Hodgkin-Huxley Equation

\begin{eqnarray} \frac{dV}{dt} &=& [I - \bar{g}_{Na} m^3 h (V-V_{Na}) - \bar{g}_K n^4 (V-V_K) - g_L (V-V_L)]/C, \\ \\ \frac{dn}{dt} &=& \alpha_n(V) (1-n) - \beta_n(V) n, \\ \\ \frac{dm}{dt} &=& \alpha_m(V) (1-m) - \beta_m(V) m, \\ \\ \frac{dh}{dt} &=& \alpha_h(V) (1-h) - \beta_h(V) h, \end{eqnarray}

where \begin{eqnarray} \alpha_n(V) = \frac{0.01 (V+55)}{1-\exp[-(V+55)/10]}, && \beta_n(V) = 0.125 \exp[-(V+65)/80], \\ \\ \alpha_m(V) = \frac{0.1 (V+40)}{1-\exp[-(V+40)/10]}, && \beta_m(V) = 4 \exp[-(V+65)/18], \\ \\ \alpha_h(V) = 0.07 \exp[-(V+65)/20], && \beta_h(V) = \frac{1}{1+\exp[-(V+35)/10]}. \end{eqnarray}
\begin{eqnarray} V &:& \qquad \mbox{membrane voltage (mV)} \\ n, m, h &:& \qquad \mbox{``gating variables" giving membrane permeability} \\ I &:& \qquad \mbox{electrical current into neuron} \end{eqnarray}

CLOSE WINDOW