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Y. Kamiyama, S. Usui; A Stochastic Spike Generation Model of the Retinal Ganglion Cell . Invest. Ophthalmol. Vis. Sci. 2003;44(13):5189.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: The ganglion cells of the vertebrate retina form the pathway by which the retina communicates with the visual cortex. The ganglion cells convert the graded potentials into a pattern of spikes whose characteristics is modulated by the synaptic and membrane currents. Voltage clamp studies of retinal ganglion cells have identified voltage- or ion-gated currents, which appear to play a role in generating spikes. In the previous studies, the ionic conductances have been modeled by means of deterministic differential equations similar to the Hodgkin-Huxley formulation (Hodgkin & Huxley, 1952, Fohlmeister & Miller, 1997). Recently, however, it was suggested that the stochastic properties of ionic channels are critical in determining the reliability and accuracy of the neuron firing (Schneidman et al., 1998). It is important, therefore, to clarify the relationship between membrane excitability and channel stochastics in the retinal ganglion cells. Methods: There are at least five ionic currents in the ganglion cell soma, namely voltage-gated sodium current (INa), calcium current (ICa), transient outward current (IA), Ca-activated current (IK(Ca)), and the delayed rectifying potassium current (IK). We developed a stochastic model of retinal ganglion cells, based on discrete stochastic ion channels represented by n-state Markov processes, i.e., Na channel by 8-states, Ca channel by 4-states, A channel by 8-states and K channel by 5-states. We assumed that K(Ca) and leakage channels do not exhibit stochastic characteristics in the present model. To simulate the channel behavior, we set random numbers for the initial state that the channel occupies, the duration of the state and the subsequent state in each time step. Results: Voltage clamp simulations show that as the size of membrane area increases, the response from the stochastic model shows a similar behavior predicted by the deterministic equations. Current clamp simulations show that the reliability and accuracy of spike patterns are highly correlated with the characteristics of the input current. Conclusions: The results suggest that the stochastic properties of ion channels play an important role in determining the firing patterns of retinal ganglion cells.
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