Article Figures & Data
Figures
- Figure 1
Schematic of the computational model of hippocampus. A, The model consisted of 3080 pyramidal cells and 20 basket cells. Eighty of the pyramidal cells received noisy synaptic input that excited the cells and could produce action potentials. Each basket cell was coupled with gap junctions to the nearest neighboring basket cells, and each sent GABAergic connections to all pyramidal cells. Basket cells received feedback AMPAergic connections from activated pyramidal cells, and they also received noisy synaptic input. All noisy input was independent from cell to cell throughout the network. B, All cells were distributed uniformly along two perpendicular axes in a plane 50 μm from the simulated recording electrode. The furthest cells were located 215 μm from the recording electrode. The voltage recorded by the electrode was generated by summing the voltage produced by the transmembrane current from every compartment of every neuron and interneuron.
- Figure 2
HFOs resulting from noisy input to the basket cell population. A, Peak network frequency (defined as peak frequency of the LFP power spectral density) increased as the intensity of noisy synaptic input to basket cells increased. Insets, Two example PSD functions. Note the difference in scale between the vertical axes of the two insets, indicating the extreme diminution of oscillation amplitude as frequency increased. Individual PSDs were obtained from 1000 ms of simulation data. B, Mean basket cell firing frequency very closely tracked peak network frequency for a given level of synaptic input. C, Total LFP power >30 Hz decreased dramatically as noisy intensity (and peak network frequency) increased. Therefore, although it was possible for noisy input to basket cells to elicit rhythms with fast ripple frequencies, such rhythms exhibited very low amplitude. All error bars represent SEM over 10 simulations.
- Figure 3
HFOs resulting from noisy input to pyramidal cell population. A, Increased noise intensity to activated pyramidal cells stimulated increases in the two highest-power frequencies observed in the LFP PSDs, which were generally bimodal (see insets). Note that the network was incapable of generating rhythms faster than 250 Hz, in contrast with simulations in which basket cells received direct input (Fig. 2A ). B, High-frequency and low-frequency spectral bumps corresponded to the mean firing rates of basket cells and pyramidal cells, respectively. C, Relative dominance between the two spectral bumps varied with noise intensity, as shown in this plot of the ratio of the maximum power of the high-frequency peak to the maximum power of the low-frequency peak. Ratios >1 (demarcated by black horizontal line) imply that the high-frequency peak dominated the low-frequency peak. D, Total LFP power >30 Hz tended to decrease somewhat with increasing noise intensity, though not nearly as dramatically as when basket cells received noisy input (Fig. 2D ). All error bars represent SEM over 10 simulations. Note that the pyramidal cells in this figure require higher levels of noise input to fire than the basket cells in Figure 2, as a result of their different input impedance. This disparity was also recently shown experimentally (Karlócai et al., 2014).
- Figure 4
Ripple generation by noisy stimulation of either basket cells or pyramidal cells. A–D, Examples of sharp-wave ripples induced by activation of the basket cell population (ID numbers 81–100 in the raster plot) with a noise intensity of 2.5 × 10–4 nA2. Note the sparsity of spiking of pyramidal cells (ID numbers 1–80 in the raster plot). LFP ripple oscillations were produced primarily by IPSPs in all 3080 pyramidal cells. (3000 of the pyramidal cells never fired and are not included in the raster plots.) E, Example intracellular voltage traces of an activated pyramidal cell (left) and an unactivated pyramidal cell (right) resulting from activation of the basket cell population. Inset, IPSP-induced membrane oscillations in the unactivated pyramidal cell. F–I, Examples of sharp-wave ripples induced by noisy synaptic stimulation of the activated pyramidal cell population (with a noise intensity of 0.77 nA2). The increased pyramidal cell spiking induced increased activity of basket cells, whose inhibitory influence restricted the dominant frequency component to ≈200 Hz. J, Example intracellular voltage traces of an activated pyramidal cell (left) and an unactivated pyramidal cell (right) resulting from noisy synaptic stimulation of the activated pyramidal cell population. Inset, IPSP-induced membrane oscillations in the unactivated pyramidal cell.
- Figure 5
Effect of diminished inhibition on fast ripple incidence. Simulations were conducted in which 50 separate sharp waves were induced by intermittently activating pyramidal cells with noisy input (using a noise intensity of 0.77 nA2). Inhibitory connections from basket cells to all pyramidal cells were progressively removed. A fast ripple was defined to occur when the peak energy in the fast ripple band (>250 Hz) exceeded the peak energy in the ripple band (100–250 Hz). A, Proportion of sharp waves which exhibited fast ripples, as a function of percent inhibitory connections removed. Fast ripple incidence increased dramatically as inhibitory connections were lost. (Error bars represent SEM over 10 simulations, each with 50 induced sharp waves.) B–D, Example LFP’s and spectrograms for three levels of intact inhibition, each with three example sharp waves. FR, Fast ripple episode; R, ripple episode.
- Figure 6
HFOs resulting from noisy input to 80 uncoupled pyramidal cells. A, Two highest-power frequency peaks in the PSD as a function of noise intensity. PSDs were generally bimodal, and grew more coherent as noise intensity increased. Note how the high-frequency peaks reached fast ripple frequencies and represent a harmonic of the low-frequency peaks. B, The low-frequency peak in the PSDs from A corresponded to the average cellular firing frequency. Insets, Representative voltage traces of individual neurons for three different levels of noise intensity. The right column shows how the entire network went into depolarization block when stimulated with high enough noise intensity. C, Ratio of peak power of the high-frequency peak-to-peak power of the lower-frequency peak. D, Total LFP power >30 Hz as a function of noise intensity. As in Figure 3, there were coherent oscillations even at high noise intensities. All error bars represent SEM over 10 simulations.
- Figure 7
Emergence of fast ripples in an uncoupled, asynchronously spiking network. Using the same parameters as the highest-frequency data in Figure 6, a 20,000 ms simulation was performed to identify the emergence of HFOs in a network of 80 uncoupled pyramidal cells driven by high levels of uncorrelated noisy input. A, LFP spectrogram of a 1000 ms interval demonstrates that both ripple (R) and fast ripple (FR) episodes emerged sporadically. B, Spike-timing histogram relative to ripple phase, averaged over all 78 observed ripple episodes. C, Spike-timing histogram relative to ripple phase, averaged over all 26 observed fast ripple episodes. Ripples occurred when the 80 cells achieved brief unimodal spike time distribution, and fast ripples occurred when the distribution was transiently bimodal. Error bars represent SEM over all observed ripple/fast ripple episodes.
- Figure 8
Fast ripple occurrence ratio for constructed LFP’s generated from AP waveforms. A, Constructed LFPs were produced by first generating trains of event times which had two sources of variation: (1) different trains had different values for their intrinsic firing rates, with greater values of σμ implying greater firing rate heterogeneity between different cells, and (2) within each train there was “jitter” in the ISI. These spike trains were then convolved with AP waveforms and summed to yield the constructed LFP. Red and blue spike trains show examples of firing times of two different “cells” with different firing rates (left) or different ISI jitter (right). B–E, Spectrograms and LFP samples from the constructed LFPs generated using the indicated parameters. Fast ripples frequently emerged from random network firing. F, Fast ripple proportion as a function of the two sources of heterogeneity in the model. Fast ripple proportion was simply the proportion of total time that the peak frequency in the 100–700 Hz band was >250 Hz.
- Figure 9
Capability of AP versus PSP events to produce HFOs of varying frequency. A, Constructed LFPs were produced by generating synchronous network bursts of either AP or PSP events at periodic intervals, with nominal frequency f and random variation defined by σjitter. B, C, Color encodes the power within the frequency band f ± 5 Hz, normalized by the maximum power observed across all parameters in each waveform. For both APs and PSPs, increased jitter caused the LFP output to become less coherent and the normalized power to drop. On the other hand, increasing frequency of network bursts had little effect on AP-dominated oscillations, but resulted in significant attenuation of PSP-dominated oscillations. D–I, Representative AP-dominated LFPs associated with the corresponding combinations of parameters indicated in B. Note how amplitude is unchanged as oscillation frequency increases. J–O, Representative PSP-dominated LFPs associated with the corresponding combinations of parameters indicated in C. Note the difference in scale bars, and how amplitude is dramatically attenuated as oscillation frequency increases. Thus, APs can robustly produce the full range of HFOs, whereas PSPs are unlikely to produce HFOs >200 Hz.
- Figure 10
Effects of synaptic parameters on HFOs. LFPs were constructed as in Figure 9C , except that GABAergic synaptic rise and decay times were modified from their standard values (τrise = 1.5 ms; τdecay = 8.0 ms). A, B, Changing τdecay had little effect on the HFO output. C, D, Very fast τrise time (0.5 ms) enabled IPSPs to produce HFOs more robustly.
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