Ph. D. Thesis, Gary R. Holt, California Institute of Technology,
Computation and Neural Systems Program, 1998.
|Table of contents
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|Chapter 1: Introduction
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|Chapter 2: Ephaptic interactions
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Ephaptic interactions (interactions through extracellular
electrical fields) are usually thought to be negligible but
they have not to my knowledge been carefully analyzed near
cell bodies. Large extracellular fields, on the order of a
few mV, occur during action potentials (see movie). I find that
these fields are sufficiently large to cause an effect on
neighboring cells which is considerably larger than a
|Chapter 3: Extracellular potassium and other diffusable
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Another way for adjacent neurons to interact
non-synaptically is through changes extracellular ionic
concentrations. In particular, the extracellular potassium
concentration is low and is therefore easier to change by
neural activity. I evaluated the magnitude of these changes
around axons on very short time scales and found the effects
to be negligible.
|Chapter 4: Shunting inhibition does not have a divisive
effect on firing rates.
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Shunting inhibition--a conductance change with a reversal
potential close to the resting potential of the cell---has
been shown to have a divisive effect on subthreshold EPSP
amplitudes. It has therefore been assumed to have the same
divisive effect on firing rates. However, shunting
inhibition actually has a subtractive effect on the firing
rate in most circumstances, for three main reasons:
Averaged over several interspike intervals, the
spiking mechanism effectively clamps the somatic membrane
potential. As a result, the average current through the
shunting conductance is approximately independent of the
firing rate. This leads to a subtractive rather than a
divisive effect for synapses which are electrotonically
close to the soma.
Shunting inhibition can only have a divisive
effect if the reversal potential of the inhibitory
conductance is at the "resting potential" of the cell.
This is usually thought to be around -70 mV. However,
when the cell is firing, the somatic voltage is clamped to
about -50 mV, which means that there is a 20 mV driving
force behind inhibition. There is therefore a subtractive
effect of distal shunting inhibition which turns out to be
much larger than any divisive effect.
Even if the reversal potential of shunting
inhibition is set properly for a divisive interaction, the
firing rate of the cell is a saturating function of the
excitatory input and as a result of this nonlinearity the
inhibition acts subtractively when the excitatory synaptic
conductance is not small compared to the inhibitory
|Chapter 5: The membrane time constant and firing rate dynamics
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The subthreshold membrane time constant governs how
quickly the membrane potential approaches equilibrium, and
has been used to estimate how quickly a neuron can respond
to its inputs. However, spiking neurons do not have an
equilibrium voltage; subthreshold dynamics do not apply to
their firing rates. In fact, a spiking neuron can respond
much faster than tau. For current step inputs, a
non-adapting spiking neuron reaches its final firing after a
single interspike interval, and an ensemble of such neurons
can respond arbitrarily fast. Firing rate dynamics are
controlled by postsynaptic conductances, adaptation, and
other processes in the cell, rather than passive properties
of the membrane. The spiking mechanism can speed up
neuronal responses, so that information can be passed to
successive stages of a feedforward network in considerably
less time than tau.
Using these considerations, we develop a formalism which
will be used to examine the dynamics of the response of a
network of integrate--and--fire units.
|Chapter 6: Adaptation and recurrent circuits
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Adaptation is thought to be useful for emphasizing
changes in input rather than the absolute level. In a
recurrent network, however, adaptation has a qualitatively
different effect. It can speed up the dynamics of the
cortical amplifier circuit significantly by cancelling out
the long tails of the recurrent EPSPs. This effect is still
significant even if parameters are set so that the tails do
not exactly cancel.
|Chapter 7: Effect of synaptic depression and facilitation on
steady state properties
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Synaptic depression has a profound effect on recurrent
circuits because any deviation from linearity is magnified
by the recurrent connections. The steady state gain of a
"cortical amplifier" falls off dramatically at higher firing
rates, even if the synapses are only weakly depressing.
Depression can be used in a cortical amplifier circuit if
it is coupled with facilitation to yield a circuit which is
linear overall. Synapses from layer 6 cells are known to
facilitate and could perhaps undo the effect of depression
in layer 4 to layer 6 synapses. The advantage of this
operation is that subtractive inhibition in layer 6 will
have a divisive effect on layer 4.
|Appendix A. Comparison of homogenized and explicitly
modeled extracellular space.
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An evaluation of the homognenous extracellular space
approximation for an array of parallel axons.
|Appendix B. Time averaged voltage in spiking cells.
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Koch et al. (1995) suggested that the spiking mechanism
can be thought of as a sort of voltage clamp which keeps the
time-averaged somatic voltage approximately constant
regardless of the firing rate. We test this hypothesis for
integrate-and-fire cells, the Hodgkin-Huxley equations, and
cortical cells in slice. In each case, to a good
approximation, the time average voltage changes very little
even though the firing rate changes significantly.
|Appendix C. Numerical methods.
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