Computational modeling of brainstem circuits controlling locomotor frequency and gait
- Drexel University, United States
- IBM TJ Watson Research Center, United States
Figures
Figure 1
Simplified schematic illustrating the model concept for the brainstem control of locomotion.
The brainstem compartment on each (left and right) side contains three major structures: the cuneiform (CnF) and pedunculopontine (PPN) nuclei, comprising the mesencephalic locomotor region (MLR), and the pontomedullary reticular formation represented by the lateral paragigantocellular nucleus (LPGi). Each of these structures contain excitatory (glutamatergic, Glu) and inhibitory (Gly/GABA) populations. The bilaterally interacting CnF and PPN control spinal circuits, including rhythm generators (RGs), by descending drives originating from their glutamatergic populations and mediated by the bilaterally located LPGi. Spinal projections from each LPGi are organized in two pathways involving two distinct glutamatergic LPGi populations: ‘1’ and ‘2’. The LPGi-Glu-1 population relays excitation from glutamatergic neurons in both CnF and PPN and projects to the rhythm generating circuits in the spinal cord. This pathway controls locomotor frequency. The LPGi-Glu-2 population relays excitation from the CnF and projects to inhibitory relay neurons (dIni) in the spinal cord controlling the activity of V0 commissural neurons securing left-right interactions between the RGs and therefore locomotor gait. For simplicity, only the left-right RGs and their connections for the cervical spinal cord are shown. Spheres represent neuronal populations and lines represent synaptic connections with arrowheads for excitatory and circles for inhibitory influences.
Figure 2
Full model schematic showing interactions between the brainstem and spinal cord (cervical and lumbar) circuits.
The structure of the cervical and lumbar circuits and their connections is taken from Danner et al. (2017). Brainstem circuits include the PPN and CnF compartments in the MLR and the LPGi compartment in the reticular formation. The LPGi project to the spinal cord via a set of interneuronal populations (see Results). Spheres represent neuronal populations and lines represent synaptic connections with arrowheads for excitatory and circles for inhibitory influences.
Figure 3 with 1 supplement
Bifurcation diagrams showing the effects of unilateral stimulation of glutamatergic (Glu) populations in the MLR and RF on locomotor frequency (top diagrams) and phase relationships between RGs controlling different limbs, representing different gaits.
(A) Unilateral stimulation of CnF Glu neurons (mCnF = 1.35; bCnF = 3.95) elicited locomotion with a wide range of frequencies with all four gaits expressed depending on stimulation strength (α). The results of these simulations closely correspond to the results of simulations using our previous model (Danner et al., 2017). Gait analyses for (A) are shown in Figure 3—figure supplement 1. (B) Unilateral stimulation of PPN Glu neurons (mPPN = 1.5; bPPN = 4) produced only lower locomotor frequencies and alternating gaits: walk and trot. (C) Unilateral activation of CnF Glu neurons (mCnF = 2.55; bCnF = 4.2), while PPN activity was suppressed bilaterally, generated all four gaits but maximum frequency was slightly reduced. (D) Unilateral activation of all LPGi Glu neurons (mLPGi = 1.1; bLPGi = 2.45) produced locomotor frequencies and gaits similar to those shown in (A). Normalized phase differences of 0.5 correspond to alternation, whereas differences of 0 and 1 correspond to synchronization. Blue and red lines indicate stable phase differences with stepwise increase and decrease of the bifurcation parameter α, respectively. Colored areas indicate the expressed gaits or regions of bistability between two adjacent gaits. Bifurcation diagrams are calculated as described in Danner et al. (2017).
Figure 3—figure supplement 1
Illustration of different gaits elicited by unilateral stimulation of glutamatergic neurons in the CnF (shown in Figure 3A).
These simulations show correspondence of the present model behavior with that of the previous model under similar conditions. (A) Rhythmic extensor activity for all four RGs and (B) phase differences for the four characteristic gaits (walk, trot, gallop and bound) when CnF- glutamatergic neurons were stimulated unilaterally (same data as in Figure 3A). These simulations are comparable with those shown in Danner et al. (2017). lh: left hind; lf: left fore; rh: right hind; rf: right fore; RG: rhythm generator. Gait analyses where performed as described in Material and methods.
Figure 4
Frequency shift in gait transitions following PPN inactivation.
(A)-(C) Comparison of model behavior when CnF glutamatergic neurons were stimulated unilaterally without (top graphs) and with (bottom graphs) bilateral inactivation of the PPN. (A) Hindlimb left-right phase differences plotted against locomotor frequency using data from Figure 3A and C. Comparison of the top and bottom diagram shows that the transition from alternating gaits - walk and trot - to synchronous gaits - gallop and bound - shifted towards lower frequencies when the PPN was bilaterally inactivated. (B) Schematic representation of this shift. Dashed lines and arrow indicate the shift of the beginning of gallop. (C) Step-by-step variability for hind left-right phase differences illustrates that synchronous gaits were also shifted to lower frequencies on a step-by-step basis. Normalized phase differences of 0.5 correspond to alternation, whereas phase differences of 0 and 1 correspond to synchronization. Blue and red lines in (A) indicate the stable phase differences with stepwise increase and decrease of the bifurcation parameter α, respectively. Colored areas indicate the expressed gaits or regions of bistability between two adjacent gaits. Bifurcation diagrams are calculated as described in Danner et al. (2017). In (C), step-by-step variability with increased noise was calculated as described in Materials and methods.
Figure 5
Frequency-dependent distribution of gaits caused by unilateral stimulation of glutamatergic neurons in the CnF, PPN, and LPGi.
(A) Unilateral stimulation of glutamatergic neurons in the CnF resulted in frequency-dependent expression of all gaits: walk, trot and gallop/bound. (B) Unilateral stimulation of glutamatergic neurons in the PPN elicited only alternating gaits, walk and trot, at a lower frequency range. (C) Unilateral stimulation of glutamatergic neurons in the LPGi resulted in frequency-dependent expression of all gaits similar to that in (A). The relative probabilities of frequency-dependent gait expression were analyzed as described in Materials and methods.
Figure 6
Role of inhibitory neurons within the CnF, PPN and LPGi in modulating locomotion.
In all simulations, locomotor oscillations were produced by bilateral activation of glutamatergic populations in the CnF by the variable excitatory drive, DCnF,ex. The other variable drive was applied unilaterally to the inhibitory population either within the CnF (DCnF,in, A and D) or within the PPN (DPPN,in, B and E), or within the LPGi (DLPGi,in, C and F). In (A), (B) and (C), the corresponding 2D diagrams were built for all three cases, and frequency was represented by color. (A) Unilateral stimulation of the inhibitory population in the CnF reduced locomotor frequency and stopped locomotion at higher stimulation intensities. (B) Unilateral stimulation of the inhibitory population in the PPN decreased locomotor frequency but was not able to arrest locomotor oscillations completely. (C) Unilateral stimulation of the inhibitory population in the LPGi decreased locomotor frequency and could also stop locomotion similar to the situation in (A). Black dotted lines indicate iso-frequency lines for 2, 4, 6, 8 and 10 Hz. White vertical dashed lines indicate the threshold for activation of the corresponding inhibitory populations. (D)-(F) Example traces of rhythmic extensor activities in all four RGs to illustrate changes in gait for the different stimulation parameters. An increase of inhibition in all cases was accompanied by sequential frequency-dependent gait transitions. Examples 1–5 in (D)-(F) are taken from the parameter combinations indicated by open circles (labeled 1–5) along the red dashed lines in (A)-(C). In all examples, DCnF,ex = 3.04, DCnF/PPN/LPGi,in are indicated for each simulation. lh: left hind; lf: left fore; rh: right hind; rf: right fore.
Tables
Table 1
Connection weights.
https://doi.org/10.7554/eLife.43587.004| Source | Target () |
|---|---|
| Within brainstem | |
| CnF-Glu | i-PPN-Glu (0.56), i-LPGi-Glu-1 (0.95), i-LPGi-Glu-2 (1.02),c-CnF-Glu (0.1), c-PPN-Glu (0.15), c-LPGi-Glu-1 (0.45),c-LPGi-Glu-2 (0.08), |
| CnF-GABA/GLY | i-CnF-Glu (−0.5), i-PPN-Glu (−0.5) |
| PPN-Glu | i-LPGi-Glu-1 (1), c-LPGi-Glu-1 (0.4) |
| PPN-GABA/GLY | i-PPN-Glu (−0.5), |
| LPGi-GABA/GLY | i-LPGi-Glu-1 (−0.5), i-LPGi-Glu-2 (−0.5) |
| Vestibular input to spinal cord | |
| VN | i-RG-E (1) |
| From brainstem to relay neurons | |
| LPGi-Glu-1 | i-Ine (1), i-CINe (1) |
| LPGi-Glu-2 | i-dIni (1), c-dIni (1) |
| LPGi-GABA/GLY | c-Ine(−0.5), c-CINe (−0.5) |
| From relay neurons to spinal circuits | |
| Ine | i-RG-F (1) |
| Ini | i-V0D (4), i-V0V (1.7), i-f-V0D-LPN (7.5) |
| CINe | c-RG-F (1) |
| Within girdle and side of the cord | |
| RG-F (fore and hind) | i-InF (0.4), i-V0D (0.7), i-V2a-lr (1), i-V3 (0.35), i-V2a-diag (0.5) |
| f-RG-F (fore only) | i-LPNi (0.7), i-V0D-LPN (0.5) |
| RG-E | i-InE (0.4), i-CINi (0.4), i-Sh2-LPN (0.5) |
| InF | i-RG-E (–1) |
| InE | i-RG-F (–0.08) |
| V2a-lr | i-V0V (1) |
| V2a-diag | i-V0V-LPN (0.9) |
| Ini | i-RG-F (–0.075) |
| Between left and right circuits within a girdle | |
| V0D | c-RG-F (–0.07) |
| V0V | c-Ini (0.6) |
| V3 | c-RG-F (0.03) |
| CINi | c-RG-F (–0.03) |
| Between fore and hind circuits | |
| f-LPNi | ih-RG-F (–0.01) |
| f-Sh2-LPN | ih-RG-F (0.01) |
| h-Sh2-LPN | if-RG-F (0.075) |
| f-V0D-LPN | ch-RG-F (–0.1) |
| f-V0V-LPN | ch-RG-F (0.02) |
| h-V0V-LPN | cf-RG-F (0.065) |
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i-, ipsilateral; c-, contralateral; f-, fore; h-, hind; CINi, inhibitory commissural interneurons; Ini, inhibitory interneurons; InE, extensor center inhibitory interneuron; InF, flexor center inhibitory interneuron; LPNi, inhibitory long propriospinal neuron; dIni, inhibitory relay neurons; Ine, ipsilaterally projecting tonically active excitatory relay neurons; CINe, commissural tonically active excitatory relay neurons; RG-F, flexor center, RG-E, extensor center. For target neurons with copies in both, the cervical and the lumbar circuits, connection weights are identical unless otherwise noted.
Additional files
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Transparent reporting form
- https://doi.org/10.7554/eLife.43587.010
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Computational modeling of brainstem circuits controlling locomotor frequency and gait
eLife 8:e43587.
https://doi.org/10.7554/eLife.43587
