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Sobell Department of Neurophysiology, Institute of Neurology, Queen Square, London, UK

	Abstract

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Threshold variability of single human motor axons was studied by delivering 0.1 ms constant current stimuli of randomly varied intensity over the ulnar nerve at the elbow, and recording all-or-none potentials from flexor carpi ulnaris. In nine normal subjects, a single unit was tested with 8–11 000 stimuli at intervals of 0.5 s. After allowing for slow changes in excitability, the probability of excitation was in all cases well fitted by a cumulative Gaussian function. The relative spread (RS) of thresholds (S.D./mean) averaged 1.65 ± 0.26% (mean ±S.D., n= 9). When threshold was tested 20 ms after the start of a polarizing current, RS increased on depolarization and decreased on hyperpolarization. The product RS x mean threshold also increased on depolarization, especially when threshold was reduced by more than 50%. When the mean was reduced by 90%, RS increased above 50% and the axon sometimes fired spontaneously. Threshold variability was simulated by a computer model of a single node of Ranvier, in which the variability arose because of the stochastic behaviour of nodal sodium channels. The observed values of RS, and potential dependence of RS, were well modelled by a node with 60 000 sodium channels, of which about 1% were modelled as persistent sodium channels. Threshold variations in the model at resting potential were not primarily due to fluctuations in the state of the node before the stimulus was delivered, but rather to the variable activation of channels by the stimulus pulse. On depolarization, however, current through (mainly persistent) sodium channels caused appreciable fluctuations in membrane potential, which increased RS and the probability of spontaneous firing.

(Received 24 May 2004; accepted after revision 20 July 2004; first published online 22 July 2004)
Corresponding author H. Bostock: Sobell Department, Institute of Neurology, Queen Square, London, WC1N 3BG, UK. Email: h.bostock{at}ion.ucl.ac.uk

	Introduction

Top Abstract Introduction Methods Results Discussion References

 
The threshold current required just to excite an axon in a steady state is not a constant quantity but appears to fluctuate from moment to moment. While stimuli that are large enough will always excite, and those that are small enough never will, there is a grey area in between where stimuli sometimes excite the axon and sometimes do not. This ‘threshold range’ has been reported to be as great as 10% of the mean threshold for human motor fibres (Bergmans, 1970). The indeterminate nature of the threshold was interpreted by Verveen (1961) as due to ‘threshold fluctuations’, and his terminology has been followed by later authors, although, as we will see later, it is somewhat misleading. Verveen also coined the term ‘relative spread’ (RS) as the coefficient of variation of the threshold (standard deviation/mean). In a detailed theoretical analysis, Lecar & Nossal (1971) estimated the contributions to threshold fluctuations from various sources of noise, and concluded that variation in sodium conductance was probably the most important factor. Using this theory, and estimates of single channel data from sodium current fluctuations measured in frog nodes, Sigworth (1980) was able to account quantitatively for Verveen's threshold fluctuations. After single channel sodium currents had been recorded directly by patch clamping, Clay & DeFelice (1983) simulated the behaviour of a population of up to 640 sodium channels, opening and closing independently with voltage-dependent kinetics, and showed how they could give rise to fluctuations in excitability. This model was extended by Rubinstein (1995) to nodes containing as many as 32 000 channels, with kinetics as described by Schwarz & Eikhof (1987) for rat nodes. Different ways of computing action potential generation with stochastic sodium channels have been published by Chow & White (1996) and Fox (1997). Mino et al. (2003) concluded that Chow and White's method was the most computationally efficient one that was accurate.

These recent advances in modelling have not been matched by data from real axons. In particular, there is very little information available on threshold variability in human motor axons, although an increasingly popular clinical technique for motor unit number estimation (MUNE) is based on threshold fluctuations. In ‘statistical’ or ‘Poisson’ MUNE (Henderson et al. 2003) the mean size of motor units is estimated from the variance in compound muscle action potential (CMAP) amplitude at three fixed stimulus intensities. This variance depends, among other factors, on the variation in threshold of individual axons, since without threshold fluctuations there would be no variance in CMAP amplitude. However, the properties of threshold fluctuations, and how their alteration in disease might affect the results of statistical MUNE have not been explored.

In this study, the pattern of threshold variability in normal single human motor units is recorded, and also how this pattern changes when axons are depolarized or hyperpolarized. The results are compared with a stochastic model of nodal excitability. Since subthreshold behaviour in human axons has been shown to be best explained by a small fraction of ‘persistent’ sodium channels (Bostock & Rothwell, 1997), such non-inactivating channels, activating at relatively hyperpolarized potentials, were incorporated into the stochastic model, and help account for the threshold fluctuations observed and their dependence on membrane potential.

	Methods

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Human nerve recording

The relationship between relative spread and membrane potential was studied in nine healthy volunteers, aged 24–54 years, with their informed consent and the approval of the National Hospital of Neurology and Neurosurgery and Institute of Neurology Joint Research Ethics Committee.

The ulnar nerve was stimulated at the elbow through a non-polarizable stimulating electrode (Red Dot, 3M Canada Inc., London, Ontario, Canada) with a larger anode 5–15 cm proximal (Fig. 1). Stimuli were generated by a purpose-built isolated current source with a maximal output of 50 mA, driven by an IBM 486DX computer, running modified QTRAC software (©Institute of Neurology, written by H.B.). Surface recording electrodes (Dantec, Medtronic, Inc., Minneapolis, MN, USA) were placed over flexor carpi ulnaris, and current pulses of 0.1 ms duration were delivered to the nerve. The stimulus intensity and positions of the stimulating and recording electrodes were adjusted manually until a single motor unit was isolated. The program delivered a pseudo-random pattern of stimulus intensities around the mean threshold intensity so that a stimulus–response curve for the axon could be well defined. The signal from the muscle was amplified and filtered by an isolated EMG amplifier before being digitized by an analogue to digital converter (DT2812-A, Data Translation Inc., Marlboro, MA, USA). The program then determined whether an action potential occurred using a simple window set by the experimenter. The effect of slow changes in the excitability of the axon, due to changes in temperature and other factors, was removed by tracking the mean threshold throughout each experiment. Threshold measurements were then normalized to this control threshold. Skin temperature was monitored periodically and remained > 32°C for all subjects.

View larger version (19K): [in this window] [in a new window]   Figure 1.  Schematic diagram of recording arrangement The computer generated a stimulus waveform, which was delivered to the ulnar nerve via a digital-to-analog converter (DAC) and an isolated voltage-to-current converter. The stimuli were 0.1 ms depolarizing pulses, some of which were superimposed on 40 ms depolarizing or hyperpolarizing currents. All-or-none motor action potentials were recorded from flexor carpi ulnaris, amplified, digitized by an analog-to-digital converter (ADC) and recorded by the computer. Stimulating and recording sites were adjusted to record an all-or-none muscle action potential (MAP) with a threshold current well below that of the next most excitable unit.

View larger version (20K): [in this window] [in a new window]   Figure 3.  Effect of membrane polarization on threshold variability Above left: time course of complete experiment in which threshold fluctuations were recorded at 3 levels of depolarization and 3 levels of hyperpolarization, with 3 stimulus conditions tested in turn: unpolarized, depolarized and hyperpolarized. Above right: expanded plot of 1 min of experiment to show individual stimuli and responses. A, amplitude of polarizing current. B, intensity of 0.1 ms test stimuli superimposed on polarizing currents at 20 ms. C, response amplitudes, plotted separately for each stimulus condition, showing that same unit was tested throughout the experiment. D, response probability for the intermediate level of depolarization () and hyperpolarization () between 29 and 49 min, collected in bins of 2% of mean threshold. The dashed curves are fitted cumulative Gaussians, corresponding to RS of 4.45% (depolarized) and 1.15% (hyperpolarized).

Model of threshold fluctuations

To model the threshold fluctuations, we modified a recent electrical model of a node of Ranvier, which provided a good description of the subthreshold excitability properties of human motor axons (Bostock & Rothwell, 1997). The deterministic and continuously variable transient and persistent sodium permeabilities (P_Na, P_Nap) were replaced by ones made up of the contributions of large numbers of single channels, each operating independently and probabilistically. However, because it is very time consuming to simulate the behaviour of each channel separately, as was done by Rubinstein (1995), we instead simulated the changes in distribution of channels between possible gating states, as was done by Chow & White (1996), since according to the modified Frankenhaeuser-Huxley kinetics used (Frankenhaeuser & Huxley, 1964), two channels in the same state and at the same membrane potential are indistinguishable. The number of distinguishable gating states for transient sodium channels in this model is 8, which can be described by the parameters H= 0–1, M= 0–3, according to the number of h and m gates open, respectively, with only the state H= 1, M= 3 conducting. (Note that each channel is controlled by 4 gates, and each gate can be either open or closed, so there are 16 different combinations, but since the m gates are indistinguishable, there are only 8 distinct states.) The state of the population of channels can therefore be defined by the numbers of channels in each of the 8 states, and the change in state of this population with time can be obtained by calculating the numbers of channels moving between each of the 8 states during each small time interval. Similar considerations apply to the persistent sodium channels, except that since they are assumed not to inactivate, only 4 states (M= 0–3, H= 1) are required.

The numbers of channels of the model node in different gating states was represented by the array N_chan (Z,H,M,S), where Z= 0 or 1 for transient or persistent Na⁺ channels, H and M are the number of h and m gates open, and S is the time step. The initial state (S= 0) was set by dividing the available channels (N_t, number of transient channels; N_p, number of persistent channels) into all possible states according to the probability of a channel being in that state. Thus the initial number of open transient channels =N_chan(0,1,3,0) =m³hN_t, where m and h are the probabilities of m and h gates being open at rest. In general,

(1)

where ₃C_M is the number of combinations of three different things, taking M at a time, i.e. 3!/(M!(3 –M)!).

The probabilities are calculated from the steady-state equations (Hodgkin & Huxley, 1952):

(2)

(3)

where the rate constants are given by:

(4)

(5)

(6)

E is the membrane potential and the constants A, B, C at 32°C (see Table 1) were calculated from Schwarz et al. (1995). A similar set of equations was used for the persistent sodium current, except that h was fixed at 1, the voltage dependence (B) was shifted 20 mV in the hyperpolarizing direction, and the rate constants (A) were reduced by a factor of 2 (see Table 1; cf. Bostock & Rothwell, 1997).

Once the number of channels in each state is determined one can calculate the nodal membrane current and hence the change in membrane potential. The complete set of equations used, modified where necessary from those in Schwarz et al. (1995), is listed here for convenience. The standard parameter values are listed in Table 1.

Membrane currents

The total ionic membrane current (I_total) is made up of contributions from transient and persistent sodium channels (I_Nat, I_Nap), fast and slow potassium channels (I_Kf, I_Ks) and the leakage current (I_leak):

(8)

where

(9)

(10)

(11)

(12)

(13)

and the potassium currents are simulated as in Schwarz et al. (1995), i.e.

(14)

(15)

(16)

(17)

where the rate constants are given by:

(18)

(19)

Membrane potential

The membrane potential was preset to a starting value, either the resting potential (–84.5 mV) or an arbitrarily depolarized or hyperpolarized potential, by adjusting E_leak so that I_total= 0. Thereafter, I_total was calculated, and the membrane potential E(S) at time St was derived by simple integration:

(20)

Model parameters

The numerical values used in the standard model are listed in Table 1. The number of sodium channels at a large mammalian node of Ranvier is not well established. Recent values in the literature vary between about 25 000 (Shrager et al. 1985) and 82 000 (Chiu, 1980). We followed the previous studies (Schwarz et al. 1995; Bostock & Rothwell, 1997) in representing the channels by a permeability of 3·5 x 10^–9 cm s^–1, so as to retain an accurate representation of subthreshold behaviour. However, a patch clamp study of human nodes indicated that single sodium channel currents follow a linear I–V relationship, at least at negative potentials, with a conductance of 13–14 pS (Scholz et al. 1993). In order to give the sodium currents the correct granularity near the threshold of spike initiation, we chose N, the total number of nodal sodium channels to be 60 000. This figure corresponds to a single-channel conductance of 13 pS at –60 mV and 32°C.

A time step of 1 µs was used for all the results presented. The model was allowed to run for a prestimulus period (normally 1 ms) after initialization before the stimulus current was applied for 0.1 ms, and a poststimulus period of up to 3 ms. The simulation was stopped when the membrane potential passed through a predefined trigger level of –20 mV (i.e. an action potential occurred) or when it returned to baseline (no action potential occurred). The program, which was written in Borland Delphi, routinely performed 1000 simulations of the nodal response to each current stimulus, to obtain a reliable estimate of response probability.

	Results

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Observations on human axons

Form of the stimulus–response probability relationship.  For each of the nine subjects, at least 2500 stimuli were delivered without polarizing currents, with the stimuli distributed symmetrically over the range of mean ±ca 2 S.D.. In Fig. 2, a 10 min section of stimuli and response amplitudes are illustrated in panels A and B, while panels C and D show results from the whole experiment. For all subjects, stimulation and recording sites could be found such that an unambiguous all-or-none muscle action potential response could be recorded from flexor carpi ulnaris (e.g. MAP in Figs 1 and 2B). The stimuli were normalized by conversion to a percentage of mean threshold, and the response probability calculated at 1% intervals (Fig. 2D). For all subjects, the data were well fitted by a cumulative Gaussian distribution. The goodness of fit was shown (a) by the fact that the 95% confidence limits for the mean probability at each 1% interval all bracketed the expected value, and (b) that a ² goodness of fit test for each subject indicated that the deviations from the theoretical curve were no greater than expected by chance. The P value for the data and fitted curve in Fig. 2D was 0.94, and in all cases was not less than 0.06. This result was expected according to Verveen's data (Verveen et al. 1967) from frog nodes, and from Rubinstein's (1995) stochastic model. The non-Gaussian distributions previously reported for human motor fibres by Bergmans (1970) and Brown & Milner-Brown (1976) therefore probably resulted from drift in mean thresholds, which was not allowed for in their methods. A skew distribution would be expected if two or more nodes were equally likely to be excited, but our data indicates that this is not normally the case. Since the stimulus–response probability function was always Gaussian, the threshold variability could be fully described by expressing the standard deviation of the Gaussian function as a percentage of the mean threshold, i.e. the relative spread (RS). RS for the data in Fig. 2D was 1.73%, and varied between subjects from 1.29 to 2.12%, with a mean of 1.65 ± 0.26% (mean ±S.D.).

View larger version (19K): [in this window] [in a new window]   Figure 2.  Part of an experimental recording showing stimuli, responses and calculated threshold distribution Top two plots show stimulus (A) and response (B) amplitudes over a period of 10 min. Stimuli are distributed symmetrically and pseudo-randomly around the mean threshold level, which was constantly tracked throughout the experiment, while responses show all-or-none behaviour of single unit. Bottom two plots show number of stimuli in bins of width 1% mean threshold (C), and fraction of stimuli in each bin that excited the unit (D). The dashed curve is a fitted cumulative Gaussian distribution, and the vertical lines are 95% confidence limits for the mean of the observed fraction. In this example, 2521 stimuli were delivered over 63 min, and the fitted Gaussian corresponded to a relative spread (RS) of 1.73%.

Figure 3D illustrates the threshold distributions and fitted cumulative Gaussian functions for the depolarized and hyperpolarized recordings between 29 and 49 min. It is clear that hyperpolarization reduces and depolarization increases RS. This was first reported by Verveen (1961) for single frog nodes of Ranvier. He also reported that the product of RS and threshold remained constant, implying that the absolute level of the threshold fluctuation is unaffected by membrane polarization. Accordingly, we defined normalized threshold (NT) as (threshold)/(resting threshold), and in Fig. 4A and B multiple estimates of both RS and RS x NT are plotted against NT for seven levels of polarization for a single subject. It is seen that the product RS x NT is only approximately constant for hyperpolarization, and increases several-fold on depolarization. Similar results were obtained from the other subjects, as shown in Fig. 4C. One subject had greater threshold fluctuations at rest, and these increased more than normal on depolarization. The computer model below suggests a possible reason for this observation.

View larger version (12K): [in this window] [in a new window]   Figure 4.  Effects of membrane polarization on threshold variability A, plot of RS against normalized threshold (i.e. threshold/resting threshold) for single subject. Threshold variability increases steeply when thresholds are halved by depolarization. B, same data replotted as RS x normalized threshold, to show change in absolute range of thresholds. C, data as in B for one motor unit in each of 9 different subjects.

View larger version (19K): [in this window] [in a new window]   Figure 5.  Effect of strong depolarizing current on threshold variability A, small dots indicate threshold for 40 ms depolarizing current that excites unit on about 10% of occasions, determined by asymmetric threshold tracking. Large dots: intensity of 0.1 ms test stimuli, superimposed on alternate depolarizing currents. B, responses to the 40 ms depolarizing currents alone, showing small proportion of stimuli above threshold. C, responses to depolarizing + test stimuli. D, numbers of stimuli, collected in bins of width 20% of mean threshold. E, proportion of stimuli that excited the unit, and fitted cumulative Gaussian, corresponding to a relative spread of 58%. Error bars indicate 95% confidence limits of the mean, as in Fig. 2D. The threshold distribution remains Gaussian, even though there is an appreciable probability of the unit firing without a test stimulus.

Model results

The behaviour of the standard model (i.e. –84.5 mV resting potential, 60 000 Na⁺ channels, 1% persistent) is illustrated in Fig. 6. Figure 6A shows the response probability as a function of stimulus amplitude, and Fig. 6B shows the superimposed responses to 10 stimuli at the level of the mean threshold (1.049 nA). As described by Rubinstein (1995), the response probability is well fitted by the cumulative Gaussian function (smooth curve in Fig. 6A). As also described by Rubinstein (1995), threshold variability is approximately inversely proportional to the square root of the number of Na⁺ channels (RS 1/N), if P_Na, the total Na⁺ permeability, is kept constant. The RS of 1.66 is close to the mean of the experimental data (1.65). We have used this model to explore the potential dependence of the threshold fluctuations, and the likely contribution of persistent sodium channels (Na_p). We have also used the model to clarify the origin of the threshold fluctuations.

View larger version (20K): [in this window] [in a new window]   Figure 6.  Threshold and membrane potential variability in model node A, probability of response of standard model, with 1% persistent sodium channels, at resting potential of –84.5 mV. Fitted curve is cumulative Gaussian with RS of 1.66%. B, membrane potentials of standard model for 10 stimuli of identical intensity, corresponding to mean threshold of 1.049 mA, showing variable response waveforms.

View larger version (13K): [in this window] [in a new window]   Figure 7.  Variation of threshold fluctuations with polarization in the model node Plot of RS x normalized threshold against normalized threshold, as in Fig. 4C, for standard model with 0, 1 and 2% persistent sodium channels at different resting potentials. Threshold variability increases with depolarization in a similar way to real motor axons, and a small percentage of persistent sodium channels make a large contribution to the variability.

View larger version (12K): [in this window] [in a new window]   Figure 8.  Relationship of excitability characteristics to membrane potential in the model node Summary of changes in threshold (A), threshold variability (B), and variability in membrane potential as a function of mean membrane potential (C). Note logarithmic scale for RS in (B).

To distinguish between the three sources of variability, we tested the effect of (a) removing the fluctuations in membrane potential by clamping the resting potential, and (b) removing the fluctuations in gating states and membrane potential by applying the stimulus at time zero, before the channels had time to be redistributed between the 8 gating states. (At time zero the number of channels in different gating states were preset to their average values.) Figure 9 illustrates the relationship between RS and NT for these three models. At normal and hyperpolarized resting potentials the effects of clamping the resting potential or gating states is small, so that most of the response variability occurs after the stimulus is delivered (3rd mechanism). On depolarization, however, the effects of clamping the membrane potential becomes more and more prominent, until by the time spontaneous activity starts, the membrane potential fluctuations play a major role.

View larger version (20K): [in this window] [in a new window]   Figure 9.  Origin of threshold variability in model node This plot indicates the contribution of membrane potential fluctuations to RS, since this contribution is removed by clamping the node at the resting potential until the stimulus is given (dotted lines). It also indicates the contribution of variations in the gating states of the sodium channels, by additionally preventing those (dashed lines). The majority of the threshold variability remains and arises from variations in the responses of the channels to the stimulation.

	Discussion

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The experimental results are satisfactorily accounted for by a stochastic model of a single node of Ranvier, in which 60 000 sodium channels are allowed to redistribute every microsecond between the 8 distinct Hodgkin-Huxley gating states. This model differed from that of Rubinstein (1995) in a number of respects, the most significant being that the ion channel parameters were based on data from human rather than frog nodes, and that a small percentage of persistent sodium channels was added, as previously shown necessary to model the subthreshold behaviour of human motor axons (Bostock & Rothwell, 1997). The model also provided a prestimulus period that allowed spontaneous fluctuations in the resting membrane potential to contribute to the threshold variability.

Nodal selection

One assumption of the modelling was that the excitation of a human motor axon normally takes place at the same node or Ranvier, so that it was only necessary to model the behaviour of the channels at a single node. This assumption was based on the extensive observations of Bergmans (1970), who pioneered the study of single human motor axons by surface stimulation. He found (a) that ‘a single motor axon can be activated from a rather large range of positions of the electrodes on the nerve trunk (up to 3 cm)’ and (b) that the ‘latency is identical (within 0.1 ms) at all locations where the nerve fibre can be activated’. He concluded that excitation takes place at preferred sites (nodes) for anatomical reasons. If excitation were equally likely at 2 (or n) nodes, then the threshold stimulus that excited the unit on 50% of occasions would be the stimulus that excited each node with probability 1 –0.5 (or 1 –ⁿ0.5), RS would be reduced, and the threshold distribution would become skewed, since the chances of a stronger than threshold stimulus exciting none of the nodes would be less than the chances of a correspondingly weaker than threshold stimulus exciting one of the nodes. Our observation that the threshold distributions are very well fitted by the (non-skewed) cumulative Gaussian function provides further evidence that only a single node is involved in the excitability measurements.

A related question is whether the selection of low threshold units by surface stimulation may have biased the results in some way. This is possible, but Bergmans (1970) found that these units were distributed over the full range of velocities of alpha motor axons, and as discussed above he concluded that the units are selected primarily by anatomical accident, rather than by axonal size or membrane properties. Also, when Bostock & Baker (1988) made the first recordings of threshold electrotonus, they used single motor axons selected by surface stimulation as in this study: the waveforms recorded, which are extremely sensitive to membrane potential (Kiernan & Bostock, 2000) were not noticeably different from those later derived from compound muscle action potential recordings (Bostock et al. 1998).

Just as other excitability properties have been found to vary between different sites on the same nerve (Mogyoros et al. 1999; Kuwabara et al. 2000), or between related sites on different nerves (Kuwabara et al. 2000), it is quite likely that threshold variability will also be found to depend to some extent on the particular axonal site tested, but we have no reason to suppose that the present results will not be found representative.

The contribution of persistent sodium channels to threshold variability

One result of the modelling, that a small percentage of persistent sodium channels can have a large effect on the threshold fluctuations, is not surprising, since they strongly affect other excitability properties (Bostock & Rothwell, 1997). This does, however, have interesting implications for sensory fibres. The strikingly different strength-duration and latent addition properties of human motor fibres and cutaneous afferents (Mogyoros et al. 1996; Panizza et al. 1994) were well modelled by the hypothesis that sensory fibres have 2.5% as against the motor fibres' 1% persistent sodium channels (Bostock & Rothwell, 1997). This hypothesis, combined with the properties of threshold fluctuations revealed by this study, could explain a puzzle about ectopic impulse generation in human nerves. During ischaemia, motor and sensory fibres increase in excitability to a similar degree, as measured by the changes in stimulus required to evoke a constant fraction of the compound motor or sensory action potential (Bostock et al. 1994). Measurements of mean threshold could not therefore account for the familiar observation that cutaneous afferents are much more likely to discharge ectopically during ischaemia, causing paraesthesiae, than are motor axons to discharge causing fasciculations. Figure 7 predicts that reducing the threshold by 25% with depolarization will increase RS to a much higher level for a sensory node with 2.5% persistent sodium channels than for a motor node with 1%, and it is a high level of RS, rather than a low level of mean threshold, that is the critical factor for the initiation of ectopic discharges.

The new results similarly help explain the effectiveness of hyperventilation in inducing paraesthesiae (Mogyoros et al. 2000). Hyperventilation, like ischaemia, causes a marked increase in strength-duration time constant, and the slow component of latent addition, indicating an increased activation of persistent sodium channels, but unlike in ischaemia this occurs without membrane depolarization (Mogyoros et al. 1997). This is presumably related to the marked increase in ‘late’ sodium currents recorded in vitro as pH increases (Baker & Bostock, 1999). Hyperventilation, like ischaemia, therefore increases RS, both by reducing the mean threshold and increasing the activation of persistent sodium currents.

From threshold variability to ectopic impulses

Recent reviews of the genesis of ectopic impulses in axons (Mogyoros et al. 2000; Baker, 2000) have concentrated on two periodic mechanisms: a ‘flip-flop’ mechanism involving regenerative potassium currents, as first proposed for postischaemic motor axons (Bostock et al. 1991), and a more sinusoidal ‘pacemaker’ mechanism, associated with demyelination, and involving persistent sodium currents and slow potassium currents (Baker & Bostock, 1992; Kapoor et al. 1997). The present study, showing how increasing resting sodium channel activity in normal motor axons increases threshold variability and can lead to spontaneous activity, provides an additional mechanism for ectopic impulse initiation. Such activity is intrinsically aperiodic, since it depends on the stochastic behaviour of a large population of sodium channels (Chow & White, 1996). However, depending on membrane potential, periodic activity might still result because of the sequence of excitability changes that follow an action potential (Bergmans, 1970; Mogyoros et al. 1996). Spontaneous activity would only be expected to approximate a purely random distribution of interspike intervals (i.e. exponential, comparable to radioactive decay) in axons depolarized to eliminate superexcitability, and with RS increased to the point that impulses occur at intervals much longer than the relative refractory period. This situation may obtain in the distal parts of human motor axons in amyotrophic lateral sclerosis, where spontaneous fasciculations arise at long and irregular intervals (Hjorth et al. 1973; Layzer, 1994).

In conclusion, this paper documents threshold variability in normal human motor axons, and shows how this increases progressively with membrane depolarization until it can be sufficient to initiate spontaneous impulses. This behaviour is well explained by a mathematical model in which the threshold variability results from the stochastic behaviour of nodal transient and persistent sodium channels. At normal resting potentials, the previously used term ‘threshold fluctuations’ can be misleading, since most of the threshold variability in the model is not related to fluctuations in the state of the node before a stimulus is given, but to the variable activation of sodium channels on stimulation. However, fluctuations in resting potential become significant when resting sodium currents are increased sufficiently for spontaneous discharges to occur.

	References

Top Abstract Introduction Methods Results Discussion References

 
Baker MD (2000). Axonal flip-flops and oscillators. Trends Neurosci 23, 514–519.[CrossRef][Medline]

Baker M & Bostock H (1992). Ectopic activity in demyelinated spinal root axons of the rat. J Physiol 451, 539–552.[Abstract/Free Full Text]

Baker MD & Bostock H (1999). The pH dependence of late sodium current in large sensory neurons. Neuroscience 92, 1119–1130.[CrossRef][Medline]

Bergmans J (1970). The Physiology of Single Human Nerve Fibres. Vander.

Bostock H & Baker M (1988). Evidence for two types of potassium channel in human motor axons in vivo. Brain Res 462, 354–358.[CrossRef][Medline]

Bostock H, Baker M & Reid G (1991). Changes in excitability of human motor axons underlying post-ischaemic fasciculations: evidence for two stable states. J Physiol 441, 537–557.[Abstract/Free Full Text]

Bostock H, Burke D & Hales JP (1994). Differences in behaviour of sensory and motor axons following release of ischaemia. Brain 117, 225–234.[Abstract/Free Full Text]

Bostock H, Cikurel K & Burke D (1998). Threshold tracking techniques in the study of human peripheral nerve. Muscle Nerve 21, 137–158.[CrossRef][Medline]

Bostock H & Rothwell JC (1997). Latent addition in motor and sensory fibres of human peripheral nerve. J Physiol 498, 277–294.[Abstract/Free Full Text]

Brown WF & Milner-Brown HS (1976). Some electrical properties of motor units and their effects on the methods of estimating motor unit numbers. J Neurol Neurosurg Psychiatry 39, 249–257.[Abstract]

Chiu SY (1980). Asymmetry currents in the mammalian myelinated nerve. J Physiol 309, 499–519.[Abstract/Free Full Text]

Chow CC & White JA (1996). Spontaneous action potentials due to channel fluctuations. Biophys J 71, 3013–3021.[Abstract/Free Full Text]

Clay JR & DeFelice LJ (1983). Relationship between membrane excitability and single channel open-close kinetics. Biophys J 42, 151–157.[Abstract/Free Full Text]

Fox RF (1997). Stochastic versions of the Hodgkin-Huxley equations. Biophys J 72, 2068–2074.[Abstract/Free Full Text]

Frankenhaeuser B & Huxley AF (1964). The action potential in the myelinated nerve fiber of xenopus laevis as computed on the basis of voltage clamp data. J Physiol 171, 302–315.[Free Full Text]

Henderson RD, McClelland R & Daube J (2003). Effect of changing data collection parameters on statistical motor unit number estimates. Muscle Nerve 27, 320–331.1002/mus.10325[CrossRef][Medline]

Hjorth RJ, Walsh JC & Willison RG (1973). The distribution and frequency of spontaneous fasciculations in motor neurone disease. J Neurol Sci 18, 469–474.1016/0022-510X(73)90140-8[CrossRef][Medline]

Hodgkin AL & Huxley AF (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117, 500–544.[Free Full Text]

Kapoor R, Li Y-G & Smith KJ (1997). Slow sodium-dependent potential oscillations contribute to ectopic firing in mammalian demyelinated axons. Brain 120, 647–652.[Abstract/Free Full Text]

Kiernan MC & Bostock H (2000). Effects of membrane polarization and ischaemia on the excitability properties of human motor axons. Brain 123, 2542–2551.[Abstract/Free Full Text]

Kuwabara S, Cappelen-Smith C, Lin CS, Mogyoros I, Bostock H & Burke D (2000). Excitability properties of median and peroneal motor axons. Muscle Nerve 23, 1365–1373.1002/1097-4598(200009)23:9\|[amp ]\|#60;1365::AID-MUS7\|[gt ]\|3.3.CO;2-T[CrossRef][Medline]

Layzer RB (1994). The origin of muscle fasciculations and cramps. Muscle Nerve 17, 1243–1249.[CrossRef][Medline]

Lecar H & Nossal R (1971). Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing. Biophys J 11, 1048–1067.[Abstract/Free Full Text]

Mino H, Rubinstein JT & White JA (2003). Comparison of algorithms for the simulation of action potentials with stochastic sodium channels. Ann Biomed Eng 30, 578–587.10.1114/1.1475343[CrossRef]

Mogyoros I, Bostock H & Burke D (2000). Mechanisms of paresthesias arising from healthy axons. Muscle Nerve 23, 310–320.1002/(SICI)1097-4598(200003)23:3\|[amp ]\|#60;310::AID-MUS2\|[gt ]\|3.0.CO;2-A[CrossRef][Medline]

Mogyoros I, Kiernan MC & Burke D (1996). Strength-duration properties of human peripheral nerve. Brain 119, 439–447.[Abstract/Free Full Text]

Mogyoros I, Kiernan MC, Burke D & Bostock H (1997). Excitability changes in human sensory and motor axons during hyperventilation and ischaemia. Brain 120, 317–325.[Abstract/Free Full Text]

Mogyoros I, Lin C, Dowla S, Grosskreutz J & Burke D (1999). Strength-duration properties and their voltage dependence at different sites along the median nerve. Clin Neurophysiol 110, 1618–1624.1016/S1388-2457(99)00087-5[CrossRef][Medline]

Panizza M, Nilsson J, Roth BJ, Rothwell J & Hallett M (1994). The time constants of motor and sensory peripheral nerve fibers measured with the method of latent addition. Electroencephalogr Clin Neurophysiol 93, 147–154.1016/0168-5597(94)90078-7[CrossRef][Medline]

Rubinstein JT (1995). Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophys J 68, 779–785.[Abstract/Free Full Text]

Scholz A, Reid G, Vogel W & Bostock H (1993). Ion channels in human axons. J Neurophysiol 70, 1274–1279.[Abstract/Free Full Text]

Schwarz JR & Eikhof G (1987). Na currents and action potentials in rat myelinated nerve fibres at 20 and 37 degrees C. Pflugers Arch 409, 569–577.[CrossRef][Medline]

Schwarz JR, Reid G & Bostock H (1995). Action potentials and membrane currents in the human node of Ranvier. Pflugers Arch 430, 283–292.[CrossRef][Medline]

Shrager P, Chiu SY & Ritchie JM (1985). Voltage-dependent sodium and potassium channels in mammalian cultured Schwann cells. Proc Natl Acad Sci U S A 82, 948–952.[Abstract/Free Full Text]

Sigworth FJ (1980). The variance of sodium current fluctuations at the node of Ranvier. J Physiol 307, 97–129.[Abstract/Free Full Text]

Verveen AA (1961). The influences of certain conditions on the fluctuations in excitability of the frog node of Ranvier. Acta Physiol Pharmacol Neerl 4, 294–295.[Medline]

Verveen AA, Derksen HE & Schick KL (1967). Voltage fluctuations of neural membrane. Nature 216, 588–589.[CrossRef][Medline]

	Acknowledgement

 
C.S.-Y.Lin is supported by a C.J. Martin Fellowship.

Author's present address
J. P. Hales: Prince of Wales Medical Research Institute UNSW, Randwick, Sydney, New South Wales, Australia.

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