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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

The PRCs are plotted for the left E, L, and C cells. Each PRC describes the resulting phase shift that occurs when that cell’s voltage is perturbed by 10−6, at various initial phases. PRCs for right E, L, and C cells are the same except for a phase shift of 0.5 due to the right–left symmetry within each oscillator
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Fig3: The PRCs are plotted for the left E, L, and C cells. Each PRC describes the resulting phase shift that occurs when that cell’s voltage is perturbed by 10−6, at various initial phases. PRCs for right E, L, and C cells are the same except for a phase shift of 0.5 due to the right–left symmetry within each oscillator

Mentions: Applying the techniques used in [29] to (1a)–(1d) the 6 intersegmental coupling functions in (3) are computed. The first step in this process is to compute the phase response curves (PRCs) for each class of neurons within a single segment. Figure 3 illustrates the PRCs for the neural model (1a)–(1d). These are the 6 neuron-to-neuron connections in half of a single oscillator. Recall that due to the spatiotemporal symmetry (seen in the connections in Fig. 1 and the simulated voltages in Fig. 2) are the same for connections between neurons on the right side of the oscillator and those on the left side. The six connections for the left E, L, and C cells are depicted in Fig. 4. Fig. 3


Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

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

The PRCs are plotted for the left E, L, and C cells. Each PRC describes the resulting phase shift that occurs when that cell’s voltage is perturbed by 10−6, at various initial phases. PRCs for right E, L, and C cells are the same except for a phase shift of 0.5 due to the right–left symmetry within each oscillator
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig3: The PRCs are plotted for the left E, L, and C cells. Each PRC describes the resulting phase shift that occurs when that cell’s voltage is perturbed by 10−6, at various initial phases. PRCs for right E, L, and C cells are the same except for a phase shift of 0.5 due to the right–left symmetry within each oscillator
Mentions: Applying the techniques used in [29] to (1a)–(1d) the 6 intersegmental coupling functions in (3) are computed. The first step in this process is to compute the phase response curves (PRCs) for each class of neurons within a single segment. Figure 3 illustrates the PRCs for the neural model (1a)–(1d). These are the 6 neuron-to-neuron connections in half of a single oscillator. Recall that due to the spatiotemporal symmetry (seen in the connections in Fig. 1 and the simulated voltages in Fig. 2) are the same for connections between neurons on the right side of the oscillator and those on the left side. The six connections for the left E, L, and C cells are depicted in Fig. 4. Fig. 3

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