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

Abstract

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.

Keywords: Ih conductance; cross-frequency coupling; phase-amplitude coupling; pyramidal neuron; theta-gamma coupling.

Figure 1

CFC analysis performed on model pyramidal neuron. (A) A 1.5 nA 40 Hz sinusoidal current was injected into the base of the apical dendrite while a 1.5 nA 4 Hz sinusoidal current was injected into the distal apical dendrite. Additonal labels include: soma, apical dendrite, and apical tuft; apical dendrite compartments 1–13 (apdend1, apdend2, …, apdend13); and the distance from soma to end of apical tuft−1,200 μm. (B) From top to bottom: membrane potential oscillations in the 11th distal apical dendrite compartment (apdend11) resulting from the 40 Hz and 4 Hz current injections, filtered 4 Hz component of the membrane potential oscillation, time series of 4 Hz phase, and filtered 40 Hz component of membrane potential oscillation (black) and amplitude envelope of 40 Hz oscillation (red). (C) Phase-amplitude plot for two complete 4 Hz cycles with a phase bin size of 5° (LG–low gamma, ~40 Hz).

Figure 2

Sensitivity analysis for the number of bins (N). MI index (solid, left ordinate) and height ratio (dashed, right ordinate) as a function of N. Values for N evaluated (10, 12, 18, 20, 36, and 72) indicated by dots.

Figure 3

Current injection amplitude sensitivity analysis. (A,C) MI and height ratio, respectively, for amplitudes of the 4 Hz current injection of 0.5, 1.0, and 1.5 nA while the amplitude of the 40 Hz injection was held constant at 1.5 nA. (B,D) MI and height ratio, respectively, for amplitudes of the 40 Hz current injection of 0.5, 1.0, and 1.5 nA while the amplitude of the 4 Hz injection was held constant at 1.5 nA.

Figure 4

(A) Distal apical dendrite 1.5 nA, 4 Hz modulation (black arrow) with 1.5 nA 40 Hz current injections in base of apical dendrite (black arrow, solid red outline), middle apical dendrite (black arrow, dashed red outline), and distal apical dendrite (black arrow, dot-dashed red outline). (B) Height ratio calculated for the soma, apical dendrite, and apical tuft in the model with exponential gradient in I_h conductance density along apical dendrite. (C) Height ratio calculated for the soma, apical dendrite, and apical tuft in model with uniform I_h conductance density. (D) Height ratio calculated for the soma, apical dendrite, and apical tuft in model with no I_h conductance. Dot symbols along the profiles in (B–D) indicate the distance from the soma of compartments along the soma-apical dendrite axis and apical tuft (measured from the beginning of each compartment).

Figure 5

(A) Perisomatic 1.5 nA, 4 Hz modulation (black arrow) with 1.5 nA 40 Hz current injections in base of apical dendrite (black arrow, solid red outline), middle apical dendrite (black arrow, dashed red outline), and distal apical dendrite (black arrow, dot-dashed red outline). (B) Height ratio calculated for the soma, apical dendrite, and apical tuft in model with exponential gradient in I_h conductance density along apical dendrite. (C) Height ratio calculated for the soma, apical dendrite, and apical tuft in model with uniform I_h conductance density. (D) Height ratio calculated for the soma, apical dendrite, and apical tuft in model with no I_h conductance. Dot symbols along the profiles in (B–D) indicate the distance from the soma of compartments along the soma-apical dendrite axis and apical tuft (measured from the beginning of each compartment).

Figure 6

Amplitude ratio and theta phase of CFC for model with exponential gradient in I_h conductance. (A) Distal 4 Hz modulation, amplitude ratio (top), and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines). (B) Perisomatic 4 Hz modulation, amplitude ratio (top) and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines).

Figure 7

Amplitude ratio and theta phase of CFC for model with uniform I_h conductance. (A) Distal 4 Hz modulation, amplitude ratio (top) and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines). (B) Perisomatic 4 Hz modulation, amplitude ratio (top), and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines).

Figure 8

Amplitude ratio and theta phase of CFC for model with no I_h conductance. (A) Distal 4 Hz modulation, amplitude ratio (top), and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines). (B) Perisomatic 4 Hz modulation, amplitude ratio (top), and theta phase (bottom) of minimum (black) and maximum (red) amplitude of 40 Hz membrane potential oscillation. Forty Hertz current injected into base of apical dendrite (solid lines), middle of apical dendrite (dashed lines), and distal apical dendrite (dot-dashed lines).

Figure 9

I_h conductance (A) activation function (B) time constant.