Limits...
Conditions for Multi-functionality in a Rhythm Generating Network Inspired by Turtle Scratching.

Snyder AC, Rubin JE - J Math Neurosci (2015)

Bottom Line: We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch.Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay.This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA, acs73@pitt.edu.

ABSTRACT
Rhythmic behaviors such as breathing, walking, and scratching are vital to many species. Such behaviors can emerge from groups of neurons, called central pattern generators, in the absence of rhythmic inputs. In vertebrates, the identification of the cells that constitute the central pattern generator for particular rhythmic behaviors is difficult, and often, its existence has only been inferred. For example, under experimental conditions, intact turtles generate several rhythmic scratch motor patterns corresponding to non-rhythmic stimulation of different body regions. These patterns feature alternating phases of motoneuron activation that occur repeatedly, with different patterns distinguished by the relative timing and duration of activity of hip extensor, hip flexor, and knee extensor motoneurons. While the central pattern generator network responsible for these outputs has not been located, there is hope to use motoneuron recordings to deduce its properties. To this end, this work presents a model of a previously proposed central pattern generator network and analyzes its capability to produce two distinct scratch rhythms from a single neuron pool, selected by different combinations of tonic drive parameters but with fixed strengths of connections within the network. We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch. Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay. This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing.

No MeSH data available.


Related in: MedlinePlus

Rostral slow phase plane. Trajectory for KE for rostral scratch projected to a single slow phase plane. Coloring of curves is identical to Fig. 8. Bottom: zoomed view near the saddle-node bifurcation where the fold in the magenta fixed point curve intersects the cyan jump up knee curve for  active
© Copyright Policy - OpenAccess
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4504876&req=5

Fig9: Rostral slow phase plane. Trajectory for KE for rostral scratch projected to a single slow phase plane. Coloring of curves is identical to Fig. 8. Bottom: zoomed view near the saddle-node bifurcation where the fold in the magenta fixed point curve intersects the cyan jump up knee curve for active

Mentions: The weights of synapses onto KE are more interesting. To understand how these are constrained, we can focus on the reduced model, which maintains four distinct synaptic weights from the interneurons onto KE. With the convenient viewpoint that we have established, it is now helpful to consider the details of the trajectories for pocket scratch (Fig. 8) and rostral scratch (shown in Fig. 9 in a two-dimensional view analogous to the bottom panel of Fig. 8) for our baseline parameter choices. Recall that in the pocket rhythm, KE activates with HE, here represented by the activation of EP. When EP becomes active and the thick black part of the trajectory starts, decreases, corresponding to the trajectory being in the active phase for KE, near a right branch of the cline. The trajectory cannot cross the curve of jump down knees (dark blue) with decreasing, because it is blocked by the green fixed point curve (which almost coincides with the dark blue one in Figs. 8 and 9). The switch of from decreasing to increasing corresponds to the activation of ER (and hence HF). The rise in pulls the trajectory across the curve of jump down knees of the cline (dark blue), terminating the active phase of KE. We then switch our view to the thick red trajectory, along which increases (and decreases), corresponding to the trajectory being in the silent phase for KE, near a left branch of the cline. The trajectory actually reaches the curve of jump up knees (cyan), and hence KE activates before the activation of EP and HE cause to increase. But shortly after this switch, EP itself activates, yielding a rise in , and we switch back to the thick black trajectory, where we started. In fact, experiments reveal a natural variability in pocket scratch patterns. There are many experimental examples of pocket rhythms in which knee extensor becomes active just before hip extensor, at the final moments of hip flexor activity, and indeed a mean pocket rhythm computed from experimentation has this property [30]. Hence, this result provides validation that the solution that we have obtained provides a reasonable reduced representation of a pocket rhythm. Fig. 9


Conditions for Multi-functionality in a Rhythm Generating Network Inspired by Turtle Scratching.

Snyder AC, Rubin JE - J Math Neurosci (2015)

Rostral slow phase plane. Trajectory for KE for rostral scratch projected to a single slow phase plane. Coloring of curves is identical to Fig. 8. Bottom: zoomed view near the saddle-node bifurcation where the fold in the magenta fixed point curve intersects the cyan jump up knee curve for  active
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4504876&req=5

Fig9: Rostral slow phase plane. Trajectory for KE for rostral scratch projected to a single slow phase plane. Coloring of curves is identical to Fig. 8. Bottom: zoomed view near the saddle-node bifurcation where the fold in the magenta fixed point curve intersects the cyan jump up knee curve for active
Mentions: The weights of synapses onto KE are more interesting. To understand how these are constrained, we can focus on the reduced model, which maintains four distinct synaptic weights from the interneurons onto KE. With the convenient viewpoint that we have established, it is now helpful to consider the details of the trajectories for pocket scratch (Fig. 8) and rostral scratch (shown in Fig. 9 in a two-dimensional view analogous to the bottom panel of Fig. 8) for our baseline parameter choices. Recall that in the pocket rhythm, KE activates with HE, here represented by the activation of EP. When EP becomes active and the thick black part of the trajectory starts, decreases, corresponding to the trajectory being in the active phase for KE, near a right branch of the cline. The trajectory cannot cross the curve of jump down knees (dark blue) with decreasing, because it is blocked by the green fixed point curve (which almost coincides with the dark blue one in Figs. 8 and 9). The switch of from decreasing to increasing corresponds to the activation of ER (and hence HF). The rise in pulls the trajectory across the curve of jump down knees of the cline (dark blue), terminating the active phase of KE. We then switch our view to the thick red trajectory, along which increases (and decreases), corresponding to the trajectory being in the silent phase for KE, near a left branch of the cline. The trajectory actually reaches the curve of jump up knees (cyan), and hence KE activates before the activation of EP and HE cause to increase. But shortly after this switch, EP itself activates, yielding a rise in , and we switch back to the thick black trajectory, where we started. In fact, experiments reveal a natural variability in pocket scratch patterns. There are many experimental examples of pocket rhythms in which knee extensor becomes active just before hip extensor, at the final moments of hip flexor activity, and indeed a mean pocket rhythm computed from experimentation has this property [30]. Hence, this result provides validation that the solution that we have obtained provides a reasonable reduced representation of a pocket rhythm. Fig. 9

Bottom Line: We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch.Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay.This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA, acs73@pitt.edu.

ABSTRACT
Rhythmic behaviors such as breathing, walking, and scratching are vital to many species. Such behaviors can emerge from groups of neurons, called central pattern generators, in the absence of rhythmic inputs. In vertebrates, the identification of the cells that constitute the central pattern generator for particular rhythmic behaviors is difficult, and often, its existence has only been inferred. For example, under experimental conditions, intact turtles generate several rhythmic scratch motor patterns corresponding to non-rhythmic stimulation of different body regions. These patterns feature alternating phases of motoneuron activation that occur repeatedly, with different patterns distinguished by the relative timing and duration of activity of hip extensor, hip flexor, and knee extensor motoneurons. While the central pattern generator network responsible for these outputs has not been located, there is hope to use motoneuron recordings to deduce its properties. To this end, this work presents a model of a previously proposed central pattern generator network and analyzes its capability to produce two distinct scratch rhythms from a single neuron pool, selected by different combinations of tonic drive parameters but with fixed strengths of connections within the network. We show through simulation that the proposed network can achieve the desired multi-functionality, even though it relies on hip unit generators to recruit appropriately timed knee extensor motoneuron activity, including a delay relative to hip activation in rostral scratch. Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay. This framework is harnessed to consider bistability and to make predictions about the responses of the scratch rhythms to input changes for future experimental testing.

No MeSH data available.


Related in: MedlinePlus