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. Author manuscript; available in PMC: 2009 Nov 28.
Published in final edited form as: Neuron. 2009 May 28;62(4):566–577. doi: 10.1016/j.neuron.2009.04.027

Instantaneous modulation of gamma oscillation frequency by balancing excitation with inhibition

Bassam V Atallah 2, Massimo Scanziani 1
PMCID: PMC2702525  NIHMSID: NIHMS121330  PMID: 19477157

SUMMARY

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.

INTRODUCTION

One of the most prominent characteristics of cortical activity is the rhythmic fluctuation of large neuronal populations in synchrony. Such oscillations occur over a wide range of frequencies, from 0.1Hz to >100 Hz depending on the behavioral state of the animals (Buzsaki, 2006; Steriade, 2006). Gamma oscillations are a particularly prominent form of rhythmic activity that results from the synchronous fluctuation of the membrane potential of cortical neurons at frequencies between 20 and 60 Hz (Jagadeesh et al., 1992; Penttonen et al., 1998; Soltesz and Deschênes, 1993). These gamma rhythms occur during wakefulness, attentive behavior (Bragin et al., 1995; Chrobak and Buzsaki, 1998; Fries et al., 2001; Womelsdorf et al., 2005) as well as in some anesthetized states (Gray and Singer, 1989; Jones and Barth, 1997; Neville and Haberly, 2003). They are evoked by external stimuli in sensory cortices (Gray and Singer, 1989; Jones and Barth, 1997; Neville and Haberly, 2003), by exploratory behavior in the hippocampus (Bragin et al., 1995), and precede motor responses in premotor areas (Pesaran et al., 2002).

Activity at gamma frequencies is thought to play a major role in the propagation of information across cortical areas (Engel et al., 2001; Sirota et al., 2008; Womelsdorf et al., 2007). By synchronizing the spiking activity of multiple neurons, gamma oscillations may allow these neurons to efficiently cooperate in the recruitment of their postsynaptic targets, thereby facilitating the transmission of information (Bruno and Sakmann, 2006; Womelsdorf et al., 2005). Indeed, odor evoked oscillations triggered in the olfactory bulb are effectively transmitted all the way through olfactory and entorhinal cortex to the hippocampus (Martin et al., 2007). Synchronous spiking during gamma activity may also regulate the efficiency by which two distinct groups of neurons recruit a third group to which they both project, thereby contributing to the merger, or “binding,” of information originating from distinct regions (Engel et al., 2001). When two groups of neurons oscillate synchronously or in-phase, they can act synergistically to recruit target neurons by exciting them simultaneously. However, even subtle changes in the phase or frequency of the oscillations in one group with respect to the other may dramatically alter this synchrony and the subsequent recruitment of downstream target neurons (Fell et al., 2001; Schoffelen et al., 2005). The transmission of information during gamma oscillations is therefore a dynamic process that depends on the precise timing of the oscillation.

Even within a specific cortical location, the instantaneous frequency of gamma oscillations changes from one moment to the next (Bragin et al., 1995; Womelsdorf et al., 2007). This ongoing modulation in oscillation frequency (or phase) affects the precise timing of neuronal spiking within that cortical location, thereby altering the efficacy with which information is transmitted to downstream regions. In fact, a recent study has shown that the precise phase of oscillatory activity can determine whether or not activity is effectively transmitted between cortical areas (Womelsdorf et al., 2007).

Despite the importance of frequency modulation in transmission of information across cortical areas, little is known about the mechanisms that drive rapid changes in oscillation frequency. Here we show that in the hippocampus the CA3 network maintains inhibition proportional to excitation during each oscillation cycle. This ongoing adjustment in the level of inhibition results in an instantaneous modulation of oscillation frequency. Thus, changes in inhibitory synaptic activity control the instantaneous oscillation frequency on a cycle-by-cycle basis.

RESULTS

Oscillation Amplitude Predicts Instantaneous Oscillation Frequency

To determine how frequency and amplitude of hippocampal activity vary in vivo, we recorded the local field potential (LFP) in area CA3 of anesthetized rats (Figure 1). A prominent feature of the recorded activity was periodicity at gamma frequencies (Bragin et al., 1995; Csicsvari et al., 2003). We observed robust rhythmic activity ranging from 26 to 41 Hz (mean frequency = 34.8 sd 5.3 Hz, n = 6 rats) corresponding to gamma oscillations. While rhythmic activity was an ongoing feature of CA3 activity, the precise amplitude and frequency varied substantially from one oscillation cycle to the next (Figure 1A, B).

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

Figure 1

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(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.

The interval between individual oscillation events (interevent interval, IEI) varied from one cycle to the next, from 12 ms to over 40 ms, corresponding to instantaneous frequencies spanning a large frequency band (25–80 Hz). Strikingly however, the changes in amplitude and frequency were not independent. We observed a substantial decrease in the instantaneous frequency of rhythmic activity following large oscillation cycles. The amplitude of an oscillation cycle was strongly correlated with the latency to the subsequent oscillation (r = 0.51 ± 0.03, n = 6 rats, Figure 1B). Consistent with oscillation amplitude predicting the latency to the next cycle the amplitude of an oscillation cycle was only weakly correlated with the latency the previous cycle (r = 0.18, n = 6 rats, discussed further in Supplementary Materials). The correlation between amplitude and interval to the subsequent cycle was not unique to gamma activity in anesthetized rats. In fact, a similar correlation existed during gamma activity recorded in area CA3 of the hippocampus of freely-moving rat (r = 0.46, Figure S1). These results demonstrate that the amplitude of an oscillation cycle predicts the instantaneous oscillation frequency.

In order to determine whether these rapid fluctuations in LFP amplitude and frequency reflect changes in the spike output of the CA3 network, we recorded multi-unit spiking activity via extracellular electrodes placed in the pyramidal cell layer of anesthetized rats. Fluctuations in LFP amplitude were accompanied by changes in spike rate (Figure 1E and S2). Spikes were precisely phase-locked to the LFP oscillation as demonstrated by the peri-oscillation time histogram (POTH, Figure 1D) (Bragin et al., 1995; Csicsvari et al., 2003; Tukker et al., 2007) and spike-LFP coherence (Figure S2). Furthermore, despite large ongoing changes in oscillation amplitude, the time window in which spikes occurred was equally narrow during both large and small amplitude cycles (full-width at half maximum, FWHM, of the POTH: 6.3 ± 1.0 ms for small cycles and 7.1 ± 1.4 ms for large cycles, n = 6 rats; Figure 1E). Taken together these data demonstrate that during gamma activity recorded in vivo the correlated fluctuations in amplitude and frequency of the LFP are precisely reported by the number and the timing, respectively, of spikes generated in the CA3 network.

What cellular mechanisms underlie the correlation between amplitude and instantaneous frequency of the LFP during gamma oscillations? To monitor synaptic events during gamma oscillations, we performed a series of experiments in acute hippocampal brain slices. First, we verified that oscillations generated in vitro also exhibited correlated changes in amplitude and frequency. Ongoing gamma oscillations were generated in area CA3 by bath application of low concentrations of kainic acid (100–500 nM) (Hájos et al., 2000) and recorded by placing a field electrode in the stratum radiatum of the CA3 region (Figure 2A). A distinct spectral peak in LFP activity occurred at frequencies between 25 Hz and 40 Hz (mean 29.8 Hz s.d. 2.4 Hz) as observed in vivo. Furthermore, rhythmic activity in vitro also exhibited large changes in both amplitude and frequency (Figure 2A). Finally, as observed in vivo, during rhythmic activity generated in vitro the amplitude of a cycle was a good predictor of the interval to the next cycle (r = 0.69 ± 0.02, n = 6 slices; Figure 2B. This correlation was not the spurious result of constructive and destructive summation of individual LFP oscillations; see Supplementary Materials and Figure S3).

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

Figure 2

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(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.

Balanced Fluctuations of Excitation and Inhibition Underlie Variation in Oscillation Amplitude

In order to determine what synaptic events underlie gamma oscillations we performed whole-cell voltage-clamp recordings from CA3 pyramidal cells while monitoring the LFP with an electrode placed in the stratum radiatum. Pyramidal cells were voltage clamped at either the reversal potential for inhibition (VH ≈ −85 mV) or for excitation (VH ≈0 mV) to isolate excitatory postsynaptic currents (EPSCs) and inhibitory postsynaptic currents (IPSCs), respectively (Figure S4). Both excitatory and inhibitory synaptic currents occurred at gamma frequencies, as shown by the power spectrum, and exhibited a pronounced peak in coherence with the simultaneously recorded LFP within the gamma frequency band (Figure S4). While the rise time of excitatory and inhibitory currents during each oscillation cycle (computed using an oscillation triggered average, Fig 2C) were similar (10–90% rise-time EPSC: 4.0 ± 0.5, IPSC 4.3 ± 0.6, t-test p = 0.7, n = 6) the decay time of IPSCs was ~ 50% longer then that of EPSCs (mono-exponential fit EPSC: 8.5± 1 ms, IPSC: 13.2 ± 2.5 ms, t-test p <0.003; n = 6).

Importantly, the amplitude of both EPSCs and IPSCs exhibited large cycle-to-cycle fluctuations that were correlated with the LFP oscillation amplitude on a cycle-by-cycle basis (r = 0.63 ± 0.05; n = 8 pairs and r = 0.65 ± 0.07; n = 8 pairs respectively, Figure S4). This suggests that cycle-by-cycle variation in excitatory and inhibitory currents may not be unique to each cell but common across the population. To address this possibility, we recorded EPSCs simultaneously in two neighboring CA3 pyramidal cells (Figure S5). We found that a substantial fraction of variation in EPSCs amplitude was common to both cells (r = 0.54 ± 0.10; n = 5 pairs, Figure S5). Similarly when both pyramidal cells were voltage clamped at the reversal potential for excitation, we observed a strong correlation between the amplitude of simultaneous IPSCs (r = 0.77 ± 0.07, n = 5 pairs, Figure S5). These data demonstrate that cycle-by-cycle fluctuations in the amplitude of excitatory and inhibitory currents are not cell specific but common across the population.

When the same approach was used to simultaneously record EPSCs and IPSCs (Figure 2C, by holding one of the pyramidal cells at the reversal potential for IPSCs and the other at the reversal potential for EPSCs) we were surprised to find that excitation and inhibition were exquisitely balanced during each cycle. That is, the amplitude of excitatory and inhibitory synaptic conductances (gE and gI, respectively), recorded simultaneously in two pyramidal cells, varied over an order of magnitude from cycle to cycle (e.g. gE: 0.5–8 nS; gI: 2–25 nS) yet strikingly remained proportional (r = 0.63 ± 0.04, slope = 5 ± 0.6, n = 8 pairs Figure 2E). Thus, independent of the amplitude changes, each excitatory synaptic event was almost instantaneously (Figure 2D, excitation led inhibition by 2.3 ± 0.3 ms, n = 8 cells; (Fisahn et al., 1998) counterbalanced by an approximately five times larger inhibitory synaptic conductance (Figure 2E and S4C).

These results show that cycle-to-cycle fluctuations in the amplitude of the LFP reflect underlying fluctuations of both excitatory and inhibitory synaptic currents, yet excitation and inhibition remain balanced such that, during each oscillation cycle, inhibition is larger than excitation.

A Simple Model Predicts the Correlation between Amplitude and Frequency

Can these large cycle-by-cycle fluctuations in synaptic conductances account for the observed changes in interval between gamma events? To test whether the determined synaptic properties may, at least in principle, account for the correlation between oscillation cycle amplitude and frequency we developed a simple model of the CA3 recurrent circuitry. Pyramidal cells and inhibitory interneurons were modeled as single-compartment neurons where intrinsic properties were matched to experimental data (Supplementary Materials). The population of pyramidal cells was reciprocally connected with itself and with a population of inhibitory neurons using physiologically realistic probabilities of connection (Figure S6). When model pyramidal cells were depolarized the network intrinsically exhibited rhythmic oscillations at gamma frequencies (Figure 3). We imposed no rhythmic pattern of depolarization; oscillations resulted from intrinsic circuit dynamics as demonstrated by other models (Bartos et al., 2007; Traub et al., 1996; Wang and Buzsáki, 1996). From the point of view of a “voltage clamped” pyramidal cell within the simulated population, EPSCs generated by the spiking pyramidal cells preceded IPSCs by 3 ms during each oscillation cycle similar to experimental results. Furthermore, during each oscillation cycle the fraction of spiking inhibitory neurons was proportional to that of pyramidal cells. Thus, the amplitude of the EPSC covaried with the amplitude of the IPSC occurring within the same cycle (Figure S6B), as observed experimentally.

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

Figure 3

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(A) Average excitatory (gE, red) and inhibitory (gI, 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 (Vm) of an individual pyramidal cell in modeled circuit (spike truncated), gE (red) and gI (cyan); dotted line illustrates the average Vm.

(D) Oscilllation cycles were binned according to gI amplitude and the OTA of Vm computed for each bin (different colors): average time course of gI in four bins of increasing amplitude (middle) and corresponding (color coded) Vm averages (top). The arrows illustrate that it takes longer for Vm to recover to the average potential (dotted line) after large amplitude cycle. (Bottom) 2D histogram of the cycle-by-cycle correlation between Vm hyperpolarization and the gI IEI. Bins in upper panels are illustrated with solid dots of respective colors.

Importantly, the model captures the correlation between oscillation amplitude and frequency observed during gamma oscillations in vivo and in vitro. In fact, at any given cycle, the larger the synaptic currents, the longer the interval to the next cycle, thereby giving rise to instantaneous frequencies ranging from 28 to 75 Hz (IEI ranging from 13 – 40 ms, Figure 3B). This variability in inter-event interval was not due to a change in the kinetics of synaptic conductance, since, in the model as in the experiment, the kinetics of both excitatory and inhibitory synaptic current remained constant despite large changes in the amplitude (Figure S7). Rather, the larger inhibitory currents produced more pronounced hyperpolarization of the membrane potential of the modeled pyramidal cells. Hence the time required for the membrane potential to recover to the mean membrane potential was increased and the start of the new oscillation cycle delayed accordingly (Figure 3C, D). Thus, the model suggests that network-wide fluctuations in the amplitude of inhibition impose a variable delay to the onset of the subsequent cycle.

To test whether, as predicted by the model, the recovery from hyperpolarization is prolonged after large oscillations as compared to small ones, we recorded CA3 pyramidal neurons in the current-clamp configuration while simultaneously monitoring oscillations with a LFP electrode placed in the stratum radiatum (Figure 4). Pyramidal neurons were systematically more hyperpolarized after larger amplitude oscillation cycles than smaller ones, as illustrated by the significant correlation between oscillation amplitude and membrane hyperpolarization in all neurons (r = 0.47 ± 0.04, n = 11 cells; Figure 4B). Furthermore, a significantly longer time was required for the membrane potential to recover to the mean potential after large oscillations as compared to small ones (Figure 4B, C).

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

Figure 4

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(A) The membrane potential (Vm) 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 Vm). Positivity is up.

(B) Oscillation cycles were binned according to LFP amplitude and the OTA of Vm computed for each bin (different colors): average time course of LFP in four bins of increasing amplitude (top) and corresponding (color coded) Vm averages (middle). Note, that Vm undergoes larger and longer hyperpolarized during large amplitude oscillation cycles. (Bottom, left) 2D histogram of the cycle-by-cycle correlation between Vm 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 Vm 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 Vm (horizontal dotted line). (Bottom) LFP IEI as a function of Vm 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.

Can the entire range of oscillation intervals observed in the LFP be accounted for by changes in the time required for pyramidal cells to recover to their mean membrane potential after each oscillation cycle? To address this question we plotted the inter-event interval recorded in the LFP against the recovery time and fit the relationship with a linear function (Figure 4C). A slope of 1 implies that the recovery time of the membrane potential spans the same range as the inter-event interval in the LFP. The slope was not significantly different from unity (mean slope = 1.16 s.d. 0.31, n = 11 cells, p < 0.12) indicating that changes in recovery time from hyperpolarization can indeed account for the entire range of oscillation intervals. These results indicate that cycle-by-cycle fluctuations in the amplitude of inhibition are likely to play a determinant role in setting the interval between consecutive gamma cycles.

Synaptic Activity during Gamma Oscillations In Vivo

To determine whether the amplitude of the IPSC predicts the interval to the next gamma oscillation cycle in vivo, as established in vitro, we performed whole-cell voltage-clamp recording from hippocampal CA3 neurons in anesthetized rats. We simultaneously monitored gamma oscillation with a LFP electrode whose tip was placed ~500 μm from the patch electrode, in the stratum radiatum (Figure 5). Both excitatory and inhibitory synaptic currents coincided with each gamma oscillation cycle, as illustrated by the coherence of EPSCs and IPSCs with the LFP in the gamma band and the OTA (7/8 cells exhibited significant coherence at gamma frequencies and were included in further analysis; Figure 5B, C), consistent with what we observed in vitro (Figure 2D and S4B). The rise and decay times of excitatory and inhibitory currents during each oscillation cycle were also similar to those recorded in vitro (10–90% rise-time EPSC: 4.7 ± 0.4, IPSC 4.3 ± 0.3; mono-exponential decay EPSC: 9.6 ± 1.1 ms, IPSC: 13.9 ± 3.3 ms, n = 7). The relative amplitudes and timing of EPSCs and IPSCs in oscillating cells also matched in vitro synaptic activity, reported above. Specifically, IPSCs recorded during gamma oscillations in vivo were on average 5 times larger (Figure 5D, E) and followed EPSCs by approximately 2 ms (Figure 5C). Furthermore, both EPSC and IPSC amplitude varied over a wide range from one cycle to the next of the gamma oscillation yet were significantly correlated with the amplitude of the simultaneously recorded LFP (r = 0.22 ± 0.04, and r = 0.33 ± 0.02, respectively, p< 0.009 n = 7 cells for excitation and inhibition). We next addressed whether the excitation and inhibition underlying gamma oscillation in vivo also fluctuate in a proportional manner. Since whole-cell recordings were made from single cells in vivo, EPSCs and IPSCs could only be recorded sequentially. In order to directly relate the two synaptic currents we made use of the simultaneously recorded LFP oscillation amplitude. That is, we subdivided LFP oscillations in separate bins according to amplitude and, for each bin averaged the simultaneously recorded EPSC or IPSCs (Figure 5D). A graph of the EPSC amplitudes plotted against the IPSC amplitudes of the corresponding bin illustrated the proportional increase of the two synaptic currents (Figure 5E). These results demonstrate that, despite large fluctuations in their amplitudes, EPSCs and IPSCs are balanced during gamma oscillation in vivo. Finally, as predicted by the model and observed in vitro, the amplitude of the IPSC during each cycle was strongly correlated with the interval to the next gamma cycle, with larger IPSCs predicting longer intervals (Figure 5F, r = 0.31 ± 0.04, p < 0.001, 6/7 cells; remaining cell, r = 0.13 p < 0.06).

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

Figure 5

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(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 (gI) and excitatory (gE) 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.

DISCUSSION

We report that gamma oscillations in the CA3 region of the hippocampus undergo rapid variability in amplitude and that, strikingly, the amplitude of each oscillation cycle predicts the interval to the next cycle. Consistent with a causal relationship between amplitude and the interval to the next cycle, the amplitude of an oscillation was not a strong predictor of the interval to the previous cycle (Supplementary Materials). Using a combination of whole-cell voltage-clamp recordings in vivo and in vitro, we show that synaptic inhibition remains proportional to synaptic excitation during each cycle, despite large cycle-by-cycle fluctuations in the amplitude of excitation. These rapid adjustments in inhibition result in instantaneous changes in the oscillation interval.

Inhibition’s Role in Rapidly Changing Oscillation Phase

Inhibition has long been held to play a role in generating fast rhythmic activity (Horowitz, 1972; Leung, 1982; Leung, 1992). Not only do interneurons participate in these fast oscillations (Buzsaki et al., 1983; Hasenstaub et al., 2005; Tukker et al., 2007) but, experimental and modeling studies have demonstrated that inhibition also plays a critical role in synchronizing neuronal activity (Cobb et al., 1995; Lytton and Sejnowski, 1991), pacing the average oscillation period (Traub et al., 1996; Whittington et al., 1995) and maintaining coherent oscillations (Mann et al., 2005; Van Vreeswijk et al., 1994; Vida et al., 2006; Wang and Rinzel, 1992; Wang and Buzsáki, 1996). Our results indicate that inhibition rapidly modulates the phase or frequency of oscillations on a cycle-to-cycle basis.

We observe that cycle-by-cycle fluctuations in the amount of synaptic inhibition are not specific to individual neurons but, on the contrary, strongly correlate among neighboring pyramidal cells within the CA3 population. The homogeneity of this gamma-modulated inhibition is thus likely to have a strong impact on the excitability of the local population on a moment-to-moment basis (both the spatial coherence of activity at gamma frequencies and interneuron axonal arbors are generally spatially localized to within a few hundred microns (Glickfeld and Scanziani, 2006; Katzner et al., 2009; Sirota et al., 2008); so it is likely that the correlation between synaptic activity in cells, and the correlation between the LFP and synaptic currents, would decrease on a similar spatial scale). Indeed, we report that one of the most direct consequences of the ongoing fluctuations in the amount of synaptic inhibition generated at each cycle is the modulation of the interval to the next cycle. We provide a mechanistic explanation for this phenomenon by showing that larger inhibitory conductances produce a correspondingly larger and longer lasting hyperpolarization of the membrane potential (Figure 4). In fact, the time it takes to recover from the hyperpolarization mediated by each cycle of synaptic inhibition not only strongly correlates with the interval to the subsequent cycle but can, in principle, completely account for the duration of the interval. What role could shunting play in modulating the interevent interval? Synaptic conductance decays as τ ~ 15 ms, thus shunting inhibition is likely to play a role in determining the minimal interval between oscillation events (~ 12 ms). Interevent intervals, however, can be as long as 45 ms (average ~ 33 ms). So pyramidal cell excitability during oscillation cycles longer than 15 ms is likely determined by membrane hyperpolarization rather than shunting since the synaptic conductances substantially decay on time scales greater than τ. These findings do not exclude the possibility that other negative feedback mechanisms, like inhibition of transmitter release via presynaptic glutamate or GABA receptor activation, may also contribute to the observed fluctuations in inter-cycle interval.

Proportional Excitation and Inhibition during Gamma Oscillations

What causes cycle-by-cycle fluctuations in the amount of synaptic inhibition? We observe that during each gamma oscillation cycle, synaptic excitation is almost instantaneously counteracted by inhibition and that the amount of inhibition is proportional to the quantity of excitation recorded at the soma. Inhibition recorded in vivo is on average 4–5 times larger than excitation at the soma (and 3–6 times larger when recorded in vitro, consistent with (Oren et al., 2006). Strikingly, this proportionality is maintained on a cycle-by-cycle basis over a range of synaptic conductances spanning more than one order of magnitude, from less than 1 nS to approximately 10 nS. Thus, the CA3 network is able to maintain a balance between excitation and inhibition despite rapidly changing activity levels during gamma oscillations.

How is balance over such a wide range of activity-levels achieved? It has been shown that even small changes in the number of active excitatory neurons can directly affect the number of active local inhibitory interneurons (Csicsvari et al., 1998; Kapfer et al., 2007; Miles and Wong, 1984; Silberberg and Markram, 2007). Thus inhibition during each oscillation cycle is likely to be recruited by recurrent excitation in proportion to the number of active excitatory neurons thereby providing a rapid balance in each cycle. In fact, we find that even a simple model of a local recurrent network, with realistic anatomical and physiological parameters and random connectivity between pyramidal cells and interneurons, results in a proportional activation of excitatory and inhibitory conductances over a relatively wide range. Consistent with the idea that recurrent networks balance excitation with inhibition, proportional changes in these two conductances have also been observed in the neocortex during non-rhythmic spontaneous activity (Okun and Lampl, 2008), high conductance states (Haider et al., 2006) and sensory evoked activity (Anderson et al., 2000; Wehr and Zador, 2003). While inhibition of the soma of pyramidal cells is likely to play a key role in maintaining the balance during gamma oscillations (Bartos et al., 2007; Hasenstaub et al., 2005; Mann et al., 2005) inhibition of other subcellular compartments may also contribute to the observed proportionality (Hajos et al., 2004).

Given the relatively constant relationship between excitatory and inhibitory conductances, why is the membrane potential of pyramidal cells more hyperpolarized after large amplitude oscillation cycles? One would expect that, despite large cycle-by-cycle fluctuations in synaptic conductances, the balance between excitation and inhibition may maintain the trajectory of a cell’s membrane potential relatively constant. The dynamics of these two opposing synaptic currents differ however such that IPSCs occur ~2 ms later and decay slower than EPSCs. These kinetic differences tip the balance towards hyperpolarization during the late phase of each oscillation cycle. These observations underscore the critical role of the fine temporal structure of excitatory and inhibitory events in controlling the membrane potential (Pouille and Scanziani, 2001) and hence the interval between oscillation cycles.

Importantly, although excitatory and inhibitory synaptic activity is proportional on a cycle-by-cycle basis these two opposing synaptic conductances are not perfectly correlated. Similarly, in neighboring neurons despite substantial co-variation of inhibition (and also of excitation) cell-to-cell variability remains. Differences in connectivity between pyramidal cells and interneurons as well as stochastic synaptic properties such as probability of release are likely to contribute to this variability. This cycle-by-cycle and cell-to-cell variability in the relative magnitude and timing of excitation and inhibition must be critical in determining the identity of cells that spike during each oscillation cycle.

So, the hippocampal circuitry tightly links the amplitude of gamma oscillation with instantaneous frequency: ongoing fluctuations in the number of active excitatory neurons are instantaneously counterbalanced by proportional changes in the number of active inhibitory neurons and the resulting inhibition is translated into variability in interevent interval or oscillation phase. The tight link between amplitude and phase is highlighted by the fact that gamma oscillations recorded under conditions ranging from acute slices to awake behaving animals, all show this fundamental relationship. Thus the hippocampal circuit constrains oscillatory dynamics so that it may not be possible to independently modulate the active number of neurons and frequency.

Synchronous spiking of neurons is an effective means to transfer of information between cortical areas (Bruno and Sakmann, 2006; Womelsdorf et al., 2005). It is believed that oscillations play a role in dynamically modulating synchronous activity to facilitate routing of information across cortical areas in a behaviorally relevant manner (Destexhe and Sejnowski, 2001; Engel et al., 2001; Womelsdorf et al., 2007). That is, distinct groups of oscillating neurons can be phase-locked at specific times and cooperatively drive postsynaptic targets, or be incoherent at other times depending on the nature of sensory stimuli, attentional state and behavior goals. In fact, the coherence between neuronal activity recorded in various sub-regions of the hippocampus undergoes rapid changes during exploratory behavior and spatial (Bragin et al., 1995; Chrobak and Buzsaki, 1998; Montgomery and Buzsáki, 2007). So it is critical to our understanding of how information is routed across different cortical areas to establish how changes in coherence are regulated. This involves determining both the cellular mechanisms that implement phase shifts within a network and how afferent projections drive these changes. We focused on the former in this study. Our results demonstrate that oscillation phase is determined on a moment-by-moment basis by inhibitory activity. We show that as oscillations fluctuate in amplitude, inhibition is adjusted to be proportional to excitation leading to rapid changes in instantaneous oscillation frequency. It will be important for future studies to identify what mechanisms underlie cycle-to-cycle fluctuations in the amplitude of excitation. Phase shifts generated by these fluctuations, by increasing or decreasing coherence between groups of oscillating neurons, may be crucial in differentially routing information to distinct hippocampal areas.

EXPERIMENTAL PROCEDURES

Surgical Procedures

All animal experiments were performed in strict accordance with the guidelines of the National Institutes of Health and the University of California Institutional Animal Care and Use Committee. In vivo experiments were performed in 6–8 week-old rats anesthetized with urethane (1.8 g/kg), and supplemented with ketamine (0.3 g/kg) and xylazine (0.03 g/kg) delivered i.p. The depth of anesthesia was as assessed by toe pinch. Skin incisions were infused with lidocaine. Body temperature was monitored and maintained at 35–37 °C using a heating pad. Animals were head-fixed using Kopf rat adapter and 18° ear-bars mounted on a custom stereotaxic fixture. After removing a section of the temporomandibular muscle a square (~4 mm2) craniotomy was performed. The craniotomy was located 4 mm caudal to the bregma and 7 mm ventrolateral to the sagittal suture along the surface of the skull (i.e. the craniotomy was located on top of the parietal-temporal suture). Two small duratomies were performed using a 30 G needle (<0.5 mm in diameter, one for the extracellular recording electrode and one for the patch pipette), separated by approximately 1 mm along the rostral-caudal axis.

Slice Preparation

Hippocampal slices (400 μm) were prepared from 4–7 week-old Wistar rats and incubated for one hour in an interface chamber at 34°C in oxygenated artificial cerebrospinal fluid (ACSF) containing (in mM): 119 NaCl, 2.5 KCl, 1.3 Na2HPO4, 1.3 MgCl2, 2.5 CaCl2, 26 NaHCO3, and 11 glucose. The slices were kept at room temperature before being placed in a submerged chamber superfused (6 ml/min in a ~1.5 ml bath) with oxygenated artificial cerebrospinal fluid at 32–34°C for recordings. Gamma oscillations were induced by bath application of 100–500 nM of kainate (Hájos et al., 2000). In subset of experiments area CA3 was severed from the dentate and CA1. Under these circumstances rhythmic activity was observed in CA3 but not in the dentate or CA1 indicating that the CA3 network alone is capable of generating gamma oscillations (Bragin et al., 1995; Csicsvari et al., 2003; Fisahn et al., 1998).

Electrophysiology

In vivo recordings

Whole-cell recordings were made with patch pipettes (3–5 MΩ) filled with (in mM): 130 Cs-Methylsulfonate, 3 CsCl, 10 HEPES, 1 EGTA, 10 phosphocreatine, 2 Mg-ATP (7.25 pH; 280–290 mOsm) and 0.2% biocytin. Extracellular recordings were performed using tungsten electrodes (~ 1 MΩ, FHC). Two extracellular electrodes were lowered into the hippocampus. One electrode (rostral duratomy) was inserted perpendicular to the pia and used to locate the CA3 pyramidal cell layer. The other (caudal duratomy) was inserted at a slight angle and advanced into the stratum radiatum such that the tip of the two electrodes, in their final positions, were separated by approximately 500 μm. The electrophysiological signature of area CA3 consisted of robust gamma oscillations in the stratum oriens followed by unit activity in the pyramidal cell layer at a depth of −2.5 to −2.8 mm from the pial surface. Gamma oscillations reversed sign in the stratum radiatum. After locating the pyramidal cell layer the rostral extracellular electrode was retracted and replaced with a patch pipette. Whole-cell recordings were obtained using the “blind” patch-clamp approach (Cang and Isaacson, 2003; Ferster and Jagadeesh, 1992; Margrie et al., 2002). Post-hoc histology was used to verify that recordings were made in CA3 pyramidal cell layer. Recordings were made at approximately −3.8 mm posterior to the bregma and lateral 4.0 mm to the midline.

In vitro recordings

Whole-cell voltage-clamp recordings were made with patch pipettes (3–5 MΩ) containing (in mM): 130 Cs-Methylsulfonate, 3 CsCl, 10 HEPES, 1 EGTA, 10 phosphocreatine, 2 Mg-ATP (7.25 pH; 280–290 mOsm) and 0.2% biocytin. Whole-cell current-clamp recordings were performed with pipettes (3–5 MΩ) filled with (in mM) 150 K-gluconate, 1.5 MgCl2, 5 HEPES, 1.1 EGTA, 10 phosphocreatine (pH 7.25; 280–290 mOsm) and 0.2% biocytin. Voltages were corrected for the experimentally determined junction potential (9.8 ± 0.2 mV; n = 3). Extracellular recordings were performed with tungsten, ni-chrome electrodes or glass pipettes (containing 1M NaCl) placed in the stratum radiatum of the CA3 region. Whole cell recordings were obtained from visually identified CA3 pyramidal cells using infrared videomicroscopy.

Data Acquisition

Whole cell and extracellular recordings, performed in vitro and in vivo anesthetized rats, were carried out using MultiClamp 700B amplifiers and digitized at 20 kHz. Whole-cell recordings were low-pass filtered (2 kHz) and extracellular recordings band-pass filtered (0.1–2 kHz). EPSC were recorded at −87 ± 0.5 mV (n = 12 cells) in vitro and −94 ± 1 mV (n = 12 cells) in vivo. IPSCs were recorded at −1 ± 4 mV (n = 7 cells) in vitro and 22 ± 4 mV (n = 7 cells) in vivo. Excitatory and inhibitory synaptic conductances (gE and gI respectively) were computed assuming that EPSCs were recorded at the reversal potential for inhibition, and that IPSCs were recorded at the reversal potential for excitation. Series resistance, assessed using an instantaneous voltage step in voltage-clamp configuration, was 12 ± 2 MΩ (n = 13 cells) for cells recorded in vitro and 11 ± 2 MΩ (n = 7 cells) in vivo; we compensated for pipette capacitance in cell-attached mode before whole-cell access. When multi-unit recordings were performed in the stratum pyramidale, the sign of the LFP was inverted to be consistent with LFP recorded in the stratum radiatum.

Data Analysis

All analysis was performed with custom routines utilizing Matlab (MathWorks). In order to analyze oscillations events, time periods when the LFP recording exhibited gamma activity were identified. A spectrogram of the broadband recording was constructed from 100 ms windows in 25 ms steps. For analysis we used time periods of at least 100 ms when greater than average power (root mean square) in gamma-band activity was recorded. The extracellular recording was band-pass filtered (5–100 Hz). Individual oscillation cycles were identified as a peak in the LFP (as illustrated in Figure 1). The oscillation cycle amplitude was defined as the peak-to-trough amplitude i.e. the difference between the peak of a given cycle to the subsequent trough of the same cycle (Figure 1). The onset of each oscillation event was defined as the time, after the peak, at which the LFP reached 10% of the oscillation cycle amplitude. The interevent interval of oscillation events was computed as the time between the onset of consequent cycles. Events with very low amplitude, less than 0.25 of the standard deviation in oscillation amplitude, were considered to be noise and omitted (these events made up only a small fraction of all events (<5%) when we reanalyzed the data including these events the results were not significantly difference). The amplitudes of EPSCs and IPSCs during an oscillation cycle were calculated, in a similar manner, i.e. as the difference between the minimum and maximum current within a given cycle (Figure 2C, D). In order to extract multi-unit spiking activity, extracellular recordings were band-pass filtered 0.3–2 kHz, and a threshold applied. A peri-oscillation time histogram (POTH) was then constructed time locked to the onset of gamma oscillation events. The POTH was then fit with a local linear regression (Chronux) in order to extract the full-width at half maximum (FWHM).

Correlation, r, was computed using Pearson’s correlation, Spearman’s rank correlation yielded quantitatively similar results. All individual r values in the reported averages were highly significant (p<0.0001) unless otherwise stated. For further description of correlation methods see Supplementary Materials.

The average time course of EPSCs, IPSCs and intracellular membrane potential during an oscillation cycle (i.e. oscillation triggered average, OTA) was determined by using a method similar to a spike-triggered average. In this case, however, the average was triggered by the onset an oscillation cycle recorded in the LFP.

The latency between EPSCs and IPSCs was computed for each individual cell by using the LFP as a time stamp. We used two different approaches to calculate this latency: first, the time lag between the trough (i.e. dI/dt = 0) of the OTA IPSC and inverted EPSC (Figure 2 & 5), and second, the time lag between the peak in the cross-correlation of the LFP-EPSC and LFP-IPSC. Additionally, in paired recordings we also computed the latency between EPSCs and IPSCs simultaneously recorded measured in two different cells. The results of the three methods were not significantly different.

To determine the relationship between sequentially recorded excitatory and inhibitory currents recorded in vivo, we evenly subdivided the LFP oscillations according to amplitude into 8 to 10 separate bins each contained at least 3 cycles (range: 3–220). Within each cell, we compared the amplitudes of EPSCs and IPSCs belonging to the same bin (Figure 5D).

Power and coherence spectra as well as confidence intervals were computed using multitapered methods (Mitra and Pesaran, 1999), the Chronux package (NIMH) and custom Matlab routines. All spectral analysis were performed on broadband recordings unless otherwise stated.

Statistical analysis was performed using the t-test and fisher transform where appropriate. Error bars are presented in terms of the standard error of the mean, unless otherwise stated.

Model

The local recurrent CA3 circuit was simulated using a model consisting of 400 pyramidal cells and 80 interneurons. Each cell was modeled as single compartment integrate-and-fire neuron with the following parameters. Parameters were chosen to match the range of intrinsic properties and synaptic connectivity patterns experimentally observed in the hippocampus. Excitatory and inhibitory synaptic conductances were modeled with instantaneous rise-times and exponential decays (τ = 5 and 8 ms respectively). Stochasticity was included in the model by the probability of release at excitatory synapses (PR = 0.5) and background synaptic activity introduced as Gaussian noise (s.d. = 50 pA). Modeled pyramidal neurons received no extrinsic rhythmic depolarization. Instead neurons’ resting potential was near threshold (similar to the experimentally recorded mean resting potential of −51.4 ± 1mV, n = 6 of pyramidal cells in vitro) and spiking activity was initiated by the stochastic background synaptic activity. The resulting rhythmic activity was a result of the network dynamics.

Although not directly imposed, the simple model exhibited several key characteristics of real oscillations in the CA3 network: the network spiked rhythmically at intervals of 28–75 ms, excitation led inhibition by 2.5 ms during each oscillation cycle, excitation and inhibition were proportional during each oscillation cycle despite large changes in excitatory conductance and finally the interval between cycles was correlated with the magnitude of inhibitory conductance during the previous cycle. See Supplementary Materials for more details.

Supplementary Material

01

Acknowledgments

We are grateful to S. Leutgeb and D. Schwindel for generously providing the freely-moving rat data. We thank J.S. Isaacson and C. Poo for their help with in vivo recording, insightful suggestions during the entire course of the project; E. Flister and for inspirational conversations; D.N. Hill and the members of the Scanziani and Isaacson laboratories for critically reading the manuscript. This work was funded by the US National Institutes of Health (MH71401 and NS061521).

Footnotes

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