The linear and non-linear relationships between action potential discharge rates and membrane potential in model vestibular neurons

Abstract

Methods for determining empirical linear transfer functions of experimentally obtained or model vestibular neurons from the modulation of their discharge firing rate by current input have been developed and shown to distinguish between regularly firing neurons with prominent after hyperpolarizations, AHP (Type A), and cells with more complex AHP's (Type B). An increase in magnitude of the modulated spike discharge rate with frequency has been observed to be greater in Type B compared to Type A neurons. In order to better interpret this finding, simulations of spike frequency modulation were done with known Hodgkin-Huxley type neuronal models consisting of non-linear differential equations that show the essential behavior of vestibular neurons, namely previously published Type A and B neuronal models (AvRon and Vidal, 1999). An empirical spike rate transfer function was obtained from the analysis of the spike rate modulation at different stimulating sinusoidal frequencies, and was compared with the theoretical linear transfer function obtained from the exact linearized equations and type B neuronal models. These linearized theoretical frequency domain functions reveal the underlying voltage dependent conductances by showing resonant behavior, increased impedance with activation of negative conductances and specific kinetic responses dependent on the time constants of the active conductances. It is shown that the theoretical linear transfer functions can be approximated by empirical spike rate transfer functions, which indicates that the basic strategy of this analysis can be applied to data from real neurons. The simulations demonstrate that such an approach is a valid experimental method that allows one to estimate membrane properties from frequency modulation of discharge rates measured extracellularly.