Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators

Abstract

Interneurons are critical for the proper functioning of neural circuits. While often morphologically complex, their dendrites have been ignored for decades, treating them as linear point neurons. Exciting new findings reveal complex, non-linear dendritic computations that call for a new theory of interneuron arithmetic. Using detailed biophysical models, we predict that dendrites of FS basket cells in both hippocampus and prefrontal cortex come in two flavors: supralinear, supporting local sodium spikes within large-volume branches and sublinear, in small-volume branches. Synaptic activation of varying sets of these dendrites leads to somatic firing variability that cannot be fully explained by the point neuron reduction. Instead, a 2-stage artificial neural network (ANN), with sub- and supralinear hidden nodes, captures most of the variance. Reduced neuronal circuit modeling suggest that this bi-modal, 2-stage integration in FS basket cells confers substantial resource savings in memory encoding as well as the linking of memories across time.

Fig. 1

Modeling tools used to study dendritic integration in FS BCs and its functional implications. a Detailed, biophysically constrained multi-compartmental models using realistic anatomical reconstructions. b Reduced two-stage integrate and fire models of FS BCs. c two-layer ANN reduction describing the FS BCs. d Reduced network model with simplified pyramidal, FS BCs and SOM + interneurons. FS BCs and SOM+ interneurons provide feedback inhibition to excitatory neurons, with FS BCs targeting the somatic subunit while SOM+ neurons target the dendritic subunits. Memory encoding afferents provide inputs to excitatory cell dendrites

Fig. 2

Bimodal dendritic integration in multi-compartmental FS BC models. Examples of hippocampal (a) and PFC (d) FS BC morphological reconstructions. Representative input-output curves from supralinear (b, e) and sublinear (c, f) dendritic branches in hippocampal (top) and PFC (bottom) models, in response to synaptic stimulation. Increasing numbers of synapses (from 1 to 20 with step = 1) are uniformly distributed within each stimulated branch and are activated with a single pulse. The y-axis shows the amplitude of the dendritic EPSP caused by synaptic activation while the x-axis shows the expected EPSP amplitude that would result from the linear summation of synaptic EPSPs. The dashed line indicates linear summation. Insets show representative traces

Fig. 3

Morphological determinants of dendritic integration mode. a, c Total length distributions of supralinear vs. sublinear dendrites in the hippocampus (a) and the PFC (c). Statistically significant differences are observed for both sub- and supra-linear dendrites, in both areas. (p-value < 0.0001 for hippocampus and p-value < 0.01 for PFC, Student's t-test). b, d Same as in a, b, for mean dendritic diameter. Statistically significant differences are observed in hippocampal (p-value < 0.0001 Student’s t-test) but not in PFC FS BCs. e, f. Dendritic Volume and dendritic Input resistance are common discriminating characteristics among supralinear (larger, with low input resistance) and sublinear (smaller, with high input resistance) dendrites, for both areas (p-value < 0.0001 Student’s t-test for hippocampus and PFC, for Volume and Input resistance respectively). g Schematic illustration of morphological features for supralinear and sublinear dendrites in hippocampus (left) and PFC (right). Traces indicate the first EPSP in supralinear and sublinear dendrites. h–j Distributions of the number of supralinear and sublinear dendrites in both areas, under control conditions (h), with the mean diameter and length of all dendrites set to the mean values of the supralinear class (i) and with mean diameter and length of all dendrites set to the mean values of the sublinear class (j). Error bars indicate the minimum and maximum values

Fig. 4

Effect of bimodal dendritic integration on neuronal firing. Firing rate responses (in Hz) from one hippocampal (a,c) and one PFC (b,d) model cell, in response to stimulation of increasing numbers of synapses (10–60) that are either randomly distributed throughout the entire dendritic tree (blue) or grouped within a few dendritic branches (pink). Synapses are stimulated with a 50 Hz Poisson spike train. In both cases, dispersed activation leads to higher firing rates. e, f Same as in c, d with dendritic diameter set to 2 μm and removal of A-type dendritic channels. Firing rates are indistinguishable between grouped and dispersed activation patterns. Insets depict representative traces from dispersed (top) and grouped (bottom) activation of 30 synapses. Red dots in a, b, show the synaptic allocation motif

Fig. 5

Reduction of multi-compartmental models into ANN abstractions. Two types of abstractions are examined: (a) a Linear ANN, in which the input from all dendrites (x_i = number of synapses in dendrite i, N = number of dendrites) is linearly combined at the cell body and (b) a two-layer modular ANN, in which the input is fed into two parallel, separated hidden layers. The supralinear-layer receives the number of inputs landing onto supralinear branches (a = number of supralinear dendrites) while the sublinear layer receives the number of inputs landing onto sublinear dendrites (b = number of sublinear dendrites). Neurons in both hidden layers are equipped with nonlinear transfer functions, a logistic sigmoid in the supralinear layer and a sublinear function in the sublinear layer. The somatic transfer functions of both ANNs are linear

Fig. 6

Challenging the point neuron dogma: FS basket cells as two-stage nonlinear integrators. Linear regression analysis for two-layer modular (a, c) and linear (b, d) ANNs for one indicative hippocampal (top) and one indicative PFC (bottom) model cell. Actual mean firing rates (Hz) correspond to the responses of the compartmental model when stimulating with 50 Hz Poisson spike trains varying numbers of synapses (1–60), distributed in several ways (grouped or dispersed) within both sub- and supra-linear dendrites. Expected mean firing rates (Hz) are those produced by the respective ANN abstraction when receiving the same input (number of stimulated synapses) in its respective sub-/supra- or linear input layer nodes. e Regression performance (measured as R²) for two-layer modular (right) and Linear (left) ANNs for all eight FS BC model cells, respectively. In all cases the two-layer modular ANN is superior to the Linear ANN. Mean R² values over all cells for the Linear (red) and two-layer modular (cyan) ANNs are shown on the left. f Same as e, applied to datasets comprised of 60 input synapses. The difference in performance between the two ANN types is higher in this challenging task

Fig. 7

Properties of memory engram encoding under different dendritic nonlinearity configurations. a Size of memory engram (percentage of excitatory neurons that respond with ff > 10 Hz during memory recall) for Linear/Bi-modal FS-BC dendritic subunits receiving dispersed (light blue) or grouped (pink) synaptic inputs. b Mean firing rate of the excitatory population under the conditions enumerated in a. c Treves–Rolls sparsity metric of the excitatory population firing rates under the conditions enumerated in a. d Percentage of overlap between two memory engrams when two memories are separated by 1 h, under the conditions enumerated in b. Dashed lines indicate the chance level of overlap for the engram sizes of the dispersed case shown in a. e As in d for 24 h separation. Box plots indicate data from 20 simulation trials for a–c, and 10 trials for d–e. ANOVA **p < 0.05, ***p < 0.005. Error bars indicate minimum and maximum values