A novel theoretical approach to the analysis of dendritic transients

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.