A Critical Reexamination of Some Assumptions and Implications of Cable Theory in Neurobiology. Ph. D. Thesis, California Institute of Technology, 1998.
Electrical Interactions via the Extracellular Potential Near Cell Bodies. G. R. Holt and C. Koch. Journal of Computational Neuroscience 6:169-184, 1999.
Ephaptic interactions between a neuron and axons or dendrites passing by its cell body can be, in principle, more significant than ephaptic interactions among axons in a fiber tract. Extracellular action potentials outside axons are small in amplitude and spatially spread out, while they are larger in amplitude and much more spatially confined near cell bodies.
We estimated the extracellular potentials associated with an action potential in a cortical pyramidal cell using standard 1-D cable and volume conductor theory. Their spatial and temporal pattern reveal much about the location and timing of currents in the cell, especially in combination with a known morphology, and simple experiments could resolve questions about spike induced polarization in a nearby passive cable. The magnitude of this induced voltage can be several mV, does not spread electrotonically and depends only weakly on the passive properties of the cable. We discuss their possible functional relevance.
Shunting Inhibition Does Not Act Divisively on Firing Rates. Holt, G. R., and C. Koch. Neural Computation 9:1001-1013, 1997.
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 reasons.
The spiking mechanism effectively holds the time-average membrane potential approximately constant, independent of the firing rate. 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.
Distal 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, which is close to the GABA A reversal potential. 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 GABA A 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 conductance.
For these reasons, regulating a cell's passive membrane conductance--for instance via inhibitory feedback--is not an adequate mechanism for normalizing or scaling its output.
A comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. G. R. Holt, W. R. Softky, C. Koch., and R. J. Douglas. J. Neurophysiol. 75:1806-1814, 1996.
A simple technique for measuring interspike interval variability when the firing rate is non-stationary. Application of this technique to data from anesthetized cat shows that variability in vivo in response to constant current injection is almost as large as variability in response to visual stimulation. Variability in response to current injection in slice is much lower.