In this paper we establish limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamics coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation, and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to numerically estimate the impact of channel noise both on frequency and spike timing coding.

We examined the functional properties of a low-voltage-activated (LVA) calcium current in ganglion cells of the neotenous tiger salamander (Ambystoma tigrinum) retina. Our analysis was based on whole-cell recordings from acutely dissociated ganglion cell bodies identified by retrograde dye injections. Using a continuously perfused cell preparation, the LVA current was isolated with the use of potassium channel blocking agents added to the bathing medium and the pipette solution, while tetrodotoxin was added to the bathing medium to block Na+ channels. Approximately 70% of ganglion cells had an easily identified LVA current. The LVA current activated at membrane potentials more positive than −90 mV, and inactivated rapidly. It was relatively insensitive to nickel (IC50 > 500 μM) and amiloride (IC50 > 750 μM). Voltage- and current-clamp studies allowed us to generate a model of this current using the NEURON simulation program. Studies were also carried out to measure the LVA Ca2+ current in ganglion cells with dendrites to confirm that it had a significant dendritic representation. Physiological mechanisms that may depend on LVA Ca2+ currents are discussed with an emphasis on the role that dendrites play in ganglion cell function.