Graphical AbstractHighlights d Neural computation relies on compartmentalized dendrites to discern inputs d A method is described to systematically derive the degree of compartmentalization d There are substantially fewer functional compartments than dendritic branches d Compartmentalization is dynamic and can be tuned by synaptic inputs In BriefMany neuronal computations rely on the compartmentalization of dendrites into functional subunits. Wybo et al. investigate the number of these subunits that can coexist on a neuron. They find that there are substantially fewer subunits than dendritic branches but that subunit extent and number can be modified by synaptic inputs. SUMMARYThe dendritic tree of neurons plays an important role in information processing in the brain. While it is thought that dendrites require independent subunits to perform most of their computations, it is still not understood how they compartmentalize into functional subunits. Here, we show how these subunits can be deduced from the properties of dendrites. We devised a formalism that links the dendritic arborization to an impedance-based tree graph and show how the topology of this graph reveals independent subunits. This analysis reveals that cooperativity between synapses decreases slowly with increasing electrical separation and thus that few independent subunits coexist. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of the subunits in a context-dependent manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features. Analysis of dendritic patch-clamp recording experiments confirmed our theoretical predictions.

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. We present a flexible and fast method to obtain simplified neuron models at any level of complexity.Through carefully chosen parameter fits, solvable in the least squares sense, we obtain optimal reduced compartmental models. We show that (back-propagating) action potentials, calcium-spikes and NMDA-spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping the affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input impedance between the ablated branches and the next proximal dendrite. Further, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions.We provide a software toolbox that automatizes the simplification, eliminating a common hurdle towards including dendritic computations in network models.

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca2+ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models.

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks, use point-neurons -neurons without a morphological component-as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal computation. In this work, we present an approach to model an artificial synapse that mimics dendritic processing without the need to explicitly simulate dendritic dynamics. The model synapse employs an analytic solution for the cable equation to compute the neuron's membrane potential following dendritic inputs. Green's function formalism is used to derive the closed version of the cable equation. We show that by using this synapse model, point-neurons can achieve results that were previously limited to the realms of multi-compartmental models. Moreover, a computational advantage is achieved when only a small number of simulated synapses impinge on a morphologically elaborate neuron. Opportunities and limitations are discussed.

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O(n) with the number n of inputs locations, contrary to the previously reported O(n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.

Signal propagation in the dendrites of many neurons, including cortical pyramidal neurons in sensory cortex, is characterized by strong attenuation toward the soma. In contrast, using dual whole-cell recordings from the apical dendrite and soma of layer 5 (L5) pyramidal neurons in the anterior cingulate cortex (ACC) of adult male mice we found good coupling, particularly of slow subthreshold potentials like NMDA spikes or trains of EPSPs from dendrite to soma. Only the fastest EPSPs in the ACC were reduced to a similar degree as in primary somatosensory cortex, revealing differential low-pass filtering capabilities. Furthermore, L5 pyramidal neurons in the ACC did not exhibit dendritic Ca 21 spikes as prominently found in the apical dendrite of S1 (somatosensory cortex) pyramidal neurons. Fitting the experimental data to a NEURON model revealed that the specific distribution of I leak , I ir , I m , and I h was sufficient to explain the electrotonic dendritic structure causing a leaky distal dendritic compartment with correspondingly low input resistance and a compact perisomatic region, resulting in a decoupling of distal tuft branches from each other while at the same time efficiently connecting them to the soma. Our results give a biophysically plausible explanation of how a class of prefrontal cortical pyramidal neurons achieve efficient integration of subthreshold distal synaptic inputs compared with the same cell type in sensory cortices.

While sensory representations in the brain depend on context, it remains unclear how such modulations are implemented at the biophysical level, and how processing layers further in the hierarchy can extract useful features for each possible contextual state. Here, we demonstrate that dendritic N-Methyl-D-Aspartate spikes can, within physiological constraints, implement contextual modulation of feedforward processing. Such neuron-specific modulations exploit prior knowledge, encoded in stable feedforward weights, to achieve transfer learning across contexts. In a network of biophysically realistic neuron models with context-independent feedforward weights, we show that modulatory inputs to dendritic branches can solve linearly nonseparable learning problems with a Hebbian, error-modulated learning rule. We also demonstrate that local prediction of whether representations originate either from different inputs, or from different contextual modulations of the same input, results in representation learning of hierarchical feedforward weights across processing layers that accommodate a multitude of contexts.

While sensory representations in the brain depend on context, it remains unclear how such modulations are implemented at the biophysical level, and how processing layers further in the hierarchy can extract useful features for each possible contextual state. Here, we first demonstrate that thin dendritic branches are well suited to implementing contextual modulation of feedforward processing. Such neuron-specific modulations exploit prior knowledge, encoded in stable feedforward weights, to achieve transfer learning across contexts. In a network of biophysically realistic neuron models with context-independent feedforward weights, we show that modulatory inputs to thin dendrites can solve linearly non-separable learning problems with a Hebbian, error-modulated learning rule. Finally, we demonstrate that local prediction of whether representations originate either from different inputs, or from different contextual modulations of the same input, results in representation learning of hierarchical feedforward weights across processing layers that accommodate a multitude of contexts.