Dendritic Compartment  Hodgkin-Huxley-A (HHA) Model  Equations for Gating Variables

Somatic Adaptation Current

  Calcium accumulation is modeled as a steeply voltage-dependent process with a long time constant, reflecting the entry of calcium ions through high-voltage activated channels during the spikes: $$\tau_{\text{adapt}} \frac{d [\text{Ca}^{2+}]}{dt} = - [\text{Ca}^{2+}] + \frac{1}{1 + \exp [ - (V+10 ) /0.5]},$$ where the time constant $\tau_{\text{adapt}} = 50$ ms is based on the work of Ahmed et al. (1997) in cat visual cortex. Since the midpoint voltage $V_{\frac{1}{2}} = -10 \; \text{mV}$ of the sigmoid is well above the firing threshold and the slope of $0.5 \; \text{mV}$ is extremely steep, calcium entry into the somatic compartment is effectively restricted to occur only during an action potential.

The linearly buffered calcium concentration drives the adaptation conductance as follows:

$$\tau_{\text{K(Ca)}} \frac{d}{dt} g_{\text{adapt}} = - g_{\text{adapt}} + A \, [\text{Ca}^{2+}]$$ where $\tau_{\text{K(Ca)}} = 1.5$ ms, and $A$ is a constant given by $A = 60.0$ $\text{mS} \; \text{cm}^{-2} \; \text{mol}^{-1}$.

 

1/14/1998