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Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

Massarelli N, Clapp G, Hoffman K, Kiemel T - J Math Neurosci (2016)

Bottom Line: This results in a simpler model yet maintains some properties of the neural model.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.

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.

No MeSH data available.


Related in: MedlinePlus

Cell classes of the neural model described in [23, 24] are excitatory interneurons (E), lateral inhibitory interneurons (L), crossed inhibitory interneurons (C), and edge cells (EC). Numbers indicates cell indices. Bars and circles indicate excitatory and inhibitory connections, respectively. Edge cells are only active in the segment at which bending occurs
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Fig1: Cell classes of the neural model described in [23, 24] are excitatory interneurons (E), lateral inhibitory interneurons (L), crossed inhibitory interneurons (C), and edge cells (EC). Numbers indicates cell indices. Bars and circles indicate excitatory and inhibitory connections, respectively. Edge cells are only active in the segment at which bending occurs

Mentions: The neural model of the lamprey CPG is based on the model developed by Buchanan [23] and Williams [24]. The model consists of a chain of coupled identical segmental oscillators, with each oscillator corresponding to one anatomical segment of the lamprey spinal cord. The segmental oscillators are modeled as in [24], except that we use a smooth approximation of the piecewise-linear threshold function of [24] (see below). Each segment is described by six variables representing the six classes of cells depicted in Fig. 1. Coupling connections exists between all oscillators, but the strength of the connections depends on their length and direction. Each segment of the CPG consists of three types of neurons: excitatory (E), lateral inhibitory (L), and crossed inhibitory (C) interneurons. Each segment exhibits left–right symmetry with each side containing one E, L, and C cell connected through intrasegmental connections, as illustrated in Fig. 1. Following [12], the effect of bending on the CPG is mediated by edge cells in the margin of the spinal cord, with connections onto CPG cells as shown in Fig. 1 [5]. We model the bending experiments of Tytell and Cohen [6] by assuming that bending activates the edge cells of only one segment. Fig. 1


Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

Massarelli N, Clapp G, Hoffman K, Kiemel T - J Math Neurosci (2016)

Cell classes of the neural model described in [23, 24] are excitatory interneurons (E), lateral inhibitory interneurons (L), crossed inhibitory interneurons (C), and edge cells (EC). Numbers indicates cell indices. Bars and circles indicate excitatory and inhibitory connections, respectively. Edge cells are only active in the segment at which bending occurs
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4835419&req=5

Fig1: Cell classes of the neural model described in [23, 24] are excitatory interneurons (E), lateral inhibitory interneurons (L), crossed inhibitory interneurons (C), and edge cells (EC). Numbers indicates cell indices. Bars and circles indicate excitatory and inhibitory connections, respectively. Edge cells are only active in the segment at which bending occurs
Mentions: The neural model of the lamprey CPG is based on the model developed by Buchanan [23] and Williams [24]. The model consists of a chain of coupled identical segmental oscillators, with each oscillator corresponding to one anatomical segment of the lamprey spinal cord. The segmental oscillators are modeled as in [24], except that we use a smooth approximation of the piecewise-linear threshold function of [24] (see below). Each segment is described by six variables representing the six classes of cells depicted in Fig. 1. Coupling connections exists between all oscillators, but the strength of the connections depends on their length and direction. Each segment of the CPG consists of three types of neurons: excitatory (E), lateral inhibitory (L), and crossed inhibitory (C) interneurons. Each segment exhibits left–right symmetry with each side containing one E, L, and C cell connected through intrasegmental connections, as illustrated in Fig. 1. Following [12], the effect of bending on the CPG is mediated by edge cells in the margin of the spinal cord, with connections onto CPG cells as shown in Fig. 1 [5]. We model the bending experiments of Tytell and Cohen [6] by assuming that bending activates the edge cells of only one segment. Fig. 1

Bottom Line: This results in a simpler model yet maintains some properties of the neural model.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.

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.

No MeSH data available.


Related in: MedlinePlus