Glissandi can occur in electrocorticography recordings from human epileptic brain in situ, prior to a seizure
An example of a preictal glissando, in a human ECoG recording, is shown in Fig. 1. As seen in Fig. 1A, there are large, slow, baseline fluctuations (marked by the horizontal bar) before the electrographic seizure. A glissando discharge is unmasked by removal of the slow baseline fluctuation with a higher pass band filter (lower trace). As seen in Fig. 1B, using a sliding window spectrogram, the glissando lasts about 4 s, and runs from ∼30 Hz to ∼125 Hz. An additional spontaneous glissando, similar to that shown in Fig. 1, was also observed in the 9 h of overnight ECoG recording analyzed.
Glissandi can be evoked in “normal” rat neocortical slices in alkaline conditions, and also when AMPA, NMDA, and GABA receptors are blocked
Transient, spatially localized alkalinization of layer V in adult rat neocortex generated ictal events lasting >30 s (Fig. 3A). The initial field potential event in each case was a low-amplitude (64 ± 12 μV) run of fast oscillations beginning 0.7 ± 0.3 s post application of alkaline solution. The initial peak frequency of this activity was 32 ± 7 Hz. The maximum frequency shifted to 180 ± 30 Hz over 0.5–2.2 s until onset of large amplitude ictaform events (Fig. 3B, p < 0.05, n = 5). Bathing slices in ACSF containing drugs to block AMPA, NMDA, and GABAA & B receptors abolished the ictal response to alkalinization in all cases; however, the initial, low amplitude fast oscillation persisted, lasting 0.6 ± 0.2 s with frequency increasing from 44 ± 8 to 220 ± 30 Hz (Fig. 3B), and latency from droplet application of 0.5 ± 0.2 s (n = 5). These initial fast oscillations resembled the glissando discharges seen in human cortex in vivo and in vitro suggesting that nonchemical intercellular transmission may play a role, and that chemical synapses are not required.
Figure 3. Experimental model of glissando discharges in normal rat neocortex: implication of pH. (A) Rat frontal cortex maintained in normal ACSF. Transient alkalinization was induced by pressure ejection of 30–70 nL ACSF containing 200 mm NaOH (asterisk). This induced a gradual increase in low amplitude spontaneous activity with an increasing peak frequency until onset of ictal event lasting >30 s. Scale bars 1 s, 2 mV. (B) Comparison of glissando discharges evoked in normal conditions and conditions with the main chemical synaptic components blocked (gabazine, CGP55845, NBQX, and D-AP5). The left trace is expanded from “A” and the corresponding spectrogram shown below. The right trace shows response to the same alkalinizing ACSF pulse in the cocktail described above. Note: no ictaform events were seen with the chemical synaptic blockers present; and there is an absence of accompanying slower frequencies as the glissando progresses during blockade of chemical synapses. Scale bars 0.1 mV, 100 msec.
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The production of a proepileptogenic low calcium environment (Haas & Jefferys, 1984) through alkalinization and subsequent precipitation of calcium ions out of the ACSF solution may, in principle, be a factor in the production of the glissandi. In order to address this issue, the fast calcium buffer, BAPTA (1 mm) was pressure ejected in the presence of the cocktail of chemical synaptic antagonists (for AMPA, NMDA, GABAA, and GABAB receptors). Following the brief application of BAPTA, no glissandi were observed (n = 3, data not shown).
The latency for a spike to cross from axon to axon is expected to depend on gap junction conductance
Furshpan and Potter (1959) showed, by direct dual recording from coupled axons, that a spike could cross from one axon to the electrically coupled other axon in <0.5 msec; this was in an invertebrate preparation (the isolated crayfish nerve cord) at room temperature. MacVicar and Dudek (1982) provided indirect evidence that spikes might cross from one hippocampal mossy fiber to another in about 0.2 msec (the reasoning behind this interpretation of their data is in Traub et al. (1999)). Mercer et al. (2006) recorded simultaneously from two CA1 pyramidal cell somata, and demonstrated that a spike in one cell could induce a spikelet in the other cell with latency about 0.5 msec; if the coupling is mediated between axons (which was not proven in the paper), then—allowing for conduction times—the axonal crossing time must be <0.5 msec. Dhillon and Jones (2000) demonstrated a similar phenomenon in entorhinal cortex. Wang et al. (2010) recorded simultaneously from two layer V pyramidal neurons, and reported spike/spikelet latencies of 0.18–1.8 msec. We are not aware of experimental data examining spike latencies that are modified by manipulations of gap junction conductance, and therefore examined this question with simulations (Fig. 4).
Figure 4. The latency for a spike to cross from axon to axon is predicted to decrease as gap junction conductance increases. Simulations of a single layer V pyramidal neuron, with a standardized prejunctional axonal spike coupled to an axonal compartment, through a conductance set at 1, 2, 3,..., 10 nS. (A) the superimposed traces of axonal potential, with the onset of the prejunctional spike at the time marked by the vertical arrow. (B) details of the axonal potential. The threshold gap junction conductance for spike transmission was between 2 and 3 nS. With conductances above 3 nS, the latency for axonal spiking decreases, although with “diminishing returns.” The largest decrease occurs between 3 and 4 nS.
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To construct Fig. 4, we first determined the waveform, V(t), of a simulated axonal action potential, over a time interval of 1.0 msec. We then simulated a current-induced spike, and injected, starting at time 10 msec (arrow in Fig. 4), the current g × V(t) into the distal axonal compartment, where g represents the putative gap junction conductance. We repeated this procedure for g = 1, 2, 3,....,10 nS. The resulting axonal responses are shown, superimposed, in Fig. 4, and are taken to represent the properties of axon-axon spike transmission as a function of gap junction conductance. (The data in Fig. 4 do not, however, capture the effects of shunting when multiple nearby gap junctions are present on an axon.) Fig. 4 shows clearly that, as expected, once a threshold conductance is reached, the latency for spike transfer diminishes as the coupling conductance increases—with “diminishing returns,” however, at larger conductances. The difference in latency to the peak of the spike, from g = 3–4 nS, is 0.08 msec; the difference in latency from g = 3–10 nS, is 0.18 msec.
We repeated the simulations of Fig. 4, injecting currents in progressively more proximal axonal compartments, rather than the most distal one (not shown). Using the penultimate axomal compartment produced results similar to Fig. 4; however, with the next, more proximal, compartment, the spread in latencies became larger, almost 1 msec. This might suggest a larger spread in glissando frequencies, but see further on.
The functional significance of these latency differences, for network behavior, can be estimated as follows: in a VFO network modeled as a random graph, oscillation periods are expected to follow the mean path length, being of order twice this quantity (Traub et al., 1999). The “mean path length,” for a connected subregion of a graph, is the average number of steps it takes to traverse a shortest path from node 1 to node 2, where both nodes are chosen randomly. In a random graph with sufficiently high connectivity, there is a single connected subregion that is much larger than all the others, called the “large cluster.” Comments below refer to the large cluster. In a random graph, the statistical structure is determined entirely by the connectivity parameter c (equal to ½ the mean number of edges, or links, emanating from a node – the “mean index”); c in turn determines the relative size of the large cluster in the graph, G(c), a number lying between 0 and 1 (Erdös & Rényi, 1960). In our case, where the mean index of the 15,000 cell random graph is 3.333, c is equal to half of this, or about 1.667, and G(c) = 0.96. That is, the large cluster is 96% of the whole network. Following Newman et al. (2001), we may estimate the mean path length as
where N is the graph size, or 15,000. This quantity is about 8.0. Therefore, a difference in latency of 0.18 msec for a spike to cross from axon to axon (see above) is expected to translate into differences in VFO periods of the order of 2 × 8 × 0.18 msec–2.9 msec. That number is sufficient to make a major difference in network frequency. Therefore, if the fastest VFO frequency in the network were, say, 160 Hz, corresponding to a period of 6.25 msec, then the network might be capable of slowing down to a period of 6.25 + 2.9 = 9.15 msec, or a frequency of 109 Hz. Simulations (see below) and experiments (see above) indicate that networks can oscillate at even lower frequencies than this. Because the above analysis does not take into account the effects of shunting caused by multiple gap junctions, and by multiple axonal K+ conductances, we cannot expect it to account for the extremes of the network frequency range.
Glissandi are predicted to occur, in a detailed network model, as gap junction conductance increases, provided gK(M) is sufficiently large
To study the effects of gap junction conductance on VFO frequency in detailed network simulations (see Methods), we performed a large number of 1-s simulations as this parameter was varied, along with a parameter scaling gK(M), the density of the M-type of K+ conductance (Fig. 5A). Chemical synaptic conductances were not simulated. We found that VFO frequency would indeed steadily rise as gap junction conductance increased—predicting the existence of a glissando—provided that gK(M) was large enough. In Fig. 5A, the scaling parameter for gK(M) needed to be ∼1.5 or larger for a glissando to be expected.
Figure 5. Parameter dependence of network frequency in model. (A) Phase plot of field oscillation frequency, as a function of M-conductance (gK(M)) and axonal gap junction conductance, based on simulations of a network of 15,000 model layer V pyramidal neurons coupled by axonal gap junctions. The model predicts that a “glissando” will occur if gK(M) is large enough, and gap junction conductance rises progressively. Network behavior is more complicated when gK(M) is small, with beta2 (∼25 Hz) oscillations predicted to occur at small gap junction conductances (Roopun et al., 2006), with a rapid “switch” to VFO with small increases in this parameter. (B) Field and intracellular behavior, 400 msec epochs, at two values of gap junction conductance and fixed large gK(M) (scaling factor 2.7, corresponding to points 1 and 2 in Fig. 5A). Note the increase in both field frequency and spikelet frequency, as gap junction conductance rises, for large enough M-conductance. Scale bars 100 msec, 50 mV (units for the fields are arbitrary, but the relative amplitudes are correct.
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Fig. 5B provides a more detailed view of network behavior, at a fixed gK(M) value (scaling factor 2.7, see Fig. 5A) for two specific values of gap junction conductance. The model predicts that spikelet frequency (in intracellular recordings) should increase as network frequency increases (compare Fig. 10.7 of Traub & Whittington, 2010).
Another parameter that influences network frequency under the conditions of Fig. 5 is axonal gK(A). Reductions of the density of this transient K+ conductance, approximately fourfold compared to Fig. 5, could lead to network frequencies approaching 300 Hz (not shown).
The network model replicates full glissandi, when gap junction conductance is increased over time, and over an appropriate range
In the simulation of Fig. 6, the gK(M) scaling factor was also 2.7 (c.f. Fig. 5), and gap junction conductance was increased from 2.0 to 12.0 nS, over a period of 2 s. Chemical synaptic conductances were not included in the simulation. The glissando thereby produced was strikingly similar to the examples recorded from patients and in in vitro slices in “nonsynaptic” conditions. We repeated this simulation (not shown) with gap junctions located in more proximal compartments, rather than the most distal axon. Use of the penultimate axon compartment led to a glissando similar to that shown in Fig. 6. Moving the gap junctions one more compartment proximally, however, and leaving all other parameters unchanged, led to a simulated field without oscillations. This can be attributed to failures of spike transmission across gap junctions, due to the impedance load of the soma and dendrites.
Figure 6. Glissando simulated by steadily rising gap junction conductance, in a network without chemical synapses. The network of Fig. 5 was used (gK(M) scaling factor 2.7, as in Fig. 5B); but axonal gap junction conductance rose progressively from 2.0 to 12.0 nS over a time interval of 2 s. Field amplitude is arbitrary, and field time scale is identical to the scale in the spectrogram below. Note the similarity to Figs 1B and 3B.
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