A Model of Reverse Spike Frequency Adaptation and Repetitive Firing of Subthalamic Nucleus Neurons

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Abstract
Subthalamic nucleus neurons exhibit reverse spike-frequency adaptation. This occurs only at firing rates of 20–50 spikes/s and higher. Over this same frequency range, there is an increase in the steady-state frequency–intensity ( F– I) curve's slope (the secondary range). Specific blockade of high-voltage activated calcium currents reduced the F– I curve slope and reverse adaptation. Blockade of calcium-dependent potassium current enhanced secondary range firing. A simple model that exhibited these properties used spike-triggered conductances similar to those in subthalamic neurons. It showed: 1) Nonaccumulating spike afterhyperpolarizations produce positively accelerating F– I curves and spike-frequency adaptation that is complete after the second spike. 2) Combinations of accumulating aftercurrents result in a linear F– I curve, whose slope depends on the relative contributions of inward and outward currents. Spike-frequency adaptation can be gradual. 3) With both accumulating and nonaccumulating aftercurrents, primary and secondary ranges will be present in the F– I curve. The slope of the primary range is determined by the nonaccumulating conductance; the accumulating conductances govern the secondary range. The transition is determined by the relative strengths of accumulating and nonaccumulating currents. 4) Spike-threshold accommodation contributes to the secondary range, reducing its slope at high firing rates. Threshold accommodation can stabilize firing when inward aftercurrents exceed outward ones. 5) Steady-state reverse adaptation results when accumulated inward aftercurrents exceed outward ones. This requires spike-threshold accommodation. Transient speedup arises when inward currents are smaller than outward ones at steady state, but accumulate more rapidly. 6) The same mechanisms alter firing in response to irregular patterns of synaptic conductances, as cell excitability fluctuates with changes in firing rate.