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Mechanisms of left-right coordination in mammalian locomotor pattern generation circuits: a mathematical modeling view.

Molkov YI, Bacak BJ, Talpalar AE, Rybak IA - PLoS Comput. Biol. (2015)

Bottom Line: The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations.We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them.The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, Indiana, United States of America.

ABSTRACT
The locomotor gait in limbed animals is defined by the left-right leg coordination and locomotor speed. Coordination between left and right neural activities in the spinal cord controlling left and right legs is provided by commissural interneurons (CINs). Several CIN types have been genetically identified, including the excitatory V3 and excitatory and inhibitory V0 types. Recent studies demonstrated that genetic elimination of all V0 CINs caused switching from a normal left-right alternating activity to a left-right synchronized "hopping" pattern. Furthermore, ablation of only the inhibitory V0 CINs (V0D subtype) resulted in a lack of left-right alternation at low locomotor frequencies and retaining this alternation at high frequencies, whereas selective ablation of the excitatory V0 neurons (V0V subtype) maintained the left-right alternation at low frequencies and switched to a hopping pattern at high frequencies. To analyze these findings, we developed a simplified mathematical model of neural circuits consisting of four pacemaker neurons representing left and right, flexor and extensor rhythm-generating centers interacting via commissural pathways representing V3, V0D, and V0V CINs. The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations. The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.

No MeSH data available.


Related in: MedlinePlus

Examples of intermittency in left-right phase relationships in the experimental preparation from mutant mice with selectively ablated V0V and V0D CINs.Recordings from left and right L2 and L5 roots in a V0V (A) and V0D (B) knockout mice at intermediate frequencies demonstrate occasional switching between left-right alternation and synchronization despite maintained values of drug concentration and average frequency.
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pcbi.1004270.g015: Examples of intermittency in left-right phase relationships in the experimental preparation from mutant mice with selectively ablated V0V and V0D CINs.Recordings from left and right L2 and L5 roots in a V0V (A) and V0D (B) knockout mice at intermediate frequencies demonstrate occasional switching between left-right alternation and synchronization despite maintained values of drug concentration and average frequency.

Mentions: A prediction generated from the bifurcation diagrams (Figs 5B, 7B, 13A, 14A) is the existence of regions where the system is bistable in cases when only one type of commissural pathway (V0V or V0D) is removed. As mentioned previously, in these regions the system can exist in qualitatively different states demonstrating different behaviors, i.e. left-right alternation or synchronization. When locomotor rhythm is generated at an intermediate frequency within the bistable area with a sufficient level of noise, the system can demonstrate occasional switching between left-right alternation and synchronization despite a constant value of drug concentration. Examples of such patterns recorded from experimental studies on knockout mice lacking V0V or V0D CINs are shown in Fig 15, panels A and B, respectively. This provides an additional indirect support for our model design.


Mechanisms of left-right coordination in mammalian locomotor pattern generation circuits: a mathematical modeling view.

Molkov YI, Bacak BJ, Talpalar AE, Rybak IA - PLoS Comput. Biol. (2015)

Examples of intermittency in left-right phase relationships in the experimental preparation from mutant mice with selectively ablated V0V and V0D CINs.Recordings from left and right L2 and L5 roots in a V0V (A) and V0D (B) knockout mice at intermediate frequencies demonstrate occasional switching between left-right alternation and synchronization despite maintained values of drug concentration and average frequency.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4430237&req=5

pcbi.1004270.g015: Examples of intermittency in left-right phase relationships in the experimental preparation from mutant mice with selectively ablated V0V and V0D CINs.Recordings from left and right L2 and L5 roots in a V0V (A) and V0D (B) knockout mice at intermediate frequencies demonstrate occasional switching between left-right alternation and synchronization despite maintained values of drug concentration and average frequency.
Mentions: A prediction generated from the bifurcation diagrams (Figs 5B, 7B, 13A, 14A) is the existence of regions where the system is bistable in cases when only one type of commissural pathway (V0V or V0D) is removed. As mentioned previously, in these regions the system can exist in qualitatively different states demonstrating different behaviors, i.e. left-right alternation or synchronization. When locomotor rhythm is generated at an intermediate frequency within the bistable area with a sufficient level of noise, the system can demonstrate occasional switching between left-right alternation and synchronization despite a constant value of drug concentration. Examples of such patterns recorded from experimental studies on knockout mice lacking V0V or V0D CINs are shown in Fig 15, panels A and B, respectively. This provides an additional indirect support for our model design.

Bottom Line: The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations.We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them.The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, Indiana, United States of America.

ABSTRACT
The locomotor gait in limbed animals is defined by the left-right leg coordination and locomotor speed. Coordination between left and right neural activities in the spinal cord controlling left and right legs is provided by commissural interneurons (CINs). Several CIN types have been genetically identified, including the excitatory V3 and excitatory and inhibitory V0 types. Recent studies demonstrated that genetic elimination of all V0 CINs caused switching from a normal left-right alternating activity to a left-right synchronized "hopping" pattern. Furthermore, ablation of only the inhibitory V0 CINs (V0D subtype) resulted in a lack of left-right alternation at low locomotor frequencies and retaining this alternation at high frequencies, whereas selective ablation of the excitatory V0 neurons (V0V subtype) maintained the left-right alternation at low frequencies and switched to a hopping pattern at high frequencies. To analyze these findings, we developed a simplified mathematical model of neural circuits consisting of four pacemaker neurons representing left and right, flexor and extensor rhythm-generating centers interacting via commissural pathways representing V3, V0D, and V0V CINs. The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations. The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. The model reproduced, and suggested explanation for, a series of experimental phenomena and generated predictions available for experimental testing.

No MeSH data available.


Related in: MedlinePlus