Inactivation mode of sodium channels defines the different maximal firing rates of conventional versus atypical midbrain dopamine neurons
Fig 4
Additional Long-term Inactivation Converts Atypical to Conventional Failure.
A. Atypical Model. During ramp stimulation, each spike produces a small uptick in occupancy in the long-term inactivated state I2 (green curves) A1. A 40 pA ramp does not induce depolarization block in the atypical model. A2. An 80 pA ramp results in depolarization block in the atypical model. B. Atypical Model with increased occupancy in the slowly inactivated state. B1. Increasing the maximum rate of the I1 to I2 transition from 26.7 s-1 to 80 ms-1 leads to failure at substantially lower frequencies for 40 pA ramp current levels. Large upticks in the level of slow inactivation (green trace) are observed for each spike. B2. A larger ramp with peak amplitude of 80 pA, beyond that required to induce depolarization block. C. Bifurcation diagrams with respect to applied current. C1. Atypical model. Oscillations terminate via supercritical Hopf. C2. Elevated cI1-I2. Oscillations terminate via saddle node of periodics (SNP) following subcritical Hopf where the unstable limit cycle (LC) originates. D, Effect of I1-I2 transition rate on entry in depolarization block. D1. Dependence of the minimum ramp amplitude required to induce depolarization block on the I1-I2 transition rate (red curve) and the frequency upon entry into depolarization block (blue curve). For the atypical value of 26.7 s-1 for the maximum I1-I2 transition rate, an 80 pA peak ramp amplitude is sufficient to induce depolarization block with a maximum frequency of about 23 Hz (vertical dashed line labeled A2). Increasing the I1-I2 maximum transition rate to 80 s-1 drops the required peak ramp amplitude to 50 pA and the maximum frequency to about 13 Hz (vertical dashed line labeled B1). D2. The larger the peak ramp current tolerated prior to entry into depolarization block, the larger the maximum frequency observed during the ramp. All parameters are set to atypical values in Table 1 except CI1-I2, which is variable.