Which formalism to use for modeling voltage-dependent conductances?
Alain Destexhe and John R. Huguenard

In: Computational Neuroscience: Realistic Modeling forExperimentalists, Edited by E. DeSchutter, CRC Press, Boca Raton FL, 2000,pp. 129-157.

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In this chapter, we compare different representations for modeling voltage-dependent currents and delineate some of the differences between these representations. In the case of sodium channels, models of increasing complexity, from simplified two-state representations to multistate Markov diagrams, can capture some of the features of sodium channels and of action potentials. Which model to chose depends on the type of experimental data available and its level of precision. It is clear that a two-state scheme cannot capture the features of single-channel recordings, which require Markov models of sufficient complexity to account for the data. On the other hand, we show that even simplified two- or three-state representations can capture phenomena such as action potentials. If the principal requirement is to generate action potentials, it is therefore not necessary to include all the complexity of the most sophisticated Markov diagrams of channels and simplified representations appears sufficient. This simplistic approach may be adequate for models involving large-scale networks of thousands of cells, for which computational efficiency is a more important concern than reproducing all the microscopic features of the channels.

In the case of the T-current, we show that various formalisms, such as empirical Hodgkin-Huxley type models, thermodynamic models and Markov models, can capture he behavior of the T-current in voltage-clamp and enerate low-threshold spikes. In this case, Markov models are probably more accurate because they also account for single-channel recordings, while Hodgkin-Huxley type models do not. The voltage-clamp data shown here were obtained in thalamic neurons and, for the particular case of these data, they were best modeled by a Hodgkin-Huxley type model in which rate constants were fit to experimental data using empirical functions of voltage. The best physically-plausible approach to capture these data is to use templates taken from nonlinear thermodynamic models, which provide a fitting of comparable quality to empirical functions. We therefore conclude that nonlinear thermodynamic models should be used to yield representations that are consistent with experimental data while having a plausible biophysical interpretation.