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

In a neuron with hyperpolarization activated current (Ih), 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 Ih. 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 (GhDer). We show that both GhDer and the current activation kinetics (characterized by the activation time constant τh) are mainly responsible for controlling the frequency and existence of resonance. The increment of both factors (GhDer and τh) greatly contributes to the appearance of resonance. We also demonstrate that resonance is voltage dependent due to the voltage dependence of GhDer. Our results have important implications and can be used to predict and explain resonance properties of neurons with the Ih current.