Mechanisms underlying the distinct K⁺ dependencies of periodic paralysis

Patients with periodic paralysis have attacks of weakness precipitated by depolarization of muscle. Each form of periodic paralysis is associated with unique changes in serum K⁺ during attacks of weakness. In hypokalemic periodic paralysis (hypoKPP), the mutation-induced gating pore current causes weakness associated with low serum K⁺. In hyperkalemic periodic paralysis (hyperKPP), mutations increase a non-inactivating Na⁺ current (Na persistent or NaP), which causes weakness associated with elevation of extracellular K⁺. In Andersen–Tawil syndrome, mutations causing loss of Kir channel function cause weakness associated with either low or high K⁺. We developed a computer model to address two questions: (1) What mechanisms are responsible for the distinct K⁺ dependencies of muscle depolarization-induced weakness in the three forms of periodic paralysis? (2) Why does extracellular K⁺ become elevated during attacks of weakness in hyperKPP, reduced in hypoKPP, and both elevated and reduced in Andersen–Tawil syndrome? We experimentally tested the model assumptions about resting potential in normal K⁺ solution in hyperKPP and hypoKPP. Recreating the distinct K⁺ dependence of all three forms of periodic paralysis required including the K⁺ and voltage dependence of current through Kir channels, the extracellular K⁺ and intracellular Na⁺ dependence of the Na/K ATPase activity, and the distinct voltage dependencies of the gating pore current and NaP. A key factor determining whether muscle would depolarize was the direction of small net K⁺ and net Na⁺ fluxes, which altered ion concentrations over hours. Our findings may aid in development of novel therapy for diseases with dysregulation of muscle excitability.