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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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Isolated SAC dynamics.Starburst amacrine cells obey Morris-Lecar dynamics with voltage term , refractory variable , sAHP variable  and acetylcholine concentration . A. Time course of individual SAC dynamics following current injections of indicated size, injected at  for 1.5 s (shown in grey). Model SACs' refractory period shows dependence on amount of current injected. B. Single cell dynamics showing sparse spontaneous depolarizations. Different colors represent different SACs. C. Distribution of inter-event intervals in stochastic simulation of isolated SAC. A threshold of −50 mV was employed. Bar plot shows mean and standard deviation.
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pcbi-1003953-g001: Isolated SAC dynamics.Starburst amacrine cells obey Morris-Lecar dynamics with voltage term , refractory variable , sAHP variable and acetylcholine concentration . A. Time course of individual SAC dynamics following current injections of indicated size, injected at for 1.5 s (shown in grey). Model SACs' refractory period shows dependence on amount of current injected. B. Single cell dynamics showing sparse spontaneous depolarizations. Different colors represent different SACs. C. Distribution of inter-event intervals in stochastic simulation of isolated SAC. A threshold of −50 mV was employed. Bar plot shows mean and standard deviation.

Mentions: As in previous models [7], [11], individual SACs are modeled according to Morris-Lecar dynamics [18], with an additional sAHP current activated by depolarization and subsequent calcium influx. The sAHP current generates recovery times on the order of a minute. Each cell is assigned the same recovery time scale, and the dynamics are such that recovery is minimally activity-dependent (Fig. 1A). Previous theoretical models [10], [11] and experimental observations [9] show that larger depolarizations increase sAHP duration. The lack of a strongly activity-dependent refractory period in our model does not affect the its ability to generate physiological waves. A noisy, excitatory current induces spontaneous depolarizations (Fig. 1B) at an average rate of once every 15 minutes per isolated cell, consistent with recordings in mice (Fig. 1C).


A reaction-diffusion model of cholinergic retinal waves.

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

Isolated SAC dynamics.Starburst amacrine cells obey Morris-Lecar dynamics with voltage term , refractory variable , sAHP variable  and acetylcholine concentration . A. Time course of individual SAC dynamics following current injections of indicated size, injected at  for 1.5 s (shown in grey). Model SACs' refractory period shows dependence on amount of current injected. B. Single cell dynamics showing sparse spontaneous depolarizations. Different colors represent different SACs. C. Distribution of inter-event intervals in stochastic simulation of isolated SAC. A threshold of −50 mV was employed. Bar plot shows mean and standard deviation.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003953-g001: Isolated SAC dynamics.Starburst amacrine cells obey Morris-Lecar dynamics with voltage term , refractory variable , sAHP variable and acetylcholine concentration . A. Time course of individual SAC dynamics following current injections of indicated size, injected at for 1.5 s (shown in grey). Model SACs' refractory period shows dependence on amount of current injected. B. Single cell dynamics showing sparse spontaneous depolarizations. Different colors represent different SACs. C. Distribution of inter-event intervals in stochastic simulation of isolated SAC. A threshold of −50 mV was employed. Bar plot shows mean and standard deviation.
Mentions: As in previous models [7], [11], individual SACs are modeled according to Morris-Lecar dynamics [18], with an additional sAHP current activated by depolarization and subsequent calcium influx. The sAHP current generates recovery times on the order of a minute. Each cell is assigned the same recovery time scale, and the dynamics are such that recovery is minimally activity-dependent (Fig. 1A). Previous theoretical models [10], [11] and experimental observations [9] show that larger depolarizations increase sAHP duration. The lack of a strongly activity-dependent refractory period in our model does not affect the its ability to generate physiological waves. A noisy, excitatory current induces spontaneous depolarizations (Fig. 1B) at an average rate of once every 15 minutes per isolated cell, consistent with recordings in mice (Fig. 1C).

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