State probabilities throughout recovery from inactivation protocol (for I_to,f) illustrates differences between acceptable and unacceptable models.

A) Recovery from inactivation protocol. B) State probabilities tracked as a function time throughout the above protocol. The 3-state model shown is representative of unacceptable I_to,f models where recovery from inactivation is slow. Green designates the rooted open state while blue and red indicate the functional hypothetical inactivated state and closed state, respectively. At the resting state (-70 mV), the red “closed” state carries about 80% of the resting state probability while the blue “inactivated” state holds the other 20%. This closed state probability spread at the holding potential essentially “locks in” the voltage-dependent rates at -70 mV as slow. After the depolarizing pulse to +40 mV for 500 ms, the “blue” inactivated state carries 99% of the probability. The 25 ms hyperpolarizing pulse to -70 mV attempts to send the state probability back to the “red” closed state. However, the rate from the blue to red state at -70 mV is quite slow and, on reapplying the depolarizing step, the open state probability is lower than expected after 25 ms of recovery. C) An analogous representation of state probabilities for a 4-state model representative of the acceptable I_to,f models where recovery from inactivation is appropriately fast. State colors are as before with the addition of 4^th purple state. At the resting potential, the hypothetical closed state holds 99% of state probability. Therefore, the other states and rates are not “locked in” to slower rates at the holding potential. After the long depolarizing pulse, most state probability is again in the blue inactivated state. In this model, however, the rate from the inactivated state back to closed at -70 mV is fast enough to allow for sufficient recovery from inactivation after 25 ms hyperpolarization (77%). The pink state thus serves as a transitory state that distances the functionally inactive (blue) state from the open state (green).

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