Resonating neurons stabilize heterogeneous grid-cell networks
- Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science, India
Figures
Figure 1 with 1 supplement
A fast virtual trajectory developed for simulating rodent run in a two-dimensional circular arena elicits grid-cell activity in a continuous attractor network (CAN) model.
(A) Panels within rectangular box: simulation of a CAN model (60 × 60 neural network) using a 589 s long real trajectory from a rat (Hafting et al., 2005) yielded grid-cell activity. Other panels: A …
Figure 1—figure supplement 1
Quantitative comparison of grid-cell firing properties obtained from CAN models simulated with virtual vs. real trajectories.
Percentage changes in average firing rate, peak firing rate, mean size, number, average grid field spacing, grid score, information rate, sparsity of grid-field rate maps obtained with a virtual …
Figure 2
Biologically prevalent network heterogeneities disrupt the emergence of grid-cell activity in CAN models.
(A) Intrinsic heterogeneity was introduced by setting the integration time constant () of each neuron to a random value picked from a uniform distribution, whose range was increased to enhance the …
Figure 3 with 3 supplements
Quantification of the disruption in grid-cell activity induced by different forms of network heterogeneities in the CAN model.
Grid-cell activity of individual neurons in the network was quantified by eight different measurements, for CAN models endowed independently with intrinsic, afferent, or synaptic heterogeneities or …
Figure 3—figure supplement 1
Quantification of the disruption of grid-cell firing by network heterogeneities across different trials of CAN-model simulations.
Figure 3—figure supplement 2
Disruption of grid-cell firing by network heterogeneities was invariant to the specific trajectory employed by the CAN models.
(A) Left to right: Virtual trajectory in a square arena (dimensions: 2 m × 2 m), which is distinct from that shown in Figure 2E, was employed to perform CAN model simulations reported in this …
Figure 3—figure supplement 3
Disruption of grid-cell activity by network heterogeneities was prevalent across CAN models of different sizes.
(A) Example rate maps of grid-cell activity for homogeneous (Column 1) and heterogeneous networks endowed with five different degrees of heterogeneities (Columns 2–6) for networks of different sizes …
Figure 4
Incorporation of biological heterogeneities predominantly altered neural activity in low frequencies.
(A–H) Left, Magnitude spectra of temporal activity patterns of five example neurons residing in a homogeneous network (HN) or in networks with different forms and degrees of heterogeneities. Right, …
Figure 5
Incorporation of an additional high-pass filter into neuronal dynamics introduces resonance in individual rate-based neurons.
(A) Responses of neurons with low-pass (integrator; blue), high-pass (black) and band-pass (resonator; red) filtering structures to a chirp stimulus (top). Equations (7–8) were employed for …
Figure 6 with 1 supplement
Impact of neuronal resonance, introduced by altering low-pass filter characteristics, on grid-cell activity in a homogeneous CAN model.
(A) Example rate maps of grid-cell activity from a homogeneous CAN model with integrator neurons modeled with different values for integration time constants (). (B) Example rate maps of grid-cell …
Figure 6—figure supplement 1
Impact of neuronal resonance (phenomenological model), introduced by altering low-pass filter characteristics, on grid-cell characteristics in a homogeneous CAN model.
(A–D) average firing rate (A), peak firing rate (B), information rate (C), and sparsity (D) of grid fields in the arena for all neurons (n = 3600) in homogeneous CAN models with integrator (blue) or …
Figure 7
Impact of neuronal resonance, introduced by altering high-pass filter characteristics, on grid-cell activity in a homogeneous CAN model.
(A) Example rate maps of grid-cell activity from a homogeneous CAN model with integrator neurons (Column 1) or resonator neurons (Columns 2–6) modeled with different values of the HPF exponent (). …
Figure 8 with 2 supplements
Neuronal resonance stabilizes grid-cell activity in heterogeneous CAN models.
(A) Example rate maps of grid-cell activity in homogeneous (Top left) and heterogeneous CAN models, endowed with resonating neurons, across different degrees of heterogeneities. (B–I) Percentage …
Figure 8—figure supplement 1
Quantification of the grid-cell activity in presence of different forms of network heterogeneities in the CAN model with phenomenological resonator neurons.
Grid cell activity of individual resonator neurons in the network was quantified by eight different measurements, for CAN models endowed independently with intrinsic, afferent, or synaptic …
Figure 8—figure supplement 2
Neuronal resonance (phenomenological) stabilizes grid-cell firing in heterogeneous CAN models.
(A) Average firing rate, peak firing rate, mean size, number, average grid field spacing, grid score, information rate, and sparsity of grid fields for all neurons (n = 3600) in heterogeneous CAN …
Figure 9
Incorporation of a slow negative feedback loop into single-neuron dynamics introduces tunable resonance in rate-based neuronal models.
(A) A mechanistic model of intrinsic resonance in individual neurons using a slow negative feedback loop. (B) Temporal evolution of the output () of an individual neuron and the state variable …
Figure 10 with 2 supplements
Impact of neuronal resonance, introduced by a slow negative feedback loop, on grid-cell activity in a homogeneous CAN model.
(A) Example rate maps of grid-cell activity from a homogeneous CAN model for different values of the feedback strength () slope of the feedback kernel (), feedback time constant (), and half …
Figure 10—figure supplement 1
Impact of intrinsic neuronal resonance, introduced by adding a negative feedback loop in the neuronal dynamics, on grid-cell characteristics in a homogeneous CAN model.
Average firing rate (Row 1), peak firing rate (Row 2), average spacing (Row 3), and mean size (Row 4) of grid fields in the arena for all neurons (n = 3600) in homogeneous CAN models and their …
Figure 10—figure supplement 2
Impact of intrinsic neuronal resonance, introduced by adding a negative feedback loop in the neuronal dynamics, on grid-cell characteristics in a homogeneous CAN model.
Number (Row 1), information rate (Row 2), and sparsity (Row 3) of grid fields in the arena for all neurons (n = 3600) in homogeneous CAN models and their dependence on the parameters of negative …
Figure 11 with 1 supplement
Resonating neurons, achieved through a slow negative feedback loop, stabilizes grid-cell activity in heterogeneous CAN models.
(A) Example rate maps of grid-cell activity in homogeneous (top left) and heterogeneous CAN models, endowed with resonating neurons, across different degrees of heterogeneities. (B–I) Percentage …
Figure 11—figure supplement 1
Phase plane analysis of spatial profiles provided visualizations of the disruption of grid-cell activity in heterogeneous integrator networks and the relative robustness of heterogeneous resonator networks.
(A) Example rate maps of grid-cell activity in homogeneous (Row 1) and heterogeneous (Row 2; all heterogeneities, degree 5) CAN models, endowed with integrator (Column 1) or phenomenological …
Figure 12
The slow kinetics of the negative feedback loop is a critical requirement for stabilizing heterogeneous CAN models.
(A) A mechanistic model of intrinsic resonance in individual neurons using a slow negative feedback loop, with the feedback time constant () defining the slow kinetics. (B) Example rate maps of …
Figure 13 with 3 supplements
Intrinsically resonating neurons suppressed heterogeneity-induced variability in low-frequency perturbations caused by the incorporation of biological heterogeneities.
(A) Normalized variance of the differences between the magnitude spectra of temporal activity in neurons of homogeneous vs. heterogeneous networks, across different degrees of all three forms of …
Figure 13—figure supplement 1
Intrinsically resonating neurons (phenomenological) suppressed low-frequency components and enhanced frequency components around resonance frequency in homogeneous CAN models.
(A–B) Ten example magnitude spectra (normalized to peak) of grid-cell activity (A) and the respective percentages of total area covered in each octave of the magnitude spectra (B) for homogeneous …
Figure 13—figure supplement 2
Intrinsically resonating neurons (mechanistic) suppressed low-frequency components and enhanced frequency components around resonance frequency in homogeneous CAN models.
(A, B) Ten example magnitude spectra (normalized to peak) of grid-cell activity (A) and the respective percentages of total area covered in each octave of the magnitude spectra (B) for homogeneous …
Figure 13—figure supplement 3
Intrinsically resonating neurons (phenomenological) suppressed heterogeneity-induced variability in low-frequency perturbations caused by different forms of biological heterogeneities.
(A–C) Normalized variance of the differences between the magnitude spectra of neurons in homogeneous vs. heterogeneous networks, across different forms and degrees of heterogeneities, plotted as a …
Tables
Table 1
Forms and degrees of heterogeneities introduced in the CAN model of grid cell activity.
| Degree of heterogeneity | Intrinsic heterogeneity () | Afferent heterogeneity () | Synaptic heterogeneity () | |||
|---|---|---|---|---|---|---|
| Lower bound | Upper bound | Lower bound | Upper bound | Lower bound | Upper bound | |
| 1 | 8 | 12 | 35 | 55 | 0 | 300 |
| 2 | 6 | 14 | 25 | 65 | 0 | 600 |
| 3 | 4 | 16 | 15 | 75 | 0 | 900 |
| 4 | 2 | 18 | 5 | 85 | 0 | 1200 |
| 5 | 1 | 20 | 0 | 100 | 0 | 1500 |
Additional files
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Source code 1
Source code for simulations reported in eLife.66804.
- https://cdn.elifesciences.org/articles/66804/elife-66804-code1-v2.zip
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Transparent reporting form
- https://cdn.elifesciences.org/articles/66804/elife-66804-transrepform-v2.pdf
