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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

Entrainment ranges as a function of the forcing position for varying intersegmental connections. Uniform coupling asymmetry is illustrated in A with , , and . All of the ascending coupling strengths are stronger than descending for all connection lengths. This coupling scheme is used to produce monotonic entrainment ranges as a function of the forcing position, seen in C. Nonuniform coupling asymmetry is depicted in B with , , , and . For our choice of parameters, ascending connections become stronger at connections of length 3. Nonuniform coupling is used to compute the entrainment range in D, where see non-monotonic entrainment ranges
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Fig9: Entrainment ranges as a function of the forcing position for varying intersegmental connections. Uniform coupling asymmetry is illustrated in A with , , and . All of the ascending coupling strengths are stronger than descending for all connection lengths. This coupling scheme is used to produce monotonic entrainment ranges as a function of the forcing position, seen in C. Nonuniform coupling asymmetry is depicted in B with , , , and . For our choice of parameters, ascending connections become stronger at connections of length 3. Nonuniform coupling is used to compute the entrainment range in D, where see non-monotonic entrainment ranges

Mentions: Figure 9 illustrates the effect of different types of intersegmental coupling on entrainment ranges plotted as a function of the forcing position. Figure 9A shows the strength of the connections plotted as a function of the connection length for both ascending and descending coupling and corresponds to Eq. (7) with parameters , , and . Strength of the ascending connections are uniformly stronger than descending connection strengths, hence we refer to this intersegmental coupling scheme as uniform coupling asymmetry. Similarly, Fig. 9B shows connection strengths, again as a function of the connection length, for both ascending and descending connections where , , , and . Note in this case, for connections of length 1 and 2, ascending strengths are stronger than descending strengths, but the curves cross transversely (at approximately coupling length 3), after which descending connections become stronger than ascending connections. We refer to this coupling scheme as nonuniform coupling asymmetry. Fig. 9


Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

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

Entrainment ranges as a function of the forcing position for varying intersegmental connections. Uniform coupling asymmetry is illustrated in A with , , and . All of the ascending coupling strengths are stronger than descending for all connection lengths. This coupling scheme is used to produce monotonic entrainment ranges as a function of the forcing position, seen in C. Nonuniform coupling asymmetry is depicted in B with , , , and . For our choice of parameters, ascending connections become stronger at connections of length 3. Nonuniform coupling is used to compute the entrainment range in D, where see non-monotonic entrainment ranges
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig9: Entrainment ranges as a function of the forcing position for varying intersegmental connections. Uniform coupling asymmetry is illustrated in A with , , and . All of the ascending coupling strengths are stronger than descending for all connection lengths. This coupling scheme is used to produce monotonic entrainment ranges as a function of the forcing position, seen in C. Nonuniform coupling asymmetry is depicted in B with , , , and . For our choice of parameters, ascending connections become stronger at connections of length 3. Nonuniform coupling is used to compute the entrainment range in D, where see non-monotonic entrainment ranges
Mentions: Figure 9 illustrates the effect of different types of intersegmental coupling on entrainment ranges plotted as a function of the forcing position. Figure 9A shows the strength of the connections plotted as a function of the connection length for both ascending and descending coupling and corresponds to Eq. (7) with parameters , , and . Strength of the ascending connections are uniformly stronger than descending connection strengths, hence we refer to this intersegmental coupling scheme as uniform coupling asymmetry. Similarly, Fig. 9B shows connection strengths, again as a function of the connection length, for both ascending and descending connections where , , , and . Note in this case, for connections of length 1 and 2, ascending strengths are stronger than descending strengths, but the curves cross transversely (at approximately coupling length 3), after which descending connections become stronger than ascending connections. We refer to this coupling scheme as nonuniform coupling asymmetry. Fig. 9

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