Computational Modeling of Spinal Locomotor Circuitry in the Age of Molecular Genetics

A spinal circuit model with asymmetric cervical-lumbar layout controls backward locomotion and scratching in quadrupeds

Locomotion and scratching are basic motor functions which are critically important for animal survival. Although the spinal circuits governing forward locomotion have been extensively investigated, the organization of spinal circuits and neural mechanisms regulating backward locomotion and scratching remain unclear. Here, we extend a model by Danner et al. to propose a spinal circuit model with asymmetrical cervical-lumbar layout to investigate these issues. In the model, the left-right alternation within the cervical and lumbar circuits is mediated by V 0D and V 0V commissural interneurons (CINs), respectively. With different control strategies, the model closely reproduces multiple experimental data of quadrupeds in different motor behaviors. Specifically, under the supraspinal drive, walk and trot are expressed in control condition, half-bound is expressed after deletion of V 0V CINs, and bound is expressed after deletion of V0 (V 0D and V 0V) CINs; in addition, unilateral hindlimb scratching occurs in control condition and synchronous bilateral hindlimb scratching appears after deletion of V 0V CINs. Under the combined drive of afferent feedback and perineal stimulation, different coordination patterns between hindlimbs during BBS (backward-biped-spinal) locomotion are generated. The results suggest that (1) the cervical and lumbar circuits in the spinal network are asymmetrically recruited during particular rhythmic limb movements. (2) Multiple motor behaviors share a single spinal network under the reconfiguration of the spinal network by supraspinal inputs or somatosensory feedback. Our model provides new insights into the organization of motor circuits and neural control of rhythmic limb movements.

Sparse Firing in a Hybrid Central Pattern Generator for Spinal Motor Circuits

Central pattern generators are circuits generating rhythmic movements, such as walking. The majority of existing computational models of these circuits produce antagonistic output where all neurons within a population spike with a broad burst at about the same neuronal phase with respect to network output. However, experimental recordings reveal that many neurons within these circuits fire sparsely, sometimes as rarely as once within a cycle. Here we address the sparse neuronal firing and develop a model to replicate the behavior of individual neurons within rhythm-generating populations to increase biological plausibility and facilitate new insights into the underlying mechanisms of rhythm generation. The developed network architecture is able to produce sparse firing of individual neurons, creating a novel implementation for exploring the contribution of network architecture on rhythmic output. Furthermore, the introduction of sparse firing of individual neurons within the rhythm-generating circuits is one of the factors that allows for a broad neuronal phase representation of firing at the population level. This moves the model toward recent experimental findings of evenly distributed neuronal firing across phases among individual spinal neurons. The network is tested by methodically iterating select parameters to gain an understanding of how connectivity and the interplay of excitation and inhibition influence the output. This knowledge can be applied in future studies to implement a biologically plausible rhythm-generating circuit for testing biological hypotheses.

Sensory Feedback and Central Neuronal Interactions in Mouse Locomotion

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyze a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behavior to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Spinal control of locomotion before and after spinal cord injury

Thoracic spinal cord injury affects long propriospinal neurons that interconnect the cervical and lumbar enlargements. These neurons are crucial for coordinating forelimb and hindlimb locomotor movements in a speed-dependent manner. However, recovery from spinal cord injury is usually studied over a very limited range of speeds that may not fully expose circuitry dysfunction. To overcome this limitation, we investigated overground locomotion in rats trained to move over an extended distance with a wide range of speeds both pre-injury and after recovery from thoracic hemisection or contusion injuries. In this experimental context, intact rats expressed a speed-dependent continuum of alternating (walk and trot) and non-alternating (canter, gallop, half-bound gallop, and bound) gaits. After a lateral hemisection injury, rats recovered the ability to locomote over a wide range of speeds but lost the ability to use the highest-speed gaits (half-bound gallop and bound) and predominantly used the limb contralateral to the injury as lead during canter and gallop. A moderate contusion injury caused a greater reduction in maximal speed, loss of all non-alternating gaits, and emergence of novel alternating gaits. These changes resulted from weak fore-hind coupling together with appropriate control of left-right alternation. After hemisection, animals expressed a subset of intact gaits with appropriate interlimb coordination even on the side of the injury, where the long propriospinal connections were severed. These observations highlight how investigating locomotion over the full range of speeds can reveal otherwise hidden aspects of spinal locomotor control and post-injury recovery.

Spinal control of locomotion before and after spinal cord injury

Thoracic spinal cord injury affects long propriospinal neurons that interconnect the cervical and lumbar enlargements. These neurons are crucial for coordinating forelimb and hindlimb movements in a speed-dependent manner. At the same time, recovery from spinal cord injury is usually studied over a very limited range of speeds. To overcome this limitation, we investigated overground locomotion in rats over the full range of speeds pre-injury and after recovery from thoracic hemisection or contusion injuries. Intact rats expressed a speed-dependent continuum of alternating (walk and trot) and non-alternating (canter, gallop, half-bound gallop, and bound) gaits. After a lateral hemisection injury, rats recovered the ability to locomote over a wide range of speeds but lost the ability to move using the highest-speed gaits (half-bound gallop and bound) and predominantly used the limb contralateral to injury as lead during canter and gallop. A moderate contusion injury resulted in a greater reduction in maximal speed, loss of non-alternating gaits, and emergence of novel alternating gaits. Analysis of the gait structure in phase space and the variability of limb coupling suggests substantial reorganization of intraspinal pathways mediating interlimb coordination following recovery of locomotion after lateral hemisection or midline contusion injuries. This reorganization appears as an increased reliance on local enlargement circuitry and suggests that speed-dependent gait changes in the forelimbs rely on ascending information from the lumbar circuitry that is impaired post-injury. These observations highlight how investigating the full repertoire of locomotor speeds can reveal otherwise hidden aspects of spinal circuitry and post-injury reorganization.

The role of V3 neurons in speed-dependent interlimb coordination during locomotion in mice

Speed-dependent interlimb coordination allows animals to maintain stable locomotion under different circumstances. The V3 neurons are known to be involved in interlimb coordination. We previously modeled the locomotor spinal circuitry controlling interlimb coordination (Danner et al., 2017). This model included the local V3 neurons that mediate mutual excitation between left and right rhythm generators (RGs). Here, our focus was on V3 neurons involved in ascending long propriospinal interactions (aLPNs). Using retrograde tracing, we revealed a subpopulation of lumbar V3 aLPNs with contralateral cervical projections. V3OFF mice, in which all V3 neurons were silenced, had a significantly reduced maximal locomotor speed, were unable to move using stable trot, gallop, or bound, and predominantly used a lateral-sequence walk. To reproduce this data and understand the functional roles of V3 aLPNs, we extended our previous model by incorporating diagonal V3 aLPNs mediating inputs from each lumbar RG to the contralateral cervical RG. The extended model reproduces our experimental results and suggests that locally projecting V3 neurons, mediating left-right interactions within lumbar and cervical cords, promote left-right synchronization necessary for gallop and bound, whereas the V3 aLPNs promote synchronization between diagonal fore and hind RGs necessary for trot. The model proposes the organization of spinal circuits available for future experimental testing.

Emergence of Extreme Paw Accelerations During Cat Paw Shaking: Interactions of Spinal Central Pattern Generator, Hindlimb Mechanics and Muscle Length-Depended Feedback

Cat paw shaking is a spinal reflex for removing an irritating stimulus from paw by developing extremely high paw accelerations. Previous studies of paw shaking revealed a proximal-to-distal gradient of hindlimb segmental velocities/accelerations, as well as complex inter-joint coordination: passive motion-dependent interaction moments acting on distal segments are opposed by distal muscle moments. However, mechanisms of developing extreme paw accelerations during paw shaking remain unknown. We hypothesized that paw-shaking mechanics and muscle activity might correspond to a whip-like mechanism of energy generation and transfer along the hindlimb. We first demonstrated in experiments with five intact, adult, female cats that during paw shaking, energy generated by proximal muscle moments was transmitted to distal segments by joint forces. This energy transfer was mostly responsible for the segmental velocity/acceleration proximal-to-distal gradient. Distal muscle moments mostly absorbed energy of the distal segments. We then developed a neuromechanical model of hindlimb paw shaking comprised a half-center CPG, activating hip flexors and extensors, and passive viscoelastic distal muscles that produced length/velocity-depended force. Simulations reproduced whip-like mechanisms found experimentally: the proximal-to-distal velocity/acceleration gradient, energy transfer by joint forces and energy absorption by distal muscle moments, as well as atypical co-activation of ankle and hip flexors with knee extensors. Manipulating model parameters, including reversal of segmental inertia distal-to-proximal gradient, demonstrated important inertia contribution to developing the segmental velocity/acceleration proximal-to-distal gradient. We concluded that extreme paw accelerations during paw shaking result from interactions between a spinal CPG, hindlimb segmental inertia, and muscle length/velocity-depended feedback that tunes limb viscoelastic properties.

A Whole-Body Musculoskeletal Model of the Mouse

Neural control of movement cannot be fully understood without careful consideration of interactions between the neural and biomechanical components. Recent advancements in mouse molecular genetics allow for the identification and manipulation of constituent elements underlying the neural control of movement. To complement experimental studies and investigate the mechanisms by which the neural circuitry interacts with the body and the environment, computational studies modeling motor behaviors in mice need to incorporate a model of the mouse musculoskeletal system. Here, we present the first fully articulated musculoskeletal model of the mouse. The mouse skeletal system has been developed from anatomical references and includes the sets of bones in all body compartments, including four limbs, spine, head and tail. Joints between all bones allow for simulation of full 3D mouse kinematics and kinetics. Hindlimb and forelimb musculature has been implemented using Hill-type muscle models. We analyzed the mouse whole-body model and described the moment-arms for different hindlimb and forelimb muscles, the moments applied by these muscles on the joints, and their involvement in limb movements at different limb/body configurations. The model represents a necessary step for the subsequent development of a comprehensive neuro-biomechanical model of freely behaving mice; this will close the loop between the neural control and the physical interactions between the body and the environment.