Chapter 2 (2) : HH Conductance Model

The previous post summarized, in somewhat qualitative terms, the HH model of the action potential. Since then, I've written up a supplement to Hille's description of their quantitative model. It is available online as HH_Conduct.pdf. It goes into a little more detail than Hille about their model. For instance, it motivates and describes the equation they actually used to fit their g_k data, thus explicitly connecting their speculative lower-level model (in terms of charged 'gating particles') to observed macroscopic conductances. The first paragraph follows.

Hodgkin and Huxley (HH) were able to reliably measure the voltage- and time-dependent changes in sodium and potassium conductance (g_na and g_k) during the action potential (Figure 2.11 [Hille]). The story that emerged from such experiments is now part of the core knowledge of all neurophysiologists. After a suprathreshold voltage step, g_na quickly rises and falls while g_k slowly increases to a steady state (Figure 2.11 [Hille]). In a cell that is not voltage-clamped, this increase in g_na causes V_m to rapidly approach E_na. However, the subsequent g_k increase, and g_na decrease, causes V_m to quickly fall back down to the resting potential near E_k. HH quantified these conductance changes in a model with explanatory and predictive power that only continues to grow. In what follows, I will describe in more detail their model of g_k and g_na.

Each time I revisit the HH corpus, I am impressed by their profound creativity, technical skills (both quantitative and experimental), and luck.