Download Membrane Potential Fluctuations in Neural Integrator

Membrane potential fluctuations in a
neural integrator
Zhao Huang
A DISSERTATION
PRESENTED TO THE FACULTY
OF PRINCETON UNIVERSITY
IN CANDIDACY FOR THE DEGREE
OF DOCTOR OF PHILOSOPHY
RECOMMENDED FOR ACCEPTANCE
BY THE DEPARTMENT OF
PHYSICS
Advisor: David W. Tank
JUNE 2009
 Copyright 2009 by Zhao Huang.
All rights reserved.
.
Abstract
How the brain is able to maintain short-term memory is an unanswered
question. The neural correlate of short-term memory is persistent discharge in the
absence of continued stimulus. This thesis describes the study of one model system
of persistent activity, the goldfish oculomotor neural integrator that integrates (in
the calculus sense) transient saccadic and vestibular signals into permanent changes
in eye position.
We use in vivo whole-cell intracellular recordings of integrator neurons in
awake goldfish to temporally resolve individual excitatory postsynaptic potentials
(EPSPs). We discovered that the EPSP rate increases with average membrane
potential and eye position. The EPSPs also form a frothy fluctuation that constitutes
a significant fraction of the total membrane voltage. This suggests that network
mechanisms play a substantial if not dominant role in the operation of these
neurons. But contrary to predictions of existing neural integration network models,
individual EPSPs do not appear to possess long time constants that were critical to
network stability and tuning.
We present numeric models that show how under some regimes, neurons
may be more responsive to fast fluctuation inputs than slow constant inputs.
These results motivate the theoretical studies of a new class of neural
integrator models that are characterized by fluctuation dominated spike dynamics.
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Acknowledgements
This work would not have been possible without building on top of the
experiences of many others. I would like to thank Tom Adelman for his support and
many innovative suggestions such as the brain clamp. I would like to thank Guy
Major for his invaluable tutelage with intracellular recordings and endless passion
for fish brains. Anton Khabbaz helped me hone my meager electronics skills and
without his help, the data would have been infinitely noisier. Thanks to Santanu
Chakraborty for teaching me electrophysiology and the art of goldfish surgery. I am
grateful to Emry Aksay for initiating me into the mysteries of Area I anatomy
I would like to thank Forrest Collman for providing many stimulating
discussions and Andrew Miri and David Markowitz who were always generous
with their time and advice. Mark Goldman also provided many helpful comments.
And most of all, I would like to thank David Tank for his endless patience
and support.
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Table of Contents
Abstract .................................................................................................................. iii
Acknowledgements................................................................................................ iv
Table of Contents.....................................................................................................v
List of Figures ....................................................................................................... vii
Appendix A: Summary plot for all eight cells .......................................................96
Bibliography ..........................................................................................................97
1 Introduction
1.0 Persistent neural activity and the oculomotor neural integrator ..................1
1.1 Biophysics of a neuron.................................................................................5
2 Models of persistent activity
2.0.0 Network models ......................................................................................13
2.0.1 Anatomical evidence for feedback in cortex and MVN, NPH .........16
2.0.2 In vitro analogue of cortical persistent activity.................................18
2.1.0 Intrinsic cellular mechanisms .................................................................19
2.1.1 Short term synaptic potentiation .......................................................19
2.1.2 Calcium wave model.........................................................................20
2.1.3 Plateau potentials ..............................................................................21
3 Goldfish Area I
3.0 Area I physiology.......................................................................................24
v
3.1 Correlations between paired Area I cells ...................................................26
3.2 Partial inactivation experiments.................................................................26
3.3 Sharp intracellular recordings ....................................................................27
4 Experimental setup
4.0 Whole-cell patch recoding .........................................................................31
4.1 Surgical preparations .................................................................................34
4.2 Vibration isolation .....................................................................................35
4.3 Electrophysiology ......................................................................................39
4.4 Eye tracking system ...................................................................................45
5 Results of whole-cell patch recordings
5.0 Comparison of whole-cell patch recordings with sharp recordings...........46
5.1 Resolved EPSPs have a short time duration ..............................................49
5.2 EPSPs increase with membrane potential and eye position.......................51
5.3 Are integrator cells driven by fluctuations in synaptic input or by the
average increase in synaptic input?............................................................65
5.4 Discussion ..................................................................................................70
6 How neurons may operate in a fluctuation dominated regime
6.0 Influences of a distal action potential initiation site on neural discharge ..74
6.1 Origin of voltage/current threshold in the Hodgkin-Huxley model...........75
6.2 Influences of cable geometry on the site of action potential initiation ......83
6.3 Numeric modeling of the properties of different locations of action
potential initiation ......................................................................................84
6.4 Discussion ..................................................................................................93
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List of Figures
1.1 Discharge characteristics of an integrator neuron ............................................3
1.2 Schematic of a neuron........................................................................................6
1.3 Electrical compartment model ...........................................................................7
1.4 Differences between extracellular and intracellular recordings ......................10
3.1 Membrane potential increases with eye position .............................................28
4.1 Different electrode geometries.........................................................................33
4.2 Schematic of experimental setup .....................................................................36
4.3 Picture of a brain clamp ...................................................................................40
5.1 Comparison of sharp vs. whole-cell intracellular recordings ..........................47
5.2 Expanded views of intracellular waveforms....................................................47
5.3 Different shapes of EPSPs ...............................................................................50
5.4 Simulated periodic EPSPs integration in a RC model .....................................54
5.5 Simulated EPSPs integration with 1 ms jitter ..................................................54
5.6 Simulated EPSPs integration with random arrival times.................................55
5.7 Simulated counting of EPSPs with random arrival times................................55
5.8 EPSP frequency increases with eye position ...................................................58
5.9 EPSP frequency increases with average membrane voltage........................... 59
5.10 EPSP frequency necessary to create fluctuations ..........................................59
5.11 Illustration of fluctuations..............................................................................60
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5.12 EPSP frequency necessary to construct entire membrane waveform............61
5.13 Dependence of frequency estimation on EPSP shape....................................61
5.14 Different EPSPs used to illustrate the shape dependence of the
frequency estimation......................................................................................62
5.15 Ratios of counted EPSPs to estimated number of EPSPs ..............................62
5.16 EPSPs cause large fluctuations in the membrane voltage .............................63
5.17 Peak-to-peak fluctuations increases with membrane voltage ........................64
5.18 Ratio of peak to peak fluctuations to the waveform ......................................64
5.19 Integrator cell operating in its normal regime................................................66
5.20 Expanded view of single action potentials.....................................................67
5.21 Moderately expanded view of single action potentials..................................67
5.22 Action potentials are initiated in the upper part of the preceding voltage
range...............................................................................................................68
5.23 Action potential threshold increases with the average membrane potential..70
6.1 Steady-state Hodgkin-Huxley gating variables as a function of membrane
voltage..............................................................................................................77
6.2 Voltage dependent time constants of the gating variables...............................78
6.3 Time course of GK and GNa after a sudden membrane change from
Vrest to Vrest + 40 mV........................................................................................78
6.4 Instantaneous I-V curve around the resting membrane potential ....................80
6.5 Slightly slower than instantaneous I-V curve around the resting membrane
potential...........................................................................................................80
6.6 Example ramp current injections into a hypothetical space clamped squid
axon..................................................................................................................82
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6.7 Relationship between the threshold current and the ramp duration necessary to
elicit an action potential in a model squid axon...............................................82
6.8 Measured somatic voltage threshold of ramp current injections to elicit an
action potential in a model squid axon ............................................................83
6.9 Current threshold vs. ramp duration for a ramp injection in a model Area I
neuron with and without dendrites...................................................................85
6.10 Somatic voltage threshold vs. ramp duration for a ramp injection in a model
Area I neuron with and without dendrites......................................................85
6.11 Frequency dependence of transferring somatic voltages to the distal axonal
compartment in the model Area I neuron ......................................................88
6.12 Influence of the location of the action potential initiation site on threshold
current ............................................................................................................89
6.13 Influence of the location of the action potential initiation site on threshold
voltage............................................................................................................89
6.14 Increasing the conductance of the action potential initiation site lowers
the current threshold ......................................................................................91
6.15 Increasing the conductance of the action potential initiation site lowers
the voltage threshold ......................................................................................91
6.16 Effects of the diameter of the axon on the current threshold.........................92
6.17 Effects of the diameter of the axon on the voltage threshold ........................92
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1 Introduction
1.0 Persistent neural activity and the oculomotor neural integrator
One basic function that all nervous systems have to accomplish is to store
information. It is hard to imagine how any computation engine with even a
modicum of complexity could operate without some form of memory storage.
In the brain, long-term memory is thought to be encoded through long-term
physical alteration of synapses and the synthesis of new proteins. The synthesis of
proteins is a slow process and would not be adequate for the storage of short-term
information.
In many working memory experiments, the ability to store short-term
information is correlated with persistent neural activities [1]. In a typical
experiment [2, 42, 46, 49], the animal is presented with a transient stimulus (a
visual pattern) and an estimation of the initial stimulus (matching previous pattern
to a new pattern) is elicited after some time delay. During the delay period, patterns
of neural activities can be found in wide spread regions of the cortex (and even subcortical regions [47, 48, 61]) that persist during the delay period (in the absence of
any stimulus), and terminates upon the behavioral response, (choosing matching
pattern). Perturbations to the persistent neural activity through either lesions or
electrical stimulations have adverse effects on the animal's ability to hold
information. Thus persistent neural activity is a necessary component of short-term
memory and might the basis for information storage in the brain.
1
In contrast to the vast literature [41] documenting working memory
paradigms and the cellular circuitry of the cortex, how the brain maintains
persistent neural activity is still a very open question. [7] Part of the difficulty in
answering the question arises from the paucity of empirical data. While it is
relatively easy to characterize the output of a neuron, it is very difficult to measure
the input that it receives. The technical difficulty of this task is particularly
accentuated in working memory paradigms, where the animal subject is awake and
is a persistent source of mechanical instabilities.
In order to ameliorate the mechanical difficulties, we have chosen to focus
our efforts on a special non-cognitive class of persistent activity known as
oculomotor neural integrators [3]. In particular, we will discuss recent progress on
recording intracellular activities in the goldfish velocity-to-position oculomotor
integrator [4]. The oculomotor integrator translates brief saccadic and vestibular
inputs (from the semicircular canals) into sustained changes in eye positions. (The
general concept of neural integrators has more applications than just the oculomotor
systems [43, 44], and it is highly probable that our work here will applicable to
other systems.)
Goldfish spontaneously move their eyes in a horizontal scanning pattern in
the dark. Their eyes fixate in one stable position for 0.5s to 5s before making quick
saccades to a different stable position. The stability of the eye is achieved in the
absence of visual and proprioceptive feedback. This necessitates some internal
persistent signal to sustain ocular muscle activity that would otherwise relax the eye
to a neutral position. The neural basis for such a persistent signal (Fig. 1) has been
2
Fig 1.1 a) Eye position b) Measured extracellular action potentials of an
integrator cell c) Instantaneous spike frequency (ISF) d) Eye position vs. average
action potential frequency
3
located in the hindbrain in a region named Area I [4]. The outputs of these
integrator cells generally possess a linear relationship between firing output and eye
position [5] with a heterogeneous mixture of slopes and thresholds.
The oculomotor system is also sensitive to rotations of the head and counter
rotates the eye to form a stable image on the retina. This is known as the vestibuloocular reflex (VOR). The semicircular canal that senses head rotation outputs
velocity and acceleration signals through vestibular neurons. These transient signals
have to be integrated into position signals by a neural integrator. Lesion experiment
and analysis of neural activity patterns suggest that the fixation and VOR
subsystems share the same integrator [45].
As angular rotation is an analog process, the ocular motor integrator must
possess graded persistence. This is an important distinction between integrators and
simpler bi-stable flip-flop behaviors. Area I integrators possess both VOR
sensitivity and graded activity patterns. Other examples of neural integrators exist.
For example, the head direction system [6] in rats is thought to integrate vestibular
(and other cues) to produce a persistent signal head direction signal.
In general, the mechanisms by which persistent activity are generated are
unknown [7]. Mechanisms generally fall into one of two camps: network
mechanisms such as positive feedback that boot-strap intrinsic cellular decay
constants to long time durations or cellular mechanisms that rely on internal biochemical dynamics to generate long lasting output.
Our work presents experimental evidence that network mechanisms play an
important role in generating persistence in the goldfish oculomotor integrator.
4
1.1 Biophysics of a neuron
Before we continue with our presentation, we will briefly describe the
anatomy of a neuron for the physicist who is unfamiliar with neuroscience
terminology. An extended overview can be found in [50].
A neuron is the ‘atom’ of the brain and in most cases can be separated into
three distinct anatomical regions. The soma (cell body) contains the major cellular
organelles and is in general the thickest part of the neuron, ranging from ~ 5 m to
10s of m in diameter in the central nervous system. While inputs from other
neurons can directly connect to the soma, the majority of inputs are received by a
neuron at the dendritic tree. The arborization of the dendritic tree can span several
hundred microns in reach and is made up of thin branches that are generally much
smaller in diameter than the soma. The output of the neuron is carried by another
thin tube, the axon, in a regenerative fashion over a distance of millimeters. Some
neurons have branching axon segments called collaterals and a single neuron can
provide input for multiple target neurons. While information generally flows from
the dendrite to the soma to the axon to the target dendrite, examples exist for direct
dendro-dendritic [51] or dendro-axonal connections [52].
Information flows into neurons through synapses. Neurotransmitter diffuse
through the synaptic cleft and gate specific ion channels with different temporal
dynamics. Some receptors like AMPA receptors [55] have short ~5 ms kinetics
while others such as NMDA [56] receptors can have long ~100 ms durations. Short
and long are referred in comparison to the membrane time constant, which is
usually about ~ 10 ms.
5
Fig 1.2 Schematic of a neuron
As the intracellular medium of a neuron is resistive, a typical neural
membrane is not an isopotential surface. Passive membranes with simplified
geometries can be described with explicit analytical solutions using Green's
functions and cable theory [57]. However, biological neurons generally show a
diversified geometry with non-linear active and passive conductances embedded
non-uniformly in the membrane. The morphology of real neurons cannot be over
trivialized as simulations suggest the physical geometry of a neuron can a large
impact on its behavior [87].
6
Fig 1.3 Electrical compartment model
In order to model realistic neurons, they are generally segmented into
compartments and modeled discreetly. For a single compartment with voltage Vm,
Kirkhoff's law gives
C
(V  Em ) (V  V0 ) (V1  V )
dV



 I channels (1.1)
dt
rT
rL
rL
I channels  k g k (t , V )(V  Ek )
RL  rL dx
RT1  rT1dx
(1.2)
C  cdx
Typical values:
c = membrane capacitance, 1F/cm2
rT = membrane resistance 30 k cm2
rL = intracellular resistance 150 cm
Many terms in Eq. 1.1 are familiar to physicists from simple cable theory.
The new terms, Vm, gk, Ek arise from the active and passive conductances of protein
channels that are embedded in the membrane. These protein channels show a rich
7
repertoire of behaviors such as voltage sensitivity, ion specific selectivity, and nonlinear temporal dynamics [53, 54].
A subgroup of these protein channels actively pumps select ions in and out
of the cell to maintain an active gradient across the membrane for several common
ion species. Taking the permeability of the membrane to each ion into account, the
resting membrane potential of a neuron can be calculated using the GoldmanHodgkin-Katz
Vm 
P [ K  ]  PNa [ Na  ]out  PCl [Cl  ]in  ...
RT
ln( k  out
) (1.3)
F
Pk [ K ]in  PNa [ Na  ]in  PCl [Cl  ]out  ...
equation. The chemical gradient and permeability of the two dominant ions Na+,
K+, are mostly responsible for setting the resting potential across the cell membrane
Vm to ~ -70 mV. (The permeability of the membrane to potassium ions is much
higher than that for sodium ions and so sets the membrane closer to the potassium
reversal potential/chemical potential.)
When a synapse is activated, select ion species are permitted to move across
the membrane in accordance their reversal potential Ek. The temporal and voltage
dynamics of the permeability of the channel is embedded in gk(t,v).
We can consider synaptic input to be charge injection if it is excitatory input
or charge extraction if it is inhibitory input. (Although inhibition can also occur
through the shunting of excitatory current.) From Eq. 1.1 it's clear that inputs can
sum temporally and spatially in an RC-circuit type fashion for passive membranes.
Membranes with active channels can produce non-linear summation.
8
In almost all neurons, there exists a special region with a particularly high
density of voltage sensitive sodium and potassium channels. Classically, this region
is associated with the axon hillock, the junction between the soma and the axon.
When the membrane voltage crosses a threshold at the axon hillock, a cascade of
voltage sensitive sodium channels is opened, resulting in a sudden depolarization of
the membrane. (The cell membrane is re-polarized by the opening of potassium
channels.) This non-linear event is known as the action potential and is the output
signal of the neuron. (The action potential travels down the axon and activates
neural-transmitters at the axon terminus, signaling other neurons.) We will present a
more detailed discussion of action potential generation in later chapters.
The large voltage swing of an action potential, ~ 100 mV, can be detected
with electrodes placed in the extracellular medium. These extracellular recordings
are sensitive to the composition of the extracellular matrix that affects the current
flow associated with the action potential. Free aqueous ions move quickly to shield
stray charges. Empirically, we can measure a 1 mV signal associated with the 100
mV action potential in the goldfish hindbrain if the extracellular electrode is within
a micron or so of the neuron for a 4" to 6" fish. The strength of the signal quickly
falls off as a function of distance, and the measurement of the AP discharge falls to
about ~100 V when the electrode is 50 m+ away. For small goldfish fish, ~1", it
is hard to detect extracellular signals greater than 100 V regardless of the
proximity of the electrode to the neuron.
Electrodes used in extracellular recordings can be fabricated from a wide
range of materials. But regardless of their construction, they generally are
9
composed of some insulated material with an exposed conductive core at the very
tip ~ 1-5 ms. Their resistances are generally on order of ~1-5 M. For the 2 M
saline-filled, 2 m open tip, glass electrode that we typically use, the rms Johnson
noise is approximately 15 V (0-10 kHz), or ~40 V peak-to-peak. This is adequate
for the detection of extracellular signals associated with action potentials. However,
such electrodes are insensitive to synaptic signals that are roughly 100 smaller in
amplitude than an action potential. Aside from being smaller in absolute voltage,
synaptic signals are also hard to measure because the extracellular waveform is a
distorted/filtered version of the true waveform (that exists across the neural
membrane) [59] and is more representative of a capacitive discharge of the
membrane.
Fig 1.4 Differences between extracellular and intracellular recordings
To obtain an electrical measurement of the sub-threshold waveform that
represents the synaptic input, the recording electrode has to be inserted through the
insulating membrane layer and into the cell. For small cells in the central nervous
10
system, this is typically done with a very fine 100 nm tip glass needle. Accordingly,
this method is known as the sharp intracellular recording technique. Alternatively,
the membrane of the neuron can be fused to the tip of a glass electrode before
penetration using a technique called whole-cell patch-clamp [60]. In the patchclamp technique, the glass electrode tip is gently pressed against the outer surface
of a neuron. A very gentle negative suction is applied to seal the neural membrane
to the inner lip of the glass electrode. If the electrode tip and neural surface are very
'clean', the two materials will fuse together to form a high resistance contact G+
contact. A more vigorous suction is made to rupture the inner membrane of the seal.
If done correctly, a hole will be made in the seal, but the outer edges of the
membrane will still be tightly coupled to the glass surface. This creates a direct
contact between the intracellular medium and the inner saline of the electrode.
However, to form a stable junction, the tip of a patch electrode should still be small
(~1 m) in comparison to the size of the neuron (~10 m) being patched.
While the relevant physical scale of extracellular recordings is on the order
of tens of microns due to the propagation of currents in the extracellular medium,
the physical scale of intracellular recordings is on order of ~1 m as set by the tip
size. Correspondingly, extracellular recordings are much less demanding in terms of
mechanical stability than intracellular recordings. The differences in difficulty are
magnified when recordings have to be made in awake behaving animals to study
short-term memory. For this reason, most measurements of short-term memory
paradigms are made using extracellular recording techniques. Thus, while we know
11
much about how the output of neurons is correlated with information storage, we do
not know much about how such output is generated.
Even without having to invoke special dynamics, a single neuron can be
said to possess a memory of its past stimulus on the time scale of its membrane time
constant ~10 ms. However, this is several orders of magnitude shorter than the time
courses of cognitive or eye fixation events that can last seconds. How then, does the
brain boost 10 ms to one second?
12
2 Models of persistent activity
2.0.0 Network models
Due to the paucity of empirical evidence, many mechanisms have been
proposed to explain how persistent activity is maintained in the brain. They
generally fall into one of two camps: positive feedback through network dynamics
or intrinsic cellular mechanisms that possess long dynamics.
It has been hypothesized for a long time [18, 19] that persistent neural
activity is maintained by positive feedback through recurrent excitatory
connections. (It is also possible to generate net positive feedback through mutual
inhibitory connections, a phenomenon known as disinhibition.)
However, positive feedback is notorious for suffering from tuning and
stability problems. We can illustrate the problems with a simple toy model. As the
firing rate of a neuron is set by its membrane potential, the decay in firing rate is
also set by the membrane time constant. Let v(t) be the firing and , the time
constant set by the decay of the membrane potential. Then
v(t )  
dv
dt
(2.1)
If positive feedback was added to the system
v(t )  
dv
 kv(t )
dt
13
(2.2)
then the apparent time constant is T 

1 k
and
dT T
 dk . Given a membrane
T

constant of 10 ms and an apparent time constant of ~10 s for eye fixation events, a
very small change in the feedback would cause a 1,000 fold change in the apparent
time constant.
Still, many models based on recurrent connections have been proposed to
explain persistent activity in the cortex [62, 63, 64] and in the oculomotor system
[12, 13, 14, 15, 83]. Most are based on linear elements that take on the general
mathematical form
 cell
N
dvi
 vi   Wij v j  f i (2.3)
dt
j 1
where vi is the instantaneous rate of action potentials of the ith neuron in the
network. cell sets the timescale of an individual neuron and is thought to correspond
to an intrinsic cellular constant such as a synaptic time constant or membrane time
constant. fi represents a basal tonic input. Wij sets the connection strength between
individual neurons.
Feedback does not imply the existence of a multi-stable or continuously
stable solution that is required for graded persistent memory systems such as the
ocular motor system. If we set
dv
 0 in Eq. 2.3, we have a system of N linear
dt
equations with N variables that in general produces one fixed solution. Thus to
produce the graded persistence seen in nature, a special topology/tuning of Wij and fi
is required.
14
Using an eigenmode analysis, Seung [11] showed that all of the published
linear models reduce to this common framework. That is, the linear models all
constrain Wij and bi in such a way to produce a solution where a continuous line of
fixed points (line attractor) represents the persistent activity observed in the neural
network.
Seung identified the general mathematical requirements necessary for a
stable solution. Wij must have a single unity eigenvalue and the left eigenvector
corresponding to the unity eigenvalue must be orthogonal to fi. A large energy gap
should also exist between the unity eigenvalue and the other N-1 eigenvalues
(whose real parts are less than one) so that the system relaxes to the line attractor
state after some small perturbation.
Put together, these conditions impose stringent precision requirements on
the parameters. The precision that is required to tune the network is on the order of
~
 cell
 network
. In the first liner models proposed by Cannon and Robinson [13, 14], cell
was identified with the membrane constant of ~5 ms. This would require a
biologically implausible tuning requirement of 0.05%. Seung proposed to identify
cell with a long NMDA N-methyl-D-aspartate receptor (NMDAR) synaptic time
constant ~100 ms [11, 12]. (Or effectively gk(t,v) has a 100 ms long time dynamic.)
NMDA has also been hypothesized to play important roles in persistent
activity in cortical models [65, 66]. The diversity and function of different NMDA
receptor subtypes has been reviewed in [67]. NMDA receptors typically exist as
heteromers composed of different subunits. Diheteromeric receptors that involve
15
the NR2D subunit can have second long deactivation time constants. Interestingly,
the NR2D subunit is moderately expressed in both the prefrontal cortex (in
mammals) and the brainstem regions (mammals and zebrafish) [68, 69, 70] and
could potentially play a role in mediating persistent activity in those areas.
2.0.1 Anatomical evidence for feedback in cortex and MVN, NPH
Feedback models are popular not only because of their mathematical
elegance, but also because there exists abundant anatomical evidence to support
their existence. Strong feed-forward and feedback connections exist within and
between cortical areas. There also exist many reciprocal cortex-subcortex loops
such as cortico-thalamic connections that could mediate recurrent feedback.
Feedback loops also appear to exist in mammalian integrator regions. We'll discuss
the physiology of those brain regions in some detail as it has the most direct
relevance to our study.
The study of ocular motor integrators originated in studies of mammalian
preparations [8]. In mammals, integration in the vertical plane involves the
interstitial nucleus of Cajal [26]. Similarly the nucleus prepositus hypoglossi (NPH)
and the medial vestibular nucleus (MVN) are important parts of the horizontal
integrator. Extracellular recording of the three regions show a heterogeneous
mixture of neurons with position and velocity sensitivities. Micro-lesions [32,34],
chemical in-activation [33, 35, 38, 40] and micro-stimulation [23] experiments
show that disruptions to those regions impair VOR and gaze-holding ability,
dropping the apparent time constant of gaze fixation from ~10 s to ~100's ms.
16
Extensive tracing studies show that the purported mammalian integration
regions contain the connectivity patterns appropriate for an integrator. Burst and
vestibular neurons project into the NIC and NPH [27, 28] that in turn project to
abducen motorneurons that directly innervate the muscle. The bilateral MVN and
PH nuclei are fully connected by internuclear projections. In addition, neurons in
the MVN and PH have recurrent collaterals that could potentially mediate
intranuclear feedback loops
The feedback loops within the integrator region appear to have important
functions as damage to the commissural connections of the MVN and PH causes
gaze-evoked nystagmus [92]. Moreover, transient micro-stimulation of the regions
can induce persistent changes in eye position [37, 39]. This effect would only be
possible if memory storage of the eye position was located in the MVN/PH or in a
downstream target. Empirical evidence suggest however that the motor nuclei
downstream of MVN/PH themselves do not store eye position memory.
While there is some anatomical evidence to support the existence of
feedback loops, in vitro studies of the guinea pig and avian MVNs have not found
any evidence for membrane bistability or other intrinsic long cellular dynamics that
could explain persistent neural activity. However, in vitro studies cannot replicate
the full physiological environment that a neuron experiences in vivo, and there
might exist some overlooked neuromodulatory mechanism that is only apparent in
vivo. It is also possible that the incorrect subset of neurons were examined as there
is no behavioral correlate in in vitro preparations to ascertain that the experiment is
truly assaying an integrator neuron.
17
2.0.2 In vitro analogue of cortical persistent activity is mediated by balanced
inhibition and excitation
While no in vitro preparation for persistent activities has been developed for
integrator brain regions, an in vitro analogue for persistent cortical activity has been
developed by the McCormick lab [73, 74]. They showed that in vitro slices of ferret
prefrontal and occipital cortex can generate recurring periods of sustained activity
that lasts between 0.5 to 3 s. These states were bistable, and undergo rhythmic
oscillations between the active (UP) and quiescent states (DOWN). Using
intracellular recording [75], it was shown that the driving current for the neural
activity came from a balance of excitatory and inhibitory current. Potential
feedback loops that could mediate such activities were also physiologically
inferred. Blocking either AMPA or NMDA receptors abolished the UP states but no
actual measurements of individual synaptic events were made and thus it's unclear
if long synaptic time constants were involved. However, in this cortical model, finetuning may not be a necessary requirement as the activity pattern appeared to be
bistable and resembled a flip-flop circuit.
It's not clear whether the in vitro bistable activity patterns accurately reflect
in vivo behavior. But it still shows that the appropriate circuitry exists and that
network dynamics can be used to generate persistence.
In general however, the network fine-tuning required to generate persistent
activity is a problem. Even if a ~100 ms NMDA-like time constant was used for
synaptic events, the network parameters would still have to be tuned within ~1% for
linear models that rely on long synaptic time constants. This stringent requirement
18
may be too difficult to achieve in noisy in vivo biological settings. In order to
address the fine-tuning problem, some researchers have introduced bi-stable or
hysteric elements to improve the robustness of the feedback model [16, 17].
The problem of robustness or t he need for positive feedback can be
completely sidestepped if there exist intrinsic cellular dynamics that can generate
persistent current. While not ubiquitous, examples of such persistent intrinsic
mechanisms exist.
2.1.0 Intrinsic cellular mechanisms
The membrane time constant of a neuron sets the rate at which synaptic
information is lost for a passive membrane. This in some sense sets the lower
temporal bound for information storage in a single neuron. While the membrane
time constant represents one intrinsic time constant for neurons, there exist other
intrinsic mechanisms that possess time constants much longer than that of the
membrane. Accordingly, these intrinsic mechanisms have been proposed to
underlie persistent activity.
2.1.1 Short term synaptic potentiation
One of the earliest models that use intrinsic cellular mechanisms was
proposed by Shen in 1989 [9]. He proposed to achieve robust integration of
synaptic input using a basic property of synapses known as short term potentiation
[71].
Short term potentiation refers to the phenomenon where repetitive
stimulation of a synapse results in increased neurotransmitter release per action
potential from the presynaptic terminal. (The mechanism for this behavior involves
19
the gradual accumulation of calcium ions in the presynaptic terminal with every
action potential. Calcium gates neurotransmitter release.)
Increased presynaptic transmitter release implies that the action potentials
that come later in an input train are more effective in eliciting a prolonged response.
If the first action potential occurred at time t=0 and increased the efficacy of the
presynaptic terminal by an amount p(t). A second stimulus increases the amount of
transmitter released by a factor of 1+ p(t). From experimental observations, p(t) was
found to assume the form e

t
p
. Shen showed that if the inter-spike interval of the
input train and the membrane constant are significantly smaller than p, then the
potentiation can effect an integration of the input. 
p have been experimentally observed to range from the tens of milliseconds
to seconds. By itself, a long p may also serve as a basis for boosting stability in
feedback models. Recently NMDA receptor dependent short term potentiation has
been observed in the NPH of in-vitro rat brainstem slices [72]. Such short term
potentiation could serve as the basis for neural integration or for boosting stability
for feedback models.
2.1.2 Loewenstein's calcium wave model
Loewenstein and Sompolinsky [40] implemented a novel mechanism for
integration using calcium bi-stability. They segmented each dendrite into
compartments. In each compartment, calcium-induced calcium release and calcium
clearance are tuned to generate local bistability of intracellular calcium
concentration. Calcium can diffuse from one compartment to the next and divides
20
the dendritic segment into zones of high and law calcium. With careful tuning of
parameters, the boundary between the two zones is stationary. Synaptic input
induces increases in intracellular calcium concentration and shifts the 'wavefront'
along the dendrite. Inhibitory input moves the wavefront in the opposite direction.
The intracellular calcium level is converted into current that triggers neural
discharge via a calcium-activated channel.
It is not clear if the parameters used in this model are robust. As calcium can
diffuse between compartments, the position of the wavefront is subject to drift.
While some robustness is gained from branching dendritic arbors that cancel out
random drift, the parameters of the model still has to be finely tuned between
calcium extrusion and release. However, it does highlight a single cell mechanism
in which integration maybe achieved.
2.1.3 Plateau potentials
While calcium bistability in the way suggested by Loewenstein and
Sompolinsky is untested, voltage bistability in the form of voltage sensitive
channels has a long track record. Various motorneurons and reticulo-spinal neurons
show intrinsic membrane bi-stability in the form of a prolonged depolarization
known as plateau potentials. These mechanisms generally involve calcium in some
fashion (although persistent sodium currents may be involved in mammals [80].)
In vitro motorneurons can produce a plateau potential that is largely
mediated by L-type Ca channels [78,79]. After an initial depolarization, these low
threshold voltage sensitive channels activate to allow calcium to flow into the
neuron, forming a self-sustaining dynamic.
21
Aside from being a source of positive current, calcium can also activate
other channels to produce a net positive current. For example, in the ‘semi-intact’
lamprey preparation [34, 35], successive stimuli to brain stem reticulospinal
neurons will activate NMDA receptors that mediate the entry of calcium into the
neuron. The calcium then activates non-specific cation channels (CAN) that
produce a long duration depolarization of the membrane. CAN current in
conjunction with various forms of neuromodulatory activation such as serotonin or
muscarinic activation can produce plateau potentials in higher brain areas such as
hippocampul CA1 cell as well [81].
More recently, a promising in vitro preparation involving the entorhinal
cortex [24] has been induced to shown graded persistence under muscarinic
activation. CAN currents provide the depolarizing drive. Moderate 0.5 s+ long
depolarization pulses can evoke transitions in firing rate of up to 40 Hz. However,
very long 5-10 s hyperpolarizations up to 80 mV are necessary to stop firing
completely. It is speculated that the persistent activity arises from a
compartmentalized model of calcium bistability. [25]
However, while the machinery for bi-stability appears to exist in many parts
of the brain, it has not been demonstrated that plateau potentials play any role in an
intact physiological setting except perhaps for the fictitious swimming behavior
induced in the semi-intact lamprey preparation.
Part of the difficulty in studying the origins of persistent activity lies with
the fact that it requires the animal subject to be awake and behaving. The awake
behavior necessarily generates mechanical vibrations that render intracellular
22
recordings difficult. Moreover, many higher forms of persistent activity are
observed during working memory tasks of primates, animals that are expensive to
perform invasive and deleterious experiments. For all of these reasons, we were led
to study the ocular motor integrator in the goldfish.
23
3 Goldfish Area I
3.0 Anatomy
The goldfish is particularly well suited for electro-physiological
experiments. A large part of its usefulness lies with its innate good nature. Unlike
common mammal preparations like mice, cats, or even other fish species such as
zebrafish, goldfish are content to be restrained in a body harness with their head
fixed for long periods of time. This makes this species particularly useful for
intracellular recordings where the pertinent characteristic size of the experiment is
on order of a micron, but endogenous behaviors produce motions on the order of
~cm.
Goldfish oculomotor behavior is also less complex and the underlying
circuit is fewer in cell numbers and localizations than mammals. Unlike mammals
that scan in both the vertical and horizontal axis, spontaneous scanning behavior in
the goldfish occurs primarily in the horizontal plane. Thus there is only one primary
integrator locus for gaze holding behavior active in a head restrained animal. This
locus has been located in the brainstem [4] and is analogous to the NPH region in
mammals. Another locus, that is insensitive to position but sensitive to velocity has
also been found, called Area II. While the mammalian integrator regions contain
thousands of cells, the goldfish integrator nucleus is purported to contain 30-40
neurons as identified by biocytin staining [4].
The discharge of Area I neurons is correlated with eye position and its
inactivation affects both gaze holding and VOR. The discharge of Area II neurons
24
is related to eye velocity and its inactivation affects VOR without affecting gaze
holding. Thus Area I is thought to be responsible for position storage while Area II
neurons is thought to responsible for ‘velocity storage.’
Area I is located within a small region in the hindbrain between
rhombomere 7 and 8. The region is a rostral-caudal column roughly 300 m long,
100 m wide, centered about 350 m from the midline. Integrator neurons in Area I
appear to be similar to the medium size neurons in the rostral NPH. In mammals,
these “principal” neurons project unilaterally and arborize within the nucleus as
well as sending projections to motorneurons in the abducen. Area I neurons receive
projections from vestibular neurons and send projections to motor neurons [30, 31].
Some Area I neurons send bilateral projections to the contralateral Area I nucleus
setting up a potential recurrent feedback loop. Correlation studies suggest that the
contralateral projections are inhibitory and therefore may be a source of net
recurrent feedback through disinhibition [21]. However experiments in the goldfish
that either inactivate Area I unilaterally or attempt to cut the projections across the
midline only produce small integrator deficits. This is in contradiction to
experiments [22, 23] in primates where midline lesions produce severe deficits in
integrator performance. This suggests that contra-lateral inhibition that has been
postulated to be important in some models, is not a critical source of feedback in the
goldfish integrator.
It is unclear if the axons of Area I position neurons arborize within the
ipsilateral nucleus. Although clearly labeled axon collaterals were not detected in
the intracellular neurobiotin injections, this may be attributed to incomplete labeling
25
and transport barriers. The axons appear to be constricted in the region where it
emanates from the soma. This in conjunction with the natural small size of axon
collaterals, suggest that insufficient dye may have diffused to visualize their
connections.
In addition, it is possible that gap junctions occur between the
dendrites of Area I neurons as this structure has been characterized in other goldfish
oculomotor nuclei [117].
3.1 Correlations between paired Area I cells
Paired and triplet recordings of position sensitive neurons [21] show that
positive correlations exist between ipsilateral pairs of neurons and negative or no
correlations exist between contra-lateral pairs. The timescale of the positive
correlations are very brief (5-10 ms) and exist in almost all ipsilateral paired
recordings. Interestingly, the correlations are pronounced at low firing rates but are
absent at higher firing rates.
It is unlikely that such correlations can exist if the driving force for
discharge only came from intrinsic cellular mechanisms as the temporal dynamics
of different cells would be independent and unlikely to produce any correlation.
While positive correlation would be a consistent signature of recurrent feedback, it
is also possible that the correlations arise from common input. (This common input
could arise from vestibular neurons discharge at a constant rate under experimental
conditions. It is possible that this could produce the observed correlations at low
rates.)
3.2 Partial inactivation experiments
26
Dual electrode drug injection and electrophysiological recording [82]
experiments show that precise partial inactivation of Area I using extracellular
application of drugs (muscimol or lidocaine) produce a sharp loss of persistence in
the remaining position sensitive neurons on the ipsilateral side.
After carefully mapping out the anatomical extent of the Area I region, one
recording electrode was positioned at the rostral periphery of the region while a
drug injection electrode was placed at a distal caudal region. As the dendrites of
Area I tend to run caudally, there should be minimal interference of the rostral
neurons by the caudal injections.
Silencing one portion of the neuron population apparently induces a loss of
persistence in the remaining neurons. This suggest that some network connectivity
might exist between the neurons because if single neurons were capable to
maintaining persistence (through plateau potentials), then knocking out a
subpopulation of the network should not affect the remaining neurons. However,
the loss in persistence was not as dramatic as predicted by line attractor models,
which suggest the system possesses some intrinsic stability.
3.3 Sharp intracellular recordings
The most important experiments that had been performed on Area I
examined the intracellular physiology of position sensitive cells using sharp intracellular electrodes [20]. (Some attempts at whole-cell recordings were made, but
the recordings were too short to provide additional information.) Sharp electrodes
are very fine, narrow glass electrodes with tips on order of 100 nm. They physically
pierce the cell membrane to measure the intracellular voltages.
27
These experiments showed that a sustained membrane depolarization is
elicited in the integrator neurons after a saccade. Artificial membrane
depolarizations elicited by current injection through the electrode suggest that the
membrane steps are of sufficient strength to produce the natural action potential
discharge. Hyperpolarizing the membrane (with injection of negative current) did
not remove the voltage steps and implied that back propagating action potentials
(into the soma and dendrite) are unnecessary for the generation of the membrane
steps.
Fig 3.1 Membrane potentials Vm increases with eye position. (Cell is
hyperpolarized to prevent spiking.)
However, transient current injections were unable to elicit permanent
changes in membrane potential or intrinsic firing rate. This is in stark contrast to
every reported example of plateau potential or membrane bistability where transient
current injections were able to elicit permanent changes in cellular activity. In
28
addition, the step changes in membrane potential remained even as the neurons
were hyperpolarized below action potential threshold, suggesting that they were
caused by steps in membrane current (or conductance.)
Along with the absence of somatic or proxi-somatic plateau potentials, no
intrinsic oscillatory pace maker currents were found either. Triangular injections of
current showed no hysteresis in current-firing rate relationship.
In about a quarter of the recordings, there was an increase in rms
fluctuations of the membrane potential as it became progressively depolarized. This
increased fluctuation amplitude could arise from an increase in EPSP rate, input
synchrony, or amplitude of the EPSPs. (In two unpublished recordings, individual
EPSPs were resolved and provided some preliminary evidence for increased EPSP
rate.)
In general, the exact origin of the fluctuations was un-resolvable from the
sharp intracellular recordings. The technical explanations for this originally was not
clear. While a sharp electrode’s impedance is very high ~100 M due to small size
of its tip, ~100nm, it doesn’t seem to be sufficiently high enough in parallel with
the electrode and amplifier capacitance ~5-10 pFs, to produce an RC time constant
that would entirely filter way individual EPSPs. (100 M x 10 pFs = 1 ms). (It is
possible that the 5-10 pFs capacitance is an underestimate as solution creep up the
shank of the electrode could have rendered a much larger portion of the electrode to
be capacitively coupled.) Sharp electrodes in general introduce a leak [86] in the
cellular membrane through the physical impalement of the cell and this may have
shunted current. The physics of salt solutions is complex and exhibits many
29
frequency dependent dielectric and conduction properties. These may be
accentuated at small scales ~100 nm by surface effects such as the Debye layer and
may produce low-pass filtering effect. All these properties of sharp recordings
could act in conjunction in reducing its temporal resolution.
30
4 Experimental Setup
4.0 Whole-cell Patching Recording
In order to increase the temporal resolution of the recording, we turned to
the whole-cell patch technique. The patch clamp technique was originally
developed to study the kinetics of ion channels [85]. Later the technique was
extended to recordings from entire cells [60].
As mentioned previously, the whole-cell patch technique consists of fusing
a relatively large pore glass pipette ~ 1.2 m to the cell membrane through an
unknown mechanism. As long as the glass surface and cell surface are relatively
clean, such seals can form spontaneously upon contact (though in practice they are
encouraged with some negative pressure.) Seal quality is assayed by measuring the
resistance of the electrode tip. Good seals measure G
The tightness of the seal confers a substantial mechanical bond between the
glass tip and cell membrane. It's not uncommon in (brain) slice preparations to see
the attached cell pulled along with the tip of the pipette during retraction of the
electrode. In the goldfish in vivo preparation however, the mechanical stability of
the seal is counteracted by instabilities associated with a large pipette tip
penetrating through the tough brain stem tissue (see Fig 4.1) The compressed brain
eventually relaxes and moves away from the pipette. Thus, virtually all recordings
are lost because of a slow (~1 min) sealing of the tip (resistance reaching G
rather than a sudden change in membrane potential and loss of apparent cell
resistance (which would be indicative of vibration problems.)
31
Electrodes were fabricated with either the P-2000 or P-87 puller (Sutter
Instruments.) Tips were drawn by the puller by heating a small uniform
1mm/1.2mm capillary tube and separating the two halves apart with tension. The
visco-elastic properties of liquid glass are such that the size of the final tip is highly
correlated with the width of the electrode shank. Sharp intracellular microelectrodes
have very tiny tips and very slender shanks. In contrast, patch electrodes are
relatively stubby. It is difficult to produce a relatively large tip opening ~ 1 m but
still slender patch pipette. Penetrating tissue with thick patch electrodes causes a
tremendous amount of built-up tension as the brain is compressed and sheared with
electrode advancement. In practice, recording from patch electrode last shorter than
that of sharp electrodes after external vibrations issues are resolved. Empirically,
sharp recordings last over 40 minutes while patch recordings last between 5-10
minutes.
It is possible to pull thicker sharp electrodes than that depicted in Fig 4.1 to
reduce capacitive coupling, but thicker shanks also increase the stiffness of the
pipette which lessens the ability of the pipette to vibrate with the tissue.
Patch electrodes convey a considerable increase in temporal sensitivity over
sharp electrodes. Unlike the small 100 nm diameter of the sharp electrodes, the
patch electrodes that we used have relatively large ~1-1.2 m openings assayed
using the bubble number test [88]. This in conjunction with the relatively stubby
taper, produces a low resistance electrode. If the internal electrode solution (~2-3M
KAc) for sharp electrodes were used for patch electrodes, the resistance of the patch
electrode would be a few hundred K. However, diffusion between the intracellular
32
Fig 4.1 Different electrode geometries a) extracellular electrode b) patch pipette
c) sharp intracellular electrode
Resistance
Tip size
extracellular electrode:
2 M
1m
patch pipette:
6 M
1 m
sharp intracellular electrode:
100 M
.1 m
Table 4.1 Dimensions and resistance of different types of electrodes
33
space and the patch electrode medium occurs rapidly (due to the large opening at
the tip), and so the electrode solution has to be matched to the intracellular medium.
The patch electrodes used in this experiment were typically between 5-6 M and
correspondingly have a much higher temporal resolution than sharp electrodes.
Capacitive coupling is also less of a problem for patch electrodes due to low
resistance tip 10 M * 10-12 pF = 0.1 ms and thicker shank. (The wall thickness of the
drawn glass is roughly proportional to the shank diameter.)
4.1 Surgical preparations
All experiments were performed in strict compliance with the Guide for the
Care and Use of Laboratory Animals. The Princeton IACUC committee approved
specific protocols.
Goldfish (Carassius auratus, 4-6”, Hunting Creek Fisheries, Thurmond
MD) were stored at 20-22 C in 75 gallon aquariums with daily exposure to light.
Prior to the experiment, a stabilizing metal bolt was attached to the exposed skull
with self-tapping screws (R-TX002, Small Parts, Miami Lakes, FL), followed by
two layers of superglue, and dental acrylic.
During the experiment, the stabilizing metal bolt was clamped with two
locking nuts to fix the goldfish head position. Two soft sponges were pressed
against the fish body to supply additional restraint. A small plastic tube was inserted
into the mouth to circulate water and to improve respiration. Unlike previous
experimenters, the operculum (bony plate over the gills) was removed to help
34
release bubbles (spontaneous cavitations) that irritate the fish. Removal of the
operculum also reduced vibration coupling between the cranium and the rest of the
body. Supersaturated levels of oxygen appeared to pacify the animal and so
carbogen (95% O2 / 5% CO2) was directly infused into the tank.
Lidocaine was used as a local anesthetic to open a small window (~1 cm) in
the cranium to allow access to the hindbrain. A small metal spatula (see next
section) was gently inserted ~500-700 ms underneath the hindbrain and fixed to a
post using fast drying hot glue. The hindbrain surface was kept free of debris and
protein buildup (from surgical wounds) using a perfusion of ACSF (in mM, 140
NaCl, 2.55 KCl, 5 NaHCO3, 0.42 Na2HPO4, 5 HEPES, 1.16 CaCl2, 1 MgCl2, pH
7.2, 270 mOsm). Excess ACSF was vacuumed using a small syringe tip. The
perfusion system was turned off during the final approach to the cell body layer to
minimize vibrations.
Fish tank water was continuously interchanged with an external five-gallon
tank.
4.2 Vibration isolation
The physical scale of the experiment is determined by the tip of the recording
electrode, ~1 m, which forms the junction with the cell. This small size implies
that excess vibration is directly detrimental to the neural recording.
Excess
vibration can also introduce spurious artifacts that are difficult to interpret and fix.
35
Fig 4.2 Schematic of experimental setup
Some previous experimenters have reported that Gseals are hard to obtain
with integrator cells. Other experimenters have reported recordings only from
‘cells’ that lack synaptic activity or membrane fluctuations but still demonstrate
robust resting membrane potentials. Taken together, the two experiences suggest
the integrator cells are tightly covered with glia (support) cells that impede the
access of the recording electrode.
Recent experience, however, suggest that the problems are not caused by
glia cells, though they may exist, but rather are artifacts of vibration related
problems. The aforementioned problems disappear once efforts have been made to
eliminate the different sources of vibration in the system.
(In light of this, it is suspected that excess vibration can impede the
formation of the Gseal between the glass electrode and the cell membrane by
36
either damaging the glass tip in transit to the recording site or by destabilizing the
junction between the glass surface and cell membrane during the seal process. (The
seal process takes a few seconds to occur.) Even after a successful seal has been
made, excess vibration may cause the membrane surrounding the seal to rip off of
the cell and reform into a self-stabilized membrane that has no synaptic activity but
still possess a voltage gradient across the membrane.)
Excess vibration will manifest itself as excess voltage/current fluctuations
when an electrode approaches a cell surface. This can be assessed by applying a
small 5 mV voltage step to the electrode while monitoring the current. As the
electrodes is advanced, decreases in current indicates blockage of the electrode tip
because of the approach of cellular mass. In stable recordings, there is no obvious
increase in the noise of the current when approaching a neuron aside from what is
expected from inherent electrical noise sources (Johnson noise.)
Some sources of vibration are intrinsic to the organic nature of the goldfish.
Undue stress from surgery or low oxygen levels will cause the goldfish to rapidly
‘gill’ and flex its jaw and forehead muscles. This effect is reduced by supersaturating the fish tank with oxygen as well as removing the operculum. Over the
course of several hours, ammonia levels can also rise in the tank from defecation.
The best course to solve this problem is to continuously replace the water with an
external tank that contains ammonia-fixating bacteria.
On a good day, the fish should be free of all visible movements (including
gilling motions) for at least 12 hrs post surgery. (Except for the months April-Sept,
37
where innate mating behaviors cause the fish to be frisky and troublesome. During
those months, Fish also develop a spongy tissue above the hindbrain)
Aside from internally generated goldfish vibrations, the experiment is also
susceptible to several external mechanical sources. One large source of mechanical
vibration comes from the motorized pump that drives water through the mouth tube.
Previous tank designs had directly connected the output of the pump to the mouth
tube using a semi-rigid plastic (Tygon) tubing. Although the strength of the motordriven vibration was not quantified, its effects could easily be felt by touching the
vibrating tubing just outside the mouth tube. Once identified, this problem was
easily solved by first pumping the water into an open top reservoir before letting
gravity smoothly feed the water down the mouth tube. This dissipated the motor
driven momentum that was most likely the greatest source of vibration in the
system.
In order to isolate the fish tank from floor vibrations, some care was also
made to suspend the fish tank inside the Helmholtz coil with a series of bungee
cords (weak springs.) The net effect of the bungee cords compare favorably with
that of a conventional air table as measured by an accelerometer (Wilcoxon P31).
Peak to peak
rms
Floor
30-40 mm/s2
7-9 mm/s2
Newport air table
4-5 mm/s2
.7-1 mm/s2
Base of goldfish tank 1.2 mm/s2
.2 mm/s2
Table 4.2 Vibration measurements of different surfaces 0-450 Hz
38
In order to stabilize the goldfish brain with respect to the animal's internally
generated motion, we inserted a 'brain clamp' underneath the hindbrain. Tom
Adelman invented this very useful device. The brain clamp is essentially a very
small hollow metal spatula, with a fine mesh grid on top. It slides underneath the
hindbrain and upon application of vacuum (~0.5 psi), holds the ventral surface of
the hindbrain lightly in place. The exact construction of the device has evolved over
time, but the most recent model was formed by 1) grinding a 1 mm stainless hollow
tube flat, 2) constructing a support well using Torr-Seal (Varian), 3) gluing on a
25x25 m nickel grid (TEM grid, samples from Imaging Facilities, Depart. of
Molecular Biology, Princeton), and 4) overlaying a very thin layer of superglue
(Loctite 4212) to waterproof the Torr-Seal.
Aside from its ability to vacuum-hold the brain in place, the brain clamp
also plays an important role as structural support. Careful post-mortem dissection of
the cranium shows that the hindbrain does not rest flat on the skull, but rather is
offset from the skeletal bone by a few hundred microns. Thus, contrary to the naked
eye, the hindbrain is not in a stable position, but is in an unstable one much like a
floating zeppelin tethered loosely by cranial nerves and the spinal cord. In such a
situation, advancement of pipettes in tissue introduces significant stresses and
instabilities.
4.3 Electrophysiology
Electrodes holders are advanced by a MP-285 manipulator (Sutter
Instruments.) The advancement was made in units of 1 m at the maximum
39
Fig 4.3 Brain clamp
advancement velocity, 2.9 mm/sec. While the MP-285 is a motor/gear driven
system, its maximal speed is comparable to piezo-driven devices. This is useful for
making quick jabs in the brain to reduce tissue-glass adhesion. If the tissue adheres
too strongly to the glass, then the brain will tend to be dragged in unison with
electrode advancement until some maximal stress is reached and a backlash occurs.
Before intracellular recordings are attempted, a gross location of the
integrator region is first mapped using thin, slender extracellular electrodes. These
electrodes are filled with 2M NaCl, ~ 1 m beveled (and sharpened) diameter tips,
and can detect extracellular currents associated with action potential discharge. The
sensitivity of the extracellular electrodes are typically ~50 V peak to peak.
However, strong signatures of extracellular activity do not correspond to
high probabilities of intracellular recordings. This is a somewhat curious
discrepancy as strong extracellular signatures are commonly associated with
somatic regions that produce the largest capacitive discharge during action potential
40
generation. In tandem, the cell soma is virtually the only region of the cell that
possesses the physical dimensions to be patched by a 1.2 m tip. Perhaps, the action
potential initiation zones for integrator cells lie far away from the soma? Thus, in
general extracellular mapping can only help determine a very rough location of the
integrator region and is most useful towards determining the rostral-caudal
coordinate of the region.
The medial-lateral coordinate of integrator cells can be precisely determined
by finding the lateral edge of the medial lateral fiber (MLF) tract which forms the
medial bound of the reticulo-column of cell bodies in the hindbrain. The edge of the
MLF is measured by monitoring the resistance of a flat 1.2 m tip electrode (patch
electrode) as a function of back pressure as it advances in tissue.
Small rectangular current/voltage pulses are used to monitor the resistance
of the electrode tip. As the tissue progressively blocks the electrode tip, the
measured resistance will increase. Pneumatic pressure (N2) can be added to the
back open end of the electrode to generate a hydrodynamic spray that dislodges the
closed tip. The MLF is characterized by the inability for a 2 psi back pressure to
separate the tissue from the tip. (In contrast, a backpressure of 0.5 psi is sufficient to
push away all normal cell surface membranes in the cell body column.)
A similar procedure can be used to determine the precise depth of the start
of the cell body column. The upper fiber tracts on the dorsal surface of the
hindbrain require 5+ psi to penetrate cleanly.
After the mapping procedure is completed, a rough sense of the lateral edge
of the integrator region, its approximate depth, and approximate medial-lateral
41
coordinate has been obtained. At this point, patch-type electrodes are inserted into
the general region with large backpressures 1-5 psi until the appropriate cell depth
has been reached. Backpressure is reduced to 0.25-0.3 psi and the electrode is
carefully advanced. When stable contact has been made with a surface that
produces a 0.3-4 M increase in electrode resistance, a small 100 ms, 0.75 psi
pressure blast is applied, before the back pressure is reduced to –0.2 psi. This
generally results in a G seal within a few seconds. Then shorts bursts of suction is
applied using a mouth tube and is used to break the electrode/membrane seal to
achieve whole-cell recording. Capacitance transients are minimized using the
capacitance compensation knob prior to break in. Series resistance compensation is
maximized by increasing the bridge balance until the measurement circuit is verge
of oscillation in voltage clamp mode or by minimizing the transient associated with
a voltage step.
Small deviations exist between the optimized in vivo protocol for patching
brainstem neurons and standard patching protocols for other preparations (e.g.
cortical slices.) Namely, the backpressures used in the in vivo experiments are much
higher. Through trial and error it has been found that advancing with smaller
standard backpressures like 0.1 psi in the cell body region, invariably results in poor
seals, quite possibly from contaminated tips. If the resistance of the electrode ever
rises to 1 M+ beyond the base resistance and is advanced in tissue for more than
50 m at that elevated resistance, the resultant seal is invariably poor. The
differences in procedure may arise from physical differences between the in vivo
brain and sliced brain. In the in vivo environment, there is a considerable
42
backpressure against the tip of the electrode because it has to push through a
considerable amount of tissue before reaching the target area. In the slice
environment, the top of the hindbrain has been removed and so there is little tissue
to create the backpressure. Thus, a large hydrodynamic pressure has to be
maintained for the in vivo recording to keep the tip clean.
The osmolarity of the optimal in vivo patch solution was also higher than
expected. Conventionally, the patch solution is kept at a lower osmolarity, -20
mOsm, than the surrounding ACSF (272 mOsm). However, it was empirically
found that solutions with ~250 mOsm did not seal well, but solutions with
osmolarities between 260 and 300 mOsm were able to make seals.
The neural tissue is quite tough in the in-vivo hindbrain, and even though
the ventral surface of the brain is gripped by the brain clamp, a ~ 45 angle exists
between the incident electrode and the brain/brain clamp. This in effect generates a
large and unavoidable shearing force in the brain. (The 45 arises from the
curvature of the bone that curves into the skull from the spinal cord, approximately
where the hindbrain begins.) Thus, brain tissue is always pushing back on the tip
with a relatively large force. The eventual relaxation of the brain is suspected of
limiting the recording times of each neuron.
Extracellular electrodes were pulled from 0.5mm/1.00 ID/OD (Sutter Calif.)
capillary tubes using a P-2000 electrode puller and beveled to 3M (using a 2M
NaCl internal solution.) Patch/sharp intracellular electrodes were pulled from either
0.6mm/1.2mm ID/OD or 0.9/1.2mm ID/OD capillary tubes (FHC) using either the
P2000 or the P87 electrode puller (Sutter Instruments) respectively. Before pulling,
43
glass for intracellular electrodes were first sonicated in 100% ethanol for 1hr. DI
water was then flowed through the capillary tubes fitted in a custom holder for
another hr. Capillary tubes were individually blown dry using nitrogen gas and
baked overnight at 80 C. The intracellular solution used for whole-cell recording
was in mM: 125 KCH3SO4, 9.6 K-Hepes, 3 Na2-ATP, 0.3MgCl2, 0.1 K2-EGTA, pH
7.3, 262 mOsm. (Sealing difficulties occurred with 250 mOsm solution.) For sharp
intracellular recordings, the internal solution was 3M K-Acetate. Goldfish sharp
electrodes were pulled thinner and longer than conventional sharp electrodes to
allow the shank to flex with excess vibration. This however, made penetration of
the upper fiber tracts difficult especially during the spring-fall months.
Patch electrodes were pulled to a tip size of 1-1.2 m (bubble number 66.4), resistance 5-7 M. This tip size is larger than what was tried before (0.60-0.70
m bubble number 4.5-5), as it was found that small tips became easily
contaminated and resulted in few good seals. Small tip electrodes generated
insufficient hydrodynamic spray at the tip to cleanly penetrate the upper fiber tracts
(regardless of the backpressure used) for 4”-6” sized goldfish.
Extracellular voltage waveforms were band pass filtered at 100 Hz - 10 kHz
using an 8-pole bessel filter (Cygnus). Current monitor signals were band pass
filtered between 0 and 5 kHz or 0 and 2 kHz. Intracellular voltage waveforms were
filtered between 0-30 kHz as set internally by the AxoClamp 2B (Axon
Instruments). All signals were sampled at 25 kHz and recorded using a Digidata
1322A (Molecular devices, Axon Instruments)
44
4.4 Eye tracking system
Eye position was measured using the sclera search-coil technique [84].
Small copper coils (5.4 mm, 40 turns, Sokymat) were sewn onto goldfish sclera
prior to the experiment using TG-100 sutures (Ethicon). Eye movements induced an
angle difference between the Helmholtz coil system (CNC Engineering, Seattle
WA) surrounding the fish tank and the eye coil. The induced coil current is
amplified by phase sensitive detectors before sampled (25 kHz) and recorded
(Digidata 1322A). The resolution of the eye tracking system is between 0.05 and
0.1. As the MP-285 introduced a substantial amount of metal into the Helmholtz
coil, the system was recalibrated using an eye coil mounted on a protractor where
the left and right goldfish eyes would normally be located
45
5 Results of intracellular measurements using
whole-cell patch recordings
5.0 Comparison of whole patch recordings with sharp recordings
We recorded eight Area I integrator cells using whole-cell patch recordings.
As seen in Fig 5.1, the whole-cell patch technique demonstrates considerable
improvement in temporal resolution over the sharp recordings. The patch
recordings reveal the existence of small 0.2-3 mV excitatory postsynaptic potentials
(EPSPs) that last ~ 5 - 10 ms.
In the sharp recordings, the EPSPs are obscured. Partly, this is because the
EPSPs generally have a prominent sharp peak (~ 1 ms) that would be highly
attenuated by the RC filter of the high resistance tip. The f3db for an RC filter is
1/2RC or about 1/2(100 )(10 pF) ~ 159 Hz. The f3db point corresponds
roughly to a reduction in voltage by ~30%. For a 1 ms, 1 kHz signal, the voltage
reduction is close to ~84%. Thus the initial peak would be nearly abolished in sharp
recordings. Without the sharp initial peak it is difficult to separate the EPSPs at
high frequencies.
For 7/8 Area I integrator cells recorded using the patch technique, the input
resistance Rcell is 6626 Mmean +/- std) (This was assessed using small
voltage pulses in voltage clamp mode immediately after breaking the seal.) The
eighth cell recorded had an unusually high input resistance of 400 M It's unclear
whether or not the high input resistance was an artifact or reflected a very small cell 
46

Fig 5.1 a) Intracellular waveform from a sharp recording b) Intracellular recording
from a whole-cell patch recording
Fig 5.2 a) Eye position b) Hyperpolarized intracellular waveform reveals steps in
membrane potential c), d) Expanded view of membrane potential
47
geometry. In comparison, previous sharp experiments [20] reported an Rm of 30
 M

The apparent resting membrane for the 8 cells was -69 +/- 5 mV (after
correcting for the liquid junction potential.) Previous sharp recordings reported -61
+/- 7 mV. The difference in membrane resistance and resting membrane potential
between the patch recordings and the sharp recordings are consistent with the
literature [86]. Sharp recordings puncture the cell and introduce a leak resistance
that
lowers
the
apparent
cell
resistance
as
well
as
depolarizes
the
membraneComparisons between the two cell resistances suggest that sharp
recordings introduce a 60 M leak resistance in goldfish integrator cells
The apparent membrane time constant as assessed by negative squarepulsed current injections was 12.0 +/- 1.9 ms for n=4 cells. This is a little bit lower
than the previously reported values of 16.3 +/- 3.9 ms.
Hyperpolarizing the membrane with negative current injections (up to -0.3
nA) reveals the existence of membrane steps that are tightly correlated with eye
position for all eight cells as expected from previous reports (Fig 5.2). For the 8
eight cells recorded, the average range for the membrane steps was 7.7 +/- 2.8 mV
over a complete left-right scanning cycle. Previously using sharp recordings, the
recorded range was 3.7 +/- 2.2 mV.
The origins of the differences between the membrane time constants and the
ranges of the membrane steps between the two techniques are unclear. (The latter
perhaps can be attributed to an increase in apparent cell resistance.) The goldfish
hindbrain is opaque, and it is not possible to target specific cell types/morphology.
48
Sharp electrodes and whole-cell patch electrodes used "blindly" may have different
biases in targeting cell types. Sharp electrodes, with their fine point, may potentially
record from all structures while patch electrode with their large ~1 um tip would
generally only record uncovered somatic regions.
5.1 Resolved EPSPs have a short time duration
The increased temporal resolution of the patch recordings revealed that the
visible portion of the waveform is composed of EPSPs. Unlike predictions made by
recurrent network models, the observed EPSPs have short time scales ~5-10 ms.
Example EPSPs waveforms are shown in Fig 5.3.
Most EPSPs possess a sharp initial peak followed by a slower phase. Some
EPSPs do not possess the fast phase, but it is possible that travel down passive
portions of the dendritic cable had smoothed out high frequency components.
Standard electrophysiology amplifiers offer two recording modes: current
clamp mode and voltage clamp mode. In current clamp mode, current is injected
into the electrode such that the total current flowing into the electrode is set to zero.
This nullifies the voltage offset that arises from the resistance of the tip. In voltage
clamp mode, current is injected into the electrode such that the voltage at the tip is
set to a constant value. This creates a uniform potential at a local region inside the
cell surrounding the tip and reduces capacitive charging of the membrane as well as
axial resistance. (In a realistic cellular morphology, the field set by the tip is not
uniform. Nor does the field extend far down the dendrite in an active cell as the
opening of local conductances from synaptic inputs shunt currents. [110])
49
Fig 5.3 Shapes of EPSPs recorded under current clamp
Nevertheless the voltage clamp mode offers some improvement in temporal
resolution over the current clamp mode. To analyze the shape of EPSP waveforms,
we chose the largest EPSPs (that are isolated n=17) under the assumption that they
represent inputs most proximal to the recording site and fitted the falling phase with
double exponentials Table 5.1.
ae
a
b
c
d

t
b
 ce

t
d
Mean
Std. Deviation
0.060 nA
0.30 ms
0.061 nA
3 ms
0.023 nA
0.17 ms
0.023 nA
2.2 ms
Table 5.1 Double exponential fit of EPSP waveform in voltage clamp mode
In contrast, under current clamp mode, the fast time constant of the falling
portion of waveform averaged 0.73 +/- 0.50 ms. The rising phase of the EPSPs
50
recorded were similar under both modes, 0.63 +/- 0.12 ms for current clamp and
0.53 +/- 0.16 ms for voltage clamp. (Unfortunately, the voltage clamp method is
not compatible with the eye tracking system as EMF from the Helmholtz coils
saturates and overloads the voltage clamp circuit.)
The peculiar sharp rise of the EPSPs suggests that mixed conductances
underlie their generation. The shape of the EPSP is similar to dendritic spikes
observed in CA1 hippocampal neurons that possess mixed NMDA, AMPA
conductances [112, 113]. Synaptic junctions of goldfish Mauthner cells that posses
mixed NMDA, AMPA components in conjunction with a gap junction also exhibits
this basic shape.
5.2 EPSPs increase with membrane potential and eye position
Network models of persistent firing predict that the number of EPSPs
increases with eye position while models of persistent firing based on intrinsic
mechanisms suggest that variations in EPSP frequency do not play a prominent
role. Thus accurately counting the EPSPs in the waveform is an important problem.
However, counting small EPSPs with short time durations is a troublesome
procedure at the high rates that are required to construct the waveform. We will
illustrate the problems with a simple model.
Suppose a neuron is a perfect single compartment RC circuit and each EPSP
represents a stereotyped current injection at t0. Then
Cm
dV
V

 I (t )
dt
Rm
(5.1)
I (t )    (t  t k )  I 0
k
51
As we observe V, we can recover the times of each input using a simple Fourier
transformation.



 F V  iwC m  1  

Rm  

1 


(
'
)
t
t
F

k

 (5.2)


F
I
0






In reality, a wide variety of EPSPs can be found and the exact distribution is
unknown. There exist many 2-3 mV EPSPs, but it is unclear whether or not they are
the dominant sources of input during the elevated membrane potentials. Moreover,
as EPSPs travel down the dendritic tree, their shapes flatten and easily blend
together. I0 is thus essentially unknown. The most serious problem with the Fourier
transform method is that it assumes an implicit mechanism, that is
I (t )    (t  t k )  I 0 . However if there exist hidden regenerative mechanisms
k
with the form of I (t )    (t  t k )  I 0  H (t  t ' ) , where H is the Heaviside
k
function, then the Fourier transform would yield an answer but it would be
incorrect. In general regenerative plateau potentials that underlie the fast
fluctuations would empirically be unobservable and presents a "hidden problem."
The fact that we can only observe the top of the waveform is a fundamental
problem and, as we have shown, a great many unknown factors affect the
construction of the whole waveform. While it is possible to attempt to brute force a
52
reconstruction of the waveform, the great number of variables that can be
manipulated to fit the waveform would make such reconstructions of dubious value.
To some extent the counting problem is alleviated by the sharp initial rise of
the EPSP that provides a prominent feature with which to count. However, at high
enough rates, even sharp peaks will tend blend together. We can see this by
simulating the integration of a realistic 1 mV EPSP using a RC model with a 12 ms
time constant.
At 300 Hz and perfect periodicity, individual EPSPs are clearly discernable.
(Fig 5.4 The green crosses denote the apex of an EPSP.) However, at 3000 Hz, the
tops of the EPSPs make a ripple that would barely be observable above the
background noise. If we add a small amount of noise, a 1 ms jitter, the top of the
waveform develops a frothy top Fig 5.5. A single sharp rise and fall of the
fluctuations can be composed of multiple EPSPs. If the arrival times are random,
Fig 5.6, then the waveform develops a significant amount of fluctuations that is
exaggerated by the asymmetric aspect ratio of the base EPSP. If we try to count the
sharp rises as indicators of EPSP frequency, then we will significantly under count
the true frequency as shown in Fig 5.7. Furthermore, in realistic cell morphologies,
the majority of EPSPs will arrive at the dendritic tree and micro-inflections that
indicate the arrival of an EPSP will be smoothed by cable properties. Thus counting
the number of EPSPs by sharp rises in the voltage membrane will always
undercount the true number of EPSPs at high frequencies.
In reality, only a fraction of the EPSPs arrive near the soma. The rest arrive
further distal in the dendritic tree and become submerged as part of the
53
Fig 5.4 Simulated periodic EPSP integration in a simple RC model at
a) 300 Hz b) 3000 Hz c) expanded view of b)
Fig 5.5 Simulate periodic EPSP integration with random 1 ms jitter at
a) 3000 Hz b) zoomed in view of a) c) further expanded zoom of a)
54
Fig 5.6 Simulate EPSP integration with random arrival times a) 3000 Hz
b) zoomed in view of a) c) further expanded zoom of a)
Fig 5.7 a) Measured number of sharp rises as a function of membrane
potential in a simulated model RC circuit b) ratio of measured frequency to
the true frequency
55
'unobservable' portion of the waveform. For the EPSPs that ride on top of the
waveform, we can count them using their initial sharp rises. The criterion for their
selection is a minimum rise rate of 2.5 mV/ms.
As the sizes of the EPSPs change with eye position, a better metric to judge
the rate of EPSPs would be to weight it by its size to produce a weighted frequency.
Fig 5.8 shows the results of the counting procedure for one cell. The frequency of
the observable EPSPs oscillates in synchrony with the average membrane voltage.
Fig 5.9 shows a plot between the EPSP frequency and average membrane voltage
(over a 100 ms period.) We see in Fig 5.9 c), d) that EPSP rate generally rises with
average membrane potential but that a leveling of the counted EPSP frequency
occurs after Vm is ~ 8 mV above the baseline voltage. The origin of this leveling
can most readily be explained by the blending of the peaks as predicted by the RC
circuit model explained earlier. That the leveling voltage occurs much later than
predicted is most likely due to smoothing of the distally arriving EPSPs via cable
properties that forms the submerged uncountable portion.
Regardless of the origins of the leveling in the apparent count of EPSP rate,
the counted EPSPs are linear over a substantial portion of the range of the
membrane voltage. This is important as the integrator has to maintain eye stability
at low rates, (low average membrane potentials), as well as it maintains stability at
high rates (high average membrane potentials). This issue will be discussed further
in the later discussion section.
Summary plots for the other 7 cells are located in the appendix A.
56
As mentioned before, many assumptions have to be made to estimate the
number of EPSPs necessary to make up the whole waveform. Nevertheless, we will
attempt to estimate this number using some conservative assumptions.
To start, while the nature of the membrane waveform underneath the frothy
fluctuations is unobservable, the fluctuations on top are clearly of synaptic origin
Fig 5.11. If we segment the waveform into 100 ms bins and attribute the waveform
above the minimum voltages of each individual segment to barrages of EPSPs, we
can estimate the number of EPSPs required to make the fluctuations using the RC
model.
I epsp t   C m
dV V  Vm  VL  Vm 


dt
Rm
Rm
 I t dt  N
 I t dt
(5.3)
epsp
0
VL is the minimum voltage of the 100 ms segment and I0 is a stereotypical 1mv
EPSP, shape a) in Fig 5.14. Rm is the input resistance of the cell and Cm is inferred
from the measured time constant of the cell. Results are shown in Fig 5.10.
We can also attempt the same procedure for the total waveform to estimate
the number of EPSPs necessary to generate the full range of membrane voltage
steps in Fig 5.12.
While the peak frequency of the counted EPSPs was between 700-800 Hz,
the estimated peak frequency of the EPSPs necessary to make the fluctuations and
the total waveform was roughly between 1300 Hz and 5500 Hz respectively.
57
Fig 5.8 a) Intracellular membrane voltage b) Counted freq. of visible EPSPs
c) Weighted freq. of visible EPSPs
58
Fig 5.9 a) Freq. of EPSPs vs. average membrane voltage (100 ms) b)
Weighted freq. of EPSPs vs average membrane voltage (100 ms)
Small variations in the shape of the stereotyped EPSPs have a large impact
Fig 5.10 Frequency of EPSPs necessary to create the fluctuations (100 ms)
of the waveform. The red line denotes the lower bound of the fluctuation.
59
on the estimation of the required EPSP frequency Fig 5.13, 5.14. The shapes of the
distal EPSPs are unknown and may possess sizes larger than the observable
proximal EPSPs.
However, even when a moderate sized EPSP is used as the stereotyped
EPSP for frequency calculations, the observable (counted) EPSPs is a significant
fraction of the estimated fluctuation EPSPs (~60%) and estimated total number of
EPSPs (~15%-20%) Fig 5.15. Thus, a substantial fraction of the synaptic input
increases with the average membrane potential and eye position as predicted by
network theories of persistent firing.
Moreover, the estimated fluctuation EPSPs themselves while not completely
counted, constitutes a formidable fraction, ~35%, of the estimated total number of
EPSPs at the most depolarized membrane levels.
Fig 5.11 Expanded view of 5.10 to illustrate the construction of the lower voltage
bound used to outline the fluctuations.
60
Fig 5.12 Frequency of EPSPs necessary to construct entire waveform
Fig 5.13 Frequency of EPSPs necessary to construct entire waveform if different
EPSP shapes are used
61
Fig 5.14 Different shapes of EPSPs used in Fig 5.13
Fig 5.15 Ratio of counted EPSPs to the total estimated number of EPSPs and the
ratio of the number of estimated fluctuation EPSPs to the total estimated number of
EPSPs. EPSP shape a) in Fig 5.14 are used for the calculation.
62
The importance of the fluctuation EPSPs can be illustrated in another way.
As can be seen in Fig 5.16, the peak-to-peak voltages that are generated by the
fluctuations can become quite large in comparison to the total range of the
membrane steps. We segment the waveform into 25 ms segments and plot the peakto-peak voltages of each segment as a function of the lower bound of the membrane
voltage of each segment Fig. 5.17 and as a function of time Fig. 5.18.
The size of the fluctuation is fairly large relative to the membrane step itself
and forms ~30-40% of the total waveform at the peak membrane step positions Fig
5.18 b). The size of the fluctuations/synaptic barrages increase with the size of the
membrane step. This can be explained in a natural way as increases in EPSP
Fig 5.16 EPSPs cause large fluctuations in the membrane voltage
63
Fig 5.17 Peak-to-peak fluctuation increases with membrane voltage
Fig 5.18 a) Peak-to-peak fluctuation oscillates with time b) Ratio of peak-topeak to VLowerBound
64
frequency will increase the probabilities that multiple EPSPs are coincident over the
time-scale of a single EPSP.
5.3 Are integrator cells driven by fluctuations in synaptic input or by the
average increase in synaptic input?
One old but still unresolved question in neuroscience is whether neurons
encode and utilize information through the average firing rate or whether or not a
time code is utilized where each action potential is individually meaningful.
Similarly, we can ask whether or not the firing of a goldfish integrator cell is
driven primarily by fluctuations in the synaptic input or by changes in the average
membrane potential. As the two variables are intimately correlated, it is hard to
distinguish the effects through purely observational measurements. But we will
offer some circumstantial experimental evidence that fluctuations may play a large
role in driving the firing of integrator cells. In the next chapter, we will present
numeric simulations using a conductance based model neuron to show how such
sensitivities may arise.
Fig 5.19 shows an example of an integrator cell operating in its normal
regime (non-hyperpolarized.) The apparent threshold of the action potential is
denoted by a green circle and exhibits a sharp kink at its onset. The membrane
voltage preceding the apparent threshold of the action potential shows a nonstereotyped behavior suggesting that it is not part of the action potential itself Fig
5.20. Every action potential is preceded by a sharp rise in the membrane voltage
(Fig 5.21) suggesting that it is preceded by a fluctuation event. Occasionally it is
65
possible to observe small inflections that are indicative of multiple EPSPs. Fig 5.22
shows that the average threshold (n=377) of action potentials always occur near the
top of the voltage range preceding it, suggesting that something must drive the
membrane above the local average to elicit the action potential Fig 5.22.
Fig
5.19 a) Integrator cell operating in its normal regime b) Expanded view of a single
action potential
The apparent threshold of the action potentials increases with the average
membrane potential Fig 5.23. This is interesting because it suggests that increases
in the average membrane potential do not reduce the threshold necessary to elicit an
action potential. The more likely explanation for this curious phenomenon is that
the action potential initiation zone is located distal from the pipette tip. As
mentioned previously, the only region that is amenable to blind patching with our
tip size ~ 1 m is the soma. Some neurons such as peripheral motor neurons and
66
Fig 5.20 Expanded view of single action potentials from Fig 5.19
Fig 5.21 Moderately expanded view of Fig 5.19
67
Fig 5.22 a) Action potential are initiated at the top of the preceding voltage range b)
Average action potentials initiation is in the upper percentile of the voltage range c)
Average action potential threshold is above the preceding average membrane
potential
68
retinal ganglion cells obey the classical picture of the action potential initiation zone
being localized in the axon hillock adjacent to the soma. However, experimental
evidence shows that many other neurons contain a distal initiation zone 40-70 ms
down the axon. The relatively narrow diameter of the axon electrically uncouples
the initiation zone from the soma. Thus charge, (in the form of a traveling action
potential), will flow from the initiation zone and will be injected on top of the
somatic waveform. This would give rise to an apparent increase in the threshold.
The sharp kink of the threshold itself is also an indication that the initiation
zone is distal of the soma. The voltage sensitive sodium and potassium channels
discovered by Hodgkin and Huxley give rise to a smoother rise for the action
potential initiation than what is found in vivo in cortical cells and here in goldfish
integrator cells. Using experimental recordings and numeric simulations
McCormick et al., showed [114] that the discrepancy arises from cable properties of
the axon. Axonal recordings showed that at the initiation site, the rise of the action
potential is smooth, but the threshold is sharpened after propagation to the soma.
We will show in the next chapter that having a distal initiation zone lowers
the threshold for action potential generation and makes the cell highly susceptible
to fluctuations in the input.
69
Fig 5.23 Action potential threshold increases with the average (100 ms) membrane
potential
5.4 Discussion
Through direct measurements, we observe increases in synaptic activity for
7/8 cells with increases in average membrane potential and eye position (see
appendix A.) For all eight cells, we observe an increase in membrane fluctuations
(that are composed of EPSPs) with increases in average membrane potential and
eye position. At the most elevated eye positions, the membrane fluctuations still
constituted a significant fraction of the total wave form, 31 % +/- 11%, (pop. range
15%-46%)
Our measurements are consistent with network theories of persistent firing
that predict an increase in synaptic rate. The sizable contribution that the
fluctuations make to the average waveform suggest that even if long lasting plateau
potentials underlie the voltage waveform, network mechanisms play an important
function in the operation of these cells.
70
The importance of coincident EPSPs in forming fluctuations can explain
some puzzling observations from previous work. Previous [21] pair recording
experiments discovered that ipsilateral Area I - Area I firing rates are correlated
over very short time scales (~ 10ms) at low firing rates, but lose their correlation as
the firing rate increases. The tight correlation times as well as the loss of correlation
at high firing rates is consistent with fast fluctuations playing an important role in
generating the output of the cells. First, if long lasting synaptic events (~100 ms)
dominate the system, then the correlation times would be expected to be on order of
the synaptic event itself ~100 ms. The observed EPSP timescale is on the order of
5-10 ms and agrees more readily with the observed correlation times of ~ 10 ms. At
low firing rates (and low synaptic input rates), highly coincident EPSPs are
necessary to push the membrane voltage across threshold and thus produce a
correlated firing rate between pairs of Area I cells.
In general, it's interesting to note that naturally occurring volatility at high
EPSP frequencies introduces a significant non-linearity into the system. Perhaps,
this is the system's method of adding robustness to network dynamics that all
theoretical models lack?
We can toy with this idea in two simple ways. If a neuron is triggered by the
average membrane potential, then the output  N , where N is the number of inputs
over a unit time. However, if a neuron is triggered by fluctuations that are caused
by coincident EPSPs, then the output  N , (where the square root comes from
the standard deviation of a poisson process.) For a stationary output, the expected
change in output for the former case is dN , while for the latter the output
71
~
1
N
dN . At high N, the non-linear neuron would buffer the system from synaptic
noise.
Earlier, we showed how a simple mathematical model v(t )  
dv
 kv(t ) ,
dt
of positive feed back using a linear term produces a solution that decays
exponentially to zero with a time constant T 
feedback to a sublinear one, such that v(t )  
two stable states 


1 k
. If we change the linear
dv
 k v(t ) , then the solution has
dt

dv
 v k  v . The concept of memory of course is a little bit
dt
different in the two models. In the former, there is only one stable state, the zero
firing rate, and the quality of the memory is associated with the time constant of the
exponential. In the later case, both zero and k2 are stable states, with k being an
attractor. Thus the quality of memory is perfect in the non linear case and we have a
basic flip-flop model. It's not clear how to extend this one dimensional model into a
network model that shows arbitrary tuning or very fine discrete steps. Nor do
integrator cells show preferred firing rates that this toy model would predict.
However, after 'training' the goldfish eyes to leak using a moving environment, and
presumably altering the synaptic weights of the network, the goldfish eyes decay to
shifting null positions. (That is the eyes do not always decay to the same neutral
position after a saccade.) Similar experiments that inactivate partial areas of the
primate integrator regions also suggest the existence of null positions [115]. These
72
suggest that the system possess inherent preferred modes that are masked while the
network is fully tuned.
Regardless of how fluctuations of synaptic input are directly impacting the
integrator circuit, the importance of fluctuations on neuronal behavior is gaining
wider acceptance in the field. Recently it was discovered that discrete synaptic
barrages are responsible for preserving contrast selectivity in orientation tuning in
the visual cortex rather than the (low) average membrane potential [116].
As integrator neurons must maintain eye stability at both nasal (low firing
rates) and temporal positions (high firing rates), network theories for persistent
activity show also explain how coincident EPSPSs that form fluctuations are
utilized..
In the next chapter, we will examine using numerical simulations how
neurons may be physiologically biased towards fluctuating inputs rather towards a
slow averaged input.
73
6 How neurons may operate in a fluctuation
dominated regime
6.0 Influences of a distal action potential initiation site
In this chapter, we will discuss how a distal action potential initiation site in
the axon may enhance a neuron's sensitivities to fluctuations. In the classical model
of a neuron, the action potential initiation site is located in the axon hillock/initial
segment adjacent to the cell body. This model is true for peripheral motor neurons
and retinal ganglion cells.
However, recent advances in electro-physiology and imaging techniques
suggest that not all neurons initiate their action potentials in peri-somatic regions.
Dual patch recordings of the soma and the initial axon fiber by Stuart et al [93],
suggest that the initiation zone in cortical pyramidal cells is located at least 30 m
distal in the axon. Later imaging studies using voltage sensitive dyes confirm that
the axon initiation zone is between 35-40 m distal from the soma [94]. In Purkinje
cells, the initiation zone is located even further down the axon, ~75 m near the
first node of Ranvier. These and other other examples [90, 91, 92, 95-98, 103],
suggest that a peri-somatic initiation zone is not necessarily a common feature of all
neurons.
As suggested in earlier chapters, certain features of Area I cells hint that the
action potentials are initiated distally as well. 1) There is little correlation between
the location of large extracellular signals and the ease of making patch recordings in
74
the region (which would be indicative of somatic surfaces) 2) The apparent increase
in action potential threshold with average membrane potential can most
parsimoniously be explained by charge injection via a distal initiation site 3) Sharp
kink at the threshold of action potential initiation suggest that the action potential
had traveled from elsewhere.
The available evidence is so far speculative, but it is informative to probe
the consequences of a distal initiation site. We will show that under certain
conditions, a distal initiation site will increase the cell's sensitivity to fast
fluctuating signals.
6.1 Hodgkin Huxley Channels
To understand how neurons transform their synaptic input into action
potential discharges, we must first discuss the origin of action potential initiation in
depth.
The mechanism was originally elucidated by Hodgkin and Huxley in 1952
[53]. In the Hodgkin-Huxley (HH) model, the total membrane current is the sum of
the capacitive current, the two voltage sensitive ion channels, INa and IK and a leak
current that is voltage insensitive.
I (t )  C m
dV
 g Na m 3 h(V  E Na )  g K n 4 (V  Ek )  g leak (V  E Leak )
dt
(6.1)
In HH's original formulation, m, h, n refer to gating particles that
independently activate/inactivate the ion channels. Each gating particle can be in
75
one of two states, permissive or nonpermissive, and the transition between the two
was hypothesized to be governed by first-order kinetics.
n
m
n 1  n
n
h
m 1 m
h 1  h
m
(6.2)
h
Mathematically, this corresponds to three first-order differential equations,
dn
  n (V )(1  n)   n (V )n
dt
dm
  m (V )(1  m)   m (V )m
dt
dh
  h (V )(1  h)   h (V )h
dt
(6.3)
Using the voltage clamp method, HH were able to experimentally determine
the values of the rate constants. Plotting the steady state values for n, m, h in Fig
6.1, we see that n and m can more properly be termed channel activation variables
while h is a channel inactivation variable. The initial exponential rise in n, and m
describes a very striking relationship between the conductances of the channels and
the membrane potential. At higher depolarization voltages, the currents saturate and
the overall level of the sodium current is reduced by the inactivation variable h.
To gain a better understanding of the temporal dynamics of the model, the
's and's of Eq. 6.3 can be transformed to a voltage dependent time constant n(V)
and a steady state value nV). Then we have
dn n  n

dt
n
n 
1
n  n
n 
n
n  n
(6.4)
While the steady state values nV), mV), hV) are monotonically
increasing and decreasing functions respectively, the voltage dependent time
76
constants have a bell shaped dependence (Fig 6.2). There is a striking discrepancy
between m (sodium activation) with h (sodium inactivation) and n (potassium
inactivation).
Fig 6.1 Steady state Hodgkin-Huxley gating variables as a function of
membrane voltage
Across all membrane voltages, n and h are approximately the same, but m is
almost an order of magnitude smaller. The consequences of this effect can be
explicitly shown if we integrate Eq. 6.4. Experimentally, this would represent
voltage clamping the neuron and very quickly bringing it from the resting state to
some voltage V'. (n0 represents the value of the gating variable at resting membrane
potential. Typically, this value is very small, ~1% for potassium.)
n(t )  n  (n  n0 )e t /  n (V ')
77
(6.5)
Fig 6.2 Voltage dependent time constants of the gating variables
Fig 6.3 Time course of GK and GNa after a sudden membrane change
from Vrest to Vrest + 40 mV.
78
The sodium current quickly rises due to the small activation time constant m but
will gradually decline as the longer inactivation time constant h sets in. The
potassium current rises more gradually than the sodium current (Fig 6.3)
We can now understand how action potentials are initiated in the HH
framework. Transient synaptic current elevates the membrane potential. This
activates sodium channels that will further depolarize the membrane. If the initial
current is strong enough, it will initiate a positive feedback between sodium channel
activation and membrane depolarization. This will create a fast sharp depolarization
of the membrane. On a longer time scale, the membrane depolarization will activate
potassium channels and inactivate sodium channels. This will eventually bring the
membrane voltage back to the resting state.
In order for the initial current to start the fast sodium cycle, it must first
cross a threshold. The origin of the threshold can be understood by considering an
instantaneous injection of current. As n and h activate fairly slowly compared to m,
we can replace them with basal constants in this thought experiment. The HH
currents can then be written as
I V   g K n0  (V  E K )  g Na m(V ) 3 h0(V  E Na )  g m (V  E Leak )  I Inj (t ) (6.6)
4
The total current ITotal makes a U-shaped bend around the x-axis. (Fig 6.4)
The point around V = 0 is an attractor. Small injections of positive currents will
shift the voltage up but the small change in INa will be balanced by larger changes in
IK and ILeak. This will generate a net outward current that will bring the membrane
voltage down. Similarly, an initial hyper-polarization of the membrane will
79
Fig 6.4 Instantaneous I-V curve near the resting membrane potential
Fig 6.5 Slightly slower than instantaneous I-V curve near the resting
membrane potential
80
generate a net inward current that will increase the membrane voltage and restore
the membrane voltage to its resting value.
However, if the initial current injection was able to bring the system pass
~2.6 mV, then the system will generate a net inward current that will continue to
increase the membrane potential, leading to runaway positive feedback.
If the initial current injection was a little bit slower, then INa will be reduced
by the inactivation variable h and this would in effect shift the threshold to the right
to a higher voltage (Fig 6.5).
The generation of the action potential is not only dependent on the initial
current being strong enough to stimulate the cell above a certain threshold, but the
threshold is also dependent on how quickly the current is injected as sodium
channels will inactivate and potassium channels will increasingly open. The full
time dependent solution is a little more complicated than the instantaneous model as
the potassium current and sodium inactivation variable h are not constant on long
time scales.
To illustrate the effect fully, we used the simulation software Neuron
developed by Hines and Carnevale [99] to numerically compute the relationship
between the threshold current and the rate of change in current to evoke an action
potential (Fig 6.6). We modeled a single compartment space clamped giant squid
axon, 500 m wide, 100 m long, with the conductance values as originally
obtained by HH. (The time step of the simulation is 5 s and the temperature is
6.3. We simulated injections of different linear ramp currents and obtained the
relationship between the threshold current and the ramp duration that is necessary to
81
Fig 6.6 Example ramp current injections into a hypothetical space clamped
squid axon. The difference between the peaks of the two ramp injections is 0.1
nA.
Fig 6.7 Relationship between the threshold current and the ramp duration
necessary to generate an action potential in a model squid axon
82
evoke an action potential. We also recorded the membrane voltage of a just-subthreshold ramp injection as the voltage threshold of that ramp duration.
In Fig 6.7, we see that a ~10 ms ramp requires the lowest peak current to
elicit an action potential. Below 10 ms, the threshold increases due to the extra
current necessary to charge the membrane in a small amount of time. Above 10 ms,
the threshold increases for the reasons we have previously mentioned.
Fig 6.8 Measured somatic voltage threshold of ramp current
injections to elicit an action potential in a model squid axon.
The threshold voltage decreases as the ramp duration is decreased,
eventually leading to the minimum instantaneous threshold.
6.2 Cable geometry on site of initiation
So far we have discussed action potential generation in a single
compartment. In a real neuron, finite cable geometries introduce complexities to the
83
problem [107, 108]. This is because a significant portion of the current that is either
injected or arise from the activation of channels flows longitudinally away from the
site of initiation. Thus less current is available for polarizing the membrane and the
effective voltage threshold is higher. Compartments such as the cell body and
dendrites are large effective current sinks. For Area I neurons, we estimate its total
capacitance to be over 150 pF from the measured membrane time constant and cell
resistance. This is reflective of the extensive dendritic tree that was revealed in
previous labeling experiments.
6.3 Numeric modeling with neuron
Our model Area I neuron is based on a simple model for cortical cells
developed by Yuguo et al, [118]. Their model is adapted for our purposes by the
addition of a tapered axon hillock and the segmentation of the axon into two parts
to study distance related effects. We used the suggested conductances values. In
Yuguo's model, the entire axon is uniformly covered with a HH conductance that is
ten times higher than the somatic conductance. We follow his example and set the
compartment with the initiation site to have ten times higher conductance than the
other compartments which otherwise have the same conductances. The dendrite
used by Yuguo provides a capacitance load of ~76pF and is an underestimate of the
dendritic capacitance. Our model neuron is simulated at 20C with 5 s time steps.
To illustrate the effects of varying the action potential initiation site, we
injected current ramps into the somatic compartment as reflective of the soma's
geometric role as the site for current integration and recorded the current threshold
and voltage thresholds necessary to elicit an action potential.
84
Fig 6.9 Current threshold vs. ramp duration for ramp injections in
a model Area I neuron with and without dendrites.
Fig 6.10 Peak somatic voltage threshold vs. ramp duration for ramp
injections in a model Area I neuron with and without dendrites.
85
The action potential initiation compartment is set by increasing its conductance to a
value ten times higher than the other compartments.
Length (m) Diameter (m) Segments gNa (ps/m2 ) gK (ps/m2 )
gLeak
Dendrite
3000
5
60
800
150
0.33
Soma
16
10
4
800
150
0.33
Hillock
10
1-10
10
800
150
0.33
Axon near
30
1
15
800
150
0.33
Axon far
30
1
15
800
150
0.33
Table 6.1 Parameters of model Area I cell. The compartment with the action
potential initiation zone is set by increasing its conductance by a factor of 10.
As a large current sink, the dendrite has a tremendous capacity to influence
neural discharge properties [87]. It also enhances differences between different
locations of the action potential initiation site. In Fig 6.9b, and Fig 6.10, we see that
without a dendrite, there is little difference <~3% between having the initiation site
located in the proximal (Near) axon segment and the distal (Far) axonal segment.
However, with the addition of a 76 pF dendrite, an 11% difference in the current
threshold and a 32% difference in somatic voltage threshold are created.
The dendrite accentuates inherent geometric differences between the two
initiation sites. The overall threshold is increased for both sites with the addition of
a dendrite as the dendrite acts as a large current sink. At short time scales the
voltage and current threshold increases less for the distal section because the
relatively large axial resistance of the proximal axonal segment uncouples the distal
86
segment from the dendrite. Thus, it is easier to generate an action potential in the
distal segment. On a longer time scale, the advantage of rapidly raising the voltage
of a low capacitance distal segment with fast sodium channels is lost and the distal
segment also has to contend with the potassium current from the proximal axonal
segment. Moreover, just as the proximal axonal segment acts as a barrier to
dendritic influences, it also acts a voltage divider to lessen the impact of the current
stimulus.
This voltage divider is also frequency dependent. Intuitively (for a
neuroscientist), this must be true as axons can propagate high frequency action
potentials but do not so readily propagate slow waveforms. By using a perturbation
scheme developed by Chandler [101], Mauro [102] showed that the HH equations
can be thought to contain an inductive component for small subthreshold voltages.
For the potassium channel he derived Eq. 6.8 (and a similar set of equations for the
sodium channel.)
dI 

 g n  L I  V
dt 

a
gn 
n  n
1
L
a
(6.8)
 d   d an   n  
a  4 g k n 3 (V  Ek )  n   n

dV

 dV  
Tithe association of an inductance with the membrane is at first a little bit
strange as ostensibly there does not appear to exist any common forms of
inductances such as coils of wires or loops of magnetism that can be associated with
87
the neural membrane. However if we return to the basic definition of inductance
V L
dI
, we can imagine how the neural system with its time and voltage
dt
dependent conductances can readily produce such a phenomenon. And it is well
known that RLC circuits will bandpass filter signals. Fig 6.11 shows the frequency
dependence of transferring a 1 mV somatic sine wave to the distal axon segment for
our model neuron.
Fig 6.11 Frequency dependence of somatic voltage transfer to the distal
axonal compartment in the model Area I neuron
Fig 6.12 and Fig 6.13 show comparisons between a hillock initiation zone
with proximal and distal axonal initiation sites for ramp injections. The more distal
the initiation zone is from the dendrites, the larger the effective threshold gap
between slow and fast injections. The absolute threshold for the fast currents also
diminishes as distance from the initiation zone.
88
Figure 6.12 Influence of the location of the action potential initiation site on
the current threshold
Fig 6.13 Influence of the location of the action potential initiation site on
the somatic voltage threshold
89
Aside from the aforementioned consequences that arise from basic circuit
theory, a distal initiation site allows the neuron two other ways to increase its
sensitivity to fluctuations. The first is a distal initiation site would allow the neuron
to increase the conductance of the initiation zone without undue perturbation to the
cell's overall conductance. This would lower the overall threshold. We simulated
this by increasing the distal axonal conductance by a factor of fifty (instead of a
factor of ten. (Fig 6.14, Fig 6.15)
The exact density of sodium channels in the initial segment is unknown
although some studies suggest that it may be as high as that at the node of Ranvier
~20-30 ns/m2 [119, 120]. A recent experiment that utilized direct patch-clamp
recordings from axon initial segments of cortical pyramidal cells suggested that the
density of sodium channels is fifty times that of the soma [120].
While the axonal channel densities of Area I neurons are unknown, it is
known from previous labeling experiments that they possess a very thin (sub
micron) initial segment. This is somewhat puzzling as Area I must project their
neurons several millimeters to the abducen nucleus and the transfer of an action
potential would be facilitated by a wider axon. A thin axon however, will increase
the isolation of an axonal initiation site and would also enhance the neurons
sensitivity to fluctuations. We examined the difference by changing the axon
diameter (for both segments) from 1 m to 0.5 m (thin) and 1.5 m (wide). (Fig 6.
16, Fig 6.17)
90
Fig 6.14 Increasing the conductance of the action potential initiation zone
lowers the current threshold
Fig 6.15 Increasing the conductance of the action potential initiation zone
lowers the somatic voltage threshold
91
Fig 6.16 Effects of axon diameter on the current threshold
Fig 6.17 Effects of axon diameter on the somatic voltage threshold
92
6.4 Discussion
The model that we have used is highly speculative as very little is known
about the parameters of actual Area I integrators. However, it is not with merit as a
recent study of the avian nucleus laminaris showed that the location of the action
potential initiation site for NL neurons is positively correlated with the ability of the
NL neuron to detect high frequency coincidence synaptic inputs [103]. This is
consistent with our model as a distal initiation site would lower the threshold
voltage/current for coincident synaptic events to trigger an action potential.
Area I neurons possess large dendritic arbors which act as significant
current sinks. This almost forces the initiation zone to be located in the axon. We
have suggested several mechanisms by which the cell's sensitivity to fluctuations
may be enhanced if this is true. (Coincidently, the observed EPSPs possess aspect
ratios which makes them more useful for forming fluctuations rather than smooth
averages.)
In the cortical in vitro analogue of persistent firing [74], it is possible to
observe transitions between up states and down states that are on the order of 20
mV. This large dynamic range however is not observed in Area I cells. Moreover,
while the cortical oscillators appear to be bistable and function in either one of two
states, Area I cells operate in many intermediate states and the neural discharge at
low rates are more easily explained by fluctuations rather than a low average
membrane potential.
That fluctuations are important beyond their average contribution to the
waveform is currently hypothetical. Future experiments can test this theory by
93
injecting current at resting/low membrane potentials (low firing rite, nasal eye
positions) in a similar fashion to what we have done for the numerical neurons.
Alternatively, as the discharge of Area I cells cannot be voltage clamped,
(consistent with the initiation site located away from the electrode tip), an exact
waveform can be imposed on the cell using voltage clamp mode to elicit action
potentials. (This would avoid the hassle of comparing current and voltages
waveform for a charging capacitor and somewhat reduce naturally occurring
fluctuations as the potential around the tip would be clamped.) Companion
experiments should also be performed to probe the sensitivity of neural discharge
with respect to changes in DC membrane voltages. Previously this latter experiment
was performed with sharp recordings, but sharp recordings introduce an effective
depolarization of the membrane potential and bias the result. If the difference, 10
mV, between the average resting membrane potential of sharp recordings and the
patch recordings is an accurate indication of this leak-induced depolarization, then
the sharp recordings may have severely biased this sensitivity test. While a single
neuron may exhibit similar behavior post-impalement as compared to preimpalement albeit at a higher frequency, it is unlikely that any network architecture
would be able to preserve its proper dynamics if every neuron in that network was
depolarized by 10 mV.
The answer to whether or not Area I is operating in a fluctuation dominated
regime is important as Area I cells must still possess stability in the form of
persistent firing at low firing rates. This suggests that network mechanisms that
attempt to explain the function of the integration must utilize the fluctuations in
94
some manner at low rates - if not at all rates. This motivates further theoretical
searches for networks that utilized fluctuation based spike time dynamics.
95
96
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