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)
