Fig 1.
Model parameters are consistent with in vivo quantities.
(A) Schematic of the connectivity pattern between excitatory neurons and inhibitory neurons in our model. (B) The probability of connection between excitatory neurons decreases as the difference between their PO increases. (C) Distribution of weights (represented as PSPs) between select neuron subtypes. Our model (filled bars) closely match the PSP distribution found by Cossell et al. [57] (left) and Znamenskiy et al. [60] (middle/right). (D) The average spontaneous firing rates in our model over 30 seconds resemble those found in vivo in anesthetized mice in Mesik et al. [63], Neill and Stryker [64], and Chen et al. [62]. Data points and error bars from in vivo data are the mean ± s.e.m. found in those studies. (E) Average resting membrane potential for each neuron subtype in our model over 30 seconds. Our results closely match those found in vivo in L2/3 of the barrel cortex in mice in Neske et al. [65] and Avermann et al. [66]. Data points and error bars from in vivo data are the mean ± s.e.m. found in those studies.
Fig 2.
Model stimulation ensemble responses are concordant with in vivo findings.
(A) Raster plot showing the firing patterns of the different neuron populations. Green dots represent evoked spikes from 30Hz stimulation of a single excitatory neuron for 250 ms. (B) Average firing rate of different neuron types during stimulation of 0 to 5 random excitatory neurons. Averages are over 20 trials (250 ms each). Error bars are mean ± standard deviation. *** indicates p < 0.001, n.s. indicates not significant. (C) Average change in membrane potential of excitatory neurons during stimulation of a single excitatory neuron. 35 neurons were individually stimulated for three 250 ms trials. The shaded region is the mean ± s.e.m of the change in membrane potential of all non-stimulated excitatory neurons in the network.
Fig 3.
K-means clustering identified ensembles of densely connected neurons.
(A) Steps to find ensembles of strongly connected neurons. Top Left: Example of network before preprocessing; Top Middle: We removed weak excitatory connections (EPSP < 0.9 mV) from the network. Top Right: The network was converted into an undirected graph. Bottom: After preprocessing, we computed a similarity matrix where each cell represented the number of shared excitatory connections between each pair of excitatory neurons. We then performed K-means clustering on this matrix to identify ensembles. (B) K-means clustering identified groups of densely connected neurons from the similarity matrix. The number of clusters was tuned such that the median size of each cluster (ensemble) was about 40 neurons (dashed lines). (C) Three examples of ensembles found in the network. We returned directionality (arrows) to the network after the ensembles were found. (D) Neurons within each ensemble had a higher probability of being bidirectionally connected than randomly selected neurons in the network. n = 10 sets of 100 neuron pairs. (E) Neurons within each ensemble were more correlated than randomly selected neurons in the network. n = 10 sets of 10 neurons. (F) Neurons within each ensemble had more similar POs than randomly selected neurons in the network. n = 10 sets of 10 neurons. *** indicates p < 0.001.
Fig 4.
Pattern Completion Capability was correlated with various graph theory parameters.
(A) Histogram of ensemble recall rate of 30 different pairs of neurons from ensemble 1. Neuron pairs with higher ensemble recall rates were better pattern completion neurons. Each pair was stimulated 800 times. The ensemble recall rate (the percent of trials where most of the ensemble was activated following stimulation) was calculated for each of the 30 pairs. (B) Probability of ensemble activation was dependent on the average membrane voltage of ensemble neurons before stimulation of the neuron pair. Neuron pairs with a higher overall ensemble recall rate were more likely to activate ensembles even at lower pre-stimulation voltages. (C) The pre-stimulation voltage needed for stimulation of a neuron pair to activate an ensemble 5% of the time was significantly and negatively correlated with the overall ensemble recall rate (p = 5.5 × 10−16, F-test, n = 29 neuron pairs). Neurons with higher overall ensemble recall rates could achieve a 5% recall rate at voltages further from threshold. (D) Graph theory parameters helped predict the pattern completion capability of each neuron pair through LASSO regression. (E) Top: Schematics representing the four network parameters calculated for each neuron pair. Bottom: The relationship between each network parameter and the pattern completion capability of each neuron pair. All variables were significantly and negatively correlated with PCC, with degree and closeness centrality having the strongest correlation (from left to right p = 4.6 × 10−9, 1.9 × 10−8, 3.3 × 10−3, 1.3 × 10−5, F-test, n = 29 neuron pairs).
Fig 5.
LASSO regression can predict Pattern Completion Capability.
(A) Correlation matrix of the network parameters for each of the 30 neuron pairs in ensemble 1 (left) and each of the 25 neuron pairs in ensemble 2 (right). (B) LASSO regression accurately predicted the PCC of each neuron pair in ensemble 1 (left) and ensemble 2 (right). Actual PCC was calculated from 800 stimulation trials for each neuron pair. Separate LASSO models were computed for each ensemble. Blue line indicates y = x. (C) Algorithm reliance for each network parameter. For both ensemble 1 (left) and ensemble 2 (right), the accuracy of LASSO regression was most reliant on degree.
Fig 6.
Modern GCaMP sensors may be able to identify efficient pattern completion neurons in vivo.
(A) Raster plots of four example ensemble recall events (from ensemble 1) evoked by stimulation of different pairs of neurons. Neurons in the ensemble activated in a sequential manner rather than simultaneously. The y-axis spans all neurons in the ensemble. (B) Scatter plot of average latency vs. PCC in ensemble 1 (top) and ensemble 2 (bottom) for all 800 trials of each neuron pair. (C) Distribution of 0–80% rise time for GCaMP8f and GCaMP7f. Data were taken from previous research that performed simultaneous calcium imaging and cell attached electrophysiology in mouse visual cortex [81]. Inset: The standard deviation of GCaMP8f’s rise time was less than that of GCaMP7f. (D) Effect of calcium indicators on Pearson r between latency and PCC when calculated with 100 trials. Error bars represent mean ± standard deviation. ** indicates p < 0.01 and *** indicates p < 0.001. (E) Accuracy of latency measurement as a function of the number of ensemble recall events for ensemble 1 (left) and ensemble 2 (right). The correlation between latency and PCC increased as the number of ensemble recall events increased and as the temporal dynamics of calcium indicators became less variable. The shaded region is the mean ± s.e.m of the correlation coefficient.
Fig 7.
Latency within ensemble activation events during spontaneous ensemble activity can identify pattern completion neurons.
(A) Top: Histogram of the number of spikes from 36 ensemble neurons over 250 seconds (using 1 second bins). Bottom: Raster plot of spontaneous ensemble activity from all 36 ensemble neurons. Arrows represent ensemble events shown in (B). (B) Zoomed-in view of three ensemble recall events. The cyan vertical line represents the median spike time, which was the reference for calculating relative latency for that recall event. Neurons are arranged and colored by latency, with earlier average latency neurons closer to the x-axis. (C) Histogram of the distribution of latency for each ensemble neuron. Latency was averaged over 41 ensemble recall events. The color gradient of the bars also serves as the colormap for individual neurons in panel (B). (D) 6 neurons that had early (negative) average latency values and 5 neurons that had late (positive) average latency values were selected to stimulate in pairs. (E) Early neuron pairs had a higher ensemble recall rate over 400 stimulation events than late neuron pairs. n = 10 neuron pairs for each group. (F) Early neuron pairs had a lower PCC than late neuron pairs. n = 10 neuron pairs for each group. (G) A scatter plot for the two forms of latency demonstrates that latency calculated from the action potential model was generally correlated with the latency calculated from the model incorporating GCaMP rise kinetics for all ensemble neurons from 41 spontaneous recall events. *** indicates p<0.001.
Fig 8.
Stimulation of five neurons can reliably activate ensemble neurons.
(A) Plot of the number of neurons stimulated vs. average ensemble recall rate for each stimulation condition, varying neuron selection and stimulation frequency. Error bars represent standard error (n = 10 neuron groups at each stimulation group size). (B) PCC from the same neuron pairs stimulated at both 20 Hz and 30 Hz (n = 20 neuron pairs). PCC from the two stimulation frequencies were well correlated. (C) The change (relative to baseline) in the number of non-ensemble excitatory neurons that fired during the stimulation period vs. ensemble recall rate. Recall rate was increased by increasing the number of stimulated ensemble neurons (n = 80 neuron groups of size 2 to 5). (D) Histogram of the probability that a non-ensemble excitatory neuron spiked as a function of their PO relative to the ensemble’s mean PO. Similar POs became more likely to spike during the stimulation period as ensemble recall rate increased (measured by number of early neurons stimulated) (n = 40 neuron groups of size 2 to 5 stimulated for fifty 400 ms periods). (E) Change in average spike rate (relative to baseline) for each inhibitory neuron group as a function of ensemble recall rate (n = 80 stimulation periods).