Solution (source code)

= Solution

Panel B steps the membrane from approximately $-80$ to $-40\,\mathrm{mV}$ and holds it there. The <sodium> current becomes inward, peaks rapidly, and decays almost to zero despite maintained <depolarization>. At $-40\,\mathrm{mV}$ the <sodium> driving <force> $V-E_{\rm Na}$ is negative, consistent with the negative current convention. A conductance description is
$$
I_{\rm Na}=N\gamma p_O(V-E_{\rm Na}),
$$
where $N$ is channel number, $\gamma$ single-channel conductance and $p_O$ the open <probability>. The trace requires rapid voltage-dependent activation followed by slower <ion-channel inactivation>[inactivation], rather than a passive pore whose only response is an instantaneous constant current. Recovery normally requires <repolarization>, helping produce a refractory period and directional propagation of excitation.

A typical eukaryotic <voltage-gated sodium channel> contains four homologous membrane-spanning domains in one large pore-forming <protein>. Charged S4 helices sense voltage; pore-associated regions form a selective pathway and activation gate. Fast <ion-channel inactivation>[inactivation] involves intracellular machinery coupled to the pore, classically the interdomain III–IV region, and should not be identified automatically with the tethered <potassium>-channel blocker. The pore permits rapid downhill electrochemical transport while maintaining selectivity against other <ions>.

Evidence separates these properties: clamp-step experiments distinguish voltage dependence and activation from decay at a fixed voltage; changing extracellular <sodium> shifts reversal potential; selective blockers isolate <sodium> current; <patch clamp>[patch-clamp] records resolve stochastic single-channel openings; and <mutations> of sensors, filter residues or the fast-<ion-channel inactivation>[inactivation] machinery alter the corresponding function. A single macroscopic trace alone cannot uniquely determine all microscopic <rate constants>.