Modeling Dendrites and Spatially-Distributed Neuronal Membrane Properties.

The first step toward understanding the brain is to learn how individual neurons process incoming signals, the vast majority of which arrive in their dendrites. Dendrites were first discovered at the beginning of the twentieth century and were characterized by great anatomical variability, both within and across species. Over the past years, a rich repertoire of active and passive dendritic mechanisms has been unveiled, which greatly influences their integrative power. Yet, our understanding of how dendrites compute remains limited, mainly because technological limitations make it difficult to record from dendrites directly and manipulate them. Computational modeling, on the other hand, is perfectly suited for this task. Biophysical models that account for the morphology as well as passive and active neuronal properties can explain a wide variety of experimental findings, shedding new light on how dendrites contribute to neuronal and circuit computations. This chapter aims to help the interested reader build biophysical models incorporating dendrites by detailing how their electrophysiological properties can be described using simple mathematical frameworks. We start by discussing the passive properties of dendrites and then give an overview of how active conductances can be incorporated, leading to realistic in silico replicas of biological neurons.