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A reaction-diffusion model of cholinergic retinal waves.

Lansdell B, Ford K, Kutz JN - PLoS Comput. Biol. (2014)

Bottom Line: Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials.In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character.The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America.

ABSTRACT
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

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Construction of traveling wave-front.A. Fast-slow dynamics in the canonical Fitzhugh-Nagumo model of action potential generation. Black curve represents a trajectory of an action potential through phase space, in which a fast transition occurs between the rest (blue dot) and excited state (green dot), followed by slow excited dynamics (green to purple dot), another fast transition between the excited and refractory state (purple to yellow), and slow dynamics while refractory (yellow to black). Red arrows represent flow lines, and the blue curve is the  cline which defines the slow manifold ( cline not drawn for clarity). B. The fast system here is described by three dynamical variables (, , and ). Shown here is the trajectory connecting the rest (blue) and excited (green) fixed points, defining the wavefront. C. Temporal voltage dynamics of the wave front.
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pcbi-1003953-g003: Construction of traveling wave-front.A. Fast-slow dynamics in the canonical Fitzhugh-Nagumo model of action potential generation. Black curve represents a trajectory of an action potential through phase space, in which a fast transition occurs between the rest (blue dot) and excited state (green dot), followed by slow excited dynamics (green to purple dot), another fast transition between the excited and refractory state (purple to yellow), and slow dynamics while refractory (yellow to black). Red arrows represent flow lines, and the blue curve is the cline which defines the slow manifold ( cline not drawn for clarity). B. The fast system here is described by three dynamical variables (, , and ). Shown here is the trajectory connecting the rest (blue) and excited (green) fixed points, defining the wavefront. C. Temporal voltage dynamics of the wave front.

Mentions: In a moving frame with speed , stationary solutions which connect the rest and excited fixed points are heteroclinic orbits which represent traveling front solutions. The basic idea of the wave front construction is outlined in Fig. 3.


A reaction-diffusion model of cholinergic retinal waves.

Lansdell B, Ford K, Kutz JN - PLoS Comput. Biol. (2014)

Construction of traveling wave-front.A. Fast-slow dynamics in the canonical Fitzhugh-Nagumo model of action potential generation. Black curve represents a trajectory of an action potential through phase space, in which a fast transition occurs between the rest (blue dot) and excited state (green dot), followed by slow excited dynamics (green to purple dot), another fast transition between the excited and refractory state (purple to yellow), and slow dynamics while refractory (yellow to black). Red arrows represent flow lines, and the blue curve is the  cline which defines the slow manifold ( cline not drawn for clarity). B. The fast system here is described by three dynamical variables (, , and ). Shown here is the trajectory connecting the rest (blue) and excited (green) fixed points, defining the wavefront. C. Temporal voltage dynamics of the wave front.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4256014&req=5

pcbi-1003953-g003: Construction of traveling wave-front.A. Fast-slow dynamics in the canonical Fitzhugh-Nagumo model of action potential generation. Black curve represents a trajectory of an action potential through phase space, in which a fast transition occurs between the rest (blue dot) and excited state (green dot), followed by slow excited dynamics (green to purple dot), another fast transition between the excited and refractory state (purple to yellow), and slow dynamics while refractory (yellow to black). Red arrows represent flow lines, and the blue curve is the cline which defines the slow manifold ( cline not drawn for clarity). B. The fast system here is described by three dynamical variables (, , and ). Shown here is the trajectory connecting the rest (blue) and excited (green) fixed points, defining the wavefront. C. Temporal voltage dynamics of the wave front.
Mentions: In a moving frame with speed , stationary solutions which connect the rest and excited fixed points are heteroclinic orbits which represent traveling front solutions. The basic idea of the wave front construction is outlined in Fig. 3.

Bottom Line: Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials.In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character.The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America.

ABSTRACT
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

Show MeSH
Related in: MedlinePlus