Passive nonlinear dendritic interactions as a general computational resource in functional spiking neural networks

Nonlinear interactions in the dendritic tree play a key role in neural computation. Nevertheless, modeling frameworks aimed at the construction of large-scale, functional spiking neural networks tend to assume linear, current-based superposition of post-synaptic currents. We extend the theory underlying the Neural Engineering Framework to systematically exploit nonlinear interactions between the local membrane potential and conductance-based synaptic channels as a computational resource. In particular, we demonstrate that even a single passive distal dendritic compartment with AMPA and GABA-A synapses connected to a leaky integrate-and-fire neuron supports the computation of a wide variety of multivariate, bandlimited functions, including the Euclidean norm, controlled shunting, and non-negative multiplication. Our results demonstrate that, for certain operations, the accuracy of dendritic computation is on a par with or even surpasses the accuracy of an additional layer of neurons in the network. These findings allow modelers to construct large-scale models of neurobiological systems that closer approximate network topologies and computational resources available in biology. Our results may inform neuromorphic hardware design and could lead to a better utilization of resources on existing neuromorphic hardware platforms.