Intrinsic and Synaptic Determinants of Spike Timing Revealed by Phase Response Analyses of a Morphological Globus Pallidus Neuron Model Público
Schultheiss, Nathan W. (2010)
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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