The spatial distribution and time course of electrical signals in neurons have important theoretical and practical consequences. Because it is difficult to infer how neuronal form affects electrical signaling, we have developed a quantitative yet intuitive approach to the analysis of electrotonus. This approach transforms the architecture of the cell from anatomical to electrotonic space, using the logarithm of voltage attenuation as the distance metric. We describe the theory behind this approach and illustrate its use. 1 INTRODUCTION The fields of computational neuroscience and artificial neural nets have enjoyed a mutually beneficial exchange of ideas. This has been most evident at the network level, where concepts such as massive parallelism, lateral inhibition, and recurrent excitation have inspired both the analysis of brain circuits and the design of artificial neural net architectures.

The spatial distribution and time course of electrical signals in neurons have important theoretical and practical consequences. Because it is difficult to infer how neuronal form affects electrical signaling, we have developed a quantitative yet intuitive approach to the analysis of electrotonus. This approach transforms the architecture of the cell from anatomical to electrotonic space, using the logarithm of voltage attenuation as the distance metric. We describe the theory behind this approach and illustrate its use. 1 INTRODUCTION The fields of computational neuroscience and artificial neural nets have enjoyed a mutually beneficial exchange of ideas. This has been most evident at the network level, where concepts such as massive parallelism, lateral inhibition, and recurrent excitation have inspired both the analysis of brain circuits and the design of artificial neural net architectures. Less attention has been given to how properties of the individual neurons or processing elements contribute to network function. Biological neurons and brain circuits have 70 Nicholas Carnevale, Kenneth Y. Tsai, Brenda J. Claiborne, Thomas H. Brown

The cold spot consisted of a high density of a Ca-activated K channel.

The cold spot consisted of a high density of a Ca-activated K channel.

We are exploring the significance of biological complexity for neuronal computation. Here we demonstrate that Hebbian synapses in realistically-modeled hippocampal pyramidal cells may give rise to two novel forms of self -organization in response to structured synaptic input. First, on the basis of the electrotonic relationships between synaptic contacts, a cell may become tuned to a small subset of its input space. Second, the same mechanisms may produce clusters of potentiated synapses across the space of the dendrites. The latter type of self-organization may be functionally significant in the presence of nonlinear dendritic conductances.

We are exploring the significance of biological complexity for neuronal computation. Here we demonstrate that Hebbian synapses in realistically-modeled hippocampal pyramidal cells may give rise to two novel forms of self -organization in response to structured synaptic input. First, on the basis of the electrotonic relationships between synaptic contacts, a cell may become tuned to a small subset of its input space. Second, the same mechanisms may produce clusters of potentiated synapses across the space of the dendrites. The latter type of self-organization may be functionally significant in the presence of nonlinear dendritic conductances.

We are exploring the significance of biological complexity for neuronal computation. Here we demonstrate that Hebbian synapses in realistically-modeled hippocampalpyramidal cells may give rise to two novel forms of self-organization in response to structured synaptic input. First, on the basis of the electrotonic relationships between synaptic contacts, a cell may become tuned to a small subset of its input space. Second, the same mechanisms may produce clusters of potentiated synapses across the space of the dendrites. The latter type of self-organization may be functionally significant in the presence of nonlinear dendritic conductances.