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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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Power-law distributed wave-size retinal waves.A. Parameter space in which avalanches are expected (gray, Equation 3) and three sample points B. Wave size distributions (points) following 5000 s of simulation on a 128128 domain for specified values of  and . Solid lines represent log-linear least-squares lines of best fit, having slopes:  (, green),  (, red) and  (, blue) C. Correlation in membrane potential between cells of a given distance apart.
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pcbi-1003953-g006: Power-law distributed wave-size retinal waves.A. Parameter space in which avalanches are expected (gray, Equation 3) and three sample points B. Wave size distributions (points) following 5000 s of simulation on a 128128 domain for specified values of and . Solid lines represent log-linear least-squares lines of best fit, having slopes: (, green), (, red) and (, blue) C. Correlation in membrane potential between cells of a given distance apart.

Mentions: In this regime, retinal wave, or forest fire, sizes are characterized by a power-law distribution with scaling exponent of approximately (simulation based [32], theoretical based [33], [34]). Parameters which have the largest and most direct impact on and are the per cell spontaneous firing rate , and the slow refractory variable (refer to Fig. 5): these are the parameters which best determine when criticality may be observed. Fig. 6 demonstrates that, within the region described by Equation (3), wave sizes distributions approximately follow a power law with an estimated exponent close to the expected . Conversely, simulations performed outside this parameter region are sub-critical and do not follow an approximate power-law. The same behaviour is observed when the distribution of wave duration (or lifetimes) are considered (Figure S4). This is further made clear by looking at the correlation in voltage activity between cells of a given distance from one another (Fig. 6C). Parameters for which power-laws are observed produce an initially high, but sharply decaying correlation function, while the sub-critical parameter set produces significantly less correlated activity. This is indicative of the smaller, more localized wave activity expected in a sub-critical system.


A reaction-diffusion model of cholinergic retinal waves.

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

Power-law distributed wave-size retinal waves.A. Parameter space in which avalanches are expected (gray, Equation 3) and three sample points B. Wave size distributions (points) following 5000 s of simulation on a 128128 domain for specified values of  and . Solid lines represent log-linear least-squares lines of best fit, having slopes:  (, green),  (, red) and  (, blue) C. Correlation in membrane potential between cells of a given distance apart.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003953-g006: Power-law distributed wave-size retinal waves.A. Parameter space in which avalanches are expected (gray, Equation 3) and three sample points B. Wave size distributions (points) following 5000 s of simulation on a 128128 domain for specified values of and . Solid lines represent log-linear least-squares lines of best fit, having slopes: (, green), (, red) and (, blue) C. Correlation in membrane potential between cells of a given distance apart.
Mentions: In this regime, retinal wave, or forest fire, sizes are characterized by a power-law distribution with scaling exponent of approximately (simulation based [32], theoretical based [33], [34]). Parameters which have the largest and most direct impact on and are the per cell spontaneous firing rate , and the slow refractory variable (refer to Fig. 5): these are the parameters which best determine when criticality may be observed. Fig. 6 demonstrates that, within the region described by Equation (3), wave sizes distributions approximately follow a power law with an estimated exponent close to the expected . Conversely, simulations performed outside this parameter region are sub-critical and do not follow an approximate power-law. The same behaviour is observed when the distribution of wave duration (or lifetimes) are considered (Figure S4). This is further made clear by looking at the correlation in voltage activity between cells of a given distance from one another (Fig. 6C). Parameters for which power-laws are observed produce an initially high, but sharply decaying correlation function, while the sub-critical parameter set produces significantly less correlated activity. This is indicative of the smaller, more localized wave activity expected in a sub-critical system.

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