Coordinated spinal locomotor network dynamics emerge from cell-type-specific connectivity patterns
- Institute of Neuroscience, University of Oregon, United States
- Discovery Brain Sciences, University of Edinburgh, United Kingdom
Figures
Figure 1
A single-population recurrent network generates rhythm, segment-to-segment propagation, and left–right alternation.
(A) Schematic connectivity diagram. Grayscale circles represent individual units at different phases of oscillation, with one unit per hemi-segment. Red lines schematically illustrate inhibitory projections from a mid-body unit. (B) Weight matrix illustrating all outgoing inhibitory projections from the mid-body unit labeled with a red dot. (C) Time dependence of network activity with all units receiving the same tonic drive. The different traces represent different units.
Figure 2
Fast and slow speed modules enable control of locomotion frequency.
(A) Connectivity schematic illustrating that fast- and slow-module units receive distinct tonic drives and project both within and between modules. (B) Map of outgoing projections from a mid-body unit (red). (C) Time-dependent activity of fast- and slow-module units given different levels of tonic drive to the two populations.
Figure 3 with 2 supplements
Speed-module recruitment enables frequency control.
(A) Locomotion frequency with different levels of tonic drive to fast and slow units. (B) Frequency along the path shown in (A). (C) Frequency-dependent recruitment of fast and slow units as a function of locomotion frequency along the path shown in (A). (D) Phase difference between left and right units within each segment (dotted line corresponds to half of a period). (E) Phase difference (where 1 corresponds to a full period of oscillation) between pairs of units on the same side in adjacent segments (dotted line corresponds to , where is the number of segments). Error bars in all panels denote standard deviation across units.
Figure 3—figure supplement 1
Recruitment of the fast module at high frequencies inhibits the slow module.
Frequency-dependent recruitment of fast and slow units as a function of locomotion frequency with constant drive to the slow population (left: small drive; right: large drive) and varying drive to the fast population.
Figure 3—figure supplement 2
Frequency determination from time series is performed through calculating the period from the autocorrelation spectrum.
(A) An example of a high-frequency rate time series from a single unit in the eight-population model. (B) The autocorrelation spectrum corresponding to the time series in (A). The global minimum and resultant period are marked in dashed and solid lines, respectively. (C) An example of a low-frequency time series from a single unit in the eight-population model. (D) The autocorrelation spectrum for the time series in (C). The global minimum and resultant period are marked in dashed and solid lines, respectively. (E) An example time series without a single dominant frequency in the eight-population model. The failure was brought about by increasing the global strength of excitatory connections to 0.5 and the modularity to 0.4. (F) The autocorrelation spectrum of the time series in (E). The global minimum and resultant period are marked in dashed and solid black lines, respectively. The first local minimum and resultant period are marked in dashed and solid red lines, respectively.
Figure 4 with 1 supplement
A model with excitatory and inhibitory populations.
(A) Schematic diagram illustrating connectivity among cell types (but not longitudinal connectivity) for the eight-population model. (B) Detailed connectivity matrices for an example mid-body unit from each population. (C) Time-dependent activity traces at slow (left) and fast (right) locomotion frequencies (traces are slightly offset for clarity).
Figure 4—figure supplement 1
Speed-module recruitment enables coordinated locomotion with frequency and amplitude control in an eight-population model.
(A) Amplitude of the fast population (left), the slow population (center), and averaged over the fast and slow populations (right). (B) Levels of tonic drive to the fast and slow populations determine locomotion frequency. (C) Average amplitude and frequency along the path shown as a solid line in (A-B). (D) Average amplitude and frequency along the path shown as a dash-dot line in (A-B). (E) Frequency-dependent recruitment of fast and slow units as a function of locomotion frequency. (F) Phase difference between units within each segment (dotted line corresponds to half of a period). (G) Phase difference between pairs of units on the same side in adjacent segments (dotted line corresponds to, , where is the number of segments). Error bars in all panels denote standard deviation across units.
Figure 5
Single-cell properties and excitatory connectivity influence locomotor frequency in an individual speed module.
(A, B) Dependence of locomotion frequency on the axonal delay per segment and membrane time constant of units ((A) shows a broad range of values; (B) shows an inset from (A)). Stars denote experimentally observed values for fast and slow excitatory V2a cells in zebrafish (Menelaou and McLean, 2019; Menelaou et al., 2022). (C) Dependence of locomotion frequency on the projection distances of excitatory connections originating from the excitatory unit labeled blue.
Figure 6
Frequency range depends on excitatory projection strength and modularity.
(A) Dependence of the range of possible locomotion frequencies on the global strength of excitatory projections relative to that of inhibitory projections. (B) Dependence of the frequency range on connectivity modularity, which quantifies the strength of inter-module (fast-to-slow and slow-to-fast) projections relative to intra-module (fast-to-fast and slow-to-slow) projections. (Missing intermediate points correspond to cases where coordinated locomotion does not appear.) (C) Dependence of the frequency range on connectivity modularity of excitatory units, where inhibitory units have modularity set to zero. (D) Dependence of the frequency range on connectivity modularity of inhibitory units, where excitatory units have modularity set to zero. (In (A), modularity is set to zero; in (B-D), strength of excitation is set to 0.4.)
Figure 7
Ablating populations affects locomotion frequency dependence of locomotion frequency (normalized to its unperturbed value) on ablation of each of the four interneuron populations during slow speed oscillations (dashed lines; fast drive = 1.0, slow drive = 1.0; frequency = 9.3 Hz) and fast speed oscillations (dotted lines; fast drive = 2.0, slow drive = 0.5; frequency = 34.0 Hz).
Asterisks mark points where the model failed to produce a coherent oscillation (see Methods).
Figure 8 with 1 supplement
A spiking network model confirms that network-based mechanisms for rhythmogenesis and frequency control are robust in stochastic settings.
(A) A raster plot from the single-population spiking model. The blue (red) dots show spikes from neurons on the left (right) side of the spinal cord. (B) A raster plot from the two-population spiking model, with spikes from the fast (slow) population shown in the left (right) panel. (C) Dependence of the frequency in the two-population spiking model on the driving rate. Given a fast drive equivalent, , the EI-balanced Poisson inputs have rates chosen to produce in an isolated fast neuron and in an isolated slow neuron. (D) Dependence of the frequency in the eight-population spiking model on the strength of excitatory connections relative to the strength of inhibitory connections. The simulations shown here use 0 modularity for all populations. (E) Dependence of the firing rate oscillations in the eight-population spiking model on the modularity of the excitatory connections. The simulation uses an excitatory connection strength of 0.4 and 0 modularity for the inhibitory connections. All spiking model simulations shown here use leaky-integrate-and-fire (LIF) neurons for each unit of the corresponding rate model and connectivity fraction .
Figure 8—figure supplement 1
Dependence of spiking model behavior on ,, and .
(A) Raster plots for the single-population spiking model at different values of . The membrane time constant is for these simulations. (B) Raster plots for the single-population spiking model at different values of . The membrane time constant is for these simulations. (C) Dependence of the frequency of firing rate oscillations in the single-population model on the membrane time constant . The spiking model was simulated with and . The rate model was simulated without synaptic time delays. (D) Dependence of the frequency of firing rate oscillations in the two-population model on and the driving frequency. The simulations used .
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Coordinated spinal locomotor network dynamics emerge from cell-type-specific connectivity patterns
eLife 14:RP106658.
https://doi.org/10.7554/eLife.106658.3
