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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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Model produces realistic cholinergic waves.A. Network dynamics showing spatiotemporal patterns of retinal waves B. Distribution of wave sizes, speeds, durations and inter-wave intervals from 2500 s of simulation. Mean wave size is 0.017 mm(0.059 mm), mean wave speed is 0.11 mm/s (0.022 mm/s), mean wave duration is 0.63 s (0.90 s), and mean inter-wave interval is 49 s (25 s). C. SACs exhibit variable participation in waves. Pearson correlation coefficient between a cell in the center of the domain and all other cells. The correlation coefficient for each variable is plotted as a function of euclidean distance between cells. Computed using one 2500 s simulation, with activity recorded every 0.1 s. Solid curve represents a loess moving average estimate of mean correlation as a function of distance. Shaded region highlights all points within one standard deviation of this mean curve.
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pcbi-1003953-g002: Model produces realistic cholinergic waves.A. Network dynamics showing spatiotemporal patterns of retinal waves B. Distribution of wave sizes, speeds, durations and inter-wave intervals from 2500 s of simulation. Mean wave size is 0.017 mm(0.059 mm), mean wave speed is 0.11 mm/s (0.022 mm/s), mean wave duration is 0.63 s (0.90 s), and mean inter-wave interval is 49 s (25 s). C. SACs exhibit variable participation in waves. Pearson correlation coefficient between a cell in the center of the domain and all other cells. The correlation coefficient for each variable is plotted as a function of euclidean distance between cells. Computed using one 2500 s simulation, with activity recorded every 0.1 s. Solid curve represents a loess moving average estimate of mean correlation as a function of distance. Shaded region highlights all points within one standard deviation of this mean curve.

Mentions: Simulations show qualitatively that the model produces realistic waves (Fig. 2A; Movie S1). Waves propagate without bias in their initiation region or direction (due to the translational and rotational symmetry of the equations), occur on average once every 60 s, propagate at an average speed of 150 per second, and exhibit a broad distribution of wave sizes, all of which are consistent with in vitro recordings of mice retinal waves [7] (Fig. 2B). The uniform distribution of initiation points is expected given the homogeneity of the connectivities (diffusion coefficient) of the model. Some studies show that both in vivo and in vitro recordings contain a directional bias in propagation [19], [20], which could be modelled with a drift-diffusion model. However, since there is presently no physiological model for how this directionality occurs, we do not attempt to address these issues here.


A reaction-diffusion model of cholinergic retinal waves.

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

Model produces realistic cholinergic waves.A. Network dynamics showing spatiotemporal patterns of retinal waves B. Distribution of wave sizes, speeds, durations and inter-wave intervals from 2500 s of simulation. Mean wave size is 0.017 mm(0.059 mm), mean wave speed is 0.11 mm/s (0.022 mm/s), mean wave duration is 0.63 s (0.90 s), and mean inter-wave interval is 49 s (25 s). C. SACs exhibit variable participation in waves. Pearson correlation coefficient between a cell in the center of the domain and all other cells. The correlation coefficient for each variable is plotted as a function of euclidean distance between cells. Computed using one 2500 s simulation, with activity recorded every 0.1 s. Solid curve represents a loess moving average estimate of mean correlation as a function of distance. Shaded region highlights all points within one standard deviation of this mean curve.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003953-g002: Model produces realistic cholinergic waves.A. Network dynamics showing spatiotemporal patterns of retinal waves B. Distribution of wave sizes, speeds, durations and inter-wave intervals from 2500 s of simulation. Mean wave size is 0.017 mm(0.059 mm), mean wave speed is 0.11 mm/s (0.022 mm/s), mean wave duration is 0.63 s (0.90 s), and mean inter-wave interval is 49 s (25 s). C. SACs exhibit variable participation in waves. Pearson correlation coefficient between a cell in the center of the domain and all other cells. The correlation coefficient for each variable is plotted as a function of euclidean distance between cells. Computed using one 2500 s simulation, with activity recorded every 0.1 s. Solid curve represents a loess moving average estimate of mean correlation as a function of distance. Shaded region highlights all points within one standard deviation of this mean curve.
Mentions: Simulations show qualitatively that the model produces realistic waves (Fig. 2A; Movie S1). Waves propagate without bias in their initiation region or direction (due to the translational and rotational symmetry of the equations), occur on average once every 60 s, propagate at an average speed of 150 per second, and exhibit a broad distribution of wave sizes, all of which are consistent with in vitro recordings of mice retinal waves [7] (Fig. 2B). The uniform distribution of initiation points is expected given the homogeneity of the connectivities (diffusion coefficient) of the model. Some studies show that both in vivo and in vitro recordings contain a directional bias in propagation [19], [20], which could be modelled with a drift-diffusion model. However, since there is presently no physiological model for how this directionality occurs, we do not attempt to address these issues here.

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