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Conceived and designed the experiments: RWB JH. Performed the experiments: RWB. Analyzed the data: RWB. Contributed reagents/materials/analysis tools: RWB SD. Wrote the paper: RWB.

The authors have declared that no competing interests exist.

In neurons, spike timing is determined by integration of synaptic potentials in delicate concert with intrinsic properties. Although the integration time is functionally crucial, it remains elusive during network activity. While mechanisms of rapid processing are well documented in sensory systems, agility in motor systems has received little attention. Here we analyze how intense synaptic activity affects integration time in spinal motoneurons during functional motor activity and report a 10-fold decrease. As a result, action potentials can only be predicted from the membrane potential within 10 ms of their occurrence and detected for less than 10 ms after their occurrence. Being shorter than the average inter-spike interval, the AHP has little effect on integration time and spike timing, which instead is entirely determined by fluctuations in membrane potential caused by the barrage of inhibitory and excitatory synaptic activity. By shortening the effective integration time, this intense synaptic input may serve to facilitate the generation of rapid changes in movements.

Spike timing in nerve cells is determined by temporal integration of synaptic potentials and intrinsic response properties. However, little is known about the timescale of this integration during functional network activity and how it is affected by synaptic events. In the absence of synaptic input the spike afterhyperpolarization (AHP) determines spike timing during repetitive firing. In motoneurons (MNs), the frequency range of this firing is well suited for force regulation in the muscle fibers they innervate

On the other hand, the AHP and other slow intrinsic properties would impede rapidly changing motor responses and it is not known how resilient they are to a noisy background of synaptic activity. Recent evidence suggests that intrinsic response properties may be shunted by synaptic conductance in cortical and sub-cortical networks _{m}) in both MNs and interneurons during spiking

For this reason, we have conducted experiments on spinal motoneurons embedded in a functionally active network during fictive motor behavior. In earlier studies the conductance increase in motoneurons during fictive locomotor and scratch network activity was first measured in vivo in the cat

We measured the effective integration time in MNs during network activity using a novel statistical approach that quantified the V_{m}-fluctuations before and after the action potential. Three temporal features were characterized: the membrane time-constant, _{m}-distribution following a spike to return to the pre-spike condition, i.e. how long it takes the cell to “forget” that a spike has occurred. We report eRT as short as 4 ms during network activity, which is more than a 10-fold decrease compared with quiescent network. Our results show that even prominent intrinsic response properties like the AHP are severely attenuated concurrent with increase in synaptic conductance. For this reason, the contribution of synaptic activity and active membrane properties to network dynamics can only be captured by a conductance-based model

(A). Red top trace: Model with constant current injection, no other input. Black middle trace: Model with added current noise with same mean current as in top trace. Blue bottom trace: Model with same mean injected constant current and noise stemming from fluctuating conductance. (B). Spike triggered superimposed spikes. Red, black (n = 243) and blue (n = 72) traces are averages of spikes from (A). Notice the current-noise average closely overlap the no-noise trace (red) whereas the conductance-noise average (blue) rapidly reach pre-spike V_{m}-level (see arrow), because of increase in total conductance. (C) and (D) illustrate the statistical quantification of the evolution of V_{m} before and after the spike for traces in (B). A template distribution of V_{m} traces is chosen at an arbitrary time prior to the spike (see arrow at t_{template}) for which the distribution at the rest of the time points is compared with. The outcome of comparison is shown as the KS-test trace below, 1 represents acceptance and 0 represents rejection of the hypothesis that they are different. Below is shown the P-values for the KS test. The distribution of V_{m} in (C) is different everywhere, whereas the distribution in (D) is only different up to and immediately after the spike. The time it takes to regain the pre-spike distribution following the spike is referred to as

The question we ask is how the surge in conductance from intense synaptic bombardment during network activity modifies intrinsic properties exemplified by the spike AHP and shrinks response time and integration time of the neuron. The sensitivity of spike generation and spike pattern to conductance is illustrated in simulations in a simple model (_{m} (blue trace,

For the purpose of making these statements applicable to quantitative evaluation of experimental data, we developed statistics to capture the temporal features of V_{m} before and after the spike. We define two measures linked to the superposition of spikes (_{m}-levels. Notice that both eRT and eSIT are absent in current noise model whereas they are present in the conductance noise model (cf.

To evaluate whether the neuronal integration time and AHP are substantially affected during intense network activity we measured eSIT and eRT in MN during scratching. The data set consisted of more than 10.000 spikes in 185 scratch epochs in 17 MNs. The analysis is organized as follows. First, we estimated the conductance increase in a sub-sample of MN to confirm that strong synaptic components were present (_{m}-fluctuations at different levels of synaptic activity. Since intensity of synaptic activity may vary among cells, we compared the eRT with indicators of input, i.e. the effective membrane time constant as well as the smallest inter-spike interval (ISI) for each MN. Finally, since the functional expression of AHP accumulation in motoneurons is spike frequency adaptation (SFA)

(A) Cutaneous stimulation via sinusoidal movements of a glass rod on the hind-limb pocket skin. (B) Electro-neurogram from hip flexor nerve. (C) V_{m} from intracellular recording. Tick mark indicates V_{m} of −100 mV. (D) Current pulses of −0.7 nA from constant current level of −1.0 nA. (E) High-pass filtered V_{m} from (C) (cut off is 2 Hz). Transient artifacts removed. (F) left, average voltage deflections from (E) during quiescence (n = 14), right during network activity (n = 14). The average increase in conductance is 340%. Notice the occurrence of two spikes. (G) The membrane conductance as a function of time. The peak conductance during network activity is >800% of the conductance during quiescence.

A scratch epoch was induced by rhythmic cutaneous stimulation of the skin in the hind-limb pocket and the concurrent synaptic conductance (

Motoneuron number | G_{quiescence} [nS] |
G_{active} [nS] |
Fraction [100%] |

2 | 73 | 320 | 438 |

3 | 45 | 181 | 405 |

10 | 71 | 224 | 314 |

13 | 20 | 40 | 200 |

14 | 55 | 258 | 470 |

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 _{template}, well before the spikes (arrows _{template} as long as it was at least 10 ms prior to the spike (

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 _{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)).

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 _{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, _{template} earlier than ∼20 ms (_{template} (_{template}. We chose to calculate the mean eRT over the range 20 ms<t_{template}<40 ms.

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 _{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.

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 (_{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 (_{m}-decay times after injected current pulses (_{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} _{eff} with this technique are listed in Data and Methods 1 in _{m} did not obey an OU-process (_{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 (

(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.

The effective synaptic integration times, the effective recovery times and the effective membrane time constants across the population of neurons are listed in _{eff} and the effective AHP (see above). However, the population average of τ_{eff} was _{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 ^{2} = 0.81), the eRT and the eSIT both had significant correlation with τ_{eff} (_{eSIT}^{2} = 0.60, p = 0.0007, R_{eRT}^{2} = 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.

(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 _{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.

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 (

The AHP contributes to spike frequency adaptation (SFA) in motoneurons at rest _{N} plotted against ISI_{N+1} displayed a ring-like pattern (^{2} = 0.17) as expected from AHP-mediated adaptation (

(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 _{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

The firing pattern in MNs during scratching was qualitatively different (_{N} and ISI_{N+1} was marginal (R^{2} = 0.03) (

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

Spike timing, the principal output of neurons, is determined by interacting synaptic and intrinsic ionic conductances. Recent decades have provided a wealth of information about the intrinsic response properties and their proposed roles in specific cell types in many parts of the nervous system

This transition has previously been referred to as a transition from temporal integration to coincidence detection in sensory perception

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

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

The role of AHPs in repetitive firing in MNs induced by depolarizing current through the recording electrode has been thoroughly investigated _{m} _{m}-fluctuations may have important computational roles

Though anatomical evidence suggests an approximate balance between inhibitory and excitatory contacts in cat motoneurons

All the experiments were performed in an integrated spinal cord-carapace preparation from the adult turtle except the heuristic control experiment of NMDA-induced spike frequency adaptation in

Red-eared turtles (_{3}; 2 MgCl_{2}; 3 CaCl_{2}; and 20 glucose, saturated with 98% O_{2} and 2% CO_{2} 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

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).

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.

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”

The data used to illustrate the difference between synaptic-current and synaptic-conductance based fluctuating inputs (^{2+} conductance and a Ca^{2+}-activated K^{+}-conductance. The synaptic noise was modeled as white current noise in the current-based regime with the heuristic expression,^{2+}-conductance were not shown here for simplicity (for complete description see _{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 _{syn}) is so large that it can no longer be considered small compared with the G_{total} _{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:_{Syn}_{AHP}^{2+}- 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 (

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}(t_{1}), is different from the distribution at a later point in time, P_{v}(t_{2}), then there has been a change in the intrinsic current generation (cf. _{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)

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 (_{m}(t) and V_{m}(t_{template}) were drawn from the same distribution. The binary test outcome was plotted (

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 _{m} (

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

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 (

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 (

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 _{N} and ISI_{N+1}, ISI_{N+2}, ISI_{N+3} etc (_{N}, ISI_{N+1})-pairs _{N} = ISI_{N+1}. If the number of points above was within a standard deviation of

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 (_{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 (

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Thanks to Jens Midtgaard for carefully reading an earlier version of the manuscript.