Electric stimulation inside and outside of individual neurons while concurrently monitoring the induced extracellular field at specific locations (for example, just outside the soma) requires multiple pipettes in a confined space. We developed a 12-pipette setup that allows independent positioning of each pipette under visual control with micrometer accuracy, with the flexibility of using an arbitrary number of these as patching, extracellularly stimulating or extracellular recording pipettes. We stimulated layer 5 neocortical pyramidal neurons in slices while recording inside and outside of their cell bodies. Typically, a single extracellular stimulation electrode (S1) was positioned 50–150 μm from the cell body (Fig. 1a). The soma was whole-cell patch-clamped with one intracellular electrode and was surrounded by a number of extracellular pipettes monitoring V e . The induced electric field as a function of distance from S1 was estimated through the spatial gradient of the best fit of all V e traces (least-squares fitting; Fig. 1b,c and Supplementary Fig. 1) assuming a point-source approximation41. V e was taken to be the potential at the extracellular recording site closest to the cell body, typically within 15 μm. The relevant V m was determined by subtracting V e from V i (Fig. 1d,e). Synaptic activity was always pharmacologically silenced using D(−)-2-amino-5-phosphonovaleric acid (AP5) to block NMDA receptors, gabazine or bicuculline to block GABA receptors, and 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) to block AMPA receptors (see Online Methods and ref. 19). Gap junctions are unlikely to contribute in any substantial manner to our results, as they are both rare among layer 5 neurons at postnatal day 14 (ref. 42), the minimum developmental age of our animals, and leave a telltale sign of spikelets, which we looked for but failed to find (Supplementary Fig. 2). Thus, any observed changes in V m can be solely attributed to the effect of the field, rather than to synapses. Finally, the extracellular stimuli that we applied were always (at least) 25–50-fold weaker than the lowest reported stimulation amplitude (5–10 μA) required to directly trigger action potentials in cortical neurons from rest43.

Figure 1: Simultaneous recordings from up to 12 electrodes inside and outside a single neuron in rat slice during intra- and extracellular stimulation. (a) Unipolar stimulation (I 0 = 200 nA at 1 Hz) in slice via an extracellular pipette (S1) near the soma of a patched pyramidal neuron (intracellular pipette, I1). (b) Seven extracellular pipettes were positioned close to the soma of the patched neuron to monitor V e (magenta, V e recordings; black, mean waveform after 9-s stimulation). The isopotentials are shown in a (blue, sink; red, source). (c) V e amplitude as a function of pipette location for I 0 = 50 (cyan), 100 (blue) and 200 (black) nA (circles, mean; error bars, s.d.). Distance is calculated from the tip of the extracellular stimulating electrode S1. Solid lines indicate the point-source approximation (least-squares fitting; typically the extracellular resistivity ρ = 2.5–3.8 Ωm, ref. 41). (d) Perturbing V e (magenta) through extracellular stimulation from pipette S1 caused V i to change (blue) through ephaptic coupling (top traces, I 0 = 100 nA and f = 1 Hz; bottom traces, I 0 = 100 nA and f = 8 Hz). (e) The membrane potential V m was defined as V m = V i − V e . Full size image

We first injected an oscillatory current I of variable strength I 0 and frequency f, with I = I 0 sin(2πft), through the extracellular stimulation electrode S1 while V e and V i were monitored and V m was calculated by subtracting V e from V i , that is, V m = V i − V e (5-s duration, 1–2 repetitions in 23 cells; Figs. 1a–c and 2a). In a perfectly homogenous resistive milieu, a point source induces a V e that oscillates at the same frequency f, and decays with 1/r where r is the distance between S1 and the measurement point41. It also induces an E that oscillates at f and decays with 1/r2. Notably, in vivo extracellular activity does not give rise to distinctive frequency bandwidths but instead scales as 1/fn, where the exponent n is approximately 1, over the whole frequency domain44. Still, linearly decomposing LFPs into their individual sinusoidal components per the Fourier theorem, although an approximation, is very widespread and not unreasonable. We chose I 0 to induce field and voltage profiles similar to LFPs measured in vivo. For extracellular stimulation at 1 Hz with I 0 = 25, 50, 100 and 200 nA, we measured fields of 0.74 ± 0.53, 1.49 ± 1.06, 2.96 ± 2.11 and 5.86 ± 4.25 mV mm−1 and V e amplitudes of 0.07 ± 0.04, 0.14 ± 0.08, 0.28 ± 0.16 and 0.55 ± 0.32 mV, respectively (mean ± s.d.; see also Supplementary Fig. 1).

Figure 2: Subthreshold extracellular field entrainment. (a) V e (first row in magenta, mean in black), V i (second row in blue) and V m (third row in green) for one neuron for three stimulation regimes: slow and fast extracellular stimulation without intracellular depolarization (left and middle, respectively), and slow extracellular stimulation combined with sustained intracellular current injection (right). (b) Amplitude and phase (circles, mean; error bars, s.e.m.) of the V e (magenta), V i (blue) and V m deflection (green) for extracellular stimulation frequencies of 1–100 Hz and constant I 0 = 100 nA (n = 23 cells). V i attenuation of an intracellular chirp without any extracellular field (blue line; chirp amplitude, 75 pA; frequency f = 3t where t (s) is time). (c) Amplitude and phase of the V e (magenta), V i (blue) and V m deflection (green) as a function of membrane polarization (n = 17 cells; circles, mean; error bars, s.e.m.; stimulation frequency f = 8 Hz). (d) Normalized cross correlation (xcorr) between V i and V e (blue) as well as V m and V e (green) of the data shown in b (line, mean; shadowed area, s.e.m.) for (left to right) f = 1, 8, 30 and 100 Hz. The difference between xcorr(V i , V e ) and xcorr(V m , V e ) for each frequency at one, two and three quarters of the inverse of the stimulation frequency was always highly significant (P < 0.001; paired t test Bonferroni-corrected for multiple comparisons). (e) xcorr(V i , V e ; blue) and xcorr(V m , V e ; green) for the data in c (line, mean; shadowed area, s.e.m.) for (left to right) I inj = −150, 0, 50 and 100 pA at f = 8 Hz. Full size image

What are the characteristics of V m entrainment to these spatiotemporal E and V e fluctuations? We first quantified ephaptic coupling when V m remained subthreshold (that is, nonspiking). Frequencies of 1, 8, 30, 60 and 100 Hz, emulating the LFP frequencies that cover delta, theta, beta and gamma bands, did not substantially alter the induced E and V e characteristics (Fig. 2b,c and Supplementary Fig. 2)41. Subthreshold oscillations in the membrane potential induced by the extracellular oscillating field through ephaptic coupling persist with equal strength up to 100 Hz (I 0 = 100 nA; for f = 1 Hz, V m amplitude of 0.16 ± 0.005 mV with a phase of 165° ± 1° between V m and V e ; for f = 100 Hz, V m amplitude of 0.14 ± 0.007 mV and a phase of 179° ± 3°; mean ± standard error mean; Fig. 2b,d). As expected, this led to an anti-phase relationship between V e (and V i ) and V m (ref. 45), as determined by the mean properties (Fig. 2b) and cross-correlation analysis (Fig. 2d). These results are in contrast with those of parallel-plate experiments, which found a strong attenuation of subthreshold V m amplitudes with increasing extracellular stimulus frequencies19. We attribute this disparity to the limited access previous experimental studies have had to the space immediately outside the soma because of the parallel plate geometry and sampling of the field by a single electrode. This made assessing the entrainment of the membrane to the field problematic, in particular given the presence of local tissue inhomogeneities19. Notably, ephaptic coupling persists for high-frequency stimuli in contrast with direct intracellular (subthreshold) current injections (Fig. 2b), whose effects on V i are substantially attenuated as a result of capacitive filtering1.

We tested whether the characteristics of ephaptic coupling persist for different levels of membrane polarization by directly injecting subthreshold currents (I inj ) into the cell (Fig. 2a). We found that the anti-phase relationship between V e (and V i ) and V m remains (Fig. 2c,e) for all membrane polarization levels (f = 8 Hz and I 0 = 100 nA; for I inj = −150 pA, the induced ephaptic amplitude was 0.13 ± 0.01 mV at a phase of 170° ± 4°; for I inj = 100 pA, the V m amplitude was 0.13 ± 0.01 mV at a phase of 151° ± 5°; mean ± s.e.m.; Fig. 2c,e). We conclude that LFP-like extracellular field activity readily entrains the subthreshold membrane potential over a hundred-fold range in frequency and at all tested membrane polarization levels.

We next examined the effect of ephaptic coupling on spiking in 25 cells. We injected a constant current for 9 s at the cell body that induced spiking (typically 2–4 Hz; Fig. 3a and Supplementary Fig. 3). Experiments were divided into two groups: control, in which the intracellular stimulus was given without any extracellular field, and extracellular stimulation, in which both intracellular and extracellular stimuli were simultaneously applied (Fig. 3a–c). We performed the control experiment immediately before each extracellular stimulation experiment using the same intracellular current step. Each pair (control, extracellular stimulation) was repeated 4–6 times for each field configuration at 1, 8 and 30 Hz.

Figure 3: Weak electric fields entrain spiking activity of individual neurons. (a) V e (magenta) and V m (green) without (control) and with an extracellular field (f = 1 Hz). (b) Normalized cross-correlation (xcorr) between V i and V e (blue) and V m and V e (green) of the low-pass (<100 Hz) suprathreshold data of an individual neuron without (top) and with extracellular stimulation (bottom) at f = 1 Hz and I 0 = 200 nA. (c) STA spectra (same data as in b; top, control; bottom, extracellular stimulation). (d) Population vector analyses for f = 1 Hz (left to right, I 0 = 25, 50, 100 and 200 nA; n = 25 neurons). Field entrainment of spikes led to nonuniform spike-phase distribution (P values by Rayleigh test) that was not attributable to changes in spike number (N(upper), control; N(lower), extracellular stimulation; Supplementary Fig. 3). (e) STA spectra (circles, mean; shadowed areas, s.e.m.) for the data in d. For the control experiments, a (virtual) V e identical to the subsequent extracellular stimulation experiment was assumed. (f) SFC (circles, mean; error bars, s.e.m.) for extracellular stimulation (black) and control (cyan) experiments at (left to right) 1, 8 and 30 Hz as a function of stimulation strength (x axis: first row, circles indicate mean V e amplitude at the soma and error bars indicate s.e.m.; second row, circles indicate mean E amplitude at the soma). Asterisks indicate statistical significance of the SFC difference between control and extracellular stimulation (paired t test, fdr-corrected for multiple comparisons; *P < 0.05, **P < 0.01, ***P < 0.001). The percentage increase in SFC relative to control is shown for statistically significant changes. STP, STA and SFC are shown for four individual neurons for all stimulation amplitudes and frequencies in Supplementary Figures 5, 7 and 9. Full size image

Although the imposed external field did not substantially change the number of spikes triggered by the current step (Supplementary Fig. 3), it did shift their timing. We employed a population-vector analysis (Fig. 3d and Supplementary Figs. 4–9) to examine whether spikes were elicited at a preferred phase of V e . We used the Rayleigh criterion to test whether the phase of spikes, relative to V e , were distributed nonuniformly in the circular phase space (0°, 360°). Indeed, increasing field strength led to an increased deformation of the spike-phase distribution. The increased entrainment manifested itself in the length of the population vector. At a stimulation frequency of 1 Hz and amplitude of 25, 50, 100 or 200 nA, the normalized length of the population vector was 0.046, 0.060, 0.098 and 0.145, respectively, and its direction was 266°, 250°, 242° and 241°, respectively. Note that the preferred spike phase for f = 1 Hz was very similar to the phase of the V m peak in the subthreshold experiments (Fig. 2a–c).

As a further measure of entrainment, we quantified the spike-triggered average (STA) of all neurons (Fig. 3c). We calculated the power spectrum of the STA as a function of frequency (Fig. 3e and Supplementary Figs. 4–9). Increasing the field enhanced the phase locking of spikes to the applied field. To confirm whether this increase is solely attributable to the presence of the field, we assumed a (virtual) V e identical to the subsequent applied extracellular field so that phases could be ascribed to the spike times of control experiments. The increase in the mean STA spectrum at f with the field (extracellular stimulation) was always greater than without it (control) (Fig. 3e).

Cross-correlation and STA depend not only on the degree of phase locking of spikes to the field but also on the amplitude of V e . We used spike field coherence (SFC), a modified version of the STA analysis28,32, to quantify the relationship between spiking and the extracellular stimulus. The SFC is defined as the STA spectrum normalized by the power spectra of all V e segments that were averaged to obtain the STA28. The latter is defined as the spike-triggered power (STP). SFC ranges between 0 and 100%, with 0% indicating no phase relationship between spikes and the imposed field and 100% indicating complete phase locking of all spikes to one particular phase. SFC is an accurate indicator of the magnitude of stereotypy of spike time relative to V e fluctuations28. Given that ephaptic coupling increased the STA spectrum at f (Fig. 3e and Supplementary Figs. 4, 6 and 8), we compared the SFC between control and experiments at f for each field configuration (Fig. 3f and Supplementary Figs. 4, 6 and 8). Indeed, the external field clearly increased the SFC by ephaptic coupling. Notably, the significance of the entrainment, as assayed through a paired t test (false discovery rate (fdr)-corrected for multiple comparisons), decreased for increasing stimulus frequency (I 0 = 50 nA; f = 1 Hz, P = 6.5 × 10−5; f = 8 Hz, P = 0.019; f = 30 Hz, P > 0.05). Thus, although an external field as small as 0.74 mV mm−1 (V e amplitude of 0.07 mV) led to statistically significant entrainment at 1 Hz (P = 6.5 × 10−5), the field had to be almost an order of magnitude larger (5.58 mV mm−1, with V e amplitude of 0.54 mV) for entrainment at 30 Hz to become significant. Ephaptically induced phase locking of spiking is thus more effective, and occurs at lower field strengths, for slow rather than fast modulations of E and V e .

The enhanced phase locking of spikes to the external field was not a result of changes in the firing rate. This was confirmed by paired t test (Bonferroni corrected for multiple comparison) that showed no statistically significant change (at q = 0.05) in the number of spikes or the spike frequency between stimulation and control experiments (Fig. 3d and Supplementary Fig. 3). The same null result was also obtained when computing the STP for stimulation and control procedures (Supplementary Figs. 4, 6 and 8). The STP quantifies the oscillations that are present in the V e signal regardless of whether or not they are related to the occurrence of spikes and is calculated by averaging the power spectrum of each individual V e segment centered on each spike28. Although the average STP of all neurons indicated the strong presence of oscillations (Supplementary Figs. 4–9), the power of the STP at f did not distinguish between extracellular stimulation and control experiments (paired t test; for all stimulation frequencies, all comparisons between the STP of control and extracellular stimulation experiments resulted in P > 0.58). Thus, the increase in phase locking is attributed to ephaptic entrainment of spikes rather than to a change in firing rate or variations in the STP.

Our results indicate that LFP-like fluctuations in the extracellular potential, V e , readily entrain both the subthreshold membrane potential and spike trains. Because the LFP extends over hundreds of micrometers, these fields could serve to synchronize thousands of neurons that would otherwise operate independently. To directly test for this, we simultaneously patched four neurons and positioned the extracellular stimulation electrode S1 close by so that all four experienced a simultaneous and similar V e fluctuation at their cell bodies. Seven extracellular recording electrodes monitored V e close to the somata of the four neurons and the space between them (Fig. 4a). We simultaneously injected a suprathreshold current step (duration of 9 s) into all four cells with or without an external field (Fig. 4b). Although the extent to which the membrane potential of each cell was modulated by the field varied (mainly as a result of the varying distance from S1), spike trains in all cells were entrained by the extracellular field, as assessed by the deviation of spike phases from uniformity. Consistent with the single-neuron data, a field oscillating at 1 Hz synchronized spikes in all four cells such that a preferred spiking-phase close to 270° emerged with increasing field strength (Fig. 4c–e). Note that all of this took place without any synaptic transmission occurring (Supplementary Fig. 10), as a result of the synaptic blockers that we used. This phase preference cannot be attributed to differences in firing rates between the two conditions (Supplementary Figs. 11–13). We observed the same outcome when simultaneously patching triplets (Supplementary Fig. 14) and pairs (Supplementary Fig. 15) of neurons.