= Solution
A <sodium>-channel gain-of-function mechanism in <Long QT syndrome> can reduce the <ion-channel inactivation>[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 $V<E_{\rm Na}$, 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.<Cardiac sodium channel mutations in patients with long QT syndrome, an inherited cardiac arrhythmia by Qing Wang and others>[Sodium-channel defects associated with the inherited repolarization phenotype]{ref}
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