Passive cable properties of dendrites

The modeling of dendritic trees was carefully presented and discussed in earlier publications; only a few points will be summarized here. In Rail, 1962 it was shown how the partial differential equation for a passive nerve cable can represent an entire dendritic tree, and how this can be generalized from cylindrical to tapered branches and trees; this paper also showed how to incorporate synaptic conductance input into the mathematical model, and presented several computed examples. In Rail, 1964 it was shown how the same results can be obtained with compartmental modeling of dendritic trees; this paper also pointed out that such compartmental models are not restricted to the assumption of uniform membrane properties, or to the family of dendritic trees which transforms to an equivalent cylinder or an equivalent taper and, consequently, that such models can be used to represent any arbitrary amount of nonuniformity in branching pattern, in membrane properties, and in synaptic input that one chooses to specify. Recently, this compartmental approach has been applied to detailed dendritic anatomy represented as thousands of compartments (Bunow et al., 1985; Segev et al., 1985; Redman & Clements, personal communication).

Significant theoretical predictions and insights were obtained by means of computations with a simple ten-compartment model (Rail, 1964). One computation predicted different shapes for the voltage transients expected at the neuron soma when identical brief synaptic inputs are delivered to different dendritic locations; these predictions (and their elaboration, Rail, 1967) have been experimentally confirmed in many laboratories (see Jack et al., 1975; Redman, 1976; Rail, 1977).