3.1 Basic aspects of spontaneous synaptic activity

In neurons recorded from the LAT of anesthetized rats, spontaneous synaptic events tend to occur in clusters. The frequency of these clusters of post-synaptic potentials (“PSP clusters”) depends on the anesthesia level, and is tightly aligned with the cortical EEG (), similar to what has been demonstrated previously (e.g. (

Pare et al., 1995b)). Because the amplitude and duration of these PSP clusters is sensitive to anesthesia level, all data used for recordings were obtained when the principal rhythmicity of the EEG was between 0.5 to 1.2 Hz. Correspondingly, the mean frequency of the PSP clusters was 0.98 ± 0.04 Hz (range 0.79 - 1.19 Hz, n=14 control neurons, measured near V

_{rest}; −75.8 ± 0.6 mV). Similarly reflective of the extrinsic origin of the frequency of these synaptic events, when the membrane potential (Vm) was shifted with direct current, there was no significant correlation between the Vm and the frequency of the PSP clusters (; Pearson r=0.20, p=0.12), indicating that the Vm had little effect on the occurrence of these clusters.

3.2 Voltage-dependence of synaptic clusters

To test whether there was a voltage-dependence of PSP cluster amplitude, Vm was shifted with direct current to a range of membrane potentials. There was a strong correlation between the peak amplitude of PSP clusters and the Vm (; Pearson r=−0.77, p<0.0001, n=14 neurons). While apparent that the cluster amplitude decreased with depolarization, there was a wide range of PSP cluster amplitudes across neurons. To obtain a more clear picture of the relationship between Vm and cluster amplitude, only neurons were included that were measured at a range of membrane potentials (>30 mV range) and non-linear and linear fits were compared. The relationship between Vm and cluster amplitude was best fit to a non-linear function (; best fit second order polynomial compared to linear; F(1,40)=4.77, p=0.035, Pearson r = 0.65, n=13 neuron).

To further facilitate comparison across neurons, the data of each individual neuron were normalized to the average amplitude of clusters measured at −90 to −100 mV in that neuron (X_{Norm}, see Methods; to be included in analysis, each neuron had to have a set of measurements between −90 and −100 mV). When reanalyzed in this manner, it is apparent that the amplitude of clusters decreases as a function of membrane voltage, and this relationship is non-linear (; best fit to second order polynomial compared to linear fit, F(1,52)=8.77, p=0.0046; polynomial goodness of fit r^{2}=0.70; n=13 neurons). While the non-linearity of this relationship is likely exagerated by normalization of the data, its presence is not the artifactual result of normalization of the data. Thus, when the best-fit relationship between Vm and cluster amplitude was examined for each individual neuron, the majority of neurons were best fit with a sublinear second order polynomial compared to a linear fit (; 10/13 neurons, p=0.002, χ^{2}=12.15, df=2, only neurons with data from at least 3 membrane potentials were included).

There are a number of factors that may contribute to this voltage-dependent decline in the amplitude of these clusters. The simplest explanation is a decrease in driving force for excitatory synaptic events. However, given the non-linearity of the relationship, it is likely that other factors contribute. Other factors may include the concurrent reduction in driving force and eventual reversal of inhibitory GABA channel-mediated synaptic events, and a change of voltage-dependent ionic conductances.

3.3 Influence of IPSPs on voltage dependence of synaptic clusters

GABAergic inhibition can strongly reduce summation of PSPs by hyperpolarization and via shunting conductances. Previous studies have demonstrated a strong GABAergic component during clusters of spontaneous synaptic activity in vivo (

Lang and Pare, 1997b;

Windels et al., 2010). To test the role of GABAergic IPSPs, separate experiments were performed with DNDS (500 μM) in the recording electrode. As demonstrated previously and replicated here, DNDS effectively blocks fast GABAergic IPSPs in LAT neurons (; Rosenkranz et al, 2010; Rademacher et al, 2011). The remaining synaptic events are likely excitatory PSPs (EPSPs). With DNDS in the recording electrode, there was still a clear voltage dependence of EPSP clusters (). Similar to control conditions, there was evidence of a suppression of PSP cluster amplitude at depolarized membrane potentials. As above, neurons with >30 mV range of data points were examined (n=9), and the relationship between cluster amplitude and Vm was found to be best-fit to a sub-linear fit (; second order polynomial compared to linear, F(1,39)=4.67, p=0.037, Pearson r = 0.53). When normalized to control for cluster amplitude variability across neurons (X

_{Norm}, see Methods), the relationship between Vm and cluster amplitude was still best fit with a sublinear function (; second order polynomial compared to linear, F(1,39)=5.60, p=0.023, Pearson r=0.78). Furthermore, when examined individually, the majority of neurons displayed a sublinear relationship between cluster amplitude and Vm (; 7/9 neurons, p=0.013, χ

^{2}=8.67, df=2). Despite the effectiveness of DNDS in blockade of IPSPs (), there was no significant difference in the voltage dependence of PSP cluster amplitudes in the presence or absence of DNDS (; best-fit functions of these treatment groups were not significantly different, F(3,88)=0.93, p=0.43).

To further explore this surprising finding, the area of PSP clusters was measured. The relationship between cluster area and Vm was best-fit to a sublinear function (; second order polynomial, F(1,39)=4.63, p=0.038, n=9 neurons). Furthermore, the majority of individual neurons displayed a sublinear relationship between cluster area and Vm (; 7/9 neurons, p=0.013, χ^{2}=8.67, df=2). Even when normalized, the best-fit curves of cluster area and Vm were sublinear (; F(1,39)=5.79, p=0.021), and were not significantly different between control and DNDS groups (F(3,82)=2.55, p=0.061). Thus, blockade of fast IPSPs with DNDS did not reverse the sublinearity of clusters at depolarized membrane potentials.

3.4 Contribution of K^{+} channels

If not explained by GABAergic inhibition, the sublinear voltage-dependence of EPSP clusters may be caused by voltage-dependent ion channels. The most likely channels to contribute to a voltage-dependent suppression of EPSP summation are potassium channels (K^{+} channels). Tetraethylammonium (TEA) is able to block a wide range of K^{+} channels, including voltage-gated K^{+} channels that are activated in ranges more depolarized than the resting membrane potential. Cesium (Cs^{+}) blocks two conductances that are highest at a range of voltages close to, or hyperpolarized to, the resting potential, and whose conductance decreases at depolarized potentials (h channels and inward rectifier K^{+} channels). To test the contribution of these two broad types of conductances to the sublinear voltage-dependency of the EPSP clusters, either Cs^{+} or TEA was included in the pipette (in both conditions with DNDS).

Addition of Cs^{+} (200 mM, along with 500 μM DNDS) to the pipette caused a significantly greater average cluster amplitude (; two-way ANOVA, Cs^{+} compared to DNDS, significant effect of treatment, p<0.0001, F(1,4)=34.0) and cluster area (two-way ANOVA, Cs^{+} compared to DNDS, significant effect of treatment, p=0.002, F(1,4)=10.3). Neurons with a >30 mV range of data points were analyzed, and a significant sublinear relationship between cluster amplitude and Vm was found (; best fit second order polynomial compared to linear, F(1,40)=4.82, p=0.034, Pearson r = 0.52), and between cluster area and Vm (; F(1,40)=5.68, p=0.022, Pearson r = 0.46). When tested on an individual neuron basis, a high proportion of neurons displayed a sublinear best-fit of the relationship between cluster amplitude and Vm (; 7/11 neurons, χ^{2}=5.09, df=2), and cluster area and Vm (; 7/11 neurons, n.s., χ^{2}=5.09, df=2). Therefore, it is unlikely that Cs^{+}-sensitive ion channels underlie the sublinear voltage-dependence of EPSP clusters. Furthermore, there was no significant difference in the normalized cluster-Vm relationship between Cs^{+} and DNDS alone conditions for amplitude (; F(3,85)=0.35, p=0.79), or area (; F(3,85)=1.90, p=0.14).

When TEA was included in the pipette (20 mM, along with 500 μM DNDS), TEA significantly increased the cluster amplitude (; two-way ANOVA, TEA (n=11) compared to DNDS (n=10), significant effect of treatment, p<0.0001, F(1,4)=81.7). and cluster area (two-way ANOVA, TEA compared to DNDS, significant effect of treatment, p<0.0001, F(1,4)=35.4). However, the voltage-dependence of cluster amplitude was best-fit with a linear instead of polynomial function (; F(1,51)=0.89, p=0.35). The same was found for cluster area (; F(1,51)=0.07, p=0.79). Furthermore, when examined on an individual neuron basis, few neurons displayed a sublinear relationship between Vm and cluster amplitude (; 1/11 neurons, n.s., χ^{2}=5.09, df=2) or cluster area (; 1/11 neurons, n.s., χ^{2}=5.09, df=2). In fact, most neurons displayed a supralinear relationship between Vm and amplitude (7/11 neurons) or area (7/11 neurons) when TEA was present. In addition, the best fit of the normalized data was significantly different for TEA compared to DNDS controls (; amplitude: F(3,101)=10.97, p<0.0001; area: ; F(3,101)=6.27, p=0.0006).

3.5 Voltage-dependence of individual PSPs

To understand what aspect of PSP integration is modulated by voltage, we next examined individual PSPs that comprise the clusters. Individual PSPs were measured with a sliding template (Methods; ). It is difficult to determine whether individual PSPs measured in vivo are in fact single synaptic events. The measured events are likely composed of single and multiple synaptic events from synapses at varying distances from the soma, leading to a wide range of measured amplitudes. Therefore, these studies do not assume that the PSPs are single synaptic events. However, this analysis assumes that the detectability of events, number of synapses, presynaptic release probability and amount of neurotransmitter released remains constant across the brief post-synaptic changes in membrane potential. Consistent with this assumption, there was no significant correlation between the membrane potential and the frequency of individual PSPs (; Pearson r=0.014, p>0.05, slope = 0.1657 ± 1.675 Hz for every 10 mV change, slope not significantly different than zero, F(1,52)=0.01, p=0.92). Therefore, voltage-dependence in PSPs is unlikely to be caused by inability to detect similar number of events at depolarized Vm.

There was a significant correlation between the amplitude of individual PSPs and the cluster amplitude (Pearson r=0.62, p<0.001, n=14 neurons), so perhaps individual PSP attributes could underlie cluster attributes. If a change in individual PSP attributes accounts for the change in clusters across membrane potentials, it is expected that individual PSPs will display the same non-linearity of voltage-dependence as PSP clusters. However, the amplitude of individual PSPs was linearly correlated with Vm (; best fit to linear compared to second order polynomial, F(1,52)=0.11, p=0.74; Pearson r=−0.54, p<0.0001, n=14 neurons) with a decrease in the amplitude of individual PSPs as the membrane potential decreases (slope=-0.11 ± 0.02 mV for every 10 mV depolarization (8.5% of mean amplitude), F(1,52)=31.0, p<0.001 slope significantly non-zero, n=14 neurons; when analyzed on a per neuron basis, the extrapolated reversal potential was 29.1 ± 4.4 mV). Furthermore, no neurons displayed a sublinear relationship between PSP amplitude and Vm (; 0/11 neurons, p=0.0023, χ^{2}=12.18, df=2), and the relationship between normalized PSP amplitude and Vm was linear (; best fit to linear, F(1,52)=2.94, p=0.09; Pearson r=−0.52, p<0.0001, n=14 neurons).

To explore the voltage-dependence of individual PSPs further, the relationship between the area of the individual PSPs and cluster area was measured, and found to correlate (Pearson r=0.35, p=0.012, slope = 179.4 ± 68.8, significantly non-zero, p<0.05, n=14 neurons). The area of individual PSPs displayed a linear relationship to Vm (; best fit to linear function compared to second order polynomial, F(1,52)=0.69, p=0.41; Pearson r=−0.30, p=0.03, slope = −0.37 ± 0.14 ms*mV for each 10 mV of change in the membrane potential, significantly non-zero, p<0.05, n=11 neurons), even when normalized (; best fit to linear, F(1,52)=3.18, p=0.081), and only 2/11 individual neurons displayed a sublinear relationship between area and Vm (, n.s.).

3.5.1 Neither voltage-dependence of individual PSP amplitude nor area mirrored the sublinear voltage-dependence of clusters. With a change in driving force and PSP amplitude, there is also expected to be a change in the half-width of individual PSPs. A significant decrease of half-width at depolarized membrane potentials would decrease the window of integration of PSPs, and could lead to reduction of cluster amplitude. However, there was not a correlation between the half-width of individual PSPs and Vm (; Pearson r= −0.17, p=0.23, n=14 neurons), and the slope of that relationship was not significantly different than zero. There was also no significant relationship between half-width and cluster amplitude (Pearson r=0.18, p=0.20, slope not significantly different than zero, n=14 neurons). Because of this surprising result we also held the Vm at predetermined membrane potentials in a separate group of neurons (−85 mV, −70 mV, and −55 mV), to facilitate comparisons across neurons and across Vm. Even when examined in this manner, there was no significant effect of membrane voltage on PSP half-width (; F(2,8)=0.84, p=0.45, one-way repeated measures ANOVA, n=9 neurons). The lack of a voltage-dependence of PSP half-width indicates that this feature of PSPs is unlikely to underlie the non-linear voltage-dependence of clusters. This finding is consistent with contribution of other factors that modulate synaptic integration in vivo, such as GABA or K^{+} channels.

3.5.2 Very similar profiles of PSPs were observed when DNDS was included in the electrode to block IPSPs. Similar to control conditions, the amplitude of individual EPSPs depended upon the membrane potential in a linear manner (; best fit to linear compared to second order polynomial, F(1,50)=0.15, p=0.70, correlation between EPSP amplitude and membrane potential Pearson r=−0.48, p<0.0001, n=10 neurons; slope =−0.136 ± 0.0346 mV for every 10 mV depolarization (9.7% of average amplitude)), as did area (; best-fit to linear compared to second order polynomial, F(1,50) = 0.015, p=0.91; correlation between EPSP area and membrane potential Pearson r=−0.36, p=0.015, n=10 neurons; slope = −0.46 ± 0.18 mV*ms per 10 mV depolarization). The voltage-dependence of the normalized amplitude and area of the individual PSPs with DNDS was not significantly different from controls (; Amplitude: control slope=-0.11 ± 0.02 mV for every 10 mV depolarization, n=14 neurons, DNDS slope =−0.136 ± 0.0346 mV for every 10 mV depolarization, n=10 neuros, not significantly different, p=0.92, F(2,93)=0.087; Area: control slope = −0.37 ± 0.14 mV*ms per 10 mV depolarization, n=14 neurons, DNDS slope = −0.40 ± 0.15 mV*ms per 10 mV depolarization, n=10 neurons, not significantly different, p=0.88, F(1,96)=0.022).

3.5.3 When Cs^{+} or TEA were included in the electrode with DNDS, the voltage-dependence of individual EPSP amplitude was still linear (; Cs^{+}: best fit to linear function, F(1,48)=0.076, p=0.78, slope = −0.164 ± 0.043 mV for every 10 mV depolarization (9.9% of average amplitude), Pearson r=−0.47, significantly non-zero, F(1,48)=14.4, p=0.0004, n=9 neurons; TEA: best fit to linear F(1,64)=1.83, p=0.18, slope = −0.137 ± 0.056 mV for every 10 mV depolarization (8.4% of average amplitude), Pearson r=−0.29, slope significantly non-zero, F(1,64)=6.12, p=0.016, n=11 neurons). When compared to DNDS control, there was no significant difference in the fits to normalized amplitude (; F(4,155)=1.24, p=0.30). The relationship between Vm and the area of EPSPs in the presence of Cs^{+} or TEA followed the same pattern and was best fit to linear functions (; Cs^{+}: best-fit to linear compared to second order polynomial, F(1,48)=0.16, p=0.69, slope = −0.45 ± 0.18 mV*ms for every 10 mV depolarization, Pearson r=−0.34, significantly non-zero, F(1,48)=6.25, p=0.016, n=9 neurons; TEA: best-fit to linear compared to second order polynomial, F(1,64)=2.96, p=0.09, slope = −0.47 ± 0.22 mV*ms for every 10 mV depolarization, Pearson r=−0.26, slope significantly non-zero, F(1,64)=4.54, p=0.037, n=11 neurons). In addition, when compared to DNDS control, there was no significant difference in the best fits to normalized data (; F(4,155)=1.02, p=0.40). This indicates that neither Cs^{+} nor TEA significantly impacted the voltage dependence of individual PSP amplitude or area. This further supports a role for factors other than EPSP amplitude or area in the sublinearity of the voltage-dependence of clusters.

3.6 Cluster-invidual EPSP relationship (Cluster_{ratio})

It is apparent from the data above that individual PSPs and the clusters do not display similar voltage-dependence, as individual PSPs were best fit with linear regressions in most conditions, whereas clusters were best fit with non-linear regressions in most conditions. This mismatch indicates that the voltage dependence of PSPs is unlikely to account for the voltage dependence of clusters. The exception is when TEA is included in the electrode, and both individual PSPs and clusters display similar voltage dependence, and implies that TEA-sensitive ion channels may underlie the sublinaerlity of the voltage-dependence of clusters. However, this inference is derived by normalizing to the peak amplitude within neurons. That approach allows comparison across groups, but it does not indicate voltage-dependence of the interaction between EPSPs and clusters. To examine this interaction, cluster amplitude was normalized by the average EPSP amplitude at each membrane potential (Cluster_{ratio}, see Methods). If voltage-dependent factors dictate the relationship between individual PSPs and clusters, Cluster_{ratio} should vary across the membrane potentials. But if voltage-dependent factors do not dictate this relationship, Cluster_{ratio} should be flat across membrane potentials. There was a strong voltage-dependence of this ratio (; Pearson r=−0.43, p=0.0012; slope significantly non-zero F(1,52)=11.7, p<0.005, n=14 neurons). To further quantify this relationship, and facilitate comparisons across neurons, we examined the amplitude Cluster_{ratio} at three predetermined values (−55, −70, −85 mV, Methods) in a separate group of neurons. There was a significant decrease in this ratio at the depolarized membrane potential, compared to other membrane potentials (; one-way repeated measures ANOVA, F(2,8)=3.36, p=0.013, n=9 neurons; post-hoc Tukey’s test −55 mV compared to −85 mV, p<0.05, q=4.56; compared to −70 mV, p<0.05, q=3.82).

The same analysis was applied to area. Similar to amplitude, there was a voltage dependence of the Cluster_{ratio} when cluster area was normalized to individual PSP area (; slope = −2.97 ± 1.06 change in area/mV change in membrane potential, significantly non-zero, p<0.01, n=14 neurons). The area Cluster_{ratio} at three predefined membrane potentials (as above, −85 mV, −70 mV, and −55 mV) in a separate group of neurons was also significantly voltage dependent (; p=0.0003, F(2,8)=13.6; one-way repeated measures ANOVA, n=9 neurons, with a significantly more shallow relationship between individual PSPs and PSP clusters at −85 mV (q=6.99) and −70 mV (q=5.53) compared to −55 mV, p<0.05; post-hoc Tukey’s tests). These data are further evidence that factors beyond just the shape and size of individual PSPs contribute to the suppression of clusters at depolarized membrane potentials, implicating the involvement of factors that reduce PSP integration, such as GABAergic IPSPs and various K^{+} channels. Because area is expected to provide a more accurate reflection of the relationship between EPSPs and clusters, it was the focus of the subsequent examination of Cluster_{ratio}.

3.6.1 When DNDS was in the pipette the area Cluster_{ratio} was also dependent upon voltage (; slope = −1.24 ± 0.56 change in ratio for every mV depolarization; significantly non-zero, F(1,50)=4.94, p=0.031, n=10 neurons), with a negative correlation (Pearson r=−0.31, p<0.05). This was further affirmed by examination of EPSP areas at predefined membrane potentials (−85, −70, and −55 mV, as above; ; one-way repeated measures ANOVA, F(2,18)=23.9, p<0.001, n=10 neurons; with significant differences between −55 mV and −80 mV (q=9.48), −55 mV and −70 mV (q=6.81), p<0.05, post-hoc Tukey’s tests). Despite blockade of fast IPSPs, DNDS did not significantly alter the voltage dependence of the Cluster_{ratio} compared to controls (; two-way repeated measures ANOVA significant effect of voltage, F(2,18)=29.98, p<0.0001; no significant effect of DNDS treatment p=0.74, F(1,18)=0.11; no significant interaction, p=0.29, F(2,18)=1.30). And, there is still a significant voltage dependence when fast inhibition is blocked (post-hoc Tukey’s tests −55 mV compared to −80 mV, q=9.48; −55 mV compared to −70 mV, q=6.81; both p<0.05). This indicates that, while GABA may modulate EPSP summation, GABA_{A}-mediated inhibition does not significantly alter the voltage dependence of the relationship between EPSPs and clusters in vivo.

3.6.2 Similarly, when Cs^{+} was in the pipette, the area Cluster_{ratio} also displayed significant voltage dependence (; slope=-2.92 ± 1.13, significantly non-zero F(1,48)=6.69, p=0.013, n=9 neurons), with a negative correlation (−0.35, p=0.013). This was further affirmed by examination of area Cluster_{ratio} at predefined membrane potentials (; −85, −70, and −55 mV, as above; one-way repeated measures ANOVA, F(2,16)=9.97, p=0.002, n=9 neurons; with significant differences between −55 mV and −85 mV (q=6.31, p<0.05), −55 mV and −70 mV (q=3.45, p<0.05), post-hoc Tukey’s tests). This indicates that Cs^{+} did not block the voltage-dependence of the relationship between EPSPs and clusters.

When TEA was present, unlike in control and Cs^{+} conditions above, the area Cluster_{ratio} was not significantly voltage dependent (; slope=-1.73 ± 1.57, slope not significantly different than zero, F(1,64)=1.23, p=0.27, Pearson r=−0.13, n=11 neurons). This was further examined at predefined membrane potentials (−85, −70, and −55 mV, as above), without a significant voltage-dependence (; one-way repeated measures ANOVA, F(2,10)=0.57, p=0.57, n=9 neurons). This is consistent with a significant role of TEA-sensitive channels in the voltage-dependence of the EPSP-cluster relationship.

3.7 Impact on integration and firing

To directly measure the effects of TEA on summation, independent from activation of synaptic input, we injected currents directly into the soma that were shaped like EPSCs (α-shaped waveform), evoking αPSPs. These αPSP trains displayed temporal integration (; 10 αPSPs at 50 Hz; in the presence of DNDS). Similar to cluster amplitude, the peak amplitude of αPSP trains displayed a sublinear relationship to Vm (; best-fit to second order polynomial compared to linear, F(1,240)=14.41, p=0.0002, n=7 neurons). Analagous to Cluster_{ratio}, the summation ratio of αPSP trains was also voltage-dependent (; summation measured as the amplitude of the last PSP/first PSP: slope = −3.26 × 10^{2} ± 0.348 × 10^{2} mV for every 10 mV depolarization, Pearson r=−0.52, slope significantly non-zero, F(1,242)=17.2, p<0.001, n=7 neurons), consistent with a reduction of PSP summation at depolarized membrane potentials. With TEA (TEA + DNDS) present the amplitude of the αPSP train across Vm was now best fit to a linear function (; F(1,246)=1.58, p=0.21, n=7 neurons). Summation was still voltage-dependent, however, the voltage-dependence was reversed and there was an increase of PSP summation at depolarized membrane potentials (; slope = 2.88 × 10^{2} ± 0.367 × 10^{2} mV for every 10 mV depolarization, Pearson r=0.45, slope significantly non-zero, F(1,228)=61.6, p<0.001, n=7 neurons). To directly compare control and TEA conditions, summation from three different membrane potentials was examined (−85 mV, −70 mV, and −60 mV; −55 mV analysis was not used for comparison because action potentials were often evoked by the αPSPs at this membrane potential when TEA was present). There was a significant effect of TEA on summation of αPSPs (; p<0.001, two-way ANOVA, F(1,36)=14.5, n=7 neurons). This is consistent with a voltage-dependent suppression of PSP summation that is mediated by TEA-sensitive ion channels.

To test if linearization of the cluster voltage-dependence led to a change of neuronal firing, action potential firing was measured during clusters. TEA led to significantly greater action potential firing during clusters than DNDS controls over a range of membrane voltages (; two-way ANOVA, TEA compared to DNDS, significant effect of treatment, p<0.0001, F(1,22)=24.6). To verify the general effectiveness of TEA, the action potential half-widths were measured. TEA significantly increased the half-widths of action potentials evoked by current steps (; DNDS control 0.93 ± 0.03 ms, TEA 1.08 ± 0.02 two-way unpaired t-test, p<0.001, t=4.57, df=157).