Modeling neuronal activity in relation to experimental voltage-/patch-clamp recordings.

A mechanism-based, Hodgkin–Huxley-type modeling approach is proposed that allows connecting the key parameters of experimental voltage-/patch-clamp data directly to the major control values of the model. The objective of this paper is to facilitate the use of mathematical modeling in supplement to electrophysiological recordings. Typical recordings from current-clamp, whole-cell voltage-clamp, and single-channel patch-clamp experiments are illustrated by means of a simplified computer model designed for life science education. These examples demonstrate that the “rate constants”, on which the original Hodgkin–Huxley equations are built up, are difficult, in most experiments even impossible, to extract from experimental data. As the combination of the two exponential rate constants leads to sigmoid activation curves, they can be replaced by sigmoid voltage dependencies, mostly presented in form of Boltzmann functions. Conversely, connecting whole-cell and single-channel patch-clamp simulations, the Boltzmann functions, can be related to exponentially voltage dependent probability factors of ion channel transition rates. The thereby introduced small variability of the activation values suggests that the power functions of the activation variables in the current equations can be neglected. Eliminating the rate constants and the power functions can be physiologically justified and makes the model easier to handle, especially in context with experimental data. Further possibilities of dimension reduction as well as model extensions are discussed.