Demonstration that sublinear dendrites enable linearly non-separable computations.

Theory predicts that nonlinear summation of synaptic potentials within dendrites allows neurons to perform linearly non-separable computations (LNSCs). Using Boolean analysis approaches, we predicted that both supralinear and sublinear synaptic summation could allow single neurons to implement a type of LNSC, the feature binding problem (FBP), which does not require inhibition contrary to the exclusive-or function (XOR). Notably, sublinear dendritic operations enable LNSCs when scattered synaptic activation generates increased somatic spike output. However, experimental demonstrations of scatter-sensitive neuronal computations have not yet been described. Using glutamate uncaging onto cerebellar molecular layer interneurons, we show that scattered synaptic-like activation of dendrites evoked larger compound EPSPs than clustered synaptic activation, generating a higher output spiking probability. Moreover, we also demonstrate that single interneurons can indeed implement the FBP. Using a biophysical model to explore the conditions in which a neuron might be expected to implement the FBP, we establish that sublinear summation is necessary but not sufficient. Other parameters such as the relative sublinearity, the EPSP size, depolarization amplitude relative to action potential threshold, and voltage fluctuations all influence whether the FBP can be performed. Since sublinear synaptic summation is a property of passive dendrites, we expect that many different neuron types can implement LNSCs.