Calcium channel dynamics limit synaptic release in response to prosthetic stimulation with sinusoidal waveforms

Extracellular electric stimulation with sinusoidal waveforms has been shown to allow preferential activation of individual types of retinal neurons by varying stimulus frequency. It is important to understand the mechanisms underlying this frequency dependence as a step toward improving methods of preferential activation. In order to elucidate these mechanisms, we implemented a morphologically realistic model of a retinal bipolar cell and measured the response to extracellular stimulation with sinusoidal waveforms. We compared the frequency response of a passive membrane model to the kinetics of voltage-gated calcium channels that mediate synaptic release. The passive electrical properties of the membrane exhibited lowpass filtering with a relatively high cutoff frequency (nominal value = 717 Hz). This cutoff frequency was dependent on intra-axonal resistance, with shorter and wider axons yielding higher cutoff frequencies. However, we found that the cutoff frequency of bipolar cell synaptic release was primarily limited by the relatively slow opening kinetics of L- and T-type calcium channels. The cutoff frequency of calcium currents depended nonlinearly on stimulus amplitude, but remained lower than the cutoff frequency of the passive membrane model for a large range of membrane potential fluctuations. These results suggest that while it may be possible to modulate the membrane potential of bipolar cells over a wide range of stimulus frequencies, synaptic release will only be initiated at the lower end of this range.