Article Figures & Data
Figures
- Figure 1.
Dense recurrent connectivity synchronizes the network but biologically plausible connectivity does not. A, Intrinsic properties of the biophysical PV+ IN model. Note that it does not have Ih, as seen in the hyperpolarizing current step. Extended Data Figure 1-2 shows the models response to a chirp current injection B, Gap junction coupling implementation. The current injected in the red neuron increases the voltage in the blue neuron. The coupling coefficient is measured at the steady-state soma-to-soma. Gap junction resistance was hand-tuned to lead to the coupling coefficient. The gap junction was placed in the middle of the proximal dendritic segment (32 μm from the center of the soma). Extended Data Figure 1-1 shows the transmission of a granule cell EPSP through an interneuron gap juction. C, The biologically plausible sigmoid connection probability functions for chemical synapses and gap junctions. These were designed to fit the data in Espinoza et al. (2018). D, Random realization from the sigmoid functions fit to the measured connection probabilities from Espinoza et al. (2018) and the distances of the ring network (see methods). E, Spike raster plots of 120 PV+ INs with biologically plausible connectivity on the left in blue (D shows a biologically plausible connectivity example) and dense (nearly full) chemical connectivity on the right in orange. Nsyn is the number of chemical synapses received by the average neuron in this example run. F, The convolved output is calculated from the spike rasters above by convolving with a synaptic kernel. Shows the partially synchronous state for the full connectivity on the right. G, shows the coherence measure k(τ) for different values of τ (see methods) for the biologically plausible on the left (blue) and the dense connectivity on the right (orange). The dashed black line shows the line between (0, 0) and
- Figure 2.
Adding PV+ IN connectivity to the ring network does not consistently increase network synchrony. A Spike raster plots (top) and convolved output (bottom) for three different conditions of the PV+ ring network. GJ-/Sy- has neither gap junctions nor chemical synapses. GJ+/Sy- has only gap junctions, GJ-/Sy+ has only chemical synapses and GJ+/Sy+ has gap junctions and chemical synapses. GJ+/Sy+ is a different random realization of the connectivity shown in Figure 1D. The convolved output does not show a partially synchronous state. B, Average frequency including all neurons of the network. Both gap junctions and chemical synapses significantly decrease the average activity of the ring network with a much larger effect of chemical synapses. Two-way ANOVA: Interaction: F = 0.0133, p = 0.9084, Main effects: GJ, F = 8.7578, p < 0.01; Sy, F = 5206.6925, p < 0.001. C–E, The three synchrony measures. Two-way ANOVA only showed significant effects for
- Figure 3.
Increasing the input drive increases network synchrony but does not reach the magnitude found with dense network connectivity. A, Spike raster plots for the PV+ ring network with biologically plausible connectivity for the standard model on the left (blue, input strength as in Figs. 1, 2), and a model with strong input drive on the right. The mean frequency fμ is calculated from all neurons in the network. B, The convolved output of the above spiking activity. C, The coherence measure k(τ) for different values of τ (see methods) for the baseline activity condition on the left (blue) and the high activity on the right (orange). The dashed black line shows the line between (0, 0) and
- Figure 4.
The PV+ IN ring network connectivity has no effect on GC synchrony and inconsistent effects on the PV+ ring network itself in the biophysical DG model. A,G, Schematic of the DG model. Green highlights the cells that are analyzed. B-F, GCs and H-L PV+ cells. Only the connectivity of the ring network was changed in the different conditions. B, Spike raster plots (top) and corresponding convolved output of EC neurons (black) and GCs. Note that the time constant of the kernel to calculate the convolved output was kept constant to the fast 1.8 ms of the PV+ neuron synapse for all cell types. C, Average frequency of the network calculated from all neurons. Two-way ANOVA showed no significant effects. D–F, The synchrony measures. Two-way ANOVA showed no significant effects. Note that in E values are large and negative. This is likely a failure of the supralinear k measure that occurs when the average frequency is slow. H, Same as B but with spike raster plots and convolved output for the PV+ INs instead of the GCs. I, Average frequency of the network calculated from all neurons. Two-way ANOVA: Interaction: F = 0.0881, p = 0.7683, Main effects: GJ, F = 1.8815, p = 0.1787; Sy, F = 30.9370, p < 0.001. J–L, The synchrony measures as in D-F but for the PV+ neurons. Two-way ANOVA showed no significant results in J. Two-way ANOVA for Supralinear K: Interaction: F = 0.9901, p = 0.3264, Main effects: GJ, F = 5.7611, p < 0.05; Sy, F = 0.0054, p = 0.9421. Two-way ANOVA for Correlation: Interaction: F = 0.2310, p = 0.6337, Main effects: GJ, F = 0.7404, p = 0.3952; Sy, F = 5.5301, p < 0.05. Extended Data Figure 4-1 shows the activity of HIPP cells and mossy cells. Extended Data Tables 4-1–4-5 contain the intrinsic parameters of the DG model. Extended Data Table 4-6 contains the synaptic parameters of the DG model.
- Figure 5.
Recurrent connectivity desynchronizes PV+ INs in the DG network model (same as in Fig. 4A,C) when the input is 30 Hz frequency modulated but not when the input is 80 Hz modulated. This figure shows results from the biophysical DG model. Results for the other cell types are shown in Extended Data Figure s 5-1 and 5-2 A, Spike raster plots (top) and corresponding convolved output of EC neurons (black) and GCs in the slow gamma (30 Hz) modulated condition. Note that the time constant of the kernel to calculate the convolved output was kept constant to the fast 1.8 ms of the PV+ neuron synapse for all cell types. B, Average frequency of the network calculated from all neurons. Two-way ANOVA: Interaction: F = 0.0215, p = 0.8842, Main effects: GJ, F = 0.0256, p = 0.8737; Sy, F = 80.9939, p < 0.001. C–E, The synchrony measures for the PV+ neurons. Two-way ANOVA for
- Figure 6.
Inhibitory recurrence does not change theta or gamma power measured through the GC membrane voltage. A, Single run examples of the average membrane potential across all granule cells. The color labeling for the conditions is between A and B and applies to both panels A & B. B, The power spectral density of the average membrane potential averaged across ten different simulation runs per condition. C, Boxplots of the summed PSD in the theta range. Two-way ANOVA showed no significant main effects or interactions for any of the conditions. D, Boxplots of the summed PSD in the gamma range. Two-way ANOVA showed no significant main effects or interactions for any of the conditions.
Extended Data
Figure 1-1
Granule cell EPSP is measurable in a coupled PV+ IN. Gap junction resistance and placement as in Figure 1 B. Download Figure 1-1, TIF file.
Figure 1-2
The PV+ IN model does not resonate below threshold. The bottom shows a chirp current that is injected into the neuron. The frequency of the chirp current rises linearly from 1 Hz to 100 Hz over 5 s. The top shows the voltage response to the current as measured at the soma. On the left, the current was injected into the soma. On the right, the current was injected into a randomly chosen proximal dendritic segment. Download Figure 1-2, TIF file.
Figure 1-3
Doubling the strength of the PV-PV synapse does not induce synchrony with biologically plausible connectivity. A shows the strenght of the PV-PV synapse as it is used throughout the paper. The postsynaptic neuron is voltage clamped to 0 mV. The peak amplitude of the IPSC is 229 pA. That is larger than most IPSCs measured by Espinoza et al. (2018). B shows the spiking activity in the PV+ ring network with doubled synaptic conductance (15.2 nS) and biologically plausible connectivity. Download Figure 1-3, TIF file.
Figure 1-4
Keeping the number of synaptic inputs homogeneous does not change measured synchrony. In these simulations, each postynaptic neuron randomly chooses Nsyn presynaptic neurons to receive input from. Therefore, each neuron receives the same number of synapses. A,B&C show the same information as in main Figure 1, but for the simulations with equal synaptic inputs. D,E&F show the synchrony measures. In black are the same data as shown in main Figure 1. In green are the simulations with equal synapse numbers. Download Figure 1-4, TIF file.
Figure 1-5
Identical neurons with identical number of incoming synapses are exhibit perfectly synchronous activity. Each neuron receives input from 8 randomly chosen other neurons in the ring network. Each neuron receives a constant somatic current injection of 300 pA. Under these conditions all neurons fire at exactly the same time, there their correlation coefficient is 1, their
Figure 1-6
Varying the reversal potential of the inhibitory synapses in the ring model does not affect synchrony measures. For reference, the equilibrium potential in the baseline model is -70 mV. Download Figure 1-6, TIF file.
Figure 1-7
A network with low variance input current is initially synchronous but desynchronizes over time. For reference, the sigma of the input current in the baseline model is 0.3 nA. Download Figure 1-7, TIF file.
Figure 2-1
Large PV + IN plane network. 4000 neurons were randomly distributed on a rectangular plane. A The spike raster plots show only every 40th neuron. Raster plot and convolved output show that the state is asynchronous. B Average frequency of all neurons in the network. Two-way ANOVA: Interaction: F = 1.893, p = 0.1743, Main effects: GJ, F = 14.0517, p < 0.001; Sy, F = 164105.4068, p < 0.001. C-D The synchrony measures. Two-way ANOVA for
Figure 2-2
Ring network simulations with PV+ INs containing Ih current. A Voltage response of the modified PV+ IN with Ih added. Top: voltage response to depolarizing current step. Middle: response to hyperpolarizing current step with the slow depolarization characteristic for Ih. Bottom: The current injections that induce the voltage responses above. B Spike raster plot and convolved output show an asynchronous state. C Average frequency of all neurons in the network. Twoway ANOVA: Interaction: F = 0.0926, p = 0.7626, Main effects: GJ, F = 1.8648, p = 0.1805; Sy, F = 5884.6182, p < 0.001. D-F The synchrony measures. Two-way ANOVA for
Figure 2-3
Ring network simulation with strong input current resulting in high average frequency. A Spike raster plot and convolved output show that some synchronous oscillations are larger when chemical synapses are added. However, this synchronous state is different from the one in Figure 1, where cells become silent during a cycle and furthermore does not reach the magnitude. B Average frequency of all neurons in the network. Two-way ANOVA: Interaction: F = 0.1127, p = 0.7391, Main effects: GJ, F = 5.3695, p < 0.05; Sy, F = 7474.6760, p < 0.001. C-E The synchrony measures. Two-way ANOVA for
Figure 4-1
Results for the HC (top) and MC (bottom), which were simulated for Figure 4 but not shown. Two-way ANOVA was done for all of the box plots but showed no significant result for any of them. Download Figure 4-1, TIF file.
Table 4-1
Parameters that are equal in all four neuron types. ccanl, intracellular calcium accumulation with exponential decay to baseline. Download Table 4-1, DOCX file.
Table 4-2
The intrinsic parameters of the granule cell model. borgka, Borg-Grahamgeneric A-type potassium channel; cagk, a voltage dependent calcium activated potassium channel; gskch, a nonvoltage-dependent calcium-activated potassium channel; ichan2, a mechanism combining Hodgkin-Huxley style sodium and potassium conductances; lca, an L-type calcium channel;ore, An N-type calcium channel (nca) was used in all cell types except for HIPP cells. T-Type calcium channels (cat) were used only in granule cells. Persistently modified h-channels (hyperde3) were used in HIPP and Mossy cells. Download Table 4-2, DOCX file.
Table 4-3
The intrinsic parameters of the basket cell model. Download Table 4-3, DOCX file.
Table 4-4
The intrinsic parameters of the mossy cell model. Download Table 4-4, DOCX file.
Table 4-5
The intrinsic parameters of the HIPP cell model. Download Table 4-5, DOCX file.
Table 4-6
The parameters of the synaptic connections. Columns: Pre, the presynaptic population; Post, the postsynaptic populations; N Target, number of nearby neurons that a neuron can connect to; Dendrite, dendrite of the postsynaptic neuron that is targeted by the synapse; Divergence, number of postsynaptic neurons that each presynaptic neuronc chooses randomly from the population defined by N Target; τ1, Decay time constant; τfacil, facilitation time constant of the Tsodyks-Markam dynamics. Download Table 4-6, DOCX file.
Figure 5-1
Cell types that were simulated in the slow gamma condition in Figure 5 but not shown. Boxplots were omitted because none of them was significant. Download Figure 5-1, TIF file.
Figure 5-2
Cell types that were simulated in the fast gamma condition in Figure 5 but not shown. Boxplots were omitted because none of them was significant with the sole exception of a significant increase of average HC frequency in the fast gamma condition when synaptic connectivity is added in the PV+ ring network: F = 5.322589, p < 0.05. Download Figure 5-2, TIF file.
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