Coincidence-detector neurons in the auditory brainstem of mammals and birds use interaural time differences to localize sounds. Each neuron receives many narrow-band inputs from both ears and compares the time of arrival of the inputs with an accuracy of 10-100 micros. Neurons that receive low-frequency auditory inputs (up to about 2 kHz) have bipolar dendrites, and each dendrite receives inputs from only one ear. Using a simple model that mimics the essence of the known electrophysiology and geometry of these cells, we show here that dendrites improve the coincidence-detection properties of the cells. The biophysical mechanism for this improvement is based on the nonlinear summation of excitatory inputs in each of the dendrites and the use of each dendrite as a current sink for inputs to the other dendrite. This is a rare case in which the contribution of dendrites to the known computation of a neuron may be understood. Our results show that, in these neurons, the cell morphology and the spatial distribution of the inputs enrich the computational power of these neurons beyond that expected from 'point neurons' (model neurons lacking dendrites).

Electrotonic structure of dendrites plays a critical role in neuronal computation and plasticity. In this article we develop two novel measures of electrotonic structure that describe intraneuronal signaling in dendrites of arbitrary geometry. The log-attenuation Lij measures the efficacy, and the propagation delay Pij the speed, of signal transfer between any two points i and j. These measures are additive, in the sense that if j lies between i and k, the total distance Lik is just the sum of the partial distances: Lik = Lij + Ljk, and similarly Pik = Pij + Pjk. This property serves as the basis for the morphoelectrotonic transform (MET), a graphical mapping from morphological into electrotonic space. In a MET, either Pij or Lij replace anatomical distance as the fundamental unit and so provide direct functional measures of intraneuronal signaling. The analysis holds for arbitrary transient signals, even those generated by nonlinear conductance changes underlying both synaptic and action potentials. Depending on input location and the measure of interest, a single neuron admits many METs, each emphasizing different functional consequences of the dendritic electrotonic structure. Using a single layer 5 cortical pyramidal neuron, we illustrate a collection of METs that lead to a deeper understanding of the electrical behavior of its dendritic tree. We then compare this cortical cell to representative neurons from other brain regions (cortical layer 2/3 pyramidal, region CA1 hippocampal pyramidal, and cerebellar Purkinje). Finally, we apply the MET to electrical signaling in dendritic spines, and extend this analysis to calcium signaling within spines. Our results demonstrate that the MET provides a powerful tool for obtaining a rapid and intuitive grasp of the functional properties of dendritic trees.

1. A novel approach for analyzing transients in passive structures called "the method of moments" is introduced. It provides, as a special case, an analytic method for calculating the time delay and speed of propagation of electrical signals in any passive dendritic tree without the need for numerical simulations. 2. Total dendritic delay (TD) between two points (y, x) is defined as the difference between the centroid (the center of gravity) of the transient current input, I, at point y[tI(y)] and the centroid of the transient voltage response, V, at point x [tV(x)]. The TD measured at the input points is nonzero and is called the local delay (LD). Propagation delay, PD(y, x), is then defined as TD(y, x)--LD(y) whereas the net dendritic delay, NDD(y, 0), of an input point, y, is defined as TD(y, 0) - LD(0), where 0 is the target point, typically the soma. The signal velocity at a point x0 in the tree, theta(x0), is defined as [1/(dtv(x)/dx)[x = x0. 3. With the use of these definitions, several properties of dendritic delay exist. First, the delay between any two points in a given tree is independent of the properties (shape and duration) of the transient current input. Second, the velocity of the signal at any given point (y) in a given direction from (y) does not depend on the morphology of the tree "behind" the signal, and of the input location. Third, TD(y, x) = TD(x, y), for any two points, x, y. 4. Two additional properties are useful for efficiently calculating delays in arbitrary passive trees. 1) The subtrees connected at the ends of any dendritic segment can each be functionally lumped into an equivalent isopotential R-C compartment. 2) The local delay at any given point (y) in a tree is the mean of the local delays of the separate structures (subtrees) connected at y, weighted by the relative input conductance of the corresponding subtrees. 5. Because the definitions for delays utilize difference between centroids, the local delay and the total delay can be interpreted as measures for the time window in which synaptic inputs affect the voltage response at a target/decision point. Large LD or TD is closely associated with a relatively wide time window, whereas small LD or TD imply that inputs have to be well synchronized to affect the decision point. The net dendritic delay may be interpreted as the cost (in terms of delay) of moving a synapse away from the target point.(ABSTRACT TRUNCATED AT 400 WORDS)

A novel theoretical framework for analyzing dendritic transients is introduced. This approach, called the method of moments, is an extension of Rall's cable theory for dendrites. It provides analytic investigation of voltage attenuation, signal delay, and synchronization problems in passive dendritic trees. In this method, the various moments of a transient signal are used to characterize the properties of the transient. The strength of the signal is measured by the time integral of the signal, its characteristic time is determined by its centroid ("center of gravity"), and the width of the signal is determined by a measure similar to the standard deviation in probability theory. Using these signal properties, the method of moments provides theorems, expressions, and efficient algorithms for analyzing the voltage response in arbitrary passive trees. The method yields new insights into spatiotemporal integration, coincidence detection mechanisms, and the properties of local interactions between synaptic inputs in dendritic trees. The method can also be used for matching dendritic neuron models to experimental data and for the analysis of synaptic inputs recorded experimentally.