NORTHWESTERN UNIVERSITY

Modeling of subthreshold voltage responses, synaptic integration and

backpropagating action potentials in CA1 pyramidal neurons

A DISSERTATION

SUBMITTED TO THE GRADUATE SCHOOL

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

for the degree

DOCTOR OF PHILOSOPHY

Field of Applied Mathematics

By

Rachel E. Trana

EVANSTON, ILLINOIS

August 2012

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© Copyright by Rachel E. Trana 2012

All Rights Reserved

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ABSTRACT

Modeling of subthreshold voltage responses, synaptic integration and backpropagating

action potentials in CA1 pyramidal neurons

Rachel E. Trana

Pyramidal neurons are composed of a cell body, or soma, extensively arborized den-

drites and a single axon. The dendrites of pyramidal neurons are the primary locations

for synaptic input, receiving tens of thousands of excitatory and thousands of inhibitory

synaptic contacts from other neurons. They also have numerous voltage-gated conduc-

tances enabling them to integrate synaptic input in a complex, nonlinear fashion to ulti-

mately regulate neuronal excitability and affect action potential firing. Dendrites typically

branch profusely, becoming narrower as they extend further away from the soma and main

apical trunk, making direct voltage recordings difficult. Computational modeling of neu-

rons can be used in combination with experimental techniques to help investigate the

properties of neuronal signaling. In this thesis, we use this combined approach to investi-

gate two topics: (1) Distance-dependent conductance scaling in CA1 pyramidal neurons,

and (2) the role of A-type potassium channels in shaping subthreshold voltage responses

in CA1 pyramidal neurons.

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As a result of the filtering properties of dendritic cables, EPSPs generated on distal

dendrites can attenuate so severely that they are unable to produce a significant somatic

voltage response. However, experimental and computational results indicate that CA1

pyramidal neurons possess a compensatory synaptic strengthening to counteract the re-

sulting attenuation, i.e., synapses more distant along the somatodendritic axis tend to be

stronger. We used computational models of biophysically realistic CA1 pyramidal neu-

rons to determine the extent to which synapses on distal dendrites could increase their

synaptic conductance to overcome attenuation. These models indicate that synapses on

more distal dendrites are unable to sufficiently increase their conductance to produce a

somatic voltage response. Consistent with these simulations, electron microscopy results

show that while AMPA receptor number increases (synaptic strengthening) in regions

more proximal to the soma, the most distal synapses in stratum lacunosum moleculare

do not exhibit this increase.

In order to better understand the complex mechanisms by which neurons integrate

synaptic input to generate action potentials, it is necessary to have compartmental mod-

els with voltage-gated conductances that reproduce experimental observations for action

potential firing as well as subthreshold events. Here we use somatic whole-cell recordings

of CA1 pyramidal neurons to investigate the subthreshold properties of A-type potas-

sium channels. Experimental results reveal a significant increase in both input resistance

and the time course of simulated somatic potentials when A-type potassium channels

were blocked with 4-aminopyridine, a selective potassium channel blocker. Incorporating

these results into a morphologically realistic CA1 neuron model not only yielded better

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fits to previous experimental results of CA1 subthreshold membrane properties, but also

accurately reproduced action potential backpropagation.

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Acknowledgements

The completion of a large research project is never the result of only one person’s

efforts. I am so pleased to have the opportunity to gratefully acknowledge the support

and thoughtfulness of everyone who helped me traverse this path.

First and foremost, I owe sincere and earnest gratitude to my advisor Bill Kath,

whose support, patience, insightful discussions and academic experience have not only

been invaluable, but without which, it would not have been possible to write this doctoral

thesis.

My co-advisor, Nelson Spruston, whose incredible ability to explain complex topics in

the simplest manner possible was only exceeded by his brilliance as a neuroscientist.

My committee members, Dr. David Chopp and Dr. William Olmstead, who have

taken the time to read this dissertation and have also provided direction and advice

throughout my graduate career.

My fellow student colleagues and friends, Yael Katz, Vilas Menon, Shannon Moore

and Joseph Hibdon, whose friendship and discussions made even the most difficult times

truly enjoyable.

Without Dan Nicholson, this thesis would be missing a chapter. I am truly grateful

for your help and your wonderful sense of humor that made all of our meetings truly

enjoyable.

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I am eternally grateful to my parents Carol and Steve, my brother Ethan, and my

uncle Sam - the eternal optimist. You have been a constant source of emotional and moral

support and your continuous love and encouragement made this thesis possible.

To my wonderful and incredibly supportive husband Donald - thank you for always

helping me to keep things in perspective.

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Dedication

This thesis is dedicated to my father, Dr. Stephen Trana. You taught me that anything

is possible. I will soar on wings like eagles, run and not grow weary, walk and not be

faint.

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Table of Contents

ABSTRACT 3

Acknowledgements 6

List of Tables 11

List of Figures 12

Chapter 1. Introduction 14

1.1. CA1 Pyramidal Neuron Morphology 16

1.2. Passive Electrical Properties 17

1.3. Influence of Dendrites: Nonisopotential Cells 20

1.4. Excitable Membranes: Ion Channels 29

1.5. Synaptic Integration 39

1.6. Work Presented 43

Chapter 2. Location-Dependent Variations in Synaptic Strength in Hippocampal

CA1 Pyramidal Neuron Models 46

2.1. Abstract 47

2.2. Introduction 48

2.3. Methods 51

2.4. Synaptic Scaling: Experimental Background 55

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2.5. Results 61

Chapter 3. A-type potassium channels shape subthreshold voltage responses in

hippocampal CA1 pyramidal neurons 82

3.1. Abstract 83

3.2. Introduction 83

3.3. Materials and Methods 85

3.4. Results 97

3.5. Discussion 114

Chapter 4. Conclusion 127

4.1. Integration of information in dendritic trees 128

4.2. Synaptic normalization in neuronal dendrites 128

4.3. Better models of voltage-gated ion channels 129

4.4. Future directions 131

References 133

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List of Tables

3.1 RN in control ACSF and 4-AP 99

3.2 Passive and active channel parameter values. 105

3.3 Na+ conductance distribution values for neuron models 110

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List of Figures

1.1 Hippocampal circuitry and pyramidal neuron morphology 18

1.2 Dendritic spine structure 19

1.3 Neuron segment used for the cable equation derivation 23

1.4 Equivalent electric circuit for multicompartmental model 27

1.5 Schematic diagram of the structure of an ion channel 30

2.1 Method of False-Position 53

2.2 Synapse ratio increases with distance from the soma 57

2.3 AMPAR Expression in Perforated and Nonperforated Synapses 59

2.4 NMDAR Expression in Perforated and Nonperforated Synapses 62

2.5 Simulated Somatic EPSPs 65

2.6 Modeling of the Synaptic Conductance Required for Normalization 69

2.7 Simulation of somatic EPSPs in a second neuron model 71

2.8 Modeling of synaptic conductances in a second neuron model 72

2.9 Modeling of synaptic conductances with active properties in a third

neuron model 75

2.10 Modeling of synaptic conductances with active properties in a fourth

neuron model 77

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3.1 RN changes in control ACSF and 4-AP 100

3.2 Somatic iEPSP area and amplitude in control ACSF and 4-AP 102

3.3 Best fits to estimated passive properties and gh distribution 106

3.4 K(A) channels are primarily responsible for lower Reff in distal locations108

3.5 Simulations of weak vs. strong backpropagation 111

3.6 Spike initiation in a CA1 pyramidal cell model 113

3.7 Model validation: Subthreshold current injections 115

3.8 Steady-state attenuation and MSE in fits to voltage transients 118

3.9 K(D) channels increase interspike intervals 125

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CHAPTER 1

Introduction

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Since as early as 4000 B.C., when an anonymous Sumerian writer described the eu-

phoric mind-altering effects of ingesting the poppy plant, the human brain has capti-

vated physicians, scientists, philosophers and the general public alike. Neuroscience, the

study of the nervous system, advances understanding of brain development and function

through critical research about molecules, neurons and the processes in and between cells.

However, even without considering the intricate interactions of large numbers of neurons

distributed throughout different regions of the brain, the study of a single neuron is ex-

traordinarily complex. To investigate these systems and individual neurons effectively,

computational methods are used in close collaboration with experimental research that

provides data to constrain these neural models, thus allowing for more accurate predic-

tions.

This thesis concentrates on the integrative properties and the underlying voltage-

gated ion channel mechanisms of individual hippocampal pyramidal neurons. A previous

experimentally constrained model of a CA1 pyramidal neuron was used to investigate the

extent to which an elaborately branched neuron can compensate for dendritic filtering

when processing synaptic inputs to influence action potential generation in the axon. In

a second project, experimental whole-cell recordings from hippocampal CA1 pyramidal

neurons are used to investigate the effect of A-type potassium and D-type potassium

channels on subthreshold voltage responses. These results are then incorporated into

the previously passive CA1 pyramidal cell model along with voltage-gated ion channel

models to create an active neuron model that accurately reproduces experimental results

on voltage attenuation and action potential backpropagation.

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1.1. CA1 Pyramidal Neuron Morphology

First characterized by Santiago Ramon y Cajal, pyramidal neurons are one the most

widely studied neurons in the brain and can be found in different regions of the brain

including the cerebral cortex, the amygdala and the hippocampus. In the CA1 region of

the hippocampus (Figure 1.1A,B), pyramidal neurons receive external excitatory input

from the entorhinal cortex via the perforant path. In addition, input from the entorhinal

cortex enters the dentate gyrus and is relayed to cells in the CA3 region, which in turn

project to neurons in the CA1 region via the Schaffer collateral pathway (Amaral and

Witter, 1989; Andersen et al., 1971). Within the hippocampus, CA1 neurons transmit

information via axons that project to neurons in the subiculum, an area that acts as an

output of the hippocampus (Amaral et al., 1991; Ramon y Cajal, 1995).

Pyramidal neurons are a main class of excitatory cells in the brain. CA1 pyramidal

neurons are easily distinguished by their triangularly shaped cell body, a long thick apical

dendrite, elaborate apical and basal dendritic arborizations, dendritic spines and a single

axon that branches extensively (Bannister and Larkman, 1995; Ramon y Cajal, 1995)

(Figure 1.1B). A single CA1 pyramidal neuron receives many excitatory (∼30,000) and

inhibitory inputs (∼1700) to its dendrites (Megıas et al., 2001). While the majority of in-

hibitory inputs target dendritic shafts, excitatory inputs primarily terminate on dendritic

spines. These dendritic spines are small extensions that protrude from the membranes of

dendrites and play a primary role in synaptic transmission and information storage. Typ-

ically characterized by their mushroom-like structure that consists of a bulbous head and

narrow neck that connects the spine to a dendritic shaft (Figure 1.2), dendritic spines vary

in size and can exhibit dynamic changes during synaptic plasticity (Harris and Stevens,

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1989; Hering and Sheng, 2001; Matsuzaki et al., 2004). The combination of an intricate

branched morphology and a large number of excitatory and inhibitory inputs located on

both dendritic shafts and spines provides a complex framework for synaptic integration

in CA1 pyramidal neurons.

1.2. Passive Electrical Properties

The electrical properties of a neuron are represented in terms of an equivalent electrical

circuit consisting of a capacitor to model the charge storage capacity of the cell membrane,

resistors that are used to model different ion channels and a battery that represents the

stored potential resulting from differing intracellular and extracellular ion concentrations.

In its simplest form, a neuron’s membrane behaves as a capacitor. It has a phospholipid

bilayer that acts as an insulator and separates the ionic charges (conductive solutions)

on each side of the membrane. Applying a voltage step across the cell membrane induces

a brief current that is proportional to the capacitance and the change of voltage with

respect to time. A given area of membrane has a fixed capacitance, called the specific

membrane capacitance (Cm), that is approximately the same for all neurons (1.0 µF/cm2).

Experimental and computational estimates of specific membrane capacitance in CA1 neu-

rons (Golding et al., 2001) are often close to this experimentally validated standard value

(Gentet et al., 2000; Major et al., 1994). The total membrane capacitance of a neuron,

cm, is proportional to the membrane surface area with the specific membrane capacitance

as the proportionality constant, cm = CmA. Therefore, the greater the membrane area,

the greater the capacitance.

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A

B

Figure 1.1. Hippocampal circuitry and pyramidal neuron morphology.A. Figure courtesy of Staff et al. (2000). The major signal pathways inthe hippocampal region. External input enters from the Entorhinal Cor-tex (EC) via the perforant path (purple) and terminate in the dentategyrus (DG) and CA3 regions. CA3 pyramidal neurons send connections tothe CA1 regions via their axons through the Schaffer collaterals (green).Granule cells in the DG send their axons (mossy fibers) to CA3 pyramidalneurons (blue). B. Figure courtesy of Yael Katz. CA1 pyramidal neuronmorphology indicating the location of inputs from the various hippocampalsignaling pathways.

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Figure 1.2. Dendritic spine structure.Spine-studded CA1 pyramidal neuron dendrites in a (figure courtesy ofWoolley et al., 1996) and b (figure courtesy of Matus, 2000). A three-dimensional reconstruction of a CA1 dendrite with spines (c, figure cour-tesy of Yankova et al., 2001), perforated and nonperforated postsynapticdensities (d, figure courtesy of Nicholson et al., 2006; Geinisman, 2000)and two-photon glutamate uncaging along a dendritic segment (e, figurecourtesy of Matsuzaki et al., 2001).

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Membrane resistance, which is reciprocally related to membrane conductance, refers

to how far the insulating properties of the membrane deviate from ideal, perfect insulation

and is determined by the density of open ion channels at resting potentials. Like membrane

capacitance, membrane conductance is proportional to membrane surface area. Thus, the

total membrane resistance is inversely related to its specific membrane resistance, rm =

Rm/A. Experimental estimates of the distribution and values of membrane resistance in

CA1 pyramidal neurons have been complicated by the technical restrictions of recording

from distal dendrites. However, recent advances in experimental techniques combined

with computational studies have suggested that the membrane resistivity of CA1 cells is

nonuniform, with a strong decrease from soma to distal apical dendrite (Golding et al.,

2005; Omori et al., 2006, 2009).

1.3. Influence of Dendrites: Nonisopotential Cells

The main equation that governs changes in neuronal membrane dynamics is the ca-

ble equation. Originally applied to calculations for the first transatlantic telegraph cable

by Lord Kelvin, the cable equation was eventually used in combination with experimen-

tal data to obtain insights on the ionic properties of the squid giant axon (Davis and

Lorente de No, 1947; Hodgkin and Huxley, 1952). In the 1950s, the advent of the glass

micro-electrode enabled researchers to gather experimental data from the cat motoneu-

ron. Initial estimates of membrane resistivity and intput resistance were about 10 times

too small due to neglecting dendritic cable properties and the size of the dendritic tree

(Coombs et al., 1955). Wilfrid Rall corrected these estimates by extending cable theory

to describe the flow of current in neurons with an extensive dendritic tree (Rall, 1959,

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1962). Rall’s calculations indicated that the electrotonic length of motoneuron dendrites

was only between one and two length constants. As a result, distal synapses could alter

somatic membrane potentials. The application of cable theory to neuron models with

extensive branching helped elucidate how electrical signals from multiple synapses at dif-

ferent locations are combined in a dendritic architecture that is composed of many different

diameters and varying electrophysiological properties. Using cable theory, neurophysiolo-

gists were able to determine that distal synaptic potentials in CA1 neurons undergo severe

attenuation as they propagate to the soma due to both axial and membrane resistance

(Golding et al., 2005; Magee and Cook, 2000; Rall, 1967).

1.3.1. The Cable Equation

For decades, neuroscientists and other researchers have been working to understand

and describe how networks of neurons process, store, integrate and relay information.

One approach to tackling the complexity of neuronal function and structure is to use

combined mathematical and computational techniques to create detailed descriptions of

functional and biologically realistic neurons (and neural systems) and their physiology

and dynamics. These computational models are used in conjunction with experimental

studies to generate hypotheses that can then be tested and/or verified by additional

experimentation to yield further insight.

1.3.1.1. Passive cable theory. At the root of compartmental modeling lies the cable

equation, which describes the variation in membrane potential along a neuronal cable

as a function of a spatial coordinate and time. To derive the cable equation, consider

a small dendritic segment (Figure 1.3A) with uniform passive membrane properties and

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longitudinal current flowing in one spatial direction (Jack et al., 1983; Rall, 1959; Segev,

1992). According to Ohm’s Law, a longitudinal current (iL) passing through the cable

segment at the location x = 0 causes a voltage drop through the resistor, such that

∆V = V(x+ ∆x)− V(x) (1.1)

∆V = −iLrL (1.2)

where V is the voltage, x is the location along the dendritic segment, rL is the longitudinal

intracellular resistance and current flowing in the direction of increasing x are defined as

positive. If the radius (a) of the dendritic segment is known, the intracellular resistivity

can be expressed in terms of specific intracellular resistivity (RL).

rL =RL

πa2(1.3)

∆V = − RL

πa2iL∆x (1.4)

Letting ∆x→ 0, the longitudinal current can be written as

iL = −πa2

RL

∂V

∂x. (1.5)

In order to derive the cable equation, Kirchoff’s current law is then used to sum all of

the currents flowing into and out of the the small dendritic segment (Figure 1.3B). These

currents, which are comprised of the longitudinal, membrane and electrode currents, are

set equal to the current that is needed to charge the membrane:

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A

B

Figure 1.3. Neuron segment used for the cable equation derivation.A. A neuron segment with length ∆x and radius a. Current is defined aspositive when flowing in the direction of increasing x. B. Currents flowinginto and out of the neuron segment that alter the rate of change of themembrane potential. Figure courtesy of William Kath.

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ic = iL

∣∣∣left− iL

∣∣∣right

+ ie − im (1.6)

2πa∆xCm∂V

∂x= −πa

2

RL

∂V

∂x

∣∣∣∣left

+πa2

RL

∂V

∂x

∣∣∣∣right

+ 2πa∆xie − 2πa∆xim (1.7)

where im is the membrane current and ie is the electrode current. Letting ∆x → 0, a

form of the cable equation can be obtained.

Cm∂V

∂t=

1

2aRL

∂

∂x

(a2∂V

∂x

)+ ie − im (1.8)

Assuming that the cable segment has constant radius and that there is no additional

current from an electrode (ie = 0), the above equation can be multiplied through by the

specific membrane resistance (Rm) to be written in the common form,

τ∂V

∂t= λ2∂

2V

∂x2− imrm (1.9)

where τ is the membrane time constant (RmCm) and λ is the electrotonic length with

units of length (λ =√aRm/2RL).

The product of the membrane capacitance and resistance is the membrane time con-

stant, τ . This quantity is independent of membrane area and as a result, can be calculated

using the specific membrane capacitance and resistance (τ = RmCm) or total membrane

capacitance and resistance (τ = rmcm). The membrane time constant is the basic fun-

damental time scale. In an isopotential cell, it describes the amount of time it takes for

a cell to reach 63% of its steady state response following a voltage change. The passive

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time constant can be used to characterize the time scale of a cell’s membrane response to

input.

In addition to membrane capacitance, signal propagation is also affected by the mem-

brane resistance and axial or longitudinal resistivity of a neuron. Axial resistivity (RL),

which is proportional to cytoplasmic resistance, also contributes to the speed and dis-

tance an impulse can travel along a neural cable. The electrotonic length constant, λ,

which describes the rate, with respect to distance, at which an electrical signal degrades

along a dendrite or axon, is dependent on both membrane and axial resistance, such that

λ =√aRm/2RL. Hence, λ increases with Rm (lower signal degradation) and decreases

with RL (higher signal degradation).

In order to apply this equation to dendritic trees, the biophysical properties of den-

drites were idealized such that dendrites could be collapsed into an equivalent single cylin-

der (Rall, 1962), allowing for an analytical solution to a transient current input. While

the equivalent cylinder model cannot capture all physiological responses of a dendritic

arborization, it nevertheless led to a broader understanding of the behavior of passive

cables. Significantly, it helped to clarify how voltage is attenuated along a neural cable

due to distance traveled from the stimulus origin, intrinsic membrane properties such

as diameter, Rm and RL, as well as signal frequency and stimulus location relative to

branching points and cable terminals.

1.3.1.2. Nonlinear cable theory. Since the idealized concept that dendritic branches

were only passive cylindrical structures was unrealistic, Rall developed a multicompart-

mental neuron model to account for nonlinearities due to synaptic currents and voltage-

dependent membrane properties. When active channels present at resting potentials are

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engaged, the superposition of passive and active properties can alter the integration of in-

puts nonlinearly, thereby triggering dendritic spikes. Mathematically, the compartmental

modeling approach uses a finite-difference approximation to the nonlinear cable equa-

tion, replacing the previous continuous cable representation of a neuron by electrically

short, isopotential and spatially uniform compartmental segments (Figure 1.4). Adjacent

compartments are connected via a longitudinal resistivity as described by the dendritic

architecture. As a result, differences in membrane properties and structure (diameter, re-

sistivity, synaptic inputs) and hence, membrane potential, occur between compartments

as opposed to within them (Holmes et al., 1992; Koch and Segev, 1998; Perkel et al., 1981;

Rall, 1964).

Thus, the nonlinear cable equation can be written as a system of coupled, first-order

differential equations (V = A~V + ~b) such that, for the jth compartment,

cjdVj

dt+ Iionj

(vj , t) + Istimj(vj , t) =

Vj−1 − Vj

rj−1 , j

− Vj − Vj+1

rj , j+1

(1.10)

where Vj is the voltage, Iionjand Istimj

are the ionic, capacitative and external current

sources, rj−1 , j is the axial resistance between the j -1 and the jth compartments. Nonlinear

voltage-gated conductances, Iionj, will be described later in this text.

1.3.1.3. Numerical Methods. If the coefficient matrix A of the above system is con-

stant, i.e. corresponding to passive properties that are not voltage-dependent, the system

can be transformed into a linear set of equations (the linear cable equation) and can be

solved analytically through the inversion of matrix A or with a stable and accurate nu-

merical integration scheme. However, when voltage-dependent conductances or synaptic

conductances that produce nonlinearities are introduced into the system, the coefficients

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j - 1 j + 1j

Vj-1 Vj Vj+1

rj-1

2

rj

2

rj+1

2

rj-1

2

rj

2

rj+1

2

i j-1, j i j, j +1

I ion j

i m j

r m jc m j

Figure 1.4. Equivalent circuit for multicompartmental model with threecylindrical segments. Figure courtesy of Koch and Segev, 1998.

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are no longer constant and numerical integration methods must be used to determine a

solution.

The NEURON simulation environment, used for all simulations described in this dis-

sertation, offers several different integration methods. The default integration method is

Backward Euler (Hines and Carnevale, 1997), a low-accuracy implicit numerical method

that can be used to solve stiff equations. All simulations described in this dissertation use

NEURON’s adaptive CVode integrator (Cohen and Hindmarsh, 1996). The CVode inte-

grator class is an interface that is implemented on top of the CVODES and IDA solvers

that are part of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation

Solvers) differential and algebraic equation solvers suite. Both the CVODES and IDA

integration methods can be used to solve stiff and nonstiff ordinary differential equation

(ODE) systems.

The CVODES suite includes a forward-sensitivity analysis (FSA) method and an

adjoint sensitivity analysis (ASA) method, in addition to the variable order, variable step

Adams-Moulton method (for nonstiff problems) and Backward Differentiation method (for

stiff problems) that comprise the regular CVODE suite (Serban and Hindmarsh, 2005).

Both sensitivity analysis methods help to determine the correlation between changes in

model parameters and the corresponding changes in model output in order to aid in model

optimization or parameter estimation.

Similar to CVODES, there is also an IDAS solver suite that includes all of the func-

tionality of the IDA suite, as well as sensitivity analysis. However, NEURON uses only

the IDA differential-algebraic equation solver suite designed for equations of the form

F (t, y, y′) = 0. IDA uses a variable order, variable-coefficient Backward Differentiation

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integration method and achieves a solution of the nonlinear system through either a Mod-

ified or Inexact Newton iteration (Hindmarsh, 2000).

1.4. Excitable Membranes: Ion Channels

The distributions and types of ion channels present in a neuron are important for

determining its firing properties and electrophysiological behavior. Ion channels are com-

plexes of transmembrane proteins (Figure 1.5) that selectively facilitate the passage of ions

into and out of a cell down their electrochemical gradient (Hille, 2001). These channels

can be classified according to the gating mechanism that allows or prevents ion movement

across the membrane, as well as their specific ion permeability. There are two primary

types of gating mechanisms: voltage-gated and ligand-gated. Voltage-gated ion channels

are activated by changes in membrane potentials, resulting in a conformational change of

the pore structure to an open or closed state. Ligand-gated channels rely on the binding

of specific ligand molecules to extracellular sites, causing a change in the structure of the

channel protein.

Axons and dendrites of pyramidal neurons have a diverse distribution of Na+, K+

and Ca2+ channels which enable a cell to sum transmembrane potentials linearly or non-

linearly to generate action potentials or other regenerative events (Magee and Carruth,

1999). In addition, dendritic ion channels may have different activation and inactivation

properties from their somatic counterparts as well as varying density distributions based

on their location (Magee, 1998; Menon et al., 2009; Migliore et al., 1999; Yuan and Chen,

2006). In combination with neuron morphology, the distribution and properties of ion

channels modulate dendritic excitability and the ability of a cell to integrate synaptic

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Figure 1.5. Schematic diagram of the structure of an ion channel.The ion channel protein structure typically involves a circular arrangementof identical or homologous membrane-spanning proteins closely arrangedaround a pore through the plane of the membrane or lipid bilayer. Figurecourtesy of Bear et al., 2001.

31

input. While this dissertation is largely concerned with synaptic scaling and A-type

potassium channels and their effect on subthreshold voltage responses, I have also included

detailed descriptions of the other ion channels used in my computational models.

1.4.1. Sodium Channels

First recorded and characterized by Hodgkin and Huxley, voltage-gated sodium cur-

rents play an important role in the initiation and propagation of action potentials in

CA1 pyramidal neurons. The core of the voltage-gated sodium channel is composed of a

large α subunit, consisting of four homologous domains that each contain six membrane-

spanning proteins. The α subunit is responsible for channel opening, ion selectivity and

rapid inactivation. In addition, sodium channels contain one or more smaller β subunits

that modify the kinetics and voltage-dependence of the channel (Catterall, 2000; Yu and

Catterall, 2003). Sufficient depolarization of the cell membrane activates Na+ channels,

allowing an influx of Na+ ions to permeate the membrane, further depolarizing the cell

and initiating the rising phase of an action potential.

1.4.1.1. Axonal Sodium Channels. Studies using local application of tetrodotoxin

(TTX) to the axon initial segment (AIS) have localized the site of action potential initia-

tion to a region proximal to the first node of Ranvier (Colbert and Johnston, 1996; Colbert

and Pan, 2002; Stuart et al., 1997). Electrophysiological and computational results sug-

gest that both a high density of Na+ channels (Kole et al., 2008) and a hyperpolarized

shift in the activation properties, relative to the soma, of Na+ channels contribute to

the low spike threshold in the AIS (Hu et al., 2009; Mainen et al., 1995; Royeck et al.,

2008). Three Na+ channel isoforms, Nav1.1, Nav1.2 and Nav1.6, have been detected at

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the AIS. Of these, the Nav1.6 subunits exhibit a unique hyperpolarized voltage of acti-

vation relative to the other Na+ channels and are targeted at the distal end of the AIS,

whereas Nav1.2 channels accumulate preferentially at the proximal end of the AIS. The

distributions of these two Na+ subunits are consistent with studies that indicate that the

distal end of the AIS is the site of action potential initiation (Colbert and Johnston, 1996;

Colbert and Pan, 2002; Stuart et al., 1997).

1.4.1.2. Dendritic Sodium Channels. From the spike initiation zone at the AIS, ac-

tion potentials propagate along the axon and also backpropagate into the dendrites. The

integration and propagation of signals in the distal dendrites of hippocampal CA1 neu-

rons is strongly mediated by the distribution, density and voltage-dependent properties of

Na+ channels in the dendrites. The voltage-dependent properties and gating kinetics of

Na+ channels were first characterized by Hodgkin and Huxley (1952) through a series of

voltage-clamp experiments. These experiments showed that Na+ channels were activated

at depolarized voltage potentials and then inactivate quickly with continued depolariza-

tion, facilitating repolarization to the resting potential. In addition to this relatively fast

form of inactivation, Na+ channels have also undergo a much slower form of inactivation,

resulting in a gradual decrease of spike amplitude during repetitive firing (Colbert et al.,

1997; Jung et al., 1997; Martina and Jonas, 1997; Rudy, 1981).

Similar to sodium channels in the AIS and nodes of Ranvier, somatic and dendritic

sodium channels also express the Nav1.2 and Nav1.6 subunits. In dendrites, these isoforms

underlie dendritic Na+ spikes and nonlinear synaptic integration (Colling and Wheal,

1994; Magee and Johnston, 1995; Golding and Spruston, 1998; Lorincz and Nusser, 2010).

33

Studies using immunogold localization of Nav subunits in the somatodendritic compart-

ments of cortical pyramidal cells have revealed a gradual decrease in the density of fast-

activating Nav1.6 channels along the primary apical dendrite (Lorincz and Nusser, 2010).

Furthermore, cell-attached recordings from the soma and dendrites of CA1 pyramidal

neurons have found that the amount of slow-inactivation of Na+ channels gradually in-

creases as a function of distance from the soma (Mickus et al., 1999). As slow-inactivation

is strongly dependent on firing frequency and history as well as the amplitude of depolar-

ization (Colbert et al., 1997; Jung et al., 1997; Martina and Jonas, 1997; Mickus et al.,

1999), these findings have important implications as to the role of Na+ channels (both

fast-activating and slowly-inactivating) in distal dendrites in mediating not only dendritic

excitability and synaptic plasticity, but also neuronal output within the hippocampal

circuit.

1.4.2. Hyperpolarization-activated Cation Channel

Hyperpolarization-activated cation currents, Ih, are inwardly-rectifying voltage-gated

ion channels equally permeable to both Na+ and K+ ions. Originally found and charac-

terized in sino-atrial node myocytes, Ih channels were referred to as ‘pacemaker’ channels

for their role in contributing to slow pacemaker depolarization and spontaneous activity

(DiFrancesco, 1986, 1993; Noma et al., 1983; Yanagihara and Irisawa, 1980). Following

their discovery in cardiac cells, Ih channels were also described in a wide number of other

neuronal cell types such as thalamic, hippocampal and cochlear nucleus neurons, where

they influence resting membrane properties (Bal and Oertel, 2000; Halliwell and Adams,

1982; Maccaferri et al., 1993; Pape and McCormick, 1989; Pape, 1996).

34

Four mammalian HCN (hyperpolarization-activated cyclic nucleotide-sensitive) genes

provide the molecular basis for Ih channels (Biel et al., 1999; Ludwig et al., 1998; Robinson

and Siegelbaum, 2003; Santoro et al., 2000). While all four of the HCN isoforms (termed

HCN1-4) give rise to hyperpolarization-activated cation currents that are modulated by

cyclic adenosine monophosphate (cAMP or cyclic AMP), each of the HCN isoforms un-

derly Ih channels with distinctly different voltage dependencies, activation kinetics, and

sensitivity to cAMP (Ludwig et al., 1999; Moosmang et al., 2001; Santoro et al., 1997;

Santoro and Tibbs, 1999; Santoro et al., 2000). In the hippocampus, HCN1 and HCN2

are expressed in both CA1 and CA3 neurons, with a stronger expression of HCN1 in

CA1 pyramidal neurons than in CA3 and a stronger expression of HCN2 in CA3 neurons

than in CA1. The HCN4 isoform is only weakly expressed in the hippocampus and is

prevalent in neurons of the thalamus, olfactory bulb and specific populations within the

basal ganglia. Of all the HCN genes, the HCN3 isoform is the most weakly expressed and

can be found in the thalamus and olfactory bulb.

HCN1, which is found predominantly in CA1 pyramidal neurons and distributed with

an over sixfold increasing gradient from soma to distal dendrite (Lorincz et al., 2002;

Magee, 1998), produces Ih channels that have the fastest activation kinetics. Ih channels

exhibit a reversal potential near -30 mV as a result of the permeability ratio of Na+ to

K+. Hyperpolarizations activate the Ih current, causing a net inward current due to Na+

ions, thus depolarizing the membrane back to the resting potential and resulting in a

membrane sag. Ih channels are active at resting potentials, thus causing the membrane to

be leakier and decreasing both the effective membrane time constant and input resistance

of a neuron. This results in a shorter electrotonic length due to having Ih channels active

35

at rest and speeds up the decay of EPSPs, effectively increasing amplitude attenuation

as they propagate from soma to distal dendrite (Berger et al., 2001; Fernandez et al.,

2002; Golding et al., 2005; Stuart and Spruston, 1998). However, because of the voltage-

dependent deactivation of Ih channels during depolarizations, a net outward current is

generated. The amplitude of this outward current increases with distance from the soma

as a result of the increasing gradient of Ih channels, thus creating a spatial normalization

for the temporal summation of EPSPs at the soma (Magee and Carruth, 1999; Williams

and Stuart, 2000).

1.4.3. Potassium Channels

Compared to Na+ channels, K+ channels activate more slowly in response to depo-

larization. However, as they have a negative reversal potential, these channels serve to

reduce the overall excitability of a cell, aid in the repolarization phase of the action poten-

tial, set the membrane resting potential and mediate high-frequency firing (Hille, 2001).

There are four main groups of K+ channels: voltage-gated, leak, inward-rectifying and

calcium-activated. For the purposes of this dissertation, I will restrict my discussion to

voltage-activated K+ channels. Voltage-gated K+ channels are homotetrameric, with four

subunits arranged symmetrically to create an ion permeation pathway which contains the

filter for ion selectivity (Bezanilla and Armstrong, 1972; Choe, 2002; Gulbis et al., 1999;

Doyle et al., 1998; MacKinnon, 1991). Between these subunits stretches two transmem-

brane helices and a loop composed of a short amino acid segment. The two helices and

the short loop are a key feature of the K+ channel family, but vary between the four K+

channel groups (Lu et al., 2001). Based on the amino terminal domain sequence of the

36

tetramer transmembrane core, the voltage-gated K+ channels can be further grouped into

four subfamilies: Shaker (Kv1), Shab (Kv2), Shaw (Kv3) and Shal (Kv4). CA1 pyramidal

neurons exhibit four main K+ currents, of which three derive from the four K+ channel

subfamilies: a delayed-rectifier K+ (Kv2), A-type K+ current (Kv4), D-type K+ current

(Kv1) and M-type K+ (KCNQ subfamily) (Chen and Johnston, 2004; Choe, 2002; Con-

forti and Millhorn, 1997; Murakoshi and Trimmer, 1999; Selyanko and Sim, 1998; Sheng

et al., 1992; Storm, 1990; Yuan and Chen, 2006).

1.4.3.1. Delayed-rectifier potassium channel. While the Kv1, Kv2 and Kv3 subfam-

ilies all give rise to various delayed rectifier potassium currents, the Shaw Kv3 subfamily

in CA1 hippocampal pyramidal neurons produces delayed rectifier potassium channels

with currents that activate relatively fast at voltages more positive than -10 mV, have no

inactivation and which deactivate very fast (Lai and Jan, 2006; Martina et al., 1998; Rudy

and McBain, 2001). These channels are activated quickly during repolarization of the ac-

tion potential and then quickly deactivate to allow further action potential generation.

This fast-activating delayed rectifier current also contributes to sustained high-frequency

firing.

1.4.3.2. A-type potassium channel. First characterized by Connor and Stevens in

gastropod neural somata (Connor and Stevens, 1971), the A-type potassium channel has

the most rapid inactivation kinetics out of all the potassium currents, as well as rapid

activation kinetics over hyperpolarized voltage ranges (Chen and Johnston, 2004; Coetzee

et al., 1999). The molecular correlates of the A-type potassium channels are Kv1.4 and

Kv4.1-3, members of the Kv4 (Shal) and Kv1 (Shaker) subfamilies. Immunohistochemi-

cal studies show that Kv1.4 proteins are primarily found in the axons of CA1 pyramidal

37

neurons (Gu et al., 2003), whereas Kv4.2 proteins are highly expressed in hippocampal

CA1 dendrites and the somatodendritic region (Serodio et al., 1996; Sheng et al., 1992;

Varga et al., 2000). Furthermore, the Kv4.1 transcript is not highly expressed in the

hippocampus and hippocampal Kv4.3 proteins have been shown to be primarily located

in interneurons (Lien et al., 2002; Rhodes et al., 2004; Serodio and Rudy, 1998), suggest-

ing that in hippocampal CA1 pyramidal neurons, the A-type potassium current (IA) is

primarily mediated by the Kv4.2 subunit. Further studies involving Kv4.2 knockout mice

have demonstrated that deletion of the Kv4.2 gene in CA1 pyramidal neurons eliminated

the IA current, supporting the previous immunohistochemical studies (Chen et al., 2006).

Distributed with an almost five-fold increasing gradient from soma to the apical den-

drites, IA plays a major role in regulating dendritic excitability (Hoffman et al., 1997). As

a result of its rapid activation and inactivation kinetics and its low activation threshold

(near resting membrane potentials), IA serves to prevent or limit large, rapid depolar-

izations. Current injections that normally produce subthreshold voltage responses have

been shown to cause suprathreshold bursts of action potentials in the presence of A-type

potassium channel blockers (Magee and Carruth, 1999), thus strongly increasing neuronal

excitability. As a result, any mechanisms, such as phosphorylation, that alter the avail-

ability of A-type potassium channels or their activation kinetics, leading to a reduction

of IA current, would modulate dendritic excitability (Anderson et al., 2000; Hoffman and

Johnston, 1998; Yuan et al., 2002). A-type potassium channels have also been implicated

in shaping action potentials and regulating action potential backpropagation (Hoffman

et al., 1997; Johnston et al., 2000; Kim et al., 2005; Migliore et al., 1999), synaptic integra-

tion (Cash and Yuste, 1999; Makara et al., 2009; Ramakers and Storm, 2002), long-term

38

potentiation (Chen et al., 2006; Frick et al., 2004; Watanabe et al., 2002) and Na+-spike

initiation and propagation (Losonczy et al., 2008).

1.4.3.3. D-type potassium channel. In CA1 pyramidal neurons, the dendrotoxin-

sensitive (DTX) D-type potassium current (ID) is a slowly-inactivating outward current

that activates in the subthreshold range, has enhanced sensitivity to 4-aminopyridine (4-

AP) and plays a prominent role in delayed excitation, regulation of calcium-dependent

spikes and reducing spike afterdepolarization (Golding et al., 1999; Metz et al., 2007;

Storm, 1988; Wu and Barish, 1992). While the molecular determinants of D-type potas-

sium channels have not yet been confirmed, colocalizations and coassociations of Kv1

subunits, such as Kv1.2 with Kvβ2, are thought to compose the basis for D-type potas-

sium channels due to their DTX-sensitivity (Monaghan et al., 2001; Rhodes et al., 1997).

The distribution of D-type potassium channels in CA1 pyramidal neurons has also yet

to be fully determined. Application of DTX to somatic nucleated patches in CA1 pyra-

midal cells has very little effect on potassium currents, indicating that D-type potassium

channels are not present in the soma. Consistent with in situ hybridization and im-

munocytochemical studies that show that Kv1.2 subunits are concentrated primarily in

dendrites (Martina et al., 1998; Sheng et al., 1994), simultaneous somatic and dendritic

current-clamp recordings with local application of DTX further suggest that the density

of D-type potassium channels are higher in distal dendrites relative to more proximal ones

in CA1 pyramidal neurons (Metz et al., 2007).

39

1.5. Synaptic Integration

CA1 pyramidal neurons have elaborate dendritic trees that receive tens of thousands of

synaptic inputs, which are then shaped and integrated through a complex combination of

factors such as membrane conductances, morphology, size and relative timing of synaptic

inputs, summation of inhibitory and excitatory inputs, as well as the location of synaptic

inputs. The ability of a neuron to computationally process the interaction of multiple

synaptic events to shape neuronal output is known as synaptic integration.

1.5.1. Excitatory synapses

Chemical synapses are either excitatory or inhibitory depending on how neurotrans-

mitter release affects the likelihood of action potential generation. Neurotransmitters are

released from presynaptic boutons following action potential invasion of the presynaptic

terminal and diffuse across the synaptic cleft to bind to receptors in the postsynaptic

membrane. The binding of neurotransmitters at an excitatory synapse causes ion chan-

nels (typically Na+ channels) to open, resulting in a depolarization of the postsynaptic

membrane and generating an excitatory postsynaptic potential (EPSP) (Chua et al.,

2010; Hille, 2001). Physically, excitatory synapses can be differentiated from their in-

hibitory counterparts by an electron-dense thickening of their postsynaptic density (PSD),

a protein-dense region attached to the postsynaptic membrane, which causes them to ap-

pear asymmetrical (Colonnier, 1968; Gray, 1959; Uchizono, 1965).

Glutamate is the main excitatory neurotransmitter in the central nervous system and

plays a primary role in long term potentiation and subsequently, learning and memory. It

40

can bind to several ionotropic and metabotropic receptors, including α-amino-3-hydroxy-

5-methyl-4-isoxazolepropionic acid (AMPA) and N -methyl-D-asparate (NMDA) receptors

(Maren and Baudry, 1995). While glutamate binds to and opens both AMPA and NMDA

receptors, NMDA receptors are blocked by Mg2+, requiring depolarization to remove the

blockade, allowing Ca2+, Na+ and K+ ions to flow through. The activation of NMDA re-

ceptors is believed to control the occurrence of long-term potentiation, underlying synaptic

plasticity and memory formation (Malenka and Nicoll, 1993).

The majority of fast excitatory synaptic transmission occurs through AMPA receptors.

In the hippocampal CA1 region, AMPA receptors are composed of heteromers comprised

of the glutamate receptor subunits GluR2, plus either GluR1 or GluR3 subunits (Dingle-

dine et al., 1999). The subunit composition of an AMPA receptor determines its perme-

ability to calcium and other cations, such as sodium and potassium. The presence of the

GluR2 subunit, evidenced in the majority of CA1 pyramidal neurons, leads to calcium

impermeability as well as low open probability and conductance, thus strongly affecting

AMPA receptor properties and hence, synaptic transmission and plasticity. Alterations to

AMPA receptor properties in CA1 pyramidal GluR2-containing neurons have suggested

that AMPA receptors play a primary role in long lasting, activity-dependent synaptic

strengthening during long-term potentiation (LTP) and depression (LTD), which are be-

lieved to be critical for the initial formation and maintenance of new memories (Derkach

et al., 2007).

41

1.5.2. Action potentials and dendritic spikes

The primary method of communication between neurons is by the collective summa-

tion and filtering of multiple excitatory and inhibitory synaptic potentials to fire an action

potential. Although a solitary EPSP may depolarize the dendritic membrane enough to

result in voltage-gated ion channels opening, the attenuation of the EPSP as it travels

passively down the dendritic tree to the soma will be insufficient to depolarize the so-

matic membrane past threshold to generate an action potential. However, if multiple

excitatory synapses are synchronously activated, the combined depolarization from the

summed input can reach a threshold level of depolarization and trigger regenerative open-

ing of voltage-gated ion channels, resulting in a dendritic spike (Golding and Spruston,

1998; Gasparini et al., 2004). Under conditions of strong synaptic stimulation from mul-

tiple locations, these dendritic spikes can forward propagate from the dendrites to the

soma, possibly inducing a somatic action potential (Gasparini et al., 2004; Jarsky et al.,

2005).

Dendrites of CA1 pyramidal neurons contain voltage-gated conductances allowing

them to generate two types of dendritic spikes via synaptic stimulation: fast Na+-

dependent spikes and slower Ca2+-dependent spikes (Golding and Spruston, 1998; Golding

et al., 1999). In CA1 pyramidal neurons, dendritic spikes can exhibit two distinct meth-

ods of forward propagation (Gasparini et al., 2004). First, regenerative spikes can remain

localized to a limited region of the dendritic tree thus having little impact on somatic

membrane potential (Golding and Spruston, 1998; Golding et al., 1999; Schiller et al.,

1997). When combined with current injection or synaptic input activated within a spe-

cific time window relative to the initiation of the dendritic spikes, regenerative potentials

42

can fully forward-propagate to the soma to generate a backpropagating action potential

that then interacts with the regenerative dendritic response (Larkum et al., 2001). Unlike

other types of neurons, such as hippocampal oriens-alveus interneurons or layer 5 pyra-

midal neurons, where dendritic voltage-gated conductances are able to reliably propagate

dendritic spikes to the soma without coincident synaptic input, distal regenerative spikes

in CA1 pyramidal neurons do not propagate reliably to the soma without membrane

depolarization (Larkum et al., 2001; Martina et al., 2000; Williams and Stuart, 2002).

1.5.3. Synaptic location independence

Combined experimental and computational studies have shown that synaptic poten-

tials evoked in distal dendrites of the CA1 stratum lacunosum-moleculare (SLM) region

are strongly attenuated by dendritic filtering properties as they propagate to the soma

(Golding et al., 2005; Rall, 1967; Williams and Stuart, 2003) and that without mecha-

nisms in place to counteract dendritic cable properties, distal inputs would be unable to

effectively influence neuronal output. If distal inputs and dendrites have no effective way

of influencing neuronal output, what is their role? To further investigate this puzzling

question, experiments in CA1 pyramidal neurons have been performed to determine the

somatic impact of EPSPs generated at increasing distances along the primary apical den-

drite (Magee and Cook, 2000; Stricker et al., 1996; Williams and Stuart, 2002). These

studies revealed that the amplitudes of locally-generated synaptic potentials increased

with distance from the soma along the primary apical dendrite. The resulting amplitudes

of somatic potentials were indistinguishable with an average somatic EPSP amplitude of

43

0.2 mV, suggesting that synapses modulate their strength as a type of distance compensa-

tion for dendritic filtering. Consistent with these studies, experiments using conventional

and postembedding immunogold electron microscopy were conducted to determine the

number and strength of AMPA receptors in excitatory synapses along the primary api-

cal dendrites of CA1 pyramidal neurons (Andrasfalvy and Magee, 2001; Nicholson et al.,

2006). These experiments show that AMPA receptor density increases with distance from

the soma such that synapse number in the distal stratum radiatum (dSR) was increased

relative to proximal stratum radiatum (pSR), but decreases in SLM relative to dSR and

pSR, indicating the synapses in stratum radiatum may compensate for their distance from

the soma through a form of synaptic strengthening.

In addition to conductance scaling, studies suggest for more distal synapses (SLM),

distance compensation may occur through dendritic spikes. The forward propagation of

dendritic spikes originating in SLM may be enhanced by moderate synaptic input from

stratum radiatum (SR) (Jarsky et al., 2005) to drive action potential generation at the

soma. Together, these two mechanisms of distance compensation may enable inputs in

more distal locations to affect somatic output.

1.6. Work Presented

There are many open questions surrounding the role of distal synaptic inputs in pro-

ducing neuronal output, as well as many questions regarding the dendritic and somatic

voltage-gated channels that contribute to integrating dendritic inputs. In this thesis, I

seek to address two important questions related to synaptic integration of subthreshold

voltage responses: (1) How do synapses in CA1 pyramidal neurons compensate for their

44

distance from the soma, and (2) What is the role of A-type potassium channels in shaping

subthreshold voltage responses in CA1 pyramidal neurons.

1.6.1. Normalization of distal synaptic inputs

To further understand the consequences of the experimentally determined distributions

of synapses and synaptic strength in CA1 pyramidal neurons (Nicholson et al., 2006), I

performed computer simulations with a passive CA1 neuron model. Initial simulations

investigated the resulting somatic potentials for given synaptic conductances (gsyn) based

on the average amplitude of miniature EPSPs (mEPSPs) in SR (Magee and Cook, 2000)

and the relative level of AMPA receptor expression. Consistent with experimental studies,

the simulation results indicate that SLM synapses are unable to overcome the effects of

dendritic filtering and subsequently produce smaller somatic EPSPs relative to responses

from more proximal inputs.

Using this same model, I also investigated how much of an increase in gsyn was neces-

sary to produce the average 0.2 mV somatic voltage response seen in previous experimental

studies of synaptic location independence (Magee and Cook, 2000). Consistent with the

electron microscopy results, synapses in pSR and dSR needed only moderate increases in

synaptic strength to effect a 0.2 mV somatic depolarization. However, synapses in SLM

required a much larger increase in synaptic strength (10 - 1000 times larger) and in some

cases, reached a local depolarization of -30 mV, a voltage above threshold for generating

dendritic spikes, at a lower conductance value than the conductance required to produce

a 0.2 mV somatic voltage response (Nicholson et al., 2006).

45

1.6.2. A-type potassium channels shape subthreshold voltage responses

Previous experimental studies and passive neuron models have suggested that mem-

brane resistance in CA1 pyramidal neurons is nonuniform, such that distal dendrites

are ‘leakier’ than dendrites located proximal to the somatic region (Golding et al., 2005).

While accurately reproducing voltage attenuation as a function of distance from the soma,

these passive models were unable to accurately reproduce specific aspects of subthreshold

voltage responses such as the time course of voltage sag for hyperpolarizing current injec-

tions. However, CA1 pyramidal neurons are not passive and have been shown to contain

a wide variety of voltage-gated conductances, such as the A-type potassium conductance,

that are open at resting potentials.

Here we combined whole-cell somatic patch clamp recordings of CA1 pyramidal neu-

rons in bath application of differing concentrations of 4-AP with computational modeling

to investigate the role of A- and D-type potassium channels in regulating subthreshold

voltage responses. The experimental results show that while pharmacological block of

D-type potassium channels did not significantly alter input resistance, pharmacological

block of A-type potassium channels yielded an almost 27% increase in input resistance as

compared to control conditions. Incorporating these results into a computational model

of a morphologically realistic neuron provides more accurate fits to subthreshold voltage

responses.

46

CHAPTER 2

Location-Dependent Variations in Synaptic Strength in

Hippocampal CA1 Pyramidal Neuron Models

47

2.1. Abstract

The ability of synapses throughout the dendritic tree to influence neuronal output is

crucial for information processing in the brain. Synaptic potentials attenuate dramati-

cally, however, as they propagate along dendrites toward the soma. Previous experimental

studies have examined whether excitatory axospinous synapses on CA1 pyramidal neu-

rons compensate for their distance from the soma to counteract such dendritic filtering.

Immungold electron microscopy was used to evaluate axospinous synapse number and

receptor expression in three progressively distal regions : proximal and distal stratum ra-

diatum (SR), and stratum lacunosum-moleculare (SLM). These experiments showed that

the proportion of perforated synapses increases as a function of distance from the soma

and that their AMPAR, but not NMDAR, expression is highest in distal SR and lowest

in SLM (Nicholson et al., 2006). Computational models of pyramidal neurons derived

from these results suggest that compensation occurs through the compartment-specific

use of conductance scaling in SR and dendritic spikes in SLM to minimize the influence

of distance on synaptic efficacy.

48

2.2. Introduction

The excitatory synaptic inputs onto a single neuron often originate in different areas

of the brain and are distributed throughout a branched dendritic tree that can extend

hundreds of microns from the soma. Activation of these synapses generates potentials

that propagate toward the soma and axon, where all electrical signaling from the den-

drites converges. In order to influence activity in these final integration zones, however,

synaptic potentials must overcome severe filtering and attenuation caused by the cable

properties of dendrites (Rall, 1977; Williams and Stuart, 2003). Because of the size and

complexity of dendrites, the impact of dendritic filtering increases with distance from

the soma and substantially reduces the influence of distal synapses on neuronal output.

Recent studies suggest, however, that CA1 pyramidal neurons can counteract this volt-

age attenuation with two different mechanisms, both of which are capable of effectively

and reliably depolarizing the soma and axon: distance-dependent conductance scaling

(Magee and Cook, 2000; Smith et al., 2003) and dendritic spikes (Golding and Spruston,

1998; Gasparini et al., 2004; Gasparini and Magee, 2006).

Conductance scaling has been studied among the CA3 → CA1 synapses of stratum

radiatum (SR), where locally generated synaptic potentials in distal dendritic regions are

larger than those generated more proximally. When these same potentials are recorded

at the soma, however, their average amplitudes are virtually indistinguishable, imparting

location independence to synapses in SR. Dendritic spikes also have been studied in detail

within apical dendritic regions, where they are triggered locally by synaptic activity and

propagate with variable reliability toward the soma. Dendritic spikes likely play an inte-

gral role in relaying synaptic signals from stratum lacunosum-moleculare (SLM) because,

49

in the absence of dendritic action potentials, inputs in this region have only a minor effect

at the soma (Golding and Spruston, 1998; Wei et al., 2001; Cai et al., 2004; Jarsky et al.,

2005). Additionally, the forward propagation of dendritic spikes originating in SLM, and

their effectiveness at driving axonal action potentials, are facilitated dramatically by very

modest synaptic activity in SR (Jarsky et al., 2005). Such findings suggest that, through

the gating action of SR synapses, dendritic spikes are the principal form of communication

between SLM and the soma/axon. These studies have contributed to the emerging view

that CA1 pyramidal neurons employ both conductance scaling and dendritic spikes to

ensure that synapses throughout the apical dendrite influence neuronal output. Virtually

nothing is known, however, regarding the cellular substrates of synaptic distance compen-

sation. In addition, the likelihood that SR and SLM synapses use the same or different

mechanisms to reduce the impact of their dendritic location has never been addressed.

To characterize the extent to which synapses are regulated in a distance-dependent

manner, especially in SLM where such a role may be masked by the technical limitations

of recording from the small-diameter dendritic tufts, conventional and postembedding im-

munogold electron microscopy was used to examine the number, as well as the AMPAR

and NMDAR expression, of synapses throughout the apical dendrite of CA1 pyramidal

neurons (Nicholson et al., 2006). At least within SR, the number or density of AMPARs

appears to be the major determinant of synaptic strength because various other param-

eters that influence excitatory postsynaptic potential (EPSP) amplitude - including cleft

glutamate concentration, the size of the readily releasable pool of vesicles, probability

of release, maximum channel open probability, single channel current, and NMDAR me-

diated currents - do not vary with distance from the soma, yet synapses in this region

50

exhibit conductance scaling (Andrasfalvy and Magee, 2001; Smith et al., 2003). Accord-

ingly, the number and density of immunogold particles for AMPARs projected onto the

postsynaptic density (PSD) was used as an estimate of the relative strength of synapses.

Computational models of CA1 pyramidal neurons were then derived from these data to

determine how distance-dependent differences in synaptic strength affect dendritic inte-

gration. Taken with results from the previous experimental studies, the modeling results

suggest that synapses on the apical dendrites of CA1 pyramidal neurons minimize voltage

attenuation by utilizing conductance scaling in SR and the generation of dendritic spikes

in SLM.

51

2.3. Methods

2.3.1. Computational Modeling

The CA1 pyramidal neuron models used for simulations were reconstructed from

stained neurons in hippocampal slices as described previously (Golding et al., 2005). All

simulations were performed using the neuronal simulator NEURON (Hines and Carnevale,

1997). The passive neuron models included only passive membrane properties, which were

constrained by direct recording of voltage attenuation from the soma to a dendritic record-

ing in the same neuron and a hyperpolarization-activated conductance (Golding et al.,

2005). Additional CA1 pyramidal neuron models with active conductances from Golding

et al. (2001) and Poirazi et al. (2003) were also used.

The distribution of leak membrane resistance in the passive neuron models was as-

sumed to be given by the expression

Rm = Rm(end) +Rm(soma) − Rm(end)

1 + exp [d− d1/2]/z(2.1)

where Rm(soma) is the membrane resistance at the soma, Rm(end) is the membrane resistance

at the distal end of the apical dendrite, d1/2 is the function midpoint value between the

two, d is distance from the soma and z is the steepness factor.

Parameters for the hyperpolarization-activated cation conductance distribution were

constrained by previous results from electrophysiological recordings (Golding et al., 2005;

Magee, 1998) yielding an increasing sigmoidal distribution as a function of distance from

the soma for the peak conductance (gh):

52

gh = gh(soma) +gh(end) − gh(soma)

1 + exp [d1/2 − d]/z(2.2)

Here gh(soma), gh(end), d1/2, d and z are parameters similar to those used in Equation 2.1.

2.3.1.1. Determining synaptic conductance values: Regula-Falsi method. The

root-finding Regula-Falsi method was used in all simulations where it was necessary to

determine a synaptic conductance (gsyn) value that produced a specific somatic or local

voltage response. Regula-Falsi, also called the False-Position method, is a linearly conver-

gent root-finding algorithm based on linear interpolation that is faster than the standard

Bisection method. Similar to the Bisection method, Regula-Falsi starts with a change

of sign interval [a,b] containing the root. Each subsequent step of the method tries to

make this interval smaller. However, unlike the bisection method, Regula-Falsi biases the

search using the value of the function to determine which side of the interval does not

contain a root. That side is then discarded to give a new, smaller interval containing the

root (Rao and Shanta, 1992).

Determining a root is as follows: If there are two points a and b such that f(a)f(b) < 0,

then there exists a root x1 such that f(x1) = 0 (Figure 2.1). The equation for the secant

line between (a, f(a)) and (b, f(b)) can be found such that

y − f(a)

x− a=f(b)− f(a)

b− a. (2.3)

Setting y = 0, the equation for the secant line can then be solved for x1.

x1 =af(b)− bf(a)

f(b)− f(a). (2.4)

53

Figure 2.1. Method of False-PositionTo use the False-Position, or Regula-Falsi, method the interval [a,b]must contain a change of sign such that f(a)f(b) < 0. The Regula-Falsi algorithm can be derived by finding the secant line or by us-ing similar triangles, i.e. EC/BC = DE/AB. Figure courtesy ofhttp://www2.lv.psu.edu/ojj/courses/cmpsc-201/numerical/regula.html

54

If f(x1) = 0, then x1 is an exact root. Otherwise, if f(x1)f(b) < 0 then the lower

boundary of the interval, a, is replaced with x1 and its corresponding functional value. If

f(x1)f(a) < 0, then the larger boundary of the interval, b, is replaced with x1. This is

repeated until f(xi) is within a specified tolerance of zero.

However, when determining the synaptic conductance value that will produce a target

somatic voltage of 0.2 mV (Magee and Cook, 2000), the root no longer occurs at y = 0,

but instead occurs at y = 0.2. In this case, the lower boundary point (a, f(a)) is (ga,Va)

where ga is the lower conductance value that sets the value for the left boundary of the

interval and Va is the resulting somatic voltage when the smaller conductance value is set

as the synaptic conductance for a synapse at a particular dendritic location. The upper

boundary point (b, f(b)) is (gb,Vb) where gb is the upper conductance value that sets

the value for the right boundary of the interval and Vb is the resulting somatic voltage

when the larger conductance value is set as the synaptic conductance for a synapse at

a particular dendritic location. Using these two boundary points, the equation for the

secant line is

y − Va

x− ga

=Vb − Va

gb − ga

. (2.5)

Setting y = 0.2 and x = gsyn1(the first iterative value for gsyn), the equation for the secant

line can then be solved for gsyn1.

gsyn1= ga +

(gb − ga)(0.2− Va)

Vb − Va

(2.6)

For each interval, the somatic and dendritic voltage changes were calculated and used to

determine a lower or upper boundary for the new interval until the somatic depolarization

55

reached 0.2 mV (within a tolerance of 0.01) or gsyn reached a maximum conductance of 1.0

nS. For simulations where local depolarizations were considered, a limit equal to -30 mV

(theoretical spike threshold) was set such that iteration was complete if the local voltage

change reached -30 mV prior to a somatic depolarization of 0.2 mV or a gsyn of 1.0 nS.

2.4. Synaptic Scaling: Experimental Background

2.4.1. Distance-Dependent Regulation of Synapse Number

The vast majority of excitatory synapses on CA1 pyramidal neurons are located

on dendritic spines (Sorra and Harris, 2000; Geinisman et al., 2004) and can be ei-

ther perforated or nonperforated (Peters and Kaiserman-Abramof, 1969; Carlin et al.,

1980), depending on the configuration of their PSD. When viewed in serial sections,

perforated synapses exhibit discontinuous PSD profiles (Figure 2.2 A-C), while nonper-

forated synapses show continuous PSD profiles (Figure 2.2 D-F). Importantly, perforated

synapses have a higher number of immunogold particles for both AMPARs and NMDARs

compared to their nonperforated counterparts (Desmond and Weinberg, 1998; Ganeshina

et al., 2004b,a). Such findings are consistent with the idea that perforated synapses, when

activated, will generate larger synaptic currents than nonperforated synapses. To clarify

the role of these two synaptic subtypes in distance compensation, experimental studies

have estimated whether the number or proportion of perforated synapses changes with

distance from the soma. The results of the estimates of the total number of perforated

and nonperforated synapses in the three zones revealed that their numbers varied in a

distance-dependent manner (Nicholson et al., 2006). Specifically, there are more perfo-

rated synapses in dSR and SLM than in pSR, and there are fewer nonperforated synapses

56

within SLM than in pSR and dSR (Figure 2.2 I). Together, these differences in synaptic

subtype number progressively increase the proportion of perforated synapses with distance

from the soma (Figure 2.2 J). That the number of perforated synapses is increased in the

dSR, and then maintained at the same elevated level in SLM (Figure 2.2 I), suggests that

perforated synapses play a pivotal role in distance-dependent synaptic scaling.

2.4.2. Synaptic AMPARs Exhibit Distance-Dependent Regulation

Because of the exceptionally high level of AMPAR immunoreactivity in perforated

synapses (Ganeshina et al., 2004b,a), the increase in their proportion might underlie the

higher incidence of large-amplitude miniature excitatory postsynaptic currents (mEPSCs)

in dSR (Magee and Cook, 2000; Smith et al., 2003). A parallel augmentation in perforated

synapse strength would account for the electrophysiological finding that the dSR contains

a subpopulation of synapses two to three times more powerful than any synapse in pSR

(Magee and Cook, 2000; Smith et al., 2003). Furthermore, perforated synapse strength

might be expected to surpass that in dSR if conductance scaling extends to SLM. As AM-

PARs mediate the majority of fast synaptic transmission and previous electrophysiological

studies have provided evidence that distance-dependent synaptic scaling is accomplished

via an increase in synaptic AMPR conductance (Magee and Cook, 2000; Andrasfalvy and

Magee, 2001; Smith et al., 2003), previous postembedding immungold electron microscopy

experiments have assessed the AMPAR immunoreactivity of axospinous synapses from the

pSR, dSR, and SLM. These studies revealed that perforated synapses are immunopositive

for AMPARs and exhibit an abundance of immunogold particles associated with their

PSD. In addition, perforated synapses had more immunogold particles for AMPARs than

57

Figure 2.2. Ratio of Perforated-to-Nonperforated Synapses Increases withDistance from the Soma in CA1 Pyramidal Neurons. Figure courtesy ofNicholson et al. (2006). Figure caption continues on the next page.

58

Figure 2.2. (A-C) A perforated synapse between a presynaptic axon ter-minal (at) and a postsynaptic spine (sp), characterized by discontinuities(arrows) in its postsynaptic density profiles (arrowheads). Scale bar, 0.25µm. (D-F) Nonperforated synapses between two presynaptic axon terminals(at1 and at2) and two postsynaptic spines (sp1 and sp2) display continuouspostsynaptic density profiles (arrowheads) in all sections. Scale bar, 0.25µm. (G) A pyramidal neuron in the hippocampal CA1 region (arrows).(H) Location of the pSR, dSR, and SLM depicted on a CA1 pyramidal neu-ron. (I) Total number of perforated (triangles) and nonperforated (circles)synapses in pSR, dSR, and SLM. pSR has fewer perforated synapses thandSR and SLM (∗); SLM has fewer nonperforated synapses than pSR anddSR (∗∗). (J) The perforated-to-nonperforated synapse ratio is higher indSR than in pSR (∗) and highest in SLM (∗∗). All values are based onpooled data from three rats (1032 perforated synapses; 7569 nonperforatedsynapses) and are presented ± SEM.

59

A B

Figure 2.3. AMPAR Expression in Perforated and Nonperforated Synapsesthroughout the Apical Dendritic Tree in CA1 Pyramidal Neurons. Figurecourtesy of Nicholson et al. (2006).(A) Mean number of immunogold particles for AMPARs per perforated(triangles) and nonperforated (circles) synapse. Perforated synapses in dSRhave the highest particle number (∗), whereas those in SLM have the lowest(∗∗). (B) Mean density of immunogold particles for AMPARs per PSD unitarea (mm2). Among perforated synapses, those in dSR have the highestparticle density (∗), and those in SLM have the lowest (∗∗). Nonperforatedsynapses in dSR have a higher particle density than those in both pSR andSLM.

60

immunopositive nonperforated synapses, regardless of whether they were in the pSR, dSR

or SLM (Figure 2.3 A,B) (Nicholson et al., 2006).

However, distance-dependent differences in AMPAR immunoreactivity were seen al-

most exclusively among perforated synapses. Perforated synapses in the dSR had the

highest particle number and density, whereas those in SLM had the lowest particle num-

ber and density (Figure 2.3 A,B). Among nonperforated synapses, neither the particle

number (Figure 2.3 A) nor the percentage of immunopositive nonperforated synapses

changed with distance from the soma. The only difference seen among nonperforated

synapses was a slightly higher particle density in those from the dSR (Figure 2.3 B).

These studies suggest that conductance scaling may be achieved by an increase in the

number and density of AMPARs, and they extend this view by demonstrating that the

upregulation of AMPARs is limited to perforated synapses. Additionally, this particular

form of conductance scaling does not appear to extend to SLM (Nicholson et al., 2006).

2.4.3. Synaptic NMDARs Do Not Scale with Distance from the Soma

Although a previous study provided compelling evidence that NMDAR-mediated cur-

rents do not change with distance from the soma in SR (Andrasfalvy and Magee, 2001),

there is evidence that the NMDAR-to-AMPAR ratio is highest in SLM (Otmakhova et al.,

2002). Moreover, synaptic currents mediated by NMDARs have slower kinetics than those

mediated by AMPARs (Hestrin et al., 1990; Spruston et al., 1995a), which, through a va-

riety of mechanisms, can be expected to decrease the impact of voltage attenuation on

potentials from very distal synapses such as those in dSR and SLM (Rall, 1977; Schiller

and Schiller, 2001; Williams and Stuart, 2003). To determine whether NMDARs play a

61

role in distance compensation, previous experiments also examined NMDAR immunore-

activity in synapses from the pSR, dSR, and SLM.

These experiments revealed that both perforated and nonperforated synapses are im-

munopositive for NMDARs (Ganeshina et al., 2004b; Nicholson et al., 2006). Perforated

synapses had a higher number, but a lower density, of immunogold particles for NM-

DARs than their nonperforated counterparts (Figure 2.4). In stark contrast to synaptic

AMPARs, however, NMDAR expression among synapses did not exhibit any distance-

dependent differences (Figure 2.4) (Nicholson et al., 2006).

2.5. Results

2.5.1. Perforated Synapses Reduce Location Dependence in SR

The results from previous experimental studies show that CA1 pyramidal neurons reg-

ulate the number of both perforated and nonperforated synapses as a function of distance

from the soma but adjust synaptic strength only among the perforated subtype, and even

then only by modifying the number of AMPARs. The selective involvement of perforated

synapses in distance-dependent synaptic scaling suggests that they are the only synaptic

subtype capable of reducing their location dependence. To provide insight into the possi-

ble functional consequences of such compartment-specific differences in synapse number

and receptor content, I used computer simulations of a morphologically reconstructed

pyramidal neuron with passive membrane properties (Golding et al., 2005).

The computer simulations were first used to model the somatic EPSPs that perfo-

rated and nonperforated synapses located throughout the apical dendrite would produce.

Synaptic conductances (gsyn) were based on the known properties of somatic EPSPs and

62

A B

Figure 2.4. NMDAR Expression in Perforated and Nonperforated Synapsesthroughout the Apical Dendritic Tree in CA1 Pyramidal Neurons. Figurecourtesy of Nicholson et al. (2006).(A) Mean number of immunogold particles for NMDARs per perforated(triangles) and nonperforated (circles) synapse. Perforated synapses havemore immunogold particles than nonperforated ones (∗) in all dendriticregions studied, but there are no distance-dependent differences. (B) Meandensity of immunogold particles for NMDARs per PSD unit area (mm2).Nonperforated synapses have a higher particle density than their perforatedcounterparts (∗), but this pattern does not change with distance from thesoma.

63

the relative number of immunogold particles for AMPARs in the two synaptic subtypes

(Figure 4 A). The average amplitude of miniature EPSPs (mEPSPs) in SR is approx-

imately 0.2 mV (Magee and Cook, 2000). This was incorporated into the model by

assuming a gsyn of 0.3 nS for nonperforated synapses, which resulted in somatic EPSPs

of 0.2 mV from the most proximal dendritic synapse locations. Based on the AMPAR

immunoreactivity of nonperforated synapses, this value was kept constant at all dendritic

locations. The gsyn value for perforated synapses was based on their relative level of AM-

PAR expression compared to nonperforated synapses, and was therefore dependent on

dendritic location. Identical gsyn values were assigned to perforated synapses in stratum

oriens (SO) and pSR, given their similar distance from the soma, and extrapolated gsyn of

perforated synapses in middle stratum radiatum (mSR) to a value intermediate to those

in pSR and dSR.

Using these values for gsyn, only the most proximal nonperforated synapses produced

somatic EPSPs near 0.2 mV (i.e., exceeding 0.16 mV), whereas somatic EPSPs from all

other locations were considerably smaller because of the lack of conductance scaling (Fig-

ure 2.5 B-E). Importantly, nonperforated synapses in dSR and SLM produced EPSPs

that were on average three to six times smaller than those in pSR (pSR: 0.13 mV; dSR:

0.04 mV; SLM: 0.02 mV), suggesting that many nonperforated synaptic potentials orig-

inating in distal dendritic regions attenuate to nearly undetectable amplitudes. When

perforated synapses were simulated, most synapses throughout SR (100% in pSR, 85%

in dSR) caused somatic EPSPs that exceeded 0.16 mV and produced relatively uniform

somatic EPSP amplitudes over a large range of dendritic locations (Figure 2.5 B-E). The

average somatic EPSP amplitude for perforated synapses in pSR (0.45 mV) exceeded that

64

of perforated synapses in dSR (0.21 mV), but these simulations suggest that somatically

recorded pSR EPSPs are likely to originate from a mixture of both perforated and nonper-

forated synapses, whereas dSR EPSPs would be produced predominantly by perforated

synapses (Figure 2.5 C-F). This would result in average pSR EPSPs being intermediate

to that of the nonperforated and perforated EPSPs (0.28 mV), and average dSR EPSPs

being derived from perforated EPSPs only (0.21 mV). Values based on such assumptions

are consistent with recording studies (Magee and Cook, 2000; Smith et al., 2003). On the

other hand, EPSPs originating in SLM (average = 0.068 mV) never exceeded 0.2 mV,

with > 90% producing somatic EPSPs below 0.1 mV and none above 0.16 mV (Figure 2.5

B-E).

The simulations of perforated and nonperforated synapses complement the electron

microscopy studies, and together they show that an increase in the proportion (Figure 2.2

A,B) and strength (Figure 2.3 A,B) of perforated synapses in dSR provides a plausible

cellular basis for synaptic location independence throughout SR. These results also show

that, despite having the highest proportion of perforated synapses (Figure 2.2 B), SLM

synapses do not effectively counteract dendritic filtering. Rather, synaptic potentials

originating in SLM attenuate so severely that they produce much smaller average somatic

EPSPs than SR EPSPs, consistent with previous recording studies (Jarsky et al., 2005).

2.5.2. Evidence for Compartment-Specific Mechanisms of Distance Compen-

sation

These simulations clearly show that conductance scaling does not extend into SLM,

implying that some other mechanism must operate in this region to reduce synaptic

65

Figure 2.5. Simulating Somatic EPSPs Generated by Nonperforated andPerforated Synapses at Different Locations on CA1 Pyramidal Neuron Den-drites. Figure courtesy of Nicholson et al. (2006). Figure caption continueson the next page.

66

Figure 2.5. (A) Synaptic conductances (gsyn) for perforated (P) and nonper-forated (NP) synapses located in stratum oriens (SO), pSR, middle stra-tum radiatum (mSR), dSR, and SLM in simulations. All gsyn values arerelative to a reference conductance (0.3 nS) necessary for a nonperforatedsynapse located in the most proximal region of pSR to generate a 0.2 mVsomatic EPSP. The values for perforated and nonperforated gsyn in pSR,dSR, and SLM derive from the results of AMPAR immunogold electronmicroscopy experiments (Nicholson et al., 2006). The value for the nonper-forated synapse gsyn at all dendritic locations was 0.3 nS, whereas the gsyn

value for perforated synapses changed with distance from the soma (pSR:1.2 nS; dSR: 1.8 nS; SLM: 1.0 nS). (B) Color-coded display of the somaticEPSP generated by synaptic conductances (gsyn) characteristic of nonper-forated (left) or perforated synapses (right) throughout various locations ofthe apical dendrite. Color map of somatic EPSP (dVsoma) is on a log-scale.(C) Percentage and cumulative percentage of perforated (gray bars, thicklines) and nonperforated (white bars, thin lines) synapses located in pSR,dSR, or SLM that produced somatic EPSPs within the ranges of amplitudesdisplayed in (B). (D) Cumulative percentages of perforated (top panel) andnonperforated (bottom panel) synapses in pSR, dSR, and SLM plotted as afunction of the depolarization (in mV) achieved in the soma. (E) Averageamplitude of somatic EPSPs caused by perforated (P) and nonperforated(NP) synaptic conductances originating in pSR, dSR, or SLM. (F) The per-centage of EPSPs in pSR, dSR, and SLM that exceeded 0.16 mV. Valuesfor average somatic EPSP amplitudes in (E) are presented ± SD.

67

location dependence. Dendritic spikes may represent such a mechanism because they are

prevalent in SLM and can be triggered relatively easily by brief bursts of synaptic activity

(Golding and Spruston, 1998; Golding et al., 2002; Gasparini et al., 2004; Jarsky et al.,

2005). Recent evidence suggests that SLM synapses indeed rely heavily on dendritic spikes

because, in their absence, SLM inputs appear to only have minimal impact on neuronal

output (Golding et al., 2005; Jarsky et al., 2005). These studies suggest that synapses

in SLM are capable of effectively counteracting dendritic filtering only via a two-stage

process: (1) SLM synaptic conductances trigger a dendritic spike; and (2) this dendritic

spike then propagates toward the soma under some conditions.

To explore the possibility that SLM synapses preferentially use dendritic spikes rather

than conductance scaling, I used the computational model to compare the conductances

necessary to achieve two different conditions: (1) a unitary EPSP of 0.2 mV at the soma;

and (2) a local depolarization to -30 mV, which can be considered sufficient to generate

a local dendritic spike (Golding and Spruston, 1998; Gasparini et al., 2004). The value

of gsyn was incrementally increased for synaptic locations throughout the dendritic tree

until each of the two conditions was achieved. I then examined whether the gsyn necessary

to achieve these two different conditions varied with distance from the soma. A unitary

somatic EPSP of 0.2 mV could be achieved with relatively moderate increases in synaptic

strength throughout pSR and dSR (Figure 2.6 A, blue). Consistent with the previous

electrophysiological studies and electron microscopic experiments showing an increase in

the number and AMPAR immunoreactivity of perforated synapses in dSR, gsyn of these

synapses needed to be increased up to 10-fold relative to the reference conductance (gref)

in pSR (0.3 nS) to normalize the somatic EPSP. Much larger gsyn values were required for

68

synapses in SLM. Specifically, synaptic conductances ranging from 100 to over 1000 times

that of more proximal synaptic locations were required to effectively counteract dendritic

filtering and produce a somatic EPSP of 0.2 mV (Figure 2.6 A, blue). Thus, the pattern

of resulting conductances is consistent with previous electron microscopic data from SR,

but not from SLM, where perforated synapses have the lowest level of AMPAR expression.

When simulating the gsyn necessary to depolarize the local membrane potential to -30 mV,

the highest values were observed for the large-diameter main apical dendrite (Figure 2.6

A, red). Much smaller values were required in the smaller-diameter apical oblique and

tuft branches (Figure 2.6 A, red). For most synapses in SLM, the conductance required

to reach -30 mV was substantially lower than the conductance required to achieve a 0.2

mV somatic EPSP (Figure 2.6 A, red). That is, when the most distal synapses - primarily

within SLM - were activated, they achieved the dendritic spike threshold of -30 mV before

they generated a 0.2 mV somatic EPSP (Figure 2.6 A-D). Importantly, this observation

is opposite to that seen in SR, where most synaptic locations produced the normalized

somatic EPSP at lower gsyn values than those required to produce a local depolarization to

-30 mV (Figure 2.6 A-D). These findings were further corroborated with a second passive

CA1 pyramidal cell model (Figure 2.7, Figure 2.8). When combined with the previous

experimental results, these simulations indicate that perforated synapses in SR scale their

strength to produce somatic EPSPs near 0.2 mV, whereas those in SLM are governed by

different rules, perhaps depending on their ability to recruit dendritic spikes, rather than

their ability to depolarize the soma (Figure 2.6 D).

69

Figure 2.6. Modeling of the Synaptic Conductance Required to Achieve aNormalized Somatic EPSP or a Large Local Depolarization. Figure courtesyof Nicholson et al. (2006). Figure caption continues on the next page.

70

Figure 2.6. (A) The synaptic conductance required to achieve a somaticEPSP of 0.2 mV throughout the dendritic tree (blue), or a local depolariza-tion to -30 mV (red). Synaptic conductance (gsyn) values were normalizedrelative to the reference conductance (gref) used for simulations of nonper-forated synapses in pSR (0.3 nS; Figure 2.5) and are plotted on a log-scale.(B) Plots, as a function of dendritic location, of the gsyn required to achieveeither a somatic EPSP of 0.2 mV (blue) or a local depolarization to -30 mV(red) first. (C) The percentage of synaptic locations that achieved a somaticEPSP of 0.2 mV first (blue) or a local depolarization to -30 mV first (red)in pSR, dSR, and SLM. (D) Average values of the synaptic conductances(gsyn) required to achieve either a somatic EPSP of 0.2 mV (blue) or a lo-cal depolarization to -30 mV (red) for synaptic locations in pSR, dSR, andSLM. The number of immunogold particles for AMPARs per perforatedsynapse (black) in pSR, dSR, and SLM is superimposed with a separateordinate. The axis for immunogold particle number is aligned such that theaverage particle number per immunopositive nonperforated synapse in pSR(3.38) is level with the average value required to achieve a 0.2 mV somaticEPSP in pSR (0.58 nS). All values are presented ± SEM.

71

Figure 2.7. Simulation of somatic EPSPs generated by nonperforated andperforated synapses at different dendritic locations in a second model of aCA1 pyramidal neuron. Figure courtesy of Nicholson et al. (2006).(A) gsyn for synapses located in stratum oriens (SO), pSR, middle stra-tum radiatum (mSR), dSR, and SLM in the simulation. All gsyn values arerelative to the reference conductance (gref ; 0.44 nS) necessary for a non-perforated synapse located in pSR to generate a 0.2 mV somatic EPSP (seetext for details). (B) Color-coded display of the somatic EPSP generatedby synaptic conductances (gsyn) located throughout the apical dendrite fora fixed gsyn characteristic of nonperforated synapses (left), or by a vari-able gsyn scaled according to the results for perforated synapses in previousimmunogold electron microscopy experiments (right).

72

3.0

2.5

2.0

1.5

1.0

0.5

0.0

8006004002000-200

Distance from soma (μm)

log

(gsy

n/g

ref)

6.0

5.0

4.0

3.0

2.0

1.0

8006004002000-200

Distance from soma (μm)

gsy

n (

nS

)

A

B

C

Figure 2.8. Modeling of the synaptic conductance required to achieve asomatic EPSP or a large local depolarization in a second model of a CA1pyramidal neuron. Figure courtesy of Nicholson et al. (2006).(A) The synaptic conductance (gsyn) required to achieve a somatic EPSPof 0.2 mV throughout the dendritic tree (blue), or a local depolarization to-30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSPof 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) Thepercentage of synaptic locations that achieved a somatic EPSP of 0.2 mVfirst (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, andSLM.

73

those in SLM need to first trigger dendritic spikes to successfully counteract dendritic

filtering.

2.6.1. Synaptic Scaling vs. Dendritic Spikes

Though not directly proven by previous experiments, the compartment-specific use of

conductance scaling and dendritic spikes to reduce synaptic location dependence is also

supported by evidence from other studies. Previous electrophysiological work has shown

that SR synapses can increase their conductance to compensate for their distance from

the soma/axon (Magee and Cook, 2000; Smith et al., 2003). These studies found that the

amplitudes of somatically recorded mEPSPs are relatively independent of their location

of origin within SR, while the distribution of dendritically recorded mEPSCs contained

substantially more large amplitude events in dSR than in pSR. These data are consistent

with the computational results presented here. For example, the larger gsyn value required

for more distal locations in the dSR to produce a 0.2 mV somatic EPSP would give rise

to larger local depolarizations at the synapse site, consistent with the findings that there

is a higher incidence of large-amplitude mEPSCs in dSR, with some mEPSCs being two

to three times larger than any seen in pSR (Magee and Cook, 2000; Smith et al., 2003).

In SLM, however, experimental evidence indicates that the AMPAR immunoreactivity of

perforated synapses was significantly lower than that in both pSR and dSR (Nicholson

et al., 2006), suggesting that perforated synapses in SLM actually may be the weakest

of all such perforated synapses on the apical dendrites. The results from the simulations

further indicate that many synapses in SLM are unable to achieve a 0.2 mV somatic

74

EPSP, even if synaptic strength is increased 100-1000 times the proximal gsyn values,

thereby indicating that conductance scaling does not extend to SLM.

Several studies indicate that dendritic spikes, rather than conductance scaling, may

be used by SLM synapses to influence neuronal output. Although EPSPs originating

in SLM attenuate the most, the small diameter of these branches (Megıas et al., 2001)

will cause local EPSPs to be larger (Rall, 1977) and therefore more likely to trigger local

dendritic spikes. This idea is consistent with computational simulations of two active CA1

pyramidal neuron models, which suggest that synaptic strength in SLM is actually scaled

down as a result of the ease with which large local depolarizations could be achieved in

this region (Figure 2.9, Figure 2.10). In one of the active models, roughly 80% of synapses

in SLM reach threshold for spike generation prior to generating a 0.2 mV somatic voltage

response (Figure 2.9). Furthermore, the synapses that are able to generate a 0.2 mV

somatic EPSP prior to dendritic spike generation in the SLM require a 15-30 fold increase

in gsyn to create a somatic depolarization of 0.2 mV (Figure 2.9). While significantly

more of the synapses in the second active model (Poirazi et al., 2003) are able to generate

a 0.2 mV somatic EPSP prior to reaching spike threshold in the SLM, these synapses

also require a 15-30 fold increase in gsyn to do so (Figure 2.10). These simulations are

also in agreement with a study using serial section electron microscopy and computational

modeling to investigate two different integration modes (global and two-stage) for synaptic

scaling in CA1 pyramidal neurons (Katz et al., 2009). The results from this study suggest

that synaptic strength increases along the primary apical dendrite, but decreases along

oblique apical dendrites. Thus, synapses at more distal locations on oblique branches

75

Figure 2.9. Modeling of the synaptic conductance required to achieve a nor-malized somatic EPSP or a large local depolarization in a third model of aCA1 pyramidal neuron with a voltage-gated Na+ conductance, a delayed-rectifier K+ conductance, and two A-type K+ conductances. Figure cour-tesy of Nicholson et al. (2006). Figure caption continued on the next page.

76

Figure 2.9. Modeling of the synaptic conductance required to achieve anormalized somatic EPSP or a large local depolarization in a third model ofa CA1 pyramidal neuron with a voltage-gated Na+ conductance, a delayed-rectifier K+ conductance, and two A-type K+ conductances.(A) The synaptic conductance (gsyn) required to achieve a somatic EPSPof 0.2 mV throughout the dendritic tree (blue), or a local depolarization to-30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSPof 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) Thepercentage of synaptic locations that achieved a somatic EPSP of 0.2 mVfirst (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, andSLM.

77

Figure 2.10. Modeling of the synaptic conductance required to achieve anormalized somatic EPSP or a large local depolarization in a model of a CA1pyramidal neuron with various passive and active conductances (Poiraziet al., 2003). Figure courtesy of Nicholson et al. (2006). Figure captioncontinued on the next page.

78

Figure 2.10. Modeling of the synaptic conductance required to achieve anormalized somatic EPSP or a large local depolarization in a model of a CA1pyramidal neuron with various passive and active conductances (Poiraziet al., 2003).(A) The synaptic conductance (gsyn) required to achieve a somatic EPSPof 0.2 mV throughout the dendritic tree (blue), or a local depolarization to-30 mV (red). (B) Plots of the gsyn that achieved either a somatic EPSPof 0.2 mV (blue) or a local depolarization to -30 mV (red) first. (C) Thepercentage of synaptic locations that achieved a somatic EPSP of 0.2 mVfirst (blue) or a local depolarization to -30 mV first (red) in pSR, dSR, andSLM.

79

may contribute to neuronal output by generating dendritic spikes during asynchronous

synaptic activation.

2.6.2. Synaptic Scaling and Gating of Dendritic Spikes

In the absence of dendritic spikes, SLM synapses are unable to generate axonal ac-

tion potentials and have only minimal impact on somatic depolarization (Golding and

Spruston, 1998; Wei et al., 2001; Golding et al., 2005; Jarsky et al., 2005). Though the

propagation of dendritic spikes in SLM can be restricted to the apical tuft (Golding and

Spruston, 1998; Wei et al., 2001; Cai et al., 2004), such spatial confinement is dramatically

reduced by modest synaptic activity in SR (Jarsky et al., 2005). In other words, synapses

in SR actively gate the propagation of dendritic spikes originating in SLM, conferring to

dendritic spikes the ability to propagate to the soma, and allowing dendritic spikes to

act as a reliable mechanism of distance compensation for SLM synapses. Together, these

findings strengthen the notion that perforated synapses in SR can communicate directly

with the soma/axon in a relatively location-independent manner by use of conductance

scaling, but that SLM synapses first need to trigger dendritic spikes, which then propa-

gate toward and ultimately depolarize the final integration zones in the soma and axon.

Importantly, dendritic spikes are not a mechanism of distance compensation exclusive to

SLM synapses. Rather, SR synapses can influence activity in the soma and axon with or

without dendritic spikes (Gasparini and Magee, 2006), whereas SLM synapses are unlikely

to impact neuronal output in their absence (Jarsky et al., 2005). Even if SLM synaptic

potentials summate with EPSPs in dSR to trigger local spikes in SR (Jarsky et al., 2005),

80

the available data are consistent with the notion that SLM synapses rely on dendritic

spikes to drive axonal action potentials, whereas SR synapses do not.

Given their small gsyn and somatic EPSP, the synchronous activation of many (>100)

nonperforated synapses would be required to trigger axonal action potentials or dendritic

spikes. And because they do not exhibit conductance scaling, the number of coincidentally

activated nonperforated synapses required to produce an axonal action potential would

increase progressively with distance from the soma. Considering the high level of AMPAR

expression in perforated synapses, they are more likely to contribute to both axonal and

dendritic spikes than their nonperforated counterparts throughout SR and SLM. The

simulations here indicate, however, that dendritic filtering of EPSPs originating in SLM

is so severe that even perforated synapses may not contribute substantially to somatic

depolarization. Rather, these synapses may instead operate together to trigger dendritic

spikes. Given their abundance of AMPARs, the relative frequency of perforated synapses

may be highest in SLM to increase the probability that synaptic input causes a local

depolarization sufficient to trigger a dendritic spike.

2.6.3. Future Directions

This study indicates that the contribution of synapses to neuronal output strongly

depends on synapse location and that conductance scaling is primarily utilized in SR,

while the generation of dendritic spikes is more likely to play a role in regulating neural

output in SLM. Forms of synaptic plasticity underlying distance-dependent regulation

of synapse number (synapse conductance) and AMPAR content, although unknown or

unverified, could serve to strength synaptic efficacy. Computational studies of a putative

81

form of synaptic plasticity, anti-STDP or anti-Hebbian has been suggested as a mechanism

by which dendritic spiking is normalized to balance it with spiking resulting from action

potential backpropagation, thus preventing runaway spiking in localized dendritic regions

and in turn, enhancing synapse strength in a positive feedback manner (Rumsey and

Abbott, 2006). These and other questions surrounding the role of synapses in SLM will

need to be addressed by future simulations and experiments to fully understand how these

distal synapses are integrated and regulated to affect neural output in CA1 pyramidal

neurons.

82

CHAPTER 3

A-type potassium channels shape subthreshold voltage

responses in hippocampal CA1 pyramidal neurons

83

3.1. Abstract

Voltage-gated potassium channels inhibit spike generation and thus play a primary

role in a cell’s ability to integrate synaptic input. I investigated the role of A- and D-

type potassium channels in shaping subthreshold voltage responses in hippocampal CA1

pyramidal neurons using somatic whole-cell patch clamp recordings and application of dif-

ferent concentrations of the A- and D-type potassium channel blocker, 4-aminopyridine

(4-AP). Inhibition of D-type potassium channels with low concentrations of 4-AP did

not significantly affect subthreshold voltage responses. Inhibition of A-type potassium

channels with high concentrations of 4-AP, however, considerably increased both somatic

input resistance and the duration of simulated somatic postsynaptic potentials compared

with control conditions, suggesting that a significant amount of A-type potassium current

is available at resting conditions in CA1 pyramidal neurons. Incorporating an A-type

potassium conductance with a substantial fraction of current that is on at rest in a re-

constructed CA1 pyramidal neuron model significantly increased the accuracy of fits to

subthreshold membrane responses while still accurately reproducing the behavior of both

action potentials and action potential backpropagation.

3.2. Introduction

Hippocampal CA1 pyramidal neurons integrate thousands of synaptic inputs, many of

which are located on distal dendrites hundreds of microns from the soma. These dendrites

contain a number of voltage-gated channels that, in combination with passive membrane

properties and neuronal morphology, directly influence spike propagation, attenuation of

84

synaptic potentials and integration of synaptic inputs. In addition, these active conduc-

tances also regulate the generation of dendritic spikes and the backpropagation of somatic

action potentials (Cash and Yuste, 1999; Christie et al., 1996; Gasparini et al., 2004; Gold-

ing and Spruston, 1998; Hoffman et al., 1997; Jaffe et al., 1992; Johnston et al., 1996, 2000;

Kamondi et al., 1998; Magee and Johnston, 1995; Magee and Carruth, 1999; Tsubokawa

et al., 1999).

One voltage-gated channel in particular, the A-type potassium or K(A) channel, plays

a prominent role in shaping backpropagating action potentials and spike initiation (Acker

and White, 2007; Hoffman et al., 1997; Johnston et al., 1999; Kim et al., 2005; Migliore

et al., 1999; Pan and Colbert, 2001). In CA1 pyramidal cells, K(A) channels are dis-

tributed with an increasing density along the somatodendritic axis (up to 5-fold larger

in distal dendrites as compared to the soma) and serve to prevent or limit large, rapid

depolarizations (Chen and Johnston, 2004; Connor and Stevens, 1971; Hoffman et al.,

1997; Kole et al., 2007; Serodio and Rudy, 1998). The large density of K(A) channels in

the dendrites not only reduces the amplitude of action potentials as they propagate from

the soma to more distal locations, but also diminishes the effect of inputs from distal

dendrites upon action potential generation. Due to difficulties associated with recording

from distal oblique apical dendrites and the dendritic tuft, a delineation of active con-

ductances (such as the A-type potassium conductance) in these distal locations is not yet

fully available.

Another tool used to explore these issues is the construction of morphologically ac-

curate computational models based on current experimental data. Many experimentally-

constrained modeling studies have demonstrated the importance of determining and using

85

pharmacological block of active conductances in order to reproduce realistic behavior in

neuronal models (Baranauskas and Martina, 2006; Gold et al., 2007; Mainen et al., 1995;

Migliore et al., 1999; Poirazi et al., 2003; Royeck et al., 2008; Varona et al., 2000; Vetter

et al., 2001).

Previous studies have also used simultaneous somatic and dendritic recordings to com-

putationally constrain estimates of membrane resistance, axial resistivity and the distri-

bution of hyperpolarization-activated cation channels (Ih) (Golding et al., 2005). Our

subsequent attempts to increase the agreement between such experimental recordings

and best-fit computational models suggested that a significant fraction of voltage-gated

K(A) channels are on at rest in these neurons. To resolve this issue, we have investigated

subthreshold voltage responses in CA1 hippocampal pyramidal neurons with somatic

whole-cell recordings both under control conditions and when K(A) channels are blocked

pharmacologically. The experimental results and associated computational models clearly

demonstrate that a K(A) current that is on at rest strongly shapes subthreshold responses

in CA1 pyramidal neurons, as well as excitatory post-synaptic potentials (EPSPs) simu-

lated by current injection. New computational models constructed using these data yield

much better fits to the experimental results and consequently provide a better framework

for future studies.

3.3. Materials and Methods

3.3.1. Slice Preparation and Electrophysiology

Hippocampal slices were prepared from 14-28 day-old male Wistar rats. The rats

were anesthetized with halothane prior to decapitation and perfused transcardially with

86

cold artificial cerebrospinal fluid (ACSF). Following decapitation, the brain was quickly

removed and immersed in cold ACSF saturated with 95% oxygen and 5% carbon dioxide.

Transverse hippocampal slices were made in 300 µm sections using a Leica vibratome

slicer and transferred to a holding chamber for storage at 35 degrees celsius (C) for 30

minutes and then held at room temperature for 30-60 minutes. For physiological recording,

slices were transferred individually to the fixed stage of a Zeiss Axioskop microscope

equipped with differential interference contrast optics and perfused in ACSF solution at

a temperature between 33 and 37 C.

Patch-clamp electrodes fabricated from borosilicate glass capillary tubes were pulled

to a resistance of 3-6 MΩ (measured in the ACSF bath) for somatic recordings. Cells in the

CA1 region were chosen based on their pyramidal morphology and low contrast appear-

ance. Upon obtaining a gigaohm seal in voltage clamp, somatic recordings were performed

in the whole-cell configuration in current-clamp mode. For all experiments, current was

applied to hold the resting potential at -67 mV. Stimulus generation, data acquisition,

and analysis were performed using custom macros written in IGOR Pro (Wavemetrics,

Lake Oswego, OR). Data from electrophysiological recordings were accepted if the series

resistance remained relatively constant (< 10% change) over the course of the recording.

All recordings were made at temperatures between 33 and 37 C. All procedures were

approved by Northwestern University Animal Care and Use Committee.

3.3.2. Solutions and Pharmacology

ACSF used during perfusion, dissection, and recording contained (in mM): 125 NaCl,

2.5 KCl, 1 MgCl2, 2 CaCl2, 25 NaHCO3, 1.25 NaH2PO4 and 25 glucose. Prior to use,

87

ACSF was bubbled with a 95% O2 - 5% CO2 mixture to oxygenate the solution. The

internal solution consisted of (in mM): 115 K-gluconate, 20 KCl, 10 Na2-phosphocreatine,

10 HEPES, 2 EGTA, 4 Mg-ATP, 0.3 Na-GTP and 0.1% biocytin for subsequent morpho-

logical identification. The synaptic blockers SR95531 (4 µM) and CGP558458A (1 µM)

were included to prevent effects from inhibition.

For all recordings, drugs were dissolved in ACSF and perfused in the bath without

interruption of flow. A concentration of 100 µM 4-aminopyridine (4-AP) was used to

block D-type K+ channels and a concentration of 6 mM 4-AP was used to block both

D-type and A-type K+ channels. Kynurenic acid (2.5 mM) was included in the 6 mM

4-AP bath solution to prevent epileptic behavior in the CA3 region of the hippocampus

due to pharmacological block of K(A) channels.

3.3.3. Data Acquisition

Current clamp recordings were obtained using a BVC-700 patch-clamp amplifier (Da-

gan Instruments) with bridge balance and capacitance compensation. Electrophysiological

data were acquired using a Power Macintosh computer with an ITC-18 interface using

custom macros written in IGOR Pro. A series of 600 ms long hyperpolarizing and depolar-

izing current injections were made at the somatic electrode, ranging in step size from -300

pA to 100 pA. These were followed by a 100 ms long subthreshold double-exponential

current waveform to elicit simulated excitatory postsynaptic potentials (iEPSP). This

protocol was repeated once a minute for the duration of each experiment (50-60 mins).

Statistical significance was determined using Student’s t-test with a significance level of

5% (P < 0.05).

88

3.3.4. Histology

In order to morphologically identify neurons during recording, 0.1% biocytin was in-

cluded in the internal pipette solution. Upon termination of experiments, the pipette was

carefully withdrawn from the cell and the cell was allowed to reseal. In order to visualize

the neuron, slices were fixed in 4% paraformaldehyde, stored for up to two weeks at 4 C

and then reacted with avidin-horseradish peroxidase 3,3’-diaminobenzadine.

3.3.5. Compartmental Modeling

Simulations were performed using the NEURON Simulation Environment (Hines and

Carnevale, 1997) with the variable time-step integration method (CVODE). A previously

reconstructed CA1 pyramidal cell morphology (Golding et al., 2005) from rat hippocam-

pus was used in all simulations. Spine density and parameters were accounted for as

described previously. Models included both passive properties (membrane resistance,

membrane capacitance and axial resistance) as well as the following active conductances:

sodium, sodium with slow recovery from inactivation (Menon et al., 2009), delayed rec-

tifier potassium, A-type potassium, D-type potassium and a hyperpolarization-activated

cation current (Ih). Passive properties were constrained with electrophysiological record-

ings for voltage attenuation (Golding et al., 2005) assuming a uniform axial resistance

(Ra) and membrane capacitance (Cm).

Apical dendrites. The distribution of leak membrane resistance in the dendrites was

assumed to be given by the expression

Rm = Rm(end) +Rm(soma) − Rm(end)

1 + exp ((d− d1/2)/z)(3.1)

89

where Rm(soma) is the membrane resistance at the soma, Rm(end) is the membrane resistance

at the distal end of the apical dendrite, d1/2 is the function midpoint value between the

two, d is distance from the soma and z is the steepness factor. Three different distributions

of Rm were tested: sigmoidally increasing from soma to dendrite (Rm(soma) < Rm(end)),

sigmoidally decreasing from soma to dendrite (Rm(soma) > Rm(end)) and uniform (Rm(soma)

= Rm(end)).

Parameters for Ih properties were constrained by previous results from electrophysio-

logical recordings (Golding et al., 2005) yielding an increasing sigmoidal distribution as a

function of distance from the soma for the peak conductance (gh):

gh = gh(soma) +gh(end) − gh(soma)

1 + exp ((d1/2 − d)/z)(3.2)

Here gh(soma), gh(end), d1/2, d and z are parameters similar to those used in Equation 3.1.

The apical dendrites also contained state-dependent Na+ channel models exhibiting

both fast and slow recovery from inactivation (Menon et al., 2009). The total Na+ conduc-

tance in the primary apical dendrites was based on previous experimental results (Hoffman

et al., 1997; Mickus et al., 1999). To produce proper activity-dependent attenuation of

backpropagating action potential trains (Menon et al., 2009), the conductance density of a

slowly inactivating sodium peak conductance (gNa(S)) was modeled as a linearly increasing

function,

gNa(S) =

gNa · sNa(s) soma (d = 0),

gNa · [d · sNa(d) +(1− d

400) · sNa(s)] d > 0.

(3.3)

90

where sNa(d) is the fraction of slowly inactivating Na+ in the distal apical dendrite, sNa(s)

is the fraction of slowly inactivating Na+ in the soma, d is distance in µm from the soma

and gNa is the total Na+ conductance at the soma (S/cm2). The non-slowly inactivating

Na+ peak conductance (gNa(F)) was modeled as a decreasing linear function,

gNa(F) =

gNa · fNa(s) soma (d = 0),

gNa · [d · fNa(d) +(1− d

400) · fNa(s)] d > 0.

(3.4)

where fNa(d) is the fraction of non-slowly inactivating Na+ in the distal apical dendrite,

fNa(s) is the fraction of non-slowly inactivating Na+ in the soma and gNa is the total Na+

conductance at the soma (S/cm2). In oblique apical dendrites, gNa(F) and gNa(S) were

set equal to half the conductance values at the junction of the oblique dendrite with

the primary apical dendrite. This was necessary to prevent spontaneous firing during

simulated block of K(A) channels was observed. The total gNa (gNa = gNa(F) + gNa(S))

decreased slightly with distance from the soma. Different rates of decrease produced

weakly and strongly backpropagating versions of the neuron model (Golding et al., 2001)

(Table 3.2). The strongly backpropagating model had a larger gNa in the distal apical

dendrite relative to the weakly backpropagating model. The sodium reversal potential

was set to ENa = +54 mV throughout the entire cell.

D-type potassium, or K(D), channels were modeled as described in Kole et al. (2007).

The peak conductance (gK(D)) was distributed with an increasing gradient along the pri-

mary apical dendrite to reflect experimental studies indicating that the primary apical

dendrite and oblique dendrites have a larger density of K(D) channels than the soma (Metz

91

et al., 2007; Raab-Graham et al., 2006; Sheng et al., 1994) (Table 3.2). This gradient was

modeled as,

gK(D) =

0 soma (d = 0),

gD(s) · (1 + 3d) d > 100.

(3.5)

where d is distance in µm from the soma and gD(s) is the conductance at 100 µm from

the soma (S/cm2). The gK(D) value in oblique dendrites was set equal to the value at the

dendritic and primary apical dendrite junctions. The K(D) channel model kinetics are,

gK(D) = gK(D) n,

n′ = (n∞ − n)/τn

n∞(V ) = 1/(1 + exp(−(V − V1/2)/− 40.1827))

τn(V ) = 2.0182 + 3.6404 · exp(−((V − (−40.1827)/30.3991)2)

(3.6)

where V is the voltage in mV and V1/2 is the half-activation voltage. The potassium

reversal potential was set to EK = −85 mV throughout the entire cell.

A model for delayed rectifier potassium current as described in Ficker and Heinemann

(1992) was also included and distributed uniformly throughout the soma, apical dendrite,

oblique dendrites and tuft. A peak conductance value was chosen so that action potentials

repolarized during simulations of pharmacological block of K(A) channels (Table 3.2). The

92

delayed rectifier K+ channel model kinetics are, gK(DR) = gK(DR) n,

n′ = (n∞ − n)/τn

n∞(V ) = 1/(1 + αn(V ))

τn(V ) = βn(V )/(0.02 · (1 + αn(V ))

αn(V ) = exp(−0.003 · (V − V1/2) · F)/(RT)

βn(V ) = exp(−0.00021 · (V − V1/2) · F)/(RT )

(3.7)

where V is the voltage in mV, V1/2 is the half-activation voltage, F is the Faraday constant,

R is the ideal gas constant and T is the temperature in degrees Kelvin.

The K(A) channel models and distribution were based on previous experimental stud-

ies (Hoffman et al., 1997; Migliore et al., 1999, 2005). Along the primary apical dendrite

and into the oblique dendrites, gK(A) was distributed with an increasing linear gradient

such that distal locations at 400 µm (or greater) from the soma exhibited a five-fold

larger gK(A) than the soma. The maximal peak conductance was adjusted to fit the aver-

age increase in input resistance (27.6 ± 9.7%) seen during pharmacological block of K(A)

channels (Table 3.2). The distribution for gK(A) was modeled as,

gK(A) = gA(s) ·

(1 + 0.015 · d) d < 400 µm,

6 d ≥ 400 µm

(3.8)

where d is distance in µm from the soma and gA(s) is the peak conductance at the soma

(S/cm2). Note that the peak conductance was allowed to increase only out to a distance

of 400 µm on the primary apical dendrite, after which point gK(A) was constant. Because

K(A) distal K(A) channels (> 100µm) have been shown to exhibit a hyperpolarized shift

in their half-activation voltage (Hoffman et al., 1997), two different K(A) channel models

93

were used to differentiate between distal and proximal K(A) channels. A proximal K(A)

channel model was used for oblique dendrites and the primary apical trunk out to a

distance of 100 µm from the soma and a distal K-A channel model with a hyperpolarized

shift in the half-activation voltage was used for locations at a distance greater than 100

µm from the soma (Migliore et al., 1999).

K(A) channel kinetics are, gK(A) = gK(A)mh (for distal and proximal models),

h′ = (h∞ −m)/τh

h∞(V ) = 1/(1 + αh(V ))

τh(V ) = 0.26 · (V + 50)

αh(V ) = exp(0.113 · (V + 56))

βh(V ) = exp(0.113 · (V + 56))

(3.9)

For proximal channels,

m′ = (m∞ −m)/τm

m∞(V ) = 1/(1 + αm(V ))

τm(V ) = 4 · βm(V )/(1 + αm(V ))

αm(V ) = exp(0.038 · zm(V ) · (V − 11))

βm(V ) = exp(0.021 · zm(V ) · (V + 56))

zm(V ) = −1.5− 1/(1 + exp((V + 40)/5))

(3.10)

For distal dendrites,

m′ = (m∞ −m)/τm

m∞(V ) = 1/(1 + αm(V ))

τm(V ) = 4 · βm(V )/(1 + αm(V ))

αm(V ) = exp(0.038 · zm(V ) · (V + 1))

βm(V ) = exp(0.015 · zm(V ) · (V + 56))

zm(V ) = −1.8− 1/(1 + exp((V + 40)/5))

(3.11)

Basal dendrites. Basal dendrites contained the following active conductances dis-

tributed uniformly: gNa(F), gNa(S), gK(A), gh and gK(DR). All active conductances in the

94

basal dendrites were set to values equivalent to their somatic values with the exception of

gNa(F) and gNa(S). The Na+ peak conductances were set to 0.15 times that of their somatic

values to prevent spontaneous dendritic spiking during simulations of pharmacological

block of K(A) and K(D) channels.

Axon. A simulated version of a myelinated axon was attached with passive properties and

active conductances distributed as described in previous computational and experimental

studies (Golding et al., 2001; Hu et al., 2009; Kole et al., 2007, 2008; Lai and Jan, 2006;

Mainen et al., 1995). In all axonal segments, the axial resistivity was set to 100 Ω-cm.

In nodal segments, the membrane resistance was set to 37.5 Ω-cm2; a value of 15,000

Ω-cm2 was used in the rest of the axon. The membrane capacitance of all axonal sections

was set to the somatic Cm, with the exception of internodal sections where Cm was set

to 0.05 µF/cm2 to simulate myelin. The following active conductances were included in

the axonal model: low-threshold Na+ (gNa(L) described below), gNa(F), gK(D) and gK(DR)

(Table 3.2).

The delayed rectifier K+ conductance was distributed uniformly in all axonal segments

with gK(DR) in the initial segment and nodes set to five times that of the somatic value so

that the axonal action potential would repolarize during simulations of pharmacological

block of K(D) channels. In all other axonal sections, gK(DR) = 0.05 (S/cm2).

The distal axonal initial segment (AIS) has been determined to be the preferred lo-

cation for action potential initiation. Therefore, to initiate action potentials in the distal

AIS, a low-threshold Hodgkin-Huxley based Na+ channel model was distributed with an

increasing linear gradient from soma to the distal AIS, with activation and inactivation

curves shifted hyperpolarized compared to the soma and dendrites (Colbert and Pan,

95

2002; Hu et al., 2009; Kole et al., 2008; Mainen et al., 1995). At the same time, gNa(F)

was distributed with a decreasing linear gradient from soma to distal AIS. The maximal

gNa(L) in the AIS increased as described from 0.007 to 0.06 S/cm2 and the maximal gNa(F)

decreased from 0.025 to 0.005 S/cm2. This resulted in a two-fold larger maximal Na+

current in the distal AIS than in the perisomatic region. Nodal and internodal sections

contained only low-threshold Na+ channels with peak conductances of 0.035 and 0.002

S/cm2, respectively.

Consistent with previous experimental findings (Kole et al., 2007), gK(D) was also

distributed in the axon with an increasing linear gradient from soma to distal AIS such

that the maximal gK(D) was 15 times that of the proximal axon initial segment conductance

(gK(D)AIS). In nodal sections, gK(D) was set to the maximum value in the initial segment

(15 · gK(D) soma).

3.3.6. Fitting of simulations to experimental data

To reproduce experimental voltage responses seen during pharmacological block of

K(A) and K(D) channels, both K(A) and K(D) channel models (Hoffman et al., 1997;

Kole et al., 2008; Migliore et al., 1999) were incorporated into a passive CA1 neuron model

(Golding et al., 2005). Peak conductances for both potassium channels were distributed

throughout the dendritic tree and axon as described above. Somatic input resistance (RN)

was determined by simulating a series of subthreshold current injections (-300 pA to +100

pA, 600 ms duration) and calculating the slope of the resulting voltage-current (V-I) curve.

To reproduce pharmacological block of K(A) and K(D) channels, application of 6 mM 4-

AP was simulated by a 92% reduction in gK(A) and a 95% reduction in gK(D) (Jackson

96

and Bean, 2007; Martina et al., 1998). A low concentration (100 µM) of 4-AP (block

of K(D) channels) was simulated by a 90% reduction in gK(D). The somatic K(A) and

K(D) conductances were then scaled (simultaneously increasing or decreasing the dendritic

values due to the linear relationship of somatic and dendritic peak conductances) until the

model results of pharmacological block of K(A) and K(D) channels matched experimental

RN values.

After initial fits for gK(A) and gK(D), models for slowly and non-slowly inactivating

Na+ channels were then incorporated into the neuron model. Peak conductances for

both Na+ channel models were determined with fits (by hand) to previous experimental

data for distance-dependent voltage attenuation of backpropagating action potentials and

distribution of slowly and non-slowly inactivating Na+ channels in CA1 pyramidal neurons

(Baranauskas and Martina, 2006; Golding et al., 2001; Mickus et al., 1999). In addition,

the axon was checked to verify that action potentials were being initiated in the distal

portion of the AIS.

Following the inclusion of active conductances, the distribution and parameters for

Ih and passive properties were reinvestigated through optimized fits to experimental sub-

threshold voltage responses recorded in the presence and pharmacological block of H-

channels (Golding et al., 2005) using NEURON’s Multiple Run Fitter.

All of the above simulations for active conductances were performed again to verify

that the model output had not changed significantly as a result of the optimization.

Parameters were adjusted and the overall process was repeated if the model results for

RN, backpropagation of action potentials or fits had changed.

97

3.4. Results

I measured the effects of pharmacological block of K(A) and K(D) channels on somatic

subthreshold voltage responses in CA1 pyramidal neurons. Experimental results suggest

that a significant fraction of K(A) channels are available near resting potentials and thus

aid in shaping voltage responses to subthreshold current injections. These experiments

were then used to constrain peak conductances for both K(A) and K(D) channel mod-

els in a previously passive compartmental neuron model. The model was then further

constrained by experimental data on voltage attenuation and action potential backprop-

agation to provide more accurate results from future simulations.

3.4.1. Experimental measurements of somatic input resistance

Using whole-cell patch clamp recordings in brain slices from adult male rats, I first

measured the effect of pharmacological block of K(A) and K(D) channels on somatic RN

in CA1 hippocampal neurons. To prevent errors in measurements due to series resistance

changes, the series resistance was monitored throughout the course of the experiment.

Only recordings that maintained a relatively constant series resistance (< 10% increase

over a duration of 50 minutes) were considered. All cells were held at a resting potential

of -67 mV for the duration of each experiment.

A series of long current injections (-300 pA to +100 pA, 600 ms duration) were made

at a somatic electrode and the resulting voltage responses were measured at the same

location. RN was calculated as the slope of the V-I curve. To investigate changes in

RN due to block of K(D) or K(A) channels, RN was measured and averaged in control

ACSF during an initial baseline period (0-10 min) at the beginning of each experiment.

98

Following this baseline period, an ACSF solution with either 100 µM 4-AP or 6 mM 4-AP

was bath applied to block K(D) channels or both K(D) and K(A) channels, respectively.

The resulting somatic RN was monitored throughout the remainder of the experiment. A

final RN value was measured and averaged 40-50 minutes into the experiment.

The average RN in control ACSF during the baseline period (0-10 min) was 51 ± 6

MΩ and did not significantly increase when measured in control ACSF (no drug appli-

cation) 40-50 minutes later (Table 3.1, Figure 3.1A). Bath application of 100 µM 4-AP

to block K(D) channels did not significantly change RN (Table 3.1, Figure 3.1B). Cells in

which 6 mM 4-AP was applied to block K(A) channels exhibited an average 27% increase

in RN from 51 ± 4 MΩ (baseline) to 64 ± 4 MΩ (final) (Table 3.1 Figure 3.1B). This

increase in RN suggests that a significant fraction of K(A) channels are open at resting

potentials. During bath application of 6 mM 4-AP, several cells required additional posi-

tive holding current to maintain a resting potential value of -67 mV, indicating that the

cells experienced a membrane hyperpolarization consistent with other studies that saw a

membrane hyperpolarization or no change in membrane potential when applying 4-AP

(Buckle and Haas, 1982; Fujiwara and Kuriyama, 1983; Li et al., 2003; Navarro-Polanco

and Sanchez-Chapula, 1997)

3.4.2. Experimental measurement of somatic iEPSPs

To elicit simulated postsynaptic potentials, somatic current injections were modeled as

double exponential functions with a rise time (τr) of either 0.2 or 0.5 ms, a decay time (τd)

of 2 or 5 ms and a maximal current of 500 or 250 pA, respectively. The peak amplitude

of the current-evoked somatic potentials (iEPSPs) remained constant over time in control

99

Baseline(0-10 min)

Final(40-50 min)

Control 51 ± 6 (8)31 - 88

52 ± 5 (8)40 - 88

100 µM 4-AP 58 ± 5 (8)36 - 74

59 ± 4 (8)36 - 74

6 mM 4-AP 51 ± 4 (9)38 - 78

63 ± 4 (9)53 - 92

Table 3.1. RN (MΩ) in control ACSF and 4-AP.Cells in control conditions or in bath application of 100 µM 4-AP did notshow a change in their somatic RN during the final test period comparedto the baseline time period. However, cells in bath application of 6 mM4-AP showed a strong increase in somatic RN during the final test periodcompared to the baseline period. Values are the mean ± s.e.m. (n) andrange.

100

A

Baseline

Final (40-50 min)

Control

100 µM 4-AP

6 mM 4-AP

70

60

50

40

403020100

RN

(M

Ω)

Time (min)

B

C

n = 80

20

40

60

n = 80

20

40

60

n = 9

0

20

40

60

***

403020100

Time (min)

70

60

50

40

70

60

50

40403020100

Time (min)

2 mV

100 ms

100 ms

10 mV

Baseline

Final (40-50 min)

-300 pA

+50 pA

RN

(M

Ω)

RN

(M

Ω)

RN

(M

Ω)

RN

(M

Ω)

RN

(M

Ω)

Figure 3.1. RN changes in control ACSF and following application of 4-AP.Somatic RN was measured and averaged in control ACSF during an initialbaseline period (0-10 min) and during a final period 40-50 minutes later.A,B,C: (Left) The measured RN (MΩ) over time (minutes) for one cell.(Middle) Averaged RN during the baseline period and the final test period.(Right) Sample somatic voltage responses to 600 ms depolarizing (+50 pA)and hyperpolarizing (-300 pA) current injections during baseline (black)and final (red) periods. Scale bars in A apply to B and C. A: Somatic RN

shows no significant change over time in control ACSF (n = 8; t-test; P> 0.05). B: Somatic RN does not change following application of 100 µM4-AP (n = 8; t-test; P > 0.05). Arrow indicates time of drug application.C: Somatic RN significantly increases following bath application of 6 mM4-AP (n = 9; t-test; P < 0.001).

101

ACSF or following application of either concentration of 4-AP (Figure 3.2A-C, middle).

In addition, there was no significant change in iEPSP amplitude between control ACSF,

100 µM 4-AP and 6 mM 4-AP cell groups (Figure 3.2D, right).

The area under the iEPSP increased an average of 10% over time in control ACSF

(s.e.m ± 3.5%, Figure 3.2A, left). After bath application of 100 µM 4-AP, iEPSP area

increased an average of 13% (s.e.m ± 2.6 %, Figure 3.2B, left). Application of 6 mM 4-

AP resulted in an average 18% increase over time (s.e.m ± 1.7%, Figure 3.2C, left). The

increase in iEPSP area following bath application of 6 mM 4-AP is significant compared

to iEPSP area increases in both control ACSF and 100 µM 4-AP (Figure 3.2D, left).

3.4.3. Simulation of subthreshold responses

The reconstructed CA1 pyramidal neuron morphology was used to investigate how

different conductances available at resting membrane potentials shape subthreshold re-

sponses. Simulations were performed using the built-in run-fitter in the NEURON envi-

ronment to reproduce experimentally measured voltage responses at both the soma and

distal apical dendrite (Golding et al., 2005) with different combinations of channel con-

ductances present. In initial fits, Ra, Cm and Rm were allowed to vary independently

without the H-conductance (gh) present in the model to simulate previous experimental

pharmacological block of H-channels with cesium (Cs+) and ZD7288. All other peak con-

ductances (gK(A), gK(D), gNa(F), gNa(S), gK(DR)) were unchanged. In addition, I examined

whether voltage responses were best fit using a uniform (constant) Rm distribution or a

non-uniform Rm distributed sigmoidally from soma to distal dendrite as described in the

Methods.

102

A

4 mV

10 ms

Baseline

Final (40-50 min)

B

C

1.4

1.2

1.0

0.8Norm

aliz

ed

iEP

SP

are

a

Time (ms)

*

20100 30 40 50

1.4

1.2

1.0

0.8

Norm

aliz

ed iE

PS

P

a

mplit

ude

Time (ms)

20100 30 40 50

1.4

1.2

1.0

0.8

Time (ms)

Norm

aliz

ed iE

PS

P

a

mplit

ude

20100 30 40 50

1.4

1.2

1.0

0.8Norm

aliz

ed

iEP

SP

are

a

Time (ms)

**

20100 30 40 50

1.4

1.2

1.0

0.8

Time (ms)

Norm

aliz

ed

iEP

SP

are

a

***

20100 30 40 50

1.4

1.2

1.0

0.8

Time (ms)

Norm

aliz

ed iE

PS

P

a

mp

litu

de

20100 30 40 50

Control

100 µM 4-AP

Control Control

100 µM 4-AP 100 µM 4-AP

6 mM 4-AP 6 mM 4-AP 6 mM 4-AP

D

0

5

10

15

20

25

iEP

SP

are

a

iEP

SP

are

ax 1

00

Con

trol

100

µM

4-A

P

6 m

M 4

-AP

*

0

2

4

6

8

10

iEP

SP

am

p.

iEP

SP

am

p.

x 1

00

Con

trol

100

µM

4-A

P

6 m

M 4

-AP

Figure 3.2. Somatic iEPSP area and amplitude in control ACSF and afterapplication of 4-AP. Figure caption continued on the next page.

103

Figure 3.2. Measurement of iEPSP area and amplitude in control ACSF,100 µM 4-AP and 6 mM 4-AP. The current injection waveform was calcu-lated as the sum of double exponentials with τr = 0.5 ms, τd = 5 ms and Imax

= 250 pA. A,B,C: (Middle) iEPSP amplitude shows no significant changeover time in control ACSF or after application of 100 µM 4-AP or 6 mM4-AP. Baseline period (0-10 min) is indicated in black and a final test period(40-50 min) is indicated in red. A: (Left) In control ACSF, the area underthe iEPSP shows a significant change increase time (n = 8; t-test; P < 0.05).At far right, sample iEPSP traces from one CA1 pyramidal neuron duringbaseline (black) and final (red) test periods. Scale bars apply to B and C.B: (Left) Bath application of 100 µM 4-AP causes a significant increase inthe area under the iEPSP (n = 8; t-test; P < 0.01). C: (Left) Over time, thearea under the iEPSP increases significantly in the presence of 6 mM 4-AP(n = 9; t-test; P < 0.001). D: (Left) The change in iEPSP area comparedacross the three cell groups is significant only following application of 6 mM4-AP (t-test; P < 0.05). (Right) There is no significant change in iEPSPamplitude between cell groups in control ACSF or application of 4-AP.

104

Simulations revealed that when the K(A) conductance was included in the model, a

uniform distribution for Rm provided equally accurate fits to voltage responses as a non-

uniform distribution (Figure 3.3 B,D). As this result for the Rm distribution differed from

previous computational studies (Golding et al., 2005), I investigated various distributions

for Rm using a model that included only passive properties and varying amounts of the

total somatic gK(A) (0.06 S/cm2). Three different distributions of Rm were modeled: uni-

form, sigmoidally increasing from soma to dendrite (Rm (soma) < Rm (end)) and sigmoidally

decreasing from soma to dendrite (Rm (soma) > Rm (end)). Consistent with the previous

studies, these simulations showed that a sigmoidally decreasing Rm distribution provides

the best fits to experimental voltage responses when a K(A) conductance is not present

in the model. However, as an increasing amount of the total gK(A) was introduced into

the passive neuron model, the normalized error in fits for the three proposed distributions

approached approximately the same value (Figure 3.3 D). Specific parameter values are

given in Table 3.2.

To further understand why a variable Rm distribution is not required to produce a re-

alistic subthreshold response when a K(A) conductance is present, the effective membrane

resistivity was calculated along the primary apical dendrite. Effective membrane resistiv-

ity (Reff) was defined as 1/Σgi where Σgi is the sum of each of the active conductances

(including the leak conductance) available at the resting potential. This calculation was

performed in the active model (both K(A) and K(D) conductances present) and in a pas-

sive model with nonuniform distributions of Rm and gh (Figure 3.4). In both models, Reff

is largest in the somatic and proximal apical dendritic regions and decreases into the distal

portion of the apical dendrite. This is consistent with experimental results indicating that

105

Passive Properties

Property Value Property Value

Rm 2.25 · 105 (Ω · cm2) gh (soma) 0.39142 (pS/µm2)

Ra 176 (Ω · cm) gh (dend) 2.6884 (pS/µm2)

Cm 1.4µF/cm2 d1/2 151.55 µm

z 24.624

Potassium Channel Properties

Property Value Property Value

gD(s) 1.5 · 10−05 S/cm2 gDAIS0.00015 S/cm2

gK(DR) 0.03 S/cm2 gK(DR)hill0.05 S/cm2

gK(DR)AIS0.15 S/cm2

gA(s) 0.06 S/cm2

Axonal Sodium Channel Properties

Property Value Property Value

gNa(L) (prox) 0.007 S/cm2 gNa(L) (dist) 0.06 S/cm2

gNa(F) (prox) 0.025 S/cm2 gNa(F) (dist) 0.005 S/cm2

Table 3.2. Passive and active channel parameter values.

106

B

C

A

Model

Experiment

1 mV

50 ms

dendrite

dendrite

soma

soma

Non-uniform Rm (dec. soma to dendrite)

Uniform Rm (constant soma to dendrite)

Non-uniform Rm (inc. soma to dendrite)

D

% gK(A) in model

E

No

rma

lize

d e

rro

r in

fits -

Ih

% gK(A) in model

5

4

3

2

1

1.00.80.60.40.20.0

No

rma

lize

d e

rro

r in

fits -

pa

ssiv

e

5

4

3

2

1

1.00.80.60.40.20.0

Figure 3.3. Best fits to estimated passive properties and gh distributionA: A morphological reconstruction of a CA1 pyramidal neuron (Golding etal., 2005). Dendritic and somatic recording electrode locations are indicatedschematically. B: Experimental somatic and dendritic voltage responses(red) to a -50 pA, 400 ms long current injection in 5 mM CsCl (to blockH-channels) and best fits (black) with a uniform Rm distribution. Scalebar also applies to C. C: Experimental voltage responses (red) to a -30 pA,400 ms long current injection in control ACSF and best fits (black) withan increasing sigmoidal distribution of gh. D: Normalized error in fits tovoltage responses for estimated passive properties and distribution (Ra, Cm,Rm) with increasing amounts of the total gK(A). Different distributions ofRm were simulated: sigmoidally increasing (black), sigmoidally decreasing(blue) and uniform (red). E: Normalized error in fits to voltage responsesfor a sigmoidally increasing distribution of gh with different distributions ofRm and increasing amounts of gK(A).

107

the effective dendritic membrane leak conductance is larger in more distal locations caus-

ing strong voltage attenuation of signal propagation in CA1 pyramidal neurons (Golding

et al., 2005). In the passive model, an increasing nonuniform Rm distribution is neces-

sary to reproduce this larger effective dendritic membrane leak conductance (lower Reff)

in more distal locations of the neuron (Figure 3.4B). However, in the active model, the

K(A) conductance creates a lower Reff due to its strongly increasing gradient from soma

to distal dendrite (Figure 3.4A). As a result, a nonuniform distribution of Rm is no longer

required to reproduce experimental results of voltage attenuation and effective dendritic

membrane leak conductance.

3.4.4. Simulation of action potential backpropagation

Previous experimental research describing action potential backpropagation in CA1

pyramidal neurons has revealed a dichotomy in the strength of action potential backprop-

agation. Some cells exhibit strong backpropagation (> 40 mV) into the distal portion of

the apical dendrite, whereas others exhibit weak backpropagation (< 25 mV). Further-

more, these backpropagating action potentials display an activity dependent attenuation

during repetitive firing due to prolonged inactivation of sodium channels (Andreasen and

Lambert, 1995; Callaway and Ross, 1995; Golding et al., 2001; Mickus et al., 1999; Sprus-

ton et al., 1995b).

To verify that this behavior was correctly reproduced in the model, I simulated action

potential backpropagation and amplitude attenuation during repetitive firing. To do this,

I incorporated a six-state Na+ model that exhibits slow recovery from inactivation and

a five-state Na+ model with fast recovery (Menon et al., 2009). These Na+ models were

108

Distance from soma (μm)

x 10-3

gi a

t V

rest (S

/cm

2) E

ffectiv

e R

m (M

Ω-c

m2)

Rm vs. gi : Active model

Distance from soma (μm)

gi a

t V

rest (S

/cm

2)

Rm vs. gi : Passive model

Effe

ctiv

e R

m (M

Ω-c

m2)

A B

x 10-3

0.25

0.20

0.15

0.10

0.05

0

20

15

10

5

0

50

100

150

200

250

300

350

400

450

0.25

0.20

0.15

0.10

0.05

0

50 100

150

200

250

300

350

400

450

20

15

10

5

0

gK(A)

gh

gK(DR)

gK(D)

gNa

Reff

gLeak

Figure 3.4. K(A) channels are primarily responsible for lower Reff in distallocationsA: Reff (right axis) and the conductance for each active current (left axis)at the resting potential are plotted against distance from the soma (µm) inan active model. B: Reff and the conductance for the leak and H-current(left axis) at the resting potential are plotted against distance from the soma(µm) in a passive model. K(A) channel conductance increases into the distalapical dendrite, accounting for the strong decrease in Reff and removing thenecessity of a nonuniform Rm distribution to reproduce accurate voltageattenuation.

109

distributed in the primary apical dendrite such that the weakly backpropagating model

had a lower Na+ conductance in the distal portion of the apical dendrite compared to

the strongly backpropagating model (Table 3.3). The only differences between the two

models were the sodium conductances in the distal apical dendrites. The model neuron

displayed strong action potential backpropagation (> 40 mV at 350 µm) with the larger

gNa and weak action potential backpropagation (< 25 mV at 350 µm) with the smaller

gNa. Both models exhibited amplitude attenuation during repetitive firing consistent

with experiments (Golding et al., 2001) due to the presence of the slowly-inactivating

Na+ channel model (Figure 3.5).

3.4.5. Simulation of somatic and axonal action potentials

In addition to fitting voltage responses for passive properties and gh distribution pa-

rameters to create a biophysically realistic model, I also included a model axon. Recent

experimental and computational studies strongly suggest that action potentials origi-

nate in the distal portion of the axon initial segment (AIS) due to a high density of

low-threshold Na+ channels (Nav1.6) that are accumulated at the distal end of the AIS.

High-threshold Na+ channels (Nav1.2) are distributed with a higher density at the proxi-

mal site of the AIS and aid action potential propagation to the soma and help determine

somatic spike threshold (Hu et al., 2009; Kole et al., 2008). In addition, the AIS has been

found to contain a 10-fold increase in Kv1 channels over the first 50 µm. The Kv1 sub-

family, which underlie K(D) channels, give rise to slowly-inactivating, low threshold K+

channels that are believed to play a significant role in shaping action potential waveform

(Kole et al., 2007). Based on these findings, we distributed the low- and high-threshold

110

Model gNa (soma) fs ss fd sd gNa (dend)

Weak bAP 0.032 (S · cm−2) 0.9 0.1 0.2 0.5 0.0288 (S · cm−2)

Strong bAP 0.032 (S · cm−2) 0.9 0.1 0.25 0.65 0.0244 (S · cm−2)

Table 3.3. Na+ conductance distribution values for neuron modelsParameter values for the distribution of both Na+ models (described inMethods), where gNa (soma) is the total Na+ conductance at the soma, fs isthe fraction of the total somatic Na+ conductance (gNa (soma)) that exhibitsfast recovery, ss is the fraction of gNa (soma) that exhibits slow inactivation, fdis the fraction of gNa (soma) at 400 µm along the primary apical dendrite thatexhibits fast recovery and sd is the fraction of gNa (soma) at 400 µm alongthe primary apical dendrite that exhibits slow inactivation. Note that inboth models, the dendritic fractions do not sum up to 1.0 due to an overalldecrease in the Na+ conductance from soma to distal dendrite. The finalcolumn gives the resulting dendritic conductance at 400 µm from the soma.

111

A

First

AP

am

pl. (

mV

)

Distance from soma (µm)

B

C

Distance from soma (µm)

La

st

AP

am

pl. (

mV

)

100

80

60

40

20

0

4003002001000

100

80

60

40

20

0

4003002001000

Weakly backpropagating

20 mV

100 ms

Strongly backpropagating

soma

soma

dendrite

dendrite

Strong (model)

Weak (model)

Experimental data

Figure 3.5. Simulations of weak vs. strong backpropagationSimulated trains of action potentials were elicited by a 900 ms long depo-larizing somatic current injection. A: The first action potential amplitude(mV) in a train of action potentials is plotted against distance from thesoma (µm) along the primary apical dendrite. Experimental data (Goldinget al., 2001) is indicated by black squares and triangles, the weakly back-propagating model in blue and the strongly backpropagating model in red.Protocol and legend apply to B and C. B: The amplitude (mV) of the lastaction potential in a train is plotted against distance from the soma (µm)along the primary apical dendrite. C: (Left) A morphological reconstructionof a CA1 pyramidal neuron. Dendritic and somatic recording electrodes areindicated schematically. (Right) Somatic and dendritic (350 µm) voltageresponses for both weakly (top) and strongly (bottom) backpropagatingmodels.

112

Na+ conductances and gK(D) in the model axon such that action potentials originated in

the distal portion of the AIS and propagated antidromically to the soma and dendrites

(Figure 3.6A). Phase plots of simulated axonal and somatic spikes, as well as calculated

somatic and axonal half-widths and maximal rates of rise (Figure 3.6 B-D) were consis-

tent with experimental and computational results (Golding et al., 2001; McCormick et al.,

2007).

3.4.6. Comparison of computational and experimental results with A-type

channel blockers

Consistent with previous studies, gK(A) was distributed with an increasing gradient

along the primary apical dendrite such that the distal portion of the primary apical den-

drite had a 5-fold larger conductance than the somatic region (Chen and Johnston, 2004;

Connor and Stevens, 1971; Hoffman et al., 1997; Magee and Carruth, 1999). Simulation

of pharmacological block of K(A) and K(D) channels revealed that a somatic gK(A) value

of 0.06 S/cm2 was necessary to reproduce the average 27% increase in RN seen during

experimental application of 6 mM 4-AP. Model voltage responses to subthreshold cur-

rent injections were compared to individual experimental voltage traces in the presence

of A-type channel blockers to verify the model accuracy (Figure 3.7).

Steady-state voltage responses during simulation of pharmacological block of K(D)

channels are in good agreement with experimental steady-state voltage responses. Note

that in Figure 3.7A, bottom, the model voltage responses are identical in both control and

simulated pharmacological block conditions such that the voltage response for simulated

block of K(D) channels completely overlays the response in the control condition. In order

113

20 mV

1 ms

A B

Axon initial segment

Soma

Axon initial segment Soma

-70 -50 -30 10

-100

100

200

300

00

-10

-100

100

200

300

0

-70 -50 -30 10-10

Voltage (mV) Voltage (mV)

dV

/dt

(V/s

)

dV

/dt

(V/s

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Soma AIS

AP

ha

lf-w

idth

(m

s)

C D

50

150

250

350

AP

ma

x d

V/d

t (V

/s)

Soma AIS

Figure 3.6. Spike initiation in a CA1 pyramidal cell modelA: Distal AIS (blue) and somatic spikes (black) in response to a 1.2 nAsomatic current injection. The action potential occurs in the distal AISfirst and then propagates the soma. B: Phase plot (dV/dt vs. V) of theaxonal and somatic spikes in A. C: AP half-width (ms) of the somatic andaxonal spikes in A. D: Maximal rate of rise (V/s) of the somatic and axonalspikes in A.

114

to achieve a slight difference in the steady-state voltage responses between control and

simulated application of 100 µm 4-AP, it was necessary to incorporate a small reduction

(∼10%) of the K(A) conductance (not shown) in the model.

Model steady-state voltage responses for both hyperpolarizing and depolarizing cur-

rent injections during simulated block of K(A) channels are also in good agreement with

experimental voltage traces. However, accurate reproduction of the time course of voltage

sag for hyperpolarizing current injections during simulation of pharmacological block of

both currents was not achieved (Figure 3.7 B). Experimental observations indicated that

iEPSP amplitude showed no significant change over time following bath application of

6mM 4-AP while the area under the iEPSP increased slightly, but significantly (∼7%),

compared to control conditions. Model voltage responses for a simulated iEPSP verify

the experimental observation that the peak of the iEPSP is essentially unchanged with

simulated block of K(A) channels (and K(D) channels), while the area under the iEPSP

increases significantly compared to control voltage responses (Figure 3.7 B, right).

3.5. Discussion

3.5.1. Passive membrane properties

In CA1 pyramidal neurons, the extent to which synaptic potentials attenuate as they

propagate from distal dendrite to soma strongly depends on the dendritic architecture and

the distribution of membrane properties within it. Cable theory indicates that smaller di-

ameter dendrites produce larger depolarizations due to having a greater input impedance,

and larger diameter dendrites produce a smaller depolarization due to a smaller input

impedance (Rall et al., 1992). At the same time, larger depolarizations often lead to

115

Experiment

Model

A

B

-300 pA

+50 pA

-300 pA +50 pA

Control

IK(D) blocked

Control

IK(D), IK(A) blocked

Experiment

Model

2 mV

5 ms

10 mV

100 ms

100 ms

2 mV

Figure 3.7. Model validation: Subthreshold current injectionsA: (Top) Experimental somatic voltage responses to a somatic hyperpolar-izing current injection (-300 pA, 600 ms), a somatic depolarizing currentinjection (50 pA, 600 ms) and a simulated somatic iEPSP (τr = 0.5 ms,τd = 5.0 ms, Imax = 250 pA) in control ACSF (black, 0-10 min) and fol-lowing bath application of 100 µM 4-AP (red, 40-50 min). (Bottom) Modelneuron voltage responses to the same current injections in simulated con-trol ACSF (black, all conductances present) and simulated block of K(D)channels (red). Scale bars and current injection amplitudes apply to Bas well. B: (Top) Experimental voltage responses to somatic current in-jections in control ACSF (black) and following bath application of 6 mM4-AP (red). (Bottom) Model neuron voltage responses in simulated controlACSF (black) and during simulated block of both K(D) and K(A) channels.

116

greater charge transfer to the soma. However, large local EPSPs produced by synapses

on distal smaller dendrites reduce the synaptic driving force, thus decreasing charge trans-

fer to the soma and strongly attenuating the synaptic potential as it travels passively to

the soma (Carnevale and Johnston, 1982; Jaffe and Carnevale, 1999). Furthermore, si-

multaneous somatic and dendritic patch-clamp recordings have suggested that membrane

resistance in CA1 neurons is nonuniform, with the distal dendrites being ‘leakier’ (lower

membrane resistance) than more proximal locations (Golding et al., 2005) causing further

attenuation of EPSPs. Therefore, the impact of a synapse on neuronal output will depend

not only on its location within the dendritic tree, but on its passive membrane properties

as well.

Our modeling results are consistent with these findings in that membrane resistivity

can be modeled as a nonuniform property in a passive neuron model, reproducing ex-

perimentally measured estimates of EPSP attenuation (Magee and Cook, 2000; Golding

et al., 2005). Initial fits in a passive model yielded best-fits with a nonuniform mem-

brane resistivity. However, it is well known that dendrites in CA1 pyramidal neurons

contain active voltage-gated channels that are important for shaping dendritic filtering

properties. The K(A) current increases 5-fold from soma to distal apical dendrite and is

available at resting potentials. With the inclusion of this large outward conductance in

the previously passive model, I found that fits to steady-state voltage responses (in the

absence of H-channel models) were equally as accurate with all three distributions for

Rm. The increasing density of A-type potassium channels available at resting potentials

in the distal portion of the apical dendrite replaced the requirement for a nonuniform

117

Rm to reproduce experimental voltage attenuation. We also tested the steady-state at-

tenuation in the fully passive model with nonuniform Rm and models that contained a

K(A) conductance and distributions of either nonuniform or uniform Rm (Figure 3.8 A).

While attenuation was greatest in the completely passive model with a nonuniform Rm

distribution, voltage attenuation in all three models fell within experimental ranges.

3.5.2. H-conductance distribution and best-fits

One problem that arises when trying to determine passive membrane properties and

their distribution is the presence of voltage-gated conductances that are active at resting

potentials. Both the hyperpolarization-activated cation conductance (gh) and the K(A)

conductance are available at resting potentials and regulate the shape of subthreshold

voltage responses.

Experimental and modeling studies in layer V and CA1 pyramidal neurons suggest

that gh is distributed with an increasing nonuniform gradient from the soma to distal

dendrites such that a more than sixfold increase in channel density is seen in more distal

locations (Berger et al., 2001; Golding et al., 2005; Magee, 1998; Stuart and Spruston,

1998; Williams and Stuart, 2000). This large conductance, which is active at resting

potentials and increases with distance from the soma, further maximizes voltage attenua-

tion of distal EPSPs. Consistent with these studies, I found that including a nonuniform

increasing gradient for gh provided accurate fits to steady-state voltage responses and

attenuation in both the passive model and the model with active conductances. Compar-

ison of steady-state attenuation in a passive model with nonuniform Rm and an H-channel

model present and neuron models with K(A) channel models, an H-channel model and

118

1.0

0.8

0.6

0.4

0.2

0.0

350300250200150100500

5 mM CsCl

50-100 µM ZD7288

Uniform Rm, 100% gK(A)Non-uniform Rm, 100% gK(A)

Non-uniform Rm, 0% gK(A)

A

B1.0

0.8

0.6

0.4

0.2

0.0

350300250200150100500

Control

100% gK(A)0% gK(A)

C0.030

0.025

0.020

0.015

0.010

0.005

0.000

1.000.750.500.250.00

Hyperpolarizing Vsag (dend)

Depolarizing Vsag (dend)

Depolarizing Vsag (soma)

Hyperpolarizing Vsag (soma)

Distance from soma (µm)

Distance from soma (µm)

Vd

en

drite

/ V

so

ma

Vd

en

drite

/ V

so

ma

% gK(A)

MS

E in

fits

Figure 3.8. Steady-state attenuation and MSE in fits to voltage transientsA: The ratio of the dendritic steady-state voltage response to the somaticsteady-state voltage response in response to a long current injection withH-channels blocked using CsCl or ZD7288. Filled circles and squares areexperimental data (Golding et al., 2005). Model steady-state attenuationsfor different distributions of Rm and varying amounts of gK(A) are indicatedby black, red and blue lines. B: Steady-state attenuation in experimen-tal control conditions are indicated by open circles (Golding et al., 2001).Model steady-state attenuation for varying amounts of gK(A) are indicatedby black and red lines. C: The mean square error (MSE) in fits to tran-sient voltage responses for somatic and dendritic voltage responses to asubthreshold current injection (depolarizing or hyperpolarizing) is plottedagainst increasing amounts of gK(A) in a passive model with an H-channelmodel present.

119

either nonuniform or uniform distributions for Rm revealed that the amount of voltage at-

tenuation is the same in all three models, in keeping with experimental results (Figure 3.8

B).

H-channels are activated by hyperpolarizing voltage responses and cause the mem-

brane potential to return to steady-state. This results in both hyperpolarizing and depo-

larizing voltage ‘sags’. Previous modeling of voltage responses to long and short current

injections was able to accurately fit the steady-state voltage responses, but was unable to

reproduce all aspects of the time course of voltage sag for depolarizing and hyperpolarizing

‘sags’. I computed the dendritic and somatic error for the depolarizing and hyperpolar-

izing voltage sags in a passive model with increasing amounts of gK(A) (Figure 3.8 C).

I found that as the amount of K(A) conductance increased in the model, the accuracy

of the fits to the transient voltages strongly improved. This suggests that the voltage-

dependent properties of K(A) channels not only serve to help regulate the amplitudes of

subthreshold hyperpolarizing and depolarizing voltage responses, but also plays a role in

modulating transient voltage sags as a result of the fast time course of activation for K(A)

channels.

3.5.3. Action potential initiation and backpropagation

Many previous experimental and modeling studies have investigated the cellular mech-

anisms that are involved in action potential initiation and backpropagation. Simultaneous

somatic and dendritic recordings, in addition to antibody staining and modeling studies,

have revealed that action potentials originate in the distal portion of the AIS due to high

densities of Na+ and K(D) channels (Colbert and Johnston, 1996; Hu et al., 2009; Kole

120

et al., 2007, 2008). After initiation in the distal AIS, action potentials backpropagate into

the dendritic tree. As they invade the dendritic tree, the amplitude of backpropagating

action potentials attenuates with distance from the soma. In CA1 pyramidal neurons, it

has been shown that a dichotomy in the strength of the backpropagating action poten-

tial occurs among neurons such that particular neurons exhibit strong backpropagation,

whereas others show weak backpropagation (Golding et al., 2001). In addition, trains of

backpropagating action potentials undergo a frequency-dependent amplitude attenuation

as they propagate from soma to the distal portion of the apical dendrite. This frequency-

dependent attenuation and the dichotomy in action potential backpropagation has been

shown to be modulated by the distribution and availability of Na+ and K(A) channels

(Bernard and Johnston, 2003; Golding et al., 2001; Hoffman et al., 1997; Mickus et al.,

1999; Pan and Colbert, 2001; Spruston et al., 1995b).

Consistent with these studies, my simulations revealed that a slight change in the total

gNa could produce either weakly or strongly backpropagating neuron models. The Na+

channel densities in both models fell within experimentally determined ranges (Hoffman

et al., 1997; Magee and Johnston, 1995). Furthermore, both models accurately reproduced

the activity-dependent amplitude attenuation of backpropagating action potentials due to

inclusion of a state-dependent Na+ model (Menon et al., 2009) that exhibited proper ki-

netics of slow inactivation. The activity-dependent attenuation disappeared upon removal

of the slowly-inactivating Na+ channel model from the neuron model. The dichotomy in

action potential backpropagation could also be reproduced in different neuron morpholo-

gies through small changes in Na+ peak conductance and distribution (not shown).

121

While I did not vary the K(A) distribution or peak conductance in our models, it is

likely that slight modulations of these channels in the distal dendrites would also give

rise to a dichotomy in action potential backpropagation without strongly altering somatic

input resistance (Golding et al., 2001; Hoffman and Johnston, 1998, 1999; Migliore et al.,

1999).

3.5.4. K(A) channels shape somatic subthreshold voltage responses

I found that pharmacological block of K(A) channels significantly increased somatic

RN by 27% compared to control ACSF. Computational simulations of pharmacological

block of K(A) channels with activation and inactivation curves as described in Hoffman

et al. (1997); Migliore et al. (1999) revealed that a large somatic gK(A) value of 0.06 S/cm2

with the described activation and inactivation kinetics was necessary to reproduce the ex-

perimental increase in somatic RN. This suggests that a large fraction of K(A) channels

are available at resting potentials. Previous experimental studies have revealed that the

large transient outward K(A) conductance strongly affects dendritic filtering properties

due to a high density of K(A) channels available in the distal dendrites. The steep increase

in the density of K(A) channels from soma to distal dendrite regulates action potential

backpropagation, raises the threshold for local spike initiation and has been implicated

in summation of subthreshold postsynaptic potentials (Hoffman et al., 1997; Frick et al.,

2004; Urban and Barrionuevo, 1998). By having a significant fraction of K(A) channels

available at rest, dendrites could effectively regulate dendritic excitability through mod-

ulation of K(A) channels by synaptic depolarization, Ca2+ influx from dendritic spiking

or by signaling cascades.

122

While my model accurately reproduced the time kinetics and steady-state behavior

of subthreshold voltage responses in control ACSF simulations, model voltage responses

during simulations of K(A) channel block exhibited a faster time course of voltage sag

than seen during experiments. In addition, model voltage responses also exhibited larger

hyperpolarizing and depolarizing voltage transients then experimental voltage responses.

The larger ‘sags’ and the faster time course of voltage sag seen in model voltage responses

during simulated block of K(A) channels is partially due to activation of H-channels at

more hyperpolarized potentials. To further refine the model, additional optimization and

experimental investigation of the H-channel model in the absence of K(A) channels would

be required.

The slower time course of voltage sag in experiments could also be partially explained

by inhibition of an inward current following application of 4-AP. Experimental studies

of 4-AP application (0.5-10 mM) in rat cerebellar granule cells and rat myoblasts have

indicated that 4-AP inhibits inward Na+ currents in a dose-dependent manner without

significantly altering the voltage-dependent activation and inactivation properties of Na+

currents (Lu et al., 2005; Mei et al., 2000). In these studies, cells in bath application of 5

mM 4-AP exhibited up to roughly 30% inhibition of Na+ currents and a significant increase

in the time to peak for maximal Na+ currents. Inhibition of an inward current or the

electrogenic Na+/K+ pump that helps regulate membrane potential could also provide

insight into the unexplained membrane hyperpolarization seen during my experiments

involving high concentrations (6 mM) of 4-AP (Gordon et al., 1990; Perreault and Avoli,

1989; Wang et al., 2003).

123

Both experimental and computational results verified that with pharmacological block

of K(A) and K(D) channels, voltage responses to a simulated EPSP-like current injection

showed a significant increase in the area under the iEPSP, but no significant alteration of

the amplitude relative to control conditions. Recent mathematical work on cable theory

for synapses on spines suggest that if synaptic conductance (or in this case, a synaptic-

like current injection) changes more rapidly than the membrane time constant, then the

amplitude of the resulting voltage response should be independent of the membrane time

constant (Harnett et al., 2012). As a result, the amplitude of the iEPSP would not be

changed during pharmacological block of K(A) and K(D) channels as the peak voltage has

already occurred prior to activation of the membrane currents (τm). However, a change

in the area under the iEPSP during block of potassium channels would be expected as

membrane currents have been activated by this point and as a result, the iEPSP would

decay more slowly as the membrane voltage returns to the resting potential.

3.5.5. Block of K(D) channels does not alter RN

My experimental results and computational modeling indicate that pharmacological

block of K(D) channels does not significantly impact RN, suggesting that K(D) channels

do not play a significant role in shaping subthreshold voltage responses. This was further

verified through model voltage responses to subthreshold current injections during simu-

lated block of K(D) channels. Voltage responses in simulations of pharmacological block

of K(D) channels did not differ from those with a K(D) channel model present. The K(D)

current (IK(D)) is a rapidly activating, very slowly inactivating current that activates in

subthreshold ranges and is strongly sensitive to 4-AP (Storm, 1988). As K(D) channels

124

are partly inactivated at resting potentials and have fast activation kinetics, it is likely

that subthreshold hyperpolarizations and depolarizations are mediated more strongly by

K(A) channels which undergo fast activation and inactivation and are available at rest.

As a result, RN, which is determined by subthreshold voltage responses, would not be

strongly affected by block of K(D) channels because K(A) channels are still present to

mediate these responses. While IK(D) may only comprise < 20% of the total potassium

current resulting from the Kv1 subfamily and appear to not have a significant impact

on RN, the slow inactivation kinetics (τ > 200 ms, recovery from inactivation: 5s at -90

mV) of K(D) channels implicate these channels in a primary role for delay during spike

firing (and intervals), slow integration of depolarizing inputs and an increase in action

potential firing frequency during prolonged current injections (Baranauskas, 2007; Guan

et al., 2006; Mitterdorfer and Bean, 2002; Shen et al., 2004).

To investigate the validity of the model during action potential firing, I used the model

to investigate the response to a sustained, low amplitude depolarizing current injection

(0.3 nA, 900 ms ) with a K(D) channel model present and during simulated block of

K(D) channels (Figure 3.9). The interspike frequency for both somatic and dendritic

action potentials produced in response to the prolonged current injection was significantly

increased with K(D) channels present in the model compared to the interspike frequency

during action potential firing in simulated block of K(D) channels. Somatic and dendritic

spike amplitudes did not change during simulated block of K(D) channels. These results

are consistent with experimental results that implicate K(D) channels in modulation of

the interspike interval. However, the onset of the first action potential in simulated control

conditions (K(D) channels present) did not appear to be delayed relative to the onset of

125

A With IK(D)

10 mV

50 ms

B Without IK(D)

Figure 3.9. K(D) channels increases interspike intervalsA: Simulated somatic and dendritic (350 µm from soma) action potentialsin response to a long depolarizing current injection () with a K(D) currentpresent in the model. B: Model somatic and dendritic (350 µm from soma)action potentials in response to a long current injection (0.3 nA, 900 ms)during simulated block of K(D) channels. The interspike frequency signifi-cantly increased with gK(D) in the model (A) compared to during simulatedblock of K(D) channels (B).

126

the first action potential during simulated block of K(D) channels as was seen in previous

experimental studies (Storm, 1988). Further simulations and research are required to

investigate and refine the role and kinetics of the K(D) channel model in the onset of

action potential firing.

127

CHAPTER 4

Conclusion

128

4.1. Integration of information in dendritic trees

CA1 pyramidal neuron dendrites receive the majority of the cell’s synaptic inputs.

However, these individual synaptic signals are typically brief and of small amplitude,

requiring a sufficient number of inputs with the correct timing in order to depolarize

a neuron to action potential threshold and generate neuronal output. In addition to

their passive electrical properties and biophysical morphology, dendrites posses voltage-

gated conductances that are activated in response to membrane potential changes, thereby

influencing the shape of synaptic potentials and the spatial and temporal summation of

inputs. The work in this thesis used an experimental and computational approach to

derive new insights about EPSP integration and attenuation in a previous passive CA1

pyramidal model (Golding et al., 2005) and to develop a more accurate CA1 pyramidal

neuron model with the addition of voltage-gated A-type potassium channel constrained

by electrophysiological recordings.

4.2. Synaptic normalization in neuronal dendrites

It is common knowledge that in CA1 pyramidal neurons, synaptic potentials on distal

apical dendrites severely attenuate as they propagate to the soma. One mechanism pro-

posed to compensate for this attenuation is distance dependent conductance scaling in

which distal synapses experience an increase in synaptic conductance with distance from

the soma to yield voltage changes at the soma (Magee and Cook, 2000). However, our

results indicate that while moderately distal synapses may exhibit an increase in their

conductance, synapses in the distal apical tuft of CA1 pyramidal neurons cannot achieve

129

synaptic efficacy via conductance scaling (Nicholson et al., 2006; Williams and Stuart,

2002).

If EPSPs generated in the apical tuft are to shape somatic output, they must do it

by a mechanism other than synaptic scaling due to the severity of synaptic potential

attenuation as they propagate to the soma. One mechanism suggested for amplifying

synaptic potentials is dendritic spiking. Temporal and spatial coactivation of distal inputs

can produce regenerative local dendritic spikes that effectively propagate to the soma when

paired with more proximal inputs such as stimulation via Schaffer collateral inputs (Jarsky

et al., 2005; Kali and Freund, 2005). Another suggested compensatory mechanism is

subthreshold resonance boosting by inward currents such as IA (Cook and Johnston, 1997,

1999; Migliore and Shepherd, 2002). A-type potassium channels are distributed with an

increasing gradient from soma to distal dendrite (Hoffman et al., 1997) in CA1 pyramidal

neurons. This high density of potassium channels in the more distal regions serves to

dampen excitability. Any decrease in the availability of these channels would cause an

overall increase in dendritic excitability (Frick et al., 2004) and hence an amplification in

the propagation of synaptic potentials.

4.3. Better models of voltage-gated ion channels

CA1 pyramidal neuron dendrites (both apical and basal) express multiple voltage-

gated conductances that affect neuronal integration of information and whose interaction

can make information processing a challenging and difficult process to understand. De-

spite the advancement of experimental techniques used to study neuronal function, many

aspects of information processing are not fully understood. To this end, computational

130

modeling of ion channels is an important tool for generating insights and addressing ques-

tions about their underlying biophysical properties and role in shaping neuronal output.

Single-channel recordings of ion channels (Sakmann and Neher, 1995) have shown that

ion channels undergo rapid transitions between open and closed states, corresponding to

conformational changes in the channel. These transitions can be described by state dia-

grams and kinetic rate equations (Hodgkin-Huxley equations) that attempt to accurately

describe the electrical properties of the ion channels (Destexhe et al., 1994; Hille, 2001).

Combining these mathematical descriptions with experimental recordings is a good way to

constrain the uncertainty in a computational model. We used this combined approach to

create a more accurate computational model of a CA1 pyramidal neuron by incorporating

a previous model of an A-type potassium channel (Hoffman et al., 1997; Migliore et al.,

1999) and constraining the amount of IA on at rest by experimental results of somatic

input resistance following pharmacological block of IA. The robustness of this model was

then further verified by investigating fits to somatic and dendritic passive properties as

well as action potential backpropagation.

Computational models can be used to predict neural behaviors that can be further

explored by experimental research. One potentially interesting finding generated by simu-

lations of action potential backpropagation in the newly constrained model was that it was

necessary to slightly decrease the overall Na+ channel conductance in the distal apical den-

drite relative to the somatic value for both strongly and weakly backpropagating models

in order to correctly reproduce the frequency-dependent attenuation (Colbert et al., 1997;

Jung et al., 1997; Martina and Jonas, 1997; Menon et al., 2009; Mickus et al., 1999) of

131

trains of backpropagating action potentials in both scenarios. Most computational mod-

els of CA1 pyramidal neurons use a constant gradient of Na+ channel conductance along

the primary apical dendrite since experimental results from cell-attached patch recordings

indicate that Na+ channel density is relatively uniform over the majority of CA1 apical

dendrites (Magee and Johnston, 1995). However, recent evidence suggests that the dis-

tribution of the primary sodium subunit in the adult hippocampus (Nav1.6) exhibits a

gradual decrease in density along the proximodistal axis (Lorincz and Nusser, 2010). This

decrease is consistent with previous studies of the distribution of RI and RII Na+ subtypes

in the CA1 region of the hippocampus (Furuyama et al., 1993; Westenbroek et al., 1989)

suggesting the possibility of a differential distribution of Na+ channel subtypes. Further

computational modeling with our constrained channel distributions in other CA1 pyra-

midal neuron morphologies, combined with additional experimental research, would help

to determine the validity of a decreased Na+ channel gradient.

4.4. Future directions

Different types of neurons have distinctive dendritic channel expressions and morpholo-

gies that give rise to cell-specific regulation of synaptic integration, long-term potentiation,

long-term depression and synaptic plasticity. The dendritic signals produced by the vari-

ations in voltage-gated channel distributions and dendritic morphologies in turn enhance

and modulate channel kinetics, further shaping how information is integrated in a partic-

ular dendritic tree. This extreme diversity is critical to neural encoding and processing of

stimuli and ultimately, cognitive function. The study of dendritic information processing

132

in multiple neuronal types using mathematical, computational and experimental tech-

niques, is a necessary step to the end goal of understanding of how all organisms process

and respond to information and stimuli, in addition to discovering potential treatments

for brain-related disorders.

133

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