Instantaneous modulation of gamma oscillation frequency by balancing excitation with inhibition

Abstract

Neurons recruited for local computations exhibit rhythmic activity at gamma frequencies. The amplitude and frequency of these oscillations are continuously modulated depending on stimulus and behavioral state. This modulation is believed to crucially control information flow across cortical areas. Here we report that in the rat hippocampus gamma oscillation amplitude and frequency vary rapidly, from one cycle to the next. Strikingly, the amplitude of one oscillation predicts the interval to the next. Using in vivo and in vitro whole-cell recordings, we identify the underlying mechanism. We show that cycle-by-cycle fluctuations in amplitude reflect changes in synaptic excitation spanning over an order of magnitude. Despite these rapid variations, synaptic excitation is immediately and proportionally counterbalanced by inhibition. These rapid adjustments in inhibition instantaneously modulate oscillation frequency. So, by rapidly balancing excitation with inhibition, the hippocampal network is able to swiftly modulate gamma oscillations over a wide band of frequencies.

Figure 1. Gamma Oscillation Amplitude Predicts Latency of Next Oscillation Cycle

(A) (Top) Broadband (gray) and gamma-band filtered local field potential (LFP, 5–100Hz) recorded in the stratum radiatum of area CA3 of an anesthetized rat. Raster plot marks the peak of each oscillation cycle. (Bottom, left) Autocorrelation of LFP and power spectral density of gamma-band LFP. (Bottom, middle) Histograms of oscillation amplitude and IEI. (Inset) LFP (from top panel; time window marked by horizontal bracket) on expanded time-scale to illustrate the measurement of peak-to-peak amplitude and IEI. Positivity is up. (B) (Top) IEI correlated against amplitude of the previous cycle illustrated in 2D histogram. (Bottom) summary of correlations, n = 6 rats. Vertical bar is average. Note the correlation between oscillation amplitude and IEI. (C) Broadband extracellular recording (top), gamma-band LFP (middle, 5–100 Hz band-pass), multi-unit spiking (red, 0.2–2 kHz) from stratum pyramidale of area CA3. Negativity is up. (D) Oscillation triggered average of LFP, peri-oscillation spike-time histogram (POTH), and local linear fit to POTH (green). (E) (Left) Average LFP and POTH fit calculated separately for large (mean amplitude = 313 μV) and small (99 μV, dotted) oscillation cycles. Arrows illustrate the increased latency between spiking events after large amplitude cycles. (Inset) Small POTH scaled to the peak of the large POTH. (Right) Summary of full-width at half maximum (FWHM) of POTH for large (solid) and small (open) oscillation cycles (n = 6 rats). Averages are illustrated with horizontal bars. Note that spiking occurs in a narrow time-window during each oscillation cycle independent of oscillation amplitude.

Figure 2. Excitation Instantaneously Balanced by Proportional Inhibition during Each Gamma Oscillation Cycle

(A) Broadband (gray) and gamma-band filtered (black) LFP recorded in the stratum radiatum of area CA3 in acute hippocampal slice. Raster plot marks the peak of each oscillation cycle. (Bottom, left) Autocorrelation of LFP and power spectral density of gamma-band LFP. (Bottom, middle) Histograms of oscillation amplitude and IEI.. (Inset) LFP (from top panel; time window marked by horizontal bracket) on expanded time-scale to illustrate the measurement of peak-to-peak amplitude and IEI. Positivity is up. (B) (Top) IEI correlated against amplitude of the previous cycle illustrated in 2D histogram. (Bottom) summary of correlations, n = 6 slices. Vertical bar is the average. Note the correlation between oscillation amplitude and IEI. (C) Dual patch-clamp recording from two neighboring CA3 pyramidal cells. Oscillations are monitored with a LFP electrode (black, positivity is up). EPSCs (red) and IPSCs (cyan) simultaneously recorded by holding two cells at the reversal potential for inhibition (−3 mV) and excitation (−87 mV) respectively. Note the correlated fluctuations in the amplitude of excitation and inhibition. (D) (Left) Average time course of EPSC and IPSC (same cell as C) during an oscillation cycle recorded in the LFP i.e. oscillation triggered average (OTA). EPSC is inverted for illustration purposes. LFPs recorded simultaneously with EPSCs and IPSCs are shown as black and gray traces respectively. (Right) Summary of EPSC-IPSC lag during an oscillation cycle. Horizontal bar is the average. (E) (Top) Cycle by cycle correlation between excitatory and inhibitory conductances recorded in pair shown in C. Summary of correlation between excitation and inhibition (bottom) and ratio of mean excitatory and inhibitory conductances (right) (n = 8 pairs). Vertical and horizontal bars illustrate respective averages.

Figure 3. Correlated Amplitude and Frequency in Simple Model of CA3 Circuit

(A) Average excitatory (g_E, red) and inhibitory (g_I, cyan) synaptic conductance received by model pyramidal cells. LFP (black) is approximated as the sum of the two conductances. (B) (Top) Autocorrelation and power spectrum of simulated LFP. (Bottom) Interevent interval correlated against amplitude of the previous cycle illustrated in 2D histogram. (C) The membrane potential (V_m) of an individual pyramidal cell in modeled circuit (spike truncated), g_E (red) and g_I (cyan); dotted line illustrates the average V_m. (D) Oscilllation cycles were binned according to g_I amplitude and the OTA of V_m computed for each bin (different colors): average time course of g_I in four bins of increasing amplitude (middle) and corresponding (color coded) V_m averages (top). The arrows illustrate that it takes longer for V_m to recover to the average potential (dotted line) after large amplitude cycle. (Bottom) 2D histogram of the cycle-by-cycle correlation between V_m hyperpolarization and the g_I IEI. Bins in upper panels are illustrated with solid dots of respective colors.

Figure 4. Larger, Longer Hyperpolarization of Pyramidal Cells following Large Amplitude Oscillation Cycles

(A) The membrane potential (V_m) of a CA3 pyramidal cell recorded using whole-cell patch clamp configuration (IC) and simultaneous LFP recording during in vitro gamma oscillations (dotted line is mean V_m). Positivity is up. (B) Oscillation cycles were binned according to LFP amplitude and the OTA of V_m computed for each bin (different colors): average time course of LFP in four bins of increasing amplitude (top) and corresponding (color coded) V_m averages (middle). Note, that V_m undergoes larger and longer hyperpolarized during large amplitude oscillation cycles. (Bottom, left) 2D histogram of the cycle-by-cycle correlation between V_m hyperpolarization and the IEI measured in the LFP. Bins in upper panels are illustrated with solid dots of respective colors. (Bottom, right) summary of correlation (n = 11 cells). (C) (Top) Oscillation cycles were binned according to LFP IEI and the OTA of V_m computed for each bin (different cell than A and B). Arrows illustrate “recovery time”, i.e. time from onset of oscillation cycle till membrane potential recovers to mean V_m (horizontal dotted line). (Bottom) LFP IEI as a function of V_m recovery time. Open circles and black line correspond to the above cell, other cells shown in grey. Note, mean slope, m = 1.16 s.d. 0.3 suggesting that changes in the time for recovery from hyperpolarization in individual cells can account for the entire range of oscillation intervals observed in the LFP.

Figure 5. Excitation Balanced by Proportional Inhibition during Gamma Oscillations In Vivo

(A) Whole-cell recording of EPSCs in CA3 cell (red) and simultaneously recorded LFP (black, positivity is up) during gamma oscillations in anesthetized rat. IPSCs (cyan) and inverted LFP recorded from the same cell. Note correlated fluctuations in the amplitude of LFP and synaptic currents (B) Coherence between LFP and IPSCs (cyan) or EPSC (red); jack-knifed 95% confidence interval (thin lines); arrows mark peak coherence frequencies. Summary of peak coherence frequency (bottom) and peak coherence (right). Average shown as a vertical or horizontal bar. (C) Oscillation triggered average (OTA) of EPSC (red), IPSC (cyan) and LFP. LFP was recorded simultaneously with EPSCs, IPSC (black and gray traces respectively). EPSC is inverted for illustration purposes. Overlaid POTH (green, data from figure 1D, aligned to the LFP also in green) illustrates spike timing during oscillation cycle. (Bottom) Summary of EPSC-IPSC lag during an oscillation cycle; vertical bar is average. (D) OTA of EPSCs (red), IPSCs (cyan) computed for four different LFP oscillation amplitudes (black; dotted and solid traces were recorded simultaneously with IPSC and EPSCs respectively, same cell as A-C). (E) Summary of correlation between average inhibitory (g_I) and excitatory (g_E) conductance in vivo; individual cells are each represented by a different color linear regression. Note, although excitation and inhibition are proportional, the inhibitory conductance is approximately 5 times larger (dotted line is at unity). (F) OTA of IPSC (middle) computed for four different LFP oscillation interevent intervals (top). Vertical arrows illustrate IPSC amplitude and horizontal arrows the correlated changes in the time to the next oscillation event (IEI). (Bottom) IPSC amplitude during an oscillation event correlated with the time to the next oscillation in the LFP (IEI); blue dots correspond to the four OTA shown above.