MiS Preprint Repository

Analysis of the firing activity of serotonergic neurons of the dorsal raphe nucleus by means of a computational model requires a knowledge of the electrophysiological properties of the various ionic components of the membrane current. In formulating such a mathematical model, whether using sets of differential equations or software packages, it is essential to have accurate data for the dynamical properties of each voltage-gated ion current, lest predictions and properties of the model be unreliable. These properties include the activation and, if present, inactivation functions which are often given as Boltzmann curves, defined by a half-activation potential and a slope factor. Experimental voltage-clamp data is often used to produce a Boltzmann function which fits the I/${\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ or G/${\mathrm{G}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ data. We outline theory for accurately obtaining the activation function in general. An illustrative example is given using voltage-clamp data for a cell of the rat dorsal raphe nucleus (DRN). We estimate the form of the current, conductance, time constants and steady state activation and inactivation functions for the fast transient potassium current ${\mathrm{I}}_{\mathrm{A}}$. It is found that for activation, the half-activation potential is -52.5 mV with slope factor 16.5 mV, whereas for inactivation the corresponding quantities are -91.5 mV and -9.3 mV. The current is of the form $\bar{g}(V-V_{rev})m^{4}h$, with $\bar{g}=20.5$ nS.