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Mechanisms underlying the response of mouse cortical networks to optogenetic manipulation

  1. Alexandre Mahrach
  2. Guang Chen
  3. Nuo Li
  4. Carl van Vreeswijk
  5. David Hansel  Is a corresponding author
  1. CNRS-UMR 8002, Integrative Neuroscience and Cognition Center, France
  2. Baylor College of Medicine, United States
Research Article
Cite this article as: eLife 2020;9:e49967 doi: 10.7554/eLife.49967
12 figures, 8 tables and 1 additional file

Figures

Effects of photostimulation of PV-positive interneurons in the mouse neocortex.

(A) Scheme of the experiment. (B–C) Normalized spike rate as a function of laser intensity in different layers and brain areas. Top, individual neuron responses of the PCs (red) and PV (blue) neurons; bottom, population average responses. (B) ALM: layer 2/3: n = 26 (PCs), n = 9(PV); (C) ALM layer 5: n = 62 (PCs), n = 12 (PV). (D) S1: n = 52 (PCs), n = 8 (PV). Mean ± s.e.m. across neurons, bootstrap. (E) Comparison of PV neurons’ normalized spike rates between ALM Layer 2/3 and Layer five at laser intensity 0.5 mW/mm2. (F).Slope of PCs and PVs’ normalized spike rate as a function of laser intensity. Data from ALM layer 5. Slopes are computed using data from 0.3 mW/mm2 and below, before the spike rate of PV neurons begin to increase. Mean ± SEM, bootstrap (Methods). (G) Same as (F) but for data from S1. In (F and G) the difference between the slopes for the PC and PV populations is not significant.

Spike rates of PCs (top) and PV neurons (bottom).

Dots correspond to individual neurons. Laser intensity is 0.5 mW/mm2. Pie charts represent the fraction of neurons with different types of changes. Mean ± s.e.m. bootstrap. Black, fraction of neurons with activity increase larger than 0.1 Hz. Light gray, fraction of neurons with activity decrease larger than 0.1 Hz. Dark gray, fraction of neurons with activity change smaller than 0.1 Hz. White, fraction of neurons with activity smaller than 0.1 Hz upon PV photostimulation.

Figure 3 with 3 supplements
Paradoxical effects in the two-population model.

(A) The network. (B–C) Responses of PCs and PV neurons normalized to baseline vs. the laser intensity, Γopto, for different values of the recurrent excitation, jEE. (B) jEE=JEE/K, the network exhibits the paradoxical effect. (C) jEE = 0, the population activity of PV neurons is almost insensitive to small laser intensities. Red: PCs. Blue: PV neurons. Thick lines: population averaged responses. Thin lines: responses of 10 neurons randomly chosen in each population. Firing rates were estimated over 100s. Parameters: NE = 57600, N1 = 19200, K = 500 N1 = 19200. Other parameters as in Tables 12. Baseline firing rates are: rE=5.7Hz, rI=11.7Hz (B) and rE=1.5Hz, rI=5.7Hz (C). At the minimum of rI in (B), rE=0.06Hz.

Figure 3—figure supplement 1
Current, Iopto, v.s. laser intensity, Γopto.

Parameters are I0=8nA, Γ0=0.5mW.mm2.

Figure 3—figure supplement 2
Effects of K on the responses of a two-population network to photoactivation of the inhibitory population.

(A) JEE = 22 μA.ms.cm-2, the inhibitory population activity always recovers when the PCs are silenced. (B) JEE = 0, as K increases, the response of the inhibitory population becomes more and more insensitive to the perturbation. Cross: K = 50; triangles: K = 100; circles: K = 500. Dashed line: . Color code and parameters as in Figure 3. Baseline firing rates: A. K = 50: rE = 10.8Hz, rI = 16.8 Hz; K = 100: rE = 8.8 Hz, rI = 14.7 Hz; K = 500: rE = 5.7 Hz, rI = 11.7 Hz; K=: rE = 3.9 Hz, rI = 8.5 Hz. B. K = 500: rE = 1.9 Hz, rI = 3.6 Hz; K = 100: rE = 2 Hz, rI = 4.8 Hz; K = 500: rE = 1.5 Hz, rI = 5.7 Hz; K=: rE = 1.4 Hz, rI = 9.1 Hz.

Figure 3—figure supplement 3
Two-population model.

The response of the PC and PV populations upon stimulation of the latter are proportional only if parameters are fine-tuned. (A) χ-I/χ-E where χ¯α=rαlight on/rα-1/Γopto estimated for Γopto=0.5mW.mm-2. The ratio is close to one only if JEEJEIJIE/JII=30μA.ms.cm-2. (B) Red star indicates the approximate center of the region with proportionality of the responses together with reasonable activities. Parameters as in Figure 3. K = 500.

Figure 4 with 2 supplements
Population activities vs. Iopto in Model 1 in the large N, K limit.

(A) The network is composed of four populations representing PCs, PV, SOM and VIP neurons. The connectivity is as in Pfeffer et al. (2013). (B) Parameters as in Table 4. The activity of PV cells increases with Iopto while for the three other populations it decreases. (C) Parameters as in Table 5. The activity of SOM neurons increases with Iopto while for the three other populations it decreases. Right panels in B and C: the activities are normalized to baseline.

Figure 4—figure supplement 1
Graphical representation of the population susceptibilities upon stimulation of PV in Model 1 (large N, E limit).

The prefactor in front of each diagram accounts for the fact that additional terms are needed to complete the loops. Note: χVI=JSEJSVχEI.

Figure 4—figure supplement 2
Population activities vsIopto in Model 1 (large N, K limit).

The activities are normalized to baseline. (A) Parameters as in Table 4. The activity of the PV (blue) population increases with Iopto . For PC (red cross), SOM (green) and VIP (gray) the activity decreases. (B) Parameters as in Table 5. In the shaded region, the network is bistable. In one stable state all the four populations are active. In the other stable state, only the PV population is active. A third state in which only the PV and SOM populations are active exists in this range of laser intensity (dotted-dashed line). This state is unstable. Baseline firing rates as in Figure 4.

Figure 5 with 3 supplements
Numerical simulations of Model 1 for JEE>JEE*.

Responses of the neurons normalized to baseline vs. the intensity of the laser, Γopto. (A) Activities of PCs and PV neurons: the PV response is not paradoxical. (B) Activities of SOM and VIP neurons. Color code as in Figure 4. Thick lines: population averaged responses. Thin lines: responses of 10 neurons randomly chosen in each population. Firing rates were estimated over 100s. Parameters: K = 500, N = 76800. Other parameters as in Tables 34. The baseline activities are: rE = 3.3 Hz, rI = 6.5 Hz, rS = 5.9 Hz, rV = 3.5 Hz.

Figure 5—figure supplement 1
Model 1 with JEE>JEE*.

Robustness with respect to change in the average connectivity, K. Triangles: K = 500; cross: K = 1000; circles: K = 2000. Nα = 10000 neurons per population. Baseline firing rates: K = 500: rE = 3.3 Hz, rI = 6.5 Hz, rS = 5.9 Hz, rV = 3.5 Hz; K = 1000: rE = 3.0 Hz, rI = 6.6 Hz, rS = 5.6 Hz,rV = 3.7 Hz; K = 2000: rE = 2.9 Hz, rI = 6.7 Hz, rS = 5.4 Hz, rV = 3.8 Hz. Rates are averaged over 10s. Color code and parameters as in Figure 5.

Figure 5—figure supplement 2
Model 1 with JEE>JEE*.

Robustness to a change of ±10% in the interaction parameters. (A) Distribution of the population activities. (B) Distribution of the activity changes upon stimulation for Γopto=0.07mW.mm-2. Color code as in Figure 5. Rates are averaged over 10s.

Figure 5—figure supplement 3
Model 1 with JEE>JEE*.

Firing statistics at baseline. (A) Distribution of the firing rates (mean: rE = 3.3 Hz, rI = 6.5 Hz, rS = 5.9 Hz, rV = 3.5 Hz). (B) Distribution of CV. Color code as in Figure 5. Parameters as in Figure 5. Individual rates are averaged over 100s with a threshold at 0.05 Hz. CVs are computed over 30s.

Single neuron firing rates in the PC and PV populations upon PV activation for two values of the light intensity (Model 1 with JEE>JEE*).

(A) Single neuron firing rates at baseline vs. at Γopto=0.5mW.mm-2. (B) Same for Γopto=1mW.mm-2. Top: PCs (red). Bottom: PV neurons (blue). Scatter plots of 300 randomly chosen PC and PV neurons. Pie charts for the whole population. The pie charts show the fraction of neurons which increase (black) or decrease (light gray) their activity compared to baseline. Dark gray: Fraction of neurons with relative change smaller than 0.1Hz. White: fraction of neurons with activity smaller than 0.1Hz upon PV photostimulation. Firing rates were estimated over 100s. Neurons with rates smaller than 0.01Hz are plotted at 0.01Hz. Parameters as in Figure 5.

Figure 7 with 5 supplements
Numerical simulations of Model 1 for JEE<JEE.

Responses of the neurons normalized to baseline vs. the intensity of the laser, Γopto. (A) Activities of PCs and PV neurons: the PV response is paradoxical. (B) Activities of SOM and VIP neurons. Color code as in Figure 4. Thick lines: population averaged responses. Thin lines: responses of 10 neurons in each population. Firing rates were estimated over 100s. Parameters: K = 500, N = 76800. Other parameters as in Tables 35. The baseline activities are: rE = 4.8 Hz, rI = 11.2 Hz, rS = 7.1 Hz, rV = 5.3 Hz.

Figure 7—figure supplement 1
Model 1 for JEE<JEE.

Proportionality of the PC and PV activity requires fine-tuning. (A) The response of the PV population is paradoxical for small Γopto and is proportional to the PC response. (B) Responses of the SOM and VIP neurons. Baseline firing rates: rE = 6.4 Hz, rI = 12.2 Hz, rS = 6.5 Hz, rV = 11.0 Hz. Color code as in Figure 7. Interaction parameters: JE0 = 40 µA. ms.cm-2; JEE = 20 µA. ms.cm-2; JEI = 32 µA. ms.cm-2; JES = 22 µA. ms.cm-2; JEV = 0; JI0 = 31 µA. ms.cm-2; JIE = 36 µA. ms.cm-2; JII = 30 µA. ms.cm-2; JIS = 20 µA. ms.cm-2; JIV = 0;JSE = 26 µA. ms.cm-2; JSI = 0; JSS = 0; JSV = 12 µA. ms.cm-2; JV0 = 22 µA. ms.cm-2; JIE = 28 µA. ms.cm-2; JVI = 24 µA. ms.cm-2; JVS = 12 µA. ms.cm-2; JVV = 0; . Other parameters as in Tables 3.

Figure 7—figure supplement 2
Model 1 with JEE>JEE*.

Robustness to a change of ±10% in the interaction parameters. (A) Distribution of the population activities. (B) Distribution of the activity changes upon stimulation for Γopto=0.07mW.mm-2. Rates are averaged over 10s. Color code as in Figure 7. Parameters as in Figure 7.

Figure 7—figure supplement 3
Model 1 with JEE<JEE*.

Robustness with respect to change in the average connectivity, K. Triangles: K = 500; cross: K = 1000; circles: K = 2000. Nα = 10000 neurons per population. Baseline firing rates: K = 500: rE = 4.7 Hz, rI = 11.2 Hz, rS = 7.1 Hz, rV - 5.2 Hz; K = 1000: rE = 4.1 Hz, rI = 10.3 Hz, rS = 7.6 Hz, rV = 4.7 Hz; K = 2000: rE = 3.7 Hz, rI = 9.7 Hz, rS = 7.8 Hz, rV = 4.4 Hz. Rates are averaged over 10s. Color code and parameters as in Figure 7.

Figure 7—figure supplement 4
Model 1.

The response of the PC and PV populations upon stimulation of the latter are proportional only if parameters are fine-tuned. (A) χ-I/χ-E where χ-A=(rAlight onrA-1)/Γopto estimated for Γopto=0.5mW.mm-2. (B) Red square indicates the region of the parameter space for which the ratio of the PC and PV slopes 1 ± 0.3 and activities are reasonable (rE < 5 Hz, 5Hz < rI < 10 Hz). Parameters as in Figure 5. K = 500.

Figure 7—figure supplement 5
Model 1 with JEE<JEE.

Firing statistics at baseline. (A) Distribution of the firing rates (mean: rE = 4.8 Hz, rI = 11.2 Hz, rS = 7.1 hz, rV = 5.3 Hz). (B) Distribution of CV. Individual rates are average over 100s with a threshold at 0.05Hz. CVs are computed over 30s. Color code as in Figure 7. Parameters as in Figure 7.

Single neuron firing rates in the PC and PV populations upon PV activation for two values of the light intensity (Model 1 with JEE<JEE).

(A) Single neuron firing rates at baseline vs. at Γopto=0.5mW.mm-2. (B) Same for Γopto=1mW.mm-2. Top: PCs. Bottom: PV neurons. Scatter plots of 300 randomly chosen PC and PV neurons. Pie charts for the whole population. Firing rates were estimated over 100s simulation time. Neurons with rates smaller than 0.01Hz are plotted at 0.01Hz. Color code as in Figure 6. Parameters as in Figure 7.

Figure 9 with 1 supplement
Network models with proportional change in the PC and PV activities upon photostimulation of the PV population.

(A) A three-population network consisting of PCs, PV and SOM neurons. SOM neurons only receive projections from the PC and PV populations. (B) Model 2 consists of four populations: PC, PV, SOM and an unidentified inhibitory population, X. The population X projects to the PC, the PV population and to itself. The PC population projects to X. (C) Population activities normalized to baseline vs. Iopto in the large N, K limit. PC and PV populations decrease their activity with Iopto in a proportional manner. Parameters as in Tables 67. Baseline firing rates are: rE = 3.0 Hz, rI = 6.7 Hz, rS = 6.4 Hz, rX = 3.8 Hz.

Figure 9—figure supplement 1
Model 2.

Graphical representation of χII (large N,K limit). Note : χEI=JSIJSEχII.

Figure 10 with 3 supplements
Numerical simulations of Model 2.

Responses of the neurons normalized to baseline vs. the intensity of the laser, Γopto. (A) Activities of PCs and PV neurons: for small Γopto, the PV response is paradoxical and the suppression of the PC and PV population activities relative to baseline are the same. (B) Activities of SOM and X neurons. Color code as in Figure 9. Thick lines: population averaged responses. Thin lines: responses of 10 neurons randomly chosen in each population. Firing rates were estimated over 100s. Parameters: K = 500, N = 76800. Other parameters as in Tables 67. The baseline activities are: rE = 4.2 Hz, rI = 6.8 Hz rS = 7.0 Hz, rX = 3.9 Hz.

Figure 10—figure supplement 1
Model 2.

Robustness with respect to change in the average connectivity, K. Triangles: K = 500; cross: K = 1000; circles: K = 2000. Nα = 10000 neurons per population. Color code and parameters as in Figure 10. Baseline firing rates: K = 500: rE = 4.2 Hz rI = 7.0 Hz, rS = 7.0 Hz, rX = 4.0 Hz, K = 1000: rE = 4.0 Hz, rI = 6.8 Hz, rS = 6.8 Hz, rX = 3.8 Hz; K = 2000: rE = 3.7 Hz, rI = 6.8 Hz, rS = 6.7 Hz, rX = 3.8. Rates are averaged over 10s.

Figure 10—figure supplement 2
Model 2.

Robustness to a change of ±10% in the interaction parameters. (A) Distribution of the population activities. (B) Distribution of the activity changes upon stimulation for Γopto=0.07mW.mm-2. Rates are averaged over 10s. Color code as in Figure 10.

Figure 10—figure supplement 3
Model 2.

Firing statistics at baseline. (A) Distribution of the firing rates (mean: rE = 4.5 HZ, rI = 10.6 Hz, rS = 7.2 hz, rV = 4.9 Hz). (B) Distribution of CV. Individual rates are average over 100s with a threshold at 0.05Hz. CVs are computed over 30s. Color code and parameters as in Figure 10.

Single neuron firing rates in the PC and PV populations upon PV activation for two values of the light intensity (Model 2).

(A) Single neuron firing rates at baseline vs. at Γopto=0.5mW.mm-2. (B) Same for Γopto=1mW.mm-2. Top: PCs. Bottom: PV neurons. Scatter plots of 300 randomly chosen PC and PV neurons. Pie charts for the whole population. Firing rates were estimated over 100s. Neurons with rates smaller than 0.01Hz are plotted at 0.01Hz. Color code as in Figure 6. Parameters as in Figure 10.

Predictions of the theory.

(A) In ALM layer 2/3, the activity of the PV population decreases upon photoinhibition of the PCs. (B) In ALM layer 2/3, photostimulation of VIP neurons increases the activity of the PV population. (C) In S1, PV and PC activity decrease proportionally upon photoinhibition of the latter. (D) In S1, the PC and PV responses are not proportional upon photoinhibition of the SOM population. (E) In S1, upon photostimulation of PV neurons and photoinhibition of the SOM population with a constant input, the PV response is paradoxical but PC and PV responses are no longer proportional.

Tables

Table 1
Connection strength matrix (rows: postsynaptic populations; columns: presynaptic populations).
JαβμA.ms.cm-2FeedforwardPCPV
PC172930
PV173636
  1. Parameters of the two-population model.

Table 2
Synaptic time constants.
ταβmsEI
E42
I22
  1. Default parameters of Model 1.

Table 3
Synaptic time constants.
ταβ (ms)PCPVSOMVIP
PC422N/A
PV224N/A
SOM2N/AN/A4
VIP424N/A
Table 4
Connection strength matrix for JEE>JEE (rows: postsynaptic populations; columns: presynaptic populations)
Jαβ (µA. ms.cm-2)FeedforwardPCPVSOMVIP
PC342026.4410
PV27442835.60
SOM0240014
VIP391235.2350
Table 5
Connection strength matrix for JEE<JEE (rows: postsynaptic populations; columns: presynaptic populations).
Jαβ (µA. ms.cm-2)FeedforwardPCPVSOMVIP
PC5217.434.432.80
PV3936.629.228.80
SOM024.20016.8
VIP3031.23114.60
Table 6
Default parameters of Model 2.

Synaptic time constants in Model 2.

ταβ (ms)PCPVSOMX
PC4224
PV2244
SOM22N/AN/A
X2N/A42
Table 7
Connection strength matrix (rows: postsynaptic populations; columns: presynaptic populations).
Jαβ (µA ms.cm-2)FeedforwardPCPVSOMVIP
PC4820303236
PV2940281632
SOM0261200
VIP242403622
Key resources table
Reagent type
(species) or resource
DesignationSource or referenceIdentifiersAdditional
information
Genetic reagent (Mus musculus)Pvalb-Ires-CreThe Jackson LaboratoryJAX #008069
Genetic reagent (Mus musculus)R26-CAG-LSL-ReaChR-mCitrineThe Jackson LaboratoryJAX #026294

Data availability

All simulation, raw, and processed data software is available on GitHub (https://github.com/Amahrach/Paper4pop; copy archived at https://github.com/elifesciences-publications/Paper4pop).

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