Article Figures & Data
Figures
- Figure 1.
Learning of two distinct inhibitory populations and postsynaptic response because of attentional switch between contexts. A, Schematic of co-active plasticity rules. A postsynaptic neuron (black triangle) receives tuned excitatory input (red population) and inhibition from two distinct populations (blue populations). The two inhibitory populations follow different synaptic plasticity rules. Δw indicates change in synaptic weight, and Δt indicates interval between presynaptic and postsynaptic spikes. B, Initially untuned inhibitory weights (blue lines) acquire different synaptic weight profiles after learning that depend on the excitatory weight profile (red dashed line). C, Contextual changes (e.g., because of attention), which we hypothesize to be responsible for modulating the activity of inhibitory populations, result in different postsynaptic responses to the same stimulus (Bathellier et al., 2012; Ruff and Cohen, 2014, 2019; Benjamin et al., 2019; Billeh et al., 2019; McClure and Polack, 2019), such that preferred (green) and nonpreferred (purple) stimuli elicit postsynaptic responses with different amplitudes.
- Figure 2.
Model details. A, Schematic of the input organization. An external signal (representing, e.g., sound) was delivered through three input populations (one excitatory and two inhibitory), with 16 input signals per population (representing, e.g., sound frequency). Each signal was simulated by 250 independent, but temporally correlated, spike trains (input afferents); 200 excitatory, and 50 inhibitory divided into two groups of 25. One postsynaptic neuron (black triangle) was the output of this system, simulated as a single-compartment LIF neuron. The firing rate of each of the inhibitory populations was modulated by a contextual cue (green and purple boxes). Excitatory and inhibitory input spike trains were generated as point processes (for details, see Materials and Methods). B, Natural input statistics. Raster plot (gray dots) of 800 neurons that take part in 4 signal groups (200 neurons per signal group), each with firing rate changing according to a modified OU process (colored lines; see Materials and Methods). C, Temporal autocorrelation (top) and distribution of the ISIs (bottom) of the presynaptic inputs. The autocorrelation of two groups are shown (green and pink), as well as the correlation between two different groups (black). Autocorrelation is computed as the Pearson coefficient with a delay (x axis). D, Pulse input schematic. A steplike increase in the firing rate of a given input group lasting 100 ms (top) with varying firing rates (grayscale). The postsynaptic response can be separated in phasic (first 50 ms), and tonic (last 50 ms), which reveals transient (middle) or persistent (bottom) types of response.
- Figure 3.
Synaptic plasticity models. A, Hebbian plasticity rule. Left, Spike-timing dependency. Δw indicates level of synaptic change, and Δt indicates interval between presynaptic and postsynaptic spikes. Coincident presynaptic and postsynaptic spikes elicit positive changes, whereas presynaptic spikes alone elicit negative changes in synaptic strength (Vogels et al., 2011). Right, Synaptic changes (Δw) as a function of postsynaptic firing rate. When the postsynaptic neuron's firing rate is above the target rate, inhibitory synapses increase in weight and, as a consequence, the postsynaptic neuron's firing rate decreases. The opposite happens for when the postsynaptic neuron's firing rate is lower than the target rate (Vogels et al., 2011) (see Materials and Methods). B, Synaptic scaling rule. Changes in synaptic strength (Δw) as a function of the postsynaptic neuron's firing rate. When the postsynaptic neuron's firing rate is lower than a lower bound threshold, inhibitory synapses decrease, proportionally to their current strength. When the postsynaptic neuron's firing rate is higher than an upper bound threshold, inhibitory synapses increase. Because of the lower and upper bounds, there is a region with no change around the target rate. C, Anti-Hebbian plasticity rule. Left, Spike-timing dependency. Presynaptic spikes elicit positive changes, whereas coincident presynaptic and postsynaptic spikes elicit negative changes in synaptic weights. Middle, Changes in synaptic efficacy (Δw) as a function of the postsynaptic firing rate. The target rate of anti-Hebbian plasticity rule is unstable. Right, Evolution of the learning rate of the anti-Hebbian plasticity model. Because of its unstable nature, we set the learning rate to decay exponentially over time.
- Figure 4.
Postsynaptic response for a model with a single inhibitory population. A, Schematic of the circuit with a single inhibitory population (top). Presynaptic spikes were generated as point processes (pp), for both excitatory (red; 16 signals) and inhibitory (blue; 16 signals) inputs, and fed into a single-compartment LIF neuron. Schematic of the synaptic weight profiles (bottom). Average weight (y axis) for different input signals (x axis); preferred signal is pathway no. 9 (gray dashed line). B, Firing rate of the preferred, and two nonpreferred inputs and mean of all inputs (top row), excitatory and inhibitory input currents (middle row), and membrane potentials (bottom row), for control (left), decreased (middle), and increased (right) inhibition. Decreased (increased) inhibition lowered (raised) inhibitory firing rates by 10%, respectively. C, CVISI, and mean and SD of the postsynaptic firing rate in response to natural input for the 3 explored cases (top), and as a function of the inhibitory firing rate (bottom). Arrowheads indicate the analyzed cases. D, Pearson correlation between postsynaptic firing rate and excitatory input firing rates for different input signals for the three conditions in B (top). Correlation between output activity and preferred (continuous line) or nonpreferred (dashed line) inputs as a function of the inhibitory firing rate (bottom). E, Response to a pulse input in the phasic (left; first 50 ms) and tonic (right; last 50 ms) periods. Firing rate computed as the average number of spikes (for 100 trials) normalized by the bin size (50 ms). Each line corresponds to a different input strength: from light (low-amplitude pulse) to dark (high-amplitude pulse) colors. Insets, Tonic response for control and decreased inhibitory firing rates.
- Figure 5.
Inhibitory plasticity acting on one inhibitory population compensates global inhibition from a second inhibitory population. A, Schematic of the synaptic weight profile for excitatory synapses (red) and different initial conditions for inhibitory synapses (pink to purple color code). Inhibitory Population 1 has its inhibitory synapses changing according to a plasticity mechanism, whereas Population 2 remains fixed. B, Time course of the postsynaptic firing rate for different initial conditions (colors as in A). Inhibitory plasticity on Population 1 is set to achieve a balanced state with target of 5 Hz (arrowhead). C, Stabilized postsynaptic firing rate as a function of the initial inhibitory synaptic weight. D, Individual synaptic weight profiles for excitatory (red), inhibitory Population 1 (blue, after synaptic stabilization), and inhibitory Population 2 (colors as in A). E, Total synaptic weight per signal (excitatory – inhibitory) for different initial conditions after stabilization of synapses from Population 1. F, Example of synaptic dynamics of inhibitory Population 1 for a given initial condition. Colors represent different signal groups. G, Final weights as a function of initial inhibitory weights. Plotted are excitatory (red), plastic inhibitory (blue), and sum of total inhibitory synapses (gray).
- Figure 6.
Postsynaptic response after stabilization of synapses from one population. A, Pearson correlation between postsynaptic firing rate and excitatory input firing rates with both inhibitory populations active. Color code as in Figure 5A. B, Pearson correlation between postsynaptic firing rate and excitatory input firing rates for different signals with both inhibitory populations active, Population 1 inactive, and Population 2 inactive. Three examples are shown.
- Figure 7.
Simultaneous learning of two inhibitory profiles via Hebbian and homeostatic scaling plasticity rules. A, Temporal evolution of inhibitory synaptic weights when one inhibitory population follows a Hebbian plasticity rule (top), and the other population follows a synaptic scaling plasticity rule (bottom). B, Initial (top) and final (bottom) weight profiles from A, with excitatory weights for reference. C, Individual synaptic weights before and after learning for synapses following the Hebbian plasticity rule (top) and synapses following the scaling plasticity rule (bottom).
- Figure 8.
Postsynaptic response for the model with co-tuned and flat inhibitory populations. A, Schematic of the circuit with two inhibitory populations (top): I1, co-tuned population; I2, flat population. Presynaptic spikes were generated as point processes (pp) and fed into an LIF. Schematic of the synaptic weight profile (bottom). Average weight (y axis) for different input signals (x axis); preferred signal is pathway no. 9 (gray dashed line). B, Firing rate of the preferred and two nonpreferred inputs and mean of all inputs (top row), total excitatory current and inhibitory currents of both populations (middle row), and membrane potential (bottom row), for control (left), co-tuned (middle), and flat (right) population inactive. C, CVISI and postsynaptic firing rate (mean and SD) in response to natural input for the 3 cases (top). Output firing rate as a function of the firing rate of the (compensatory) active inhibitory population (bottom). Arrowheads indicate the analyzed cases where output rate is equal to 5 Hz (i.e., where the green and purple lines cross the black line). D, Pearson correlation between postsynaptic firing rate and excitatory input firing rates for different input signals for the three conditions in B. Correlation between output activity and preferred (continuous line) or nonpreferred (dashed line) as a function of the inhibitory firing rate of each inhibitory population (bottom). E, Response to a pulse input in the phasic (left; first 50 ms) and tonic (right; last 50 ms) periods. Firing rate computed as the average number of spikes (for 100 trials) normalized by bin size (50 ms). Each line corresponds to a different input strength: from light (low-amplitude pulse) to dark (high-amplitude pulse) colors. Insets, Tonic response for control firing rates.
- Figure 9.
Simultaneous learning of two inhibitory profiles via Hebbian and anti-Hebbian plasticity rules. A, Temporal evolution of inhibitory synaptic weights when one inhibitory population follows a Hebbian plasticity rule (top), and the other population follows an anti-Hebbian plasticity rule (bottom). B, Initial (top) and final (bottom) weight profiles from A, with excitatory weights for reference. C, Individual synaptic weights before and after learning for synapses following the Hebbian plasticity rule (top) and synapses following the anti-Hebbian plasticity rule (bottom).
- Figure 10.
Postsynaptic response for the model with co- and counter-tuned inhibitory populations. A, Schematic of the circuit with two inhibitory populations (top): I1, co-tuned; I2, counter-tuned population. Presynaptic spikes were generated as point processes (pp) and fed into an LIF. Synaptic weight profile (bottom). Average weight (y axis) for different input signals (x axis); preferred signal is pathway no. 9 (gray dashed line). B, Firing rate of the preferred and two nonpreferred inputs and mean of all inputs (top row), total excitatory current and inhibitory currents of both populations (middle row), and membrane potentials (bottom row), for control (left), co-tuned (middle), and counter-tuned (right) population inactive. C, CVISI and postsynaptic firing rate (mean and SD) in response to natural input for the 3 cases (top). Output firing rate as a function of the firing rate of the (compensatory) active inhibitory population (bottom). Arrowheads indicate the analyzed cases where output rate is equal to 5 Hz (i.e., where the green and purple lines cross the black line). D, Pearson correlation between postsynaptic firing rate and excitatory input firing rates for different input signals for the three conditions in B. Correlation between preferred (continuous line) or nonpreferred (dashed line) with the output activity as a function of the inhibitory firing rate of each inhibitory population (bottom). E, Response to a pulse input in the phasic (left; first 50 ms) and tonic (right; last 50 ms) periods. Firing rate computed as the average number of spikes (for 100 trials) normalized by the bin size (50 ms). Each line corresponds to a different input strength; from light (low-amplitude pulse) to dark (high-amplitude pulse) colors. Insets, Tonic response for control firing rates.
- Figure 11.
Comparison of postsynaptic responses receiving co-tuned & flat or co-tuned & counter-tuned inhibitory populations. A, Performance index as the difference in input/output correlation between preferred and nonpreferred signal. Ideal outcome is ΔC = 0 for control case (gray), ΔC > 0 for co-tuned population inactive (purple), and ΔC < 0 for flat or counter-tuned populations inactive (green). We added the values for a single inhibitory population with control (gray), weak (purple), and strong (green) inhibitory inputs for comparison. B, Pearson correlation between postsynaptic firing rate and excitatory input firing rates for different signal indices from Figures 4D, 8D, and 10D, replotted for reference. C, Signals recovered in the pulse input paradigm. Signals represented are calculated as the percentage of signal afferents that activate the postsynaptic neuron with more than half the spikes of the maximum response for the 3 cases considered for the circuits analyzed together. D, Normalized phasic response to a pulse input of 40 Hz, from Figures 4E, 8E, and 10E, replotted for reference. Horizontal line indicates 50% of maximum response.
Tables
Parameter Symbol Value Figures Membrane time constant τm 30 ms 4–11 Resting potential urest –65 mV 4–11 Excitatory reversal potential EE 0 mV 4–11 Inhibitory reversal potential EI –80 mV 4–11 Excitatory time constant τE 5 ms 4–11 Inhibitory time constant τI 10 ms 4–11 Spiking threshold uth –50 mV 4–11 Reset potential ureset –65 mV 4–11 Refractory period τref 5 ms 4–11 Simulation time step Δt 0.1 ms 4–11 Parameter Symbol Value Figures No. of excitatory afferents NE 3200 4–11 No. of inhibitory afferents NI 800 4–11 No. of signal groups P 16 4–11 Refractory period for excitatory afferents τEref 5 ms 2, 4–11 Refractory period for inhibitory afferents τIref 2.5 ms 2, 4–11 OU time constant τOU 50 ms 2, 4–11 OU update time step ΔT 1 ms 2, 4–11 Excitatory firing rate amplitude for OU νE0 5 Hz 2, 4–11 Inhibitory firing rate amplitude for OU νI0 10 Hz 2, 4–11 Excitatory background firing rate νEbg 2 Hz 2, 4–11 Inhibitory background firing rate νIbg 4 Hz 2, 4–11 Pulse amplitude reference ν* 5 Hz 4, 8, 10, 11 Excitatory ratio for pulse input 
1 4, 8, 10, 11 Inhibitory ratio for pulse input 2 4, 8, 10, 11 Synaptic weight profile amplitude r0 4 4–11 Synaptic weight profile slope b 0.25 4–11 Preferred pattern index μ0 9 4–11 Synaptic weight profile power c 2 4–11 Simulation time step Δt 0.1 ms 2, 4–11 Parameter Symbol Value Figures Excitatory baseline weight wE0 0.5 4–11 Noise parameter for excitatory weights 0.01 4–11 Inhibitory baseline weight (one inhibitory population) wIF 0.4 Data not shown Noise parameter for inhibitory weights (one inhibitory population) 0.01 Data not shown Inhibitory baseline weight wIF Varying 5, 6 Noise parameter for inhibitory weights 0.01 5, 6 Inhibitory baseline weight (Hebbian & scaling) wIF 0.8 7 Noise parameter for inhibitory weights (Hebbian & scaling) 0.3 7 Inhibitory baseline weight (Hebbian & anti-Hebbian) wIF 0.55 9 Noise parameter for inhibitory weights (Hebbian & anti-Hebbian) 0.01 9 Correcting factor for plot αw 4.4 5, 7, 9 Parameter Symbol Value Figures STDP time constant τSTDP 20 ms 5, 7, 9 Hebbian learning rate ηH 10−3 5, 7, 9 Hebbian decay term αH 0.2 5, 7, 9 Firing rate setpoint ρ0 5 Hz 5, 7, 9 Scaling time constant τscaling 1000 ms 7 Scaling learning rate ηs 10−7 7 Scaling learning rate weight wIs 0.8 7 Scaling threshold parameter αs 2 7 Anti-Hebbian initial learning rate 10−3 9 Anti-Hebbian learning rate time constant τaH 250 s 9 Anti-Hebbian increase term αaH 0.165 9 Anti-Hebbian peak time t0 0 ms 9 Simulation time — 30 min 5, 7, 9 Parameter Symbol Value Figures Presynaptic time constant τZ 10 ms 4, 6, 8, 10, 11 Postsynaptic time constant τY 250 ms 4, 6, 8, 10, 11 Simulation time — 30 min 4, 6, 8, 10, 11
