Interplay of activation kinetics and the derivative conductance determines resonance properties of neurons

Abstract

In a neuron with hyperpolarization activated current (I_{h}), the correct input frequency leads to an enhancement of the output response. This behavior is known as resonance and is well described by the neuronal impedance. In a simple neuron model we derive equations for the neuron's resonance and we link its frequency and existence with the biophysical properties of I_{h}. For a small voltage change, the component of the ratio of current change to voltage change (dI/dV) due to the voltage-dependent conductance change (dg/dV) is known as derivative conductance (G_{h}^{Der}). We show that both G_{h}^{Der} and the current activation kinetics (characterized by the activation time constant τ_{h}) are mainly responsible for controlling the frequency and existence of resonance. The increment of both factors (G_{h}^{Der} and τ_{h}) greatly contributes to the appearance of resonance. We also demonstrate that resonance is voltage dependent due to the voltage dependence of G_{h}^{Der}. Our results have important implications and can be used to predict and explain resonance properties of neurons with the I_{h} current.