Abstract

Integration of excitatory post synaptic potentials (EPSPs) in dendrites can be locally non-linear. In a dendritic branch, synchronous EPS Ps can cause a local voltage response which overshoots their arithmetic sum, the so-called dendritic spike. This leads to the theoretical proposal that a neuron can be seen as a network of non-linear subunits, a model with a higher computational capacity than classic models. However, in practice dendritic morphology can severely reduce the number of possible subunits. This can be an issue, because the number of independent subunits directly determines the increase in computational capacities. Thus, in this study, we take the most conservative hypothesis: we suppose the existence of a single non-linear dendritic subunit on top of linear somatic integration. To model this hypothesis we use a binary neuron model, the threshold linear unit also known as the Perceptron, and we add to it a non-linear subunit. This subunit locally sums its synaptic inputs, and passes it though an all-or-none transfer function, modeling a dendritic spike. We use systematic parameter searches on this model to answer two questions: Are they computations – Boolean functions – enabled by a non-linear subunit ? How well a computation which is possible with a non-linear subunit can be approximated without ? We made two observations: first, a non-linear subunit coupled with linear integration enables original computations, for instance the feature binding problem; second, this computation is the hardest to approximate without a non-linear subunit. We use these observations to implement the binding problem in a proof of principle biophysical model made of a soma and a single dendritic compartment. This demonstrates that a very simple dendritic morphology, a single branch, already enhances the computational capacities of single neuron.