Article Figures & Data
Figures
- Figure 1.
Ongoing activity is characterized by sequences of states. A, Four representative trials from one ensemble of nine simultaneously recorded neurons, segmented according to their ensemble states (HMM analysis). Black vertical lines indicate action potentials. States are color-coded: smooth colored lines represent the probability for each state; shaded colored areas indicate intervals where the probability of a state exceeds 80%. Below each single-trial population raster, average firing rates across simultaneously recorded neurons are plotted (states are color-coded). x-axis for population rasters: time preceding the next event at (0 = stimulus delivery); x-axis for average firing rates panels: firing rates (spikes/s); y-axis for population rasters: left, ensemble neuron index, right, probability of HMM states; y-axis for firing rate panels: ensemble neuron index. B, Distribution of number of states per ensemble across all sessions (only states lasting >50 ms are included). x-axis, number of states per ensemble; y-axis, frequency of occurrence. C, Distribution of state durations across all sessions together with the least-squares exponential fit (red line; see Materials and Methods). x-axis, state duration; y-axis, frequency of states occurrence.
- Figure 2.
Single-neuron coactivation drives ensemble transitions. A, Change points (CPs), represented by red dots, and state transitions (vertical dashed green lines) are superimposed to a raster plot of simultaneously recorded neurons (same trials as the first three in Fig. 1A). x-axis for top, time preceding taste delivery (0 = stimulus delivery); y-axis, ensemble neuron index. B, CPTA of ensemble transitions for the empirical dataset (black) and for the trial-shuffled dataset (blue). Shaded bounds represent SE. Thick black line below traces indicates p < 0.05 (bin-wise t test with multiple-bin Bonferroni correction). x-axis, time lag from CP (seconds); y-axis, probability of a transition given a CP at t = 0. C, Fraction of transitions co-occurring with CPs within a 200 ms window before the state transition (significant window from B). x-axis, number of single neuron's CPs divided by the ensemble size; y-axis, fraction of transitions co-occurring with CPs (%). D, Correlation (φ2 statistics) between the signs of single neurons' and ensemble firing rate changes for the empirical (“Data”) and simulated datasets. In the latter, 90%, 50%, and 0% of simulated neurons had firing rate changes matched to those of the whole ensemble (boxes in box-plots represent 95% CIs). y-axis, φ2 statistics. E, Firing rate distributions across states for representative neurons 2 and 3 from the ensemble in Figures 1A and 2A (color-coded as in Fig. 1A; each curve represents the empirical distribution of firing rates in each state). x-axis, firing rate (spikes/s); y-axis, probability density of states. F, Number of different firing rates per neuron across all sessions: 42% of all neurons had ≥3 different firing rates across states. x-axis, minimal number of different firing rates across states; y-axis, fraction of neurons (%).
- Figure 3.
Attractor landscape of the spiking network model. A, Network architecture. Excitatory (E) and inhibitory (I) LIF neurons are recurrently connected (black lines), with E neurons organized in Q clusters; intracluster synaptic connections are potentiated (thick arrows), intercluster connections are depressed. Line thickness illustrates relative synaptic weight strength. B, Mean field theory analysis of the network in A. Firing rates for excitatory clusters attractor states (diamonds) are shown as a function of the intracluster potentiation parameter J+ (in units of JEE). Below the critical point J′ = 4.2 (i.e., left most vertical dotted line), the only stable state has low firing rate ∼5 spikes/s (blue diamonds). At J+ = J′, a bifurcation occurs whereby states with active clusters at higher firing rate coexist (top diamond). There are in total Q such states. As J+ is further increased, states with ≥2 active clusters exist. For each state, all active clusters have the same firing rate (reported on the vertical axis). Vertical green line at J+ = 5.2 indicates the value chosen for the spiking network simulations. Vertical red lines indicate critical points where a new configuration appears with an increased number of active clusters. x-axis, intracluster synaptic potentiation (J+); y-axis, firing rate (spikes/s). C, Number of active clusters as a function of J+. Notations are as in B. For J+ = J′, all attractor states have only one active cluster; for J+ = 5.2 (green line), there are 7 possible configurations of attractor states, with 1, 2, …, 7 active clusters, respectively. x-axis, intracluster synaptic potentiation (J+); y-axis, firing rate (spikes/s).
- Figure 4.
Dynamics of the spiking network model during ongoing activity. Simulation of the network in Figure 3 with 4000 excitatory and 1000 inhibitory LIF neurons, Q = 30 clusters at intracluster synaptic potentiation J+ = 5.2. A, Incoming PSC to an excitatory (PSCE, top plot) and an inhibitory (PSCI, bottom plot) neuron: EPSC (blue trace), IPSC (red trace), external current (green line), and total current (black trace) are in a balanced regimen. x-axis, time (seconds); y-axis, PSC (nA). B, Membrane potential from representative excitatory (VE, top plot) and inhibitory (VI, bottom plot) neurons. Vertical bars represent spikes. Horizontal dashed lines indicate threshold for spike emission. x-axis, time (seconds); y-axis, membrane potential V (mV). For illustration purposes, V was linearly transformed to obtain the threshold for spike emission at −45 mV and the reset potential after a spike at −60 mV. C, Representative rasterplot from excitatory clustered neurons. Each dot represents a spike (background population not shown). Clusters of neurons that are currently active appear as darker regions of the raster. x-axis, time (seconds); y-axis, neuron index. D, Time course of the number of active clusters from the representative trial in C. x-axis, time (seconds); y-axis, number of active clusters. E, Average firing rates in the active clusters as a function of the number of active clusters across all simulated sessions. Error bars indicate SD. x-axis, number of active clusters; y-axis, average cluster firing rate (spikes/s). Inset, Occurrence of states with different counts of active clusters for 5% stimulus amplitude. x-axis, number of active clusters; y-axis, frequency of occurrence (% of total time). F, Instantaneous cluster firing rate in three representative clusters (red, blue, and green lines) from trial in C. x-axis, time (seconds); y-axis, firing rate (spikes/s).
- Figure 5.
Ongoing activity in the model is characterized by sequences of states. A, Two representative trials from an ensemble with 30 neurons from Figure 4C, one neuron per cluster (notations as in Fig. 1A). Raster plots (top) are overlaid with HMM states, together with their firing rates across neurons (bottom). Top, x-axis, time preceding the next event (0 = stimulus delivery); y-axis, left: ensemble neuron index; right: probability of HMM states. Bottom, x-axis, firing rates (spikes/s); y-axis, ensemble neuron index. B, Three representative trials of simulated data after keeping only 9 randomly chosen neurons, together with a representation of the corresponding HMM states (bottom). Notations are as in A. C, CPTA of ensemble transitions for the simulated dataset (black) and for a trial-shuffled dataset (blue). Same conventions as in Figure 2B. Thick black line indicates p < 0.05 (t test with multiple-bin Bonferroni correction). x-axis, time lag from CP (seconds); y-axis, probability of a transition given a CP at t = 0. D, Fraction of transitions co-occurring with CPs within the 200 ms significant window from B. x-axis, number of single neurons' CPs divided by the ensemble size; y-axis, fraction of transitions co-occurring with CPs (%). E, Number of different firing rates per neuron across all sessions: 44% of all model neurons had ≥3 different firing rates across ensemble states (compare with Fig. 2F). x-axis, minimal number of different firing rates across states; y-axis, fraction of neurons (%).
- Figure 6.
Taste-evoked activity: reduction of multistability and trial-by-trial variability in the experimental data. A, Two representative examples of population rasters together with their segmentation in HMM states during evoked activity in GC, in response to citric acid (left) and sucrose (right) delivery, respectively. Red arrow indicates taste delivery at t = 0. The remaining notations are as in Fig. 1A. Top, x-axis, time relative to taste delivery (0 = stimulus delivery); y-axis, left, ensemble neuron index, right, probability of HMM states. Bottom, x-axis: firing rates (spikes/s); y-axis, ensemble neuron index. B, Fraction of multistable neurons across all states during ongoing (left) and evoked activity (right) in GC. **p < 0.01 (χ2 test). x-axis, ongoing and evoked conditions; y-axis, fraction of multistable neurons (%). C, Time course of the mean-matched FF in a time interval around taste delivery (occurring at time t = 0) across all data. Shaded bounds represent 95% CIs. The thick horizontal black line indicates bins where the evoked FF is significantly different from baseline (*p < 0.05, see Materials and Methods). x-axis, time (seconds); y-axis, FF.
- Figure 7.
Taste-evoked activity: reduction of multistability and trial-by trial variability in the model. A, Two examples of population rasters together with their segmentation in HMM states during evoked activity in the model network, in response to two surrogate stimuli. Clusters may be selective to more than one stimulus. Middle bottom, Dark circles and colored areas represent, respectively, individual clusters and their selectivity to the two different stimuli A (blue) and B (red). The remaining conventions are as in Figure 6A. Model stimuli (middle top) consist of double exponentials peaking at 30% of vext (50 ms rise time and 500 ms decay time). x-axis, time (seconds); y-axis, stimulus amplitude (%). B, Fraction of multistable neurons across all states during ongoing and evoked activity in the model. **p < 0.01. x-axis, ongoing and evoked conditions; y-axis, fraction of multistable neurons (%). C, Time course of the mean-matched FF in a time interval around stimulus presentation (occurring at time t = 0) across all simulated sessions (same conventions as in Fig. 6C, *p < 0.05). x-axis, time (seconds); y-axis, FF.
- Figure 8.
Mean field predictions of evoked activity and comparison with model simulations. A, Attractor states of the model during evoked activity predicted by mean field theory for J+ = 5.2 and as a function of stimulus amplitude. Diamonds represent mean firing rate in active clusters for each attractor state, featuring the number of active clusters indicated by the red numbers (see also Fig. 3B). Stimulus amplitude varied from 1% to 45% of vext. Vertical dashed lines indicate attractor states for stimuli of 5%, 25%, and 45%. The firing rate range decreases as the stimulus amplitude is increased, and it reduces to a single configuration with 15 active clusters for stimuli >30%. x-axis, stimulus increase (%); y-axis, firing rate (spikes/s). B, Mean firing rates in active clusters in simulations of the model for the three stimuli marked by vertical lines in A. Error bars indicate SD. x-axis, number of active clusters; y-axis, average cluster firing rate (spikes/s). Inset, Frequency of configurations with different numbers of active clusters for 5% stimulus. x-axis, active clusters; y-axis, frequency of occurrence (% of total simulation time across all simulations). C, Rasterplot of spike trains from excitatory clustered neurons (background excitatory population not shown) in a representative trial encompassing both periods of ongoing and evoked activity (compare with Fig. 4C), using a “box” stimulus with amplitude at 30% of vext in the [0, 2]s interval (ongoing activity corresponds to the [−2, 0]s interval). Vertical red line indicates stimulus onset. x-axis, time (seconds); y-axis, neuron index. D, Number of active clusters versus time (same representative trial as in C). Notations as in Fig. 4D. x-axis, time (seconds); y-axis, active clusters.
