Optimal current transfer in dendrites

Abstract: Integration of synaptic currents across an extensive dendritic tree is a prerequisite for computation in the brain. Dendritic tapering away from the soma has been suggested to both equalise contributions from synapses at different locations and maximise the current transfer to the soma. To find out how this is achieved precisely, an analytical solution for the current transfer in dendrites with arbitrary taper is required. We derive here an asymptotic approximation that accurately matches results from numerical simulations. From this we then determine the diameter profile that maximises the current transfer to the soma. We find a simple quadratic form that matches diameters obtained experimentally, indicating a fundamental architectural principle of the brain that links dendritic diameters to signal transmission. Author Summary: Neurons take a great variety of shapes that allow them to perform their different computational roles across the brain. The most distinctive visible feature of many neurons is the extensively branched network of cable-like projections that make up their dendritic tree. A neuron receives current-inducing synaptic contacts from other cells across its dendritic tree. As in the case of botanical trees, dendritic trees are strongly tapered towards their tips. This tapering has previously been shown to offer a number of advantages over a constant width, both in terms of reduced energy requirements and the robust integration of inputs at different locations. However, in order to predict the computations that neurons perform, analytical solutions for the flow of input currents tend to assume constant dendritic diameters. Here we introduce an asymptotic approximation that accurately models the current transfer in dendritic trees with arbitrary, continuously changing, diameters. When we then determine the diameter profiles that maximise current transfer towards the cell body we find diameters similar to those observed in real neurons. We conclude that the tapering in dendritic trees to optimise signal transmission is a fundamental architectural principle of the brain