= Solution
A <Two-state ion-channel gating>[two-state] closed–open scheme at fixed <voltage> relaxes monotonically and cannot by itself produce a sodium-current transient during a maintained step with constant driving <force>. A minimal <sodium> scheme therefore includes an unavailable state: $C\rightleftarrows O\rightleftarrows I$, with voltage-dependent activation, <Ion-channel inactivation>[inactivation] and recovery; closed-state recovery pathways may be added when needed. Opening is initially rapid, occupancy then accumulates in $I$, and recovery on repolarization restores an activatable population.
For the illustrated <potassium> current, a closed–open model gives sustained opening, but several activation steps can account for its initial delay. A conventional illustrative coarse-grained description is
$$
I_{\rm Na}=\overline g_{\rm Na}m^3h(V-E_{\rm Na}),\qquad
I_{\rm K}=\overline g_{\rm K}n^4(V-E_{\rm K}),
$$
with each gate following $\dot q=\alpha_q(V)(1-q)-\beta_q(V)q$. Fast $m$ activation, subsequent decrease of $h$, and slower increase of $n$ produce the two qualitative records. The powers are phenomenological gate assumptions, not values uniquely inferred from these traces or an exact structural count for every cardiac channel.
A 1-Hz cardiac rhythm has about a second between successive activations, whereas a 100-Hz neuronal rhythm has only $10\,\mathrm{ms}$; the available resting interval is shorter still after subtracting the <action potential>. Recovery or deactivation with a timescale comparable to that interval can then leave residual <Ion-channel inactivation>[inactivation] or <potassium> activation, giving use-dependent changes and <Neuronal refractory period>[refractoriness]. Millisecond or faster relaxation usually completes much more readily during a long diastolic interval. The particular <Two-state ion-channel gating>[two-state] A and B in <4/d> would both nearly equilibrate over a full $10\,\mathrm{ms}$ at their stipulated constant rates; their values alone do not demonstrate high-frequency failure. Real comparison requires voltage-dependent recovery rates and the different cardiac and neuronal waveforms. A frozen-rate model cannot quantitatively predict either firing pattern from frequency alone.
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