A critical reexamination of some assumptions and implications of cable theory in neurobiology

Citation

Holt, Gary R. (1998) A critical reexamination of some assumptions and implications of cable theory in neurobiology. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HPPC-S237. https://resolver.caltech.edu/CaltechETD:etd-09122006-135415

Abstract

Linear cable theory lies at the core of our understanding of how an individual neuron works. Cable theory usually assumes that neurons do not interact significantly except at specific, anatomically specialized locations (synapses and gap junctions). An analysis of the extracellular electrical fields shows that spikes in one neuron could cause a depolarization of several mV in a dendrite or axon passing by its initial segment. This is somewhat larger than typical chemical synapses; such ephaptic interactions could possibly play a role in controlling action potential failure at branch points.

Applying conclusions of linear cable theory to nonlinear spiking neurons has led to incorrect ideas about neural function. For example, in linear cable theory changing the membrane conductance can be used to scale the amplitude of EPSPs. Shunting inhibition has therefore been repeatedly proposed as a mechanism for division or normalization. This mechanism does not work if the neuron is spiking, i.e., when the output is firing rate rather than EPSP amplitude. When a neuron spikes, its time-averaged voltage does not increase much even if the firing rate goes up; therefore current through a shunt resistance is independent of firing rate, and shunting inhibition acts subtractively rather than divisively.

Cable theory also predicts that EPSPs are low-pass filtered by the membrane resistance and capacitance, and investigators have therefore assumed that the membrane time constant determines how fast a neuron can respond. Again, because of the spiking mechanism, the membrane potential never reaches steady state, so the time constant is not obviously relevant. The dynamics of firing rates may be better described by currents than voltages.

Applying this principle to the dynamics of simple feedback networks shows that a key factor in the response time of a network is the adaptation current. Without adaptation, the network time constant can belong because it is the gain of the network multiplied by the synaptic time constants. Adaptation can cancel out the long tails of synaptic current, significantly speeding up response times. Recurrent inhibition has a similar effect.

Another key factor determining input current is synaptic depression and facilitation. Recurrent networks are especially sensitive to synaptic depression because of the feedback; within a very short period of time the network behaves like a feedforward network because the recurrent synapses have been depressed away. However, facilitation and depression can act together to provide a log-exponential transform, allowing subtractive inhibition at one stage to have a divisive effect at another.

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