Modelling Dendrite Shape from Wiring Principles
The primary function of a dendrite is to connect a neuron to its inputs. In this chapter, I describe a model that captures the general features of dendritic trees as a function of the connectivity they implement. This model is based on locally optimising connections by weighing costs for total wiring length and conduction times. The model was used to generate synthetic dendrites that are visually indistinguishable from their real counterparts for all dendrite types tested so far. Dendrites of different cell types vary only in the shape of the volume that they span and in the weight between costs for wiring length versus conduction times. Using the model, an equation was derived that relates total dendrite length, number of branch points, spanning volume and the number of synapses, measures that are among the most commonly employed in the study of the molecular and genetic background of dendrite morphology and growth. This equation holds true for all neurons measured so far and confines the possible computations a dendrite is capable of. Finally, beyond the consequences for neuronal morphology and computation, an outlook is given on a number of ways to scale up the single cell model to study the formation of larger neural circuits.
The work presented here was a collaborative effort together with Alexander Borst, Friedrich Förstner, Jürgen Haag, Michael Häusser, Alexandre Mathy and Idan Segev. I would like to thank Peter Jedlicka for constructive criticism on this manuscript.
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