Assessing the Impact of I_h Conductance on Cross-Frequency Coupling in Model Pyramidal Neurons

Large cortical and hippocampal pyramidal neurons are elements of neuronal circuitry that have been implicated in cross-frequency coupling (CFC) during cognitive tasks. We investigate potential mechanisms for CFC within these neurons by examining the role that the hyperpolarization-activated mixed cation current (I_h) plays in modulating CFC characteristics in multicompartment neuronal models. We quantify CFC along the soma-apical dendrite axis and tuft of three models configured to have different spatial distributions of I_h conductance density: (1) exponential gradient along the soma-apical dendrite axis, (2) uniform distribution, and (3) no I_h conductance. We simulated two current injection scenarios: distal apical 4 Hz modulation and perisomatic 4 Hz modulation, each with perisomatic, mid-apical, and distal apical 40 Hz injections. We used two metrics to quantify CFC strength-modulation index and height ratio-and we analyzed CFC phase properties. For all models, CFC was strongest in distal apical regions when the 40 Hz injection occurred near the soma and the 4 Hz modulation occurred in distal apical dendrite. The strongest CFC values were observed in the model with uniformly distributed I_h conductance density, but when the exponential gradient in I_h conductance density was added, CFC strength decreased by almost 50%. When I_h was in the model, regions with much larger membrane potential fluctuations at 4 Hz than at 40 Hz had stronger CFC. Excluding the I_h conductance from the model resulted in CFC either reduced or comparable in strength relative to the model with the exponential gradient in I_h conductance. The I_h conductance also imposed order on the phase characteristics of CFC such that minimum (maximum) amplitude 40 Hz membrane potential oscillations occurred during I_h conductance deactivation (activation). On the other hand, when there was no I_h conductance, phase relationships between minimum and maximum 40 Hz oscillation often inverted and occurred much closer together. This analysis can help experimentalists discriminate between CFC that originates from different underlying physiological mechanisms and can help illuminate the reasons why there are differences between CFC strength observed in different regions of the brain and between different populations of neurons based on the configuration of the I_h conductance.