Parameter optimization methods were used to quantitatively analyze frequency-domain-voltage-clamp data of NMDA-activated lamprey spinal neurons simultaneously over a wide range of membrane potentials. A neuronal cable model was used to explicitly take into account receptors located on the dendritic trees. The driving point membrane admittance was measured from the cell soma in response to a Fourier synthesized point voltage clamp stimulus. The data were fitted to an equivalent cable model consisting of a single lumped soma compartment coupled resistively to a series of equal dendritic compartments. The model contains voltage-dependent NMDA sensitive (INMDA), slow potassium (IK), and leakage (IL) currents. Both the passive cable properties and the voltage dependence of ion channel kinetics were estimated, including the electrotonic structure of the cell, the steady-state gating characteristics, and the time constants for particular voltage- and time-dependent ionic conductances. An alternate kinetic formulation was developed that consisted of steady-state values for the gating parameters and their time constants at half-activation values as well as slopes of these parameters at half-activation. This procedure allowed independent restrictions on the magnitude and slope of both the steady-state gating variable and its associated time constant. Quantitative estimates of the voltage-dependent membrane ion conductances and their kinetic parameters were used to solve the nonlinear equations describing dynamic responses. The model accurately predicts current clamp responses and is consistent with experimentally measured TTX-resistant NMDA-induced patterned activity. In summary, an analysis method is developed that provides a pragmatic approach to quantitatively describe a nonlinear neuronal system.

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