Somatic Adaptation Current  Hodgkin-Huxley-A (HHA) Model  Voltage Equation

Equations for Gating Variables

The gating variables $m, h, n, a$ and $b$ that control the flow of current through the voltage-dependent conductances obey the equations
$$\begin{gather*}\frac{d m}{dt} = \phi \bigl[ \alpha_m(V) (1-m) - \beta_m(V) ... ...a_\infty(V) - a \qquad \tau_b(V) \frac{db}{dt} = b_\infty(V) - b \end{gather*}$$
where $\phi = 3.8$ is a temperature factor reflecting the difference between $6.3\deg \text{C}$ of the original Hodgkin-Huxley experiments and the $18.5\deg \text{C}$ of the Connor & Stevens' crustacean experiments.
 

$$\begin{align*}a_{\infty}(V) & = {\biggr\{\frac{ 0.0761 * \exp \bigl[ (V +... ...24 + \frac{2.678}{ 1 + \exp\bigl[ (V+50) \bigr/16.027 \bigr]} \end{align*}$$

This choice of somatic spiking conductances allows spiking to occur at arbitrarily low firing rates, as is typically observed in cortical cells. (For further details, see the section on the current-discharge relationship.)

1/14/1998