Mitchell-Schaeffer Revised

To make the Mitchell-Schaeffer look more like a cardiac ionic model, take

$$C_m{dv\over dt} = g_{Na}hm^2(V_{Na}-v) +g_K(V_K-v),$$ (23)

$${dh\over dt} = a_h(v)(1- h) - b_h(v)h$$ (24)

where

$$m(v) = \left\{\begin{array}{cc} 0, &v<0\\ v,&0<v<1\\ 1,&v>1\end{array}\right.$$ (25)

To match the M-S model, we take

$${g_{Na}\over C_m} = {1\over \tau_{in}} = {1\over 0.3} = 3.33... ...\over C_m} = {1\over \tau_{out}} = {1\over 6} = 0.16 /{\rm ms}$$ (26)

We also take

$$a(v) = {1-f\over\tau_{open}+(\tau_{close}-\tau_{open})f},\qquad b(v) = {f\over\tau_{open}+(\tau_{close}-\tau_{open})f}$$ (27)

where

$$f(v) = {1\over 2}(1+\tanh(\kappa(v-v_{gate})),$$ (28)

so that $h_\infty = 1-f(v)$, and $\tau_h = {\tau_{open}+(\tau_{close}-\tau_{open})f}$. If $\kappa \rightarrow \infty$, this reduces exactly to the M-S model. In the M-S model, $\tau_{open} = 120$ms, $\tau_{close} = 150$ms, and $v_{gate} = 0.13$.

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