A spinal circuit model with an asymmetric cervical-lumbar layout for limb coordination and gait control in quadrupeds

doi:10.1007/s10483-025-3282-9

摘要/Abstract

Abstract:

In quadrupeds, the cervical and lumbar circuits work together to achieve the speed-dependent gait expression. While most studies have focused on how local lumbar circuits regulate limb coordination and gaits, relatively few studies are known about cervical circuits and even less about locomotor gaits. We use the previously published models by Danner et al. (DANNER, S. M., SHEVTSOVA, N. A., FRIGON, A., and RYBAK, I. A. Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds. eLife, 6, e31050 (2017)) as a basis, and modify it by proposing an asymmetric organization of cervical and lumbar circuits. First, the model reproduces the typical speed-dependent gait expression in mice and more biologically appropriate locomotor parameters, including the gallop gait, locomotor frequencies, and limb coordination of the forelimbs. Then, the model replicates the locomotor features regulated by the M-current. The walk frequency increases with the M-current without affecting the interlimb coordination or gaits. Furthermore, the model reveals the interaction mechanism between the brainstem drive and ionic currents in regulating quadrupedal locomotion. Finally, the model demonstrates the dynamical properties of locomotor gaits. Trot and bound are identified as attractor gaits, walk as a semi-attractor gait, and gallop as a transitional gait, with predictable transitions between these gaits. The model suggests that cervical-lumbar circuits are asymmetrically recruited during quadrupedal locomotion, thereby providing new insights into the neural control of speed-dependent gait expression.

Key words: locomotor control, cervical-lumbar asymmetrical spinal circuit, computational modeling, ionic current, gait

中图分类号:

O175.1

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(8): 1433-1450.

Qinghua ZHU, Fang HAN, Qingyun WANG. A spinal circuit model with an asymmetric cervical-lumbar layout for limb coordination and gait control in quadrupeds[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(8): 1433-1450.

图/表 14

Parameter	Value
Membrane capacitance	$C$ = 10 pF
Maximal conductance	$g NaP$ = 4.5 nS, $g M$ = 0.3 nS, $g SynE$ = 1.0 nS, $g SynI$ = 1.0 nS,
	$g L$ = 4.5 nS for RG neurons; $g L$ = 2.8 nS for other neurons
Reversal potential	$E Na$ = 50 mV, $E K = − 80$ mV, $E SynE = − 10$ mV, $E SynI = − 75$ mV,
	$E L = − 62.5$ mV for RG neurons; $E L = − 60$ mV for other neurons
Threshold/maximum voltage	$V thr = − 50$ mV, $V max$ = 0 mV
Half-voltage	$V 1/2,NaP = − 40$ mV, $V 1/2, τ = − 35$ mV, $V 1/2,h = − 45$ mV, $V 1/2,M = − 44$ mV
Slope	$k NaP = − 6$ mV, $k τ$ = 15 mV, $k h = 4$ mV, $k τ M = 25$ mV, $k M = 2.0$ mV
Time constant	$τ 0$ = 80 ms, $τ max$ = 210 ms, $τ M 0$ = 35 ms, $τ noise$ = 10 ms

Target	$m$	$d$
E	0.0	1.0
F	1.0	0.0
c- $V0 D$	2.5	0.0
$V0 D$ -diag	2.5	0.0
l- $V0 D$	4.5	0.0
l- $V0 V$	2.5	0.0
F: flexor center; E: extensor center; c: cervical; diag: diagonal; l: lumbar

Scope	Source	Target ( $w i j$ )
Within cervical and lumber circuits	F	E (0.01), V2b (4.0), V3 (3.5), $V0 D$ (7.0)
	E	F (0.01), V1 (4.0), Sh2 (5.0), CINi (4.0)
	V1	F $(− 0.8)$
	V2b	E $(− 10.0)$
	CINi	F $(− 0.3)$
	V3	F (0.3)
Within cervical circuits	c-F	LPNi (7.0), IIV2a-diag (5.0), $V0 D$ -diag (5.0)
	$V0 D$	c-F $(− 3.0)$
	IIV2a-diag	$V0 V$ -diag (9.0)
Within lumber circuits	l-F	IV2a (10.0), IV2a-diag (5.0)
	IV2a	$V0 V$ (10.0)
	$V0 V$	InI (6.0)
	InI	l-F $(− 0.7)$
	$V0 D$	l-F $(− 0.7)$
	IV2a-diag	$V0 V$ -diag (9.0)
Between cervical-lumber homolateral circuits	c-Sh2	l-F (0.1)
	l-Sh2	c-F (1.25)
	LPNi	l-F $(− 0.1)$
Between cervical-lumber diagonal circuits	$V0 D$ -diag	l-F $(− 0.45)$
	c- $V0 V$ -diag	l-F (0.2)
	l- $V0 V$ -diag	c-F (0.1)

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Gait	Left-right fore	Left-right hind	Homolateral	Diagonal
Walk	[0.25,0.75]	[0.25,0.75]	[0.1,0.4)/(0.6,0.9]	[0.1,0.4)/(0.6,0.9]
Trot	[0.25,0.75]	[0.25,0.75]	[0.25,0.75]	[0.0,0.1]/[0.9,1.0]
Gallop	[0.25,0.75]	(0.0,0.25]/[0.75,1.0)	[0.25,0.75]	(0.15,0.4)/(0.6,0.85)
Bound	[0.0,0.025]/(0.975,1.0]	[0.0,0.025]/(0.975,1.0]	[0.25,0.75]	[0.25,0.75]