hippocampal theta-driving cells revealed by granger causality

Hippocampal Theta-Driving Cells Revealed by Granger Causality

Lu Zhang, Guifen Chen, Ruifang Niu, Wei Wei, Xiaoyu Ma, Jiamin Xu,Jingyi Wang, Zhiru Wang, and Longnian Lin*

ABSTRACT: The two-dipole model of theta generation in hippocam-pal CA1 suggests that the inhibitory perisomatic theta dipole is gener-ated by local GABAergic interneurons. Various CA1 interneurons firepreferentially at different theta phases, raising the question of how thesetheta-locked interneurons contribute to the generation of theta oscilla-tions. We here recorded interneurons in the hippocampal CA1 area offreely behaving mice, and identified a unique subset of theta-lockedinterneurons by using the Granger causality approach. These cells firedin an extremely reliable theta-burst pattern at high firing rates (�90 Hz)during exploration and always locked to ascending phases of the thetawaves. Among theta-locked interneurons we recorded, only these cellsgenerated strong Granger causal influences on local field potential (LFP)signals within the theta band (4–12 Hz), and the influences were persis-tent across behavioral states. Our results suggest that this unique typeof theta-locked interneurons serve as the local inhibitory theta dipolecontrol cells in shaping hippocampal theta oscillations. VVC 2012 WileyPeriodicals, Inc.

KEY WORDS: hippocampus; theta oscillations; theta-lockedinterneurons; theta-driving cells; Granger causality

INTRODUCTION

Network oscillatory activity reflects the dynamic interactions ofensemble neurons in information coding (O’Keefe and Recce, 1993;Skaggs et al., 1996; Buzsaki, 2002; Foster and Wilson, 2006; O’Neillet al., 2008). Theta rhythm is a dominant oscillatory pattern of localfield potentials (LFPs) in rodent hippocampus during voluntary behav-iors as well as rapid-eye-movement (REM) sleep (Grastyan et al., 1959;Jouvet, 1969; Vanderwolf, 1969; Ranck, 1973). The classic theta genera-tion model postulates that at least two theta dipoles are generated in thehippocampal CA1, one by somatic inhibitory postsynaptic potentials(IPSPs) on CA1 pyramidal cells and the other by dendritic excitatorypostsynaptic potentials (EPSPs), (Kocsis et al., 1999; Montgomery et al.,2009). In addition, it has been widely accepted that the medial septum-diagonal band of Broca (MS-DBB) is the ultimate rhythm generator oftheta, and that MS-DBB GABA-containing efferents to the hippocam-

pus innervate most of the GABAergic interneurons(Freund and Antal, 1988). Therefore, hippocampallocal interneurons are generally believed to be criticalin generating theta oscillations (Fox, 1989; Ylinenet al., 1995; Kamondi et al., 1998; Wang, 2010).

Hippocampal CA1 theta cells (Ranck, 1973) wereoriginally identified by their characteristic firing pat-terns relative to theta oscillations in freely moving ratsand were later classified mainly as inhibitory inter-neurons (Fox and Ranck, 1975, 1981). Phase relationsbetween these theta-locked interneurons and thetawaves have been further studied in both anesthetizedand freely behaving animals. In freely moving rats,interneurons in both the pyramidal layer and the stra-tum oriens/alveus fired preferentially on the negativephases of the theta waves (Csicsvari et al., 1999). CA1theta-locked interneurons were recently classified intofour groups based on their preferred firing thetaphases (Czurko et al., 2011). In anesthetized rats, dis-tinct types of hippocampal interneurons also fired atdistinct phases of the theta cycle (Klausberger et al.,2003; Klausberger and Somogyi, 2008). However,theta phase-locked firing itself does not answer thequestion of whether and how distinct types of theta-locked interneurons contribute to the generation oftheta oscillations. For example, CA1 pyramidal cellsalso have phase-locked firing to the theta waves duringexploration, but their theta phase-locked firing is gen-erally believed to be important in temporal coding,but not involved directly in the generation of thetheta dipoles in hippocampal CA1 (O’Keefe andRecce, 1993; Skaggs et al., 1996; Buzsaki, 2002;Foster and Wilson, 2006; O’Neill et al., 2008).

Granger causality is a statistical concept of causalitybased on prediction (Granger, 1969; Geweke, 1982,1984). Recently, it has been reported that Grangercausality analysis can be applied to evaluate the causalinfluence among simultaneous neural signals (Brovelliet al., 2004; Chen et al., 2006; Seth and Edelman,2007; Gregoriou et al., 2009). If hippocampal theta-locked interneurons were involved directly in thetageneration, we would expect that the time series oftheir spike activity should exhibit theta rhythmic spik-ing and their rhythm should precede the theta rhythmof LFPs. Thus the temporal relationship can bedetected by the Granger causality test. We thereforeemployed the Granger causality method to identifydirectionality of neuronal interactions between spikeactivity of theta-locked interneurons and simultaneous

Key Laboratory of Brain Functional Genomics (Ministry of Education),Institute of Brain Functional Genomics, East China Normal University,3663 Zhongshan Road N., Shanghai, ChinaGrant sponsor: National Natural Science Foundation of China; Grantnumber: 30990262; Grant sponsor: Innovation Program of Shanghai Mu-nicipal Education Commission; Grant number: 09ZZ44.*Correspondence to: Longnian Lin, Institute of Brain FunctionalGenomics, East China Normal University, Shanghai 200062, China.E-mail: [email protected] for publication 30 January 2012DOI 10.1002/hipo.22012Published online in Wiley Online Library (wileyonlinelibrary.com).

HIPPOCAMPUS 00:000–000 (2012)

VVC 2012 WILEY PERIODICALS, INC.

LFPs, in hope of pinpointing the contributions of these cells togenerating theta oscillations.

MATERIALS AND METHODS

Subjects

All procedures involving experimental animals were carriedout in accordance with the Animals Act, 2006 (China) andassociated procedures. Twenty-six male C57BL/6J mice (4- to7-months old, 25–35 g at implantation) were used for record-ing, and were singly housed in plastic buckets (55 cm diameter3 42 cm height), with free access to food and water, on a 12h light-dark cycle.

Microdrive Making and Surgery

We designed a recording microdrive, which allowed us toimplant two independently adjustable electrode bundles of 12tetrodes into both sides of dorsal hippocampi. The detaileddescription has been published (Lin et al., 2006). Theimplanted electrodes can be slowly advanced towards therecording position by turning the small screw nuts on themicrodrive. Tetrodes were constructed from four twisted 13-lm nichrome wires (California Fine Wire, Grover Beach, CA).Before implantation, the tips of electrodes were plated withgold to reduce their impedance to 500–800 KX at 1 kHz.

For implant, mice were anesthetized with i.p. injection ofpentobarbital sodium (40 mg kg21), and the body temperaturewas kept constant by a small animal thermoregulation device(FHC, Bowdoin, ME). Then skull was exposed for implantingelectrodes. The positions for two bundles of tetrodes (2.3 mmposterior to bregma and 2.0 mm lateral to bregma on bothsides) were measured and marked, and then holes at these posi-tions were drilled in the skull. After that, two-independentlyadjustable bundles of 12 tetrodes were positioned and loweredthrough the drilled holes into the cortex above the dorsal hip-pocampi. The gaps between the electrodes and holes were filledwith softened paraffin and the microdrive was secured to theskull using dental cement.

In Vivo Recording

After implant, mice were normally singly housed in the‘‘homecages’’ (plastic buckets), and were allowed to recover forat least 3 or 4 days. Then the connector pin arrays on themicrodrive were attached to preamplifiers with extended cablesto allow for the monitoring of neuronal signals using the 96-channel Plexon system (http://www.plexon.com, Dallas, TX).To enable the mouse move freely when recording, a helium-filled mylar balloon was tied to the cables for alleviating theweight of the apparatus and cables. The tetrode bundles wereadvanced slowly toward the hippocampal CA1 region in dailyincrements of about 0.07 mm until the tips of the electrodesreached the hippocampal CA1, which we deduced from localfield potentials and neuronal activity patterns.

The extracellular signals from electrodes were filteredthrough the preamplifiers to separate spike activity and localfield potentials. The spike signals (Sampling at 40 KHz) andthe LFP signals (Sampling at 1 KHz) were filtered online at400–7,000 Hz and 0.7–300 Hz, respectively. Spike waveforms,time stamps, and local field potentials were saved to Plexondata (*.plx) files.

Animals were recorded in their homecages during sleeping,eating, and quiet awake and in the square box (40 cm 3 40cm 3 20 cm) for 15-min active exploration.

After experiments, histological staining with 1% cresyl echtviolet was used to confirm the electrode positions (Fig. 1).

Spike Sorting and Cell Classification

Spike sorting was conducted manually in a three-dimensionalparameter space at Offline Sorter (http://www.plexon.com,Dallas, TX). Two major criteria were used to separate inter-neurons from pyramidal cells including firing rates and spikedurations. In general, pyramidal cells have lower firing rates(<5 Hz) and longer spike durations, whereas interneurons havehigher firing rates and shorter spike durations (Fig. 1).

Detection of Theta, Gamma, and RippleOscillations

For detecting theta oscillations, the original LFP was firstband-pass filtered (4–12 Hz), then theta (5–10 Hz)/delta (2–4Hz) ratio was calculated by sliding 2-s window. More than

FIGURE 1. Discrimination of putative hippocampal pyramidalcells and interneurons. Red circles: putative pyramidal cells (n 5216), blue circles: interneurons (n 5 308) identified by waveformsand firing rates. Green solid circles: five theta-driving cells. Inseton the upper left, temporal parameters used in the clustering pro-cess (x, half-amplitude duration; y, duration from trough to peak).Inset on the upper right, a Nissl-stained sagittal brain sectionshowing the recording locations in the dorsal hippocampal CA1,the red dots indicate the final positions of the electrode tips. Inseton the lower right, 800-ls average waveforms (mean 6 SD, n 5500) of a typical pyramidal cell (red; M14C01), an interneuron(blue; M10C29), and a theta-driving cell (green; M03C37). Scalesare 0.3 mV for the largest amplitude waveforms from tetrodesdenoted by the gray squares. [Color figure can be viewed in theonline issue, which is available at wileyonlinelibrary.com.]

2 ZHANG ET AL.

Hippocampus

three consecutive time windows in which the ratio was greaterthan four were identified as theta episodes (Csicsvari et al.,1999). Only 30-s continuous theta episodes were included infurther analysis for active exploration and rapid-eye-movementsleep unless specified otherwise.

For gamma oscillations, the original LFP was digitally band-pass filtered at 30–80 Hz. Gamma power (root mean square)of the filtered signal was calculated by sliding 25 ms windowevery 1 ms, and then two standard deviations above the back-ground mean power was used as the threshold of detectinggamma episodes (Csicsvari et al., 2003).

To detect ripples, the original LFP was digitally band-passfiltered at 100–250 Hz. The power (root mean square) of thefiltered signal was calculated by sliding 10 ms window every 1ms. Epochs with five standard deviations above the backgroundmean power were designated as ripple episodes. And then thetime window was moved forward and backward to detect thebeginning and the end of each ripple episode, the thresholdwas two standard deviations above the background mean power(Csicsvari et al., 1999; Klausberger et al., 2003).

Power Spectrum, Coherence, andCrosscorrelation Analysis

Augmented Dickey-Fuller test was applied for stationary testand only stationary data were included in further analysis. Powerspectral density and squared coherence spectrum analyses were per-formed on both the spike and LFP signals using Welch’s averagedperiodogram method with 512-ms nonoverlapping Hanning win-dow. The discrete spike signals were converted into continuous sig-nals by firing rate histograms with 1-ms window. Cross-correlationfunctions were obtained using MATLAB xcorr function. Eachanalysis period was 30-s unless specified otherwise.

Theta Phase-Locking Firing Analysis

The theta-filtered (4–12 Hz) LFP y(t) was first decomposedinto instantaneous amplitude q(t) and phase u(t) componentssuch that y(t) 5 Re(q(t)eju(t)) by using Hilbert transform.Then given the spike train {ti | i 5 1, 2, . . ., n}, spike phasewas calculated by ui 5 u(ti). To evaluate the presence of phaselocking, Rayleigh test for circular uniformity was performed tocompute the significance (P < 0.001) of phase locking and cor-responding preferred phase (Siapas et al., 2005). Unit phasewas fit with a von Mises distribution. In hippocampal CA1,ripples have maximum amplitude in stratum pyramidale.Therefore, LFP with highest ripple power (root mean square offiltered LFP in ripple band) recorded among all electrodes inipsilateral hippocampal CA1 was chosen as reference as well asin other analysis of spike-field relationship unless specified oth-erwise. The analysis period was 30 s.

Pair-Wise Granger Causality Analysis

Granger causality analysis was implemented to further evalu-ate the causal interactions between two time series (Brovelliet al., 2004; Chen et al., 2006). For two time series x1t and x2t,

x1t Granger caused x2t if knowing that the passive informationof x1t helps to predict x2t. In our case, both LFP and spike sig-nals were time series and were normalized by z score to removethe first-order nonstationarity before applying further analysis;and Granger causality spectrum was computed only for station-ary signals.

Denoting spike and LFP signals at time t by X ðtÞ ¼ x1t ;x2tð ÞT,where T stands for matrix transposition, then, the multivariateauoregressive (MVAR) model of order m is:

Xmk¼0

AkX ðt � kÞ ¼ EðtÞ ð1Þ

where Ak is 232 coefficient matrices and estimated by solvingthe multivariate Yule–Walker equations via the Levinson-Wiggins-Robinson (LWR) algorithm. EðtÞ is temporallyuncorrelated residual error with 232 covariance matrix S. Theoptimal order m is determined by the minimum of AkaikeInformation Criterion (AIC) (Akaike, 1974). The value of theorder m normally fell into a range from 100 to 120 for theta-driving cell during AE, and orders of 100, 110, and 120 madeconsistent results. Thus 110 was selected as a tradeoff betweensufficient spectral resolution and overparameterization.

Then the spectral decomposition of the spectral density of Xcan be represented as

Sðf Þ ¼ X ðf ÞX �ðf Þh i ¼ H ðf ÞRH �ðf Þ

where * denotes complex conjugate and matrix transpose, andH ðf Þ ¼ ðPm

k¼0 Ake�2pikf Þ�1 is the transfer function of thesystem.

According to the Geweke’s formulation of Granger causality inthe spectral domain (Geweke, 1982, 1984; Brovelli et al., 2004).The causal influence from x2t to x1t at frequency f is given by

Ix2t!x1t ðf Þ ¼ � ln 1� ðR22 � R122

R11Þ H12ðf Þj j2

S11ðf Þ

!;

where R11, R12, and R22 are elements of S, and S11ðf Þ ispower spectrum of x1t at frequency f. Similarly, the causal influ-ence from x1t to x2t at frequency f is given by

Ix1t!x2t ðf Þ ¼ � ln 1� ðR11 � R122

R22Þ H21ðf Þj j2

S22ðf Þ

!:

Conditional Granger Causality Analysis

In trivariate time series case Z ðtÞ ¼ x1t ;x2t ; x3tð Þ, there isdirect causal component from x2t to x1t if Joint autoregressiverepresentation of ZðtÞ ¼ x1t ;x2t ; x3tð ÞT makes better predictionof x1t than that of Y ðtÞ ¼ x1t ;x3tð ÞT ; if not, the causal influen-ces from x2t to x1t in pair-wise Granger Causality analysis ismediated entirely by x3t. Then the joint autoregressive represen-tations of both Y ðtÞ and ZðtÞ could be written in normalizedterms (Chen et al., 2006) as followed respectively

HIPPOCAMPAL THETA-DRIVING CELLS REVEALED BY GRANGER CAUSALITY 3

Hippocampus

XmY

k¼0

BkY ðt � kÞ ¼ EY ðtÞ ð2Þ

XmZ

k¼0

CkZðt � kÞ ¼ EZ ðtÞ ð3Þ

where Bk and Ck are the coefficient matrices of 232 and 333,respectively; mY and mZ are the corresponding model orders;EY ðtÞis temporally uncorrelated residual error with 232 covari-ance matrix C for Eq. (2) and EZ ðtÞ is temporally uncorrelatedresidual error with 333 covariance matrix R̂ for Eq. (3). BothC and R̂ are diagonal matrices based on the normalized proce-dures (Chen et al., 2006).

All model parameters are estimated in the same way as thosein pair-wise Granger causality analysis above. To compute con-ditional Granger causality in frequency domain, Fourier trans-formations of Eqs. (2) and (3) are performed and written byEqs. (4) and (5) as follows respectively:

x1ðf Þx3ðf Þ

� �¼ G11ðf Þ G12ðf Þ

G21ðf Þ G22ðf Þ� �

E_

Y ðf Þ ð4Þ

whereE_

Y ðf Þcould be represented by H1ðf Þ;H2ðf Þð ÞT

x1ðf Þx2ðf Þx3ðf Þ

0@

1A ¼

H11ðf Þ H12ðf Þ H13ðf ÞH21ðf Þ H22ðf Þ H23ðf ÞH31ðf Þ H32ðf Þ H33ðf Þ

0@

1AE

_

Z ðf Þ ð5Þ

Combine (4) and (5), we have

H1ðf Þx2ðf ÞH2ðf Þ

0B@

1CA ¼

G11ðf Þ 0 G12ðf Þ0 1 0

G21ðf Þ 0 G22ðf Þ

0B@

1CA

�1

3

H11ðf Þ H12ðf Þ H13ðf ÞH21ðf Þ H22ðf Þ H23ðf ÞH31ðf Þ H32ðf Þ H33ðf Þ

0B@

1CAE

_

Z ðf Þ

¼Q11ðf Þ Q12ðf Þ Q13ðf ÞQ21ðf Þ Q22ðf Þ Q23ðf ÞQ31ðf Þ Q32ðf Þ Q33ðf Þ

0B@

1CAE

_

Z ðf Þ ð6Þ

where Qðf Þ ¼ G�1ðf ÞH ðf ÞFinally, the conditional Granger causality from x2t to x1t con-

ditional on x3t at frequency f is represented as

Ix2t!x1t jx3t ðf Þ ¼ lnW11

Q11ðf ÞR̂11Q11�ðf Þ��

where W11 is element of C and R̂11 is that of R̂.Permutation test was performed for coherence, pairwise

Granger causality and conditional Granger causality analysis byusing surrogate data. The surrogate data were generated fromshuffling non-overlapping 100-ms data for 1,000 times. Thethreshold of significance was P 5 0.001. The computing periodfor Granger causality analysis was 30 s unless specified otherwise.

TABLE 1.

Coherence and Granger Causality of Theta-Related Interneurons During Exploration

Type (number) Firing rate (Hz)

Coherence Granger causality

LFP ? UnitUnit—LFP Unit ? LFP

Peaka f (Hz) Peaka f (Hz) Peaka f (Hz)

Theta-locked interneurons (105) 36.48 6 16.67 0.39 6 0.10 7.92 6 0.89 0.06 6 0.05 8.33 6 2.22 0.31 6 0.12 7.59 6 0.67

Theta-driving cells (5) 88.05 6 4.45 0.82 6 0.06 8.40 6 0.41 0.94 6 0.08 8.46 6 0.22 0.19 6 0.04 6.59 6 1.12

Other cells recorded by the same tetrode

Int. Pyr.

M03C37 0 0 80.85 6 4.48 0.81 6 0.06 8.16 6 0.54 0.98 6 0.10 8.68 6 0.47 0.20 6 0.07 6.56 6 0.96

M05C19 0 0 91.59 6 6.21 0.88 6 0.03 8.58 6 0.26 1.03 6 0.16 8.86 6 0.52 0.26 6 0.07 6.14 6 1.09

M10C53 1 0 91.43 6 8.09 0.84 6 0.02 8.51 6 0.48 0.95 6 0.10 8.16 6 0.61 0.16 6 0.03 6.63 6 1.01

M11C41 1 0 89.31 6 5.78 0.85 6 0.03 8.51 6 0.38 1.04 6 0.18 8.79 6 0.40 0.14 6 0.03 6.63 6 1.32

M24C85 0 0 93.16 6 6.32 0.79 6 0.03 8.30 6 0.28 0.96 6 0.11 8.30 6 0.00 0.24 6 0.08 5.30 6 0.59

Each value (mean 6 SD) on the first two rows was averaged over cells within types from thirty-second epoch.Each value for individual theta-driving cell was averaged from seven thirty-second epochs.aNote the peaks of coherence and Granger causality within the theta band.f s Note the frequencies corresponding to peaks.Int.: Interneurons; Pyr.: Pyramidal cells.

4 ZHANG ET AL.

Hippocampus

RESULTS

Strong Granger Causal Influence ofTheta-Driving Cells on LFP Theta

Of the 110 theta-locked putative interneurons recorded frommice hippocampal CA1, five showed extremely high firing rates

(88.05 6 4.45 Hz, mean 6 SD, n 5 5, Table 1) and reliabletheta-rhythmic-bursts with 5–15 spikes per theta cycle duringexploration (Figs. 2A,B and 3A,B). Particularly, all of the fivecells preferred the ascending phases of theta oscillations of thereference LFP with highest ripple power among all electrodesin ipsilateral hippocampal CA1 (details in Materials and Meth-ods), and the mean preferred firing phase was 1178 6 608

FIGURE 2. Firing features of theta-driving cells. A, Burst firingpattern of a theta-driving cell (M10C53) observed in interspike inter-val histogram (IIH). Notice the bimodal distribution of intervals (twopeaks indicated by red arrows) reflecting the intraburst and interburstintervals. B, Spike autocorrelogram of the cell in A was characterizedby a high level of theta rhythmicity. C, All the five theta-driving cells(dark blue, M05C19; purple, M24C85; green, M10C53; red,M03C37; light blue, M11C41 as the same in D) had significant peaksaround the theta frequency band in the power spectral density plots.

The gray area indicates the density averaged from the five cells. D,Phase relationship between the five theta-driving cells and theta waves.The gray area shows the average from the five cells. The upper redtrace: the averaged LFP theta wave. E, Spiking activity of two theta-driving cells and corresponding LFP recorded from the same tetrodesduring SWS were shown on the left; while averaged LFP were alignedto the negative peaks of ripples on the right. Scales: LFP, 0.5 mV; rip-ple (filtered 100–250 Hz), 0.1 mV. [Color figure can be viewed in theonline issue, which is available at wileyonlinelibrary.com.]


Hippocampus

(mean angle 6 angular deviation, n 5 5; Fig. 2D). The fivecells were recorded in isolation from pyramidal cells (Table 1),which indicated that their cell bodies were not located in thepyramidal layer. Besides, the positive-going sharp waves (SPW)and large-amplitude ripple events could be observed in corre-sponding LFPs during SWS (Fig. 2E), which also promptedthat the locations of the five cells were probably in the stratumoriens of the CA1 area close to stratum pyramidale.

The power spectra of spike activity showed prominent peaksin the theta frequency range (4–12 Hz, Fig. 2C), the same asthat of LFP (Fig. 3C). Unit-LFP coherence also peaked withinthe theta frequency range (permutation test, P < 0.001; Fig.3D), but no significant coherence was found in the gammaband (30–80 Hz; permutation test, P > 0.05). Moreover, thepeak coherence value averaged from the five cells was 0.82 60.06 (n 5 5) at the frequency of 8.40 6 0.41 Hz, which wassimilar to the peak frequency of the power spectra of LFPs(8.40 6 0.22 Hz, n 5 5; P 5 1.00, paired t test; Table 2).However, theta phase-locked firing and high theta coherencedid not reveal detailed information about the interactionsbetween theta-locked interneurons and LFP theta. We furtherexamined Granger causal relationship between spike activityand LFP signals in the frequency domain (Brovelli et al., 2004;

Gregoriou et al., 2009). Granger causality values showed over-threshold (permutation test P < 0.001) peaks within the thetaband, and the peak in the Unit-to-LFP direction (peak 50.90) was much higher than that in the reverse direction (peak5 0.20; Fig. 3E). The average values from the five cells con-firmed the asymmetric directional influence (Unit-to-LFP: 0.946 0.08 vs. LFP-to-Unit: 0.19 6 0.04, n 5 5, P < 0.001,paired t test; Fig. 3E and Table 1). Furthermore, higherGranger causality values in the Unit-to-LFP direction in thetheta band were also found in the interactions between spikeactivity and the concurrent LFPs recorded from all of the ipsi-lateral CA1 (Fig. 4). Overall the results suggested that theactivity of the five theta-locked interneurons had a unidirec-tional significant Granger causal influence on LFP theta.

The theta coherence between spike activity and LFPs wasalso observed in other theta-locked interneurons, although theaverage peak values (0.39 6 0.10, n 5 105) were quantita-tively lower than that of the five cells (0.82 6 0.06, n 5 5;P < 0.001, Wilcoxon rank-sum test; Table 1). We examinedthe Granger causal relationship between the remaining 105theta-locked cells and LFPs. Surprisingly, the theta Granger cau-sality values in the Unit-to-LFP direction (peak 5 0.06 6 0.05,n 5 105) were not only below the significance levels (permutation

FIGURE 3. Theta-locked firing of theta-driving cells and theirstrong Granger causal influences on LFP theta. A, Spike activity(Action potentials, APs) of a theta-driving cell (M10C53) and LFPrecorded simultaneously in CA1 during exploration. The theta-driving cell fired preferentially on the ascending phases of thetawaves. Scales: LFP, 0.5 mV; theta (filtered 4–12 Hz), 0.2 mV; APs,0.5 mV, 200 ms. B, The perievent spike raster (the upper panel)and histogram (the lower panel) of M10C53 referenced to thetroughs of the averaged theta waves (the middle red trace). A 10-sdata was calculated by using 2-ms bin width. The vertical dottedline indicates the time zero corresponding to the negative peak ofthe averaged theta. C, Dominant theta powers in both activity of

M10C53 and LFP are showed via 60-s spectrograms. D, Theta co-herence between activity of theta-driving cells and LFPs (M10C53and the same population data shown in E). Dotted line indicates asignificance threshold at P 5 0.001 (permutation test). Inset, theaverage Unit-LFP coherence values from the five theta-driving cells(n 5 5). E, Strong Granger causal influences of the theta-drivingcells on LFP theta. Directions of influences are indicated by thearrows (significance thresholds P 5 0.001, permutation test).Inset, the average Granger causality values from the five theta-driv-ing cells (n 5 5). [Color figure can be viewed in the online issue,which is available at wileyonlinelibrary.com.]

6 ZHANG ET AL.

Hippocampus

test P < 0.001) but also significantly lower than those in theLFP-to-Unit direction (peak 5 0.31 6 0.12, n 5 105; P <0.001, paired t test; Fig. 5A and Table 1), despite the fact thatsome of these theta-locked cells fired at different phases of thetheta cycle (Fig. 5B). These Granger causal relationships demon-strated that among the recorded theta-locked interneurons, onlythe five cells could generate strong Granger causal influences onLFP signals within the theta band. Therefore, we called these fivetheta-locked interneurons ‘‘theta-driving’’ cells.

It is commonly believed that LFP represents the synchronousmembrane potential fluctuations of nearby pyramidal cells, so itseemed not interpretable that LFP theta could have a Grangercausal influence on the activity of theta-locked interneurons. Oneof the possibilities is that the effect represents an indirect interac-tion between these two signals. It has been reported that condi-tional Granger causality analysis can evaluate whether the causalrelationship between two signals is direct when considering athird signal (Chen et al., 2006). In two animals, we simultane-ously recorded theta-driving cells and other theta-locked cells(Fig. 6A), thus we could evaluate the conditional Granger causal-ity among LFP and those cells (Fig. 6E). The conditional Grangercausal influence of theta-driving cells on LFP, with other theta-locked cells taken into account, was slightly reduced (peak values:0.85 6 0.11, n 5 14, seven 30-s durations 3 2 cells, M10C53and M11C41) but still well above significant levels (permutationtest P < 0.001), compared with the influence without theta-locked cells (peak values: 0.95 6 0.14, Fig. 6E left). However,the conditional Granger causal influence of LFP on other theta-locked cells, with the theta-driving cells taken into account, wasgreatly reduced (peak values: 0.02 6 0.01, n 5 14, seven 30-sdurations 3 2 cells) and even fell below significant levels (permu-tation test P < 0.001), compared with the influence without thetheta-driving cell (peak values: 0.33 6 0.13, Fig. 6E middle).The comparisons suggested that the Granger causal influence ofLFP theta on other theta-locked cells was more likely to be indi-rect (Fig. 6F). Meanwhile, no significant Granger causal relationwas found between theta-independent interneurons and LFPtheta in either direction (Fig. 6D). The above results indicatedthat among CA1 interneurons, theta-driving cells could play aunique role in entraining theta oscillations.

Persistent Granger Causal Influence ofTheta-Driving Cells on LFP Theta AcrossBehavioral States

Previous studies suggest that oscillation patterns of LFPs dif-fer across behavioral states (Vanderwolf, 1969; O’Keefe andNadel, 1978; Buzsaki et al., 1992). In particular, theta andgamma oscillations occur primarily during active exploration(AE) and rapid-eye-movement (REM) sleep, while ripples occurmainly during slow-wave sleep (SWS). Strong Granger causalinfluence of theta-driving cells on LFP theta during explorationraises the question of their interactions in other behavioralstates. SWS is one of the typical non-theta states when thetarhythm is not prominent and only small ‘‘residual’’ theta canbe detected (Fig. 7A). We first investigated the activity patternsT

ABLE2.

FiringProperties

ofTheta-D

rivingCells

Under

Distinct

BehavioralStates

Power

(LFP)

Power

(Unit)

Coheren

ceGranger

causality

LFP?

Unit

Unit—

LFP

Unit?

LFP

State

Firingrate

(Hz)

Peak

f(H

z)Peak

f(H

z)Peak

f(H

z)Peak

f(H

z)Peak

f(H

z)

AE

88.056

4.45

228

.716

7.87

8.40

60.22

228

.156

2.34

8.30

60.00

0.82

60.06

8.40

60.41

0.94

60.08

8.46

60.22

0.19

60.04

6.59

61.12

REM

69.586

6.38

229

.346

6.91

7.08

60.49

229

.666

1.21

7.08

60.49

0.80

60.05

7.32

60.4

0.98

60.18

7.41

60.63

0.23

60.08

5.41

61.72

QW

41.476

6.79

232

.286

6.38

7.08

60.49

233

.826

1.94

7.08

60.49

0.64

60.10

7.57

60.63

0.48

60.06

7.21

61.10

0.14

60.07

6.19

61.26

SW

S52

.496

6.71

––

233

.326

1.37

6.10

60.63

0.38

60.12

7.69

61.08

0.25

60.09

7.14

61.04

0.06

60.03

5.03

60.66

Eachvalue(m

ean6

SD)was

averaged

from

a30

-sduration

sof

allfive

theta-drivingcells

(n5

5).


Hippocampus

of theta-driving cells and their relationship with LFPs duringSWS. Although the theta-rhythmic bursting pattern of theta-driving cells became irregular during SWS (Fig. 7A), the burstfiring remained locked to the ‘‘residual’’ theta (Fig. 7D) andhad no correlation with the ripples (Fig. 7C). Interestingly, theaverage peak value (0.38 6 0.12, n 5 5) of Unit-LFP theta co-herence during SWS decreased by about 60% compared with

that during AE (0.82 6 0.06, n 5 5; Table 2), but it was stillsignificantly above chance level (permutation test, P < 0.001;Fig. 7E). Granger causality analysis further revealed that theta-driving cells still had a significant Granger causal influence onLFP theta during SWS (peak 5 0.28 at 6.84 Hz, permutationtest, P < 0.001; Fig. 7F), and the average peak value ofGranger causality from the five theta-driving cells in the Unit-

FIGURE 4. Strong Granger causal influences of theta-drivingcell (M10C53) on the concurrent LFP traces recorded from the ip-silateral hippocampal CA1. A, Four LFP traces simultaneouslyrecorded in the ipsilateral CA1. Slight variations in amplitude andphase were observed probably due to the difference of recordinglocations. A theta-driving cell was identified from the same tetrodeas LFP_3. Scales: LFP, 0.5 mV, 100 ms. B, The theta-driving cell

(in grey) fired locked to the different phases of theta waves (fil-tered from the original LFPs in A), peak firing occurred at 608 ofLFP_1, 1158 of LFP_2, 1408 of LFP_3, and 2408 of LFP_4. C,Strong Granger causal influence of the theta-driving cell on simul-taneously recorded LFP theta from all four electrodes. [Color fig-ure can be viewed in the online issue, which is available atwileyonlinelibrary.com.]

FIGURE 5. Granger causality between theta-locked interneur-ons and LFP theta. A, LFP signals have significant Granger causaleffects on theta-locked interneurons. Dotted lines indicate a signif-icance threshold at P 5 0.001 (permutation test). Insets, phaserelations between spikes and LFP theta (M15C61, M14C45,

M07C85, M25C69, M26C31, M08C77, M02C87, and M07C25ranked from left to right in the top row and then at bottom). B,Preferred theta phases of these theta-locked interneurons. [Colorfigure can be viewed in the online issue, which is available atwileyonlinelibrary.com.]

8 ZHANG ET AL.

Hippocampus

to-LFP direction was 0.25 6 0.09 (n 5 5; Table 2). These resultssuggested that theta-driving cells retained their influence on LFPtheta even during SWS although the strength decreased.

We further separated a wake-sleep cycle into four character-ized behavioral states: active exploration (AE), quiet waking(QW), rapid-eye-movement (REM) sleep, and slow-wave sleep(SWS), and compared the relationships between the activity oftheta-driving cells and LFPs across these states (Fig. 8 and Ta-

ble 2 showing the comparison of the four characteristic behav-ioral states, and Fig. 9 showing the consecutive 2,000-s data).The average firing rate of the theta-driving cells changed acrossvarious behavioral states (one-way analysis of variance, P <0.001); it climbed to the highest during AE (88.05 6 4.45Hz, n 5 5) and plunged to the lowest during QW (41.47 66.79 Hz, n 5 5; Table 2). The analysis of the consecutive2,000-s data clearly demonstrated the persistence of Unit-LFP

FIGURE 6. Diverse Granger causal relationships between hip-pocampal interneurons and LFP theta. A, Four interneuronsincluding Unit 1 (M10C53): a theta-driving cell; Unit 2(M10C41): a theta-locked interneuron; Unit 3 (M10C45) andUnit 4 (M10C33): two theta-independent interneurons) wererecorded simultaneously in the ipsilateral CA1 during REM sleep,together with the LFPs recorded simultaneously. Scales: LFP, 0.5mV; theta (filtered 4–12 Hz), 0.3 mV, 300 ms. (Color code foreach unit was the same in B–F) B, Phase relations between thefour units and the LFP theta. Discharge probabilities of the fourunits are shown. For clarity, two theta cycles are shown; 08, 3608,and 7208 mark the troughs of theta cycles. C, Coherence betweenLFPs and the four units. Dotted line indicates a significance

threshold at P 5 0.001 (permutation test). D, Granger causal rela-tions between LFPs and the four units. Directions of influence areindicated by the arrows. Dotted lines indicate a significancethreshold at P 5 0.001 (permutation test). Note the unidirectionalinfluence from LFP to Unit 2 (theta-locked interneuron) in thetheta frequency range (the second panel). E, Conditional Grangercausality (the red lines) among LFP theta, Unit 1 (a theta-drivingcell) and Unit 2 (a theta-locked interneuron). F, Schematic illustra-tion of direct Granger causal influence from theta-driving cells(Unit 1) to both LFPs and other theta-locked cells (Unit 2), indi-rect Granger causal influence from LFPs to Unit 2. [Color figurecan be viewed in the online issue, which is available atwileyonlinelibrary.com.]


Hippocampus

theta coherence and Unit-to-LFP causal influence (Fig. 9)across behavioral states. The peak values of both coherence andGranger causality within the theta band fluctuated acrossbehaviors, and the fluctuation always reflected the changingpower of LFP theta (Fig. 8 and Table 2). These results sup-ported the idea that the activity of theta-driving cells couldhave a persistent influence on the theta component of LFP sig-nals across behavioral states.

DISCUSSION

It has been observed that many hippocampal interneuronsfired phase-locked to theta waves (Ranck, 1973; Lawson andBland, 1993; Csicsvari et al., 1999; Klausberger et al., 2003;Klausberger and Somogyi, 2008); however, the theta phase-locked firing revealed no details about the effect of theta-lockedinterneurons on generating theta oscillations. Using Grangercausality analysis, we identified a unique type of theta-lockedinterneurons: theta-driving cells. These cells can be distin-guished from other interneurons during in vivo recording basedon their characteristic theta-burst firing patterns and extremely

high firing rates. Even during slow-wave sleep, the high averagefiring rates maintained at 52.49 6 6.71 Hz, and the firing alsoremained phase-locked to residual theta. Table 1 showed thesignificant difference of these firing patterns between the theta-driving cells and other theta-locked cells. Overall the resultsshowed that theta-driving cells exclusively exhibited strongGranger causal influences on LFP theta, although they onlyconstituted a tiny percentage (4.5%, 5 out of 110) of theta-locked interneurons we recorded. Therefore, we concluded thattheta-driving cells could be involved in the generation of thetaoscillations via their unique theta bursting patterns.

Granger causality analysis is a statistical tool for causalityanalysis which was initially applied in economics (Granger,1969; Geweke, 1982, 1984). It has recently been reported asan efficient approach for detecting the directionality of neuralinteractions (Brovelli et al., 2004; Seth and Edelman, 2007;Gregoriou et al., 2009). In principle, considering time Series Aand B, A is counted as a Granger-cause of time series B only ifA shares information with succeeding B, in another word, in-formation of A is useful for predicting B. The significantGranger causal influence of theta-driving cells on LFP thetatherefore suggested that the theta rhythmicity of cell firing notonly correlated well with, but also preceded rhythmic theta

FIGURE 7. Influence of theta-driving cell (M10C53) on thetacomponent of LFPs during slow-wave sleep (SWS). A, A theta-driving cell reliably fired at rhythmical bursts preferentially on theascending phases of theta waves (the shaded areas) during SWS.Scales: LFP, 0.5 mV; ripple (filtered 100–250 Hz), 0.1 mV; theta(filtered 4–12 Hz), 0.2 mV; APs, 0.5 mV, 200 ms. B, Power spec-tral density plot of LFPs (red) and spike activity (blue). Red arrowindicates the peak for ripples in LFP signal. C, The perievent spikeraster (the upper panel) and histogram (the lower panel) refer-enced to the average ripple trace (the middle red trace). A 500-sdata was calculated by using 1-ms bin width. The vertical dottedline indicates the time zero corresponding to the maximal negative

peak of the average ripples. D, The perievent spike raster (theupper panel) and histogram (the lower panel, bin width: 2 ms) ref-erenced to the troughs of LFP theta waves (the middle red trace).The vertical dotted line indicates the time zero corresponding tothe negative peak of the average LFP theta. E, Theta coherencebetween the theta-driving cell and LFPs during SWS. Dotted lineindicates the significance threshold at P 5 0.01 (permutation test).F, Granger causal influence of the theta-driving cell on LFPs in thetheta band remained significant during SWS. Directions of influ-ence are indicated by the arrows (significance thresholds at P 50.001, permutation test). [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]

10 ZHANG ET AL.

Hippocampus

activity of LFPs. Furthermore, we also noticed that the Unit-to-LFP Granger causality values remained significant regardingall ipsilateral concurrent LFPs, although their firing phase rela-tionship to LFP theta varied as a function of recording depth(Fig. 4). The results suggested that the theta rhythmic firing oftheta-driving cells preceded all concurrent ipsilateral CA1 LFPtheta regardless of the recording depth. Thus, we believed thatsuch theta-driving cells might play a crucial role in thetageneration.

Our analysis indicated that the rhythmic activity of thetheta-driving cells had a strong Granger causal influence onLFP theta, which led us to the question of what the physiologi-cal correlates of this effect are. The classic model of hippocam-pal theta generation proposes that hippocampal interneurons,paced by septal GABAergic afferents, induce rhythmic inhibi-tory postsynaptic potentials (IPSPs) in pyramidal cells, whichgenerate an inhibitory theta dipole in the CA1 region (Buzsaki,2002). We hypothesized that theta-driving cells could function

FIGURE 8. Firing features of theta-driving cell (M10C53) dur-ing distinct behavioral states including A: active exploration (AE);B: rapid-eye-movement sleep (REM); C: quiet awake (QW);D: slow-wave sleep (SWS). The traces on the top are originalLFPs, and the underneath spike raster plots show simultaneouslyrecorded spike activity of the theta-driving cell. Scales: LFP, 0.5mV, 250 ms. The bottom panels show power spectral analysis ofLFPs (the black curves) and spike activity (the blue curves), unit-LFP coherence (the green circles), and unit-LFP Granger causality(unit-to-LFP: red open diamonds; LFP-to-unit: pink diamonds).

Dotted lines marked the peak values of power spectral densities ofspike activity. The peaks of the four curves (the black, blue, green,and red) aligned up at the same frequency value during AE (A),REM (B), and QW (C), although the peak values varied across be-havioral states. During SWS (D), peak activity remained aroundthe theta frequency band, suggesting that the activity of the theta-driving cell was always correlated with the theta component of theLFP signal during SWS. [Color figure can be viewed in the onlineissue, which is available at wileyonlinelibrary.com.]


Hippocampus

as these interneurons as shown by the high Granger causalityvalues from the theta-driving cells to LFP theta.

It was surprising that most of the theta-locked interneurons,excluding the theta-driving cells, were Granger-causally influ-enced by, rather than imposing the influence on, LFP theta.These cells usually fired at lower rates (Table 1) in a less rhyth-mic pattern than the theta-driving cells (Fig. 6A), and theyphase-locked to varied phases of LFP theta, mostly to thetroughs of theta waves (Fig. 5). The difficulty of seeking thephysiological explanation of the LFP-to-Unit Granger causalinfluence led to our hypothesis that the influence might beindirect. This hypothesis was supported by the result of ourconditional Granger causality analysis on simultaneouslyrecorded theta-driving cells and theta-locked cells with LFP.

Moreover, the Granger causal influence of the theta-drivingcells on LFP theta varied across behavioral states as a functionof LFP theta power. Meanwhile, the theta-driving cells showed

no significant correlation with either ripples or gamma oscilla-tions. On the basis of these results we concluded that the activ-ity of the theta-driving cells correlated well with the theta com-ponent of LFPs regardless of the behavioral states.

Acknowledgments

The authors thank L. Rui for his comments on the manuscript.

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FIGURE 9. Persistent influence of the theta-driving cell(M10C53) on theta component of LFPs during different states.On the right column, the top bar indicates distinct behavioralstates; the underneath five panels are spectrogram of LFP, spectro-gram of Unit, phase relationship, Unit-LFP coherence and Unit-to-LFP Granger causality, respectively. A 30-s sliding window wasused to calculate the 2,000-s wake-sleep cycle (sliding shift: 1 s).The yellow contour line in the bottom panel indicates 0.25 in thevalue of Granger causality. On the left column, the red and blue

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hippocampal theta-driving cells revealed by granger causality

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