= Solution
Add an unavailable nonconducting inactivated state to the two-state gating scheme, for example
$$
C\mathrel{\mathop{\rightleftarrows}^{k_o(V)}_{k_c(V)}}O
\mathrel{\mathop{\rightleftarrows}^{k_i(V)}_{k_r(V)}}I.
$$
The probabilities obey
$$
\dot p_O=k_op_C-(k_c+k_i)p_O+k_rp_I,\qquad
\dot p_I=k_ip_O-k_rp_I,\qquad p_C+p_O+p_I=1.
$$
<Depolarization> increases activation, initially raising $p_O$; subsequent transfer to $I$ reduces current while voltage is held constant. Slow recovery at the depolarized voltage permits most channels to become unavailable. <Repolarization> promotes recovery and deactivation. More closed states and closed-state <ion-channel inactivation>[inactivation] may be needed for quantitative data, but this minimal extension already explains the rise followed by decay that fixed-rate $C\leftrightarrow O$ gating cannot produce from a closed population.
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