Highlights

  • Neural computation relies on compartmentalized dendrites to discern inputs

  • A method is described to systematically derive the degree of compartmentalization

  • There are substantially fewer functional compartments than dendritic branches

  • Compartmentalization is dynamic and can be tuned by synaptic inputs

Summary

The 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.

Graphical Abstract

Figure thumbnail fx1 {focus_keyword} Electrical Compartmentalization in Neurons

Keywords

  • neural computation
  • dendrites
  • compartmentalization
  • independent subunits
  • branch-specific learning
  • dendritic computation

Introduction

Brain function emerges from the orchestrated behavior of billions of individual neurons that transform electrical inputs into action potential (AP) output. This transformation starts on the dendritic tree, where inputs are collected, and proceeds to the axon initial segment where APs are generated before they are transmitted to downstream neurons through the axon. While axons appear to merely communicate the neuronal output downstream, dendrites collect and nonlinearly transform the input. This phenomenon, termed dendritic computation, has been shown to occur in vivo and to be required for normal brain function (

). In both experimental and theoretical work, an abundance of dendritic computations have been proposed (

,

,

). Nearly all of them assume that dendrites are compartmentalized into independent subunits: regions on the dendritic tree that can integrate inputs independently from other regions.

The computational significance of these subunits arises from their ability to support independent regenerative events, such as N-methyl D-aspartate (NMDA), Ca2+, or Na+ spikes (

Wei et al., 2001

  • Wei D.-S.
  • Mei Y.-A.
  • Bagal A.
  • Kao J.P.Y.
  • Thompson S.M.
  • Tang C.-M.

Compartmentalized and binary behavior of terminal dendrites in hippocampal pyramidal neurons.

). These events, where an initial depolarization is enhanced supralinearly by subsequent synaptic inputs and/or voltage-dependent ion-channel currents (

Major et al., 2013

  • Major G.
  • Larkum M.E.
  • Schiller J.

Active properties of neocortical pyramidal neuron dendrites.

), significantly strengthen the computational power of neurons. They enable the local decoding of bursts of inputs (

Polsky et al., 2009

  • Polsky A.
  • Mel B.
  • Schiller J.

Encoding and decoding bursts by NMDA spikes in basal dendrites of layer 5 pyramidal neurons.

) and hence, through branch-specific plasticity (

Golding et al., 2002

  • Golding N.L.
  • Staff N.P.
  • Spruston N.

Dendritic spikes as a mechanism for cooperative long-term potentiation.

,

Govindarajan et al., 2011

  • Govindarajan A.
  • Israely I.
  • Huang S.-Y.
  • Tonegawa S.

The dendritic branch is the preferred integrative unit for protein synthesis-dependent LTP.

,

Losonczy et al., 2008

  • Losonczy A.
  • Makara J.K.
  • Magee J.C.

Compartmentalized dendritic plasticity and input feature storage in neurons.

,

Weber et al., 2016

  • Weber J.P.
  • Andrásfalvy B.K.
  • Polito M.
  • Magó Á.
  • Ujfalussy B.B.
  • Makara J.K.

Location-dependent synaptic plasticity rules by dendritic spine cooperativity.

), drive the clustering of correlated synaptic inputs (

Gökçe et al., 2016

  • Gökçe O.
  • Bonhoeffer T.
  • Scheuss V.

Clusters of synaptic inputs on dendrites of layer 5 pyramidal cells in mouse visual cortex.

,

,

Lee et al., 2016

  • Lee W.-C.A.
  • Bonin V.
  • Reed M.
  • Graham B.J.
  • Hood G.
  • Glattfelder K.
  • Reid R.C.

Anatomy and function of an excitatory network in the visual cortex.

). A recent finding that distal apical dendrites can spike 10-fold more often than somata (

Moore et al., 2017

  • Moore J.J.
  • Ravassard P.M.
  • Ho D.
  • Acharya L.
  • Kees A.L.
  • Vuong C.
  • Mehta M.R.

Dynamics of cortical dendritic membrane potential and spikes in freely behaving rats.

) suggests an important role for this branch-specific plasticity. Independent subunits furthermore allow different input streams to be discriminated from each other (

Johenning et al., 2009

  • Johenning F.W.
  • Beed P.S.
  • Trimbuch T.
  • Bendels M.H.K.
  • Winterer J.
  • Schmitz D.

Dendritic compartment and neuronal output mode determine pathway-specific long-term potentiation in the piriform cortex.

), and they facilitate sensory perception through feedback signals (

Takahashi et al., 2016

  • Takahashi N.
  • Oertner T.G.
  • Hegemann P.
  • Larkum M.E.

Active cortical dendrites modulate perception.

).

When triggered independently, these local regenerative events are predicted to enable individual neurons to function as two-layer neural networks (

,

Poirazi et al., 2003b

  • Poirazi P.
  • Brannon T.
  • Mel B.W.

Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell.

). This in turn should enable neurons to learn linearly nonseparable functions (

Schiess et al., 2016

  • Schiess M.
  • Urbanczik R.
  • Senn W.

Somato-dendritic synaptic plasticity and error-backpropagation in active dendrites.

) and implement translation invariance (

Mel et al., 1998

  • Mel B.W.
  • Ruderman D.L.
  • Archie K.A.

Translation-invariant orientation tuning in visual “complex” cells could derive from intradendritic computations.

). On the network level, independent subunits are thought to dramatically increase memory capacity (

Poirazi and Mel, 2001

  • Poirazi P.
  • Mel B.W.

Impact of active dendrites and structural plasticity on the memory capacity of neural tissue.

), to allow for the stable storage of feature associations (

Bono and Clopath, 2017

  • Bono J.
  • Clopath C.

Modeling somatic and dendritic spike mediated plasticity at the single neuron and network level.

), represent a powerful mechanism for coincidence detection (

Chua and Morrison, 2016

  • Chua Y.
  • Morrison A.

Effects of calcium spikes in the layer 5 pyramidal neuron on coincidence detection and activity propagation.

,

Larkum et al., 1999

  • Larkum M.E.
  • Zhu J.J.
  • Sakmann B.

A new cellular mechanism for coupling inputs arriving at different cortical layers.

), and support the back-prop algorithm to train neural networks (

Guerguiev et al., 2017

  • Guerguiev J.
  • Lillicrap T.P.
  • Richards B.A.

Towards deep learning with segregated dendrites.

,

Sacramento et al., 2017

Sacramento, J., Costa, R.P., Bengio, Y., and Senn, W. (2017). Dendritic error backpropagation in deep cortical microcircuits. arXiv, arXiv:1801.00062v1.

,

).

Thus, abundant data show that dendritic trees consist of a multitude of subunits, and both experimental and theoretical work suggests an important computational role for these subunits (

Major et al., 2013

  • Major G.
  • Larkum M.E.
  • <