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

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.