Simplified computational model of the BK channel–spermine interaction

Spermine blocks large-conductance voltage- and calcium-activated potassium channels (BK channels). In recent years, interest in this interaction has increased because of its involvement in both physiological and pathological processes. This study aimed to develop a simplified mathematical model of the BK current and its blockade by spermine and to implement it in a computational simulator. To this end, a Hodgkin–Huxley-type mathematical model of the BK current was used, in which the steady-state channel activation follows a Boltzmann function that depends on membrane voltage and intracellular calcium concentration. Spermine block depended on the concentration of this polyamine and on the fraction of spermine molecules entering the channel as a result of the electrostatic attraction between the positive charges of spermine and the negative charges within the channel pore. This process was described, in a simplified manner, by a Boltzmann function with a behavior different from that of the activation function. The simulator reproduced the voltage and calcium dependence of the BK channel. Depending on the spermine concentration, channel block produced inward rectification of the BK current followed by a partial recovery of the current, indicating partial channel blockade. In conclusion, all variables of the mathematical model can be modified to evaluate their effects on the BK channel–spermine interaction. Careful selection of these variables, while maintaining values within electrophysiological ranges, allows the model to approximate several experimentally observed responses.