Experimental Setup

Our experimental results are based on a new available versatile setup49, enabling complex multiple extracellular stimulations and recordings from a micro-electrode array (MEA), simultaneously with a patch-clamp stimulation and recording of a single neuron, selected from a cultured neural network (Figs 2A and B and Methods). Specifically, the in-vitro apparatus measurement (Fig. 2A) consists of an array of 60-electrodes with a diameter of 30 μm each, typically separated by 200 μm from each other38,50 (in a limited number of cultures separated by 500 μm, see Methods) and cover an area of (1.4 mm) X (1.4 mm) (Fig. 2A 2 ) of the entire ~5 cm2 cortical tissue culture (gray circle in Fig. 2A 1 ). The spontaneous spiking activity51 of the patched neuron as well as the nearby culture, sampled by the MEA, was typically silenced by the addition of synaptic blockers (Methods). Synchronized bursts activity49 was measured in the neuronal cultures before the addition of synaptic blockers. After the addition of synaptic blockers, no intra- or extra-cellular activity were observed over tens of minutes. In addition, repeated extracellular stimulations to the culture did not provoke cascades of neuronal responses (recorded extra- or intra- cellular). The stability of the neuronal response latency (Fig. 2E), much below a variance of a millisecond, also strongly excluded the possibility of leftover sparse connectivity in the culture. The stimulations and the recording of the intra- and the extra- cellular signals were done by two independent systems (Fig. 2B and Methods), and required a careful synchronization of their clocks. A sustained 20 μs matching between the two clocks was achieved using careful analysis of the relative drift of the two clocks and by using leader-laggard triggers for synchronization (Fig. 2B and Supplementary Fig. S1).

Figure 2 The Experimental Setup and Principles of Measurements. (A) A micro-electrode array (MEA) consisting of 60 electrodes (see Methods for details). (A 1 ) The gray circle with a diameter of ~2.2 cm represents the tissue culture area of ~1.3 million cortical neurons (Methods). (A 2 ) Zoom-in of the blue square in (A 1 ) showing the arrangement of the 60 extracellular electrodes, separated by 200 µm. A patched neuron, indicated by a yellow intracellular electrode, and two nearby extracellular electrodes (pink and green) are demonstrated. (A 3 ) A snapshot of a section of a neuronal culture with an intracellular patch electrode and four extracellular electrodes, similar to (A 2 ), allowing simultaneously recording and multiple stimulations. (A 4 ) A reconstruction of a fluorescence image (Methods) of a patched neuron and its dendrites (red), growing to different directions. The typical distance to the nearest extracellular electrode (black circles) is much less than 100 µm. (B) A simplified scheme of the experimental setup according to A 2 (see Methods and Supplementary Fig. S1 for more details). The extracellular and the intracellular electrodes are capable of recording and stimulating simultaneously in a time resolution of 20 μs using their controlled unit (color-coded). A trigger from the extracellular electrodes to the control unit of the intracellular electrode is used to synchronize their clocks. (C) An example of the developed experimental method for finding a subset of extracellular electrodes which reliably generate evoked spikes measured by the intracellular electrode. The 60 extracellular electrodes are stimulated serially at 2 Hz and above-threshold, where each electrode is stimulated several times (twice in this demonstration) and the voltage of the first 30 ms after each stimulation is presented. Red electrodes in the raster plot indicate electrodes which result in reliable evoked spikes. (D) A zoom-in of the green area in (C), presenting evoked spikes originated from 2 different extracellular stimulating electrodes. The neuronal response latency (NRL), measuring the time-lag between the extracellular stimulation and the intracellularly recorded evoked spike (measured following threshold crossing, see Methods), is exemplified. The NRL of the same neuron varies among extracellular stimulating electrodes; however, for a given stimulating electrode it is reproducible (for low stimulation frequencies), as can be qualitatively seen in (C). (E) The stability of the NRL is quantitatively demonstrated for 40 consecutive stimulations from a given electrode at 1 Hz. The orange dashed line represents the average NRL, and the orange bar (and light-orange area) represents the standard deviation, ~0.1 ms. See also Supplementary Fig. S1. Full size image

The dense cultured MEA enables the possibility for effective stimulations from different spatial directions with resulted evoked spikes recorded intracellularly from a patched neuron (Fig. 2). An example of a reconstructed fluorescence image of a patched neuron and its dendrites (Fig. 2A 4 ) illustrates dendrites growing to different directions, where the distance to the nearest extracellular electrode (black circles) is much less than 100 µm, as expected in the case of 200 µm between electrodes. An efficient and fast procedure was developed to identify the subset of extracellular electrodes which can reliably evoke spikes recorded intracellularly (Fig. 2C and Methods). In this procedure, a stimulation is given by an extracellular electrode and repeated several times at 2 Hz (twice in Fig. 2C), and then proceeds to the next extracellular electrode until all the 60 electrodes are stimulated. For convenience, time-slots of the first 30 ms after stimulations are demonstrated (Fig. 2C). The time-lag between the extracellular stimulation and the intracellular recorded evoked spike is defined as the neuronal response latency (NRL) for a given stimulating electrode, and typically ranges between 1–15 ms, and varies between neurons and stimulating electrodes for a given neuron (Fig. 2C and D). Nevertheless, at low stimulation frequencies, e.g. 2 Hz, the duration of the NRL is reproducible for a given neuron and stimulating electrode (Fig. 2C), with fluctuations that can be scaled down much below a millisecond (Fig. 2E). This subset of electrodes reproducing reliably intracellularly recorded evoked spikes with a stable NRL is a necessary prior demand for the implementation of the following three types of experiments. In each experiment we have verified that there were no changes, before and after performing the experiment, in the properties and the environmental conditions of the patched neuron (e.g., NRL and intra- and extra-cellular thresholds).

There are several phenomena which strongly support the assumption that the extracellular stimulations in blocked cultures (see Methods) affect the membrane potential via dendrites and not directly the soma or via the axon. The first evidence is the stretching of the NRL by several milliseconds as the stimulating frequency is enhanced (Supplementary Fig. S4). Moreover, the absolute value of the NRL can exceed 10 ms. These phenomena do not exist when stimulating the soma or antidromic the axon. In addition, the appearance of neuronal response failures at low stimulating frequencies, e.g. 1–10 Hz, occur exclusively via dendritic stimulations.

First Type of Experiments – Variability in the Spike Waveforms

The first type of experiments consists of alternating stimulations of a patched neuron by two extracellular electrodes (green and pink as illustrated in Fig. 2A 2 ) which were detected to reliably generate evoked spikes (Fig. 2C). We select a very low stimulating frequency, 0.5 Hz, of alternating stimulations (Fig. 3A) to ensure that there are no accumulative effects along the sequence of stimulations, as indicated for instance by the time-independent recovered resting potential (Fig. 3B). In addition, the alternating stimulations scheduling excludes the possibility that some changes in the measured neuron occurred during the transition from a sequence of stimulations by the first electrode to the second one. The symmetry between the pair of stimulating electrodes is preserved, including the resting periods before and after stimulations.

Figure 3 Variability in the Spike Waveform as a function of the Stimulation Location. (A) The alternating stimulation scheduling for this type of experiments. The patch neuron is alternatingly stimulated by two extracellular electrodes (green and pink, see also Fig. 2A 2 ) at a low frequency, 0.5 Hz. Each colored rectangle represents a stimulation by the corresponding extracellular electrode (the width is arbitrary, see Methods for details), similar to the realization illustrated in Fig. 2A 2 . (B) An example of intracellular recording from a patch neuron stimulated alternatingly, as in (A), showing two different well-separated spike waveforms. The voltage is presented from 5 milliseconds prior to the threshold crossing, which is defined at -50 mV. (C) An illustration of a neuron stimulated above-threshold either via the green dendrite (C 1 ) or via the pink dendrite (C 2 ), where each one generates a different waveform for the spike (colored coded). The suitable neuronal model for the presented experimental results is model III in Fig. 1C, where when the green weight crosses its spring threshold a “green” spike is evoked, while when the pink weight crosses its spring threshold a “pink” spike is evoked. (D) Examples of different spike waveforms recorded intracellularly and generated by two extracellular stimulating electrodes (pink and green) with reliable evoked spikes (Fig. 2C). Each one of the eight panels is associated with a different neuron, and for each two electrodes two evoked spikes are plotted to illustrate the reproducibility of the spike waveform. Full size image

The waveforms of the spikes, plotted 5 ms prior to the first time the membrane potential crosses -50 mV (Fig. 3B), lead to the following conclusions. The shape of the spikes originated from stimulations from either the green or the pink extracellular electrode have a well define reproducible waveform (see also Fig. 2D). However, the two stimulating electrodes generate two distinguishable sets of waveforms. The differences between the bunch of the green and the pink waveforms are evident in the rise shape, the values and the timings of the maximal membrane potential and in the shape of the decay of the voltage after the spike. It is clear that the two distinguishable sets of spike waveforms (green and pink) cannot become identical under either translation or rescaling of the voltage of one of the sets. We note that the waveform of spikes is robust to changes in the amplitude and the duration of the stimulations, as long as it is above the relative threshold of each one of the stimulating electrodes, hence the different waveforms cannot be attributed to the precise stimulation shape, i.e. duration with time-dependent amplitudes. Results clearly indicate (see Statistical analysis in Methods) that for a given neuron the waveform of a spike is not independent of the origin of the stimulation (Fig. 2A 4 ) and its relative direction (as illustrated in Fig. 3C and D). It is evident that the outcome of this type of experiments is in contradiction with the scheme of a unique central excitable mechanism within the neuron; therefore, it can hardly fit with the scheme of model I and model II (Fig. 1C). However, this observation and conclusions, based on the stimulation of a neuron from several directions independently, require an additional support and especially to include scenarios where the neuron is stimulated simultaneously from several directions.

Second Type of Experiments – the Absence of Anisotropic Spatial Summation

Spatial summation52,53,54,55,56,57 is one of the eminent mechanisms to control and to maintain the activity of neural networks, since most of the synapses are much below a neuronal threshold. A neuron receives many sub-threshold electrical inputs via its dendrites and the possibility to generate a spike relies on the fact that the neuron integrates the incoming signals using a time-dependent weighted function. Consequently, threshold crossings occur with non-negligible probability. The current assumption is that the neuron integrates the incoming signals in an isotropic manner, independent of their arriving routes to the soma.

Following the observation in the above-mentioned first type of experiments, that the spike waveform depends on the origin of the stimulation, we designed a second type of experiments in order to explore whether the spatial summation is implemented isotropically or anisotropically by the neuron (Fig. 4A). The designed experiments consist of two extracellular electrodes (green and pink as illustrated in Fig. 2A 2 ) which were detected to reliably generate evoked spikes recorded intracellularly (Fig. 4B), with preferably different spike waveforms (Figs 4C and 2C). In the first step of the experiment, the NRL was estimated for each one of the two electrodes (Fig. 4B) as well as the threshold amplitude for 2 ms stimulation durations (Fig. 4D and Methods). In the second step, based on the prior measured NRLs of the two electrodes, the neuron was repeatedly stimulated by the two extracellular electrodes, where the arrival time-lag of the two stimulations to the soma was tuned (Fig. 4E and Methods). Results indicate (see Statistical analysis in Methods) that the neuron does not generate evoke spikes even in the most favored scenario, where the two stimulations (green and pink) arrive simultaneously to the soma from two different directions, and their amplitude sum significantly exceed the threshold. We note that the properties of the patched neuron, i.e. the threshold of each one of the two electrodes, are practically unchanged for stimulation duration of 1–2 ms (Methods), hence even a partial overlap between the arrivals of the two stimulations is expected to be sufficient to exceed the threshold. In addition, since the NRL of each electrode is different, a pair of stimulations for the two electrodes were typically given in different timings, reducing the possibility of some electrical reciprocal influence between them. Results clearly exclude model I (Fig. 1C) and might fit model II where the thresholds to transmit the incoming signals from the dendrite to the soma (e.g. Th 1 and Th 2 for the green and pink dendrites, respectively) typically exceed a half of the threshold to generate an evoked spike from each electrode separately. The feasibility of model II seems somehow artificial, since such a powerful dendritic barrier, exceeding 0.7 of the threshold to generate an evoked spike (Fig. 4E) was repeatedly observed in all experiments, and practically excluded efficient spatial summation (in the formulation of the neuronal equation of model II (Fig. 2C), the dendritic thresholds always obey Th i >0.7·Th). In addition, model II also consists of a unique centralized excitable mechanism which does not fit to the anisotropic spike waveforms as observed in the first type of experiments. We turn now to the third type of experiments to further support model III over model II.

Figure 4 The Absence of Spatial Summation in Simultaneous Stimulations from Two Different Sources. (A) Possible scenarios for a neuronal computational model, where the neuron is simultaneously stimulated by two sub-threshold stimulations arriving from two extracellular electrodes. The amplitude of each sub-threshold stimulation is significantly above one half of its threshold. Left scenario demonstrates the lack of spatial summation, where each dendrite is coupled to an independent threshold mechanism. Although the sum of the two signals is above-threshold an evoked spike is absent (Model III in Fig. 1C). The right scenario presents a spike generated by the central threshold mechanism which sums all incoming signals (Model I or II in Fig. 1C). (B) The measured NRL for the two extracellular electrodes (green/pink in B 1 /B 2 ), showing the stability of the NRLs around a different value for each one of the extracellular electrodes. (C) Intracellular recordings of the spike waveforms for the green and the pink extracellular electrodes (similar to Fig. 2A 2 ) when stimulated above-threshold. The distinct different spike waveforms are visible. (D) The threshold of each one of the two electrodes was estimated using stimulation pattern of 2 ms duration and varied amplitudes (see Methods). For both electrodes reliable evoked spikes were observed at an amplitude of 800 mV, where at an amplitude of 500 mV no evoked spikes were observed. Hence, the threshold is in the range of (500, 800) mV and a stimulation of 500 mV is significantly above a half of the threshold. (E) The neuron is stimulated by the two extracellular electrodes, using a stimulation patterns of 2 ms as in (D) and 550 mV (~0.8 of the threshold, Th, of each electrode), and recorded intracellularly. Based on the prior knowledge of the NRLs in (B), the time-lags between the two stimulations were dynamically adjusted by relatively shifting the stimulation timings of the green electrode (see Methods). Specifically, the green stimulation was adjusted from a partial overlap with the pink stimulation, to a complete overlap and finally to non-overlapping timings (left). All scenarios did not result in evoked spikes, but in a negligible local depolarization independent of the relative timings between the two extracellular stimulations (right). Full size image

Third Type of Experiments – the Absence of Intra- and Extra- Summation and Subtraction

The second type of experiments indicated that spatial summation is most probably performed anisotropically. We examine now this feature from a different perspective, where the neuron is stimulated by two sub-threshold stimulations, extracellular and intracellular, which their arithmetic sum is above-threshold (Fig. 5A). We expect that if the neuron functions as a centralized excitable mechanism (models I and II in Fig. 1C), an evoked spikes will be generated, otherwise the feasibility of model III is most likely (Fig. 1C).

Figure 5 The Absence of Spatial Summation in Simultaneous Intracellular and Extracellular Stimulations. (A) Possible scenarios for a neuronal computational model, where the neuron is simultaneously stimulated by two sub-threshold stimulations, one arriving from an extracellular electrode (green) and the second from an intracellular electrode (orange). The sum of the two sub-threshold stimulations is significantly above the threshold. Left scenario demonstrates the lack of spatial summation, where each dendrite is coupled to an independent threshold mechanism (Model III in Fig. 1C). The right scenario presents a spike (combined colors) generated by the central threshold mechanism which sums all incoming signals (Model I or II in Fig. 1C). (B) The scheme of the performed experiment. Orange and green rectangles represent the stimulations from the intracellular electrode, 3 ms duration, and the extracellular electrode, 2 ms duration, respectively. Both stimulations are sub-threshold, ~75% of their threshold, as demonstrated by their relative amplitude in comparison to their threshold (dashed orange and green lines). The stimulation scheduling of the intracellular stimulation (orange) was shifted successively by 0.5 ms relative to the timing of the extracellular stimulation (where the NRL is omitted, green). Three possible scenarios between the two stimulations (partial overlapping, overlapping or non-overlapping) are illustrated. (C) The intracellular recorded voltage from the neuron according to the three scenarios in (B). All three scenarios exemplify similar shallow local depolarization and without an evoked spike, indicating the absence of summation of the intra- and the extra- cellular stimulations. (D) The scheme of the performed experiment, similar to (C), but the duration of the extracellular stimulation is 0.2 ms, since the patched neuron was close to the stimulating electrode (see Methods). Nevertheless, the stimulation was extracellular, since as the stimulation frequency was enhanced an increase in the NRL and in its fluctuations around an average value were observed (Supplementary Fig. S4). (E) A rare counter example, where the intracellular and the extracellular stimulations are summing up, both spatially and temporally. This behavior represents rare events, following our experimental evidence, and probably requires that the intra- and the extra- cellular spike waveforms will be identical (Supplementary Fig. S3), i.e. generated by the same local threshold mechanism. See also Supplementary Figs. S2–S4. Full size image

The added value of this type of experiments is twofold. The timing of the intracellular stimulation is precisely known and is independent of the NRL, hence fluctuations in the relative timings of the stimulations are reduced. In addition, the direct intracellular stimulation of the soma is expected to be more accurate and to fluctuate less than an indirect extracellular stimulation. We selected long durations for the intracellular stimulations (3 ms) and for the extracellular stimulations (2 ms) (Fig. 5B) in order to precisely control the overlap in time of the two stimulations, and for each stimulation the threshold was measured (see Methods). In addition, the NRL of the extracellular stimulation was carefully estimated in order to control the relative timings of the stimulations of the soma. The time-lag between the extracellular stimulation (green) and the intracellular stimulation (orange) was tuned by intervals of 0.5 ms, and for each interval several pairs of intra- and extra- cellular stimulations were given. Almost all experiments of this type were found to be in agreement with the second type of experiments and with model III (Fig. 1C). For all relative timings and stimulations no evoked spikes were observed (Fig. 5C), although both the extracellular and the intracellular stimulations exceed 75% of their thresholds, indicating the lack of summation between the intra- and the extra- cellular stimulations. Nevertheless, in rare experiments (less than one out of ten) a spike was observed even when there was a time-lag of several ms between the intra- and the extra- cellular stimulations (Fig. 5D and E). The duration of the extracellular stimulation in this case was reduced to 0.2 ms to avoid artifacts in the spike waveform, as the extracellular electrode was only several dozens of μm away from the patched neuron and the NRL was less than 2 ms (see Methods). A similar result was observed also for a larger NRL and 2 ms duration of the extracellular stimulation (Supplementary Fig. S2). These rare results indicate that a spatial summation between extra- and intra- cellular stimulations can occur under some circumstances, probably the excitation of the same threshold element within the neuron, and present a benchmark to support the correctness of our experimental design.

The lack of summation between the intracellular and the extracellular stimulation (Fig. 5 and Statistical analysis in Methods), hints that a subtraction between the stimulations is also ineffective. The subtraction is implemented by stimulation with a negative amplitude for the intracellular electrode, resulting in a temporary drop in the membrane voltage for several ms (Fig. 6A). We now simultaneously stimulate the neuron by an extracellular stimulation which is slightly above the threshold and by an intracellular stimulation which is slightly above the minus threshold amplitude (Fig. 6B). The relative timings between these two stimulations, with the exclusion of the NRL, were carefully tuned (Fig. 6B and Methods). These two stimulations almost annihilate each other arithmetically (Fig. 6B), however, an evoked spike was observed even when they completely overlapped (Fig. 6B, middle panel). A prior prolonged hyperpolarizing pre-pulse just before the depolarizing pulse might enhance the excitability of the neuron and reduce temporarily the threshold. However, in the presented experiments the pulse is short and the lack of evoked spike is observed even when the intra- and the extra- cellular stimulations are given simultaneously, indicating that a subtraction between the two stimulations does not occur.

Figure 6 The Absence of Spatial Subtraction in Simultaneous Intracellular and Extracellular Stimulations. (A) Left: The intracellular threshold amplitude is represented by the upper dashed horizontal orange line and correspondingly the minus threshold amplitude, the lower dashed orange line. An intracellular stimulation with a duration of 0.5 ms and an amplitude of approximately -90% of the threshold amplitude is represented. Right: A temporary drop of several ms in the membrane voltage by such a short pulse with a negative amplitude (left) is presented. (B) Left: A neuron is simultaneously stimulated by a slightly above-threshold extracellular stimulation, a duration of 0.5 ms and an amplitude of 110% of the threshold (green), and by a negative intracellular amplitude slightly above the minus amplitude of the threshold as in (A) (orange). The relative timing between these two stimulations was tuned by shifting the timing of the intracellular stimulation by 0.5 ms every three pairs of such intra- and extra- cellular stimulations (see Methods). Three possible scenarios are presented (upper/middle/lower panels), where the extracellular stimulation, with the exclusion of the NRL, is slightly before/ at the same time/ after the intracellular stimulation. Right: An evoked spike is recorded for all three scenarios, indicating that there is no subtraction between the two stimulations. Full size image

Nonlocal Time Interference between the Intra- and Extra- Cellular Spiking Activities

The lack of additivity of two stimulations arriving at a neuron from two different stimulation locations is the main evidence so far for multiple independent threshold elements composing the computation dynamics of a neuron. These experiments require a careful tuning and dynamical maintenance of the arrival timings of the stimulating signals at the neuron almost simultaneously. We present below another supplemental type of experiments, where the precise timings of the stimulations and their NRLs are irrelevant.

The following experiment (see Statistical analysis in Methods) consists of a neuron with two extracellular stimulating electrodes reproducing reliably evoked spikes recorded intracellularly, each at 2 Hz (as in Fig. 2C), and for a much longer period of alternating stimulations between the two extracellular electrodes (Fig. 7A), resulting at 1 Hz stimulation frequency for each electrode. A comparison between the typical spike waveforms generated by each one of these two electrodes (green and pink) and the intracellular one (orange) (Fig. 7B) leads to the following conclusions. The spike waveforms generated by the two extracellular electrodes are different (green and pink), where one of them (green) has a very similar waveform as the one generated by an intracellular stimulation (orange). This observation suggests that the following two scenarios are most likely (Fig. 7C). Either each one of the three stimulation sources generates an independent spike (Fig. 7C 1 ) or the generation of spikes by the two sources with similar spike waveforms (green and orange) are coupled (Fig. 7C 2 ). This coupling is illustrated by two springs pulling in parallel the same threshold element and are capable to generate combined colored spike. waveforms will be identical (Supplementary Fig. S3), i.e. generated by the same local threshold mechanism. See also Supplementary Figs S2–S4.

Figure 7 Non-Overlapping Time-Dependent Extra- and Intra- Cellular Stimulations Induce Interference in the Spiking Activity. (A) Intracellular recordings of a neuron stimulated alternately at 2 Hz by two extracellular electrodes (green and pink) with reliable evoked spikes. (B) The spike waveforms generated by the stimulations of the two extracellular electrodes (green and pink) and by an intracellular stimulation (orange). It is evident that the green and the orange waveforms are very similar, whereas the pink waveform is different. (C) Two possible scenarios for the spike generation. (C 1 ): The neuron consists of three threshold elements associated with intracellular stimulations and with each one of the two extracellular stimulation locations, represented by different spike colors. (C 2 ): The intracellular stimulation and the green extracellular stimulation activate the same sub-neuronal threshold element, represented by the two springs connected to the threshold spring and by a two-color spike. (D) Recorded spike train with the stimulating scheduling. The pink extracellular electrode was stimulated every 1 s and in between 8 intracellular stimulations were given separated by ~100 ms. The spike color is associated with the origin of the corresponding type of the stimulation. The duration/amplitude was 2 ms/800 mV for an extracellular stimulation and 3 ms/600 pA for an intracellular stimulation. (E) Similar to (D), but with the stimulation of the green extracellular electrode results in response failures. See also Supplementary Figs S5,S6. Full size image