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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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Modeling biophysical manipulations.A. Synaptic connection strength  is varied. Sub plots from left to right: speed of wave front  at rest (when ) as a function of conductance , velocity indicates maximum wave-front speed since  and  is monotonically decreasing, point at which  becomes zero represents excitability threshold; wave-front speed as function of refractory variable  for three different values of ; from 5000 s of simulation of model with indicated values of  interwave-inteval; wave speed distribution; and mean wave size. B. Sub plots from left to right: dynamics of refractory variable  of individual SAC following depolarization with different sAHP timescales , black line indicates refractory value above which  and thus represents an absolute refractory time period in which SAC is not sufficiently excitable to participate in future wave activity; from 5000 s of simulation of model with indicated values of inter-wave interval; wave speed distribution; and mean wave size.
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pcbi-1003953-g005: Modeling biophysical manipulations.A. Synaptic connection strength is varied. Sub plots from left to right: speed of wave front at rest (when ) as a function of conductance , velocity indicates maximum wave-front speed since and is monotonically decreasing, point at which becomes zero represents excitability threshold; wave-front speed as function of refractory variable for three different values of ; from 5000 s of simulation of model with indicated values of interwave-inteval; wave speed distribution; and mean wave size. B. Sub plots from left to right: dynamics of refractory variable of individual SAC following depolarization with different sAHP timescales , black line indicates refractory value above which and thus represents an absolute refractory time period in which SAC is not sufficiently excitable to participate in future wave activity; from 5000 s of simulation of model with indicated values of inter-wave interval; wave speed distribution; and mean wave size.

Mentions: It is important to understand that this analysis is only for the case of a domain uniformly at rest. Of course, we would like to consider the existence of waves within a medium that is not uniformly recovered but for which some of the domain may be refractory from previous activity. Our analysis provides a necessary condition for the existence of propagating activity in this more general case: a network incapable of supporting wave propagation at rest is a network incapable of supporting wave activity when some of its cells are refractory. In this more general case, waves propagate not only if SACs are sufficiently excitable, but also if neighboring SACs are sufficiently recovered from prior depolarizations. The wave speed is then modulated by the refractory state as well (e.g.Fig. 5).


A reaction-diffusion model of cholinergic retinal waves.

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

Modeling biophysical manipulations.A. Synaptic connection strength  is varied. Sub plots from left to right: speed of wave front  at rest (when ) as a function of conductance , velocity indicates maximum wave-front speed since  and  is monotonically decreasing, point at which  becomes zero represents excitability threshold; wave-front speed as function of refractory variable  for three different values of ; from 5000 s of simulation of model with indicated values of  interwave-inteval; wave speed distribution; and mean wave size. B. Sub plots from left to right: dynamics of refractory variable  of individual SAC following depolarization with different sAHP timescales , black line indicates refractory value above which  and thus represents an absolute refractory time period in which SAC is not sufficiently excitable to participate in future wave activity; from 5000 s of simulation of model with indicated values of inter-wave interval; wave speed distribution; and mean wave size.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003953-g005: Modeling biophysical manipulations.A. Synaptic connection strength is varied. Sub plots from left to right: speed of wave front at rest (when ) as a function of conductance , velocity indicates maximum wave-front speed since and is monotonically decreasing, point at which becomes zero represents excitability threshold; wave-front speed as function of refractory variable for three different values of ; from 5000 s of simulation of model with indicated values of interwave-inteval; wave speed distribution; and mean wave size. B. Sub plots from left to right: dynamics of refractory variable of individual SAC following depolarization with different sAHP timescales , black line indicates refractory value above which and thus represents an absolute refractory time period in which SAC is not sufficiently excitable to participate in future wave activity; from 5000 s of simulation of model with indicated values of inter-wave interval; wave speed distribution; and mean wave size.
Mentions: It is important to understand that this analysis is only for the case of a domain uniformly at rest. Of course, we would like to consider the existence of waves within a medium that is not uniformly recovered but for which some of the domain may be refractory from previous activity. Our analysis provides a necessary condition for the existence of propagating activity in this more general case: a network incapable of supporting wave propagation at rest is a network incapable of supporting wave activity when some of its cells are refractory. In this more general case, waves propagate not only if SACs are sufficiently excitable, but also if neighboring SACs are sufficiently recovered from prior depolarizations. The wave speed is then modulated by the refractory state as well (e.g.Fig. 5).

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