Effect of weak EF on membrane voltage. (A) Slow oscillation in active neocortical slice. Top: LFP. Bottom: Multiunit signal. (B) Endogenous EFs. In vitro and in vivo group data for maximum, minimum, and average of the absolute values of maximum and minimum EF peaks for (all significantly different). (C) In vitro, the endogenous EF generated by neuronal activity is considerably weaker (“feedforward”) and thus facilitates the study of the “feedback pathway” in relative isolation by application of external EFs. (D) External EF was generated by two parallel AgCl wires on the two sides of the slice such that field lines were vertical to the cortical layers. Change in transmembrane voltage was recorded by subsequent measurements of intra- and extracellular voltage with the same sharp glass microelectrode at the offset of constant field application. (E) Simultaneous extracellular multiunit (top) and intracellular (bottom) recording of slow oscillation in vitro. (F) Zoom-in on single Up state from (E). Intracellular recording truncated. (G) Left: Schematic representation of applied fields (2 mV/mm and 4 mV/mm). Right: Averaged sample traces that show effect of 2 mV/mm and 4 mV/mm field on somatic transmembrane voltage. Vertical line represents field artifact from switching off field. (H) Group data. Average change in transmembrane voltage ΔV_m for 2 and 4 mV/mm. See also Figure S2.

Sine-wave EFs enhance slow oscillation. (A) Multiunit recording in control condition (0 mV/mm; dashed line: “virtual extension” of field waveform) and with frequency-matched external sine-wave field (4 mV/mm). (B) Autocorrelograms of multiunit firing reveal enhanced oscillatory characteristics during field application (enhanced sideband peak, SB). CP: Central peak. (C) Left: CP was significantly increased for fields with 1.0–4.0 mV/mm amplitude (median modulation index). Right: SB/CP was significantly increased for fields with 1.0–4.0 mV/mm amplitude (median modulation index). (D) Sine-wave fields with three different periods (T) successfully entrained slow oscillation (top: control, top middle: T = 13.3 sec, bottom middle: T = 10.0 sec, bottom: T = 6.7 sec). (E) Correlograms show enhancement of oscillation at all field periods applied. Dashed lines mark SB peaks. Arrows indicate period of applied EFs. (F) Across experiments, network period matched the period of the applied field (n = 8). See also Figure S4.

In vivo field waveform guides network activity in vitro. (A) Time excerpt from representative example experiment. Left: Control condition (no field applied). Right: In vivo field applied. Top: Applied field waveform. Middle: Multiunit traces from consecutive trials. During control periods, Up states occur at random points in time. In presence of in vivo field, Up states occur preferentially aligned with applied field waveform. Bottom: Multiunit activity averaged across all trials. (B) Top: Applied in vivo field waveform (duration: 60 sec). Bottom: Multiunit activity averaged across experiments for control condition (black) and for condition with in vivo field (red). Multiunit activity is normalized to the average activity level during control epochs. (C) Zoom in from panel (B) as indicated by dashed box. Averaged multiunit (red) and applied EF (black). (D) Relative enhancement of the instantaneous multiunit activity as a function of the instantaneous applied field strength (binned in 0.25 mV/mm intervals). Population average across experiments (n = 7). Black: Control. Red: In vivo field applied, fitted with exponential function. Curves significantly diverge for field strengths of 0.50 mV/mm and higher (all points p <0.005). See also Figure S6.

Computational network model supports global small somatic depolarization as mechanism for activity modulation by EFs. (A) Network model with 2D layers of pyramidal neurons (PYs, green) and inhibitory interneurons (INs, blue). Constant, sine-wave and feedback fields were simulated by according somatic current injections into both PYs and INs to cause depolarization that mimicked the measured effect of EFs on the somatic membrane voltage of neurons. (B) Sine-wave EF entrains slow oscillation. Top: Raster plot of PY cell spiking (two-dimensional network structure was linearized for presentation purposes). Red: Applied sine-wave EF waveforms. Black: “Virtual extension”. Bottom: Representative PY membrane voltage trace. (C) Average PY membrane voltage V_m. No field applied (control, top) and sine-wave field application with different oscillation periods (2nd from top to bottom). Entrainment occurs for oscillation periods close to intrinsic oscillation period. (D) Feedback field enhances slow oscillation structure. Top: Sample membrane voltage trace (black: control, red: with feedback field). Bottom: Average PY V_m (left: control, right: with feedback field). See also Figure S7.

Structured neocortical network activity and associated endogenous EF. (A) Extracellular recording in primary visual cortex in anesthetized ferrets exhibits the slow oscillation. Top: Broadband LFP recording. Bottom: High-pass filtered multiunit activity. Network activity is structured into alternating epochs of activity and quiescence (Up and Down states). (B) EF is the spatial gradient of the LFP determined from simultaneous multi-site recordings. Top: LFP traces of two neighboring electrodes (spacing: 150 μm). Bottom: Corresponding EF. (C) Sample experiment: LFP (left) and EF (right) exhibit spatio-temporal pattern that reflects the oscillatory nature of the ongoing network activity. Averaged traces are aligned on Up state initiation at time 0 sec. Depth 0 mm corresponds to the most superficial electrode site where extracellular multiunit activity was first detected. (D) Group data: Maximum, minimum, and average of the absolute values of maximum and minimum EF peaks. (E) Conceptual framework: Neuronal network activity generates an EF (“feedforward”). This EF in turn may influence neuronal activity (“feedback”). See also Figure S1.

Constant EF enhances slow oscillation by decreasing oscillation period and shortening of Down states. (A) Frequency of Up states increased in presence of constant field. Top: Control. Bottom: With constant field. Up states are numbered to facilitate comparisons between conditions. (B) Left: Oscillation period is significantly decreased in presence of external field with 2 or 4 mV/mm amplitude. Middle: Down state duration is significantly decreased for 2 mV/mm and 4 mV/mm. Right: Up state duration remains unaffected for all field amplitudes used (2.0 and 4.0 mV/mm shown). See also Figure S3.

Sine-wave field entrains Up states. (A) Left (black): Slow oscillation in control condition (0 mV/mm; no applied field). Dashed line represents “virtual extension” of applied sine wave. Right (red): Slow oscillation with sine-wave EF (4 mV/mm). Up states are marked with a label and their respective phases are shown. (B) Representative examples of Up state phase as a function of cycle number of the Up state. (C) Left: Schematic representation of preferred phase as an attractor. If the phase assumes a value outside the basin of attraction for a given Up state (e.g. Up state “D”), the phases of the consecutive Up states rapidly change such that they converge back to preferred phase. Right: Schematic representation of phase difference |Δϕ| as the absolute value of the difference between the two phases of two consecutive Up states. (D) Up state phase distribution for control, 2 mV/mm, and 4 mV/mm applied sine wave fields (Pr: Probability). Peak of phase histogram indicates preferred phase (n = 10). Normalized entropy H measures how uniform the phase distribution is. (E) Absolute phase difference |Δϕ| of all consecutive Up state pairs (ϕ₁, ϕ₂) as a function of phase ϕ₁ is largest for values that are farthest from the preferred phase. See also Figure S5.

Activity-dependent, positive feedback electrical field enhances slow oscillation. Negative feedback field decreases rhythmic structure of the slow oscillation. (A) Feedback loop is provided by real-time field simulator that provides an EF based on the ongoing multiunit activity. Top: Sample multi-unit trace. Bottom: Simulated EFs. (B) Representative positive feedback sample experiment. Slow oscillation is more regular in presence of the feedback loop (bottom) than in absence (control, top). (C) Correlogram of multiunit activity shows both an enhanced central peak (CP) and a more pronounced side-band peak (SB) in presence of the positive feedback (red) in comparison to control condition without feedback (black). (D) Group data correlograms (n = 7). Activity levels (left) and slow oscillation structure (right) were enhanced in presence of positive feedback field with median relative increase in CP amplitude: 120% (p = 0.016) and SB/CP ratio: 150% (p = 0.031). (E) Negative feedback experiments. Left: Endogenous EF in vitro (black) and EF in presence of negative feedback field (red). Right: Positive peak field strength at onset of Up state was reduced to 47% of control (p = 0.0078, n = 8). (F) Coefficient of variation of both Up and Down state duration decreased in presence of positive feedback EF (red, Up: 86%, p = 0.016; Down: 83%, p = 0.016) but increased in presence of negative feedback EF (blue, 111% of control for both, n = 8, p = 0.0039 and p = 0.0078, respectively).