voltage-dependent potassium channels).
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FIG. 4.
Effect of intracellular cesium injection on input resistance (RN). A: relationship between RN and membrane potential for 2 populations of motoneurons: a control group recorded with potassium acetate electrodes ( , control) and a second group whose characteristics were determined after injection of cesium (). B: changes in RN and membrane potential recorded over the duration of the recording from individual cells. Each line represents data obtained from 1 cell. The start of each line indicates values recorded shortly after penetration of the motoneuron with a potassium acetate electrode; and end of line (at the arrowhead) shows values recorded just before withdrawal of the electrode, 10-40 min later (only cells with 
2 measurements over this period are included; thus some of the cells shown in A are not included). C: each line starts with data obtained before or after 1 short injection of cesium and ends (arrowhead) with data obtained after the maximum accumulated injection of cesium (only cells with >40 nA*min are included).
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FIG. 5.
Effect of intracellular cesium injections on specific membrane resistivity on the soma (Rms)/specific membrane resistivity on the dendritic tree (Rmd). A: relationship between Rms/Rmd and membrane potential for control cells recorded with potassium acetate electrodes ( ) and from motoneurons whose characteristics were determined after injection of cesium (). Solid and dashed lines: regression lines fitted to the control data (r2 = 0.81, P < 0.001) and to data from cesium-loaded motoneurons (r2 = 0.32, P < 0.001), respectively. B and C: changes in Rms/Rmd and membrane potential recorded from control cells (B) and from cells loaded with >40 nA*min cesium (C). Same format as Fig. 4.
1 mV). Changes in Rms/Rmd and membrane potential of motoneurons over the course of the cesium injections followed a different direction (Fig. 5C). Rms/Rmd increased in all cells (>25% in 8 of 10 cells) and this increase was coupled to a depolarization (9 of 10 cells) or no change in membrane potential (1 cell). These results support the hypothesis that cesium causes a uniform increase in Rms and Rmd and, over the period of the recording, there is an improved seal between the electrode and motoneuron (1st explanation).
0
0 (cf. Durand 1984). However, a comparison of the effect of cesium on the relationship between 0 and membrane potential for control and cesium-loaded motoneurons showed that 0 was unaffected by the injection of cesium (analysis of covariance, F = 0.60, not significant). Moreover, in individual cesium-loaded motoneurons, 0 did not change over the course of the injections (0 shortly after impalement, 5.6 ± 1.3 ms; 0 after >40 nA*min of cesium, 6.1 ± 1.7 ms; t-test, not significant).
0 is not consistent with the assumption that voltage-dependent potassium channels are distributed equally on the soma and dendritic tree. The data are compatible, however, with a nonuniform distribution of these channels in which most of the open channels are concentrated on the somatic or proximal dendritic membrane (i.e., an increase in Rms due tothe block of somatic voltage-dependent potassium channels by cesium). More direct evidence in support of a somatic distribution of open voltage-dependent potassium channels was provided by estimates of GDa and GK (see METHODS).
7 S and 1.87 ± 0.81 × 107 S, respectively; t-test, not significant). Control motoneurons showed a strong negative correlation between GDa and membrane potential (r2 = 0.80; Fig. 6A). This relationship is consistent with the expected effect of damage caused by electrode impalement and was confirmed by following changes in GDa over the course of the recording period (Fig. 6B). Decreases in GDa (5 cells) were invariably coupled with a hyperpolarization; increases in GDa (2 cells) were matched with a depolarization and small changes in GDa (2 cells) were associated with little change in membrane potential (<2.5 mV). Compared with control cells at similar membrane potentials, GDa appeared to be reduced in cesium-loaded motoneurons, but this reduction was not statistically significant (Fig. 6A; analysis of covariance, F = 1.80, P = 0.19). Within cesium-loaded cells, changes in GDa were not related to changes in membrane potential that occurred over the course of the injections (Fig. 6C). Membrane potential usually depolarized, but GDa decreased in three cells, increased in two cells, and changed <0.5 × 107 S in five cells. Calculations of RN after removal of GDa (i.e., GN GDa) for the data shown in Fig. 4A showed that RN of cesium-loaded motoneurons was significantly larger than RN of control motoneurons (2.19 ± 0.56 M and 1.77 ± 0.55 M, respectively; t-test, P < 0.05).
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FIG. 6.
Effect of intracellular cesium injections on the conductance due to electrode impalement (GDa). A: relationship between GDa and membrane potential for cells recorded with potassium acetate electrodes ( ) and from motoneurons whose characteristics were determined after injection of cesium (). Solid and dashed lines: regression lines for the control data (r2 = 0.80, P < 0.001) and for data from cesium-loaded motoneurons (r2 = 0.51, P < 0.001), respectively. B and C: changes on GDa and membrane potential recorded from control cells (B) and from cells loaded with >40 nA*min cesium (C). Same format as Fig. 4.
70 mV. In cesium-loaded motoneurons, this correlation was disrupted (Fig. 7A; r2 = 0.0002). GK was significantly smaller in cesium-loaded motoneurons compared with control motoneurons at corresponding membrane potentials (analysis of covariance, F = 14.6, P < 0.001). After large injections of cesium there was a decrease in GK (8 of 10 cells; Fig. 7C) that was associated with a depolarization. In contrast, decreases in GK in control cells were always coupled with a hyperpolarization (Fig. 7B). These results demonstrate that cesium acts primarily to increase Rms because of a block of somatic potassium channels that is tonically active at membrane potentials positive to 70 mV.
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FIG. 7.
Effect of intracellular cesium injections on the somatic conductance attributable to voltage-dependent potassium channels (GK). A: relationship between GK and membrane potential for cells recorded with potassium acetate electrodes ( ) and for motoneurons whose characteristics were determined after injection of cesium (). Solid line: regression line for the control data (r2 = 0.74, P < 0.001). The relationship between GK and membrane potential for cesium-loaded cells was not significant (r2 = 0.0002). B and C: changes in GK and membrane potential recorded from control cells (B) and from cells injected with >40 nA*min cesium (C). Same format as Fig. 4.
; Gustaffson and Pinter 1984; Ito and Oshima 1965; Zengel et al. 1985) and has been attributed to a hyperpolarization-activated inward current, Ih (Bayliss et al. 1994; Chandler et al. 1994; Engelhardt et al. 1995; Larkman and Kelly 1992; Takahashi 1990). In seven control cells, the response to current pulses of 4 nA was compared with the response to other steps of current ranging from 2 to 8 nA. Estimates of electrotonic structure obtained from these responses were similar. However, the magnitude of the sag, quantified as shown in Fig. 8A, was found to be voltage- dependent. Cells recorded at more hyperpolarized membrane potentials had a larger degree of sag than cells recorded at more depolarized membrane potentials (Fig. 8B). This relationship was altered in cesium-injected motoneurons. The magnitude of the sag seen in cesium-injected motoneurons was less than that in control motoneurons at corresponding membrane potentials (analysis of covariance, F = 7.1, P = 0.012).
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FIG. 8.
Effect of intracellular injections of cesium on sag. A: calculation of sag. The magnitude of sag was defined as V150/Vpeak, where V150 is the change in membrane potential 150 ms after the start of a 4-nA current step and Vpeak is the maximum hyperpolarization evoked by the same current step. B: relationship between sag and membrane potential for control cells recorded with potassium acetate electrodes () and for cells whose characteristics were determined after injection of cesium (). Solid and dashed lines: regression lines for the control data (r2 = 0.60, P < 0.001) and for data from cesium-loaded motoneurons (r2 = 0.57, P < 0.001), respectively.
0. This result may be attributed to the difficulty of detecting the small increase in 0 anticipated for neurons, like motoneurons, that have a large and a value of Rms/Rmd in the range of 0.05-0.1 (cf. Holmes and Rall 1992a). In addition, there was a small, but consistent, decrease in md following the injection of cesium. This decrease was not detected in the comparison of cesium-loaded motoneurons and those recorded with potassium acetate electrodes (although there was a tendency for md of cesium-injected motoneurons to be less than md of control motoneurons at corresponding membrane potentials; analysis of covariance, F = 0.3, not significant). However, md decreased over the course of the recordings in 7 of 10 cesium-loaded motoneurons. These differences were usually small, 1-2 ms (representing a 10-15% decrease; ms increases were usually >40%), but a paired t-test revealed that the differences were statistically significant (P = 0.038). This decrease was not due to the depolarization seen in the cesium-injected motoneurons, because in control cells decreases in md that occurred over the duration of the recording were associated with a hyperpolarization (4 of 5 cells).
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Clements and Redman 1989; Fleshman et al. 1988; Iansek and Redman 1973; Rose and Vanner 1988). The results of the present study suggest that part of this shunt is due to tonic activation of voltage-dependent potassium channels on or near the soma. The validity of this conclusion rests on two critical assumptions: 1) that the somatic shunt model is appropriate for the study of motoneuron electrotonic structure, and 2) that the coefficients and time constants of the multiexponential voltage response can be estimated reliably, despite the presence of noise due to synaptic activity and artifacts introduced by the nonideal properties of the electrode. Simulations (described in the APPENDIX) demonstrated that the methods used in thepresent study to extract C0, C1, 0, and 1 provided, under most circumstances, a robust (i.e., largely insensitive to noise and electrode characteristics) estimate of the cable properties of the somatic shunt model. The most serious error was an overestimate of Rms/Rmd if is large, and this may partially explain the larger values of Rms/Rmd found in the present study compared with previous estimates (Burke et al. 1994; Clements and Redman 1989; Fleshman et al. 1988). Nevertheless, GSh was estimated accurately in these models and the estimates of relative Rms/Rmd were correct. Thus the critical assumption is that the behavior of neck motoneurons can be approximated by the somatic shunt model.
; Rall 1959). First, it is assumed that the voltage response to a step of current is free from the influence of time- and voltage-dependent conductances during the measurement period. Second, the dendritic tree is assumed to meet several geometric criteria. Finally, the somatic shunt model, as proposed by Durand (1984), assumes that all of the shunt is restricted to the soma of the neuron. The following discussion considers the validity of each of the assumptions as they pertain to neck motoneurons.
; Chandler et al. 1994; Ito and Oshima 1965; Larkman and Kelly 1992; Takahashi 1990). Thus membranes of motoneurons are not passive at subthreshold membrane potentials and a fundamental condition of the somatic shunt model is not satisfied. However, the more pertinent question is whether the presence of this nonlinearity could explain the increase in Rms/Rmd and the decrease in GK in the absence of a nonuniform distribution of activated voltage-dependent potassium channels. In the present experiments, the degree of sag was usually reduced after the injection of cesium, compared with control motoneurons at corresponding membrane potentials. This change should lead to an underestimate of Rms/Rmd and GK, if it has any effect at all. Engelhardt et al. (1995) recently reported that blocking or reducing the sag response of trigeminal neurons had little effect on the coefficients and time constants used to estimate cable properties. Moreover, Rose and Dagum (1988) demonstrated that when an Ih-like conductance was introduced into somatic shunt models, Rms/Rmd was overestimated. Thus a reduction in sag should lead to decrease in Rms/Rmd. These simulations suggest that the block of voltage-dependent potassium channels by intracellular cesium injections might have more potent effects on Rms/Rmd than were found in the present study, because these effects were partially masked by the decrease in the sag response.
), this current is a property of trigeminal motoneurons (Chandler et al. 1994). Inactivation of this current by hyperpolarizing current steps at depolarized membrane potentials, such as those recorded after the injection of cesium, would generate the equivalent of an additional hyperpolarizing current. Thus RN would be overestimated. The effect on other cable properties is more difficult to predict, because it would depend on the time course of the deactivation, data that are not currently available. Currents generated by tonic synaptic activity would also be altered. For example, inhibitory currents due to tonically active inhibitory synapses would be reduced during the current step, leading to an apparent positive inward current, opposite to the current generated by the deactivation of the persistent sodium current. Until additional studies are performed that either block these currents or model their effects, the reservation discussed previously regarding the inability to measure the absolute values of electrotonic properties under the circumstances of the present experiments should be reinforced.
; Burke et al. 1994; Cameron et al. 1985; Clements and Redman 1989; Fleshman et al. 1988; Kernell and Zwaagstra 1989; Moore and Appenteng 1991; Nitzan et al. 1990; Rose et al. 1985; Ulfhake and Kellerth 1981, 1984; Ulrich et al. 1994). Both of these characteristics can cause major errors in the estimation of electrotonic parameters (Holmes and Rall 1992a; Holmes et al. 1992; Rose and Dagum 1988). The ideal solution to this problem would be to combine anatomic and electrophysiological data to construct a compartmental model of the motoneuron dendritic tree and apply either the constrained inverse computation procedure developed by Holmes and Rall (1992b) or the optimization technique described by Major et al. (1994). However, this combined approach suffers from a serious drawback. Because of the difficulty of obtaining high quality morphological and electrophysiological data from the same neuron and the time-consuming nature of the morphological analysis, estimations of electrotonic structure in these types of studies have rarely been performed on more than a few neurons (e.g., Fleshman et al. 1988; Major et al. 1994). Thus there is a potential problem of a sampling bais. In contrast, a strategy based solely on an electrophysiological approach, as used in the present study, can be applied to a large number of neurons. Moreover, the deviations of motoneuron dendritic trees from the characteristics expected of an equivalent cylinder approximation have well-known and predictable effects on the estimations of Rms/Rmd and GSh. Dendritic tapering and dendrites with unequal electrotonic lengths both lead to an overestimate of Rms/Rmd and thus an underestimate of GSh (Holmes and Rall 1992a; Holmes et al. 1992; Rose and Dagum 1988). This error, however, will not effect estimates of the relative values of Rms/Rmd and GSh. Indeed, the analysis of data derived from the same cell over the period of cesium injections removes the confounding effect of comparing cells with different geometrics, because each cell serves as its own control. Therefore the mismatch between the geometry of neck motoneurons and the equivalent cylinder approximation does not compromise the conclusion that part of the somatic shunt of neck motoneurons is due to the tonic activation of voltage-dependent potassium channels.
). This suggests that voltage-dependent potassium channels are concentrated only at the soma. Such an abrupt transition is unlikely. Instead, it is more plausible that the gradient in Rm and change in density of potassium channels is gradual. The identical voltage response can be generated in compartmental models of motoneurons that incorporate either an abrupt change in Rm at the somatodendritic junction or a monotonic or sigmoidal increase in Rm from the soma to the distal dendrites (Clements and Redman 1989; Fleshman et al. 1988). These simulations suggest that voltage-dependent potassium channels are not concentrated solely on the somata of neck motoneurons, but are distributed more widely. This suggestion agrees with the experiments of Clements et al. (1986) in which voltage-dependent potassium channels were blocked by intracellular injections of tetraethylammonium. The amplitude and time course of dendritic excitatory postsynaptic potentials were increased, a finding that is most simply explained by the presence of voltage-dependent potassium channels near the synapses on the dendritic tree. It is apparent, however, that under the circumstances of the present experiments, the density of open voltage-dependent potassium channels is greater proximally than distally.
).
). However, cesium is often used as a broad-spectrum blocker of voltage-dependent potassium channels (e.g., Grega and Macdonald 1987) and probably blocks other voltage-dependent potassium channels, such as the A channel. Both the delayed rectifier and A channels contribute to the fast repolarization phase of action potentials in motoneurons (Barrett et al. 1980; Takahashi 1990). Delayed rectifier channels in motoneurons are rarely activated at membrane potentials negative to 60 mV, but A channels are activated between 70 and 60 mV (Safronov and Vogel 1995; see also Barrett et al. 1980). Thus, assuming that the voltage dependence of GK seen in the present study accurately reflects the voltage dependence of potassium channels in neck motoneurons, it is likely that a block of both delayed rectifier and A potassium channels contributes to the increase in Rms/Rmd and the decrease in GK.
reported that large intracellular injections of cesium blocked calcium-activated potassium channels. In the present study, AHPs were not altered after multiple injections of cesium, and it is therefore unlikely that these channels were affected. Intracellular cesium can also block -aminobutyric acid-B (GABAB)-receptor-mediated channels (Gähwiler and Brown 1985). However, the effect of GABA on mammalian motoneurons via GABAB receptors appears to occur presynaptically rather than postsynaptically (Pinco and Lev-Tov 1993, 1994; see Matsushima et al. 1993 for evidence of GABAB receptors on lamprey spinal motoneurons). Finally, M channels are blocked by extracellular cesium, but the effect of intracellular cesium is not known (Coggan et al. 1994).
reported that intracellular injections of tetraethylammonium caused an amplification of dendritic synaptic potentials by unmasking a positive inward current. This activation may be related to the unexpected absence of a significant change in 0, an observation initially reported by Clements et al. (1986) and confirmed in the present study. Neck motoneurons receiving multiple injections of cesium demonstrated a small, but significant, decrease in md. This decrease is consistent with the presence of a shunt on distal dendrites due to the activation of other types of voltage-dependent channels by excitatory postsynaptic potentials (Clements et al. 1986). This suggestion is also supported by the disproportionately large depolarizations seen in some motoneurons relative to the small changes seen in GK and GDa.
). Because Rms is dependent on the membrane potential at the soma, due to the presence of voltage-dependent potassium channels, the attenuation of synaptic potentials will be regulated in a voltage-dependent fashion. As the membrane potential of the soma depolarizes, more voltage-dependent potassium channels will open, causing a larger somatic shunt. Thus the physiological effects of this shunt will be most evident as the membrane potential approaches threshold for action potentials.
). Thus voltage-dependent potassium channels may alter the responsiveness of neck motoneurons by several mechanisms.
), conductances generated by tonic synaptic activity that is localized to proximal regions of the dendritic tree (Bernander et al. 1991; Rapp et al. 1992; Rose and Vanner 1988), and other types of voltage-dependent conductances, such as those responsible for Ih. Thus the absolute value of GK may be smaller than estimated in the present study and its role in regulating motoneuron input/output properties may be subtle. On the other hand, it is likely that the methods employed in the present studies underestimated GSh. Calculations based on compartmental models of intracellularly stained spinal motoneurons indicate that Rms/Rmd is ~0.01 (Burke et al. 1994; Clements and Redman 1989; Fleshman et al. 1988). If other electrotonic properties are similar to those reported here, a value of 0.01 for Rms/Rmd would more than double the estimate of GSh. GK would also increase. But, in the absence of information about the contribution of other conductances contributing to GSh, it is difficult to estimate the absolute size of GK. Thus the presence of tonically active voltage-dependent potassium channels on the soma of neck motoneurons provides a mechanism by which motoneuron electrotonic structure can be regulated dynamically, but the importance of this regulation as a means of altering synaptic potentials must still be determined.
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ACKNOWLEDGEMENTS |
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The authors acknowledge the excellent technical support of M. Neuber-Hess and D. Hamburger and the helpful comments of Drs. P. Zarzecki, F. Richmond, and M. Bisby on an earlier draft of this manuscript.
This research was supported by the Medical Research Council of Canada. D. M. Campbell received a Ontario Graduate Award and a Queen's University Fellowship.
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APPENDIX |
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Validation of methods for estimating electrotonic structure
Several methods have been developed to estimate electrotonic parameters of neurons on the basis of electrophysiological data with the assumption that the behavior of the neurons is consistent with the properties of a somatic shunt model with Rms Rmd (Ali-Hassan et al. 1992; D'Aguanno et al. 1986, 1989; Fleshman et al. 1988; Jack and Redman 1971; Rall 1969; Rose and Dagum 1988; White et al. 1992). All of these methods are designed to extract C0, C1, 0, and 1 from the voltage response to a step or pulse of current, although the strategies used to accomplish this goal differ. A critical test of the utility of these strategies is the ability of the technique to estimate accurately the electrotonic structure of models with known electrotonic parameters on the basis of an analysis of noise-free simulated voltage responses. Several of the methods have been shown to meet this objective (Ali-Hassan et al. 1992; D'Aguanno et al. 1986, 1989; Rose and Dagum 1988). However, the addition of noise due to ongoing synaptic activity, movement artifacts, and data acquisition methodology (e.g., DCC mode vs. bridge mode) can lead to serious errors in estimates of electrotonic parameters (Holmes et. al. 1992; White et al. 1992). Thus the methods for estimating electrotonic parameters used in the present study were subjected to two tests: 1) the accuracy of electrotonic parameters estimated from an analysis of noise-free simulations of the voltage response of somatic shunt models with known electrotonic parameters; and 2) the sensitivity of the estimates of electrotonic parameters to the presence of noise in the voltage response where the noise characteristics are similar to those seen in the present experiments. These tests were conducted on 10 model neurons whose electrotonic properties matched the experimental range of values for md (8-12 ms), (0.56-8.0, corresponding to different somatic shunts on models with s of 8 or 16 in the absence of a somatic shunt), L (1.0-1.8), Rms/Rmd (0.07-1.0), and GSh (0-4.0 × 107 S). For the purposes of this study, the accuracy of estimates of Rms/Rmd and GSh was of paramount importance, and the analysis therefore concentrates on these parameters.
Address for reprint requests: P. K. Rose, MRC Group in Sensory-Motor Neuroscience, Dept. of Physiology, Queen's University, Kingston, Ontario, K7L 3N6 Canada. Received 18 January 1996; accepted in final form 3 December 1996.
7 S. However, over this range, the maximum error was 1.0 × 107 S and this was a small error relative to the GSh measured in the present experiments.
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FIG. A1.
Accuracy of estimates of Rms/Rmd (A) and GSh (B) for 10 model neurons without ( ) and with () the addition of Gaussian noise to the voltage responses to a 4-nA current step. Rms/Rmd and GSh were estimated with the use of the protocol described in METHODS. Gray and dashed lines: regression lines fitted to estimates of Rms/Rmd and GSh based on noise-free responses and noisy responses, respectively.
4-nA hyperpolarizing current step, the average SD of the noise was 0.31% (range 0.11-1.04%). To examine the impact of this noise on the reliability of estimates of Rms/Rmd and GSh, Gaussian noise with an SD of 0.31% of the maximum voltage response to the simulated current step was added to the response of three models. Rms/Rmd and GSh of these models spanned the range encountered experimentally. The results of a Monte Carlo analysis (10 runs per model) are summarized in Fig. A2. For all models examined, the average estimate of Rms/Rmd and GSh were within 7% of the estimates obtained from an analysis of noise-free responses. Most significantly, the variability of the estimates was low. For the models with Rms/Rmd = 0.1 or 0.04, the coefficients of variation (CV) for Rms/Rmd were 3.6% and 6.0%. CVs for GSh were 3.7% and 2.0%. For the model with Rms/Rmd = 0.1, doubling the magnitude of noise led to a small increase in variability (Rms/Rmd, CV 5.2%; GSh, CV 5.1%). The most variable estimates were found in the model with Rms/Rmd = 0.4 (Rms/Rmd, CV 25.6%; GSh, CV 42.0%), but none of the errors were large enough to obscure the difference between a model with a small somatic shunt (i.e., Rms/Rmd = 0.4) and a model with an intermediate somatic shunt (i.e., Rms/Rmd = 0.1).
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FIG. A2.
Estimates of Rms/Rmd and GSh in 3 models (M1, M2, M3) with L = 1.4, md = 8.0 or 12 ms (8.0 ms for M3), (no shunt) = 8, andRN = 1.5 M. Rms/Rmd = 0.4 (M1), 0.1 (M2), or 0.04 (M3) with corresponding value of GSh = 0.95 × 107 S (M1), 3.33 × 107 S (M2),and 4.85 × 107 S (M3). Gray lines: estimates of Rms/Rmd and GSh in noise-free models. Each circle represents an estimate of Rms/Rmd or GSh after the addition of noise (10 runs per model). For M2 these estimates were obtained with 2 amplitudes of noise, SD = 0.31% of the maximum voltage response (left) and SD = 0.62% of the maximum voltage response (right).
, md = 12 ms, L = 1.4, = 0.8, Rms/Rmd = 0.1, and GSh = 3.33 × 107 S. This model was chosen because it represented the electrotonic parameters of a "typical" neck motoneuron. The characteristics of the extracellular responses (i.e., SD of the noise, time constant, and magnitude of the steplike shift) of the five extracellular responses were representative of the extracellular responses recorded with potassium-acetate- and cesium-acetate-filled electrodes.
7 S). No compensation for the extracellular response was therefore not a viable option. As an alternative, 100% of the fit to the extracellular response was subtracted from the sum of the model and extracellular responses. This tactic led to accurate and consistent estimates of Rms/Rmd and GSh (Fig. A3b1): Rms/Rmd, mean 0.096, CV 4.1%; GSh, mean 3.34 × 107 S, CV 4.4%). In comparison, the variable percentage method used to subtract the extracellular responses in the present experiments resulted in equally accurate, but more variable, estimates of Rms/Rmd and GSh (Fig. A3c1: Rms/Rmd, mean 0.104, CV 9.1%; GSh, mean 3.54 × 107, CV 8.5%). As described in METHODS, the response of the electrode recorded extracellularly may not be an accurate record of its intracellular response. To explore this problem, the extracellular response was halved or doubled and added to the model response. Rms/Rmd and GSh were estimated with the use of two strategies: subtraction of 100% of the fit to the extracellular response (i.e., change in voltage response due to the electrode not taken into account), and subtraction of a variable percentage of the fit to the extracellular response with the use of the protocol described in METHODS. The latter strategy was accurate and more consistent (Fig. A3, b2 and c2: Rms/Rmd, 100% subtraction, mean 0.097, CV 44.2%; variable percentage subtraction, mean 0.102, CV 13.4%; GSh, 100% subtraction, mean 3.47 × 107 S, CV 11.3%; variable percentage subtraction, mean 3.58 × 107 S, CV 10.6%). As a final test, the parameters used to compensate for the electrode response were deliberately selected from the different extracellular response than the one added to model response. This test was designed to determine the consequence of changes in the magnitude and time course of the electrode response recorded intracellularly compared with the responses recorded extracellularly. Once again the variable percentage subtraction procedure proved to be less prone to spurious estimates of Rms/Rmd and GSh (Fig. A3, b3 and c3): Rms/Rmd, 100% subtraction, mean 0.095, CV 45.7%; variable percentage subtraction, mean 0.098, CV 35.0%; GSh, 100% subtraction, mean 4.01 × 107 S, CV 19.3%; variable percentage subtraction, mean 3.76 × 107 S, CV 10.9%). These results indicate that the variable percentage subtraction protocol provides the best protection against incorrect estimates of Rms/Rmd and GSh due to changes in electrode characteristics between extracellular and intracellular locations.
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FIG. A3.
Estimates of Rms/Rmd and GSh in a model neuron with L = 1.4, md = 12.0 ms, (no shunt) = 8, and Rms/Rmd = 0.1 (GSh = 3.33 × 107 S). In the noise-free model with no additional voltage signal due to the electrode, estimates of Rms/Rmd and GSh were 0.91 and 3.52 × 107 S, respectively (gray lines). Symbols: estimates of Rms/Rmd and GSh after addition of the extracellular responses recorded from 5 electrodes. a: no compensation procedure. b: 100% of extracellular response subtracted. c: variable percentage of extracellular response subtracted based on the criterion described in METHODS. For b and c, estimates were obtained under 3 circumstances: 1) addition of 100% of the extracellular response, 2) addition of 50% (open symbols) or 200% (filled symbols) of the extracellular response, and 3) addition of an extracellular response that was different from the extracellular response used to calculate m, b, and s (see METHODS).
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FIG. A4.
Effect of procedure for subtraction of extracellular response on estimates of Rms/Rmd and GSh in a model neuron with L = 1.4, md = 12.0 ms, (no shunt) = 32, and Rms/Rmd = 0.1, 0.04, or 0.01 (corresponding to GSh = 1.43 × 107 S, 2.81 × 107 S, and 5.00 × 107 S). Open circles and gray lines: estimates with no extracellular response added to the simulated response. These estimates were close to the parameters assigned to the models (- - - : line of identity). Estimates shown by the filled symbols linked by black lines were based on analysis of voltage responses consisting of the model response and the extracellular response recorded from 5 electrodes (symbols: data obtained with different electrodes). For 3 of the responses, goodness of fit did not reach a minimum, and thus there was no solution for Rms/Rmd and GSh.
is large (e.g., 32), as might be expected for motoneurons with a large dendritic tree and small soma, the ratio of the two slopes shown in Fig. 1 will exceed the 10-15% criterion used to determine the percentage of the extracellular response subtraction. Under these circumstances, adopting the 10-15% criterion will lead to an overcompensation for the extracellular response (i.e., RN will be underestimated). The consequences of this overcompensation on three models with (no shunt) = 32 and Rms/Rmd = 0.1, 0.04, and 0.01 are shown in Fig. A4. Rms/Rmd, with one exception, was overestimated, usually by a factor of 4-6. Errors in the estimates of GSh were small. These results suggest that the estimates of Rms/Rmd reported in RESULTS may be incorrect. However, the error in the experimental data may not be as serious as shown in Fig. A4. The percentage of extracellular responses subtracted always exceeded 100% for the simulations shown in Fig. A4. The mean percentage subtracted for the five extracellular responses was 157%, 191%, and 285% for the respective models with Rms/Rmd set at 0.1, 0.04, and 0.01. Experimentally, the mean percentage subtracted was 111%.
FOOTNOTES
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
-motoneurons of the cat.
J. Physiol. Lond.
356: 401-431, 1984.an electrophysiological study of neck and shoulder motoneurons in the cat.
J. Neurophysiol.
59: 149-166, 1988.-motoneurones.
Brain Res.
307: 167-179, 1984.[Medline]
0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society
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P. A. Nunez-Abades, J. M. Pattillo, T. M. Hodgson, and W. E. Cameron Role of Synaptic Inputs in Determining Input Resistance of Developing Brain Stem Motoneurons J Neurophysiol, November 1, 2000; 84(5): 2317 - 2329. [Abstract] [Full Text] [PDF]
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W. E. Cameron, P. A. Nunez-Abades, I. A. Kerman, and T. M. Hodgson Role of Potassium Conductances in Determining Input Resistance of Developing Brain Stem Motoneurons J Neurophysiol, November 1, 2000; 84(5): 2330 - 2339. [Abstract] [Full Text] [PDF]
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D. W. Robinson and W. E. Cameron Time-Dependent Changes in Input Resistance of Rat Hypoglossal Motoneurons Associated with Whole-Cell Recording J Neurophysiol, May 1, 2000; 83(5): 3160 - 3164. [Abstract] [Full Text] [PDF]
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 J. C. Rekling, G. D. Funk, D. A. Bayliss, X.-W. Dong, and J. L. Feldman Synaptic Control of Motoneuronal Excitability Physiol Rev, April 1, 2000; 80(2): 767 - 852. [Abstract] [Full Text] [PDF]
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R. K. Powers and M. D. Binder Summation of Effective Synaptic Currents and Firing Rate Modulation in Cat Spinal Motoneurons J Neurophysiol, January 1, 2000; 83(1): 483 - 500. [Abstract] [Full Text] [PDF]
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