## Which formalism to use for modeling voltage-dependent conductances ?

#### Alain Destexhe and John R. Huguenard

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

## Abstract:

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 the behavior of the T-current in voltage-clamp and generate
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.

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