Synaptic conductance

A scratch epoch was induced by rhythmic cutaneous stimulation of the skin in the hind-limb pocket and the concurrent synaptic conductance (Figure 2A, B) was estimated from the voltage deflections to injected current pulses (Figure 2C–F) for a subset of MN. Conductance due to action potentials is a potential source of error in these measurements [25]. We therefore avoided spikes by injecting a steady hyperpolarizing current (typically −2 nA) or selected a part of the scratch episode without spikes. The pair of spikes in Figure 2F was left in for illustration, but the sweep was not included in the final estimate. Even with this conservative approach, the estimated conductance increased 2–5 times during scratching (table 1 and Figure 2G)[9]. We attribute this increase to balanced inhibitory and excitatory synaptic input [13] and conclude that temporal processing in MNs could be affected by synaptic conductance during network activity.

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Table 1. Total input conductance for 5 MN during both quiescence and active network.

https://doi.org/10.1371/journal.pone.0003218.t001

Effective synaptic integration time

We first considered the V_m-statistics prior to spikes. The time of the earliest statistical sign of depolarization prior to action potentials we dub “the effective synaptic integration time” (eSIT). This depolarization may be caused by a rise in excitatory conductance or a fall in inhibitory conductance. For each cell, the eSIT was estimated by comparing a template distribution of V_m with distributions of V_m as a function of time prior to action potentials, as in figure 1. The comparison was attained using a KS-two-sample test at each point in time (method, Figure 3). The template distribution was chosen at a time, t_template, well before the spikes (arrows Figures 3A and B). The eSIT did not depend systematically on the choice of t_template as long as it was at least 10 ms prior to the spike (Figure 3C) even though the number of samples in the distribution decreased (Figure 3D).

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Figure 3. Effective recovery time and synaptic integration time during scratching.

Peri-spike V_m distribution in quiescence (A) (n = 50) and during scratching (B) (n = 29). Top, superimposed data traces (gray) with mean V_m in black. Middle, KS-test. Bottom, P-values for the KS test. The effective synaptic integration time (eSIT) and effective recovery time (eRT), defined as the time periods before and after the spike, in which the V_m distribution is significantly different from a template distribution (arrows), i.e. gray areas in the KS-graphs in the middle. P-vaules of the test is plotted below. (C) Estimates of eSIT and eRT versus position of the template distribution relative to the spike from (B) (broken lines represent mean values eSIT = 12.1 ms, eRT = 8.7 ms). (D) The number of traces in template distribution decreases with window length (from same data as in (B) and (C)).

https://doi.org/10.1371/journal.pone.0003218.g003

Memory of a spike–eRT

The same statistical test was used to evaluate the impact of a spike by comparing the V_m-distribution after action potentials with template distributions well before the spike (arrow Figure 3B). In the graph of the KS-test, the gray area represents rejection of the null hypothesis that the V_m-distribution before and after the spike was statistically similar to the template distribution. When the V_m-distribution after the spike was indistinguishable from the template distribution, we considered the impact of a spike to have ceased (graph of P-values, Figures 3A and B). Both eRT and eSIT had no clear dependence on t_template earlier than ∼20 ms (Figure 3C). Since the number of spikes in the distribution decreased with t_template (Figure 3D) the eRT estimate should not be performed with a high t_template. We chose to calculate the mean eRT over the range 20 ms<t_template<40 ms.

Impact of τ_eff and AHP on recovery time

Right after the occurrence of an action potential V_m is hyperpolarized. The time it takes for V_m to re-polarize back to the level prior to the spike depends on the AHP and on the passive effective time-constant of the membrane, which we refer to as τ_eff. In our attempt to sort out which part of the re-polarization is due to the passive decay of V_m and which is due to the cessation of AHP conductance, it is important to estimate τ_eff during network activity. The increase in total conductance will also diminish the relative importance of the AHP conductance and the AHP will appear shorter. To quantify the vestige of the AHP under different levels of input conductance we define the effective After-Hyperpolarisation Period (eAHP). This period represents the time it takes until the AHP ceases to affect the V_m trajectory. If there is no overlap between the passive membrane decay and the eAHP, the eRT is just the sum of τ_eff and eAHP, while if there is overlap eRT will be less than the sum:

It is important to emphasize the eRT also represents the upper bound on both eAHP and τ_eff, i.e. eRT≥eAHP and eRT≥τ_eff. Hence, it was important to determine τ_eff for each cell in order to determine the contribution of AHP to the integration process.

Estimating τ_eff during activity

For the spinal motor activity we differentiated three situations: The quiescent state with little or no synaptic input; the on-cycle with motor nerve activity and spike activity in motoneurons; and the off-cycle, which is at the low point in between the on-cycles (Figure 4A–C). As expected the effective membrane time constant decreased significantly during scratching. For representative data, τ_eff was 27 ms in the quiescent state, while it was only 2.8 ms in the On-cycle and 5.2 ms in the off-cycle (Figure 4C–E). Membrane time constants during quiescence are ordinarily estimated from V_m-decay times after injected current pulses (figure S2). During the dynamic and intense synaptic input in the on-cycle and off-cycle, this method was both difficult and imprecise. Instead, if V_m is assumed to follow a stochastic process known as Ornstein-Uhlenbeck-process (OU-process), then maximum likelihood estimation would be the proper way to obtain τ_eff [26], [27]. The estimated values of τ_eff with this technique are listed in Data and Methods 1 in Data and Methods S1 and see Figures S1pone.0003218.s003–S3. It turned out that V_m did not obey an OU-process (Figure S4) and these estimates of τ_eff were systematically much higher than eRT and eSIT. Therefore, τ_eff was instead estimated empirically by fitting an exponential decay to the initial part of the auto-correlation sequence (Figure 4F). It was necessary to fit to the initial part (from 0 to 3 ms, vertical gray line) to assure that the auto-correlation lag was small compared to the total length of the sample (200 ms), since the premise of exponential decay is infinite-length of data trace (see Data and Method S1).

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Figure 4. Temporal characteristics of sub-threshold V_m-fluctuation in motoneurons during quiescence and in the on- and off-cycle during scratching.

(A) Hip-flexor nerve recording during scratch. (B) Concurrent V_m in MN, spikes avoided with −2.5 nA hyperpolarizing current. Shaded regions mark the selected area of on- and off-cycle illustration below. Sample trace of V_m in quiescence (C) (note time-course of spontaneous synaptic potentials) and in the on-cycle (D) and off-cycle (E). D and E are from the shaded boxes in B. (F) The auto-correlation sequence of each sample trace. Blue is from quiescent trace (C), gray is from the off-cycle trace (E), and red is the on-cycle trace (D). The effective time constant of each trace is obtained by fitting an exponential decay function (broken lines) to the initial 3 ms (until the vertical gray line). The time constants are τ_eff = 2.8 ms (on-cycle activity), τ_eff = 5.2 ms (off-cycle activity) and τ_eff = 27.0 ms (quiescence). C–E are on the same time scale.

https://doi.org/10.1371/journal.pone.0003218.g004

Temporal features for the population

The effective synaptic integration times, the effective recovery times and the effective membrane time constants across the population of neurons are listed in Figure 5A. The average eSIT was μ = 7.7±0.8 ms and the average eRT was μ = 7.5±0.7 ms (mean±SE, n = 17). The median of eSIT and eRT were both 7.7 ms. The eRT was assumed to be approximately equal to the sum of τ_eff and the effective AHP (see above). However, the population average of τ_eff was μ = 9.3±1.4 ms (mean±SE, n = 17) while the median of τ_eff was 7.0 ms. In some cases (41%, n = 7/17) τ_eff was longer than the corresponding eRT, which suggests two things. First, the reset potentials were closer to the steady state mean V_m than the natural fluctuations of V_m around the mean, so the decay from reset back to the mean was faster than τ_eff. Secondly, the eAHP was close to zero or no more than a couple of milliseconds. This value of eAHP is a dramatic decrease from the 200 ms AHP duration previously reported during quiescence [4], [24]. Further, not only did the population spread in eRT across cells correlate with the population spread in eSIT (R² = 0.81), the eRT and the eSIT both had significant correlation with τ_eff (Figure 5B) (R_eSIT² = 0.60, p = 0.0007, R_eRT² = 0.47, p = 0.005, when ignoring the two outliers, cell 7 and 16). Since eRT is dependent on both τ_eff and eAHP, while eSIT is only dependent on τ_eff, these strong correlations also indicate that the contribution of eAHP to eRT must be minor in most cells.

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Figure 5. Time constants across the population of MNs.

(A) The average τ_eff (for ON-cycle), eRT and eSIT (mean±SE) as triplets bars for each cell. Horizontal lines represent population averages, μ = 9.5 ms for τ_eff, μ = 7.5 ms for eRT, and μ = 7.7 ms for eSIT. Cell 3 is marked with a ★ and the sample cell used in figures 3, 4, 5. (B) eRT and eSIT plotted against τ_eff show significant correlation. The lines are linear least square fits. (C) The shortest ISI at zero current injection plotted against the average eRT for each MN. Gray line is where x = y.

https://doi.org/10.1371/journal.pone.0003218.g005

Hence, the population spread in eRT, eSIT, and τ_eff probably reflected different levels of synaptic intensity in different cells. Since the eRT is the major contribution to the refractory period, we expected most of the inter-spike intervals (ISI) to be longer than or equal to the eRT. If this is the case, the data points in a plot of the shortest ISI versus eRT in each cell should fall at the 45°-line or below. Indeed, all points were within their error bars or below (Figure 5C). In this way, the inverse of the eRT represents an upper bound for the spike frequency during network activity.

Absence of spike frequency adaptation

The AHP contributes to spike frequency adaptation (SFA) in motoneurons at rest [4], [24]. A classical example of SFA in absence of synaptic input is during bursting induced by N-Methyl-D-Aspartic acid (NMDA). We therefore performed a heuristic comparison between NMDA-bursting in MNs in slices with the bursting induced by synaptic input in functional networks (cf. Figures 6A and 6B). During each burst in the case of NMDA-bursting (Figure 6Aa), spike frequency peaked at onset and adapted to a lower level at the end of the burst (Figure 6Ab). The histogram of interspike-intervals confirmed similarity in firing rate distribution between NMDA-bursting and network bursting [28] (cf. Figure 6Ac and 6Bc). ISI_N plotted against ISI_N+1 displayed a ring-like pattern (Figure 6Ad), as expected from adapting spike trains in each successive burst [29]. Note that the vast majority of points (83%/17%, SE = 6%) are above the 45°-line, which is a consequence of SFA, presumably in large part produced by the prominent AHP. Under these conditions neighboring ISIs were significantly correlated (R² = 0.17) as expected from AHP-mediated adaptation (Figure 6Ae).

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Figure 6. Presence and absence of spike frequency adaptation (SFA) during bursting.

(Aa) SFA in intracellular recording from motoneuron in slice during NMDA induced bursting. (Ab) Single burst highlighted in (Aa) show gradual increase in ISI. (Ac) Histogram of ISI. The mean ISI is 55 ms (arrow). (Ad) Plot of ISI_N against ISI_N+1 shows significantly greater proportion of points above than below the ISI_N = ISI_N+1 line (83.2% above, total N = 239), which is evidence of spike frequency adaptation. In addition, ISIs are correlated with their neighbors (correlation coefficient = 0.41), as expected when ISI are influenced by AHP conductance and the burst pattern is reproduced after 10 spikes (Ae). Gray area represents the 5% confidence limit (Ba) Recording from a MN in a functional spinal network during rhythmic motor activity. (Bb) A hightligted cycle from (Ba) shows irregular spike times and no SFA. (Bc) Histogram of ISI. The mean ISI is 34 ms (arrow) (Bd) A plot of ISI_N against ISI_N+1 illustrates no discrepancy of points above and below the ISI_N = ISI_N+1 line (51.3% above, total N = 362), which demonstrates absence of SFA. Furthermore, there is only a marginal correlation of ISI with neighbors (correlation coefficient = 0.18), as expected with negligible AHP conductance (Be). Gray area represents the 5% confidence limit . Tick marks to the left represent −80 mV (A) and −60 mV (B). Inter-burst-intervals are omitted in analysis.

https://doi.org/10.1371/journal.pone.0003218.g006

The firing pattern in MNs during scratching was qualitatively different (Figure 6Ba). Though the distribution of ISI times resembled the NMDA-bursting (cf. Figure 6Bc and 6Ac), spike timing was irregular (Figure 6Bb) and points scattered nearly symmetrically around the 45°-line in the return map (51%/49%, SE = 6%) (Figure 6Bd). This shows that spike frequency acceleration was as prevalent as spike frequency adaptation during bursts [29] and therefore that the AHP and other intrinsic mechanisms for adaptation or acceleration in spike frequency did not have a detectable influence on the firing pattern during network activity. Furthermore, the correlation between ISI_N and ISI_N+1 was marginal (R² = 0.03) (Figure 6Be), which shows that spikes were driven by a stochastic process rather than by deterministic intrinsic properties. In all 17 motoneurons SFA was insignificant during depolarizing waves, i.e. the numbers above the line were not significantly higher than 50% (Figure 7). Thus, we conclude that the mechanisms causing SFA such as AHP accumulation were not pervasive enough to overcome the increase in synaptic conductance during motor activity.

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Figure 7. Spike frequency adaptation during NMDA induced bursts but absent during scratching.

The number of points above the ISI_N = ISI_N+1 –line in a ISI-return map (Figure. 7Ad and 7Bd) divided by the total number of intervals (×100%) for all MNs including the NMDA induced bursting data from slice experiment for comparison. The network induced bursting have little or no SFA since there is an even amount of points above as below. In contrast, the NMDA-activated bursting has a much larger fraction above the line reflecting the high degree of SFA. Error bars are , where K total number of ISI.

https://doi.org/10.1371/journal.pone.0003218.g007

Coincidence detection

This transition has previously been referred to as a transition from temporal integration to coincidence detection in sensory perception [33]. Konig and colleagues defined a coincidence detector as a neuron in which the integration time for synaptic potentials is short compared with the average ISI, and a temporal integrator if the reverse is true. Adopting this definition, the motoneurons in the present study were all coincidence detectors during motor activity, since their eSIT and eRT on average are an order of magnitude shorter than their average ISI (cf. Figure 5A and 6Bc, and see Figure S5). The functional effect and benefit of MNs working as coincidence detectors could be to minimize aberrant firing due to the background barrage of noisy synaptic input [28]. The potentially undesirable consequence of having such a coincidence detection scheme is irregular spike patterns, which we indeed did observe (Figure 6). However, irregular patterns are not likely to be a problem, since muscle fibers are slow integrators, and therefore the exact temporal structure of the MN firing, whether irregular and yet fast coincidence detectors or slow regular temporal integrators, is unimportant for securing a smooth contraction.

Origins of spike pattern

The network mechanisms underlying the phasic spike activity in motoneurons during rhythmic motor behaviors are unknown. It has been hypothesized that certain intrinsic properties are crucial mediators of bursting rhythms in spinal networks [3], [5], [34]. It is also widely accepted that the after-hyperpolarization in MN secures repetitive firing at low rates appropriate for regulation of muscle contraction [3], [4]. The high conductance state, however, compromises the ability to fire repetitively during steady depolarization [11]. This is probably a direct consequence of the reduced slow AHP since the same effect is observed when the AHP is reduced by blocking the underlying ionic current pharmacologically rather than by shunting [35]. Nevertheless, MNs still fired in a broad range of rates in the high conductance state while driven by rapid fluctuations in membrane potential during motor activity (Figure 6B) [13]. Further evidence for fluctuation driven irregular firing is the fact that the shortest ISIs in the active network are longer than the eRT (and thus eAHP) (Figure 6C). This is in contrast to the regular firing and frequency adaptation in motoneurons in slices during NMDA induced bursting (Figure 6A). The reduced AHP amplitude, increased spike time variability and the absence of adaptation during locomotor network activity have also been observed in MNs in the decerebrate cat [36]. In the light of our findings it will be interesting to investigate if the underlying mechanism is modulation of intrinsic properties [1], [24], [37] or parallel increase in excitatory and inhibitory synaptic activity [13], [38].

In conclusion, the rhythm-generation could have two origins: a pattern generating subset of neurons elsewhere in the network in which intrinsic response properties are protected from shunting by intense synaptic bombardment or alternatively, the motor rhythm can be an emergent distributed network phenomenon as suggested for respiratory rhythms [39], [40], i.e. the network bursting hypothesis. Decisive experimental tests of these hypotheses are still missing.

Caveats of constant current protocols

The role of AHPs in repetitive firing in MNs induced by depolarizing current through the recording electrode has been thoroughly investigated [4], [5], [24]. Based on the linear summation of synaptic potentials under certain experimental conditions [41], [42] this approach takes injected current as a simplifying representation of synaptic input. However, important aspects of synaptic input are overlooked in this approach. First, synaptic variability adds fluctuations as a second moment to V_m [22]. Synaptic V_m-fluctuations may have important computational roles [43]–[45]. Secondly, the effect of surge in conductance from synaptic input is unaccounted for in the constant current protocol (Figure 1). Therefore the functional role of the AHP and other intrinsic response properties should be assessed either in functional networks with real synaptic input, as in the present study, or by dynamic clamp analysis in neurons at rest [7], [8], [46] if a valid estimate of the temporal structure of the functional synaptic conductances is available.

Balanced state in the spinal cord

Though anatomical evidence suggests an approximate balance between inhibitory and excitatory contacts in cat motoneurons [4], the circuit substrate for variations in the balance of inhibition and excitation during motor activity and its prevalence in other spinal networks is yet unresolved. High-conductance states produced by parallel increase in inhibitory and excitatory synaptic activity is a common occurrence in other functional networks [6], [38], [47]–[51]. In the neocortex, the link between excitation and inhibition is provided by feed-forward and recurrent pathways [48], [49], [52]–[55]. In the spinal cord, recurrent inhibition is unlikely to contribute significantly to the high conductance state in MNs since recurrent collaterals are scarce in the turtle [56], [57] and Renshaw inhibition has not been documented. Feed-forward inhibition provided by Ia inhibitory interneurons can produce synaptic conductance that clearly reduces intrinsic response properties in cat MNs in vivo [58]. However, reciprocal inhibition contributes insignificantly to the high conductance state in MNs during breathing [38] and scratching [13]. We propose that inhibitory input to MN is mostly due to local feedforward inhibitory connections, but it remains to be seen if balanced spinal motor networks resemble architectures of the much better investigated networks in other parts of the nervous system [6], [38], [48], [51], [55].

Integrated preparation

Red-eared turtles (Trachemys scripta elegans) were placed on crushed ice for 2 hrs to ensure hypothermic anesthesia. Animals were killed by decapitation and blood substituted by perfusion with a Ringer solution containing (mM): 120 NaCl; 5 KCl; 15 NaHCO₃; 2 MgCl₂; 3 CaCl₂; and 20 glucose, saturated with 98% O₂ and 2% CO₂ to obtain pH 7.6. The carapace containing the D4-D10 spinal cord segments was isolated by transverse cuts and removed from the animals, similar to studies published elsewhere [19], [20]. The surgical procedures complied with Danish legislation and were approved by the controlling body under the Ministry of Justice.

Slice preparation

One mm thick slices of the turtle spinal cord were placed in a chamber for intracellular recording and submerged in and perfused with oxygenated Ringer solution. The pharmacological agent N-methyl-D-aspartate (NMDA) was added to the ringer medium to induce bursting activity (10 µM).

Recordings

Intracellular recordings in current-clamp mode were performed with an Axoclamp-2A amplifier (Axon Instruments, Union City, CA). Glass pipettes (part no. 30-0066, Havard Apparatus, UK) were pulled with a electrode puller (model P-87, Sutter instrument co., USA) and filled with a mixture of 0.9 M potassium acetate and 0.1 M KCl. Intracellular recordings were obtained from neurons in segment D10. Recordings were accepted if neurons had a stable membrane potential more negative than −50 mV. Data were sampled at 20 kHz with a 12-bit analog-to-digital converter (Digidata 1200, Axon Instruments, Union City, CA), displayed by means of Axoscope and Clampex software (Axon Instruments, Union City, CA), and stored on a hard disk for later analysis. Hip flexor nerve activity was recorded with a differential amplifier Iso-DAM8 (WPI) using a suction pipette. The bandwidth was 100 Hz–1 kHz.

Activation of network

Mechanical stimulation was performed with the fire polished tip of a bent glass rod mounted to the membrane of a loudspeaker in the cutaneous region known to elicit “pocket scratch” [12] which results in a broad activation of cells [59]. The duration, frequency, and amplitude of the stimulus were controlled with a function generator (Figure 2A). This tactile stimulus induced the scratch-like network activity, which was monitored by the suction electrode nerve recordings from the Hip-flexor nerve (Figure 2B).

Model data

The data used to illustrate the difference between synaptic-current and synaptic-conductance based fluctuating inputs (Figure 1) was based on a one-compartment model simulation [22] supplemented with Ca²⁺ conductance and a Ca²⁺-activated K⁺-conductance. The synaptic noise was modeled as white current noise in the current-based regime with the heuristic expression,where the fast conductances of the action potential and Ca²⁺-conductance were not shown here for simplicity (for complete description see Data and Methods S1) and the total membrane conductance waswhich contains no synaptic component. In this scheme, the synaptic input was represented as a current, I_syn. The membrane capacitance is C, and G_leak, E_leak, G_AHP, E_K are conductance and reversal potential of leak and AHP, respectively.

In a more realistic regime, the high intensity synaptic input was modeled as a conductance [22]. Here, the AHP was reduced as a consequence of the increase in total input conductance (Figure 1). The conductance-based regime applies when the synaptic conductance (G_syn) is so large that it can no longer be considered small compared with the G_total [6]. Heuristically expressed similar to the synaptic current modelwhere E_syn is the weighted reversal potential of excitatory and inhibitory synaptic reversal potentials and G_syn is the sum of both conductances. G_syn is competing with G_AHP in controlling inter-spike intervals, and if it is large enough it can render G_AHP insignificant at steady state:when G_Syn≫G_AHP. The action potentials were largely unaffected by the conductance increase, since fast Na/K conductances of the action potential were much larger. In a simple Hodgkin-Huxley-model added AHP- and Ca²⁺- conductances and including synaptic input as either current noise (I_syn = 12 nA, σ_syn = 3 nA, OU-simulated with time-constant = 1 ms and D = 0.0005) or conductance noise we verified the theoretical importance of synaptic conductance (Figure 1). The conductance noise was a mixture between inhibition and excitation balanced at −60 mV (see Data and Method S1 for details).

Evolution of V_m-distribution

The variable constituting the estimation of effective eSIT and eRT was the membrane potential (V_m). This variable was stochastic and a sample measurement drawn from an underlying probability distribution function (P_V), which we assumed had the same statistics in all interspike intervals. The probability distribution depends on time after occurrence of spike and this dependence was a manifestation of intrinsic current generators like SK-channels. Because of the large synaptic fluctuations, it was necessary to look at the distribution P_V instead of just isolated instances of V_m. These fluctuations were assumed uncorrelated from trial to trial, so we could estimate P_v by superimposing spikes.

The key assumption is, if the distribution at some given point in time, P_v(t₁), is different from the distribution at a later point in time, P_v(t₂), then there has been a change in the intrinsic current generation (cf. Figure 3A and B). We selected P_v at one point in time (t = t_template) as a template distribution, which all distributions P_V(t≠t_template) were compared with. The P_V(t_template) was chosen more than 10 ms before the spike, since this region constitute a background V_m, and was compared via the Kolmogorov-Smirnov-2 sample test (KS-test) [60] expressed formally as:

F(V, t) is the empirical cumulative probability distribution function of V_m. N is the total number of traces (and spikes) used to estimate the distribution at time t (Figure 3D). The maximal difference between the cumulatives, D(t), was the measure for rejecting or accepting the null hypothesis. If the difference was larger than a critical value, then we rejected the null hypothesis that V_m(t) and V_m(t_template) were drawn from the same distribution. The binary test outcome was plotted (Figure 3A and B) where 1 represented rejection (gray area) and 0 represented no rejection of null hypothesis, at a 5% confidence limit. The p-value of the test was plotted below.

Effective Recovery time

The first point in time after the spike, where the KS-test was zero (i. e. no rejection of hypothesis of same distribution) was where we defined the AHP conductance and other transient intrinsic current generators no longer had a significant impact on the V_m and the passive diffusive spread had reach steady state. We dubbed this period effective recovery time (eRT, arrow in Figure 3B) in analogy to the effective membrane resistance and effective membrane time constant [14], [16], [21], [22]. This recovery time told us how long time after the spike had occurred that there was still a memory of the spike in V_m (Figure 3B).

Effective synaptic integration time

Similar to eRT, we could ask how long time prior to the spike, that P_v was different from the template distribution. This point represented a net depolarization caused either by reduced inhibition or increased excitation. We named this period effective synaptic integration time (eSIT) indicating the time prior to the spike where its occurrence can be predicted (arrow in Figure 3B).

Location of template

Obviously, the choice of template distribution is important. The template is always chosen prior to the spike. The earlier before the spike we choose the template, the more independent it is. However, there is a trade off, since the inter-spike interval has to be longer than the window between the template distribution and the spike. As a result, the larger the window is, the fewer spikes in a finite dataset will participate in the distribution (Figure 3D). Fortunately, the estimation of both eRT and eSIT is largely independent on the window size (Figure 3C). We chose to average the values of eRT and eSIT from templates 20 to 40 ms prior the spike, since these locations gave nearly constant values (Figure 3C).

Critique of method

The above described statistical testing of the evolution of P_v only accounts for changes that are locked to the occurrence of a single action potential, such as the AHP. Accumulative events that build up over several spikes as e.g. spike frequency adaptation or plateau potentials are not easily accounted for using this statistics. One way to test for slow changes would be to divide the spikes according into several different groups depending on their position in the epoch. These groups could then be compared to evaluate if the distributions have changed. However, we decided this was outside the scope of the present study and it was not necessary since the test of spike frequency adaptation (Figure 6) came out negative.

Inter-spike interval analysis

The inter-spike intervals were extracted from the intracellular recording during scratch episodes and processed. The auto-correlations were calculated as the normalized covariance function [26], [61] between ISI_N and ISI_N+1, ISI_N+2, ISI_N+3 etc (Figure 6d). The test for spike frequency adaptation (Figure 6e) was performed assuming statistical independence of observation of (ISI_N, ISI_N+1)-pairs [29] and thus a binomial distribution with chance of 50% above and 50% below the line ISI_N = ISI_N+1. If the number of points above was within a standard deviation ofof the 50%-line, as expected from an even binomial distribution [61], there was no significant spike frequency adaptation. K is the total number of points and p is the probability of a point being above the line, when assuming no correlation.

Data processing

All analysis was performed in Matlab (version 7.3, Mathworks). The data was converted from Axoclamp format to matlab and the spikes were identified and superimposed (Figure 3) to study the V_m statistics before and after the spike as described above. KS-testing of the V_m distributions was done with the matlab procedure “kstest2.m”. The custom made procedures for calculating eRT and eSIT has been uploaded to mathworks code sharing web site (http://www.mathworks.com/matlabcentral/) with the name “eRT.m” for the interested reader. The remaining matlab code is available on request.