Cell class-specific electric field entrainment of neural activity

Abstract

Electric fields affect the activity of neurons and brain circuits, yet how this interaction happens at the cellular level remains enigmatic. Lack of understanding on how to stimulate the human brain to promote or suppress specific activity patterns significantly limits basic research and clinical applications. Here we study how electric fields impact the subthreshold and spiking properties of major cortical neuronal classes. We find that cortical neurons in rodent neocortex and hippocampus as well as human cortex exhibit strong and cell class-dependent entrainment that depends on the stimulation frequency. Excitatory pyramidal neurons with their typically slower spike rate entrain to slow and fast electric fields, while inhibitory classes like Pvalb and SST with their fast spiking predominantly phase lock to fast fields. We show this spike-field entrainment is the result of two effects: non-specific membrane polarization occurring across classes and class-specific excitability properties. Importantly, these properties of spike-field and class-specific entrainment are present in cells across cortical areas and species (mouse and human). These findings open the door to the design of selective and class-specific neuromodulation technologies.

Figure 1:. Cellular and cell type-specific characterization of ES effects.

a, Top: Simultaneous ES, V_i and V_e recordings from eight electrodes near the soma of a whole-cell patched neuron. Bottom: Experiment in mouse cortical slice (yellow: extracellular ES, green: patched cell soma of layer 5 pyramidal neuron; blue: intracellular electrode recording V_i; red: extracellular electrodes recording V_e at multiple locations within 150 um from soma). b, Left: V_e amplitude as function of distance between ES and recording electrodes (ES: amplitude is 25–200 pA; ES frequency: 8 Hz; circles: V_e mean amplitude; error bars: V_e amplitude st.d.) Trendlines are least-squares fit of the point source approximation. c, V_e and electric field amplitude elicited by the ES at the extracellular recording electrode closest to the whole-cell patched soma (approx. 15 μm). Blue: V_e amplitude for each experiment (n=59); Black: mean and st.d. across experiments. d, Sample fluorescent images, cellular morphology, electrophysiology responses, and response curves (spike frequency vs. current input, f-I) from identified neocortical cells (colored lines: individual neurons; black: median). Three cell types: (left) excitatory pyramidal, (middle) inhibitory Pvalb, and (right) inhibitory SST. e, Experiments with simultaneous ES (delivered at 8, 30, and 140 Hz for all cells) and intracellular DC current injection I_inj to elicit spiking. Sample electrophysiology traces from three cells. top, V_e close to the soma; bottom: V_i from inside the soma of a spiking neuron responding to I_inj (5 s of I_inj shown here). Left to right: traces from a pyramidal, a Pvalb and an SST neuron. f, Introduction of spike time analysis and quantification of spike-field entrainment. Spikes are ascribed a phase by mapping the spike time to the V_e phase from the electrode closest to the spiking cell. Spike phase distributions shown in polar plots. g, Top: Polar plots of the spike-phase distribution for a pyramidal cell (green), Pvalb cell (red), and SST cell (orange) in the absence (Control) and presence of ES (200 pA; 8 Hz, 140 Hz, 30 Hz ES for pyramidal, Pvalb, and SST cells, respectively). The population vector length (black line) reflects the degree of entrainment. The presence of ES skews the spike-phase distribution and entrains the neurons. Bottom: Spike phase distributions under ES for a pyramidal (green; ES: 200 pA, 8 Hz), a Pvalb (red; ES: 200 pA, 140 Hz) and an SST neuron (yellow, ES: 200 pA, 30 Hz). # of spikes, Pyr: Control: 52, ES: 56; Pvalb: Control: 702, ES: 864; SST: Control: 216, ES: 218.

Figure 2.. Cell class-specific entrainment of spiking to ES.

a, Simultaneous spiking induced by a suprathreshold DC stimulus I_inj co-occurs with sinusoidal ES. Despite its relatively small amplitude (see Figure 1c and Figure 2), the subthreshold effect entrains neuronal spike timing (left to right: traces from a pyramidal, a Pvalb and an SST neuron) without affecting the spike rate (see Figure S1). b, Spike-phase distribution for pyramidal (green), Pvalb (red), and SST (orange) cell classes for varying ES parameters. (Rows) ES frequency (top to bottom): 8, 30, to 140 Hz. (Columns) ES amplitude (left to right): 0 (Control), 50, 100 and 200 nA. “Control” indicates no ES is applied (ES amplitude: 0 nA). Control experiments show symmetric spike-phase distribution, i.e., no inherent preferred spike-phase in the absence of ES, as assessed by Rayleigh’s test (p>0.05, see Table S2). Increasing (but subthreshold) ES amplitude generally increases spike-phase entrainment. Different ES frequencies have a distinct, cell class-specific effect on spike phase entrainment. Summary statistics for the highest amplitude (in yellow box) plotted in c. c-e, Spike entrainment to ES assessed via the Rayleigh’s test (c) and the population vector length (d-e) against the ES frequencies (ES amplitude: 200 nA). c, p-values calculated for pyramidal, Pvalb, SST spikes (left to right) via Rayleigh’s test as function of ES frequency show statistically significant spike phase entrainment (*p < 0.05, **:p < 0.01, ***p < 0.001, ****p < 0.0001, see Table S2). Dashed pink line: p-value at 0.05. Pyramidal spiking entrains to slow (8 Hz), medium (30 Hz), and fast (140 Hz) ES frequencies while Pvalb and Sst are most strongly entrained by high ES frequencies (140 Hz). d, The population vector length plotted for each cell (gray circles) within each class (left to right: Pyramidal, Pvalb, SST). Purple and blue lines: mean and median values, respectively; error bars: st.d. e, The population vector length for each cell (from d) across each ES frequency is compared against control conditions (no ES) to assess degree of entrainment (paired t-test, false discovery rate (FDR)-corrected for multiple comparisons: *p<0.05, **p<0.01, ****p<0.0001) Pyramidal: N=21 cells for 8, 30 Hz, N=13 for 140 Hz; Pvalb: N=22 cells for 8, 30 Hz, N=12 for 140 Hz; Sst: N=13 for 8, 30 Hz, N=10 for 140 Hz.

Figure 3.. Non-specific, ES frequency-independent subthreshold entrainment of excitatory and inhibitory cell classes to ES.

a, Entrainment of V_i to ES, for pyramidal (green), Pvalb (red), and SST (orange) cells. Gray traces: V_e measured at the closest extracellular location (15 μm) from the cell soma. The subthreshold sinusoidal ES is delivered 50 μm from cell soma (frequency: 8 Hz, amplitude: 100 nA). b, c ES effect on neurons at resting potential (ES amplitude: 100 nA, frequency: 1 to 100 Hz). Amplitude (b) and phase (c) of the ES where V_e (gray), V_i (green, red, or orange), and V_m (blue) for each cortical cell type (circles: mean; error bars: std; left to right: pyramidal, Pvalb, SST). The three cell classes exhibit ES frequency independence with induced V_i, V_e and V_m amplitude and phase remaining constant for ES frequencies ranging 1–100 Hz (one-way ANOVA, p>0.05 for Pyr, Pvalb, and SST). d, ES effect on hyper- and depolarized neurons held at a range of membrane potentials via injection of depolarizing or hyperpolarizing current I_inj (from −90 to 90 pA). The sinusoidal ES is simultaneously applied with I_inj (ES amplitude: 100 nA, frequency: 8 Hz). e, f Amplitude (e) and phase (f) of the ES-induced V_e (gray), V_i (green, red, or orange), and V_m (blue) for each cortical class for hyper- and depolarizing I_inj (circles: mean; error bars: std; left to right: pyramidal, Pvalb; right: SST). The induced ES effect on V_i, V_e and V_m amplitude and phase are broadly independent of membrane polarization and remain constant across a range of 40 mV for the three classes. N=24 cells (Pyramidal), N=22 cells (Pvalb), N=6 cells (SST).

Figure 4.. Cell class-specific ES entrainment of spiking correlates with spike rate properties of the individual classes.

a, Schematic diagram demonstrating the instantaneous spike rate for each spike, calculated as the inverse of the interspike interval (ISI). ISI: time between a spike and the next consecutive spike. b, Histogram of the instantaneous spike rate distribution for all spikes recorded in pyramidal (green), Pvalb (red), and SST (orange) cell classes. (Pyramidal : N=21 cells, Pvalb: N=22 cells, SST: N=13). c, Degree of spike entrainment (as evaluated by population vector length) to ES (8 Hz and 200 nA) for each recorded cell’s spikes in the pyramidal class containing only spikes within a specific spike-rate range/bin (vector length means bootstrapped for 10000 trials). Bin size (boundaries) are designated by the spike rate to be analyzed (a “Center” Frequency) within a frequency-window range (ranging from ±1 to ±6 Hz). Tighter spike-frequency ranges are on the left, with the range widening towards the right. Boxplots: quartiles; purple and blue lines: mean and median values, respectively; whiskers: remaining distribution. d, Plot of -log₁₀ p-values (Welch’s t-test; null-hypothesis: the two populations have equal means) for comparison between the same-spike-range bins (e.g., 8±1 Hz Control vs 8±1 Hz ES bins) between Control and ES (in c)). Dashed pink line: p=0.05; #: effect size (Cohen’s d) where d>0.8. e, Degree of spike entrainment (expressed as % of the normalized vector length, 0–1) to Control (no ES; left column) or ES application for spikes within specific spike-rate bins, in pyramidal (green), Pvalb (red), and SST (orange) classes (right column). Results shown for ES (200 nA) at 8 Hz for Pyr, 140 Hz for Pvalb, and 30 Hz for SST. f, Percentual increase in spike entrainment (vector length) in ES vs. Control for Pyr, Pvalb, and SST. Pyramidal: N=21 cells for ES frequencies 8, 30 Hz and N=13 for 140 Hz; Pvalb: N=22 cells for ES frequencies 8, 30 Hz and N=12 for 140 Hz; SST: N=13 for ES frequencies 8, 30 Hz and N=10 for 140 Hz.

Figure 5.. Computational modeling suggests spike rate differences rather than individual conductances as the major contributor to class-specific spike-field coupling.

a, (Top left) A bio-realistic model of a pyramidal neuron (cell ID: 488698341) is used to emulate the experimental setup accounting for the sinusoidal ES. Intracellular DC current is combined with weak sinusoidal ES of various frequencies (8, 30 and 140 Hz) such that, just as in the experiments, the spike rate remains unperturbed by the ES). (Bottom left) Model ISI distribution (Control). (Right) Spike-phase relationship for the simulations (ES at 200 pA, top-to-bottom: 8, 30 and 140 Hz ES). Weak ES gives rise to strong spike-phase coupling in the presence but not in the absence of ES. (Top right) Same setup as for panel a but using a bio-realistic inhibitory Pvalb model (cell ID: 569998790; see also Figure S8). The Pvalb model shows preferential entrainment to fast ES while the pyramidal model readily entrains to both slow and fast ES (Figure S9). b, Top, Hall of fame (hof) models of the pyramidal (left)_and Pvalb (right) cell from panel a exhibit the robustness of the spike-field coupling (40 hof models per cell; Figure S8). Identical setup like in panel a for each hof model (spike-field entrainment: population vector length; thin lines: vector length for each hof model; thick line: mean vector length across hof models; cyan: control, no ES). With Pvalb spiking faster than pyramidal models (spike rate distributions in panel a), ES strongly entrains all hof models when ES frequency matches the spike rate. b, Bottom, Spike phase entrainment at the preferred ES frequency (pyramidal: 8 Hz; Pvalb: 140 Hz) across hof models for two pyramidal (pyramidal A: 488698341; pyramidal B: 354190013) and two Pvalb cells (Pvalb A: 569998790; Pvalb B, 471077857). c, Correlation between model conductances and spike-phase entrainment at the preferred ES frequency (for pyramidal neurons: 8 Hz; Pearson correlation across hof models; 40 hof models per cell; panel b, bottom row). Green boxes: statistically significant correlations (p<0.0017 for pyramidal and p<0.002 for Pvalb models). No conductance consistently correlates across the two pyramidal cells (i.e., compare locations of green boxes left vs. right column) despite the strong spike-phase coupling of individual hof models (panel b).

Figure 6.. Sub- and spiking ES entrainment of human neurons.

a, Top (left): Human ex vivo cortical slice obtained via neurosurgical tissue resections. (Right) Sample intracellular electrophysiology trace of human pyramidal neuron after depolarizing and hyperpolarizing current injections. Bottom (left): Human cortical slice with extracellular electrodes recording V_e at multiple locations 50–120 μm from pyramidal soma (white spot: soma of recorded cell filled with biocytin and dye for identification). (Middle): Pyramidal cell morphology of recorded cell visualized with post-hoc biocytin-HRP staining. (Right): f-I curves of recorded cells. b, Left: V_e amplitude as function of distance between ES and recording electrodes (ES amplitude: 25–200 pA; ES frequency: 8 Hz; circles: V_e mean amplitude; error bars: V_e amplitude st.d.) Trendlines: least-squares fit of the point source approximation. c, V_e and electric field amplitude elicited by the ES at the extracellular recording electrode closest to the whole-cell patched soma (approx. 15 μm). Blue: V_e amplitude for each experiment (n=5); Black: mean and st.d. across experiments. d, Sample trace of a human pyramidal neuron showing entrainment of V_i (green trace) to subthreshold ES. V_e (gray trace) measured at the closest extracellular location (15 μm) from the cell soma. The subthreshold sinusoidal ES is delivered 50 μm from cell soma (frequency: 8 Hz, amplitude: 100 nA). e, Simultaneous spiking induced by a suprathreshold DC stimulus I_inj that co-occurs with sinusoidal ES in human neurons. Despite its relatively small amplitude (see also c), the subthreshold ES affects neuronal spike timing without altering the spike number or frequency. f, Spike rate distribution for all spikes recorded from the human pyramidal neurons (N=4 cells). g, Subthreshold ES effect at resting potential (top) and at hyper- and depolarized potentials (bottom). Neurons were held at a range of membrane potentials via injection of depolarizing or hyperpolarizing current I_inj (from −90 to 90 pA). (ES amplitude: 100 nA, ES frequency: 1 to 100 Hz). V_e (gray)-, V_i (green)- and V_m (blue outlined circle)-amplitude (left) and phase (right) are shown (circles: mean; error bars: std). Human pyramidal neurons exhibit ES-frequency independence with induced V_i-, V_e- and V_m-amplitude and -phase remaining constant across ES frequencies 1–100 Hz (top). The induced ES effect on V_i, V_e and V_m amplitude and phase remain constant across a range of 40 mV polarization (bottom). h, Spike-phase distribution for varying ES parameters. (Rows) ES frequency (top to bottom): 8, 30, to 100+ Hz. (Columns) ES amplitude (left to right): 0 (Control), 50, 100 and 200 nA. Increasing ES amplitude increases spike-phase entrainment across slow (8 Hz), medium (30 Hz), and fast (100+ Hz) ES frequencies. i-k, Summary statistics for ES amplitude=200 nA (yellow box in h). i, Spike phase entrainment of human pyramidal neurons to ES assessed via Rayleigh’s test (****p < 0.01; dashed pink line: p=0.05). j, The population vector length for each cell. Purple and blue lines: mean and median values, respectively; error bars: st.d. k, The population vector length for each cell (from j, each line represents a cell) across ES frequencies (paired t-test, false discovery rate (FDR)-corrected for multiple comparisons: *p<0.05, see Table S4). l, Spike entrainment (vector length) in Control (i.e. no ES, left) and ES (8 Hz and 200 nA) experiments (right) for each recorded human pyramidal cell, containing only spikes within a specific spike-rate range/bin. Bootstrap means of spikes within each cell obtained with 10000 trials. Bin size (boundaries) are designated by the spike rate (a “Center” Frequency) within a frequency-window range (ranging from ±1 to ±6 Hz). m, Spike phase entrainment assess via -log₁₀ p-values (Welch’s t-test) for comparison between the same-spike-range bins (e.g. 8±1 Hz Control vs. 8±1 Hz ES bins) between Control vs. ES (in k). Dashed pink line: p=0.05; #: effect size (Cohen’s d) where d>0.8.