= Solution
An <ion channel> can disturb cellular electrical activity by changing unitary <electrical conductance>, open <probability>, gating kinetics or the number delivered to the <cell membrane>. A useful organizing relation is
$$
I_j=N_j\gamma_jP_{o,j}(V,t)(V-E_j),\qquad
C_m\dot V=I_{\rm applied}-\sum_jI_j.
$$
Here outward <electric current> is positive. Altering one channel's biophysical behavior changes the balance governing <membrane potential> and hence the timing or recurrence of <action potentials>.
\b[<Long QT syndrome>, type 3.] Certain disease-associated SCN5A variants impair fast <ion-channel inactivation> of the cardiac <voltage-gated sodium channel> NaV1.5. Instead of vanishing promptly after the upstroke, a small persistent inward sodium <electric current> remains during the plateau and <repolarization>. Because $V<E_{\rm Na}$ in this phase, the residual <electric current> is inward and opposes the outward <electric currents> that would terminate the cardiac <action potential>. The ventricular <action potential> lasts longer, extending the QT interval on the <electrocardiogram>. Excessively prolonged or uneven <repolarization> permits early afterdepolarizations and dangerous ventricular rhythm disturbances.
Genetic association identifies the channel, while <voltage clamp> distinguishes defective <ion-channel inactivation> from a mere increase in channel abundance. Recordings of disease-associated channels show persistent or bursting openings; coupling measured mutant sodium <electric current> into an otherwise modeled cardiac membrane through <dynamic clamp> tests whether that kinetic defect prolongs the <action potential>. The phenotype is variant-specific: not every SCN5A variant increases late <electric current> or causes <long QT syndrome>.<Cardiac sodium channel mutations in patients with long QT syndrome, an inherited cardiac arrhythmia by Qing Wang and others>[Human Molecular Genetics 4, pp. 1603–1607: familial variants affecting the inactivation machinery]{ref}<Long-QT syndrome-related sodium channel mutations probed by the dynamic action potential clamp technique by Géza Berecki and others>[Measured mutant-channel currents coupled to a ventricular-cell model test action-potential prolongation]{ref}
\b[<Myotonia congenita>.] CLCN1 encodes the skeletal-muscle ClC-1 <chloride channel>, which normally supplies a large resting stabilizing <electrical conductance>. Because the chloride <reversal potential> is near the resting <membrane potential>, that pathway resists small depolarizing disturbances. Loss of functional channels, reduced <electrical conductance>, or a shift in opening toward more positive <membrane potential> reduces the resting electrical shunt. <Potassium> accumulation in the transverse-tubule space during activity can then produce larger depolarizing afterpotentials and trigger further muscle <action potentials> after the intended stimulus has ceased. Continued electrical firing sustains contraction and delays relaxation: this is myotonia, rather than a primary inability of the contractile apparatus to relax.
Patient-family linkage and variant analysis connect the disease to ClC-1. Functional recordings of disease-associated channels demonstrate shifted voltage dependence and reduced availability near resting <membrane potential>; single-channel and noise measurements also resolve two conductive protopores and their gating behavior. Different variants can act through different mechanisms, so a gating shift is an example rather than an explanation of every case.<The skeletal muscle chloride channel in dominant and recessive human myotonia by Manuela C. Koch and others>[Science 257, pp. 797–800: familial disease linked to the muscle chloride-channel gene]{ref}<Mutations in dominant human myotonia congenita drastically alter the voltage dependence of the ClC-1 chloride channel by Michael Pusch and others>[Neuron 15, pp. 1455–1463: disease-associated changes in voltage dependence]{ref}<The muscle chloride channel ClC-1 has a double-barreled appearance that is differentially affected in dominant and recessive myotonia by Caterina Saviane and others>[Single-channel and fluctuation analysis of ClC-1 and myotonia-associated gating changes]{ref}
These examples connect contrasting current defects to their consequences: persistent inward sodium <electric current> prolongs cardiac <action potentials>, whereas loss of stabilizing resting chloride <electrical conductance> permits repetitive skeletal-muscle <action potentials>. Both causal chains require functional channel measurements in addition to a disease-associated sequence change.
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