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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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Parameter regimes which produce propagating activity.Numerical determination of retinal wave excitability threshold for different timescales  and excitability threshold determined through singular perturbation analysis, both as functions of , . Each point on each curve indicates a point in parameter space in which the wavefront transitions from propagating to receding. Points in parameter space below each curve are therefore not excitable, while those above are excitable.
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pcbi-1003953-g004: Parameter regimes which produce propagating activity.Numerical determination of retinal wave excitability threshold for different timescales and excitability threshold determined through singular perturbation analysis, both as functions of , . Each point on each curve indicates a point in parameter space in which the wavefront transitions from propagating to receding. Points in parameter space below each curve are therefore not excitable, while those above are excitable.

Mentions: Parameters for which a heteroclinic orbit exists for a positive speed are parameters which support propagating activity. Parameters at the transition between a propagating, positive speed, traveling front and a receding, negative speed, traveling front (that is, when ) represent an excitability threshold. Fig. 4 demonstrates this excitability threshold over a two dimensional parameter space, computed using the above framework and, for comparison, computed using numerical simulations of the model for different values of (the separation of fast and slow time scales). The analysis and simulations exhibit the same general behavior. The analysis method presented here is a more direct method for determining wave propagation because it is not necessary to set up and solve numerically a solution for each point in parameter space to be queried. Refer to Methods for more detail on the numerical simulations.


A reaction-diffusion model of cholinergic retinal waves.

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

Parameter regimes which produce propagating activity.Numerical determination of retinal wave excitability threshold for different timescales  and excitability threshold determined through singular perturbation analysis, both as functions of , . Each point on each curve indicates a point in parameter space in which the wavefront transitions from propagating to receding. Points in parameter space below each curve are therefore not excitable, while those above are excitable.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003953-g004: Parameter regimes which produce propagating activity.Numerical determination of retinal wave excitability threshold for different timescales and excitability threshold determined through singular perturbation analysis, both as functions of , . Each point on each curve indicates a point in parameter space in which the wavefront transitions from propagating to receding. Points in parameter space below each curve are therefore not excitable, while those above are excitable.
Mentions: Parameters for which a heteroclinic orbit exists for a positive speed are parameters which support propagating activity. Parameters at the transition between a propagating, positive speed, traveling front and a receding, negative speed, traveling front (that is, when ) represent an excitability threshold. Fig. 4 demonstrates this excitability threshold over a two dimensional parameter space, computed using the above framework and, for comparison, computed using numerical simulations of the model for different values of (the separation of fast and slow time scales). The analysis and simulations exhibit the same general behavior. The analysis method presented here is a more direct method for determining wave propagation because it is not necessary to set up and solve numerically a solution for each point in parameter space to be queried. Refer to Methods for more detail on the numerical simulations.

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