= Solution
In the <Hodgkin-Huxley model>, $V$ is the intracellular-minus-extracellular <membrane potential>, $C_m$ is the <membrane capacitance> per unit area, and $I_{\mathrm{app}}$ is the applied inward <electric current> per unit area. A <space clamp> makes $V$ spatially uniform, leaving temporal <ordinary differential equations>. With outward ionic <electric current> positive, the <capacitance> balance is $C_m\dot V=I_{\mathrm{app}}-I_i$.
The variables $m,n,h$ lie between zero and one. They describe <sodium> activation, <potassium> activation and availability against <sodium> inactivation, respectively. Thus larger $h$ means less inactivation. Their voltage-dependent limiting values are $m_\infty,n_\infty,h_\infty$, and $\tau_m,\tau_n,\tau_h$ are their positive relaxation <time constants>.
Each ionic term has the <Ohm's law> form conductance times driving potential. The <sodium> term has instantaneous <electrical conductance> $g_{\mathrm{Na}}m^3h$, the <potassium> term has instantaneous <electrical conductance> $g_{\mathrm K}n^4$, and the leak term has constant <electrical conductance> $g_{\mathrm L}$. Here the $g$ constants are maximal <electrical conductances> per area, and $V_{\mathrm{Na}},V_{\mathrm K},V_{\mathrm L}$ are the corresponding <reversal potentials>. The factors $m^3h$ and $n^4$ arise from <independent permissive gates in an ion channel>. A conducting channel carries zero net ionic <electric current> at its <reversal potential>.
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