According to the classical view, axons are seen as conduction cables that reliably transmit action potentials (APs) between synaptically connected neurons in a digital (all-or-none) fashion (Hodgkin and Huxley, 1952). However, more recently, a growing body of evidence suggest that a more refined view of axonal conduction might be appropriate. A number of experimental and modeling studies provided insights into different mechanisms that might fine-tune information processing in mammalian axons, and, thereby, affect synaptic transmission (Debanne, 2004; Bucher and Goaillard, 2011; Debanne et al., 2011; Sasaki et al., 2011). It has been shown that a modest increase in the somatic membrane potential of presynaptic cortical neurons leads to a proportional increase in the amplitude of axonal action potential (Shu et al., 2006). An increase in the AP amplitude facilitated synaptic release and increased the average amplitude of the postsynaptic potential (Shu et al., 2006; Alle and Geiger, 2006). In addition, it was found that gating dynamics of voltage-gated ion channels can regulate the length of axonal AP waveforms and, thereby, modulate the synaptic release. For example, slow inactivation of voltage-gated K⁺ channels in mossy fiber boutons was found to mediate activity-dependent broadening of APs during high-frequency neuronal activity, which facilitated synaptic transmission (Geiger and Jonas, 2000). Contrary to a classical notion that information flows from the dendritic membrane toward the axon terminals, parallel patch-clamp recordings from soma and axons revealed that axons possess a certain level of functional independence from the presynaptic input. Thus, for example, during gamma oscillations of pyramidal cells, ectopic APs were found to be generated in the distal axon but did not invade the soma (Dugladze et al., 2012). Moreover, it has been shown that hippocampal interneurons can share the output across a coupled network of axons and can respond with persistent firing even in the absence of input to the soma or dendrites (Sheffield et al., 2011).

Moreover, the temporal precision with which APs arrive at a neurons’ synapses is essential for encoding and computing neural information (Rieke, 1999). E.g., cortical neurons are specialized to detect coincident arrival of APs on the order of milliseconds (Stuart and Häusser, 2001). In contrast, theoretical studies suggest that ion channel noise (Hodgkin and Huxley, 1952; Clay and DeFelice, 1983; White et al., 2000) introduces random variability in axonal AP waveforms (Neishabouri and Faisal, 2014), decreases the temporal precision of AP propagation (Faisal and Laughlin, 2007), and compromises the reliability of the conduction itself (Faisal and Laughlin, 2007; Skaugen and Walløe, 1979; Strassberg and DeFelice, 1993; Rubinstein, 1995; Schneidman et al., 1998). Taken together, the role of these effects for neural information processing are not yet well understood, and clarification of their exact influence will require experimental access to individual APs across entire axonal arbors.

Mainly due to methodological limitations to track individual APs across multiple sites of mammalian axons, it was not yet possible to record the temporal evolution of a single AP throughout entire axonal arbors. Whole-cell patch-clamp of axonal blebs (Shu et al., 2006), boutons (Alle and Geiger, 2006), or the Calyx of Held (Forsythe, 1994) enables recording of individual axonal signals, however, the technique is invasive and limited to recording from a single site. Axon-attached patch clamp allows for experimental access to intact axons and enables simultaneous recordings from two axonal sites, but stable recording is only possible for less than 60 min and with success rates of ∼50% (Sasaki et al., 2012). Owing to the small diameter of neocortical axons (0.08 to 0.4 µm diameter) (Debanne et al., 2011), classical electrophysiological tools, such as patch clamp, cannot be used to spatially track the propagation of action potentialat more than a couple sites. Over the past decades, optical microscopy techniques and application of fluorescent indicators, sensitive to voltage (Peterka et al., 2011) or calcium (Grienberger and Konnerth, 2012), have become popular means for recording electrical activity from neuronal processes in invertebrates (Stepnoski et al., 1991; Fromherz and Müller, 1994; Antić and Zecević, 1995; Zecević, 1996; Antic et al., 2000) and vertebrates (Antic et al., 1999; Antic, 2003; Djurisic et al., 2004; Kampa and Stuart, 2006; Palmer and Stuart, 2006; Canepari and Vogt, 2008; Djurisic et al., 2008; Acker and Antic, 2009; Palmer and Stuart, 2009; Holthoff et al., 2010; Foust et al., 2010; Popovic et al., 2011; Popovic, 2015). Advances in optical electrophysiology techniques (Popovic, 2015; Lin and Schnitzer, 2016) contributed to accumulating a body of knowledge about neuronal functions (Popovic, 2015): voltage-sensitive-dye-based techniques enabled the imaging of individualaction potential propagating into axon collaterals of Purkinje cells, although the cells remained viable for only a few seconds of total illumination (Popovic et al., 2011); fluorescence resonance energy transfer (FRET)-based genetically encoded voltage indicators (GEVI) (St-Pierre et al., 2015) allowed for tracking of APs with high temporal fidelity (Chanda et al., 2005; Wang et al., 2010; Ghitani et al., 2015); (FRET)-based GEVIs targeted at mammalian axons (Wang et al., 2012; Ma et al., 2017) enabled to discern axonal APs from the background noise after averaging 10 recording trials (Ma et al., 2017). However, optical techniques did not yet provide sufficient temporal resolution and signal quality that would allow for the reliable detection of single individual APs in mammalian axons over longer periods of time.

In the present study, we present a method to noninvasively record individual axonal APs in rat cortical neurons cultured over complementary-metal-oxide-semiconductor (CMOS) –based high-density microelectrode arrays (HD-MEAs) (Frey et al., 2010). We use template matching to detect individual axonal APs by combining the simultaneously recorded signals from multiple electrodes. We show recordings of individual APs as they propagate across hundreds-of-micrometer-long-cortical axons at high spatiotemporal resolution. Using the developed method, we measure (I) latencies and temporal precision of AP initiation in response to extracellular voltage stimulation; (II) temporal precision of arrival times of individual APs as they propagate along axonal branches; (III) gradual changes in velocities and temporal precision of propagating APs during high-frequency neuronal activity. We use live imaging to assign the measured extracellular electrical activity to the morphology of individual neurons in the network.

We recorded cultures of neurons from rat cortex using a state of the art HD-MEA system (Frey et al., 2010) (see Figure 1—figure supplement 1). Owing to the low-noise recordings provided by our CMOS-based HD-MEAs, averaging over multiple recordings of a single neurons’ APs allows for discerning small-amplitude axonal signals from the background noise (Bakkum et al., 2013; Müller et al., 2015; Radivojevic et al., 2016). However, the reliable detection of single axonal APs is needed to investigate the consistency, reliability and precision of axonal conduction, as averaging across multiple APs removes the AP-to-AP variability. Nevertheless, we found that a single axonal AP can be observed if the very same AP is recorded simultaneously on several neighboring electrodes. The detectability of axonal APs can be further improved by combining the signals recorded from multiple electrodes via a matched filtering technique, which we will refer to throughout this work as ‘template matching’. In brief (see Materials and methods section for details), the method works by first establishing the prototypical waveform of a neurons’ or axons’ AP, called its template, on each recording electrode. A multi-electrode filter is then computed from a multi-electrode template that is optimally matched to the individual electrode templates (Franke et al., 2015). The filter is then convolved with each (non-averaged) period of recorded data and is analyzed for the presence, or absence, of the neuron’s or axon’s AP (Franke et al., 2015). If the AP is present, the filter will give a large response that is detected by thresholding (see Figure 2a). To estimate the template, we first performed a set of recordings and analytical steps in order to electrically identify axonal arbors of individual neurons within cell cultures of cortical neurons. For this purpose, the high-spatial-resolution of our electrode arrays facilitated ‘spike sorting’ of extracellular APs which was used for identifying individual neurons and their axons (Franke et al., 2015; Jäckel et al., 2012). Furthermore, the applied techniques enabled the electrical identification of the respective axon initial segments (AIS), which co-localize with the largest-amplitude and first-emerging extracellular AP traces (Figure 2—figure supplement 1a) (Radivojevic et al., 2016).

Spatiotemporal distribution of average extracellular APs captures electrical activity across an entire neuron

For each neuron presented in this study, we used spike-triggered averaging, triggered by the strong extracellular signals recorded close to the neuron’s AIS, to capture the neuron-wide AP propagation (Figure 1a) (Müller et al., 2015; Radivojevic et al., 2016). After each spike detected at the AIS, we recorded a 10 ms time window on all electrodes that we refer to as a ‘single trial’. As only 126 of the array’s 11,011 electrodes can be read out at the same time, for each neuron, we recorded its spontaneous extracellular activity by scanning ~200 different configurations of recording electrodes, in 2 min recordings per configuration, covering the entire array. All ~200 electrode configurations had a small number of electrodes in common. These electrodes were located close to the neurons’ AIS and were used for spike detection. For each electrode configuration, we averaged 40 single trials to compute the single-electrode templates. The set of all single-electrode templates provided an array-wide spatiotemporal distribution of the extracellular APs, referred to as an AP ‘footprint’ or ‘electrical image’ (Figure 1a). The presented footprint spread over 1200 electrodes. Averaging of 40 trials per electrode was needed in order to discern small-amplitude APs of axons and proximal dendrites (Bakkum et al., 2013; Müller et al., 2015; Radivojevic et al., 2016). Reconstructed waveforms of averaged signals recorded in different neuronal regions are presented in the four insets of Figure 1a. Neuronal morphology was revealed by lipofection. For details on spike-triggered averaging and lipofection of individual neurons in the network, see the Materials and methods section.

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We found a strong dependence between average AP amplitudes on a given electrode and the Euclidean distance of the electrode to the neuron’s AIS only within a 100 µm radius. Euclidean distance refers to the geometric distance between the electrode that recorded the largest-amplitude AP waveform and the respective recording electrode. The average decrease in amplitude was ~350 µV at a distance of 100 µm from the AIS. However, we did not find strong decrease in amplitudes over distances between 100 to 1,400 µm from the AIS, showing that distal axonal branches produced similar signals as more proximal branches. Average AP amplitudes varied across an axonal arbor (from ~3 to ~100 µV) independently from the distance of the recording site to the AIS (Figure 1b). For the corresponding analysis, we reconstructed AP footprints of 20 neurons (from 18 different preparations) and extracted average AP amplitudes recorded by 26,925 electrodes in total. The spatial profile of the extracellular AP amplitudes is presented in Figure 1b. Examples of AP traces and noise recordings are presented in Figure 2—figure supplement 1a.

Detection of single AP trials across an entire neuron

We used template matching to detect APs within individual trials recorded across the entire neuron. To estimate our capability to detect individual APs in single axonal branches, we used the strong signal on the electrodes close to the AIS as a ground truth of the presence of a given AP. We then tried to detect the same AP independently, only relying on the recording of groups of neighboring electrodes located close to an axonal branch, using several detection strategies: either thresholding individual electrodes or template matching using one, or groups of three or six neighboring electrodes (see Figure 2 and example in Figure 2—figure supplement 1b). In general, we used multiple electrodes to independently detect signals that propagated across an individual axonal branch. This enabled us to discriminate detection errors (i.e., some of the electrodes along a branch do not detect an AP) from possible conduction failures (i.e., none of the electrodes along a branch or axonal segment detects an AP). Template matching strongly improved the detection performance as compared to single electrode thresholding and allowed for detecting a single AP simultaneously and independently in multiple axonal branches with high precision (>90% detection performance). In general, reliable detection of large APs, recorded near the AIS, can be attained by using a simple amplitude threshold set to 5σ_noise (Quiroga et al., 2004) (Figure 2—figure supplement 1a). However, a simple threshold is inadequate to detect the much smaller APs from axonal arbors, leading to omitted spikes if a high threshold is used, or to false positives due to noise crossing a low threshold.

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Performances pertaining to separability of the signal from the noise using template-matching-based detection and simple threshold-based detection are compared in Figure 2a. In this example, three neighboring electrodes near an axonal terminal are used to detect axonal spikes. For each electrode, the template matching filter was convolved with the raw data. While the filtering on individual electrodes provided sufficient signal-to-noise ratio for a reliable detection of higher amplitude APs within noisy data (see filter output per electrode in Figure 2a), low-amplitude APs buried within the noise might still be missed by the detection, even after template matching. Detection of small-amplitude APs could be facilitated by constructing a multi-electrode filter from templates captured over a local group of neighboring electrodes (Franke et al., 2015), which further improved detection performance (see filter output from three electrodes in Figure 2a).

We compared performances of the different detection strategies across the entire neuron and found significantly better detectability rates, when template-matching -based detection was used (Figure 2b). For the simple threshold-based detection on raw data, recordings from each electrode were treated independently, and the threshold was set to 5σ_noise.

To demonstrate the performance of simple threshold-based detection and template-matching -based detection (using inputs from one, three and six neighboring electrodes) over Euclidean distances of recording sites from the soma or AIS, we compared percentages of electrodes that could be used to identify individual APs (Figure 2c). Data used for this analysis was obtained from 20 neurons and 23,423 electrodes in total. The grids in Figure 2—figure supplement 1b illustrate how electrodes were grouped for the template-matching -based detection.

So far, we only characterized the detection performance in terms of correct detection or misses (false negatives). To assess the fraction of false-positive detections of the template-matching -based technique, trials with APs were mixed with ‘noise trials’ that have been recorded during inactive neuronal states in a 2:1 ratio (40 AP trials and 20 noise trials per electrode). The false-positives were then expressed as percentage with respect to the total number of detections per electrode (or group of 3 or six electrodes). We found that false-positive detection was generally less than 5%, whereas an increase in the number of electrodes used for template matching (from 1 to 6) reduced the false-positive detections to ~3% (Figure 2—figure supplement 1c). Despite the fact that 40 AP trials were mixed with 20 noise trials, template matching did not yield any false-negative detections in this analysis.

Precise detection of AP occurrence times

We used template-matching-based detection to extract occurrence times of axonal APs, triggered by extracellular stimulation at the AIS, and we were able to measure neuronal activation latencies caused by different stimulation voltages (Figure 3). We selectively stimulated a neuron near the AIS by using positive-first bi-phasic voltage pulses (see Materials and methods section) and we recorded the triggered responses from the axonal arbor of the same neuron (Figure 3a). We chose the AIS as a reference stimulation site because, in comparison to other neuronal sites, it requires the lowest voltage for effective and selective activation of individual neurons in the network (Radivojevic et al., 2016). A range of voltages (between ±40 and ±80 mV, stepped by ±10 mV) was used to stimulate the neuron. Each voltage was randomly applied 40 times at 1 Hz using the same stimulation electrode. We then recorded stimulation-triggered responses from 25 electrodes placed along a segment of an axonal arbor (Figure 3a). Recorded traces (40 trials per stimulation voltage; 200 trials in total) were temporally aligned with respect to the downswing of the stimulation pulses (Figure 3b, first column). The alignment between successive triggered AP waveforms then depended on the promptness and on the temporal precision of the neuronal responses to extracellular stimulation (see below). As supra- and sub-threshold voltages were used to stimulate the neuron, the triggered recordings included evoked APs (Figure 3b, second column) and stimulation failures, i.e., situations in which no AP was elicited in the neuron (Figure 3b, third column).

Figure 3

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We were able to extract precise arrival times of the elicited APs with respect to the downswing of respective stimulation pulses at each electrode location. Precise detection of AP arrival times was possible, because the peak of the filter output was found to be a robust estimate of the true temporal position of the AP within the raw data (Franke et al., 2015). However, the extracted arrival times represent the result of the summation of two different time spans: (I) the timespan needed for neuronal activation in response to extracellular stimulation (referred to as activation latency) and (II) the timespan needed for an elicited AP to propagate from the stimulation site to the respective recording site (referred to as AP propagation time). To show the activation latencies that have been obtained by applying different stimulation voltages, the APs, triggered by a given voltage, were aligned with respect to the peaks of their filter outputs (Figure 3b, fourth column). The temporal shift of the spikes in this alignment procedure reflects its activation latency (larger latencies for smaller stimulation voltages).

Increase in the stimulation voltage decreases the latency and increases the precision of neuronal activation

We investigated the effect of stimulation voltage amplitudes on the arrival times of the triggered APs (Figure 4a–d) and found that an increase in the stimulation voltage decreases neuronal activation latency (Figure 4c) and, at the same time, increases temporal precision of the activation itself (Figure 4d). To obtain the data for this analysis, individual neurons were stimulated near their AIS, and the triggered APs were recorded from the proximal part of the neuron’s axon (Figure 4a). We selected recording electrodes at ~100–500 µm distance from the stimulation site in order to avoid interference of the stimulation artifact with the recorded APs (Radivojevic et al., 2016). We used stimulation voltages between ±10 and ±300 mV, with steps of ±10 mV, in order to reconstruct precise excitability profiles across a broad range of stimulation voltages (Figure 4b). The different stimulation voltages were applied at 1 Hz in a randomized sequence, using the same stimulation electrode near the AIS. We stimulated 60 times with each voltage. Stimulation-triggered APs were captured by up to three recording electrodes near the proximal part of the axon. In order to obtain good signal quality, we chose electrodes that exhibited comparably large signal-to-noise ratio and used template-matching-based detection to distinguish elicited APs from activation failures. The minimum voltage that triggered an AP in 100% of the stimulation trials was defined as the stimulation threshold (Figure 4b). We assigned the obtained excitability profiles to three categories: (I) a sub-threshold regime included stimulation voltages that did not activate the neuron in any of the trials; (II) an intermediary regime included stimulation voltages that were lower than the threshold, but activated the neuron in at least one trial; (III) a supra-threshold regime included stimulation voltages that activated the neuron in 100% of the trials (Figure 4b).

Figure 4

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To analyze the effect of the stimulation voltage on the neuronal activation latency and activation precision, we first extracted the arrival times of the APs elicited by different voltage magnitudes (Figure 4a). The arrival time represents a summation of the activation latency and the propagation time between the stimulation and recording site. Therefore, to calculate activation latencies, we subtracted the estimate of the propagation time from the measured arrival times (see Materials and methods section for details). Using this calculation, we obtained a range of activation latencies for stimulation voltages within intermediate and supra-threshold regimes (Figure 4c). We averaged over 60 trials per stimulation voltage (N = 8 neurons from eight different preparations) to obtain AP arrival times and to obtain the estimates of the propagation time.

To analyze the effect of the stimulation voltage on the jitter of the neuronal activation, we first expressed the jitter of the AP arrival time as the standard deviation of arrival times for the respective voltage magnitudes. The jitter of the AP arrival time represents a summation of the neuronal activation jitter and the AP propagation jitter. Therefore, to calculate the jitter of the neuronal activation, we subtracted the estimate of the AP propagation jitter from the jitter of the AP arrival times (see Materials and methods section for details). We used 60 trials per voltage (N = 8 neurons from eight different preparations) to calculate jitters of AP arrival times and to obtain the estimate of the propagation jitter.

In order to demonstrate changes in activation latency and activation precision over different stimulation voltages, we normalized voltages with respect to the intermediate regime of the respective excitability profile. Such normalization was necessary, because excitability profiles obtained from different neurons varied in their intermediate regimes (slopes in (b)) and stimulation thresholds (see inset in Figure 4c). The difference between the minimum and maximum voltages of the intermediate regime was used as the normalization unit to compare between neurons: for each neuron, we normalized the stimulation voltages, ${\displaystyle V}$, by setting the first voltage to elicit a spike (onset of intermediate regime), ${\displaystyle V_{inter}}$, to zero, and the threshold (onset of super threshold regime), ${\displaystyle V_{thr}}$, to one. The normalized voltages were then computed as:

${\displaystyle {\mathrm{V}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=(\mathrm{V}-{\mathrm{V}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}})/({\mathrm{V}}_{\mathrm{t}\mathrm{h}\mathrm{r}}-{\mathrm{V}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}).}$

Although different neurons had different stimulation voltage ranges associated with the intermediary regime (see inset in Figure 4c), their normalized voltage profiles were very similar.

An increase in the stimulation voltage decreased activation latencies (Figure 4c; 60 trials per stimulation voltage; N = 8 neurons from eight different preparations). The strongest drop in latencies was within the intermediate regime of the excitability profile (~130 µs drop between minimum and maximum voltage of the intermediate regime). A further increase in the voltage magnitude above the threshold did not drastically decrease activation latencies (~40 µs drop between threshold voltage and supra-threshold voltage at three unit values of the normalized voltage).

An increase in the stimulation voltage beyond the threshold initially increased the precision of neuronal activation (Figure 4d; N = 8 neurons from eight different preparations). An increase in the precision by ~12 µs was noticed between threshold voltage and supra-threshold voltage at two unit values of the normalized voltage. A further increase in the voltage magnitude did not drastically increase activation precision. In all stimulation experiments, we used bath application of synaptic blockers in order to avoid possible interference of synaptic inputs with the arrival time estimations of triggered APs.

High-frequency neuronal activity decreases velocity and increases jitter of AP propagation

We also investigated propagation times of single APs during high-frequency activation and found a decrease in velocity and an increase in the jitter of AP propagation (Figure 5). To obtain data for this analysis, we selectively stimulated individual neurons at the AIS while recording triggered APs from the axonal arbor (Figure 5a). Neurons (N = 5 neurons from five different preparations) were repetitively stimulated at 100 Hz, using threshold voltages. Stimulation protocols were organized in 100 stimulation episodes, whereas, each episode was composed of 100 stimuli applied at 100 Hz. Therefore, we obtained 100 single trials (from 1st to 100th) per each stimulation episode. An interval of 60 s separated consecutive stimulation episodes. Electrical stimulation near the AIS was effective for each stimulation for the given protocol, which was confirmed by observing an equal number of stimulations and triggered AP events recorded from the axonal arbor (Radivojevic et al., 2016). Stimulation-triggered APs were captured by 20–120 recording electrodes selected along multiple axonal branches, which exhibited high SNR.

Figure 5

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To investigate whether repetitive neuronal activation at 100 Hz affects propagation velocities and jitter, triggered APs were grouped with respect to the stimulation count (from 1st to 100th). We used template-matching-based detection to extract the arrival times of individual AP across all stimulations. Arrival times were measured with respect to AP arrival times recorded from a proximal axonal site (alignment site, indicated as electrode one in Figure 5a), which enabled us to compare AP waveforms (Figure 5a), propagation times (Figure 5b) and propagation jitters (Figure 5c) across different stimulation trials (from 1st to 100th).

Repetitive stimulation at 100 Hz decelerated AP propagation gradually across 100 successive stimulations (Figure 5b). 100 Hz stimulation also increased AP propagation jitter across successive stimulations (Figure 5c). Axial distances were measured along the specific observed axonal branch with all its turns; axial distances are also depending on the inter-electrode pitch (17.8 µm center-to-center pitch). Data presented in Figure 5b–d and Figure 2—figure supplement 1a,b were obtained from the neuron shown in Figure 5a.

The same analysis was repeated on 12 branches of 5 neurons from five different preparations (Figure 5e,f). We used linear regression to obtain propagation velocities and propagation jitter of APs triggered by the 1st, 25th, 50th and 100th stimulation. Repetitive neuronal activation at 100 Hz induced a decrease in AP propagation velocity by 20.7% (0.14 ± 0.2 m/s (mean ± SEM), p<0.001, paired t-test, N = 12) between the 1st and 100th stimulation event (Figure 5e). Estimated velocities were 0.71 ± 0.07, 0.65 ± 0.06, 0.62 ± 0.06 and 0.57 ± 0.05 m/s (mean ± SEM) for 1st, 25th, 50th and 100th stimulation event, respectively (inset in Figure 5e). Propagation jitter increased by 11.7% or 11.7 ± 5.24 µs/mm (mean ± SEM, p=0.03, paired t-test, N = 12) between the 1st and 100th stimulation event (Figure 5f). The estimated propagation jitter was 111 ± 4.32, 115 ± 4.55, 121 ± 3.82 and 124 ± 8.34 µs/mm for the 1st, 25th, 50th and 100th stimulation event, respectively (inset in Figure 5f).

We cultured neurons taken from whole primary neocortices of rats over HD-MEAs and developed a method to noninvasively detect single individual APs propagating across hundreds-of-micrometer-long cortical axons. Live imaging was used to correlate extracellular electrical activity to the morphology of individual neurons in the network.

Spike-triggered averaging of extracellular APs, triggered by signals recorded near the AIS, enabled the reconstruction of AP footprints - a spatiotemporal representation of the average electrical activity recorded across an entire neuron (Figure 1a). This was possible owing to: (I) electrical identification of the AIS based on the extracellular activity pattern of the neuron (Bakkum et al., 2013; Radivojevic et al., 2016); (II) reliable detection of the comparably large AIS signals that served as a trigger for the averaging (Figure 2—figure supplement 1a), and (III) low-noise recording provided by the array (Frey et al., 2010), which allowed to discern small-amplitude APs of the neurites after averaging (Bakkum et al., 2013; Radivojevic et al., 2016). In general, an AP footprint captures electrical activity across the AIS, axonal trunk and lower-order branches, which enables to electrically visualize large portions of the axonal arbor and to track AP propagation in multiple axonal branches (Bakkum et al., 2013; Müller et al., 2015; Radivojevic et al., 2016). The soma and proximal dendrites provide minor contributions to the extracellular footprint, which are typically masked by the much larger AIS signals (Radivojevic et al., 2016). Owing to their small extracellular signals, distal dendrites seem not to be detectable with the HD-MEA devices used here (Bakkum et al., 2013).

We analyzed AP footprints obtained from 20 neurons and observed a strong decrease in the average amplitude of the extracellular APs over a 100 µm Euclidean distance from the AIS (Figure 1b). This can be explained by the electrical contribution of voltage-gated ion channels, whose concentration is high at the AIS and significantly drops moving towards somatodendritic and axonal compartments (Debanne et al., 2011).

We found that AP amplitudes broadly varied across neurites, however, such variation was largely independent of the Euclidean distance of the recording site to the AIS (Figure 1b). The amplitude of an extracellular AP is proportional to the sum of all transmembrane currents (Gold et al., 2007) weighted by the relative proximity of the current sources to the recording electrode, the filter properties of medium and electrode, and the characteristics of the analog filters in the recording circuitry and of the digital filters used for data analysis. Whereas the filter properties can be safely assumed to be identical for all electrodes (Obien et al., 2014), the distance between the membrane and electrode likely varies across axonal arbors and recording sites. Therefore, axonal compartments that are tightly attached to the electrode surface could provide large signal amplitudes, whereas axonal sections that are between electrodes could render much smaller amplitudes. In addition, the electrode-neuron interface could be affected by local interactions between axons and glial cells. Thus, for example, glial cells may elevate axons away from the array’s surface, making them less accessible to recording. Alternatively, they might cover an axon over an electrode, and thereby tighten the electrode-axon contact and increase signal heights. Supporting evidence from our previous study shows that axonal sensitivity to extracellular stimulation also varies across an axonal arbor, which might be caused by similar factors (Radivojevic et al., 2016). Besides the quality of the electrode-neuron contact, the biophysical properties of an axon itself could explain amplitude variations along the arbor. Differences in the distributions of voltage-gated ion channels and various morphological features, such as branching points and axonal varicosities, could, for example, play a role in determining AP amplitudes (Debanne et al., 2011).

In general, APs recorded near the AIS were, on average, approximately 10 times larger in their amplitudes compared to those captured near axonal arbors and dendrites (Figure 1b; Figure 2—figure supplement 1a). The extracellular amplitude depends on the transmembrane currents of each neural compartment, but also on the spatial arrangement of the compartment with respect to the specific electrode that is recording the signal. This means that one cannot directly derive quantitative information about the transmembrane currents from the extracellular recording. The high density of electrodes and the availability of a multitude of electrodes at different distances from a signal-generating source or neuronal compartment, however, do enable to derive a spatial profile of signal intensity. The high amplitudes at the AIS signals could be reliably detected within a single trial using simple threshold-detection (Figure 2—figure supplement 1). Reliable detection of signals from the AIS can then be used to facilitate detection of small-amplitude signals recorded from the axonal arbor. Under the assumption that AP propagation velocity is, within certain boundaries, constant over subsequent trials (Bakkum et al., 2013; Bakkum et al., 2008), it can be expected that individual electrodes near distal axons always captured APs at approximately the same time with respect to the time of the AIS signal. In this sense, the large-amplitude signal from the AIS could serve as a ground truth for the detection of small-amplitude signals (Figure 2—figure supplement 1a), however, it did not allow for discerning individual APs within the background noise. Therefore, averaging over 40 trials was previously needed to discern small-amplitude signals recorded from the axonal arbor (Bakkum et al., 2013; Müller et al., 2015; Radivojevic et al., 2016).

By using template matching with multi-electrode templates, we were now able to detect individual APs propagating across an entire neuron (Figure 2b), including APs recorded near axonal terminals hundreds of micrometers away from the AIS (Figure 2a). This was possible using the optimal matched filter, a finite impulse response filter, which maximizes the signal-to-noise ratio of a given transient signal in the background noise when convolved with the recordings (Franke et al., 2015). Consequently, separability of the signal from the noise obtained through template-matching-based detection was significantly better compared to that provided by a simple threshold-detection (Figure 2a). Both, detection failures and false-positive detections could be strongly reduced by constructing a multi-electrode filter using signals recorded by a group of three or six neighboring electrodes (Figure 2; Figure 2—figure supplement 1b,c).

We found that an increase in stimulation voltage decreased activation latency (Figure 4c) and increased precision of the activation itself (Figure 4d). A decrease in the latency could be explained by the fact that more charge activates a higher number of ion channels at once, leading to faster recruitment of other channels in the membrane and eventually to faster activation of the AIS.

In our measurements, AP propagation jitter accumulated during axonal conduction (Figure 4g,h). We determined the arrival time jitter to be 100 µs per mm axonal length. Arrival time jitter of individual APs will impact the reliability of coincidence detection of multiple PSPs at the postsynaptic neuron and will, therefore, impact neural-network computations based on a temporal code (König et al., 1996). However, for unmyelinated axons of less than a few mm length, other sources of variability, such as temporal imprecision of synaptic transmission, synaptic transmission failure, or PSP amplitude variability, seem to contribute to a larger extent to imprecision in information transmission (Ribrault et al., 2011; Krächan et al., 2017).

The inconsistency in AP propagation time could be attributed to the thermodynamic noise inherent to the gating dynamics of voltage-gated ion channels in axons (Hodgkin and Huxley, 1952; White et al., 2000; DeFelice, 2012). Supporting evidence from modeling studies suggests that such noise can cause threshold fluctuations in axonal membrane and affect reliability of AP initiation in membrane patches (Skaugen and Walløe, 1979; Strassberg and DeFelice, 1993; Rubinstein, 1995; Schneidman et al., 1998). Considering theoretical studies, the accumulation of AP jitter along a conduction path may be influenced by two factors: (I) the cumulative afflux of the noise along the propagation path, and (II) more noise being introduced, as the axonal diameter decreases from proximal regions towards axonal terminals (Faisal et al., 2005). Other phenomena, such as ephaptic coupling and the presence of gap-junctions could also be a source of electrical noise in unmyelinated axons, although we did not observe any related evidence. Furthermore, axonal morphology is not uniform along the arbor, and it is possible that branching points and axonal varicosities locally impact on AP propagation. We also noticed that cortical axons conducted single action potentials with high reliability: in more than 8,000,000 recorded action potentials we did not observe any conduction or branch-point failure.

In a next set of experiments, we found that the high-frequency regime of neuronal activity induced a decrease in velocity and an increase in jitter of the AP propagation (Figure 5). Previous studies have reported deceleration of AP propagation velocities during repetitive electrical stimulation (Soleng et al., 2003; Raastad and Shepherd, 2003; Shimba et al., 2015), but, to the best of our knowledge, this is the first time that the propagation jitter, accumulated during AP conduction, and its increase by high firing rates were measured. Repetitive neuronal activation at high frequency leads to an increase in the intracellular Na⁺ concentration (De Col et al., 2008), which hyperpolarizes the axonal membrane through activation of Na⁺/K⁺ ATPase (Soleng et al., 2003). Such hyperpolarization could explain the deceleration of AP propagation during high-frequency stimulation (Soleng et al., 2003; Shimba et al., 2015). Alternatively, accumulation of extracellular K⁺ could contribute to Na⁺ channel inactivation by keeping the membrane depolarized for a longer time after a stimulus (Malenka et al., 1981; Poolos et al., 1987), the decrease in AP propagation velocities could then be attributed to more time needed for Na⁺ channels to recover from inactivation.

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Author details

1. Milos Radivojevic

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Contributed equally with

   Felix Franke

   For correspondence

   rmilosh@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8828-9475

2. Felix Franke

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Conceptualization, Software, Formal analysis, Methodology, Writing—review and editing

   Contributed equally with

   Milos Radivojevic

   Competing interests

   No competing interests declared

3. Michael Altermatt

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Conceptualization, Software, Formal analysis, Validation, Investigation, Visualization

   Competing interests

   No competing interests declared

4. Jan Müller

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Software, Methodology

   Competing interests

   No competing interests declared

5. Andreas Hierlemann

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared

6. Douglas J Bakkum

   Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

   Contribution

   Conceptualization, Resources, Software, Supervision, Funding acquisition, Methodology, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared

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