Decreased Neuronal Synchronization during Experimental Seizures

MATERIALS AND METHODS

Experimental preparation. Sprague Dawley rats 10–20 d old were deeply anesthetized with diethyl-ether and decapitated. The brains were removed and placed into chilled artificial CSF (ACSF). Slices 350 μm thick were cut using a tissue chopper and perfused with ACSF containing (in mm): 130 NaCl, 1.2 MgSO₄, 3.5 KCl, 1.2 CaCl₂, 10 dextrose, 2.5 NaH₂PO₄, 24 NaHCO₃. Slices were aerated with 95% O₂–5% CO₂ at 7.2 pH in an interface holding chamber until used. For experiments, single slices were transferred to a submersion chamber (Warner Instruments) mounted on a fixed stage microscope (Ziess Instruments, Axioskop).

Weak synchronization in CA1 was created by elevating potassium from 3.5 to 5.5 mm. Strong synchronization, sufficient to generate reliable seizures in CA1, was created by infusing 100–200 μm 4-amino-pyridine (4AP) at normal potassium concentrations. For 4AP experiments in which CA1 seizures were to be isolated from smaller bursts that propagated into the CA1 from CA3, the Schaffer collateral fibers were cut with an eyebrow knife. Such study of seizures in isolation from burst activity is aided by using 4AP rather than high [K⁺]_o to generate the seizure-like events (Barbarosie and Avoli, 1997). We observed similar events with or without low Mg in the perfusate.

Dual simultaneous whole-cell patch-clamp recordings in CA1 were made with differential infrared contrast microscopy (Sakmann and Neher, 1995). Patch electrodes were made from borosilicate micropipettes pulled to 5–7 MΩ and filled with (in mm): 0.1 CaCl, 1.1 EGTA, 2 MgATP, 10 HEPES, 130 potassium gluconate (in potassium experiments), or 130 KCl (in slices bathed with 4AP), 5% biotin, and titrated to pH 7.2 with KOH. Cells selected for patching were between 30 and 200 μm of each other. To prevent spiking, cells in potassium experiments were either voltage clamped (at holding potentials between −50 and −90 mV) or hyperpolarized under current clamp (<100 pA). Experiments in 4AP were performed using current clamp without hyperpolarization, and spikes were prevented by adding 100 μm QX-314 to the electrode solution (Connors, 1982). In 4AP experiments with bursts and seizures, an extracellular electrode was placed in the vicinity of the patched cells to provide a measure of the network ensemble activity. In addition, to bring out synchronous behavior that was both inhibitory and excitatory, recording electrodes in 4AP experiments contained 130 mmchloride to set the chloride reversal potential near 0 mV, making all inhibitory synaptic input depolarizing rather than hyperpolarizing or neutral shunting (Prida and Sanchez-Andres, 1999). In preliminary experiments (data not shown) (in low Mg/4AP), we observed similar depolarizing seizure-like events using patch electrodes without elevated chloride.

Membrane potential was amplified and low-pass filtered at 3 kHz using an Axoclamp 2A amplifier (Axon Instruments), digitized at 10 kHz using a Digidata 1200A analog-to-digital converter (Axon Instruments), and stored using pClamp software (Axon instruments). Before analysis, each window of data analyzed was linearly detrended to improve spectral estimation, detrending the entire window for short windows (<100 msec), and serially detrending for longer data segments. After detrending, the data were bandpass filtered from 1 to 500 Hz and notch filtered at 60 Hz and its harmonics (120, 180,… , 480 Hz).

Power spectral density. Power spectral density (PSD) was calculated after applying a Hanning window and bandpass filtering the data, and total power was calculated by summing the absolute magnitude of the squared Fourier components in frequency bands from 1 to 500 Hz.

Cross-correlation. The sample cross-correlation (CC) between two channels is:

where X₁(t) andX₂(t) are the two time series of length N, with sample means μ₁and μ₂, and sample standard deviations ς₁ and ς₂ (Bendat and Piersol, 1986). This sample CC is equivalent through the Wiener–Khinchine Theorem to the inverse Fourier transform of the product of Fourier transform first time series, X₁(ω), times the complex conjugate of the Fourier transform of the second time series, X ${}_2^{\ast }$(ω):

where ⇔ indicates a Fourier transform pair (Press et al., 1992). This formula for cross-correlation was used for computational efficiency.

Because finite length autocorrelated time series will have spurious cross-correlation even if uncoupled, the Bartlett estimator (Bartlett, 1946; Box and Jenkins, 1976) was used to calculate the expected variance of the CC at a given lag l as:

where CC_i,i are the autocorrelation values of channel i at lags τ.CC_1,2(τ) values were considered significant if they were greater than the twice the expected standard deviation (2 · $\sqrt{\text{var}(\text{l}))}$ for lags <100 mS. This confidence represents the probability <0.05 that such aCC_1,2(τ) value would be generated from uncoupled time series by chance.

Mutual information. Mutual information (MI) is a measure of how much information is known about the distribution of the values of time series B by knowing how it varies with the distribution of time series A. The information capacity, I, of a single voltage trace, V_A(t), is:

where N bins were used to partition the data, andP_VA(i) is the probability that the voltage values of time seriesV_A will fall within bin i(Shannon and Weaver, 1964). The MI from two channels can be calculated as:

This measure of MI is an estimate that must be less than the true amount of information in the system. This systematic bias can be compensated for by estimating the errors introduced by the partitioning into bins. The corrected MI is:

where B_X,B_Y,B_X,Y are the number of bins that have points in them from the A data set,B data set, and the combined data set AB, andN is the number of points in each time series (Roulston, 1999).

Unfortunately, we still lack an analytical means to estimate the variance of these bias-corrected MI values. To estimate the variance and test whether a given MI is significantly different from the uncoupled state, we therefore use a bootstrap statistic. Mutual information at short lags (<100 mS) were compared with mutual information calculated between the channels with randomly selected long lags (>4 sec). These “shift surrogate data” sets were generated by time shifting one data set relative to the other and wrapping the extra values around to the beginning of the data set. Shift surrogates have an advantage in that they preserve the statistical structure of the original time series but destroy the correlations between them. Twenty different time shift lags were chosen randomly with the restriction that time shifts be >4 sec. We considered the MI detected between the two channels significant if the value was greater than two SDs from the mean MI calculated on 20 shift surrogates.

Mutual information in two dimensions. Mutual information can be calculated in more than one dimension. If two data sets are each multivariate in two dimensions (i,j for one data set andk,l for the other) or are univariate but embedded in two dimensions by time-delay embedding (Takens, 1981; Abarbanel, 1996), the MI of the combined system must be calculated in four dimensions. If the systems and their coupling are nonlinear, then MI in higher dimension may reveal the coupling with more sensitivity than the standard univariate approach. Mutual information in two dimensions (MI2D) is calculated as:

For time-delay embedding, delays were chosen on the basis of the decay of mutual information between a signal and a time-shifted version of itself (Frazer and Swinney, 1986).

Phase correlation: broad band. Similar to the correlation between amplitudes measured with CC, phase correlation (PC) measures the correlation between phases. A growing body of work suggests that PC can detect weak correlations in nonlinear neuronal systems to which CC may be insensitive (Tass et al., 1998; Varela et al., 2001).

Our signals are not simple sines and cosines, where the assignment of phase would be straightforward. To assign a phase to each time point of the data, the signal is first passed through a Hilbert transform:

The values of the Hilbert transform become the imaginary part or phase of a new combined signal, X(t) +iH(τ). Such a complex signal can be expressed as an amplitude A(t) and phase ϕ(t), asA(t)e^φ(t)where φ(t) = arctan (H(t)/X(t)) (Bendat and Piersol, 1986).

To quantify phase correlation, mutual information was calculated between the phase angles of the two data sets:

whereP(φ ${}_{\text{i}}^A$,φ ${}_{\text{j}}^B$) is the joint probability that channel A has phase angle φ ${}_{\text{i}}^A$ while channel B has phase angle φ ${}_{\text{j}}^B$. As above, one time series can be time shifted and a surrogate MI calculated. The phase correlation between the data sets is significant if the MI for the unshifted phase angles is greater than two SDs from the mean calculated from 20 time shift surrogates.

To visually display phase differences between channels i andj, histograms of phase difference,p_φi,j(θ),

were calculated modulus 2π. If the signals are uncoupled, such histograms will be flat from uniformly random associations of phase, and if coupled, such histograms will be peaked.

Phase correlation: narrow band. The above description of PC used the Hilbert transform to assign a phase to the original signal that contained all of the relevant frequencies between 0.1 and 500 Hz. The phase assigned was therefore broad band (BB). Nevertheless, phase can be assigned to narrowly bandpass-filtered data, and PC has been used in narrow band analysis in several applications of PC to neural systems (Tass et al., 1998; Varela et al., 2001). Because systems may demonstrate synchronization only in specific frequency bands, for such systems narrow band phase is the preferred method of analysis (DeShazer et al., 2001). Following DeShazer et al. (2001), we created narrow band data by filtering in the Fourier domain with a Gaussian spectral filter with adjustable mean frequency and adjustable variance. There is a balance between the length of the data set and how narrow the bandpass Gaussian filtering can be. A guideline we have found useful is to choose the SD, ς, of the Gaussian filter, such that N · ς/r > 10, where N is the length of the data set and r is the acquisition rate.

Burst detection. Burst-firing events were detected by filtering extracellular recordings between 0.1 and 10 Hz and selecting events by threshold detection. Bursts were required to have minimum and maximum durations of 10 msec and 1 sec, but bursts were generally <100 msec and not observed to last longer than 300 msec. The 1 sec upper limit in duration served to effectively discriminate all seizure-like events from the shorter bursts. A minimum interval was imposed between burst offset and onset of the next burst of 200 msec. Bursts within 5 sec before or 20 sec after a seizure were excluded. All burst onset times were checked by visual inspection and corrected manually if indicated.

Seizure detection. Seizures had complex and variable waveforms, with high-frequency activity superimposed on a DC potential shift, and lasted several seconds. The variability precluded reliable automated onset detection, and all seizure onsets were set by visual inspection as the earliest detectable change associated with the event.

RESULTS

DISCUSSION

We examined how various synchrony detection tools responded to weak synchronization in this neuronal system. Weak synchronization was studied in elevated [K⁺]_o in the period of time before an extracellularly detected burst discharge and in the period of time leading up to seizure-like events. Because neurons are floridly nonlinear elements, and their synaptic connections have nonlinear transmission properties as well, we anticipated that we would easily demonstrate that nonlinear methods are more powerful than the linear tools. Quite the contrary, we found that for elevated [K⁺]_o, linear cross-correlation was more sensitive than any other method for detecting synchronization, whereas in the pre-burst period, nonlinear methods were the best choice. None of these methods detected an increase in synchrony before the seizure-like events, suggesting no well defined pre-seizure state. Our findings suggest strongly that it is a mistake to make a priori assumptions regarding the type of synchrony detection required for a coupled neuronal system. Applying a battery of powerful tests that examine different aspects of dynamical synchronization seems a sensible approach.

With the increasing interest in using phase synchronization for the detection of synchrony, our findings highlight another open issue: relying on broad versus narrow band phase for synchrony detection. In several studies of neuronal data (Tass et al., 1998; Rodriguez et al., 1999), narrow band phase was used. Indeed, in the seminal work demonstrating that phase was a more sensitive determinant of synchronization in weakly coupled nonlinear systems (Rosenblum et al., 1996), the theoretical system that was used was one with a very strongly defined dominant frequency and phase. A similarly strong dominant set of frequencies and phase demonstrated that the synchrony between coupled lasers was best defined in narrow band (DeShazer et al., 2001). Nevertheless, our data clearly demonstrate that when faced with compound synaptic potentials, with features that emerge from the baseline time series with a unidirectional deflection from baseline, that synchronization may be best characterized in broad band. In retrospect, because such unidirectional deflections require superimposition of sines and cosines (the basis functions used to decompose such signals in Fourier analysis) at multiple frequencies, finding that detecting synchronization requires the broad band signal should have come as no surprise.

On the other hand, our findings for narrow band phase correlation were problematic. We identified several instances in low [K⁺]_o where narrow band PC suggested coupling where all other methods failed. However, PC-NB also was the only method that suggested a discrepant decrease in synchronization as [K⁺]_o was elevated. Although it may well be that subtle nonlinear couplings in low [K⁺]_o were identified only with PC-NB, we have proceeded cautiously with this method and did not apply it to the seizure data.

We were careful to use an estimate of the expected cross-correlation if the time series were uncoupled, given the autocorrelation and length of our time series. Although the statistical requirements have been known for more than half a century [Bartlett (1946); see extensive discussion in Jenkins and Watts (1968)], we are hard pressed to find within the vast neuroscience literature examples in which such statistics were applied appropriately to either intracellular or extracellular multi-electrode data. The use of either the variance estimate for uncoupled cross-correlation as we have used here, or prewhitening data with a best linear filter (Chatfield, 1989; Ljung and Glad, 1994), should be routine for correlation analysis of neuronal data.

In human epilepsy several pre-seizure changes occur such as electrodecremental events (Alarcon et al., 1995), linear increases in spectral power (Litt et al., 2001), and nonlinear signal changes (Lehnertz and Elger, 1998; Martinerie et al., 1998). Despite an extensive search, we detected no pre-seizure state in our 4AP seizures.

Bursts in our experiments were found to demonstrate an increase in synchronization between neurons on fast time scales, a degree of synchrony that was not accounted for by the simultaneous increase in synaptic activity measured in the neurons. An increase in synchrony was also detected before bursts. Such gradual buildups for these synchronous events are consistent with other reports in high [K⁺]_o (Chamberlin et al., 1990), 4AP (Perreault and Avoli, 1991), and before spontaneous neonatal bursts (Prida and Sanchez-Andres, 1999).

Completely unexpected was the finding that the seizure-like events in this preparation demonstrated a decrease in synchronization between neurons. Such a decrease in synchrony was detected when compared with the interictal baseline before the seizure, and in preparations with both bursts and seizures, in comparison with the bursts preceding the seizure. There are several lines of evidence, both theoretical and experimental, that are consistent with our findings of a synchrony decrease in such seizures.

Recent theoretical work using computational models suggests that neuronal networks might be capable of sustaining a higher level of population activity if the neurons are asynchronous (Gutkin et al., 2001). Indeed, excessive synchronization of neurons in an ensemble leads to both a communal refractory period, and a unified response from the recurrent inhibitory neurons that are ubiquitous in many regions of cortex and subcortical areas. Additional theoretical work supports the hypothesis that persistent neuronal network activity may require asynchrony (Golomb, 1998). Our findings are the first direct experimental evidence consistent with such theoretical predictions.

Other theoretical work has studied the asynchronous state in networks of strongly coupled neurons (Golomb and Hansel, 2000; van Vreeswijk, 2000). When sparsely coupled networks demonstrate inhomogeneous landscapes of connectivity, increasing coupling serves to increase asynchrony because the coupling becomes strong enough to force the inhomogeneities to dominate the dynamics (Golomb and Hansel, 2000).

In addition, there are converging lines of evidence, both theoretical (Izhikevich, 2000; van Vreeswijk, 2000) and experimental (Elson et al., 1998), that show that as neurons become more strongly coupled they may synchronize on slow time scales (such as bursts), yet remain asynchronous on faster time scales. Our results with seizures may reflect such a phenomenon, because we focused on the synaptic events at faster time scales.

Furthermore, experimental work has shown that the CA1, with direct excitatory connections between pyramidal cells <1% (Bernard and Wheal, 1994; Deuchars and Thomson, 1996), is more sparsely coupled synaptically than CA3, where such connections approach 2–5% of cells (Traub and Miles, 1991). The differences in the degree of connectivity may be intimately related to the generation of bursts in CA3, and seizures in CA1, when subject to the same epileptogenic manipulations whether elevating [K⁺]_o (Traynelis and Dingledine, 1988) or introducing 4AP (Barbarosie and Avoli, 1997).

In addition, there is experimental work demonstrating that the increased synchronization imposed on an epileptic region from bursts may reduce the likelihood of seizures (Bragdon et al., 1992; Barbarosie and Avoli, 1997). Indeed, periodic pacing at the natural frequencies of bursts can suppress seizures in the high [K⁺]_o hippocampal slice (Jerger and Schiff, 1995) or in the 4AP slices when the Schaffer collateral tract is severed (Barbarosie and Avoli, 1997). It is also possible that the desynchronization that we observed at the beginning of these events was related to a GABAergic process similar to the long-lasting depolarization events observed to trigger seizure-like events in entorhinal cortex (Lopantsev and Avoli, 1998).

Our synchronization was measured between synaptic currents in patch-clamped excitatory neurons that had suppressed spike-generating mechanisms. Each neuron thus served to sample the neighborhood of neurons directly connected to it from within the network. Our results suggest that as these seizure-like events initiated and built up, the correlation length within the network shrunk about the neurons, decreasing the apparent synchronization between sampled neuronal pairs. As the seizures abated, our findings are consistent with a simultaneous increase in apparent correlation length within the network. Such a decrease and increase in correlation lengths within this network may be created by the level of activity and synchronization within the inhibitory neuronal network. Examination of the previous work of Perez Velazquez and Carlen (1999) is fully consistent with this idea. In their work, dramatic synchronization was visually evident between the GABAergic interneurons and CA1 pyramidal cells as the seizure-like events matured and turned into afterdischarges before termination (Perez Velazquez et al., 1999, their Figs. 1, 6, 7). In contrast, visual inspection of their data suggests that these tetanus-induced ictal events initiated without such apparent synchronization.

If a decrease in synchronization is essential for the initiation and maintenance of epileptic seizures, and if synchrony is associated with seizure termination, then methods directed at increasing such synchronization may be useful in controlling seizures.