Intrinsic and Synaptic Determinants of Spike Timing Revealed by Phase Response Analyses of a Morphological Globus Pallidus Neuron Model Open Access

Schultheiss, Nathan W. (2010)

Permanent URL: https://etd.library.emory.edu/concern/etds/dr26xx804?locale=en
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Abstract

In neuronal systems the phase response curve (PRC) describes how synaptic
inputs to a neuron at different times during the spike cycle affect the timing of subsequent
spikes. The shapes of neuronal PRCs have been related extensively to entrainment of
spiking to correlated or periodic input and to the emergence of synchronous modes in
synaptically-coupled networks of neurons. Using a full morphological model of a globus
pallidus (GP) neuron, the studies presented here explore differences in PRC shape that
result 1) when stimuli are targeted to different regions of the neuronal morphology; 2)
when the densities of active conductances in the neuronal membrane are varied; and 3)
when intrinsic spiking is driven to different frequencies either by tonic somatic current
injection or by ongoing synaptic background activity. We demonstrate that during
intrinsic spiking, somatic PRCs for our GP neuron model are type I, indicating that
excitatory inputs at all phases of the spike cycle advance the spontaneous spiking rhythm.
In contrast, we show that distal dendritic PRCs are type II, i.e. excitatory inputs at early
phases of the spike cycle can delay subsequent spiking as a consequence of dendritic
activation of the small conductance calcium-activated potassium current, SK. Further
analyses presented in this dissertation demonstrate the robustness of somatic and
dendritic PRC shapes against stochastic barrages of excitatory and inhibitory synaptic
inputs. We also analyze on a trial-by-trial basis how PRC stimuli interact with
fluctuations in the synaptic background activity resulting in added or skipped spike
events, and we derive phase response-variance curves (PRVCs) illustrating a major
source of spike time variability that can be expected across populations of GP neurons in
vivo
. Lastly, we develop a tool, the cumulative PRC, for differentiating the contributions
of intrinsic mechanisms and synaptic backgrounds to the responses of the model across
multiple spike cycles. Taken together our results highlight the need to consider different
effects of somatic and dendritic synapses in the control of network activity, and we
identify a potential role for dendritic SK conductance in the orchestration of normal
pallidal activity as well as the pathological β-frequency synchronization accompanying
Parkinson's disease.

Table of Contents

Table of Contents


Chapter 1............................................................................................................................. 1
General Introduction ........................................................................................................... 1
Computation by Neurons and Networks......................................................................... 3
Neuronal Excitability and Active Membrane Conductances...................................... 3
Dendritic integration. .................................................................................................. 6
Phase Response Curve Analysis ..................................................................................... 8
Phase reduction. .......................................................................................................... 8
PRC derivation............................................................................................................ 8
Weak coupling and the infinitesimal PRC.................................................................. 9
Averaging.................................................................................................................. 10
Active Conductances and PRC Modulation. ............................................................ 12
Modulation of the Globus Pallidus. .......................................................................... 12
High conductance states of neurons in vivo. ............................................................ 14
Phase Response Analysis of a Morphological GP Neuron Model ............................... 15
Morphological GP neuron model.............................................................................. 16
Morphological modeling approach to PRC analysis of GP. ..................................... 17
Chapter 2........................................................................................................................... 19
Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration ........................ 19
Abstract ......................................................................................................................... 19
Introduction................................................................................................................... 21
Methods........................................................................................................................ 23
GP Neuron Model ..................................................................................................... 23
Morphology and Passive Electrical Properties. ........................................................ 23
Active Conductances. ............................................................................................... 24
Conductance Distributions and Density Tuning. ...................................................... 25
Simulation Protocols................................................................................................. 26
PRC Stimulation Protocol......................................................................................... 26
Faster Spiking and Higher-Order PRCs.................................................................... 27
Categorization of PRCs as type I or type II. ............................................................. 28
Membrane potential and channel current analysis.................................................... 29
Results.......................................................................................................................... 30
Responses to Weak Phasic Inputs............................................................................. 30
Responses to Larger Somatic Current Injections and Realistic Synaptic Inputs ...... 32
Type II PRCs from Stronger, More Distal Dendritic Inputs..................................... 34
Strong AMPA Inputs to D2D Evoked Outward SK Current in Excess of Combined Inward Synaptic and Membrane Currents. ............................................................... 36
Comparison of voltage-gated and synaptic currents explains somatic type I and dendritic type II PRCs............................................................................................... 38
The Type II Character of Distal Dendritic PRCs Directly Reflects Local SK Conductance.............................................................................................................. 39
Spike Frequency Dependence of Somatic and Dendritic PRCs ............................... 40
Dendritic Conductance Densities Modulate Dendritic PRCs ................................... 44
Dendritic SK conductance. ....................................................................................... 46
Type II Dendritic PRCs are robust within a large range of SK activation parameters.................................................................................................................................. 47
Discussion..................................................................................................................... 48
Phase Response Curve Analysis of a Morphological GP Neuron Model................. 49
GP model construction.............................................................................................. 49
Dendritic properties. ................................................................................................. 50
Dependence of PRC shape on physiological properties. .......................................... 51
Implications of PRC Behavior for GP Network Interactions ................................... 51
Chapter 3........................................................................................................................... 90
During in vivo-like high conductance states, synaptic background activity and intrinsic mechanisms interact to control spike timing and responses to synaptic input. ................ 90
Introduction................................................................................................................... 90
Results.......................................................................................................................... 92
Simulation of High Conductance States ....................................................................... 93
Synaptic Background Parameters Determine Frequency and Regularity of Spiking93
PRC Analysis During High-Conductance States...................................................... 95
Interactions of Phasic Synaptic Inputs with Ongoing Synaptic Backgrounds.......... 98
Added spikes, skipped spikes, and divergence events.............................................. 99
Discussion................................................................................................................... 108
Methods....................................................................................................................... 113
GP Neuron Model ................................................................................................... 113
Morphology and Passive Electrical Properties. ...................................................... 113
Active Conductances and Model Tuning................................................................ 114
PRC Analysis During High Conductance States .................................................... 115
Synaptic Backgrounds. ........................................................................................... 115
PRC Stimulation Protocol....................................................................................... 116
Chapter 4......................................................................................................................... 134
General Discussion ......................................................................................................... 134
Compartmental modeling approach to PRC analysis. ............................................ 135
Experimental PRCs................................................................................................. 135
Weak coupling and active membrane conductances. ............................................. 136
Conductance Interactions and Modulation of PRCs............................................... 139
Potential Effects of Inhibition................................................................................. 140
SK Controls Dendritic Processing of Synaptic Inputs to GP.................................. 142
Future Directions .................................................................................................... 142
References...................................................................................................................... 144

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