Article Figures & Data
Figures
- Figure 1.
Dominant electrophysiological features of L1 interneuron subtypes. A, Examples of traces that show four different types of features: A1, IR firing, A2, Acc in the firing rate, A3, OB, and A4, Adap in the firing rate. A2, Inset, 1/ISI and the corresponding fitted line. A3, Inset, Zoomed-in traces during the first 100 ms. Traces with ∼10 APs are selected as examples. B, Scatter plot of the L1 INs from four subtypes in an E-feature space (n = 69). Each dot represents one IN. Only the cells with a sweep that has ∼9 APs from 100 ms to 1 s are analyzed in this panel (average firing rate <ν> = nAP/0.9 s = 10 Hz). x axis shows the normalized change of the instantaneous firing rate (ν = 1/ISI) from the last to the first ISI between 100 ms and 1 s. y axis is the onset firing rate, calculated by the first ISI. The size of the point represents the CV ISI (>200 ms) of that sweep. Arrows indicate the cells from A. Dashed boxes represent the “hero” cells to model except the α7 cell (for details, see main text). C, Distribution of the four features in C1, Canopy cells, C2, NGFCs, C3, α7 cells, and C4, VIP cells. *IR2 and Acc2 features are classified by looser criteria than IR and Acc, respectively (see main text). Cells with IR2 or Acc2 are only marked in the canopy cells and NGFCs for simplicity. Eleven of 27 canopy cells, 4 of 21 NGFCs, 9 of 22 α7 cells, and 8 of 13 VIP cells have an IR2 feature. All VIP cells are classified as having an IR or IR2 feature. Five of 27 canopy cells, 8 of 21 NGFCs, 0 of 22 α7 cells, and 0 of 13 VIP cells are classified as having an Acc2 feature. D, Two sweeps from an example cell with an Acc2 feature. The cell shows acceleration in the firing rate when the injection current is low, while Adap when the injection current is high. E, F, **The cells that do not show any feature are indicated as other1 or other2. The other2 cells are late-spiking, but the other1 cells are not.
- Figure 2.
Electrophysiological features of the L1 interneurons. Bars above suggest the corresponding pair is significantly different (p < 0.001, Mann–Whitney U test). Mean ± SD. Scatters shows the values measured from individual cells. Jitters are added for better visualization. Rheobase and FI slope are measured by fitting the spike-count curve to an ReLU function. Lines are aligned by the rheobase. Bold black lines indicate the ReLU function with the mean FI slope. Gray lines indicate individual spike-count curves of individual cells.
- Figure 3.
Modeling IR spiking of a canopy cell with an SIK channel. A, The voltage trace of an example canopy cell at Iinj = 376 pA. B, Phase diagram of the cell. Inset, The corresponding zoom-out diagram. y axis is the slope of the voltage trace, which is proportional to the net current to the cell. Red arrows indicate where we estimate the value of reset, curvature, and firing threshold of the corresponding model. C, D, The trace and the phase diagram at Iinj = 380 pA. E, The sketch of the canopy cell model (left) and the equilibrium value of the gating variables of the SIK channel (right). F, Δb estimation. Left, The shapes of all the APs from all the sweeps of the same cell. We exclude the first two APs in every sweep. APs are aligned at the maximum of the voltage. Dashed lines indicate t = –0.4, 1.6 ms, respectively. Voltage traces of these 2 ms time windows are used to calculate the jump of the slow inactivation variable Δb. Right, The histogram of Δb with an initial value binit = 0.28. The value binit = 0.28 is the average value after 3 s of injection in the simulation. The average change is <Δb> = –0.0020. G, The voltage SD measured between 500 ms and 1 s during the current injection from the data (black) and the model (red). H, I, The voltage trace and the phase diagram of the canopy cell model at Iinj = 370 pA. J, The voltage trace at Iinj = 380 pA. K, The comparison of irregularity from the data and the model by IR score (left) and by CV ISI (right). L, The comparison of firing rate from the data, estimated by the number of APs during the 1 s current injection, and from the model, estimated by the steady-state firing rate. Red arrows indicate Iinj = 376, 380 pA. M, The initial dynamics are not considered in this model. Top, The voltage trace that includes the initial transient part when Iinj = 380 pA. Bottom, The transient dynamics of gating variables of the SIK channel. Black and red lines indicate the fast and slow variables a and b, respectively.
- Figure 4.
A fast-slow analysis of the canopy cell model shows that the irregularity results from the square-wave bursting. A, Sample simulation when Iinj = 375 pA without noise. Black line indicates the voltage trace. Red line indicates the difference between b and bmin. Red dashed line is at b – bmin = 0, suggesting the boundary between the resting state and the firing state of the cell. B, Nullclines when Iinj = 375 pA, b = 0.27. The intersections indicate the fixpoints of the fast manifold. C, The bifurcation diagram when varying b with Iinj = 375 pA. The system undergoes an SNIC. Black solid line indicates the stable branch. Dashed line indicates the unstable branch. Blue line indicates the simulation of the canopy cell model while we remove the noise term σ = 0. Red dashed line indicates the minimum b that the fast manifold has a global SS. Arrows indicate the direction of the dynamics. C1, Dynamics of the entire AP range. C2, Zoomed-in dynamics around the bifurcation point.
- Figure 5.
Modeling the acceleration and late-spiking of an NGFC with a smaller SIK conductance. A-C, Voltage traces of the selected NGFC at Iinj = 198, 188, 190 pA. D, The phase diagram of the cell at Iinj = 190 pA. E, The histogram of Δb with an initial value binit = 0.4. The average change is <Δb> = –0.0040. F, The voltage SDs of the data and the model. G, The instantaneous firing rate ν = 1/ISI over time. We fit the ISIs (dot) to an exponential decay curve (line) for different injection currents Iinj = 188, 190, 194, 198, 202, 206 pA (color). H, The initial firing rate (black) and the last (red) firing rate at different injection currents. I, The sketch of the NGFC model. J-M, Model results correspond to B-D, A. N, The time of the first spike decreases fast when increasing the injection current in both the data and the model. O, P, The instantaneous firing rate ν increases over time in the model. Organized as in G, H.
- Figure 6.
Recovering dynamics of the NGFC model. A, Simulation of the two voltage steps Vclamp = –40 mV with a resting time Δtime = 200 ms. From top to bottom, the voltage of the model, gating variables a (black) and b (red), SIK current ISIK. B, Simulation of the two current steps Iinj = 188 pA with a resting time Δtime = 200 ms. From top to bottom, injection current, gating variables a (black) and b (red), the voltage of the model. C, The peak SIK current and delay of the first spike recover with a long resting time Δtime. The recover ratio of the peak SIK current (red) is calculated by comparing the maximum ISIK during the second voltage step to that during the first voltage step. The delay of the first spike is calculated from the current steps (black).
- Figure 7.
Modeling the OB of an α7 cell with a T-type calcium channel. A, The voltage trace at Iinj = 262 pA. B, Phase diagram of the cell. Red arrow indicates the trajectory from the first AP within the OB period. C, Instantaneous firing rate shows a sudden drop in the first 40 ms of the injection period. Colors represent sweeps with different injection currents, Iinj = 252, 262, 272, 282, 292 pA. D, The sketch of the α7 cell model. E, The voltage SDs of the data and the model. F, The firing rates from the data and the model. G-I, Modeling results organized as in A-C.
- Figure 8.
Reproducing the OB, IR firing patterns, and adaption simultaneously in a VIP cell model. A-D, Voltage traces at Iinj = 91, 121, 261 pA, which are examples to show OB, IR, and Adap, respectively. E, The instantaneous firing rates ν from 0 to 100 ms that show the OB. Colors represent sweeps with different injection currents Iinj = 91, 131, 171, 212, 251, 291 pA. F, The histogram of Δb with an initial value binit = 0.25. The average change is <Δb> = –0.0009. G, The ISI ratio (black) and CV ISI (red) curves that show the irregularity. H, The instantaneous firing rates ν between 100 ms and 1 s that show the Adap. Color coding is the same as in D. I, Sketch of the VIP cell model. J-P, Corresponding modeling results. M, SD of the voltage of the data and the model.
- Figure 9.
More results of the VIP cell model. A, B, The voltage traces of the model in 3 s at Iinj = 121, 141 pA. C, The voltage traces of the model at Iinj = 235, 237 pA. The jump in the curve of the initial firing rate is because of the diminishing of the silent period after the OB. D, The comparison of the firing rates ν of the data and the model. The ν of the model is measured as the number of APs during 1 s current injection. The initial and last (steady-state) firing rates ν of the model are measured from 100 to 1500 ms. E, The AI from the data (black) and the model (red), measured based on the fitting of 1/ISI from 100 ms to 1 s. F, Voltage traces when varying the time constant of fast activation variable τa = 40, 80 ms with an injection current Iinj = 141 pA. The firing pattern around 100 ms is more comparable between the data and the model. However, τa is not biologically plausible anymore (original τa = 4 ms).
- Figure 10.
The fast-slow analysis of the VIP cell model shows that the irregularity results from the square-wave bursting. A, The sample simulation when Iinj = 170 pA. Black line indicates the voltage trace. Red line indicates the difference between b and bmin. Red dashed line is at b – bmin = 0, suggesting the boundary between the resting state and the firing state. B, Nullclines of the fast manifold when Iinj = 170 pA, Cca = 10, b = 0.3. The intersections indicate the fixpoints of the fast manifold. C, The bifurcation diagram when Iinj = 170 pA, Cca = 10. Black solid line indicates the stable branch. Dashed line indicates the unstable branch. Red dashed line indicates the minimum of b that the fast manifold has a global SS. D, The bifurcation diagram of the whole system and the simulation when Iinj = 170 pA. Red dashed line, bmin(Cca), indicates the SNIC bifurcation line. Only the region above which has a global SS. Black line indicates the simulation of the VIP cell model without noise (σ = 0).
- Figure 11.
The IR firing of VIP cells is more easily observed in experiments because of a large IR width introduced by the interaction between ISIK and Iadap. A, The ISI ratio (color) over different injection currents and Adap strength γ when gSIK = 150 nS. B, Same as in A, but gSIK = 50 nS. C, The sample ISI ratio when gSIK = 150 nS, γ = 0.1. The range of injection current when CV ISI is above the threshold 0.6 is defined as the IR width. D, The irregularity visibility is high only when the gSIK and γ are both large. Top, The IR width curves over gSIK. Different lines indicate results with different Adap strength γ. Dots and arrows indicate the parameters of the VIP cell model (top right), the canopy-like case (bottom right, shown in E), and the NGFC-like case (left, shown in F). Bottom, The IR area-under-curves, defined as the area under the curve of ISI ratio and above the ISI ratio threshold 0.6. E, The model results when set γ = 0, gSIK = 150 nS look like a canopy cell. Left, The IR score. The drop of the curve is sharp when increasing the injection current, and the IR width is small. Right, Voltage trace at Iinj = 121 pA. F, The model results when setting γ = 0, gSIK = 90 nS looks like an NGFC. The IR width is further reduced compared with A. In this case, we remove the T-type CA2+ current for better visualization.
- Figure 12.
The VIP model resonates with theta/alpha band input only when the average input is around the resting. A, Simulation results of the VIP model when varying the average injection current. In this panel, σ = 50 pA. Gray lines model results while excluding the T-type Ca2+ channels. Top, The average firing rate ν shows two non-zero branches. Middle, The voltage's SD decreases when the injection current increases. Bottom, The average voltage of the model. B, The normalized DG when the injection current is at the sub-rheobase region (Iinj = 20 pA, black arrow in A) and around the resting (Iinj = 105 pA, red arrow in A). The DG shows an unexpected high-gain range around the theta/alpha band when the model is around the resting regimen. The high-frequency profile was described as f–α with a cutoff frequency f0 and α, shown as a dashed gray line. The two thin black lines indicate the simulation with average firing rates <ν> = 3, 7 Hz, respectively. Solid gray line indicates the 95% confidence level generated by bootstrapping the shuffled ISIs. Top, f0 = 58.9 Hz, α = 0.99. Bottom, f0 = 67.6 Hz, α = 0.69. C, Simulation results of VIP model with reduced noise σ = 5 pA. Top, The average firing rate. Bottom, The SD of the voltage. D, The DG around the resting still shows a high gain range around the alpha band (Iinj = 25 pA, red arrow in C) when the input noise is drastically reduced (f0 = 41.7 Hz, α = 1.52). E-G, The normalized DG for the canopy cell model (Iinj = 282 pA, σ = 90 pA, f0 = 77.6 Hz, α = 0.62), NGFC model (Iinj = 170 pA, σ = 80 pA, f0 = 14.8 Hz, α = 0.65), and α7 cell model (Iinj = 200 pA, σ = 65 pA, f0 = 38.9 Hz, α = 0.51) when the average input current is at sub-rheobase. H, The α7 cell model also has a non-zero firing branch around the resting that shows high gain around the theta/alpha band frequency (Iinj = 25 pA, σ = 65 pA, f0 = 83.2 Hz, α = 1.10).
Tables
Canopy NGFC α7 VIP Resistance R (mΩ) 86 163 120 400 Capacity C (pF) 80 80 80 80 Reversal potential VL (pF) –67 –70 –70 –69 Threshold VT (pF) –38 –40 –39 –40 Reset voltage VT (pF) –52 –52 –50 –50 Curvature ΔT (mV) 1 1 0.5 1 Noise std σ (pA) 20 8 10 10 Conductance gSIK (nS) 120 30 — 150 Jump of slow gating variable Δb –0.002 –0.004 — –0.001 Conductance gT (nS) — — 8 10 Adap strength γ (nS) — — — 0.1 Rheobase (pA) 366.2 177.5 244.3 177.7 f-I slope (Hz/pA) 1.64 0.933 1.28 0.33 ↵aThe rheobase and f-I slope are measured by fitting the curve of firing-rate at the steady state to a ReLU function.
Canopy (n = 27) NGFC (n = 21) α7 (n = 22) VIP (n = 13) Timescale (ms) 8.23 ± 1.72 9.53 ± 1.84 8.37 ± 3.86 18.34 ± 6.45 Resistance (mΩ) 133.5 ± 38.2 185.4 ± 50.4 135.3 ± 57.3 336.6 ± 83.0 Capacity (pF) 64.4 ± 14.0 53.3 ± 10.1 62.6 ± 12.5 45.1 ± 16.0 Delay (ms) 29.3 ± 15.1 497.9 ± 249.9 37.4 ± 17.4 113.8 ± 42.7 Rheobase (pA) 233.9 ± 70.1 139.10 ± 46.2 212.6 ± 82.1 25.0 ± 25.6 fI slope (Hz/pA) 1.04 ± 1.26 0.94 ± 1.19 0.25 ± 0.11 0.58 ± 0.32 IR widthb (pA) 17.9 ± 25.3 — 91.8 ± 104.2 99.0 ± 121.9 AP rise (mV/ms) 365.3 ± 83.8 419.7 ± 78.2 398.3 ± 99.9 480.1 ± 221.1 AP decay (mV/ms) −98.0 ± 23.9 −88.5 ± 19.8 −99.5 ± 29.3 −185.9 ± 67.7 AP halfwidth (ms) 0.610 ± 0.107 0.657 ± 0.158 0.659 ± 0.189 0.456 ± 0.151 AP reset (mV) 50.0 ± 3.6 −52.9 ± 2.5 −47.8 ± 3.2 −52.8 ± 6.6 AP threshold (mV) −34.9 ± 3.0 −32.4 ± 1.7 −33.8 ± 2.3 −35.2 ± 4.9 AP max Volt (mV) 32.0 ± 6.4 35.6 ± 5.0 34.8 ± 5.8 38.9 ± 11.5 ↵aData are mean ± SEM.
↵bThe IR width is only measured for the cells with an IR feature within each subtype (n = 7, 9, and 5 for canopy, α7, and VIP cells, respectively) (for details, see Materials and Methods). The values are not exactly the same as the previous study (Schuman et al., 2019) because we exclude the cells with <10 APs in the sweep with the maximum injection current.
Table 1-1
The analysis on individual L1 INs. Download Table 1-1, XLSX file.
