Hearing, vision, touch: underlying all of these senses is stimulus selectivity, a robust information processing operation in which cortical neurons respond more to some stimuli than to others. Previous models assume that these neurons receive the highest weighted input from an ensemble encoding the preferred stimulus, but dendrites enable other possibilities. Nonlinear dendritic processing can produce stimulus selectivity based on the spatial distribution of synapses, even if the total preferred stimulus weight does not exceed that of nonpreferred stimuli. Using a multi-subunit nonlinear model, we demonstrate that stimulus selectivity can arise from the spatial distribution of synapses. We propose this as a general mechanism for information processing by neurons possessing dendritic trees. Moreover, we show that this implementation of stimulus selectivity increases the neuron's robustness to synaptic and dendritic failure. Importantly, our model can maintain stimulus selectivity for a larger range of loss of synapses or dendrites than an equivalent linear model. We then use a layer 2/3 biophysical neuron model to show that our implementation is consistent with two recent experimental observations: (1) one can observe a mixture of selectivities in dendrites that can differ from the somatic selectivity, and (2) hyperpolarization can broaden somatic tuning without affecting dendritic tuning. Our model predicts that an initially nonselective neuron can become selective when depolarized. In addition to motivating new experiments, the model's increased robustness to synapses and dendrites loss provides a starting point for fault-resistant neuromorphic chip development.

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.

The integration of excitatory inputs in dendrites is non-linear: multiple excitatory inputs can produce a local depolarization departing from the arithmetic sum of each input's response taken separately. If this depolarization is bigger than the arithmetic sum, the dendrite is spiking; if the depolarization is smaller, the dendrite is saturating. Decomposing a dendritic tree into independent dendritic spiking units greatly extends its computational capacity, as the neuron then maps onto a two layer neural network, enabling it to compute linearly non-separable Boolean functions (lnBFs). How can these lnBFs be implemented by dendritic architectures in practise? And can saturating dendrites equally expand computational capacity? To adress these questions we use a binary neuron model and Boolean algebra. First, we confirm that spiking dendrites enable a neuron to compute lnBFs using an architecture based on the disjunctive normal form (DNF). Second, we prove that saturating dendrites as well as spiking dendrites also enable a neuron to compute lnBFs using an architecture based on the conjunctive normal form (CNF). Contrary to the DNF-based architecture, a CNF-based architecture leads to a dendritic unit tuning that does not imply the neuron tuning, as has been observed experimentally. Third, we show that one cannot use a DNF-based architecture with saturating dendrites. Consequently, we show that an important family of lnBFs implemented with a CNF-architecture can require an exponential number of saturating dendritic units, whereas the same family implemented with either a DNF-architecture or a CNF-architecture always require a linear number of spiking dendritic unit. This minimization could explain why a neuron spends energetic resources to make its dendrites spike.