Abstract
Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment.
Highlights
The central pattern generator (CPG) for vertebrate locomotion consists of a circuit of neurons in the spinal cord that produces the basic oscillatory rhythmic output necessary for locomotion such as walking and swimming [1]
Nonuniform coupling asymmetry produces qualitatively the same entrainment ranges as a function of the forcing position as the experimental data and supports the hypothesis of Previte et al [15] that non-monotonic entrainment ranges as a function of the forcing position are not a generic property of coupled oscillators but rather depends on intersegmental coupling properties
The lamprey central pattern generator for locomotion is considered to be a model system for studying vertebrate locomotion because it is a primitive vertebrate with relatively few neurons [37, 38]
Summary
The central pattern generator (CPG) for vertebrate locomotion consists of a circuit of neurons in the spinal cord that produces the basic oscillatory rhythmic output necessary for locomotion such as walking and swimming [1]. Tytell and Cohen [6] found that the experimental entrainment ranges were approximately twice as large for bending stimuli applied near the middle of the preparation as those for stimuli applied at the ends This experimental result motivated the study of entrainment in CPG models in order to determine the mechanisms responsible for entrainment ranges which are non-monotonic as function of the forcing position. Parametric and non-parametric modeling, and concepts from control theory can be used to understand how the open-loop properties of a system’s component determine its closed-loop behavior [18, 19] This approach has been used to study, for example, blowflies [20] and electric fish [21, 22] and motivates our interest in the open-loop effect of bending on the lamprey CPG.
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