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INTRODUCTION |
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
, 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).
A somatic shunt in motoneurons was first described by Iansek and Redman (1973) 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.
Damage caused by electrode impalement would be expected to depolarize the motoneuron in the absence of activation of voltage-dependent channels (Durand 1984; 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).
In the present study the electrotonic structure of neck motoneurons was estimated with the use of the equivalent cylinder model developed by Rall (1977) 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).
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METHODS |
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
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.
Intracellular recordings were obtained with the use of glass micropipettes with sharp 1.9- to 2.1-µm diam tips. The electrodes were filled with 2.5 M potassium acetate or 2.0 M cesium acetate (pH adjusted to 8.3 with 10 M NaOH). Because of the large diameter of the electrode tip, electrode resistances were low, 2.2-4.0 M
, 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.
Motoneurons were identified antidromically by stimulation of the C2 or C3 nerves innervating splenius, biventer cervicis, and complexus. Antidromic action potentials were recorded at intervals throughout intracellular impalement to measure the height and duration of the action potentials and the magnitude and duration of the afterhyperpolarization (AHP).
Cesium was injected with currents of 5-10 nA for 2-10 min. The amount of injected cesium was expressed in nA*min (the product of the current, in nA, and the duration of current injection, in min). The block of voltage-dependent potassium channels by cesium was monitored by measuring the duration of the action potential recorded between cesium injections. The difference between the time at which the rising phase of the spike was 10% of its maximal value and the time at which the falling phase decayed to 20% of the spike height was used as a measure of the duration of the action potential. This technique avoided ambiguities in defining the precise onset and end of the action potential due to spontaneous fluctuations in membrane potential and slow, delayed depolarizations (e.g., Fig. 3).
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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 ( ).
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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 
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.
During collection of the responses to consecutive sets of short and long current pulses, the resting membrane potential did not fluctuate by >2-3 mV. However, the resting membrane potential of motoneurons recorded over 10-30 min with potassium acetate electrodes often hyperpolarized or depolarized (up to 15 and 8 mV, respectively), presumably because of changes in the quality of electrode impalement. Additional records of the responses to current steps were therefore obtained at intervals throughout the impalement. For cells recorded with cesium acetate electrodes, the responses to consecutive sets of short and long current pulses were recorded after each injection of cesium.
At least 32 consecutive extracellular voltage responses to the 150-ms current steps were also recorded just after exiting the cell. The extracellular voltage response was used to estimate the contribution of the electrical characteristics of each electrode to the response recorded inside the motoneuron. Data were stored on magnetic tape with an instrumentation tape recorder (Racal-Thermionic, Store 4, frequency response 0-10 kHz). Each set of voltage responses (n = 128 or 32) was averaged with the use of a Brain Wave Systems software package. The averaged response produced by the software package consisted of a data file that contained 625 pairs of time and voltage data points.
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
![<IT>f</IT>(<IT>t</IT>) = <IT>m</IT>[1 − exp(−<IT>bt</IT>)] + <IT>s</IT>](/content/vol77/issue3/fulltext/1470/img001.gif)
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(1)
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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.
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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%.
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If the intracellular and extracellular electrical characteristics of the electrodes are the same, the contribution of the motoneuron to the intracellularly recorded response can be obtained by simply subtracting f(t) from the averaged intracellular response. However, the response of the electrode to a current pulse inside a cell may not be the same as the response recorded extracellularly (Burke et al. 1994; 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%).
Data analysis
The voltage response to a hyperpolarizing step of current (I) decays in a multiexponential fashion as described by Rall (1969)
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(2)
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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).
The derivative of (Eq. 2) can be expressed as
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(3)
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where an = Cn/
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.
1) A five-point moving average of the voltage response was performed much that
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(4)
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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.
2) For calculation of the slope of the voltage response, a subset of the data points in the original data file (625 data points) was selected as follows. Starting at 0.2 ms after the onset of the current step, data points were selected at an initial sample interval of 4-6% of Vpeak until the response equaled 1/3 of Vpeak. For data points >1/3 of Vpeak and <2/3 of Vpeak, the voltage interval between data points was 2/3 of the initial sample interval. Finally, over the last 1/3 of the voltage response, the data were selected with the use of 1/3 of the initial sample interval. The final data file contained 39-45 data points (Fig. 2A). The initial data points were separated by the shortest time intervals, 0.08 ms. Time intervals over the phase of the response where 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.
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3) The slope of the voltage response was calculated from the following equation
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(5)
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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.
4) In an effort to reduce further the effects of cardiac, respiratory, and synaptic noise, a three-point moving average of the slope at tn was estimated with the use of the equation
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(6)
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The procedure was applied twice.
The coefficients and time constants of the two slowest exponential components of Eq. 3 were estimated with the use of a nonlinear regression analysis (based on the Marquardt-Levenberg algorithm, Sigmaplot 5.0) of the slope of the voltage response. The equation used in this regression analysis
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(7)
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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, 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.
The estimates of a0, a1, 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).
In practice, the regression analysis is imperfect because the contribution of faster exponential components will vary and therefore estimates of a1 and 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 response of each model was compared with the experimental data beginning at 0.45-0.50 ms after the onset of the response and ending at the time at which the membrane potential was 85-95% of Vpeak (Fig. 2, B and C). This time period typically included 120-160 data points from the original data file (after subtraction of the extracellular response but no 5-point moving average, time intervals between successive data points were equal). This range was used for two reasons; the subtraction procedure designed to compensate for voltage shifts caused by the electrode characteristics was based on extracellular responses that began 0.4-0.6 ms after the start of current step and thus the subtraction procedure could not be applied to earlier data; data points at times >85-95% of Vpeak included a nonlinear voltage response (see RESULTS). The model whose response produced the closest match to the experimental response was chosen as having the set of electrotonic characteristics that best described the motoneuron. The goodness of fit (GOF) was determined by the equation
![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)
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(8)
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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).
Calculation of somatic shunt conductances
According to the somatic shunt model of Durand (1984) the shunt conductance at or near the cell body is
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(9)
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where GN = 1/RN.
Durand (1984) 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
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(10)
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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
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(11)
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This is equivalent to
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(12)
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where E is recorded membrane potential; Epas is estimated membrane potential of a motoneuron with no damage or voltage-dependent activity (e.g., 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
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(13)
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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., 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.
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RESULTS |
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) 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.
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; Clements et al. 1986; Connors et al. 1982; Hille 1992; Puil and Werman 1981; Schwindt and Crill 1980; Takahashi 1990).
The effect of cesium on action potential duration was evident after a single injection of cesium (Fig. 3C). Action potentials recorded in motoneurons before cesium injections had a duration of 1.00 ± 0.20 (SD) ms. After injections of 9-20 nA*min cesium, the duration increased to 1.95 ± 0.49 ms. These results indicate that small injections of cesium cause a detectable block of voltage-dependent potassium channels. Additional injections of cesium led to further increases in action potential duration (Fig. 3C). Action potentials in motoneurons with cumulative injections of cesium that totaled 21-40 nA*min were 2.34 ± 1.32 ms long. After cumulative injections of 44-93 nA*min, action potential duration increased to 2.98 ± 0.77 ms. On a per nA*min basis, the increase in action potential duration became progressively smaller as the accumulated injection size increased (9- to 20-nA*min range, 63 µs per nA*min; 21- to 40-nA*min range, 46 µs per nA*min; and 44-93 nA*min, 29 µs per nA*min). Thus the duration of the antidromic action potential approached a plateau with injections of >40 nA*min, suggesting a near-maximal block of voltage-dependent potassium channels.
Araki et al. (1962) 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.
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 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).
Effect of cesium on RN
RN of control motoneurons (1.48 ± 0.49 M) 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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1) The increase in RN is due to a combination of an improved seal between the electrode and motoneuron and a uniform increase in Rms and Rmd caused by the cesium block of voltage-dependent potassium channels. The latter effect causes a depolarization that exceeds the hyperpolarization expected as a consequence of reduced electrode penetration damage.
2) The increase in Rms and Rmd due to the actions of cesium leads to a net increase in RN despite a deterioration in the quality of electrode impalement. Both of these changes act in concert to depolarize the motoneuron.
3) The damage caused by electrode penetration remains static and thus the increase in RN and the depolarization are attributed exclusively to the block of voltage-dependent potassium channels by cesium.
These explanations lead to specific predictions for the effect of cesium on Rms/Rmd. An increase in Rms/Rmd is consistent with the first explanation; the second explanation predicts a decrease in Rms/Rmd, and Rms/Rmd should remain the same for the third explanation. Additional explanations involving a nonuniform distribution of voltage-dependent potassium channels will be considered later.
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).
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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.
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For control motoneurons these data support the earlier suggestion that changes in RN with respect to membrane potential are due to changes in the quality of electrode impalement. This suggestion is reinforced by the pattern of Rms/Rmd changes recorded over time in control cells (Fig. 5B). Cells that showed an increase in Rms/Rmd (5 of 9 motoneurons), presumably because of an improvement in the electrode penetration, hyperpolarized by >2 mV over the course of the recording. The converse was also observed (2 cells). For the remaining two control cells, the change in Rms/Rmd was small (<25%) and this was associated with little change in membrane potential (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).
Effect of cesium on 0
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 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).
Effects of cesium on Gk and Gda
The combination of effects of cesium on membrane potential, RN, Rms/Rmd, and 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).
Estimates of GDa of motoneurons recorded with potassium acetate electrodes and motoneurons injected with cesium were similar (1.26 ± 1.25 × 107 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.
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The estimates of GDa indicated that the depolarization and the increase in Rms/Rmd and RN seen over the course of the cesium injections cannot be attributed to changes in the quality of electrode impalement. Evidence linking these changes to a decrease in GK is shown in Fig. 7. In control cells there was a close correlation between GK and membrane potential (Fig. 7A; r2 = 0.74), GK increasing with depolarizations from 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.
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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; 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.
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As described earlier, one of the factors that did not change was 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).
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DISCUSSION |
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; 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.
Applicability of somatic shunt model
The somatic shunt model places several constraints on the electrical and morphological properties of the neuron (Durand 1984; 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.
There is widespread evidence that a step of hyperpolarizing current will activate a slow positive inward current, Ih, that manifests itself in the slow sag of the voltage response (Bayliss et al. 1994; 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.
The results of the present study indicate that hyperpolarizing current steps will deactivate voltage-dependent potassium channels over most of the subthreshold voltage range. Thus a fast positive inward current will be superimposed on the hyperpolarizing current injections. The effect of this current on the voltage response and, thus, estimates of electrotonic parameters, is not known. However, simulations employing somatic shunt models or compartmental models based on the geometry of reconstructed neck motoneurons with Hodgkin-Huxley-type potassium channels on the soma demonstrate that a reduction in the density of potassium channels always leads to an increase in Rms/Rmd and a decrease in GK (Rose, unpublished observations). More importantly, simulations of compartmental models of reconstructed neck motoneurons with a uniform distribution of potassium channels indicate that Rms/Rmd decreases when potassium channel density is reduced uniformly, opposite to the results reported in this study. Although these simulations also show that the absolute values of many of the electrotonic properties may be in error, they demonstrate that deactivation of potassium channels by hyperpolarizing current steps does not alter the ability of the somatic shunt approximation and associated techniques to detect a block of voltage-dependent potassium channels on the cell soma.
It is unlikely that Ih- and voltage-dependent potassium channels are the only channels that will be affected by either the current steps used to measure electrotonic structure or the changes in membrane potential caused by electrode damage and/or block of voltage-dependent potassium channels by cesium. Although a persistent sodium current has not yet been found on spinal motoneurons (Safronov and Vogel 1995), 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.
Morphological evidence from many studies indicates that the dendritic trees of motoneurons in general, and neck motoneurons in particular, do not satisfy two key constraints characteristic of the equivalent cylinder approximation; first, motoneuron dendrites are not cylindrical, instead, they taper between branch points; and second, unlike the equivalent cylinder model, dendrites of motoneurons terminate at different electrotonic lengths (Barrett and Crill 1974; 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
Abstract
Introduction
Abstract
