Why Neurons Have Thousands of Synapses, A Theory of Sequence Memory in Neocortex

Neocortical neurons have thousands of excitatory synapses. It is a mystery how neurons integrate the input from so many synapses and what kind of large-scale network behavior this enables. It has been previously proposed that non-linear properties of dendrites enable neurons to recognize multiple patterns. In this paper we extend this idea by showing that a neuron with several thousand synapses arranged along active dendrites can learn to accurately and robustly recognize hundreds of unique patterns of cellular activity, even in the presence of large amounts of noise and pattern variation. We then propose a neuron model where some of the patterns recognized by a neuron lead to action potentials and define the classic receptive field of the neuron, whereas the majority of the patterns recognized by a neuron act as predictions by slightly depolarizing the neuron without immediately generating an action potential. We then present a network model based on neurons with these properties and show that the network learns a robust model of time-based sequences. Given the similarity of excitatory neurons throughout the neocortex and the importance of sequence memory in inference and behavior, we propose that this form of sequence memory is a universal property of neocortical tissue. We further propose that cellular layers in the neocortex implement variations of the same sequence memory algorithm to achieve different aspects of inference and behavior. The neuron and network models we introduce are robust over a wide range of parameters as long as the network uses a sparse distributed code of cellular activations. The sequence capacity of the network scales linearly with the number of synapses on each neuron. Thus neurons need thousands of synapses to learn the many temporal patterns in sensory stimuli and motor sequences.Comment: Submitted for publicatio

Generation of directional selectivity by individual thin dendrites in neocortical pyramidal neurons

Patterned 2-photon glutamate uncaging and local GABA iontophoresis were used to test, in brain slices, whether basal and oblique dendrites possess the biophysical machinery to contribute to the directional selectivity exhibited by many sensory neocortical neurons. On average, Distal-to-Proximal (DP) sequences of glutamate stimuli along individual dendrites produced ~1.5-fold larger responses than the same stimuli in reverse order (PD). Proximal inhibition consistent with spatially-offset receptive subfields, preceding PD but following DP sequences, enhanced directionality to ~2.1-fold

Electrical Compartmentalization in Neurons

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.Peer reviewe

The Decade of the Dendritic NMDA Spike

In the field of cortical cellular physiology, much effort has been invested in understanding thick apical drites of pyramidal neurons and the regenerative sodium and calcium spikes that take place in the apical trunk. Here we focus on thin dendrites of pyramidal cells (basal, oblique, and tuft dendrites), and we discuss one relatively novel form of an electrical signal (“NMDA spike”) that is specific for these branches. Basal, oblique, and apical tuft dendrites receive a high density of glutamatergic synaptic contacts. Synchronous activation of 10–50 neighboring glutamatergic synapses triggers a local dendritic regenerative potential, NMDA spike/plateau, which is characterized by significant local amplitude (40–50 mV) and an extraordinary duration (up to several hundred milliseconds). The NMDA plateau potential, when it is initiated in an apical tuft dendrite, is able to maintain a good portion of that tuft in a sustained depolarized state. However, if NMDA-dominated plateau potentials originate in proximal segments of basal dendrites, they regularly bring the neuronal cell body into a sustained depolarized state, which resembles a cortical up state. At each dendritic initiation site (basal, oblique, and tuft) an NMDA spike creates favorable conditions for causal interactions of active synaptic inputs, including the spatial or temporal binding of information, as well as processes of short-term and long-term synaptic modifications (e.g., long-term potentiation or long-term depression). Because of their strong amplitudes and durations, local dendritic NMDA spikes make up the cellular substrate for multisite independent subunit computations that enrich the computational power and repertoire of cortical pyramidal cells. We propose that NMDA spikes are likely to play significant roles in cortical information processing in awake animals (spatiotemporal binding, working memory) and during slow-wave sleep (neuronal up states, consolidation of memories

Location-Dependent Effects of Inhibition on Local Spiking in Pyramidal Neuron Dendrites

Cortical computations are critically dependent on interactions between pyramidal neurons (PNs) and a menagerie of inhibitory interneuron types. A key feature distinguishing interneuron types is the spatial distribution of their synaptic contacts onto PNs, but the location-dependent effects of inhibition are mostly unknown, especially under conditions involving active dendritic responses. We studied the effect of somatic vs. dendritic inhibition on local spike generation in basal dendrites of layer 5 PNs both in neocortical slices and in simple and detailed compartmental models, with equivalent results: somatic inhibition divisively suppressed the amplitude of dendritic spikes recorded at the soma while minimally affecting dendritic spike thresholds. In contrast, distal dendritic inhibition raised dendritic spike thresholds while minimally affecting their amplitudes. On-the-path dendritic inhibition modulated both the gain and threshold of dendritic spikes depending on its distance from the spike initiation zone. Our findings suggest that cortical circuits could assign different mixtures of gain vs. threshold inhibition to different neural pathways, and thus tailor their local computations, by managing their relative activation of soma- vs. dendrite-targeting interneurons

Gradient estimation in dendritic reinforcement learning

We study synaptic plasticity in a complex neuronal cell model where NMDA-spikes can arise in certain dendritic zones. In the context of reinforcement learning, two kinds of plasticity rules are derived, zone reinforcement (ZR) and cell reinforcement (CR), which both optimize the expected reward by stochastic gradient ascent. For ZR, the synaptic plasticity response to the external reward signal is modulated exclusively by quantities which are local to the NMDA-spike initiation zone in which the synapse is situated. CR, in addition, uses nonlocal feedback from the soma of the cell, provided by mechanisms such as the backpropagating action potential. Simulation results show that, compared to ZR, the use of nonlocal feedback in CR can drastically enhance learning performance. We suggest that the availability of nonlocal feedback for learning is a key advantage of complex neurons over networks of simple point neurons, which have previously been found to be largely equivalent with regard to computational capability

Synaptically activated Ca2+ waves and NMDA spikes locally suppress voltage-dependent Ca2+ signalling in rat pyramidal cell dendrites

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of The Physiological Society for personal use, not for redistribution. The definitive version was published in Journal of Physiology 589 (2011): 4903-4920, doi:10.1113/jphysiol.2011.216564.Synaptically activated changes in dendritic [Ca2+]i affect many important physiological processes including synaptic plasticity and gene expression. The location, magnitude, and time course of these changes can determine which mechanisms are affected. Therefore, it is important to understand the processes that control and modulate these changes. One important source is Ca2+ entering through voltage gated Ca2+ channels opened by action potentials backpropagating over the dendrites (bAPs). Here we examine how [Ca2+]i changes, caused by regenerative Ca2+ release from internal stores (Ca2+ waves) or by regenerative Ca2+ entry through NMDA receptors (NMDA spikes) affect subsequent bAP evoked [Ca2+]i changes. These large [Ca2+]i increases suppressed the bAP signals in the regions where the preceding [Ca2+]i increases were largest. The suppression was proportional to the magnitude of the large [Ca2+]i change and was insensitive to kinase and phosphatase inhibitors, consistent with suppression due to Ca2+ dependent inhibition of Ca2+ channels.Supported in part by NIH grant NS-016295.2012-08-1

Active dendrites enable strong but sparse inputs to determine orientation selectivity

The dendrites of neocortical pyramidal neurons are excitable. However, it is unknown how synaptic inputs engage nonlinear dendritic mechanisms during sensory processing in vivo, and how they in turn influence action potential output. Here, we provide a quantitative account of the relationship between synaptic inputs, nonlinear dendritic events, and action potential output. We developed a detailed pyramidal neuron model constrained by in vivo dendritic recordings. We drive this model with realistic input patterns constrained by sensory responses measured in vivo and connectivity measured in vitro. We show mechanistically that under realistic conditions, dendritic Na+ and NMDA spikes are the major determinants of neuronal output in vivo. We demonstrate that these dendritic spikes can be triggered by a surprisingly small number of strong synaptic inputs, in some cases even by single synapses. We predict that dendritic excitability allows the 1% strongest synaptic inputs of a neuron to control the tuning of its output. Active dendrites therefore allow smaller subcircuits consisting of only a few strongly connected neurons to achieve selectivity for specific sensory features.</jats:p