frequency-dependent properties of neurons and synapses in

Frequency-dependent properties of neurons and

synapses in an oscillatory network

by Hua-an Tseng

A Dissertation submitted to the

Graduate School-Newark

Rutgers, The State University of New Jersey

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

Graduate program in Biology

written under the direction of

Professor Farzan Nadim

and approved by

Newark, New Jersey

October, 2011

ii

Abstract of the Dissertation

Frequency-dependent properties of neurons and

synapses in an oscillatory network

by Hua-an Tseng

Dissertation Director:

Dr. Farzan Nadim

The oscillatory activities from neural networks are involved in many

behaviors, and animals need to be able to control the frequencies of these

activities to respond to the environmental challenges. Neurons in many systems

have frequency-dependent properties and preferred frequencies (also known as

resonance). We hypothesize that the activity frequency of an oscillatory network

is determined by the preferred frequencies of the neurons and of the synapses in

the network. We examined this hypothesis by investigating the frequency-

dependent properties of the neurons and of the synapses in the pyloric network

in the crab Cancer borealis. We also examined what factors affect the preferred

frequencies and how changing in these factors influence the frequency of the

network activity.

We first showed that the preferred frequency of neurons could be

measured with the voltage-clamp technique. Measuring the preferred frequency

with the voltage-clamp technique allowed us to have a full control of the voltage

iii

range and the waveform of the oscillation. By shifting the voltage range of the

oscillation, we found that the pacemaker PD neuron has a higher preferred

frequency when it is oscillating at a higher voltage range, and the preferred

frequency of the follower LP neuron is only affected by the upper bound of the

oscillation. The PD neuron also has different preferred frequencies when

oscillating with different waveforms. Specifically, one waveform parameter, the

75 - 100% rising slope, showed a negative correlation with the preferred

frequency.

After knowing that the voltage range and the waveform of the oscillation

are correlated with the preferred frequency, we used dynamic clamp to alter the

voltage range and the waveform of the PD oscillation during the ongoing activity

and measured the pyloric frequency. Based on our hypothesis, we expected the

voltage range and the waveform would have similar effects on the pyloric

frequency as they do on the preferred frequency. Indeed, our result showed that

the shifts in the pyloric frequency during the dynamic clamp experiments could

be explained by the changes in the voltage range and in the waveform

parameters.

Finally, we examined the frequency-dependencies of the amplitude and

the phase of the synaptic current. The amplitudes of the synaptic currents

between the AB/PD and LP neuron showed preferred frequencies. Interestingly,

the preferred frequencies of the synapses were significantly lower than those of

the presynaptic neurons and also than the pyloric frequency. While the voltage

iv

range of the presynaptic PD oscillation did not affect the preferred frequency of

the AB/PD to LP synapse, the preferred frequency of the LP to PD synapse was

higher when the upper bound, but not the lower bound, of the LP oscillation was

increased. Moreover, the strength of the synaptic resonance depended on the

upper bound of the presynaptic oscillation. To produce the strongest resonance,

the upper bound of the presynaptic oscillation needs to be within the voltage

range at which the synapse is most sensitive to the presynaptic membrane

potential. In addition to the amplitude, the phase of the synapses also showed

frequency-dependence. At low frequencies (< 1 Hz), the synaptic current reached

its peak before the presynaptic membrane potential did, and this phase

relationship reversed at high frequencies (> 1 Hz).

Overall, in this study, we demonstrated that many properties of the

neurons and synapses depend on the frequency of the oscillation and have

preferred frequencies. Moreover, these preferred frequencies can be regulated

by many factors, including the voltage range and the waveform of the oscillation.

Because some of these frequency-dependent properties are able to influence the

network frequency, the factors affecting their preferred frequencies could change

the network frequency in the same way. As a result, the frequency of an

oscillatory network is not determined by a single factor, but by the dynamic

interactions among the frequency-dependent properties of the network

components.

v

Acknowledgements

First, I would like to thank my advisor Dr. Farzan Nadim for his inspiration

and guidance. He taught me much of my scientific knowledge, many experiment

skills and most importantly his critical approach to research. Everything I learned

from him throughout my PhD years helped me a lot.

I would also like to thank my thesis committee, Drs. Jorge Golowasch,

Amitabha Bose and Dirk Bucher, for their advice and suggestions on my thesis.

Thanks to everyone in the Nadim lab and in the Golowasch lab. We had

such a good time working together.

Finally, I would like to thank my parents and my sister for their love. All my

accomplishments would never be possible without their endless support.

vi

Table of contents

Abstract .............................................................................................................. ii

Acknowledgements ............................................................................................ v

Table of contents ............................................................................................... vi

List of figures ...................................................................................................... x

Chapter 1: General introduction

...................................................................................................................... 1

The stomatogastric nervous system .............................................................. 2

The pyloric network and its tri-phase activity ................................................. 3

Ion channels in neurons of the pyloric network ............................................. 6

Neurotransmitter release in the pyloric network ............................................ 7

Neuromodulations in the pyloric network ...................................................... 8

Frequency-dependent properties in neuron .................................................. 9

Short-term dynamics of synapses ............................................................... 11

Frequency-dependent properties in synapse .............................................. 12

vii

Frequency-dependent properties of neuron and synapse determine the

frequency of network activity ....................................................................... 13

Chapter 2: Materials and methods

Preparation .................................................................................................. 16

Impedance amplitude profile (ZAP) function ............................................... 17

Software ...................................................................................................... 18

Chapter 3: Voltage range of oscillations affects the preferred frequency of an

oscillatory neuron

Introduction ................................................................................................. 19

Materials and methods ................................................................................ 21

Results ........................................................................................................ 22

Discussion ................................................................................................... 28

Chapter 4: Correlations between the waveform parameters and the preferred

frequency of an oscillatory neuron

viii

Introduction ................................................................................................. 39


Results ........................................................................................................ 42

Discussion ................................................................................................... 45

Chapter 5: The changes in voltage range and in waveform have similar effects on

the preferred frequency of pacemaker PD neurons and the network frequency

Introduction ................................................................................................. 55


Results ........................................................................................................ 58

Discussion ................................................................................................... 62

Chapter 6: Frequency-dependence of the action potential phase

Introduction ................................................................................................. 70


Results ........................................................................................................ 71

Discussion ................................................................................................... 72

ix

Chapter 7: The frequency-dependence of the IPSC amplitude

Introduction ................................................................................................. 75


Results ........................................................................................................ 80

Discussion ................................................................................................... 86

Chapter 8: Frequency-dependence of the IPSC phase

Introduction ............................................................................................... 105

Materials and methods .............................................................................. 106

Results ...................................................................................................... 107

Discussion ................................................................................................. 109

Chapter 9: Discussion .................................................................................... 117

Chapter 10: Future directions ......................................................................... 122

Reference ....................................................................................................... 125

Curriculum vitae .............................................................................................. 131

x

List of figures

Chapter 3: Voltage range of oscillations affects the preferred frequency of an

oscillatory neuron

Figure 3.1 Frequency-dependent impedance profile ................................... 34

Figure 3.2 Preferred frequency measurements in the current clamp and the

voltage clamp .............................................................................................. 35

Figure 3.3 Preferred frequency of the PD neuron increases with the voltage

range of oscillation ...................................................................................... 36

Figure 3.4 Preferred frequency of the LP neuron increases with the upper

bound of the oscillation only ........................................................................ 38

Chapter 4: Correlations between the waveform parameters and the preferred


Figure 4.1 Realistic waveforms of the PD neuron ....................................... 49

Figure 4.2 Preferred frequencies of PD neurons with realistic waveforms

.................................................................................................................... 50

xi

Figure 4.3 Correlations between the normalized preferred frequencies

(Normalized fmax) of the PD neurons and the waveform parameters ........... 52

Figure 4.4 Preferred frequencies of LP neurons with realistic waveforms

.................................................................................................................... 54

Chapter 5: The changes in voltage range and in waveform have similar effects on

the preferred frequency of pacemaker PD neurons and the network frequency

Figure 5.1 Dynamic clamp experiment setup .............................................. 65

Figure 5.2 Low-threshold dynamic clamp current ........................................ 66

Figure 5.3 High-threshold dynamic clamp current ....................................... 67

Figure 5.4 Waveform parameters during the dynamic clamp current injection

.................................................................................................................... 69


Figure 6.1 Action potentials during an oscillation ........................................ 73

Figure 6.2 The phases of the action potential show more delay as the

frequency increases .................................................................................... 74

xii


Figure 7.1 Frequency-dependent profile of IPSC amplitude........................ 94

Figure 7.2 Preferred frequency of the AB/PD to LP synapse was not affected

by the presynaptic PD voltage range .......................................................... 96

Figure 7.3 Only the upper bound of the presynaptic LP oscillation affects the

preferred frequency of the LP to PD synapse ............................................. 98

Figure 7.4 Correlations between the preferred frequencies of the presynaptic

neurons and the synapses ........................................................................ 100

Figure 7.5 The strength of resonance depends on the upper bound of the

presynaptic oscillation ............................................................................... 101

Figure 7.6 Correlations between the voltage for maximal R and the half-

activation voltage of synapse .................................................................... 102

Figure 7.7 The upper bound of the LP slow-oscillation during the ongoing

pyloric activity reached the dynamic range of the synaptic current ........... 104


Figure 8.1 Frequency-dependent profile of the synaptic phase difference

.................................................................................................................. 113

xiii

Figure 8.2 The AB/PD to LP synaptic phase differences were affected by the

lower bound, but not the upper bound, of the presynaptic PD oscillation

.................................................................................................................. 114

Figure 8.3 The LP to PD synaptic phase differences were affected by the

upper bound, but not the lower bound, of the presynaptic LP oscillation

.................................................................................................................. 115

Figure 8.4 The synapses oscillating with realistic waveforms generate a wider

range of phase differences ........................................................................ 116

Chapter 9: Discussion

Figure 9.1 The interactions between the pyloric frequency, preferred

frequencies and properties of neurons and synapses ............................... 121

1

Chapter 1: General introduction

Many behaviors result from coordinated and rhythmic neural activities.

Some examples include the swimming in lamprey, heartbeat in leech, feeding in

crab and walking and breathing in vertebrate. Neural networks underlying these

rhythmic behaviors are known as central pattern generators (CPGs). The activity

of a CPG can arise from the intrinsic properties of neurons or from the synaptic

interactions between neurons in the network (Marder and Calabrese, 1996;

Marder and Bucher, 2001). In some CPGs rhythmic activities arise from synaptic

interactions which are usually inhibitory while in other CPGs, network activities

are driven by pacemaker neurons.

Because CPG activities are involved in many essential activities of the

animal’s day by day life, how CPGs generate rhythmic activity becomes an

important question. Additionally, the knowledge gained from studying an

anatomically simple CPG, such as the pyloric network used in this study, helps

us understand the connections between different levels of neuroscience, from the

intrinsic properties of neuron and synapse to the neural network activity. By

characterizing, identifying and finally modifying the underlying cellular and

synaptic mechanisms in a CPG, researchers can investigate how the properties

of the neurons and synapses affect the network activity, which provides a great

entry point for bringing different levels of neuroscience together and reveals the

big picture of neural networks.

2

A fundamental and important characteristic of an oscillatory activity is its

frequency. As CPGs are involved in many behaviors, the frequencies of their

activities have to be regulated. In particular, the CPG may need to maintain its

activity at a certain frequency or to change the frequency in response to various

environmental challenges. For example, animals can change their walking speed

as needed. Therefore, what factors determine the frequency of CPG activity

becomes an important question. In this thesis we hypothesize that the frequency-

dependent properties of the neurons and synapses in an oscillatory network

determine the frequency of the network activity. Based on this hypothesis, we

examined the neurons and synapses in the pyloric network of the stomatogastric

nervous system of the crab Cancer borealis to understand their frequency-

dependent properties and preferred frequencies, and to investigate how the

changes in these properties affect the frequency of network activity.

The stomatogastric nervous system

The stomatogastric nervous system (STNS), whose activity is responsible

for the feeding behaviors in crustacean, has become a well-studied model

system in the past years. The STNS is located on top of the foregut stomach and

includes four ganglia, including two commissural ganglia, one oesophageal

ganglion and one stomatogastric ganglion (STG). The commissural and the

oesophageal ganglia neurons project their axons to the STG via stomatogastric

nerve (stn) and their axonal terminals release neuromodulators required for the

3

STG to produce the rhythmic activities. We will refer to these as descending

(modulatory) projection neurons.

Located in the STG, there are two CPGs, the gastric mill network and the

pyloric network. The gastric mill activity is slow (around 0.1 Hz) and responsible

for chewing, while the pyloric activity is fast (around 1 Hz) and responsible for

filtering of chewed food. The pyloric network and the gastric mill network are not

independent from each other and interact both through local synapses and

through feedback to descending projection neurons (Bartos et al., 1999; Wood et

al., 2004).

As an experiment model system, STNS has many advantages. First,

STNS produces similar activities in vitro and in vivo, and the network activity lasts

for days in vitro. Second, each type of neuron can be easily identified by

comparing the intracellular recording with the corresponding extracellular

recording on the corresponded nerve. Third, the connections between neurons,

including gap junctions and chemical synapses, are well known. Finally, many

neuromodulators are present in and modify the outputs of the STNS and can be

used as tools to modify the properties of neurons and synapses to study how

these properties affect the network activity.

The pyloric network and its tri-phase activity

The pyloric network in crab is responsible for the filtering the chewed food

and its activity can be detected extracellularly on the motor nerves. There are 7

4

types of neurons, totaling around 11-13, in the pyloric network. These neurons

can be divided into two groups, the pacemaker group and the follower group. The

pacemaker group includes one anterior burster (AB) neuron and two pyloric

dilator (PD) neurons. The AB neuron has intrinsic oscillatory properties and,

under proper neuromodulation, is able to generate endogenous bursting

oscillations. The PD neurons do not typically generate oscillatory activity in

isolation but are strongly coupled to the AB neuron via gap junctions. As the

result of the strong electrical coupling, the AB and PD neurons become a

pacemaker kernel and produce bursting oscillation at the same phase (Marder

and Eisen, 1984b). The rhythmic bursting activity of the pacemaker kernel drives

the whole pyloric activity via inhibitory synapses, and the frequency of the

pacemaker bursting activity is the primary determinant of the frequency of the

network activity. In crab, the two lateral posterior gastric neurons (LPGs) show

rhythmic activity synchronized with the pyloric pacemakers and are sometimes

considered part of the pyloric network but will not be further discussed in this

thesis.

The follower lateral pyloric (LP) pyloric constrictor (PY), inferior cardiac (IC)

and ventral dilator (VD) neurons receive the inhibitory synapses from the

pacemaker neurons. Pyloric network contains one LP, VD and IC neuron and

three to five electrically coupled PY neurons. Without the synaptic input from the

pacemaker neurons, the follower neurons loss their bursting oscillatory activities

and become silent or fire tonically. Beside the synapses from the pacemaker

neurons, the LP and PY neurons also have a gap junction and reciprocal

5

inhibitory synapses between each other and therefore their bursting activities are

out of phase.

All chemical synapses within the pyloric network are inhibitory and can be

divided into two types based on the neurotransmitters they use: the dilator PD

and VD neurons have cholinergic synapses and all other pyloric neurons have

glutamatergic synapses (Marder and Eisen, 1984a). The pacemaker neurons

make chemical synapses to the follower neurons. Although both the AB and PD

neurons have synapses to the follower neurons, their synapses are quite

different in many ways. Besides using different neurotransmitters, they also show

different dynamics. The synapse from the AB to the LP neuron activates and

decays faster than those from the PD to the LP neuron (Rabbah and Nadim,

2007) and, in crab, the synapse from AB appears to be the major synapse

received by the LP neuron (Martinez, Golowasch and Nadim, unpublished). The

pacemaker group receives its sole chemical feedback from the follower neurons

through the LP to PD synapse, and the timing of the feedback can alter the cycle

frequency and also limit the variability of the pyloric frequency (Mamiya and

Nadim, 2004, 2005). Between the follower LP and PY neurons, there are also

synaptic connections; notably, these synapses are a combination of chemical

inhibitory synapses and electrical synapses which are rectifying in the LP to PY

direction (Mamiya et al., 2003a).

The pyloric network generates a tri-phase rhythmic activity. The AB/PD

neurons burst periodically and hyperpolarize the follower LP and PY neurons via

inhibitory synapses. The LP and PY neurons rebound at different phase due to

6

their different intrinsic properties (Rabbah and Nadim, 2005) and the inhibitory

synapse from the LP to PY neuron (Mamiya and Nadim, 2005). After the AB/PD

bursts, there is a short delay and then the LP neuron rebounds from the inhibition

and starts bursting, followed by the PY neurons. The strong inhibitory synapses

from the PY neurons to the LP neuron allows the bursting of PY neurons to end

the LP burst (Rabbah and Nadim, 2005). Finally, the AB/PD neurons begin to

burst again and terminate the PY burst. The tri-phase pattern repeats itself at the

frequency around 1 Hz. Besides the LP and PY neurons, the other follower

neurons in the pyloric network include the VD and IC neurons and are not

discussed in this thesis.

Ion channels in neurons of the pyloric network

Neurons in the pyloric network carry a wide range of voltage-gated ion

channels (Golowasch and Marder, 1992b), including transient potassium A-

current (IA), Ca2+-sensitive K+ channel (Ouyang et al., 2010) and

hyperpolarization-activated inward current (Ih) channel (Goeritz et al., 2011). The

conductance of different types of potassium channel can vary several folds

among individuals (Golowasch et al., 1999; Golowasch et al., 2002) and are not

independent from each other and from other channels. In PD neurons, the

expression of high-threshold potassium currents (IHTK), IA and Ih are correlated

with each other at the mRNA level (Schulz et al., 2007) and at the conductance

level (MacLean et al., 2005; Khorkova and Golowasch, 2007). Modeling results

7

show that similar neural activity can arise from different relative levels of ion

channel compositions (Goldman et al., 2001).

The interactions and dynamics of these voltage-gated ion channels are

important in determining the activity of each neuron. For example, an increase in

the A-current will delay the onset of the PY burst (Zhang et al., 2008). Therefore,

the bursting waveform of each neuron can be seen as representing the

combination of its ion channel composite and synaptic inputs it receives.

Neurotransmitter release in the pyloric network

Neurotransmitter release can be spike-mediated; when an action potential

reaches the axon terminal, it triggers the release of neurotransmitter. This type of

release is common in most synapses. In the stomatogastric nervous system as in

other invertebrate networks and the retina, there is another type of

neurotransmitter release, graded release (Raper, 1979; Graubard et al., 1980;

Johnson and Harris-Warrick, 1990). The synaptic terminal could release

neurotransmitter even without action potentials, and the amplitude of the release

depends on the presynaptic membrane potential. An activation curve of graded

release is usually constructed by plotting the amplitude of the postsynaptic

response to presynaptic voltage pulses of different amplitude.

8

Neuromodulation in the pyloric network

Neuromodulation has been reported in many CPG systems, including the

locomotion, respiratory system and the pyloric network (Christie et al., 1997;

Fenelon et al., 1999; Li et al., 2003; Dickinson, 2006; Harris-Warrick, 2011). The

neurons and synapses in the pyloric network are targets of neuromodulation

(Beltz et al., 1984; Hooper and Marder, 1984; Marder et al., 1986; Stein, 2009).

Many neuromodulators are released in the STG by descending projection

neurons of the commissural and oesophageal ganglia. These neuromodulators

are required for the pyloric network to generate proper rhythmic activity; blocking

the of action potential in the stn by either applying TTX or transecting the nerve

causes the removal of neuromodulator release and the pyloric network stops

producing rhythmic activity. Besides for maintaining the rhythmic activity, a recent

study shows that neuromodulators are also involved in controlling correlations

between ionic current expression in pyloric neurons (Khorkova and Golowasch,

2007).

At network level, the neuromodulators can alter the network activity during

bath application. For example, serotonin, pilocarpine and proctolin are able to

increase the frequency of the activity when bath-applied (Marder and Eisen,

1984b; Hooper and Marder, 1987). At the cellular level, one of the best known

features of many neuromodulators in the STG, in particular the peptidergic

modulators, is their ability to induce a specific voltage-dependent inward current

(Swensen and Marder, 2000), which was first identified in response to proctolin

(Golowasch and Marder, 1992a). Besides activating the modulatory inward

9

current, the neuromodulators can also regulate other intrinsic properties of pyloric

neurons. For example, dopamine increases Ih in the AB, PY and VD neurons

(Peck et al., 2006). Finally, in some cases, the neuromodulators also alter the

synaptic properties. The peptide proctolin increases the amplitude of the LP to

PD synapse and also modifies its short-term dynamics (Zhao et al, 2011 in

review). Overall, the neuromodulators play important roles in regulating the

pyloric activity.

Frequency-dependent properties in neuron

Neurons in many systems show frequency-dependence in impedance

measurements (Hutcheon and Yarom, 2000). The traditional way to measure the

impedance during the oscillation is using the impedance amplitude profile (ZAP)

waveform, a sweeping-frequency sinusoidal function whose oscillatory amplitude

is fixed but whose frequency increases with time. The neuron is usually injected

with a ZAP current in current clamp and the membrane impedance is calculated

as a ratio of membrane potential to injected current as a function of frequency. In

some neurons, the impedance first increases and then decreases as the

frequency of neural subthreshold oscillation increases. This type of impedance

profile is called resonance and such a neuron has highest impedance when it is

oscillating at a unique frequency. We refer to this frequency as the preferred

(resonant) frequency. Resonance is observed in many neurons in a variety of

neural systems (Hutcheon et al., 1996a, b; Fisher et al., 2011; van Brederode

10

and Berger, 2011), including the pacemaker neurons in the pyloric network of

crab Cancer borealis (Tohidi and Nadim, 2009).

The preferred frequency results from the interactions between passive

membrane properties and voltage-gated ion channels (Hutcheon and Yarom,

2000). The passive membrane has capacitive properties. When oscillatory

current is injected into the neuron at high frequency, the current charges and

discharges the membrane capacitor without much affecting the membrane

potential. Therefore, the membrane potential only changes when the current is

injected at low frequencies and the cellular membrane acts as a low-pass filter.

On the other hand, the voltage-gated ion channels, specifically those with large

time constants and reversal potentials around the resting membrane potential,

can act as high-pass filters. During low-frequency oscillations, these channels

activate and counter the change in the membrane potential when the potential

slowly drifts away from the resting potential. However, when the neuron is

oscillating at high frequency, these channels fail to activate due to their large time

constant. Therefore, these channels diminish the change in membrane potential

only at low frequencies and act as high-pass filter. Examples of this type of

voltage-gated channels include Ca2+ channel (Tohidi and Nadim, 2009), Ca2+-

sensitive K+ channel (Fisher et al., 2011) and hyperpolarization-activated inward

current channel (Orio et al., 2009; Tohidi and Nadim, 2009; Zemankovics et al.,

2010). The combination of cellular membrane and voltage-gated ion channels

with properties mentioned above is sufficient to generate resonance. Finally,

some voltage-gated ion channels, such as persistent Na+ channel, can act as an

11

amplifier for resonance (D'Angelo et al., 2001). These channels have short time

constants and reversal potentials away from the resting membrane potential.

They activate when the oscillation reaches its peak and enhance the amplitude of

the oscillation (Hutcheon and Yarom, 2000).

Many studies have shown correlations between the preferred frequency of

a neuron in the network and the frequency of network activity. In the rat

cerebellum, granule cells have resonant frequency around the theta-frequency

(3-12 Hz) (D'Angelo et al., 2001). In the pyloric network, the preferred frequency

of the pacemaker PD neuron is correlated with the frequency of pyloric activity

(~1 Hz) (Tohidi and Nadim, 2009). These findings imply that the preferred

frequency of the neurons in a network could be a good predictor for the network

frequency.

Short-term dynamics of synapses

With repetitive depolarizing presynaptic pulses, the amplitude of synaptic

output can show short-term dynamics and either increase (facilitation) or

decrease (depression). Short-term dynamics are a common feature of synapses

in both vertebrate and invertebrate nervous systems (Nadim and Manor, 2000;

Rabbah and Nadim, 2005; Connelly et al., 2010; Doussau et al., 2010;

Kandaswamy et al., 2010) and play important roles in determining network

activity (Connelly et al., 2010). In a simple oscillator-follower model network,

short-term depression of the synapse from the oscillator to the follower neuron

12

acts to promote phase maintenance in response to changes in network

frequency (Manor et al., 2003). Also, short-term depression of synapses enables

an oscillatory network to have bistable states, which is a possible mechanism for

prolonged effects of neuromodulators (Nadim et al., 1999; Manor and Nadim,

2001). The degree of facilitation or depression usually depends on the frequency

of repetitive stimulation (Connelly et al., 2010; Kandaswamy et al., 2010).

In the stomatogastric nervous system, graded synapses are known to

show depression (Mamiya and Nadim, 2005). Individual synapses, even those

from the same presynaptic neuron, can have different dynamics of short-term

depression, which could be important for producing proper network activity

(Mamiya and Nadim, 2005). Many factors, including the neuromodulation and

presynaptic waveform, can modify the short-term depression of the synapses

(Rabbah and Nadim, 2007). Finally, while short-term depression of graded

synapses is found in many synapses in the pyloric network, facilitation has only

been reported in the graded synapse from the LP to PD neuron with low-

amplitude presynaptic depolarization pulses in the presence of proctolin (Zhou et

al., 2007).

Frequency-dependent properties in synapses

Short-term synaptic dynamics provide possible mechanisms to generate

frequency-dependent responses in the amplitude of synaptic output in an

oscillatory network. As the frequency of presynaptic oscillation increases, the

13

amplitude of synaptic output can either increase or decrease due to facilitation or

depression, respectively. More interestingly, resonance in synaptic amplitude can

occur if the synapse shows facilitation during low-frequency oscillation and

depression during high-frequency oscillation. As a result, the synapse generates

a larger output when the presynaptic neuron is oscillating at the preferred

frequency.

Another possible frequency-dependent property is the phase of the

synaptic current in the oscillatory cycle. In an oscillatory network, the phase of

synapses can affect the properties of network oscillations. For example, in pyloric

network, the synapses from the LP to PD neuron can shorten or extend the

pyloric period depending on the phase of the synaptic input (Prinz et al., 2003;

Mamiya and Nadim, 2004, 2005). The pyloric frequency is influenced by this

synaptic phase, and if this synaptic phase has the frequency-dependence, then

there will be a two-way interaction between the pyloric frequency and the

synaptic phase, instead of simply one determines the other.

Frequency-dependent properties of neuron and synapse determine the

frequency of network activity

In this thesis, we are interested in factors that determine the frequency of

CPG activity. We hypothesize that the frequency-dependent properties of the

neurons and synapses in an oscillatory network determine the frequency of the

network activity. To examine this hypothesis, we designed a series of

14

experiments using the pyloric network of the crab Cancer borealis as our model

system. Among the neurons in the pyloric network, we focus on the PD neuron,

which is part of the pacemaker group, and the LP neuron, which is a follower

neuron with the sole chemical feedback synapse to the pacemaker group. Our

study requires a precise control of membrane potential and waveform, which is

not possible if we measure the resonance with current-clamp technique. Instead,

we use voltage-clamp to generate the oscillation with the designed voltage range

in (presynaptic) neurons and measure the cellular and synaptic preferred

frequencies.

In general, the preferred frequencies of neurons increase with higher

oscillatory voltage range and, in PD neuron, is correlated with the top 25% slope

of oscillatory waveforms. When a current is injected into the pacemaker PD

neuron with dynamic clamp to modify its voltage range and waveform, the

network frequency will shift in the same direction as the preferred frequency of

the neuron predicted by the knowledge of the voltage range and waveform. The

synapses between the pacemaker neurons and follower LP neuron show

resonance and preferred frequencies. Interestingly, the preferred frequency of

the synapses is lower than that of the neurons and is also lower than the network

frequency. Among the synaptic properties, the synaptic preferred frequency from

the pacemaker neurons to the follower LP neuron is not affected by the voltage

range of the presynaptic oscillation; on the other hand, the one from the LP

neuron to the PD neuron moves to a higher value as the upper bound of the LP

oscillation increases. The phase of synaptic current also shifts with the

15

presynaptic frequency. At low frequency, the peak of synaptic current occurs

before the peak of presynaptic voltage (negative phase), but at high frequency,

the peak of synaptic current lags behind the peak of presynaptic voltage (positive

phase). In conclusion, the network frequency affects many properties of neurons

and synapses, and these properties, in turn, have feedback on the network

frequency. Therefore, the network frequency is determined by a recurrent map of

dynamic interactions between the frequency itself and frequency-dependent

properties.

16

Chapter 2: Materials and methods

This chapter elaborates the general materials and methods used during

the course of the dissertation. The specific methods for different chapters are in

the corresponding chapters.

Preparation

Adult male crabs Cancer borealis were purchased from the local seafood

supermarkets and kept in tanks filled with artificial sea water at ~12°C until use.

Before dissection, crabs were put on ice for 20-30 minutes to anesthetize them.

The dissection was done using the standard protocol as described in (Tohidi and

Nadim, 2009). After dissection, the nervous system, including the commissural

ganglia, the esophageal ganglion, the stomatogastric ganglion (STG), the nerves

connecting these ganglia and the motor nerves were pinned down in a 100 mm

Petri dish coated with the silicon elastomer Sylgard (Dow Corning). The STG was

then desheathed to expose the neurons for impalement. During the experiment,

the whole dish was superfused with normal crab saline (11 mM KCl, 440 mM

NaCl, 13 mMCaCl2∙2H2O, 26 mM MgCl2∙6H2O, 11.2 mM Trizma base, 5.1 mM

maleic acid; pH 7.4) and maintained at 10 - 14°C. The PD and LP neurons were

identified by matching their intracellular activity with the extracellular action

potentials on the corresponding motor nerves.

17

The electrodes were prepared by using the Flaming–Brown micropipette

puller (P97; Sutter Instrument) and filled with 0.6 M K2SO4 and 0.02 M KCl. For

current injection, the resistance of the electrode was kept at 10 – 20 MΩ; for

membrane potential measurements, the resistance of the electrode was 20 – 35

MΩ. Extracellular recording from the motor nerves was done using a differential

AC amplifier model 1700 (A-M Systems) and intracellular recording was done

with Axoclamp 2B amplifiers (Molecular Devices).

Impedance amplitude profile (ZAP) function

The ZAP function was calculated as follows:

where A is the amplitude of the oscillation and f(t) is a monotonically increasing

function that determines the range of the sweeping frequencies (in Hz) and is

defined as:

where Fmax and Fmin were the maximum and minimum sweeping frequencies,

respectively; dur is the duration of the sweep; and L is the rate of the exponential

rise in frequency (the exponential rise in frequency is used so that lower

frequencies are sampled sufficiently). Because time was measured in

18

milliseconds, the scaling factor 10-3 was used to convert the frequency units to

Hz. All experiments were done with Fmin = 0.1 Hz, Fmax = 4 Hz, and dur = 100

seconds. To avoid transients at the beginning of the oscillations, the ZAP

waveform was preceded with three cycles of a sinusoidal waveform injected at

the lowest frequency Fmin, which transitioned smoothly into the ZAP function,

bringing the total duration of each sweep to 130 seconds. The first sinusoidal

waveform was phase-shifted to start at its minimum value.

Software

Data were recorded with pClamp (vesion 9.2) and Scope (version 7.75)

softwares. Dynamic clamp experiments were performed with Dynamic Clamp

software (version 1.55). Analysis was done with Readscope and Matlab. Scope,

Dynamic Clamp and Readscope were developed in the lab of Dr. Farzan Nadim

and are available for download at http://stg.rutgers.edu/software.

19

Chapter 3: Voltage range of oscillations affects the preferred


Introduction

Membrane resonance in neurons results from interactions between the

passive membrane properties and voltage-gated ionic currents. Two voltage-

gated currents, the hyperpolarization-activated inward current and Ca2+-sensitive

K+ current, are commonly involved in resonance and their expression have been

reported in the pyloric neurons (Ouyang et al., 2010; Goeritz et al., 2011). Indeed,

removal of the Ih or the Ca2+-sensitive K+ channel reduces the resonance in the

AB and PD neurons in the pyloric network (Tohidi and Nadim, 2009). Ih activates

when the neuron is hyperpolarized to -80 mV and has reversal potential around -

30 mV. Analyzing the neural response to the ZAP current injection shows that Ih

is responsible for the lower envelope of the oscillating membrane potential and

IK(Ca) shapes the upper envelope (Tohidi and Nadim, 2009). The activation and

inactivation of the voltage-gated ion channels depend on the membrane potential;

when the neuron is oscillating at different voltage ranges, the compositions of

activated voltage-gated ion channels may vary, resulting in different frequency-

dependent response profiles. Therefore, it is interesting to see if there is a

change in the preferred frequency of the neuron with different voltage ranges of

oscillation. In an oscillatory network, slow-oscillations of neurons can be

extracted from the bursting activity by removing the action potentials with a low-

20

pass filter. The voltage range of the oscillation can then be measured from the

slow-oscillation. Under natural conditions, the voltage range of the oscillating

neurons in the pyloric network can be regulated by many factors, including

synaptic inputs and neuromodulation. For example, follower neurons receive

inhibitory synapses from the pacemaker AB/PD neurons; with stronger synaptic

inhibition, the lower bounds of the voltage range of follower neurons will be

pushed to a more hyperpolarized level. The feedback chemical synapse received

by the pacemaker PD neurons from the follower LP neuron can similarly

determine the lower bound of the PD neuron voltage range. Neuromodulators

can also influence the voltage range of the oscillation by modifying the intrinsic

properties of neurons and by altering the strength or dynamics of synapses.

We used voltage-clamp to generate a ZAP oscillation (0.1 to 4 Hz) of sine

wave in the PD and LP neurons of the pyloric network, and calculated their

frequency-dependent impendence profiles as well as their preferred frequencies

under different voltage ranges of oscillation. While increases in both the upper

bound and the lower bound of the voltage range resulted in higher preferred

frequency in the PD neuron, only the upper bound of the oscillation had a similar

effect on the preferred frequency of the LP neuron. The results suggest that 1)

the composition and the dynamics of voltage-gated ion channel might be different

in the PD and LP neuron, and 2) the preferred frequency can be modulated by

altering the voltage range of the oscillatory neuron.

21

Materials and methods

Impedance measurement

To measure the impedance of the PD and LP neuron, after identifying the

neuron, we used 10-7 M TTX (tetrodotoxin, Biotium) to remove the

neuromodulatory inputs and, therefore, the endogenous oscillatory activity. Two

electrodes were inserted into the neuron; one used for current injection and the

other used for recording the membrane potential. In the current-clamp

experiments, the current injected was a ZAP function with the frequency

sweeping from 0.1 to 4 Hz. The amplitude of the injected current was adjusted to

produce a 30 mV difference in the membrane potential when the neuron was

oscillating at 0.1 Hz. To make the results comparable to those from the voltage-

clamp recordings, when necessary, we also injected a bias DC current to bring

the baseline membrane potential to -60 mV.

The voltage-clamp experiments were done in two-electrode voltage clamp

mode. In each sweep, the membrane potential was clamped first at a holding

value (equal to the minimum value of the ZAP function), followed by the ZAP

function. The voltage range of oscillation varied depending on the experiment.

The PD neuron produces bursting oscillations at a frequency of ~1 Hz with a

slow-wave profile that ranges approximately between -60 and -30 mV. We

therefore focused our study around these voltages and frequency ranges. In the

experiments in which the effect of the lower bound was examined, the lower

bound was shifted by ±10 mV (-70, -60 and -50 mV) while the upper bound was

22

kept at -30 mV. When examining the effect of the upper bound, this bound was

shifted by ±4 mV (-34, -30 and -26 mV) while the lower bound was kept at -60

mV. We limited the shift of the upper bound to ±4 mV, which resulted, on average,

in a shift of preferred frequency that was similar to that seen when the lower

bound was shifted by ±10 mV.

Calculation of impedance power and preferred frequency

The impedance profile was calculated with Matlab scripts. For each cycle

of recording, the script measured the frequency as well as the changes in voltage

and current. The impedance profile was generated by calculating the impedance

power (the ratio of voltage over current) as a function of frequency. During each

experiment, each oscillatory condition was repeated three times. The impedance

profiles from three repeated trials are then re-sampled and averaged together to

minimize any possible noise. The preferred frequency was defined as the

frequency at which the impedance power was maximal. In this thesis, we refer to

the impedance power as impedance.

Results

The pyloric network produces tri-phasic activity with frequency around 1

Hz. A previous study has shown that the pacemaker PD neuron shows

resonance in current-clamp and has preferred frequency close to the pyloric

23

frequency. Moreover, the preferred frequency of the PD neuron is also correlated

with the pyloric frequency (Tohidi and Nadim, 2009). To measure the frequency-

dependent impedance, we first removed the endogenous pyloric oscillation by

bath applying TTX. TTX blocks both action potential generation and

neuromodulator release, resulting in a silent pyloric network. Our experiment

required precise control of voltage ranges and waveforms; therefore, instead of

using current-clamp, we used voltage-clamp to generate ZAP oscillations of the

membrane potential in neurons and recorded the injected current simultaneously.

During the ZAP oscillation, the neuron was oscillating with the sine wave at a

fixed voltage range and continuously varying frequencies (figure 3.1A, upper

trace, voltage range: -60 to -30 mV, frequency: 0.1 to 4 Hz). The current required

for generating the oscillation with fixed voltage range varied with the frequency

(figure 3.1A, lower trace). The preferred frequency is the unique frequency at

which the neuron exhibits maximum impedance. When the voltage clamped

neuron was oscillating at the preferred frequency, the injected current was

minimal (figure 3.1A, arrow). The plot of the impedance against the frequency at

each oscillatory cycle showed that the impedance first increases and then

decreases (figure 3.1B), and that the maximum impedance occurred at the

preferred frequency (figure 3.1B, arrow).

Traditionally, the frequency-dependent impedance profile is measured

with the current-clamp technique. We were interested to know if the

measurements we obtained with the voltage-clamp technique were comparable

with those obtained with the current-clamp technique. We adjusted the amplitude

24

of the current in the current-clamp experiments to produce the ZAP oscillation,

whose voltage range at 0.1 Hz matching the voltage range we used in the

voltage-clamp experiments (-60 to -30 mV). The frequency-dependent

impedance profile was produced in the same neuron with the voltage-clamp

technique (figure 3.2A) and with the current-clamp technique (figure 3.2B). The

measurement results from both techniques were similar and were not statistically

different (N = 7; voltage-clamp: 1.28±0.51 Hz, current-clamp: 1.36±0.38 Hz;

paired Student’s t-test, p = 0.742; figure 3.2C). In all following experiments, we

measured the preferred frequency with the voltage-clamp technique.

The activation and inactivation of voltage-gated ion channels depend on

the membrane potential, and the dynamics of these channels are required to

generate resonance. Therefore, the different voltage ranges of oscillation could

potentially produce different frequency-dependent responses. To examine the

effects of voltage range on frequency-dependent responses and preferred

frequencies, we altered either the upper bound or the lower bound of the

oscillations in PD and LP neurons. As our control, we used the voltage range of -

60 to -30 mV, which was similar to the voltage range of pyloric neurons during

natural oscillation. The upper bound was shifted by ±4 mV during the upper

bound experiment, and the lower bound was shifted by ±10 mV during the lower

bound experiment. The different values for the upper bound and lower bound

were chosen because in preliminary experiments, these two values generated a

similar level of change in the preferred frequency.

25

First, we examined how the frequency-dependent impedance profile in the

pacemaker PD neuron responded to changes in voltage range. When the PD

neuron was oscillating at a fixed lower bound (-60 mV) but various upper bound

(-34, -30 and -26 mV), the frequency-dependent impedance profiles showed that

the peak of impedance shifted toward higher frequency as the upper bound of

voltage range became more depolarized (figure 3.1A1). A 4 mV increase (from -

30 to -26 mV) in the upper bound shifted the preferred frequency of the PD

neuron toward the higher value by ~27% (from 1.14±0.23 Hz to 1.44±0.36 Hz)

compared with control. Similarly, decreasing the upper bound by 4 mV (from -30

to -34 mV) dropped the preferred frequency by ~23% (from 1.14±0.23 Hz to

0.88±0.25 Hz) compared with the control. Summary of results from 15

experiments showed that moving the upper bound to a more depolarized level

shifted the preferred frequency to a higher value (N = 15; one-way ANOVA, p <

0.001; figure 3.3A2).

Similarly, the preferred frequency also moved with the lower bound of the

voltage range in the oscillating PD neuron. As the lower bound became more

depolarized, the peak of the frequency-dependent impedance profile moved

toward a higher value (figure 3.3B1). When the lower bound was increased by 10

mV (from -60 to -50 mV), the preferred frequency of the PD neuron increased by

~18% (from 1.02±0.24 Hz to 1.18±0.26 Hz) compared with control. Likewise,

decreasing the lower bound by 10 mV (from -60 to -70 mV) resulted in a drop in

the preferred frequency by ~30% (from 1.02±0.24 Hz to 0.74±0.36 Hz) compared

with control. Results from 12 experiments showed that moving the lower bound

26

of the voltage range higher or lower shifted the preferred frequency in the same

way (N = 12; one-way ANOVA, p < 0.05; figure 3.3B2).

Although both shifting the upper bound and the lower bound of the voltage

range could alter the preferred frequency in the PD neuron, they might have

different efficiency. To examine which one is more efficient in shifting the

preferred frequency, we compared the sensitivity of the preferred frequency to

the changes in the upper bound or the low bound of the voltage range. The

sensitivity was calculated as the ratio of the change in preferred frequency to the

change in the voltage. We found that changing the upper bound of the voltage

range was more efficient than the lower bound in shifting the preferred frequency

in the PD neuron (upper bound: N = 15, 0.07±0.044 Hz/mV; lower bound: N = 12,

0.02±0.017 Hz/mV; Student’s t-test, p = 0.001).

We also shifted both the upper and the lower bound simultaneously by ±4

mV. The voltage amplitude of the oscillation was kept at 30 mV and the peak of

the frequency-dependent profile increased as the voltage range became more

depolarized (figure 3.3C1). Moving the voltage range of the PD neuron toward a

depolarized level by 4 mV (from -60 – -30 mV to -56 – -26 mV), increased the

preferred frequency by ~29% and moving toward the hyperpolarized level by

4mV (from -60 - -30 mV to -64 - -34 mV) decreased the preferred frequency by

~25% (N = 9; one-way ANOVA, p < 0.001; figure 3.3C2). Interestingly, the

change in the preferred frequency due to shifting both upper and lower bounds

by 4 mV was close to and not significantly different from shifting the upper bound

by 4 mV alone (upper bound: N = 15, frequency increase: 26.9±25.5%; both

27

upper and lower bound: N = 9, frequency increase: 28.5±18.9%; Student’s t-test,

p = 0.876).

Besides the pacemaker PD neuron, we also investigated the frequency-

dependent impedance profile in the follower LP neuron. Shifting the upper bound

of the voltage range in the oscillating LP neuron had a similar effect as we saw in

the oscillating PD neuron. When the upper bound of the voltage range increased,

the peak of the frequency-dependent impedance profile shifted toward the higher

frequency (figure 3.4A1). Increasing the upper bound by 4 mV (from -30 to -26)

increased the preferred frequency by ~24% (from 1.53±0.40 Hz to 1.90±0.48 Hz)

and decreasing the upper bound by 4 mV (from -30 to -34) decreased the

preferred frequency by ~29% (from 1.53±0.40 Hz to 1.08±0.30 Hz; N = 10; one-

way ANOVA, p < 0.001; figure 3.4A2).

Unlike changing the upper bound of the voltage in the oscillating LP

neuron, changing the lower bound had no effect on the preferred frequency. We

shifted the lower bound by 10 mV in both directions (from -60 to -50 mV or to -70

mV) and the peak of the frequency-dependent impedance profile was unchanged

(figure 3.4B1). Further analysis showed that the preferred frequencies during the

oscillation with all three lower bound (-70, -60 and -50 mV) were not significantly

different from each other (-70 mV: 1.56±0.56 Hz; -60 mV: 1.33±0.43 Hz; -50 mV:

1.50±0.45 Hz; N = 8; one-way ANOVA, p = 0.72; figure 3.4B2).

28

Discussion

Resonance in neurons involves cellular membrane and voltage-gated ion

channels. The activation and deactivation of the voltage-gated ion channels

depends on the voltage value of the membrane potential. Therefore, it is likely

that the frequency-dependence of the impedance and the preferred frequency of

the neuron are affected by the voltage range of its oscillation. Indeed, modifying

the voltage range changes the preferred frequency. In general, when the voltage

range becomes more depolarized, the preferred frequency will move to a higher

value.

The traditional way of measuring the frequency-dependence of impedance

is to inject the ZAP current into the neuron in current clamp and to record the

membrane potential simultaneously. During the ZAP current injection, the neuron

is oscillating at various voltage ranges, depending on the oscillatory frequency.

Because we were interested in the effects of voltage range on the preferred

frequency, the voltage-clamp technique, which allowed us to have full control of

the voltage range of the oscillation, is a better choice for the impedance

measurement than the current-clamp technique. The fact that the voltage clamp

technique and the current clamp technique give the same preferred frequency at

similar voltage ranges further proves that the voltage clamp technique is a

feasible alternative way to measure the preferred frequency. In future

experiments, we will have the ability to explore the details of the behavior of ionic

currents during the oscillation because we will have precise control of the

membrane potential under the voltage clamp. In voltage clamp, the amplitude of

29

the ionic current of voltage-gated ion channels can be measured by comparing

the amount of the injected current with and without an ion channel blocker. The

amplitude of Ih, for example, can be obtained by subtracting the injected current

under CsCl (an Ih blocker) treatment from the one without the CsCl treatment.

The ability to measure the preferred frequency with the voltage clamp technique

opens new possibilities in understanding the role of each ionic current during

oscillation.

Increasing either the upper bound or the lower bound of the voltage range

of the oscillating PD neuron increases its preferred frequency. However, the

preferred frequency shows different sensitivities between the upper bound and

the lower bound changes. It is known that different types of voltage-gated ion

channels are responsible for the reactions at the upper portion and the lower

portion of the oscillation. The upper portion of the oscillation is shaped by the Ica

while the lower portion is shaped by the Ih (Tohidi and Nadim, 2009). Because

these two types of ion channels have distinct dynamics, they can respond to the

voltage change differently, resulting in different sensitivities of the preferred

frequency.

Many factors, including ionic currents, neuromodulation and synaptic

inputs, influence the voltage range of an oscillation. In a PD neuron model,

increasing the conductance of Ih makes the baseline of the membrane potential

more depolarized and also increases the preferred frequency of the model

(Tohidi and Nadim, 2009). These findings are consistent with our experimental

results that a more depolarized voltage range will give a higher preferred

30

frequency. Neuromodulators also play an important role in determining the

voltage range of oscillating neurons. Many neuromodulators, including dopamine,

serotonin and pilocarpine, depolarize the AB neuron when bath applied (Marder

and Eisen, 1984b). Interestingly, these neuromodulators also increase the

frequency of the AB oscillation (Marder and Eisen, 1984b). For PD neurons,

some neuromodulators, such as dopamine, hyperpolarize the membrane

potential while others, such as octopamine and pilocarpine, depolarize it (Marder

and Eisen, 1984b; Harris-Warrick et al., 1998; Kloppenburg et al., 1999; Goaillard

et al., 2004). Moreover, ionic currents involved in generating resonance can be

the target of neuromodulation directly. For example, Ih current is modulated by

dopamine, octopamine and serotonin (Peck et al., 2006; Ballo et al., 2010).

Although the effects of neuromodulators on pyloric frequency have been shown

in many studies, how neuromodulators will affect the preferred frequency is still

unclear.

In addition to the ionic currents, the strength of inhibitory synapses

between neurons is also regulated by neuromodulators and therefore can shift

the lower bound of the voltage range to different levels. Dopamine enhances the

graded release component of the synapse from the LP to the PD neuron but

reduces the overall synaptic output (Ayali et al., 1998). Another neuromodulator,

red pigment concentrating hormone, enhances both the graded release

component and the overall output of the LP to PD synapse (Thirumalai and

Marder, 2002). Because the pyloric frequency is correlated with the preferred

frequency of the PD neuron (Tohidi and Nadim, 2009) and the factors shifting the

31

preferred frequency shifts the pyloric frequency in the same direction (see

chapter 5), we expect that the inhibitory synapse from the LP to PD neuron is

able to control the pyloric frequency. However, previous studies have shown that

removing (by hyperpolarizing the LP neuron) or enhancing (with neuromodulators)

this synapse has almost no effect on the pyloric frequency (Mamiya and Nadim,

2004; Thirumalai et al., 2006). One explanation is that the strength of the

synaptic input from the LP neuron does not produce enough of a shift in the

lower bound of the PD voltage range, so the changes in both the preferred

frequency and the pyloric frequency are not significant, especially considering

that the preferred frequency is less sensitive to the shift in the lower bound of the

voltage range. It is also possible that changing the strength of the LP to PD

synapse not only shifts the lower bound, but also alters the PD waveform in a

way of counteracting the effect of shifting the lower bound; resulting in a limited

change in the preferred frequency and the pyloric frequency.

Finally, the neuromodulator can activate a voltage-dependent inward

current (IMI) (Swensen and Marder, 2000). A recent study shows that using

dynamic clamp to inject the negative-conductance region of the IMI or a negative

leak current into the PD neuron is sufficient to recover the pyloric oscillation in

the absent of the neuromodulation (Zhao et al., 2010). The negative leak current

could have two possible effects on the resonance and the preferred freqeuncy of

the PD neuron. By reducing the leak current, the neuron could have a higher

impedance and therefore an enhanced resonance, which may help the recovery

of the pyloric oscillation. Also, the negative leak current has the reversal potential

32

at -68 mV, so increasing its conductance would depolarize the neuron, resulting

a higher preferred frequency and a higher pyloric frequency.

Interestingly, the preferred frequency in the LP neuron behaves differently

to the shift in the voltage range. The LP and PD neurons play different functional

roles in the pyloric network; the PD neuron is part of the pacemaker kernel while

the LP neuron belongs to the group of followers. Their voltage-gated ion

channels can be composed of different combinations thus respond differently to

the shift of voltage range. The preferred frequencies of neurons in many other

systems have varied responses to the shift in the voltage range. In some, like

the pyloric neurons, the preferred frequency increases as the membrane

potential becomes more depolarized (Gutfreund et al., 1995). In others, the

preferred frequency could decrease with a more depolarized membrane potential

(Hutcheon et al., 1996b) or is not affected by the voltage range at all

(Zemankovics et al., 2010).

When we put all our measurements from voltage range of -60 to -30 mV

together, we found that there was a three-fold variability in the preferred

frequencies of the PD or LP neurons (PD: min = 0.75 Hz, max = 2.10 Hz; LP: min

= 0.71 Hz, max = 2.56 Hz), which is similar to the variabilities in the ionic currents

(Golowasch et al., 2002; Khorkova and Golowasch, 2007). Interestingly, the

pyloric frequencies cross animals are also variable, while the phases are

relatively more constant (Bucher et al., 2005). Because the pyloric frequency is

correlated with the preferred frequency of the PD neuron (Tohidi and Nadim,

2009), the variability in the preferred frequency could reflect on the pyloric

33

frequency, and there are other mechanisms help stabilizing the phase of the

pyloric activity.

Overall, in this part of my thesis, we demonstrate that the voltage range

can be an important factor in determining the preferred frequency of the neurons

in the pyloric network. In the following chapters, we will explore other possible

factors.

34

Figure 3.1 Frequency-dependent impedance profile. A. The ZAP oscillation was

generated in the PD neuron with voltage clamp. To avoid transient effects, the

first three cycles of oscillations in the membrane potential were kept at 0.1 Hz,

and then the frequency was increased from 0.1 Hz to 4 Hz in 100 seconds (upper

trace). At the preferred frequency, the neuron required less current for the

oscillation with the same amplitude (arrow). B. The frequency-dependent

impedance profile was constructed by plotting the impedance versus the

frequency at each cycle. The maximal impedance occurred when the neuron was

oscillating at its preferred frequency (arrow).

35

Figure 3.2 Preferred frequency measurements in the current clamp and the

voltage clamp. The same neuron oscillated under the voltage clamp (A) or the

current clamp (B). C. The preferred frequencies measured under the voltage

clamp and the current clamp were not statically different (N = 7; paired Student’s

t-test, p = 0.742).

36

Figure 3.3 Preferred frequency of the PD neuron increases with the voltage

range of oscillation. A1. The impedance profiles when a PD neuron is oscillating

between different upper bounds (-34, -30 and -26 mV) and a fixed lower bound (-

37

60 mV). A2. The preferred frequency of the PD neuron increases as the upper

bound becomes more depolarized (N = 15; one-way ANOVA, p < 0.001). B1.

The impedance profiles when a PD neuron is oscillating between a fixed upper

bound (-30 mV) and various lower bounds (-70, -60 and -50 mV). B2. The

preferred frequency of the PD neuron increases as the lower bound becomes

more depolarized (N = 12; one-way ANOVA, p < 0.05). C1. The impedance

profiles when a PD neuron is oscillating at different voltage range (-64 to -34 mV,

-60 to -30 mV and -56 to -26 mV) with the same amplitude. C2. The preferred

frequency of the PD neuron increases with the voltage range of the oscillation (N

= 9; one-way ANOVA, p < 0.001).

38

Figure 3.4 Preferred frequency of the LP neuron increases with the upper bound

of the oscillation only. A1. The impedance profiles when a LP neuron is

oscillating between various upper bounds (-34, -30 and -26 mV) and a fixed

lower bound (-60 mV). A2. The preferred frequency of the LP neuron increases

when the upper bound becomes more depolarized (N = 10; one-way ANOVA, p <

0.001). B1. The impedance profiles when a LP neuron is oscillating between a

fixed upper bound (-30 mV) and different lower bounds (-70, -60 and -50 mV). B2.

The preferred frequency of the LP neuron is not affected by the voltage of the

lower bound of the oscillation (N = 8; one-way ANOVA, p = 0.72).

39

Chapter 4: Correlations between the waveform parameters and

the preferred frequency of an oscillatory neuron

Introduction

The bursting activity of the neurons in the pyloric network can be simplified

to slow-oscillation waveforms by filtering out the action potentials on the recorded

waveform using a low-pass filter. The slow-oscillation waveform represents the

change of membrane potential of the oscillatory neuron and is the result of

dynamic interactions between a number of ion channels. I have discussed one

parameter of the slow-oscillation waveform, the voltage range, in the previous

chapter. Besides the voltage range, the slow-oscillation waveform can also be

described by many other parameters, including duty cycle, rising and falling

slopes and peak phase. Duty cycle is the portion of the cycle above the average

value. Slope can be either rising or falling and is the rate of the change in

membrane potential. Peak phase is the phase at which the membrane potential

reaches its peak during the cycle. In general, the slow-oscillation is how the

membrane potential changes during the activity. Because many voltage-gated

ion channels are involved in generating neural resonance, different slow-

oscillation waveforms may recruit different levels of activation of voltage-gated

ion channels and result in different frequency-dependent responses and

preferred frequencies.

40

We recorded the membrane potential during the ongoing activity and used

a low-pass filter to filter this recording at 10 Hz to generate slow-oscillation

realistic waveforms. We then measured the preferred frequencies by voltage-

clamping the neuron with the realistic waveform and sine wave (which serve as

reference). In the PD neuron, the preferred frequencies vary with different

realistic waveforms and are negatively correlated with the top 75-100% of the

rising slope. However, the preferred frequencies of the LP neuron oscillating with

different realistic waveforms show no statistical difference.


Generation of the slow-oscillation realistic waveform

The representative realistic waveforms were extracted from the

experimental recordings using the Readscope software (version 7.75) as

described below. Five consecutive cycles of the selected recording were

analyzed. The voltage trace was low-pass filtered at 10 Hz to reveal the slow

oscillation. The average membrane potential in the five cycles was used as the

voltage threshold to align and average these cycles and produce a single

averaged waveform. The averaged waveform was sampled at 1000 points and

rescaled to be between 0 and 1. Finally, the waveform was shifted so that the

minimum point 0 became the start point of the waveform. These representative

realistic waveforms were then used in the waveform analysis and in the

experiments. The experiments in which the waveform was used to voltage clamp

41

the neuron and measure the corresponding preferred frequency were performed

by replacing the sine function in the ZAP equation (see chapter 2) with the

realistic waveform using the Scope software.

The realistic waveforms used in this study were selected as described

below. The seven PD realistic waveforms were extracted from randomly selected

recordings. For the LP realistic waveforms, we collected a group of the LP

waveforms and performed the principal component analysis. We then chose

seven LP realistic waveforms showing the most variations on the first and second

principal components.

Waveform analysis

The waveform analysis was done using Matlab scripts. The waveform duty

cycle was defined as the fraction of time that the waveform was above its mean

value. We also calculated the portions of the waveform above 75% or below 25%

of the peak value. The peak phase is the phase at which the maximum value (1)

occurs when the minimum (0) is used as the reference point. Area refers to the

area underneath the waveform curve where the duration of the waveform is

normalized to 1. The various slopes were calculated from different parts of the

waveform after dividing the waveform into a rising and a falling interval. The

rising interval is the portion of the waveform from between the start point 0 and

the peak point 1 and the falling interval is between the peak and the end point.

Each interval was divided into different slope ranges. The rising slopes used

42

were as follows: 0-100, 0 -25, 25-50, 50 -75, and 75-100%; the falling slopes

were as follows: 100-0, 100-75, 75-50, 50-25, and 25-0%. These parameters

were not meant to be independent or exhaustive descriptions of the waveforms.

These were selected from among a larger set of parameters because they

provide a relatively distinct and comprehensive description of the waveforms.

Results

In the pyloric network, each type of neuron has a singular slow-oscillation

waveform. The same type of neuron from different preparation, however, has a

similar (not exactly the same) waveform. The slow-oscillation waveform

represents how the membrane potential changes during each oscillation cycle

and can be dissected into several parameters, including the duty cycle, peak

phase, the portion above a certain threshold, the rising and falling slopes, etc. As

the activation and inactivation of voltage-gated ion channels depend on the

membrane potential, and the dynamics of the voltage-gated ion channels is

responsible for resonance in neurons, the same neuron oscillating with different

slow-oscillation waveforms could have different preferred frequencies. Moreover,

the preferred frequency could be correlated with the parameters of the waveform.

We explored the possible correlations between the preferred frequency in

the PD neuron and the waveform parameters. One way to approach this question

is to measure the preferred frequency with a set of waveforms, which have

differences in the desired parameters. Instead of creating separate sets of

43

waveforms for each parameter, we took advantage of the fact that the slow-

oscillation waveform of PD in each individual has different parameters during the

ongoing pyloric activity. We selected seven PD neurons in different individuals

and extracted the slow-oscillation waveforms from their recorded bursting

activities. The pre-recorded bursting activity (figure 4.1A, blue trace) was low-

pass filtered at 10 Hz to remove action potentials, and the filtered waveform

(figure 4.1A, red trace) was averaged over several cycles to generate the unitary

slow-oscillation waveform (we called it the realistic waveform) representing this

recording. We collected a set of seven unitary realistic waveforms (figure 4.1B, a-

g) and also included the sine waveform as our reference waveform. Although all

realistic waveforms were from real PD recordings, they looked different from

each other (figure 4.1C, compare the realistic waveforms a and g).

In each experiment, we drove the voltage-clamped PD neurons, in

separate runs, with ZAP functions constructed from the realistic waveforms and

the sine waveform, making them oscillate from 0.1 to 4 Hz and with a voltage

range between -60 and -30 mV. The example traces of the same neuron

oscillating with different realistic waveforms, waveforms a and g, were shown in

figure 4.2A. The frequency-dependent impedance profiles showed that different

realistic waveforms generate the peak of impedance at different frequencies

(figure 4.2B). To focus on the effects of different realistic waveforms in the same

neuron and to eliminate the variations between individuals, we normalized the

preferred frequency obtained from the realistic waveform oscillation to that

obtained from the sine waveform oscillation. The normalized preferred

44

frequencies were clearly different when the neurons were oscillating with different

realistic waveform (N = 7; one-way ANOVA, p < 0.001; figure 4.2C).

The realistic waveform can be described with several parameters,

including duty cycle, peak phase, the portions above certain thresholds, rising

and falling slopes, etc. We would like to know which of these parameter(s) can

be correlated with the preferred frequency. We calculated the parameters of the

seven realistic waveforms we used in the preferred frequency measurement and

checked if there was any correlation between the realistic waveform parameters

and the normalized preferred frequency. Surprisingly, most of the parameters

only showed slight or no correlations with the normalized preferred frequency

(figure 4.4). However, few specific parameters did stand out and draw our

attention. Amongst them, the rising slope of the waveform at 75 -100% amplitude

gave us a strongest negative correlation with statistically significant p value

( Pearson Product Moment Correlation, correlation coefficient = -0.59, p < 0.001;

figure 4.3J). In addition to the 75-100% rising slope, the total waveform area

(figure 4.3C) and the portion above 75% amplitude of the waveform (figure 4.3D)

also showed a good correlation with normalized preferred frequency (Pearson

Product Moment Correlation; area: correlation coefficient = 0.43, p < 0.05; portion

above 75%: correlation coefficient = 0.45, p < 0.05). Altogether, the analysis of

waveform parameters indicated that other than the upper bound and the lower

bound of the voltage range, other factors also influence the preferred frequency.

In particular, when the rising slope of the top portion of the waveform became

steeper, the preferred frequency became smaller.

45

As described in chapter 3, in contrast to the PD neuron, the preferred

frequency in the LP neuron responded differently to the shift in voltage range. We

therefore examined if the preferred frequency in the LP neuron is correlated to its

waveform parameters in a similar manner as the PD neuron, and if not, what are

the differences. We generated a set of seven realistic waveforms of LP neuron

from the LP bursting activity in different preparations. Even though the seven

realistic waveforms of the LP neuron looked similar, there were differences in the

waveform parameters (figure 4.4A, h-n). The oscillations were generated in the

LP neuron with these seven realistic waveforms and the sine wave, and their

frequency-dependent impedance profiles were calculated in the same manner as

described above for the PD neuron. In some cases, as the example shown in

figure 4.4B, the impedance in the same LP neuron oscillating with different

realistic waveforms could peak at different frequencies. However, the results

from seven experiments showed that there is no statistical difference in the

normalized frequencies obtained from different realistic waveforms (N = 7; one-

way ANOVA, p = 0.57; figure 4.4C).

Discussion

In the previous chapter, we used sine waveforms to examine the effects of

voltage range on the preferred frequency. To study the effects of other

parameters, we switched to realistic oscillation waveforms, which show variability

in several waveform parameters. The realistic slow-oscillation waveforms of PD

46

or LP neurons were extracted from recorded traces in several experiments.

Among different individuals, the pyloric activity has shown consistence in its

phase relationships (Bucher et al., 2005). Despite the consistence in the phase

relationship, the waveforms of the same type of neuron in different individuals

could be quite distinct (see figure 4.1 and 4.4). When comparing the waveform

parameters of each waveform to the preferred frequency, the rising slope of top

75- 100% of the waveform showed the strongest negative correlation with the

preferred frequency in the PD neuron. In contrast, for the LP neuron, oscillations

with different realistic waveforms produced a similar preferred frequency.

The slow-oscillation waveform represents how the membrane potential

changes during the oscillation cycle. The activation and inactivation of voltage-

gated ion channels depend on the value and the change rate (slope) of the

membrane potential. The same type of voltage-gated ion channels could behave

differently when the neuron is oscillating with different waveform. For example, in

leech heart interneurons, waveforms with different rising slopes produce different

amounts of ICa and Ih (Olsen and Calabrese, 1996). These differences in the

dynamics of ion channels can in turn affect the preferred frequency of neurons.

On the other hand, the slow-oscillation waveform of a neuron results from

the interactions between the dynamics of ion channels in the neuron. In the PD

neuron, over-expression of Ih changes its waveform by reducing the time to first

spike, increasing duty cycle and producing more action potentials per burst

(Zhang et al., 2003), whereas an increase in transient potassium current (IA)

delays the post-inhibitory rebound (Tierney and Harris-Warrick, 1992). In other

47

neurons, modeling results show that increasing IA reduce the duration of the PY

active phase (Zhang et al., 2008). Because many ion channels undergo

neuromodulation, neuromodulators also influence the slow-oscillation waveform.

The neuromodulator dopamine enhances the rebound of the LP and PY neurons

(Johnson et al., 2005), shortens the LP bursting duration (Johnson et al., 2011)

and increases the burst duration and duty cycle of the PY neuron (Johnson et al.,

2005). The last contributors to the waveform are the synaptic inputs. Stronger

inhibitory synapses creates a larger delay in the rebound after inhibition, due to

the removal of IA inactivation (Tierney and Harris-Warrick, 1992). Working

together, ionic currents, neuromodulators and synaptic inputs determine the

slow-oscillation waveform and therefore the preferred frequency of the PD

neuron.

As in responses to voltage range described in chapter 3, the preferred

frequency of the LP neuron behaves differently from the PD neuron in response

to changes in the slow waveform. Unlike The PD neuron, the LP neuron has a

similar preferred frequency even when oscillating with different realistic slow-

oscillation waveforms. One possible but unlikely explanation is that the preferred

frequency of the LP neuron is not related to any waveform parameters. However,

it is also possible that the preferred frequency is affected by certain waveform

parameters, but these parameters are similar in the waveforms we used. When

we selected the LP waveforms, we did the principal component assay and picked

up the ones far away from each other on the first and second principal

components. If there is a specific waveform parameter correlated with the

48

preferred frequency and not showing variations in the waveform we used, it is

likely that that specific waveform parameter does not vary much in normal

conditions.

So far, we demonstrate that the voltage range of the oscillation and the

rising slope of top 75-100% of the waveform have great influence on the

preferred frequency of the PD neuron. Because the preferred frequency of the

PD neuron is correlated with the pyloric frequency, we would like to know if

modifying the voltage range and the rising slope of the PD neuron during ongoing

activity could change the pyloric frequency in the same way as it changes the

preferred frequency. This possibility will be examined in the next chapter.

49

Figure 4.1 Realistic waveforms of the PD neuron. A. The PD membrane

potential recording (blue trace) is low-pass filtered at 10 Hz to remove the action

potentials and the slow-oscillation (red trace). B. We select seven realistic

waveforms (a - g) and also include the sine waveform as the reference. C. The

overlapped comparison of the waveforms a and g is showed here as an example

of the differences between the realistic waveforms.

50

Figure 4.2 Preferred frequencies of PD neurons with realistic waveforms. A. We

use the voltage-clamp technique to generate the ZAP oscillation with realistic

waveforms in the PD neuron. Shown here is the same PD neuron oscillating with

51

the realistic waveform a (left) and waveform g (right). B. The frequency-

dependent impedance profiles from the recording shown in A. C. To eliminate

variations between individuals, we normalize the preferred frequency from the

realistic waveforms to that from sine waveform in the same neuron. The

normalized preferred frequencies vary with the realistic waveforms (N = 7; one-

way ANOVA, p < 0.001).

52

Figure 4.3 Correlations between the normalized preferred frequencies

(Normalized fmax) of the PD neurons and the waveform parameters. A–O, Fifteen

53

properties of waveform were analyzed, including duty cycle (A), peak phase (B),

area under the waveform (C), portion above 75% (D), portion below 25% (E), and

slope within different parts of the waveform (F–O). Among these properties, the

rising slope at the 75–100% amplitude (J) showed the strongest (negative)

correlation. Each yellow dot shows the measurement at that value of the

parameter in a single experiment.

54

Figure 4.4 Preferred frequencies of LP neurons with realistic waveforms. A.

Seven realistic waveforms were generated from pre-recorded LP oscillation. The

sine waveform was included as reference. B. The frequency-dependent

impedance profiles of the same neuron oscillating with waveform h and n. C. The

normalized preferred frequency does not change when the LP neuron is

oscillating with different realistic waveforms (N = 7; one-way ANOVA, p = 0.57).

55

Chapter 5: The changes in voltage range and in waveform have

similar effects on the preferred frequency of pacemaker PD

neurons and the network frequency

Introduction

In the pyloric network, the preferred frequency of the pacemaker PD

neuron is correlated with the pyloric frequency (Tohidi and Nadim, 2009). As we

showed in previous chapters, factors such as the voltage range and the rising

slope could influence the preferred frequency of the PD neuron. It is possible that

these factors also affect the pyloric frequency and that the pyloric frequency can

be regulated by targeting these parameters.

We use the dynamic clamp technique to alter the PD oscillation in an

ongoing pyloric network and measure the response in the pyloric frequency. As

shown in chapters 3 and 4, both the voltage range and the top 75-100% slope of

the waveform affect the preferred frequency of the PD neuron. In this chapter we

show that changing the voltage range and waveform of the PD oscillation in the

ongoing pyloric activity have similar effects on both the preferred frequency of the

PD neuron and the pyloric frequency. Therefore, with the understanding that the

preferred frequency of the PD neuron is correlated with the voltage range and the

waveform parameters, we can predict how the changes in voltage range and

waveform of the pacemaker neuron affect the pyloric frequency.

56


Dynamic clamp

The Dynamic Clamp software (version 1.55) was used to produce artificial

ionic conductances to shift the voltage range of an oscillating PD neuron during

its ongoing network activity. The current was injected into the PD neuron in

discontinuous current-clamp mode. In the upper-bound shift experiments, the

artificial current had a reversal potential at 0 mV and activated when the PD

membrane potential was above a given threshold; in the lower-bound shift

experiments, the artificial current had a reversal potential at -80 mV and activated

when the PD membrane potential was below a given threshold. In each

experiment, we used two different thresholds. The lower threshold was set at the

voltage at which the inhibitory synapse from the LP neuron activated (around -55

mV; figure 5.1, blue line), whereas the higher threshold was always set 10 mV

higher than the lower threshold (figure 5.1, red line). The dynamic clamp current

was assumed to activate with first-order activation kinetics and no inactivation:

The activation variable followed equations:

57

Here, vth is the activation threshold, k was set to -1 mV to produce a sharp

m) was set to a constant value of 1 ms.

By adjusting the maximal conductance gmax (range, 5–35 nS), we could move the

upper bound or the lower bound of the PD neuron membrane potential to

different levels. In the upper and lower bound shift experiments, we limited the

value of gmax so that only the upper or lower bounds, respectively, were affected.

This restriction resulted in a smaller possible range of gmax values for the low

threshold activation inward current and thus a more limited shift in the upper

bound when compared with the high threshold activation current.

Waveform parameter comparison

For each recording, we used Readscope software to extract five

consecutive cycles of the PD membrane potential before dynamic current

injection and five cycles during the injection. The analysis of the extracted

waveforms was done as described in chapter 4. To show how the waveform

parameters change during the dynamic current injection, we calculated the ratio

of the value of the waveform parameter during the dynamic current injection to

that before the injection. A ratio larger than one indicates the waveform

parameter increases during the current injection while a value less than less than

one indicates that parameter decreases.

58

Results

Our goal is to understand what factors determine the frequency of pyloric

activity. The preferred frequency of the PD neuron has been shown to be

correlated with the pyloric frequency (Tohidi and Nadim, 2009). So far, we have

demonstrated that the voltage range and the waveform of the PD neuron can

influence its preferred frequency. Therefore, we hypothesized that any

modifications changing the preferred frequency of the PD neuron will change the

pyloric frequency in the same way. Specifically, the changes in the voltage range

and in the waveform parameters of the PD neuron during ongoing activity can

alter the pyloric frequency. We predicted that when the voltage range of the PD

oscillation went higher, the frequency of the pyloric activity would also go higher,

just like the preferred frequency of the PD neuron.

To alter the voltage range of the PD neuron during ongoing activity, we

used dynamic clamp to generate an additional voltage-gated current in the PD

neuron. We changed the upper bound of the voltage range in the PD neuron by

designing a dynamic current that activates when the PD membrane potential is

over a certain threshold. Because the PD neuron in different individuals had

slight differences in voltage range, instead of a fixed voltage for all experiments,

we used a threshold based on the features of the PD bursting waveform. One

prominent feature of the PD bursting waveform is the drop in the membrane

potential caused by the inhibitory synaptic input from the LP neuron (figure 5.1,

arrow). As shown in figure 5.1, we used the voltage at which the PD neuron

receives the synaptic input from the LP neuron as the threshold (referred as low-

59

threshold) for the dynamic current. The dynamic clamp current had a sharp

activation curve and a reversal potential of 0 mV. When the membrane potential

of the PD neuron increased and crossed the low-threshold, dynamic clamp

started the current injection and pushed the upper bound of the voltage range

higher without affecting the lower bound (figure 5.2 A1). By adjusting the maximal

conductance value of the dynamic clamp current, we pushed the upper bound of

the voltage range to the different levels. In each experiment, we pushed the

upper bound of the PD voltage range to several different levels and compared

the frequency of the pyloric activity before and during the dynamic current

injection. Because we wanted to focus on the upper bound of the voltage range,

any traces with shifts in the lower bound of the voltage range were discarded and

were not included in this analysis. As we predicted from our hypothesis, the

increase in the upper bound of the voltage range in the PD neuron resulted in a

higher pyloric frequency (N = 6; Pearson Product Moment Correlation, correlation

coefficient = 0.45, p < 0.05; figure 5.2A2).

Shifting the lower bound of the voltage range in the PD neuron during the

ongoing activity also gave us the results as we predicted from the preferred

frequency. In the shifting the lower bound experiment, the dynamic current had

the reversal potential of -80 mV and activated when the PD membrane potential

was below the low-threshold, making the lower bound of the PD voltage go lower

(figure 5.2B1). Again, we adjusted the maximal conductance value of the

dynamic clamp current so that the lower bound of the voltage range could reach

different voltage levels. Any traces with shifted upper bounds were discarded.

60

When the lower bound of the voltage range in the PD neuron became more

hyperpolarized, the frequency of the pyloric activity decreases (N = 6; Pearson

Product Moment Correlation, correlation coefficient = 0.61, p < 0.001; figure

5.2B2). Overall, these results showed that shifting the voltage range has similar

effects on the preferred frequency of the PD neuron and the frequency of the

pyloric activity.

The choice of the low-threshold, although based on the features of the PD

bursting waveform, was arbitrary. We therefore examined the effect of this

threshold value by using another threshold (referred as the high threshold), which

was 10 mV higher than low-threshold, for the dynamic clamp current. In the

upper bound shift experiment, the high-threshold current altered the upper bound

of the voltage range as the low-threshold current did (figure 5.3A1). Surprisingly,

even though the upper bound was shifted during the dynamic clamp current

injection, unlike the low-threshold dynamic current, the high-threshold dynamic

current failed to increase the pyloric frequency (N = 6; Pearson Product Moment

Correlation, correlation coefficient = 0.06, p = 0.67; figure 5.3A2).

In the lower bound shift experiments, the high-threshold current generated

similar results to those generated by the low-threshold current. During the high-

threshold dynamic current injection, the lower bound was brought to more

hyperpolarized levels (figure 5.3B1) and the pyloric frequency also slowed down

(N = 6; Pearson Product Moment Correlation, correlation coefficient = 0.35, p <

0.05; figure 5.3B2).

61

In the previous chapters, we showed that the voltage range of the

oscillation in the PD neuron was not the only factor affecting its preferred

frequency. Additionally, the rising slope of 75-100% of the waveform was also

strongly negatively correlated with the preferred frequency. The dynamic current

not only shifted the voltage range, but also altered the PD waveform. To

understand how the dynamic current affects the waveform, we extracted the

slow-oscillation realistic waveform from the PD busting activities before and

during the dynamic current injection. The low-threshold current and the high-

threshold current modified the realistic waveforms in different ways, especially

the top portion of the waveforms (figure 5.4A).

To compare the slow-oscillation waveform before and during the dynamic

clamp current injection, we measured the effects of the dynamic clamp current by

calculating the ratio of the given waveform parameter during injection to that

before injection. A ratio higher or lower than one indicated the waveform

parameter increased or decreased, respectively. The rising slope of the 75-

100% portion of the waveform, one of the most correlated parameters to the

preferred frequency, reacted differently during the low-threshold and high-

threshold injection. As the high-threshold current pushed the upper bound of the

voltage range higher and increased the rising slope at the same time; on the

other hand, the low-threshold current shifted the upper bound but slightly

reduced rising slope (low-threshold: N = 6, r = 0.36, p < 0.05, slope = -0.03; high-

threshold: N = 6, r = 0.39, p < 0.01, slope = 0.13; figure 5.4B). The other two

parameters, the area and the portion above 75%, showed an increase when the

62

upper bound of the voltage range was pushed higher during both dynamic clamp

current injections. However, the values measured with low-threshold current

injection were higher (figure 5.4C and D). The low- and high-threshold dynamic

clamp currents affected the waveform parameters differently, which could provide

a possible explanation of their different effects on pyloric frequency.

Discussion

In chapter 3 and 4, we demonstrated that a more depolarized voltage

range resulted in a higher preferred frequency while a steeper rising slope of top

75- 100% of the waveform gave a lower preferred frequency. The preferred

frequency of the PD neuron has been correlated with the pyloric frequency. We

therefore expected to observe that changing the voltage range and the waveform

parameters would have the same effects on the pyloric frequency as the

preferred frequency of the PD neuron. To examine how the voltage range of the

PD neuron during ongoing pyloric activity affects the pyloric frequency, we used

dynamic clamp to shift the voltage range of the oscillating PD neurons in intact

networks. The dynamic clamp technique induces an artificial current into the cell

based on given equations and is a great tool for mimicking ionic currents or

synaptic currents (Sharp et al., 1993a, b; Prinz et al., 2004). In our experiments,

we used the dynamic clamp technique to add an inward or outward current to

shift the voltage range of the PD neuron up or down, respectively, and we

examined the pyloric frequency during these manipulations.

63

During the low-threshold dynamic current injection, the upper bound

shifted to more depolarized levels and as our hypothesis predicted, the pyloric

frequency also increased. Similarly, when the lower bound became more

hyperpolarized, the pyloric frequency decreased. One may argue that by injecting

the inward current, the PD neuron became more depolarized and the excitability

of the PD neuron increased, resulting in a higher pyloric frequency. However,

when we moved the threshold of the dynamic current to a higher value, shifting

the upper bound failed to increase the pyloric frequency. These results indicated

that the voltage range of the PD neuron was not the only factor affecting the

pyloric frequency.

In the upper-bound shift experiments, when the dynamic clamp current

was injected in the low-threshold condition, the voltage range became more

depolarized and the top 75-100% slope decreased. Both changes in the voltage

range and the top 75-100% slope would produce a higher preferred frequency,

and as we expected, the pyloric frequency increases. On the other hand, the

dynamic current in the high-threshold condition makes the voltage range more

depolarized and the top 75-100% slope steeper at the same time. The

depolarized voltage range would increase the preferred frequency but the

steeper slope would decrease the preferred frequency; the changes in these two

factors counteracted each other and resulted in an unchanged or slightly lower

preferred frequency and pyloric frequency. In the pyloric network, it has been

shown that the properties of neurons and synapses can vary several fold, and it

is not uncommon for properties, either at the cellular or synaptic level, to

64

compensate each other and generate a similar output (Marder, 2011; Marder and

Taylor, 2011). Overall, the preferred frequency and the pyloric frequency are not

determined by a sole factor, but by the combination effects of many parameters.

We demonstrated that some factors influence the preferred frequency and

the pyloric frequency in the same way. However, these results do not necessary

mean the preferred frequency determines the pyloric frequency directly. It is

possible that the preferred frequency and the pyloric frequency share some

common underlying mechanisms, such as voltage-gated ion channels, and that

changes in the voltage range and the top 75-100% slope modify these underlying

mechanisms which in turn alter the preferred frequency and the pyloric frequency

together. Nevertheless, we provide an example that the properties (the voltage

range and the top 75-100% slope) of the neuron in the network can be good

indicators for the properties (pyloric frequency) of the network's activity.

65

Figure 5.1 Dynamic clamp experiment setup. During the ongoing pyloric activity,

the PD membrane potential shows inhibitory postsynaptic potential (IPSP) due to

the inhibitory synapse from the LP neuron. The low-threshold (blue line) was set

at the voltage at which the PD neuron receives the IPSP (arrow), and the high-

threshold was set at 10 mV higher than the low-threshold (red line).

66

Figure 5.2 Low-threshold dynamic clamp current. A1. The dynamic clamp

current injection shifted the upper bound of the PD oscillation to a more

depolarized level. A2. The pyloric frequency increases when the upper bound

became more depolarized (N = 6; Pearson Product Moment Correlation,

correlation coefficient = 0.45, p < 0.05). B1. The dynamic clamp current injection

shifted the lower bound of the PD oscillation to a more hyperpolarized level. B2.

The pyloric frequency decreases as the lower bound became more

hyperpolarized (N = 6; Pearson Product Moment Correlation, correlation

coefficient = 0.61, p < 0.001).

67

Figure 5.3 High-threshold dynamic clamp current. A1. The high-threshold

dynamic clamp current shifted the upper bound of the PD oscillation to a more

depolarized level as the low-threshold one did. A2. As the upper bound of the PD

oscillation became more depolarized, the pyloric frequency was unchanged (N =

6; Pearson Product Moment Correlation, correlation coefficient = 0.06, p = 0.67).

B1. The high-threshold dynamic clamp current shifted the lower bound of the PD

oscillation to a more hyperpolarized level as the low-threshold one did. B2. As

the lower bound became more hyperpolarized, the pyloric frequency decreased,

68

as in the low-threshold dynamic clamp experiments (N = 6; Pearson Product

Moment Correlation, correlation coefficient = 0.35, p < 0.05).

69

Figure 5.4 Waveform parameters during the dynamic clamp current injection. A.

The waveforms during the low-threshold (left) and high-threshold dynamic

current injection were overlapped with the waveforms before the injection. The

top 75-100% slope became steeper during the high-threshold dynamic current

injection but not during the low-threshold dynamic current injection. B. During the

high-threshold dynamic current injection, the top 75-100% slope became steeper

when the upper bound of the oscillation was pushed higher (N = 6, r = 0.39, p <

0.01, slope = 0.13). The top 75-100% slope slightly decreased during the low-

threshold dynamic current injection (N = 6, r = 0.36, p < 0.05, slope = -0.03). C

and D. The area and the portion above 75% increased during both the low-

threshold and high-threshold dynamic current injection, although they increased

more during the low-threshold situation.

70


This chapter describes preliminary results of ongoing experiments dealing with

the phase of action potentials.

Introduction

Most neurons, beside the AB neuron, in the pyloric network are motor

neurons, and in the crab their action potentials directly control the muscle around

the stomach (Marder and Bucher, 2007). The phases of the action potentials in

the pyloric network, therefore, are important for proper feeding behavior. Studies

have shown that the same type of pyloric neuron generates the burst of action

potentials at similar phases among different individuals (Bucher et al., 2005).

However, it is still unclear how the phase of the action potential changes with the

frequency within the same individual.

In this study, we looked at the phase of the action potential of a neuron

when it was oscillating at different frequencies. We showed that the phase of the

first action potential depended on the oscillatory frequency. Because the onset of

the first action potential is the start of the burst, our results indicate the phase of

the burst changes with the frequency of the oscillation.

71


In order to remove the endogenous oscillations while preserving the

neurons' ability to generate action potentials, we transected the modulatory nerve

(stn), instead of bath-applying TTX. The neuron was voltage-clamped with the

ZAP function (frequency: 0.1 to 4 Hz; voltage range: -60 to -30 mV) while the

amplitude of the injected current was recorded simultaneously (figure 6.1). The

injected currents which counteracted the action potential, could be detected in

the current recording (figure 6.1B, example: arrow pointed at the first action

potential). We used the lowest point (-60 mV) of the sine wave as our reference

point for each cycle and calculated the phase of every action potential, which

the period.

Results

In the PD neuron, the onset of the first action potential, which coincided

with the onset of the PD burst, showed a greater delay when the neuron was

oscillating at a higher frequency. The onset of the last action potential (the end of

the PD burst) was at about 0.75 phase of the cycle, except at the very high

frequency (~4 Hz) (figure 6.2A). Similarly, the onset of the LP burst occurred at a

later phase when the frequency of the oscillation became higher, but the LP burst

always ended around 0.75 of the phase (figure 6.2B). The onset of the PD burst

seemed more consistent between individuals; the phase of the first action

72

potential from three experiments overlapped with each other. On the other hand,

the onset of the LP burst was more variable.

Discussion

Traditionally, action potentials are generated when the membrane

potential reaches a certain threshold. Accordingly, we would expect that the first

action potential occurs at a fixed phase at all frequencies during the ZAP

oscillation, because the sine waveform always crosses a certain voltage at a

certain phase, regardless of the frequency. However, our results show that the

onset of the first action potential depends on the frequency. One possible

explanation is that along with the voltage, the slope of the membrane potential

also influences the initiation of the action potential. In the ZAP oscillation, the

slope of a certain phase in each cycle increases as the frequency goes higher.

This can be further determined by voltage-clamping the neuron with ramp

waveforms having different slopes and measuring the voltage and the slope at

which the first action potential occurs.

In conclusion, we have shown that the phase of the first action potential,

and therefore the onset of the burst, depends on the frequency of the oscillation.

This frequency-dependence might be related to the slope of the membrane

potential. However, the detailed mechanism and functional significance of this

frequency-dependence needs further investigation.

73

Figure 6.1 Action potentials during an oscillation. A. The neuron was voltage-

clamped with the ZAP oscillation (top trace; frequency: 0.1 to 4 Hz; voltage range:

-60 to -30 mV) and the injected current was recorded simultaneously (bottom

trace). B. A close-up of one cycle shown in A. Under the voltage-clamp, the

current recording showed the inward current of action potential. The arrow

indicates the first action potential in the cycle.

74

Figure 6.2 The phases of the action potential show more delay as the frequency

increases. The phases of the action potentials show frequency-dependences in

the PD (A) and LP (B) neurons. The data is pooled together from three

experiments (black, red and blue) with each dot representing one action potential.

75


Introduction

Synaptic interactions play an important role in shaping neural network

output. In an oscillatory network, the interactions between the neural intrinsic

properties and the synaptic outputs could be crucial for generating the rhythmic

activity or for determining the properties (i.e., frequency and phase pattern) of

network activity. In the pyloric network, inhibitory synapses from the oscillatory

pacemaker neurons drive the follower neurons to produce rhythmic activity;

without synaptic inputs from the pacemaker neurons, the follower neurons either

become silent or fire tonically. Because the synaptic interactions are critical for

the network activity and the neurons in the network are constantly oscillating, it is

important to understand how the synaptic outputs respond to the presynaptic

oscillation at different frequencies.

Short-term plasticity of synapses has been reported in both vertebrates

and invertebrates (Connelly et al., 2010; Doussau et al., 2010; Kandaswamy et

al., 2010). The amplitude of the synaptic current can either increase (facilitation)

or decrease (depression) during repetitive stimulation, and the level of facilitation

or depression is dependent on the frequency and duration of the stimulus

(Rabbah and Nadim, 2005; Connelly et al., 2010; Kandaswamy et al., 2010). In

the pyloric network, short-term synaptic depression has been reported in the

synapses from the pacemaker AB/PD neurons to the follower LP and PY

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neurons (Rabbah and Nadim, 2005) and from the LP neuron to PD and PY

neurons (Mamiya and Nadim, 2005). The characteristics of short-term

depression of individual synapses are important for proper network activity

(Mamiya and Nadim, 2005). In a simple inhibitory oscillator-follower model,

synapses without short-term depression result in a fixed delay between the

oscillator and follower bursting and fail to maintain a proper phase relationship.

With short-term depression, the phase relationship is maintained over a wide

frequency range of oscillation (Manor et al., 2003; Bose et al., 2004). A similar

result is also observed in a more realistic PD-LP/PY model (Mouser et al., 2008).

These findings indicate that the synaptic amplitude could vary depending on the

frequency of the presynaptic oscillation.

Here we show that the synapses between the AB/PD and LP neuron

produce larger currents when the presynaptic neurons were oscillating at certain

(preferred) frequencies than at other frequencies. The preferred frequency of the

LP to PD synapse became higher when the upper bound of the presynaptic

voltage waveform was shifted to a more depolarized level. The preferred

frequency of this synapse was also positively correlated with the preferred

frequency of the LP neuron. Finally, to have the strongest resonance, the upper

bound of the presynaptic oscillation has to be within the dynamic range of the

synaptic current. Overall, the synaptic output depends on the frequency of

oscillation, and this frequency-dependence varies with the voltage range of the

presynaptic oscillation.

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Frequency-dependence of synaptic current

The preparation bathed in saline containing 10-7 M TTX (tetrodotoxin,

Biotium) to remove the endogenous oscillations and the spike-mediated

neurotransmitter release. The presynaptic neuron was voltage-clamped with the

ZAP oscillation while the postsynaptic neuron was voltage-clamped at -40 mV to

measure the postsynaptic current. The ZAP oscillation started with three 0.1 Hz

pre-cycles and then the frequency increased from 0.1 to 4 Hz in 100 seconds.

The voltage ranges of presynaptic oscillation depended on experimental design.

For the upper-bound shift experiment, we used three values for the upper bound

(-34, -30 and -26 mV) and a fixed lower bound at -60 mV. The lower-bound shifti

experiments were done with a fixed upper bound (-30 mV) and various lower

bounds (-70, -60 and -50 mV). The frequency-dependence profiles were

generated with Matlab scripts as described below. We discarded the pre-cycles

to avoid any possible transient effects. The ZAP oscillation of the membrane

potential was divided into individual cycles, and we extracted the frequency and

the amplitude of postsynaptic current from each oscillatory cycle. The remaining

data was then fit with a 7-variable polynomial equation. The preferred frequency

was defined as the peak frequency of the fit curve.

The strength of synaptic resonance

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When the upper bound of the presynaptic oscillation was set to different

voltage values, synaptic resonance only occurred at some voltages but not at

others. To quantify the power of resonance, we calculated the slope from the

peak of the fit curve to both ends (0.1 and 4 Hz) and multiplied the absolute

values of the two slopes. We refer to this quantity as the strength of resonance

(R). A larger R value indicated a more prominent resonance response whereas if

the amplitude of the synaptic current increased or decreased monotonically with

the frequency, the R value would be zero.

Activation curve of synaptic current

We first used 10-7 M TTX to remove the endogenous oscillation and spike-

mediated neurotransmitter release. The presynaptic neuron was voltage-clamped

with the holding potential at -60 mV and then depolarized with five pulses

(duration: 500 ms; interpulse interval: 500 ms) of the same amplitude. The

postsynaptic neuron was voltage-clamped at -40 mV to record the synaptic

current during the presynaptic pulses. The peak amplitude of synaptic current

during the 5th pulse was measured as the steady-state value. To obtain the

activation curve, we measured the values of steady-state synaptic current with

varying levels of the presynaptic pulse, from -50 to 0 mV, in 5 mV intervals. The

resulting synaptic currents were then fit with Boltzmann equation:

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where Isyn was the amplitude of the synaptic current at membrane potential Vm,

Imax and Imin were the maximal and minimal values of synaptic current,

respectively, Vth was the half-activation voltage and k was a constant. When the

presynaptic neuron was depolarized to its half-activation voltage (Vth), the

synaptic current was at 50% of its maximal value.

Neuromodulator

A stock solution of the peptide proctolin was prepared in distilled water at

a concentration of 10-3 M and stored in small aliquots at -20 °C. During proctolin

treatment, the final concentration of 10-7 M proctolin in physiological saline was

superfused for a minimum of 20 minutes before measurements were obtained.

The LP voltage range and the synaptic activation curve during the ongoing

activity

To measure the voltage range of the LP neuron during the ongoing activity,

we low-pass filtered the LP membrane potential recording at 10 Hz to reveal the

LP slow-oscillation. The voltages of the upper and lower bounds of the LP slow-

oscillation were measured using the Readscope software. To calculate the

activation curve of the LP to PD synapse, we voltage-clamped both the

presynaptic LP neuron and the postsynaptic PD neuron and measured the

steady-state synaptic current with depolarized pulses at different voltages as

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described above. However, without TTX treatment, we lacked good control of

membrane potential when it was close to 0 mV. Therefore, when performing the

Boltzmann fit, we used the voltage value measured from the actual membrane

potential recording, not those set in the protocol.

Results

In oscillatory networks, the neurons and synapses may possess

frequency-dependent properties, and these properties could play an important

role in determining the characteristic of network activity. Previous chapters have

shown that the neurons in the pyloric network exhibit preferred frequencies, and

that there are correlations between the preferred frequency of the pacemaker

neuron and the frequency of the network. In this and subsequent chapters, we

investigated the possible frequency-dependence of the synaptic properties,

specifically the synaptic currents of graded synapses (this chapter) and the peak

phase of the synaptic current (chapter 8) between the pacemaker AB/PD

neurons and the follower LP neuron.

First, we examined whether there is a frequency-dependence of the

graded synapse by measuring the synaptic current after TTX treatment. The

application of TTX removed both the endogenous oscillation of the network

activity and the production of action potentials, leaving only the graded

component of the synaptic current. Oscillations were imposed in the presynaptic

neuron by voltage-clamping the presynaptic neuron with a ZAP function

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(frequency: 0.1 to 4Hz, voltage: -60 to -30 mV) and the postsynaptic current was

recorded simultaneously (PD to LP: figure 7.1A; LP to PD: figure 7.1B). The

amplitude of the synaptic current in each cycle during the ZAP function was then

plotted against the frequency to produce the frequency-dependence profile of the

synaptic current. The profile showed that, in both the AB/PD to LP synapse and

the LP to PD synapse, as the frequency of presynaptic oscillation increased, the

graded-synaptic currents also increased at the beginning and then decreased

over time (PD to LP: figure 7.1A; LP to PD: figure 7.1D). The synaptic currents

showed resonance, and there were preferred frequencies at which the synaptic

currents reached their peak values (red arrow in figure 7.1C and 7.1D). The

preferred frequencies of the graded-synaptic currents were lower than the

preferred frequencies of the respective presynaptic neurons and the natural

pyloric frequency (N = 16; one-way ANOVA, *: p < 0.05; PD to LP: 0.49±0.11 Hz,

LP to PD: 0.70±0.13 Hz, PD: 0.97±0.18 Hz, LP: 1.42±0.41 Hz, network:

1.24±0.33 Hz; figure 7.1E).

The neurotransmitter release of graded synapses are dependent on the

presynaptic membrane potential, so we were interested to determine how the

different voltage ranges of presynaptic oscillation affect the preferred frequency

of the synaptic current. To address this question, we shifted the upper bound of

the oscillating voltage to different levels (-34, -30 and -26 mV) while keeping the

lower bound at a fixed value (-60mV) or, alternatively, shifted the lower bounds (-

70, -60 and -50 mV) while kept the upper bound fixed (-30 mV). For the synaptic

current from the AB/PD to LP neuron, the peaks of the frequency-dependence

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profile were similar in all voltage ranges tested (upper bound: figure 7.2A1; lower

bound: figure 7.2B1) and shifting the lower or upper bounds of the presynaptic

oscillation had no significant effect on the synaptic preferred frequency (upper

bound, N = 11, one-way ANOVA, p = 0.700, -34 mV: 0.51±0.08 Hz, -60 mV:

0.49±0.12 Hz, -26 mV: 0.52±0.12 Hz, figure 7.2A2; lower bound: N = 10, one-

way ANOVA, p = 0.191, -70 mV: 0.49±0.09 Hz, -60 mV: 0.51±0.06 Hz, -50 mV:

0.56±0. 09 Hz; figure 7.2B2). We also tested the presynaptic PD oscillations with

more depolarized upper bounds, and the synaptic preferred frequency was

unchanged even when the upper bound was as high as -15 mV (N = 5; one-way

ANOVA, p = 0.648; figure 7.2C).

On the other hand, the synaptic current from the LP to PD neuron had

different responses to changes in the voltage range. The peaks of the frequency-

dependence profile did not move when the lower bound was shifted (figure 7.3B1)

but increased as the upper bound became more depolarized (figure 7.3A1).

Analysis showed that while changing the lower bound of LP oscillations did not

significantly affect the preferred frequency of the synaptic current from the LP to

PD neuron (N = 10; one-way ANOVA, p = 0.751; -70 mV: 0.76±0.19 Hz, -60 mV:

0.75±0.18 Hz, -50 mV: 0.81±0.20 Hz; figure 7.3B2), moving the upper bound of

the LP oscillation to a higher level increased the preferred frequency (N = 9; one-

way ANOVA, p < 0.001; -34 mV: 0.44±0.10 Hz, -60 mV: 0.70±0.13 Hz, -26 mV:

0.84±0.07 Hz; figure 7.3A2).

Because both neurons and synaptic currents exhibit preferred frequencies,

whether there is any correlation between their preferred frequencies become an

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interesting question. We combined the data from all the voltage ranges examined

above (three voltage ranges per experiment) and compared the synaptic

preferred frequencies to the preferred frequencies of the presynaptic neuron.

While the preferred frequency of the PD to LP synapse showed no correlation

with the preferred frequency of the PD neuron (N = 15; Pearson Product Moment

Correlation, correlation coefficient = 0.26, p = 0.08; figure 7.4A), the LP to PD

synapse with a higher preferred frequency tended to pair with the LP neuron with

the higher preferred frequency (N = 18; Pearson Product Moment Correlation,

correlation coefficient = 0.63, p < 0.001; figure 7.4B).

The synapse from the LP to PD neuron is the sole feedback synapse to

the pacemaker neurons, and its frequency-dependent properties show more

sensitivity to the upper bound of the presynaptic LP oscillation. Therefore, we

further examined the frequency-dependent property of this synapse in a larger

range of the upper bound of the presynaptic oscillation, from -40 to 0 mV, in 5

mV intervals. An example is shown in figure 7.5. When the upper bound was at

or below -35 mV, the synaptic current was small and the frequency-dependent

profile showed no resonance (figure 7.5A, yellow line). As the upper bound

increased to -30 mV, the resonance started to emerge (figure 7.5A, blue line).

Increasing the upper bound to -25 mV produced clear resonance (figure 7.5A,

red line). However, further pushing the upper bound above -20 mV resulted in a

flatter profile (figure 7.5A, black line). Because the frequency-dependent profiles

of the synaptic current changed radically as the upper bound moved from -40 to

0 mV, we used "the strength of resonance" (R, figure 7.5B; see Methods) to

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characterize these profiles. When the frequency-dependence profile decreases

or increases monotonically, the peak will be at the end of the profile and one

slope is zero; thus, the R value will be zero. The larger the synaptic current at the

preferred frequency compared with the current at other frequencies, the higher

the R value will be. The result showed that the R value is voltage-dependent on

the upper bound of presynaptic oscillation (figure 7.5C). When the upper bound

of oscillating voltage increased, the R value first increased and then decreased,

and there existed a specific upper bound value for the presynaptic oscillation at

which the synaptic current showed strongest resonance (-35 mV for the example

shown in figure 7.5C).

We noticed that the upper bound required for the strongest synaptic

resonance was different between individuals. One possibility is that the voltage-

dependence of the resonance is related to other voltage-dependent properties of

synapse. A well-known voltage-dependent property of graded synapses is the

amount of neurotransmitter release, which can be represented by the activation

curve of the synaptic current. The activation curve shows the amplitudes of

steady state synaptic current when the presynaptic neuron is voltage-clamped

with repetitive pulses, which depolarize the presynaptic neuron to different

voltage levels. There is a voltage (half-activation voltage) at which the synaptic

current reaches the 50% of its maximum value. In the voltage range (dynamic

range) around the half-activation voltage, the synaptic current increased or

decreased rapidly with the voltage. We hypothesized that the strongest synaptic

resonance occurs when the upper bound of the presynaptic oscillation is within

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the dynamic range of the synapse. This hypothesis predicts that when the

activation curve is modified and there is a shift of the half-activation voltage, the

voltage of the upper bound producing the strongest resonance should move in

the same direction as the shift of the half-activation voltage. To test this

hypothesis, we measured the R values and the half-activation voltage of the

synaptic current in 13 experiments in control and during the 10-7M proctolin

treatment. The neuromodulator proctolin is known to enhance the LP to PD

synaptic current (Zhao et al., 2011). Among the 13 experiments, most showed

shifts of the half-activation voltage toward more hyperpolarized levels during the

proctolin treatment (figure 7.6A), and, as our hypothesis predicted, the voltages

of the upper bound producing the strongest resonance also moved to lower

voltages (figure 7.6B). In a few experiments, the proctolin treatment had no effect

on the half-activation voltage, and the voltage of the upper bound producing the

strongest resonance also remained the same in the control condition and during

the proctolin treatment, which also agreed with our hypothesis. Furthermore,

there was a correlation between the half-activation voltage and the voltage of the

upper bound producing the strongest resonance (N = 13; Pearson Product

Moment Correlation, correlation coefficient = 0.50, p < 0.01; figure 7.6C). Thus,

the half-activation voltage of the synapse could be a good indicator for the

voltage of the upper bound required for producing the strongest resonance.

Finally, proctolin also enhanced the maximal R value of the synaptic current by

563% (N = 13; paired Student's t-test, p = 0.002; figure 7.6D).

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Because the resonance of the synaptic current only occurs when the

presynaptic neuron is oscillating at certain voltage ranges, we examined if the

upper bound of the LP oscillation is within the dynamic voltage range of the LP to

PD synapse during the ongoing pyloric activity. If yes, then it is likely that the

resonance of the LP to PD synapse plays a functional role during ongoing pyloric

activity. To address this, we recorded the LP membrane potentials during the

ongoing pyloric activity (figure 7.6A, blue trace) and then filtered these recordings

with a 10 Hz low-pass filter to generate the slow-waves of the LP neuron (figure

7.6A, red trace). The voltage ranges of the slow waveform were measured with

the Readscope software, and the upper bounds of the slow waveforms were

compared with the half-activation voltages of the LP to PD synaptic current in the

same preparation. Our results showed that the voltage range of the LP slow

waveform included the half-activation voltage of the synaptic current, indicating

that synaptic resonance likely exists in the pyloric network under naturally

ongoing activity (figure 7.6B).

Discussion

Synapses and neurons are two fundamental components of every neural

network. Short-term synaptic dynamics allow the synaptic current to vary its

amplitude based on the presynaptic neuron’s activity. In an oscillatory network,

the presynaptic neuron could oscillate at different frequencies and voltage ranges.

As a result, knowing how the synapses respond under different frequencies is

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critical to understand how an oscillatory network maintains its function. Our study

shows that the amplitude of the synaptic current is frequency-dependent. More

importantly, in some synapses, these frequency-dependencies are adjustable by

altering the voltage range of the presynaptic neuron and/or modulating the

activation curve of the synapse, thus providing the network possible ways to

regulate the frequency-dependence of its synapses in response to different

needs.

Synaptic dynamics have been shown to be present in many neural

systems. Repetitive stimulation can either increase (facilitation) or decrease

(depression) the amplitude of the synaptic current, and the levels of increase or

decrease depend on the frequency of the stimulation. If facilitation occurs at low

frequencies and depression happens at the high frequencies, the frequency-

dependence profile of the synaptic current will have a preferred frequency

(Izhikevich et al., 2003). During the repetitive pulse stimulation, the graded

synapse from the LP to the PD neuron exhibits short-term depression (Mamiya

and Nadim, 2005) and facilitation in modulatory conditions (Zhou et al., 2007).

When stimulated with an oscillatory realistic waveform, the inhibitory postsynaptic

potential (IPSP) shows resonance. One possible explanation is that as the

frequency increase, the inactivation of Ca2+ channel decreases, resulting in a

initial increase in the postsynaptic potential before the depression occurs (Manor

et al., 1997).The IPSP is generated by the interactions between the synaptic

current and the voltage-gated ion channels in the postsynaptic neuron. By

measuring the synaptic current, we showed that the synapse itself has

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resonance and the resonance in the IPSP is not solely from the voltage-gated ion

channels in the postsynaptic neuron.

The preferred frequency of the pacemaker PD neuron increases when the

voltage range of the oscillation increases, while the preferred frequency of the LP

neuron is only affected by the upper bound of the voltage range. The preferred

frequency of the PD to LP synapse is not affected by the presynaptic PD voltage

range, and only shifting the upper bound of the LP oscillation has effects on the

LP to PD synaptic preferred frequency, not the lower bound. One possible

explanation is that we generated the oscillation in the PD neuron, not in the AB

neuron, whose synapse produces the major synaptic current from the pacemaker

to the follower neurons in crab. The 4 mV shifts in the upper bound of the PD

oscillation might only have little changes on the upper bound of the AB neuron

and therefore had no significant influence on the preferred frequency of the

AB/PD to LP synapse. However, shifting the upper bound of the PD neuron to a

more depolarized level (from -30 to -15 mV), which should move the AB upper

bound higher, still fails to generate any significant change in the frequency-

dependent properties of the AB/PD to LP synapse. Therefore, a lack of an effect

of changing the upper bound of the PD oscillation is not because we failed to

alter the upper bound of the AB neuron.

Unlike the preferred frequency of the PD neuron, which closely resembles

the frequency of the network output during ongoing network activity (about 1 Hz),

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the preferred frequencies of both the AB/PD to LP and the LP to PD synaptic

currents are significantly lower than the pyloric frequency and the preferred

frequency of the presynaptic neurons. However, the synaptic current still shows

frequency-dependence around the natural frequency of the pyloric activity. When

the pyloric frequency becomes slower than 1 Hz, the synaptic current from the

LP to PD neuron gets larger and occurs at an earlier phase, which is consistent

with the change in the postsynaptic potential previously reported by our lab

(Mamiya and Nadim, 2004). As a result, the LP to PD synapse generates a

greater compensation if the perturbation decreases the frequency of the pyloric

activity.

An interesting question is the connection between the preferred frequency

of the synapse and that of the presynaptic neuron. The preferred frequency of

the LP to PD synapse has been correlated with the preferred frequency of the

presynaptic LP neuron. Shifting the upper bound of the oscillation has similar

effects on both the neural and the synaptic preferred frequencies, while shifting

the lower bound has no effect on either. These similarities indicate that the same

type of ion channel, possibly the Ca2+ channel, may be involved in both the

preferred frequencies of the LP neuron and of the LP to PD synapse. The

preferred frequency of the PD neuron and of the AB/PD to LP synapse showed

no correlation and responded differently to the shift of voltage range, indicating

that different types of ion channel are behind these preferred frequencies.

The activation of graded synapses depends on the presynaptic membrane

potential. A typical method to measure the activation of a synapse is to record

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the steady state synaptic current during repetitive pulse stimulation with the

different upper bounds. The voltage-dependence of the synaptic current can be

divided into three ranges: non-activation, dynamic and saturated. No activation

occurs when the upper bound of the pulse is low and there is no synaptic current.

The dynamic range occurs as the upper bound of the pulse becomes more

depolarized and the amplitude of the synaptic current increases rapidly from its

minimum to its maximum value. The saturated range occurs after the membrane

potential reaches a certain voltage where further depolarizing the membrane

potential results in no increase in the synaptic current and the synaptic current

maintains its maximal value. The midpoint voltage of the dynamic range is near

the half-activation voltage of the synaptic current. The synaptic current has the

largest voltage-sensitivity around the half-activation voltage; any depolarization

or hyperpolarization of membrane potential from the half-activation point will,

respectively, increase or decrease the amplitude of the synaptic current. On the

other hand, the amplitude of the synaptic current is maintained at its minimum

when membrane potential is in the low non-activation range and at its maximum

when the membrane potential is in the saturated range.

The voltage-dependence of the strength of synaptic resonance in our

experiment is correlated to the voltage-dependent activation of the graded

synapse. The presynaptic oscillation with upper bound in the non-activation

range of the synaptic activation curve produced a minimal, close to zero, synaptic

current, and even if it is enhanced at a certain frequency, the difference is barely

detectable. The oscillation with the upper bound in the saturated range pushes

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the synaptic current close to its maximum value, so after a small increase in the

synaptic current, the current reaches it maximum and cannot be enhanced more,

resulting in less resonance in the frequency-dependent profile. Only when the

upper bound of the presynaptic oscillation is within the dynamic range of the

synaptic activation curve, the synaptic current is large enough that the

enhancement in the current is noticeable, and small enough that it will not reach

its maximum. Thus, the strongest resonance occurs when the upper bound of the

presynaptic oscillation is at the half-activation point of the synapse, where the

synaptic current has the largest freedom to either increase or decrease.

The observation that the strength of the resonance of a synaptic current

depends on the voltage of presynaptic oscillation shows a possible way for a

neural network to regulate the synaptic resonance within the network. By shifting

the voltage range of oscillations, the network can switch the synaptic resonance

on and off, or change the frequency-dependence of the synaptic current. Another

way to regulate the frequency-dependent response of synaptic current is by

altering the activation curve of the synapse. As we have shown in this study,

when the activation curve shifts towards the hyperpolarized or depolarized

voltage, the half-activation voltage follows and so does the voltage for the

strongest resonance. Under natural conditions, many factors can affect the

voltage range of the neuron, the activation curve of synapse or both

simultaneously. For example, neuromodulators such as proctolin are able to shift

the membrane potential of the neuron to a depolarized level and also enhance

the synaptic current. Therefore, regulation of the frequency-dependence of

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synaptic current in the intact pyloric network may be complicated and result from

different sources.

Because the existence of synaptic resonance requires certain presynaptic

voltage ranges, it becomes an interesting question to know if it occurs in the

pyloric network during the ongoing activity. However, due to the interference of

the endogenous oscillation, it is difficult to measure the frequency-dependent

response of the synaptic current directly without TTX treatment. An alternative

way is to examine if the presynaptic neuron is oscillating at the dynamic range of

the synaptic activation curve. Our results have shown that the half-activation

voltage of synaptic current from LP to PD neuron is close to the upper bound of

the LP oscillation under natural neuromodulation. Therefore, it is likely that

resonance and hence the frequency-dependence of synaptic current exist in the

pyloric network during ongoing activity.

In conclusion, we demonstrated that the synapses in an oscillatory

network exhibit frequency-dependencies. The synaptic current could increase

with frequency of presynaptic oscillation and then decrease, producing

resonance and also have a maximal value at the preferred frequency. The

preferred frequency of the synaptic current is influenced by the oscillating voltage

of the presynaptic LP neuron; the higher the upper bound of LP oscillation is, the

higher the preferred frequency of synaptic current. Moreover, the strength of

synaptic resonance is correlated with the activation curve of the synapse, and the

strongest resonance occurs when the presynaptic neuron is oscillating with the

upper bound at the dynamic range of synapse. The frequency-dependence of the

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synaptic current can be modified by shifting the voltage range of the presynaptic

neuron and by altering the activation curve of the synapse. Overall, this study

characterizes the frequency-dependent properties of the synaptic current and

demonstrates the potential ways for the neural network to regulate the amplitude

of the synaptic current when needed.

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Figure 7.1 Frequency-dependent profile of IPSC amplitude. A. The presynaptic

PD neuron was voltage-clamped with the ZAP oscillation (voltage range: -60 to -

30 mV; frequency: 0.1 to 4 Hz). The amplitude of the synaptic current from the

PD to the LP neuron first increased with the oscillatory frequency and then

decreased. C. The amplitude of the synaptic current from the PD to LP neuron

was plotted against the presynaptic oscillatory frequency and fitted with a

polynomial curve. When the presynaptic PD neuron was oscillating at the

preferred frequency (arrow), the fitting curve was at its maximal value. The

synaptic current from the LP to the PD neuron also showed resonance (B) and

the synaptic preferred frequency (D, arrow). E. The synaptic preferred

frequencies were significantly lower than the preferred frequencies of the

presynaptic neurons and the pyloric frequency (N = 16; one-way ANOVA, p <

0.05).

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Figure 7.2 Preferred frequency of the AB/PD to LP synapse was not affected by

the presynaptic PD voltage range. A1. The frequency-dependence profiles of the

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AB/PD to LP synapse showed resonances when the PD neuron was oscillating

between various upper bounds (-34, -30 and -26 mV) and a fixed lower bound (-

60 mV). However, the peak of the synaptic current occurs at the very similar

frequencies. A2. The synaptic preferred frequency was not affected by the upper

bound of the presynaptic oscillation (N = 11; one-way ANOVA, p = 0.700). B1.

When the presynaptic PD neuron was oscillating between a fixed upper bound (-

30 mV) and various lower bound (-70, -60 and -50 mV), the frequency-

dependence profiles of synaptic current had the peaks at a similar presynaptic

frequency. B2. Shifting the lower bound of the presynaptic oscillation has no

effects on the synaptic preferred frequency (N = 10; one-way ANOVA, p = 0.191).

C. The synaptic preferred frequency was still not affected by the upper bound

even when the upper bound was as high as -15 mV (N = 5; one-way ANOVA, p =

0.648).

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Figure 7.3 Only the upper bound of the presynaptic LP oscillation affects the

preferred frequency of the LP to PD synapse. A1. When the upper bound of the

presynaptic LP oscillation shifted to a more depolarized level, the peak of the

synaptic current moved to a higher frequency range (arrow). A2. The synaptic

preferred frequency increased when the upper bound of the presynaptic LP

oscillation became more depolarized (N = 9; one-way ANOVA, p < 0.001). B1.

The frequency-dependence profiles with various lower bounds (-70, -60 and -50

mV) showed the peaks of the synaptic current at the similar frequency. B2. The

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synaptic preferred frequency was not affected by the lower bound of the

presynaptic oscillation (N = 10; one-way ANOVA, p = 0.751).

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Figure 7.4 Correlations between the preferred frequencies of the presynaptic

neurons and the synapses. A. The preferred frequencies of the synaptic current

from the PD to LP synapses showed no correlation with the preferred

frequencies of the presynaptic PD neurons (N = 15; Pearson Product Moment

Correlation, correlation coefficient = 0.26, p = 0.08). B. When the LP to PD

synapses had higher preferred frequencies, the presynaptic LP neuron also

exhibited higher preferred frequencies (N = 18; Pearson Product Moment

Correlation, correlation coefficient = 0.63, p < 0.001). Each dot shows the

measurement at one voltage range in a single experiment. There were three

voltage ranges per experiment.

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Figure 7.5 The strength of resonance depends on the upper bound of the

presynaptic oscillation. A. The frequency-dependence profiles changed when the

LP neuron was oscillating at different upper bounds. The most significant

resonance occurred when the upper bound was at -25 mV. B. We multiplied the

absolute values of the slopes from the preferred frequency to the minimal and

maximal frequency (S1 and S2, respectively) as the strength of resonance (R). C.

We calculated the R value of the experiment in A. The maximal R value

happened when the upper bound was at -25 mV.

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Figure 7.6 Correlations between the voltage for maximal R and the half-

activation voltage of synapse. A. Bath-application of neuromodulator proctolin

shifted the activation curve. The amplitude of the maximal synaptic current

increased and the half-activation voltage also became more hyperpolarized. B.

The voltage of the upper bound producing the maximal R value shifted to a more

hyperpolarized level during the proctolin treatment. C. The synapse with higher

value of half-activation voltage required a higher upper bound to produce the

strongest resonance. Each experiment generated two data points; one in the

control condition and the other during the proctolin treatment (N = 13; Pearson

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Product Moment Correlation, correlation coefficient = 0.50, p < 0.01). D. Proctolin

also enhanced the synaptic resonance. The maximal R value increased during

the proctolin bath-application (N = 13; paired Student's t-test, p = 0.002).

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Figure 7.7 The upper bound of the LP slow-oscillation during the ongoing pyloric

activity reached the dynamic range of the synaptic current. A. The LP slow-

oscillation (red trace) is revealed by low-pass filtering the LP ongoing activity

(blue trace) at 10 Hz. B. The upper bound of the LP oscillation reached the

dynamic range of the LP to PD synaptic current.

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Introduction

The activation of a graded synapse depends on the voltage of the

presynaptic membrane potential. Moreover, neurotransmitter release is not

instantaneous and requires a response time for the synapse to reach its peak,

even when the presynaptic depolarization occurs instantly (Rabbah and Nadim,

2007). Therefore, the shape of the synaptic current may not exactly follow the

presynaptic membrane potential, and there could be a timing difference between

the peaks of the synaptic current and the presynaptic membrane potential.

The synapse from the LP to PD neuron is the only chemical synapse

providing feedback from the pyloric follower neurons to the pacemaker kernel.

This synapse reduces the variation of the pyloric frequency by increasing or

decreasing the network frequency depending on its phase. The frequency of the

pyloric network increases when the peak of the synaptic current occurs in the

early phase of the cycle and decreases when the peak occurs in the late phase

(Mamiya and Nadim, 2004, 2005). As a result, the phase of this feedback

synapse is critical in regulating the pyloric frequency.

Here we examined the shape of the synaptic current during oscillations

and showed that the peaks of synaptic current and of the presynaptic membrane

potential could occur at different times. We used the peak of presynaptic

membrane potential as the reference point and calculated the phase difference of

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the peak of the synaptic current. The phase difference depends on the frequency

of the presynaptic oscillation. With low frequency oscillations, the synaptic

current reaches its peak before the presynaptic membrane potential does while,

with high frequency oscillations, the synaptic current peaks after the membrane

potential. Overall, the frequency-dependence of the peak phase in the feedback

synapse can be a mechanism to maintain the pyloric activity at a certain

frequency.


Phase analysis

The synaptic current during the ZAP oscillation was recorded as described

in chapter 7 and analyzed with Matlab scripts. For each cycle in the ZAP

oscillation, we measured the duration of the cycle (period) and the peak time of

the presynaptic membrane potential (TV) and the synaptic current (TC). The

phase difference was calculated as:

A negative phase difference indicated that the synaptic current reached its

peak before the presynaptic membrane potential did, and a positive phase

difference indicated that the peak of the synaptic current occurred after the peak

of the presynaptic membrane potential.

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To simplify the analysis, we divided the frequency range (0.1 to 4 Hz) into

0.5 Hz intervals. For each interval, we referred to the averaged phase difference

from all cycles in the interval as the phase difference of that interval.

Results

In the pyloric network, the phases of synaptic current have important roles

in maintaining the proper network activity. We investigated if the frequency of

presynaptic oscillation has any effect on the phase of the synaptic current peak.

The phase difference is defined as the time difference (from the peak of the

postsynaptic current to the peak of the presynaptic voltage) divided by the period.

At low frequency, the phase difference is negative, indicating that the peak of the

postsynaptic current occurred before the peak of the presynaptic voltage (figure

8.1A, left); at high frequency, the peak of postsynaptic current has occurred after

the peak of the presynaptic membrane potential, and the phase difference is

positive (figure 8.1A, right). To provide a simple analysis, we divided the

frequency range of the ZAP function (0.1 to 4 Hz) into eight 0.5 Hz interval bins

and averaged the phase differences of every cycle in each frequency region.

When the presynaptic neurons were oscillating between -60 and -30 mV, both

synaptic currents showed negative phase differences at the lowest frequency

range (0.1 to 0.5 Hz); as the presynaptic frequencies went higher, the phase

difference turned into a positive value and increased. Moreover, the synaptic

current from the AB/PD to LP neuron showed more delay than that from LP to

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PD neuron in all frequency ranges except the lowest one (N = 16; two-way

ANOVA, frequency: p < 0.001, *: the difference between two synapses has p <

0.001; figure 8.1B).

In general, the phase differences of the synaptic current increased with

the frequency of the presynaptic oscillation in all voltage ranges examined.

However, shifting the upper or the lower bound of the presynaptic oscillation had

different effects on the phase differences of the synapses between the AB/PD

and LP neurons. For the AB/PD to LP synapse, shifting the upper bound had no

effect (N = 11; two-way ANOVA, frequency: p < 0.001, upper bound: p = 0.624);

figure 8.2A) while increasing the lower bound of PD neuron resulted in a slightly

larger phase delay (N = 10; two-way ANOVA, frequency: p < 0.001, lower bound:

p = 0.043; figure 8.2B). On the other hand, when the LP neuron was oscillating

within the range of the natural pyloric frequency (0.5 to 2 Hz), moving the upper

bound of the LP neuron to a higher value increased the delay of the synaptic

current from the LP to PD neuron (N = 9; two-way ANOVA, frequency: p < 0.001,

*: the difference between upper bounds has p < 0.05; figure 8.3A). Changing the

lower bound of LP oscillation had no effect on the phase difference (N = 10; two-

way ANOVA, frequency: p < 0.001, upper bound: p = 0.099; figure 8.3B).

Although the sine waveform is a common choice for generating

oscillations in neurons, there are few similarities between the sine waveform and

the LP neuron realistic waveform. To get a better idea about the phase difference

under natural situations, we further generated the ZAP oscillation (-60 to -30 mV,

0.1 to 4 Hz) in the LP neuron with the LP realistic waveforms along with the sine

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waveform and measured the phase difference of the LP to PD synapse (figure

8.4). The LP realistic waveforms were the same set of waveforms used in

chapter 4. The oscillations with sine waveform produced phase differences within

the range of -0.1 and 0.1. The oscillations with the LP realistic waveforms, on

the other hand, had the phase difference as low as -0.25 at a low frequency and

as high as 0.39 at a higher frequency. These results indicated that, during the

ongoing pyloric activity, the value of the phase difference could have a wider

range and have more influence on the pyloric frequency.

Discussion

Previous studies in lobster have reported the different frequencies of the

presynaptic oscillations produce different peak phases in the postsynaptic

potential of the AB/PD to LP synapse (Rabbah and Nadim, 2007), the AB/PD to

PY synapse (Rabbah and Nadim, 2007), the LP to PD synapse (Manor et al.,

1997) and the LP to PY synapse (Mamiya et al., 2003b). Moreover, the duty

cycle of the presynaptic waveform can influence the frequency-dependence of

the postsynaptic potential peak. The postsynaptic potential results from the

combination of the synaptic properties and the intrinsic properties of the

postsynaptic neuron. Here we focused on the frequency-dependence of the

synaptic properties by measuring the synaptic current instead of the postsynaptic

potential. Whether the peak phases of the synaptic current share exactly the

same frequency-dependences with the peak phases of the postsynaptic potential

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and the contributions of the postsynaptic neural properties to the peak phases of

the postsynaptic potential are still unclear and require further experiments.

Our results show that the phase differences changed from negative to

positive values and then increased as the frequency of presynaptic oscillation

became higher. In the AB/PD to LP synapse, shifting the lower bound of the

presynaptic oscillation had a small but statically significant effect on the

frequency-dependence of the phase difference. However, the functional role of

this frequency-dependence is still in question. Unlike the peak phase of the

AB/PD to PY synapse showing the correlation with the PY burst phase, the peak

phase of the AB/PD to LP synapse has no correlation with the LP burst phase

(Rabbah and Nadim, 2007). In addition, the LP to PD postsynaptic potential,

which controls the lower bound of the PD oscillation, is usually only a few mVs

and therefore may not be large enough to alter the frequency-dependence of the

peak phase.

On the other hand, the peak phase of the LP to PD synapse is known to

affect the frequency of the PD oscillation (Mamiya and Nadim, 2005). When the

peak occurs during the early phase of the PD oscillatory cycle, the frequency of

the next oscillatory cycle will increase (Mamiya and Nadim, 2004); if the peak

occurs during the later phase, the frequency will decrease. These studies provide

a hypothesis regarding how the inhibitory synapse from the LP to PD neuron

stabilizes the frequency of the network activity. During natural pyloric oscillations,

the LP to PD synapse is active in the middle of the PD cycle, a phase with no

effect on the network frequency (Oprisan et al., 2003). When the perturbation

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changes the PD frequency without changing the frequency of LP, the inhibitory

synapse from the LP neuron will occur at relatively early or later phases and thus

push the PD oscillation back to its original frequency (Nadim et al., 2011). Our

results provide another way to explain how the LP to PD synapse helps

maintaining the pyloric frequency. Based on our results, the peak phase of

synaptic current is frequency-dependent. When the pyloric frequency becomes

slower, the peak of the synaptic current will occur earlier in the oscillatory cycle

and therefore increase the pyloric frequency. Similarly, when the pyloric

frequency becomes faster, the peak occurs later and slows down the frequency.

As a result, there is a default frequency at which the peak phase of the LP to PD

synapse is in the middle of the oscillatory cycle.

When the LP neuron is voltage clamped with a sine waveform, the phase

differences of the LP to PD synapse are within only the range of ±0.1. Although

the phase of the LP to PD synapse can affect the pyloric frequency, it is doubtful

if such small phase differences can have a large effect. The realistic waveforms,

which are more similar to the LP natural waveform, produced the phase

differences in a wider range (from -0.25 to 0.39), suggesting that under more

realistic conditions frequency may have a much larger influence on the peak

synaptic phase.

In conclusion, we showed that the peak phases of the synapses between

the AB/PD and LP neuron depend on the presynaptic frequency. These findings,

combined with previous studies that the peak phase of the LP to PD synapse can

shift the pyloric frequency, demonstrate that the potential ability of the pyloric

112

network to control the variability of its cycle frequency via the frequency-

dependence of the peak synaptic phase.

113

Figure 8.1 Frequency-dependent profile of the synaptic phase difference. A. The

traces of the PD membrane potential and the PD to LP synaptic current were

selected from low frequency region (left, around 0.1 Hz) and high frequency

region (right, around 4 Hz) in the same ZAP oscillation (voltage range: -60 to -30

mV). At low frequency, the peak of the synaptic current occurred before the peak

of the membrane potential, and the order of the peaks was reversed at high

frequency. B. As the presynaptic frequency increased, the phase differences also

increased from negative values to positive values. Moreover, the synaptic current

from the PD to LP neuron showed more delay than those from the LP to PD

neuron (N = 16; two-way ANOVA, frequency: p < 0.001, *: the difference

between two synapses has p < 0.001).

114

Figure 8.2 The AB/PD to LP synaptic phase differences were affected by the

lower bound, but not the upper bound, of the presynaptic PD oscillation. A. The

phase differences of the AB/PD to LP synaptic current increased with the

frequency of the presynaptic PD oscillation and were unchanged by shifting the

upper bound (N = 11; two-way ANOVA, frequency: p < 0.001, upper bound: p =

0.624). B. The higher lower bound produced a slightly larger phase difference (N

= 10; two-way ANOVA, frequency: p < 0.001, lower bound: p = 0.043).

115

Figure 8.3 The LP to PD synaptic phase differences were affected by the upper

bound, but not the lower bound, of the presynaptic LP oscillation. A. In the

physiological frequency range of the pyloric activity, a more hyperpolarized upper

bound produced a more positive phase difference (N = 9; two-way ANOVA,

frequency: p < 0.001, *: the difference between upper bounds has p < 0.05). B.

The phase differences were unchanged by shifting the lower bound of the

presynaptic oscillation (N = 10; two-way ANOVA, frequency: p < 0.001, upper

bound: p = 0.099).

116

Figure 8.4 The synapses oscillating with realistic waveforms generate a wider

range of phase differences. While the sine oscillation produced the phase

difference between -0.1 and 0.1, the phase difference during the oscillation with

the realistic waveforms can reach -0.25 at low frequencies and 0.39 at high

frequencies (N = 4; two-way ANOVA, frequency: p < 0.001, waveform: p < 0.001).

117

Chapter 9: Discussion

Oscillatory activity controls many aspects of animal behavior like feeding,

breathing and locomotion. In order to respond to changing environments,

animals may need to adjust the frequency of the behavior, and the way the

frequencies are regulated becomes important. We hypothesized that the

frequency of an oscillatory activity is determined by the frequency-dependent

properties of the neurons and synapses in the network. We tested this

hypothesis by examining the frequency-dependent properties of the neurons and

synapses in the pyloric network of crab Cancer borealis. The impedances of the

pacemaker PD neuron and the follower LP neuron show frequency-dependences,

and the impedances reach a maximum value when the neurons are oscillating at

their preferred frequencies. Factors, such as the voltage range and waveform

parameters, could shift the preferred frequency and the network frequency in the

same way. The frequency-dependent properties can also be found in the

amplitude and peak phase of the synaptic current. The synapse generates a

larger current when the presynaptic neuron is oscillating at the synaptic preferred

frequency. During a low frequency oscillation, the synaptic current reaches its

peak before the membrane potential does, and the opposite occurs at a high

frequency of oscillation. Overall, we showed that preferred frequencies exist in

neurons and synapses of the pyloric network, and there are many factors could

potentially affect these preferred frequencies.

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Since the preferred frequencies exist in both the neurons and the

synapses, it would be of interest to know which has more influence on the pyloric

frequency . Considering that we demonstrated a clear correlation between the

pyloric frequency and the preferred frequency of the pacemaker PD neuron and

that other studies show that removal of the LP to PD synapse has little effect on

the pyloric frequency, it is likely the preferred frequency of the neuron, at least of

the pacemaker neurons, plays a major role in determining the pyloric frequency.

Notably, the factors affecting the preferred frequencies are not

independent from each other and there are continuous interactions between

them. For example, the voltage range and the waveform, both of which show

correlation with the neural preferred frequency, are shaped by the activation of

voltage-gated ion channels. However, the activation of the voltage-gated ion

channels itself, depends on the voltage range and waveform of the membrane

potential. These relationships, therefore, are not simple one-directional

interactions, but rather complex two-way interactions between the voltage-gated

ion channel and the waveform. The waveform of a neuron is also affected by the

synaptic input it receives. Modeling results show that the short-term depression

of the inhibitory synapses and the dynamics of transient potassium A-current

control the rebound properties of the follower neurons in an inhibitory oscillator-

follower system; more importantly, there are interactions between the inhibitory

synaptic input and the activation of A-current (Bose et al., 2004). When the

inhibitory synapse becomes stronger and pushes the membrane potential lower,

more inactivation of A-current is removed, resulting in a larger A-current during

119

the rebound process. As a result, it is hard, if not impossible, to only modify one

factor without altering the other factors.

The pyloric network receives many neuromodulatory inputs from

projection neurons, and each neuromodulator can affect many properties of the

network at the same time. One example is the neuromodulator dopamine.

Dopamine shifts the activation curve of Ih channel to a depolarized level and

reduce its conductance, resulting in a combined effect of the depolarization of PD

axon (Ballo et al., 2010). Dopamine also affects the waveform of the LP neuron.

It shortens the LP bursting duration (Johnson et al., 2011) and enhances the LP

rebound (Johnson et al., 2005). Besides the intrinsic properties of neurons,

neuromodulators also influence multiple synaptic properties, such as the strength,

the short-term depression and the peak phase (Johnson et al., 2011). Many of

these properties affect neural and synaptic resonance so bath-application of

neuromodulators could affect resonance properties in a complex way.

By putting all these relationships together, we can obtain a roadmap that

shows how the pyloric oscillation frequency relates to various properties of

neurons and synapses in the network (figure 9.1). Many feedback loops can be

seen in the map. For example, the pyloric frequency affects the amplitude of the

LP to PD synapse, which in turn shifts the lower bound of the PD neuron

oscillation and then influences the pyloric frequency. The pyloric frequency is not

determined by one single factor, but by the dynamic interactions between many

factors. The work in this thesis provides the groundwork for further mathematical

120

modeling and biological experiments to understand the importance of each

individual factor.

121

Figure 9.1 The interactions between the pyloric frequency, preferred frequencies

and properties of neurons and synapses. Several feedback loops can be seen in

the map. Red color indicates results from this thesis.

122

Chapter 10: Future directions

Regulating the frequency of a bursting neuron through connections to a resonant

neuron via gap junctions

Among the neurons in the pacemaker kernel, only the AB neuron is an

intrinsicoscillator. The PD neuron oscillatory activity is primarily due to the strong

gap junction coupling between the AB and PD neurons. Therefore, how the

intrinsic properties, especially the preferred frequency, of the PD neuron affect

the frequency of the oscillation becomes an interesting question. This question

could be examined with mathematical modeling or biological experiments. In the

model, we could construct an oscillator and connect this oscillator to a resonance

model neuron. Similarly, we could first isolate the AB neuron experimentally and

then use dynamic clamp to connect the AB neuron to a resonant model neuron.

The voltage of the resonant model neuron need to be carefully adjusted to the

voltage level so that when it connects to the resonant neuron, the voltage range

of the oscillator or the AB neuron will not be shifted. By using resonant neurons

with various preferred frequencies, we expect that the oscillatory frequency

would shift by shifting the preferred frequency of the connected resonant neuron.

Connecting to a resonant neuron with a preferred frequency higher than the

oscillatory frequency of the isolated oscillator should increase the overall

frequency, and connecting to one with lower preferred frequency should bring

down the overall frequency. These results help us understand how the network

123

frequency is regulated with the gap junctions between an oscillator and a

resonant neuron.

Ionic currents contributed to resonance

Many ionic currents are involved in resonance, and the behaviors of these

ionic currents during the oscillatory activity are still unclear. To address this

question, we could measure the ionic currents during the oscillation by

comparing the voltage-clamp current with and without the blocker to the specific

ion channels. For example, CsCl can block the Ih and could be used to study the

amplitude of the Ih during the oscillation. Other blockers include CdCl2 for calcium

currents and 4-aminopyridine for the IA. By applying these blockers, we could

understand the roles of individual ionic current in generating the resonance. In

addition to the removal of ionic currents, we could also use neuromodulators to

alter the properties of the currents. By combining the blockers and the

neuromodulators, we would be able to identify the effects of neuromodulator

result from which ionic current. Finally, by comparing the amplitudes of different

ionic current when the neuron is oscillating at different voltage ranges, we will be

able to understand the underlying mechanisms responsible for the changes of

the preferred frequency with voltage ranges.

The functional role of synaptic resonance in determining the network activity

124

We showed that the synapses have preferred frequencies, and these

preferred frequencies are lower than the network frequency. To examine how

shifting the synaptic preferred frequency affects the network frequency, we could

block the endogenous synapses in the biological network by applying

tetraethylammonium (cholinergic synapse blocker) and picrotoxin (glutamatergic

synapse blocker), and then use dynamic clamp to introduce artificial synapses.

The amplitude of the artificial synapse should have a frequency-dependent

profile and show a preferred frequency. By adjusting the profile and the preferred

frequency, we can examine how the differences in the synaptic resonance

influence the frequency of the network activity.

125

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Curriculum vitae

Hua-an Tseng

Ph.D. in Biology, Rutgers University, NJ, USA (July 2011)

M.S. in Neuroscience, National Yang-Ming University, Taipei, Taiwan (2003)

B.S. in Life Science, National Tsing-Hua University, Hsinchu, Taiwan (2001)

frequency-dependent properties of neurons and synapses in

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