Model concept.

A. Organization of the spinal locomotor circuitry (intact). B, C. Neural structures affected by thoracic hemisection (B) or contusion (C) injuries. Spheres represent neural populations involved in commissural and long propriospinal pathways. Descending drives and synaptic interactions are shown by arrowheads. Decreased color intensity in C signifies partial disruption of pathways by contusion injury. CINs, commissural interneurons; LPNs long propriospinal interneurons.

Detailed model schematic.

Spheres represent neural populations. Excitatory drives and connections are marked by arrowheads; inhibitory connections are marked by circles. RG, rhythm generator; In, interneuron; CINs, commissural interneurons; LPNs, long propriospinal neurons; a-, ascending; d-, descending. See text for details. Adapted from Danner et al. (2017) and Zhang et al. (2022) with modifications.

Gait expression in pre-injury/intact model and rats.

A1, A2 Extensor/stance phases (upper panels) and instantaneous normalized phase differences (bottom panels) of representative bouts for the model (A1) and a rat (A2). B1, B2 Average extensor/stance phases for each gait (upper panels) and circular plots of average normalized phase differences for each gait (bottom panels) expressed in the intact model (B1) and rats (B2). Detailed statistical results for rats are reported in Danner et al. (2023). H.-b., Half-bound; RG, rhythm generator.

Frequency-dependent distribution of normalized phase differences, gaits, and phase durations in the model and in rats.

A1, A2 Scatter plots of normalized phase differences against frequency of locomotor oscillations in the intact model (A1) and rats (A2). Each dot represents one step cycle. Gaits are classified for each step cycle and color-coded. B1, B2 Distribution of gaits vs. locomotor frequency in the model (B1) and rats (B2). Due to the low prevalence of lateral-sequence and canter steps, these gaits were omitted in B1 and B2. C1, C2 Flexor and extensor phase duration in the model (C1) and duration of swing and stance in rats (C2) against frequency of locomotor oscillations. Same number of step cycles are shown for the model and animals; model step cycles were randomly sampled. l-, left; r-, right; -f, fore RG/limb; -h, hind RG/limb; lat. seq., lateral-sequence; hbound, half-bound; RG, rhythm generator.

Gait prevalences, variability of interlimb coordination, and gait transition probabilities in model and rats.

A1 Prevalence of gaits in the intact model and following simulated recovery from hemisection and contusion injury. A2 Prevalence of each gait across intact rats and rats after recovery from hemisection and contusion injury (recalculated from Danner et al. (2023)). B1, B2 Means of the deviations from the moving average of each phase differences for intact case and after recovery from hemisection and contusion injuries for the model (B1) and rats (B2). Detailed statistical results for rats are reported in Danner et al. (2023). C1–C3 Matrices of gait transition probabilities in the intact model and following recovery from hemisection and contusion injury. D1–D3 Gait transition graphs, where nodes represent gaits (size is proportional to their prevalence) and edges represent gait transitions (line widths are proportional to their frequency of occurrence). l-, left; r-, right; -f, fore RG/limb; -h, hind RG/limb; nd, not-defined; diag., diagonal; lat., lateral; seq., sequence; RG, rhythm generator.

Conceptual schematic of the impact of hemisection injury on the spinal locomotor circuitry (A) and its reorganization after recovery from hemisection predicted by the model (B).

In B, affected long propriospinal neuron (LPN) connections recovered functionally through detour pathways. Drives to lumbar and cervical commissural interneurons (CINs) were altered to strengthen left-right alternation. Drive to the ipsilesional lumbar rhythm generator (pink arrow at the bottom) was substituted by regenerated brainstem input and/or afferent feedback.

Gait expression in the model and rats following recovery after hemisection.

A1, A2 Extensor/stance phases (upper panels) and instantaneous normalized phase differences (bottom panels) of representative bouts the model (A1) and a rat (A2). B1, B2 Average extensor/stance phases (upper panels) and circular plots of average normalized phase differences for each gait (bottom panels) expressed in the post-hemisection model (B1) and rats (B2). Detailed statistical results for rats are reported in Danner et al. (2023). C1 Prevalences of lead RG in the intact model and following simulated recovery after hemisection for gallop and canter. C2 Prevalence of leading limbs (left or right forelimb that touches down second) pre-injury (intact) and after recovery of hemisection for gallop and canter in rats. Adapted from Danner et al. (2023). T., trot; C., canter; RG, rhythm generator.

Frequency-dependent distribution of normalized phase differences in the model and in rats following recovery after hemisection.

A1, A2 Scatter plots of normalized phase differences are plotted against frequency of locomotor oscillations. Each dot represents one period/step cycle. Gaits are classified for each period/step cycle and color-coded. B1, B2 Distribution of gaits versus locomotor frequency in the post-hemisection model (B1) and rats (B2). Same number of step cycles are shown for the model and animals; model step cycles were randomly sampled. l-, left; r-, right; -f, fore RG/limb; -h, hind RG/limb; nd, not-defined; lat. seq., lateral-sequence; hbound, half-bound; RG, rhythm generator.

Bifurcation diagrams of the intact model (A1), following simulated recovery after hemisection (A2), and for model versions where only LPN connections were affected (40% of the pre-injury values; A3) or only brainstem drive to the ipsilesional hind RG was reduced (to 90% of the pre-injury value; A4).

Diagrams are plotted against the bifurcation parameter α and with reduced noise, σNoise = 5 fA. Normalized phase differences of 0.5 correspond to alternation, whereas phase differences of 0 or 1 correspond to synchronization. B1–B4 Dependency of frequency of locomotor oscillations on parameter α. Blue and red lines indicate stable phase differences or frequency with stepwise increase and decrease of parameter α, respectively. Colored areas indicate the expressed gait. l-, left; r-, right; -f, fore RG/limb; -h, hind RG/limb; lat. seq., lateral sequence; hbound, half-bound; RG, rhythm generator.

Conceptual schematic of the contusion injury (A) and following recovery after contusion in the model

(B). The weights of the long propriospinal neuron (LPN) connections between the cervical and lumbar compartments were significantly reduced. Brainstem drive to the lumbar rhythm generators (RGs) was substituted with additional drives to these RGs (pink arrows at the bottom). Brainstem drives to the cervical RG were adjusted to match oscillation frequency of lumbar RGs (gray arrows at the top). Inhibitory drives to cervical V0v commissural interneurons (CINs) were reduced to secure fore left–right alternation (pink arrows at the top). Commissural pathways in the lumbar compartment were reorganized to secure hind left–right alternation (pink arrows at the bottom).

Gait expression in the model and rats following recovery after hemisection.

A1, A2 Extensor/stance phases (upper panels) and instantaneous normalized phase differences (bottom panels) of representative bouts the model (A1) and a rat (A2). B1, B2 Average extensor/stance phases for each gait (upper panels) and circular plots of average normalized phase differences for each gait (bottom panels) expressed in the post-contusion model (B1) and rats (B2). Detailed statistical results for rats are reported in Danner et al. (2023). D.sq., diag. seq., diagonal-sequence; lat. seq., lateral-sequence; RG, rhythm generator.

Frequency-dependent distribution of normalized phase differences in the model (A1) and in rats (A2) following recovery after contusion.

A1, A2 Scatter plots of normalized phase differences are plotted against frequency of locomotor oscillations. Each dot represents one period/step cycle. Gaits are classified for each period/step cycle and color-coded. B1, B2 Distribution of gaits vs. locomotor frequency in the model (B1) and rats (B2). l-, left; r-, right; -f, fore RG/limb; -h, hind RG/limb; nd, not-defined; diag. seq., diagonal-sequence; lat. seq., lateral-sequence; RG, rhythm generator.

Connection weights in intact model

Hemisection: differences to pre-injury model

Contusion: differences to pre-injury model

Idealized gaits