Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration

Abstract

Synchronization of globus pallidus (GP) neurons and cortically entrained oscillations between GP and other basal ganglia nuclei are key features of the pathophysiology of Parkinson's disease. Phase response curves (PRCs), which tabulate the effects of phasic inputs within a neuron's spike cycle on output spike timing, are efficient tools for predicting the emergence of synchronization in neuronal networks and entrainment to periodic input. In this study we apply physiologically realistic synaptic conductance inputs to a full morphological GP neuron model to determine the phase response properties of the soma and different regions of the dendritic tree. We find that perisomatic excitatory inputs delivered throughout the interspike interval advance the phase of the spontaneous spike cycle yielding a type I PRC. In contrast, we demonstrate that distal dendritic excitatory inputs can either delay or advance the next spike depending on whether they occur early or late in the spike cycle. We find this latter pattern of responses, summarized by a biphasic (type II) PRC, was a consequence of dendritic activation of the small conductance calcium-activated potassium current, SK. We also evaluate the spike-frequency dependence of somatic and dendritic PRC shapes, and we demonstrate the robustness of our results to variations of conductance densities, distributions, and kinetic parameters. We conclude that the distal dendrite of GP neurons embodies a distinct dynamical subsystem that could promote synchronization of pallidal networks to excitatory inputs. These results highlight the need to consider different effects of perisomatic and dendritic inputs in the control of network behavior.

Figure 1.

GP model morphology, conductances, and electrophysiological properties reproduce those of recorded GP neurons. A, Neurolucida (MicroBrightField) reconstruction of the GP neuron morphology used for all versions of the GP model. Somatic (S) and proximal, mid, and distal dendritic stimulus locations for PRC analysis are indicated by oval labels. B, Matching of model spike shapes to physiological recordings. The model spike trace (solid line) matched the average recorded spontaneous spike trace (dashed line) well within the biological variability (gray lines) for of spike onset, spike height, and spike width, and AHPs. Average spikes from 50 recorded neurons (gray lines) are anchored to the population mean voltage 5 ms before spike peaks (black arrowhead) to illustrate the variability of AHPs across neurons. C, Somatic voltage- and calcium-gated currents during a spontaneous action potential of GP_base. Note that the NaF current peak is curtailed by the x-axis to better distinguish the other current traces. H-current is not shown because it had minimal activation. D, Frequency-current (FI) curves for the base model compared with the average experimentally measured FI curve.

Figure 2.

Physiologically realistic inputs to GP are outside somatic and dendritic domains of weak coupling. A, Voltage traces illustrating spontaneous 7.9 Hz spiking of the model and voltage deflections and spike advances elicited by 100 pA somatic stimuli delivered at one of three points in phase (indicated by asterisks). Note, spike advances persist indefinitely (3 spike cycles shown). B, Expansion of A highlighting spike advances resulting from stimuli delivered at different phases. The earliest stimulus (indicated in A–C by the lightest gray asterisk) yields the smallest spike advance, and the latest (black asterisk) yields the largest. C, Normalized PRCs for somatic current injections between 1 pA (solid black line) and 100 pA (dotted black line). Larger somatic stimuli yield PRCs with peaks occurring earlier in phase. The shape of normalized somatic PRCs converges for stimuli weaker than 7.5 pA. D, Normalized PRCs derived by stimulating the distal region of dendrite 3 (D3_D) with current pulses between 0.5 pA and 10 pA (dotted black line). The shape of normalized D3_D PRCs converges for stimuli ≤1 pA (solid black line) with an r-value of 0.0675 indicating that the iPRC for D3_D is type I. This can be seen most readily by examining the negative peaks of these PRCs occurring at a phase of ∼0.025 (box and inset). E, Normalized PRCs for negative somatic current injections between −1 pA (solid black line) and −100 pA (dotted black line). Larger negative stimuli yield PRCs with more right-shifted peaks. Note by comparison to C, 1 pA and −1 pA somatic PRCs are symmetrical across zero. F, Normalized PRCs for D3_D current injections between −0.5 pA and −10 pA (dotted black line). The shapes of these normalized D3_D PRCs converge for stimuli of or greater than −1 pA (solid black line). This can be seen most readily by noting the positive peaks of PRCs at a phase of ∼0.025 (box and inset). G, Domains of somatic and D3_D weak coupling illustrated by plotting the relationships between features of the PRCs and stimulus strength. For somatic current injections of 7.5 pA or less, the phase at which the peak of PRCs occurs (left y-axis) has converged. For D3_D current injections of 1 pA or less, the negative peak of PRCs (right y-axis) has converged. H, Domains of somatic and D3_D weak coupling illustrated by plotting a measure of PRC asymmetry (obtained by summing together PRCs for positive and negative current injections of equal magnitude at all points in phase) against stimulus strength. Excitatory somatic PRCs for stimulus strengths >5 pA are increasingly asymmetric with inhibitory somatic PRCs of equal strengths. Excitatory D3_D PRCs for stimulus strengths >1 pA are increasingly asymmetric with inhibitory D3_D PRCs of equal strengths. I, Infinitesimal PRCs (1 pA and −1 pA) for all stimulus locations are type I.

Figure 3.

PRC shape depends both on stimulus location and strength. A, Somatic PRCs are always type I for square-pulse positive current injections and for simulated excitatory synaptic AMPA conductances. Somatic PRCs have peaks that scale approximately linearly with stimulus magnitude, and larger stimuli cause more of the late-phase PRC to approach the limit of spike advancement. B, Small excitatory synaptic inputs to the end of a shorter dendrite (D2_D) yield type I PRCs, however, larger inputs to D2_D yield PRCs of increasing type II character. Both positive and negative peaks of D2_D PRCs increase in size with stimulus strength. C, Excitatory synaptic inputs to the end of the longest dendrite (D3_D) yielded type II PRCs for all input strengths tested in this set of experiments. D, Somatic PRCs are always type I for square-pulse negative current injections and for simulated inhibitory GABA_A synaptic conductances. E, F, Distal dendritic PRCs for inhibitory synaptic input (to D2_D in E; to D3_D in F) are type I.

Figure 4.

Different input strengths evoke different contingents of membrane currents at the distal dendrite. Shown are stimulus-evoked voltage and current transients for 0.5 nS and 2 nS excitatory inputs to D2_D. A, Voltage deflections elicited by 0.5 nS excitatory synaptic input to D2_D at phases of 0.25, 0.5, or 0.75 (red dashed lines, indicating phase advances). Importantly, these stimuli yield a type I D2_D PRC. The unstimulated voltage trajectory at D2_D (black trace) illustrates the back-attenuated voltage oscillation driven by spontaneous axosomatic spiking. Small spike advancements are evident in the stimulated D2_D voltage traces relative to the control trace (red _*), particularly for the late-phase stimulus. B, Voltage deflections elicited by 2 nS excitatory synaptic input to D2_D at phases of 0.25, 0.5, or 0.75 (dashed blue or red lines, indicating phase delays or advances, respectively). Importantly, these stimuli yield a type II D2_D PRC. C, Difference currents (I_Diff) local to 0.5 nS D2_D stimuli were calculated by the subtraction of control current traces from stimulated current traces. The five largest difference currents are shown, and of these, I_Diff-SK (green traces) is both the largest and longest lasting. Only slight differences are evident in the currents evoked by stimuli at difference phases (here, and in D), because the control voltage trajectory at D2_D is relatively flat. Note that for visual clarity, I_Diff traces in C are curtailed at the time of the next spike. D, Difference currents local to 2 nS D2_D stimuli. A fourfold increase in input strength (compared with C) yields a much larger transient increase in I_Diff-NaF which amplifies the voltage deflection (red traces) and a 20-fold increase in peak I_Diff-SK (green traces). Note that the spike advancement caused by the late-phase stimulus results in a second peak in I_Diff-SK (_*).

Figure 5.

Targeting identical stimuli to different regions of the model evokes different contingents of membrane currents. Shown are stimulus-evoked voltage and current transients for 1 nS excitatory inputs to the soma vs the most-distal region of dendrite, D3_D. A, Voltage deflections elicited by 1 nS excitatory synaptic input delivered to the soma at phases of 0.25, 0.5, or 0.75 (dashed or solid black lines, as indicated). Importantly, these stimuli yielded a type I somatic PRC. The unstimulated somatic voltage trajectory (gray line) covers approximately a 10 mV range between the depth of the AHP and spike threshold. As in Figure 4, spike advancements relative to control are evident, particularly for the late-phase stimulus. B, Voltage deflections elicited by 1 nS excitatory synaptic input to D3_D at phases of 0.25, 0.5, or 0.75 (dashed or solid black lines, as indicated) are more than 10-fold larger than those elicited by equivalent somatic inputs, because D3_D input resistance is much higher. Importantly, these stimuli yield a type II D3_D PRC. Slight spike delays and advancements relative to control are again evident (_*). C, Difference currents local to 1 nS somatic stimuli. The pattern of evoked currents differs depending on input phase, because the control somatic voltage trajectory is not flat. As in Figure 4, I_Diff traces are curtailed at the time of the next spike. D, Difference currents local to 1 nS D3_D stimuli. D3_D stimuli yielded a peak I_Diff-SK (green traces) that is five times greater than that elicited by identical somatic stimuli. Minimal differences are evident in the pattern of currents evoked by stimuli at difference phases, because the control voltage trajectory at D3_D is flat. E, The synaptic current of the stimulus overwhelms membrane currents evoked at the soma. The sum of all somatic difference currents and difference leak are negligible relative to the synaptic current of a 1 nS AMPA input which is ∼70 pA. F, A 1 nS AMPA input to D3_D yields a smaller synaptic current than the equivalent conductance input applied to the soma, because the D3_D voltage deflection is much larger, reducing the synaptic driving force. The sum of all D3_D difference currents, of which NaF and SK are the major contributors (D), is sufficiently large (and long-lasting) to rival the synaptic current.

Figure 6.

Tandem local up- and downregulation of Ca_HVA and SK modulates the depth of the negative peak of distal dendritic PRCs. A, SK difference currents evoked by 2 nS excitatory synaptic input to D2_D in models where the densities of Ca_HVA and SK have been dialed up or down in the compartments composing the D2_D stimulus site. (Note that since the manipulation of conductance densities was limited to the 25 compartments of the D2_D site, the spontaneous spiking behavior of the model was unaffected.) Traces are aligned such that stimulus onsets are at zero. B, D2_D PRCs transition from type I to type II as Ca_HVA and SK are upregulated local to stimulus delivery. Visually identical type I PRCs result when either Ca_HVA or SK are eliminated from D2_D (gray and dashed black lines). The negative region of D2_D PRCs (asterisk) that remains when the Ca_HVA/SK mechanism had been locally disabled (by eliminating either Ca_HVA or SK) stems from compartments neighboring D2_D where the mechanism was left intact and that also experience significant voltage deflection evoked by the stimulus. C, Ca_HVA difference currents evoked by 2 nS excitatory synaptic input to D3_D in models where the densities of Ca_HVA and SK have been dialed up or down in the compartments composing the D3_D stimulus site. Traces are aligned such that stimulus onsets are at zero. D, The negative region of D3_D PRCs is deeper for models where Ca_HVA and SK has been upregulated local to stimulus delivery. Elimination of either Ca_HVA or SK from D3_D yields visually identical type II PRCs, and like the D2_D case, the remaining negative regions of these PRCs (asterisk) stems from compartments adjacent to the stimulated region where the Ca_HVA/SK mechanism remains intact.

Figure 7.

Spike frequency affects somatic but not distal dendritic SK activation. A, Faster spiking elevates baseline levels and augments stimulus-evoked transients of somatic SK current. A1, When spiking was driven from 10 Hz (black trace) to 30 Hz (red trace) by increasing somatic applied current, the mean voltage at the soma (dashed black and red lines) was elevated ∼5 mV. A2, Driving faster spiking with somatic applied current elevated the baseline level of somatic SK current. Note that a 2 nS AMPA stimulus (red and black arrowheads) elicited immediate initiation of a spike when applied to the soma during 30 Hz spiking but not when applied during 10 Hz spiking. The stimulus applied during 30 Hz spiking evoked a larger peak in SK current (red asterisk) than is evoked by spontaneous spikes (red dashed traces). A3. During 10 Hz spiking, the somatic stimulus (black arrowhead) shortened the ISI during which it was delivered, but did not affect the subsequent ISI. A4. During 30 Hz spiking the somatic stimulus (red arrowhead) shortened the ISI during which it was delivered. However, the subsequent ISI was longer in duration, reflecting the larger SK current evoked by the stimulus during faster spiking. B, The time course of distal dendritic SK current flow is unaffected by spike frequency, spanning additional spike cycles during faster spiking. B1, During 10 Hz spiking, the local depolarization transient elicited by a 2 nS AMPA input to D3_D (solid black line) was ∼55 mV relative to the control voltage trace (dashed black line). (Note that the ripples in the control voltage trace which demarcate the 100 ms spike cycles reflect attenuated spikes reaching the distal dendrite.) B2, During 30 Hz spiking, the local depolarization transient elicited by a 2 nS AMPA input to D3_D (solid red line) was also ∼55 mV relative to the control voltage trace (dashed red line). B3, The peak and time course of the SK difference current (∼30 pA) evoked locally by AMPA inputs to D3_D was not dependent on spike frequency. Difference current traces for 10 Hz (black) and 30 Hz (red) spiking overlay one another nearly perfectly.

Figure 8.

Faster axosomatic spiking changes the shapes of somatic and dendritic PRCs, and it is necessary to consider stimulus effects that outlast a single spike cycle. A1, When the model is driven faster (from 10 Hz to 30 Hz) by increasing applied current to the soma, excitatory synaptic inputs of 2 nS yield somatic PRCs with larger, earlier peaks and less skewness. A2, Permanent PRCs are calculated by summing single cycle PRCs F1 through F5. At higher spike frequencies the peak of the permanent somatic PRC is reduced, occurs earlier in phase, and is less skewed. B1, Like the somatic case, during faster spiking the positive peak of distal dendritic (D3_D) PRCs, occurs earlier in phase. The negative region present in F1 PRCs for D3_D inputs delivered during slower spiking (green arrowhead) is pushed into F2 when spiking is driven faster (blue arrowhead). B2, Permanent PRCs for D3_D inputs have only a slight positive peak for the slowest spike frequencies, and at 15 Hz or faster, the entire permanent PRC is negative. C1, Single-cycle PRCs for inputs to D2_D show an amalgam of the effects of somatic or D3_D stimulation. The red and blue arrowheads correspond to the red arrowhead in A1 and the blue arrowhead in B1. C2, The permanent PRCs for D2_D inputs are type II for all spike frequencies up to 60 Hz, and they vary smoothly as a function of spike frequency. For high spike frequencies a negative region develops for stimuli late in phase.

Figure 9.

Distal dendritic PRCs are robustly type II against significant variation of dendritic conductance densities. A, Single-cycle PRCs (A1, F1–F4) and the permanent PRC (A2) for models with 0, 1, and 4 times the base dendritic density of NaP. For models with greater dendritic densities of NaP the positive peak in the F1 PRC and both of the negative peaks in the F2 PRC were increased. B, Single-cycle PRCs (B1, F1–F4) and the permanent PRC (B2) for models with 0.5, 1, and 1.5 times the default dendritic density of the 4 spike conductances (NaF, NaP, KV3, and KV2). For models with greater dendritic densities of the spike conductances, the positive peak in the F1 PRC and both of the negative peaks in the F2 PRC were increased. C, Single-cycle PRCs (C1, F1–F4) and the permanent PRC (C2) for models with 0.5, 1, 1.5, and 2 times the base dendritic density of SK. For models with greater dendritic densities of SK, the positive peak in the F1 D2_D PRC and the early-phase negative peak (blue arrowhead) is reduced, whereas the late-phase negative peak in the F2 D2_D PRC (solid red arrowhead) is increased. Complete removal of SK conductance from the dendrite (red traces in C1 and C2) eliminates the late-phase negative peak in the F2 D2_D PRC (red box arrowhead) and the corresponding permanent PRC is purely positive.