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\begin{document}
\Large
Nerve cells (Hodgkin-Huxley Equations)

\begin{equation}
 C_m {d\phi\over dt} =  - \bar g_{Na} m^3h(\phi - V_{Na}) -  \bar g_K n^4(\phi -
    V_K) - g_L(\phi - V_L) + I_{\rm app}, \label{eq:HH}
\end{equation}

\noindent
and
\begin{eqnarray}
    {dm \over dt} &=& \alpha_m(1-m) - \beta_m m,\label{excit12}\\
    {dn \over dt} &=& \alpha_n(1-n) - \beta_n n,\label{excit13}\\
    {dh \over dt} &=& \alpha_h(1-h) - \beta_h h.\label{excit14}
\end{eqnarray}
The specific functions $\alpha$ and $\beta$ proposed by Hodgkin and 
Huxley were (in units of ms$^{-1}$)
%
\begin{eqnarray}
    \alpha_m &=& 0.1\, {25 - \phi \over \exp\left({25 -\phi \over
                                  10}\right)-1},      \label{eq:am}\\ 
    \beta_m &=& 4\, \exp\left({-\phi \over 18}\right),      \label{eq:bm}\\
    \alpha_h &=& 0.07\, \exp\left({-\phi\over 20}\right),    \label{eq:ah}
        \\
    \beta_h &=& {1\over\exp({30-\phi\over 10})+1},       \label{eq:bh} \\
    \alpha_n &=& 0.01\, {10-\phi\over \exp({10-\phi\over
                        10})-1},                    \label{eq:an}\\ 
    \beta_n &=& 0.125\, \exp\left({-\phi\over 80}\right).  \label{eq:bn}
\end{eqnarray}
\newpage

Equations for $m, n, h$ can be written as
\begin{equation}
    \tau_n(\phi){dw \over dt} = w_\infty(\phi) - w, w = m, n, {\rm or} h\label{excit7}
\end{equation}

\end{document}
