Quasi-active Approximation of Nonlinear Dendritic Cables
The quasi-active approximation of a dendritic cable is a linearized description of a cable with voltage-dependent membrane conductances. It is an extension of classical passive cable theory relying on linearization of the voltage-dependent conductances around a reference membrane potential (typically the resting potential). The current thereby acquires a linear current–voltage relationship but still has an activation time constant associated with it that determines its gating dynamics. This approximation accurately describes the frequency-dependent filtering of the nonlinear cable for sufficiently small voltage deflections around the reference potential.
The use of linearized descriptions of voltage-dependent membrane conductances in point neuron models has a rich history, e.g., Hodgkin and Huxley (1952) already used this to analyze the subthreshold (oscillatory) response of the space-clampedsquid giant axon. However, the first use of such methods in a...