Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

Design Principles for Central Pattern Generators With Preset Rhythms

This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.

Analytical CPG model driven by limb velocity input generates accurate temporal locomotor dynamics

The ability of vertebrates to generate rhythm within their spinal neural networks is essential for walking, running, and other rhythmic behaviors. The central pattern generator (CPG) network responsible for these behaviors is well-characterized with experimental and theoretical studies, and it can be formulated as a nonlinear dynamical system. The underlying mechanism responsible for locomotor behavior can be expressed as the process of leaky integration with resetting states generating appropriate phases for changing body velocity. The low-dimensional input to the CPG model generates the bilateral pattern of swing and stance modulation for each limb and is consistent with the desired limb speed as the input command. To test the minimal configuration of required parameters for this model, we reduced the system of equations representing CPG for a single limb and provided the analytical solution with two complementary methods. The analytical and empirical cycle durations were similar (R 2 = 0.99) for the full range of walking speeds. The structure of solution is consistent with the use of limb speed as the input domain for the CPG network. Moreover, the reciprocal interaction between two leaky integration processes representing a CPG for two limbs was sufficient to capture fundamental experimental dynamics associated with the control of heading direction. This analysis provides further support for the embedded velocity or limb speed representation within spinal neural pathways involved in rhythm generation.

State-dependent rhythmogenesis and frequency control in a half-center locomotor CPG

The spinal locomotor central pattern generator (CPG) generates rhythmic activity with alternating flexion and extension phases. This rhythmic pattern is likely to result from inhibitory interactions between neural populations representing flexor and extensor half-centers. However, it is unclear whether the flexor-extensor CPG has a quasi-symmetric organization with both half-centers critically involved in rhythm generation, features an asymmetric organization with flexor-driven rhythmogenesis, or comprises a pair of intrinsically rhythmic half-centers. There are experimental data that support each of the above concepts but appear to be inconsistent with the others. In this theoretical/modeling study, we present and analyze a CPG model architecture that can operate in different regimes consistent with the above three concepts depending on conditions, which are defined by external excitatory drives to CPG half-centers. We show that control of frequency and phase durations within each regime depends on network dynamics, defined by the regime-dependent expression of the half-centers' intrinsic rhythmic capabilities and the operating phase transition mechanisms (escape vs. release). Our study suggests state dependency in locomotor CPG operation and proposes explanations for seemingly contradictory experimental data. NEW & NOTEWORTHY Our theoretical/modeling study focuses on the analysis of locomotor central pattern generators (CPGs) composed of conditionally bursting half-centers coupled with reciprocal inhibition and receiving independent external drives. We show that this CPG framework can operate in several regimes consistent with seemingly contradictory experimental data. In each regime, we study how intrinsic dynamics and phase-switching mechanisms control oscillation frequency and phase durations. Our results provide insights into the organization of spinal circuits controlling locomotion.