Voltage-Clamp Frequency Domain Analysis of Nmda-Activated Neurons
Authors: Moore L. E. , Hill R. H. , Grillner S. 
Published: April 2021

Voltage and current-clamp steps were added to a sum of sine waves to measure the tetrodotoxin-insensitive membrane properties of neurons in the intact lamprey spinal cord. A systems analysis in the frequency domain was carried out on two types of cells that have very different morphologies in order to investigate the structural dependence of their electrophysiological properties. The method explicitly takes into account the geometrical shapes of (i) nearly spherical dorsal cells with one or two processes and (ii) motoneurons and interneurons that have branched dendritic structures. Impedance functions were analysed to obtain the cable properties of these in situ neurons. These measurements show that branched neurons are not isopotential and, therefore, a conventional voltage-clamp analysis is not valid. The electrophysiological data from branched neurons were curve-fitted with a lumped soma-equivalent cylinder model consisting of eight equal compartments coupled to an isopotential cell body to obtain membrane parameters for both passive and active properties. The analysis provides a quantitative description of both the passive electrical properties imposed by the geometrical structure of neurons and the voltage-dependent ionic conductances determined by ion channel kinetics. The model fitting of dorsal cells was dominated by a one-compartment resistance and capacitance in parallel (RC) corresponding to the spherical, non-branched shape of these cells. Branched neurons required a model that contained both an RC compartment and a cable that reflected the structure of the cells. At rest, the electrotonic length of the cable was about two. Uniformly distributed voltage-dependent ionic conductance sites were adequate to describe the data at different membrane potentials. The frequency domain admittance method in conjunction with a step voltage clamp was used to control and measure the oscillatory behavior induced by N-methyl-D-aspartate (NMDA) on lamprey spinal cord neurons. Voltage-clamp currents and impedance functions were measured at different membrane potentials. The impedance functions had a voltage-dependent resonance and phase shift characteristic of a negative conductance. These measurements provide a quantitative analysis of the conductances induced by NMDA in central neurons of the lamprey spinal cord and directly establish the basis of the non-linear oscillatory behavior previously observed in the presence of NMDA. NMDA was shown specifically to activate a negative and a positive conductance, both of which were markedly affected by the membrane potential. It is shown that the net current in the presence of NMDA must be considered as the algebraic sum of currents in opposite directions. The impedance functions at membrane potentials hyperpolarized by −10mV or more were described by passive properties. However, at less negative potentials the neurons showed a non-resonating enhancement of the impedance magnitude with a clear negative conductance revealed by a phase function more negative than −90°. For modest depolarizations of less than 10mV, a sharp resonance and phase function were observed. Finally, at greater depolarizations, a broader resonance with a less abrupt phase change occurred. In the potential range of NMDA-induced oscillatory behavior, the observed impedance resonance peaks were in the range of the oscillation frequencies of neurons seen under current-clamp conditions. The NMDA-induced negative conductance was reduced by the removal of Na+ without blocking an NMDA-enhanced positive conductance, which is consistent with the hypothesis that NMDA directly induces a voltage-dependent conductance to both Ca2+ and Na+. The NMDA-induced positive conductance remaining after Na+ removal is probably a consequence of the activation of a potassium conductance by increased intracellular calcium levels. The frequency of the NMDA-induced resonance was decreased by the removal of Na+. In the presence of Na+ and NMDA, the resonance is a mixture of outward and inward current kinetics, the combination of which leads to a lower peak frequency the greater the inward current. These experiments show that activation of the NMDA receptor leads to an inherently unstable condition where a negative conductance depolarizes the cell. This then turns on a repolarizing positive conductance. The activation of both the NMDA-induced inward current and a positive conductance contributes to a resonance in the impedance that will influence the inherent oscillation frequency. Finally, the voltage-dependent impedance markedly affects the cable properties of the neurons and their ability to propagate synaptic potentials.