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Write the instantaneous electrical conductance as $g_K(t)={\bar{g}}_{K}n(t{)}^4$. Here ${\bar{g}}_K$ is the maximal electrical conductance of the recorded membrane, $n$ is the activation variable, $V_m$ is inside-minus-outside membrane potential, and $V_K$ is the potassium Nernst equilibrium potential. The factor $V_m-V_K$ is the electrochemical driving voltage; positive $I_K$ conventionally denotes outward positive charge. For an electric current density, ${\bar{g}}_K$ must instead be an electrical conductance per area.

In the Hodgkin-Huxley model, four equivalent independent activation gates must all be permissive, each with probability $n$, so their joint opening probability is $n^4$. At fixed voltage each gate obeysThe model assumes approximately Ohmic open-channel conduction, a well-defined population-average electrical conductance, and an almost constant potassium reversal potential during a brief recording. Four phenomenological gates should not be mistaken for a proof of four physically independent molecular transitions. The simple delayed-rectifier description also omits ion-channel inactivation.

Reducing the available electrical conductance can weaken repolarization, broaden an action potential and alter repetitive firing. Depending on channel class and tissue, excess excitability or impaired recovery can follow; persistent depolarization can also reduce voltage-gated sodium channel availability. Cardiac potassium-current reductions can prolong the action potential and contribute to Long QT syndrome. These are conditional physiological consequences, not a claim that every potassium-current reduction has the same clinical effect.

An increased late inward sodium current can delay repolarization if fast inactivation is incomplete or slowed, if channels reopen excessively, or if the voltage range of persistent/window current is enlarged. A larger brief peak current alone is not equivalent to a sustained depolarizing current. Conversely, reduced outward potassium current can prolong the action potential through fewer functional surface channels, reduced conductance, slower or less favourable activation, or altered deactivation/availability. Either change shifts the balance towards inward current during repolarization.

These are distinct biophysical routes to Long QT syndrome, not claims that every subtype has the same channel defect.^[ref] The experimental association of sodium-channel abnormalities with inherited disease supports the inward-current mechanism.^[ref]

A sodium-channel gain-of-function mechanism in Long QT syndrome can reduce the inactivation rate $k_i$ or increase recovery/reopening from inactivated states, leaving a small persistent open population. The resulting late inward sodium current opposes repolarizing outward currents while $V<E_{\mathrm{Na}}$, prolonging the cardiac action potential. Slower entry into $I$ would also extend the typical conducting episode relative to its normal duration. The altered effect is prolonged sodium entry, not reversal of sodium's charge or a pump-driven uphill flux through the channel.

The precise rate change depends on the mutation: the clinical label alone does not uniquely specify one transition constant. Long QT syndromes also include other channel mechanisms; the question here concerns its stated sodium-channel variant.^[ref]

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 isHere 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.

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 $V<E_{\mathrm{Na}}$ 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.^[ref][ref]

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.^{[ref][ref][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.