A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon

Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with maximum likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF gating currents, and single-channel first latency densities over a wide voltage range. Best models have five closed states before channel opening, with inactivation from at least one closed state as well as the open state. Forward activation rate constants increase with depolarization, and deactivation rate constants increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At negative potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more positive potentials, the time to first opening and burst duration together produce the macroscopic current.