Spatiotemporally Graded NMDA Spike/Plateau Potentials in Basal Dendrites of Neocortical Pyramidal Neurons

Bidirectional NMDA receptor plasticity controls CA3 output and heterosynaptic metaplasticity

NMDA receptors (NMDARs) are classically known as coincidence detectors for the induction of long-term synaptic plasticity and have been implicated in hippocampal CA3 cell-dependent spatial memory functions that likely rely on dynamic cellular ensemble encoding of space. The unique functional properties of both NMDARs and mossy fiber projections to CA3 pyramidal cells place mossy fiber NMDARs in a prime position to influence CA3 ensemble dynamics. By mimicking presynaptic and postsynaptic activity patterns observed in vivo, we found a burst timing-dependent pattern of activity that triggered bidirectional long-term NMDAR plasticity at mossy fiber-CA3 synapses in rat hippocampal slices. This form of plasticity imparts bimodal control of mossy fiber-driven CA3 burst firing and spike temporal fidelity. Moreover, we found that mossy fiber NMDARs mediate heterosynaptic metaplasticity between mossy fiber and associational-commissural synapses. Thus, bidirectional NMDAR plasticity at mossy fiber-CA3 synapses could substantially contribute to the formation, storage and recall of CA3 cell assembly patterns.

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

NMDA and GABAB (KIR) conductances: the "perfect couple" for bistability

Networks that produce persistent firing in response to novel input patterns are thought to be important in working memory and other information storage functions. One possible mechanism for maintaining persistent firing is dendritic voltage bistability in which the depolarized state depends on the voltage dependence of the NMDA conductance at recurrent synapses. In previous models, the hyperpolarized state is dependent on voltage-independent conductances, including GABA(A). The interplay of these conductances leads to bistability, but its robustness is limited by the fact that the conductance ratio must be within a narrow range. The GABA(B) component of inhibitory transmission was not considered in previous analyses. Here, we show that the voltage dependence of the inwardly rectifying potassium (KIR) conductance activated by GABA(B) receptors adds substantial robustness to network simulations of bistability and the persistent firing that it underlies. The hyperpolarized state is robust because, at hyperpolarized potentials, the GABA(B)/KIR conductance is high and the NMDA conductance is low; the depolarized state is robust because, at depolarized potentials, the NMDA conductance is high and the GABA(B)/KIR conductance is low. Our results suggest that this complementary voltage dependence of GABA(B)/KIR and NMDA conductances makes them a "perfect couple" for producing voltage bistability.

Passive dendrites enable single neurons to compute linearly non-separable functions

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.

Classical views on single neuron computation treat dendrites as mere collectors of inputs, that is forwarded to the soma for linear summation and causes a spike output if it is sufficiently large. Such a single neuron model can only compute linearly separable input-output functions, representing a small fraction of all possible functions. Recent experimental findings show that in certain pyramidal cells excitatory inputs can be supra-linearly integrated within a dendritic branch, turning this branch into a spiking dendritic sub-unit. Neurons containing many of these dendritic sub-units can compute both linearly separable and linearly non-separable functions. Nevertheless, other neuron types have dendrites which do not spike because the required voltage gated channels are absent. However, these dendrites sub-linearly sum excitatory inputs turning branches into saturating sub-units. We wanted to test if this last type of non-linear summation is sufficient for a single neuron to compute linearly non-separable functions. Using a combination of Boolean algebra and biophysical modeling, we show that a neuron with a single non-linear dendritic sub-unit whether spiking or saturating is able to compute linearly non-separable functions. Thus, in principle, any neuron with a dendritic tree, even passive, can compute linearly non-separable functions.

Dopaminergic regulation of dendritic calcium: fast multisite calcium imaging

Optimal dopamine tone is required for the normal cortical function; however it is still unclear how cortical-dopamine-release affects information processing in individual cortical neurons. Thousands of glutamatergic inputs impinge onto elaborate dendritic trees of neocortical pyramidal neurons. In the process of ensuing synaptic integration (information processing), a variety of calcium transients are generated in remote dendritic compartments. In order to understand the cellular mechanisms of dopaminergic modulation it is important to know whether and how dopaminergic signals affect dendritic calcium transients. In this chapter, we describe a relatively inexpensive method for monitoring dendritic calcium fluctuations at multiple loci across the pyramidal dendritic tree, at the same moment of time (simultaneously). The experiments have been designed to measure the amplitude, time course and spatial extent of action potential-associated dendritic calcium transients before and after application of dopaminergic drugs. In the examples provided here the dendritic calcium transients were evoked by triggering the somatic action potentials (backpropagation-evoked), and puffs of exogenous dopamine were applied locally onto selected dendritic branches.

A fast model of voltage-dependent NMDA receptors

NMDA receptors are among the crucial elements of central nervous system models. Recent studies show that both conductance and kinetics of these receptors are changing voltage-dependently in some parts of the brain. Therefore, several models have been introduced to simulate their current. However, on the one hand, kinetic models-which are able to simulate these voltage-dependent phenomena-are computationally expensive for modeling of large neural networks. On the other hand, classic exponential models, which are computationally less expensive, are not able to simulate the voltage-dependency of these receptors, accurately. In this study, we have modified these classic models to endow them with the voltage-dependent conductance and time constants. Temperature sensitivity and desensitization of these receptors are also taken into account. We show that, it is possible to simulate the most important physiological aspects of NMDA receptor's behavior using only three to four differential equations, which is significantly smaller than the previous kinetic models. Consequently, it seems that our model is both fast and physiologically plausible and therefore is a suitable candidate for the modeling of large neural networks.

Hippocampal place fields emerge upon single-cell manipulation of excitability during behavior

The origin of the spatial receptive fields of hippocampal place cells has not been established. A hippocampal CA1 pyramidal cell receives thousands of synaptic inputs, mostly from other spatially tuned neurons; however, how the postsynaptic neuron's cellular properties determine the response to these inputs during behavior is unknown. We discovered that, contrary to expectations from basic models of place cells and neuronal integration, a small, spatially uniform depolarization of the spatially untuned somatic membrane potential of a silent cell leads to the sudden and reversible emergence of a spatially tuned subthreshold response and place-field spiking. Such gating of inputs by postsynaptic neuronal excitability reveals a cellular mechanism for receptive field origin and may be critical for the formation of hippocampal memory representations.

Extrasynaptic glutamate receptor activation as cellular bases for dynamic range compression in pyramidal neurons

Repetitive synaptic stimulation overcomes the ability of astrocytic processes to clear glutamate from the extracellular space, allowing some dendritic segments to become submerged in a pool of glutamate, for a brief period of time. This dynamic arrangement activates extrasynaptic NMDA receptors located on dendritic shafts. We used voltage-sensitive and calcium-sensitive dyes to probe dendritic function in this glutamate-rich location. An excess of glutamate in the extrasynaptic space was achieved either by repetitive synaptic stimulation or by glutamate iontophoresis onto the dendrites of pyramidal neurons. Two successive activations of synaptic inputs produced a typical NMDA spike, whereas five successive synaptic inputs produced characteristic plateau potentials, reminiscent of cortical UP states. While NMDA spikes were coupled with brief calcium transients highly restricted to the glutamate input site, the dendritic plateau potentials were accompanied by calcium influx along the entire dendritic branch. Once initiated, the glutamate-mediated dendritic plateau potentials could not be interrupted by negative voltage pulses. Activation of extrasynaptic NMDA receptors in cellular compartments void of spines is sufficient to initiate and support plateau potentials. The only requirement for sustained depolarizing events is a surplus of free glutamate near a group of extrasynaptic receptors. Highly non-linear dendritic spikes (plateau potentials) are summed in a highly sublinear fashion at the soma, revealing the cellular bases of signal compression in cortical circuits. Extrasynaptic NMDA receptors provide pyramidal neurons with a function analogous to a dynamic range compression in audio engineering. They limit or reduce the volume of “loud sounds” (i.e., strong glutamatergic inputs) and amplify “quiet sounds” (i.e., glutamatergic inputs that barely cross the dendritic threshold for local spike initiation). Our data also explain why consecutive cortical UP states have uniform amplitudes in a given neuron.

Location-dependent excitatory synaptic interactions in pyramidal neuron dendrites

Neocortical pyramidal neurons (PNs) receive thousands of excitatory synaptic contacts on their basal dendrites. Some act as classical driver inputs while others are thought to modulate PN responses based on sensory or behavioral context, but the biophysical mechanisms that mediate classical-contextual interactions in these dendrites remain poorly understood. We hypothesized that if two excitatory pathways bias their synaptic projections towards proximal vs. distal ends of the basal branches, the very different local spike thresholds and attenuation factors for inputs near and far from the soma might provide the basis for a classical-contextual functional asymmetry. Supporting this possibility, we found both in compartmental models and electrophysiological recordings in brain slices that the responses of basal dendrites to spatially separated inputs are indeed strongly asymmetric. Distal excitation lowers the local spike threshold for more proximal inputs, while having little effect on peak responses at the soma. In contrast, proximal excitation lowers the threshold, but also substantially increases the gain of distally-driven responses. Our findings support the view that PN basal dendrites possess significant analog computing capabilities, and suggest that the diverse forms of nonlinear response modulation seen in the neocortex, including uni-modal, cross-modal, and attentional effects, could depend in part on pathway-specific biases in the spatial distribution of excitatory synaptic contacts onto PN basal dendritic arbors.

Pyramidal neurons (PNs) are the principal neurons of the cerebral cortex and therefore lie at the heart of the brain's higher sensory, motor, affective, memory, and executive functions. But how do they work? In particular, how do they manage interactions between the classical “driver” inputs that give rise to their basic response properties, and “contextual” inputs that nonlinearly modulate those responses? It is known that PNs are contacted by thousands of excitatory synapses scattered about their dendrites, but despite decades of research, the “rules” that govern how inputs at different locations in the dendritic tree combine to influence the cell's firing rate remain poorly understood. We show here that two excitatory inputs contacting the same dendrite interact in an asymmetric nonlinear way that depends on their absolute and relative locations, where the resulting spectrum of location-dependent synaptic interactions constitutes a previously unknown form of spatial analog computation. In addition to suggesting a possible substrate for classical-contextual interactions in PN dendrites, our results imply that the computing functions of cortical circuits can only be fully understood when the detailed map of synaptic connectivity – the cortical connectome – is known down to the subdendritic level.

Long-lasting small-amplitude TRP-mediated dendritic depolarizations in CA1 pyramidal neurons are intrinsically stable and originate from distal tuft regions

In several regions of the nervous system, neurons display bi- or multistable intrinsic properties. Such stable states may be subthreshold and long-lasting, and can appear as a sustained afterdepolarization. In hippocampal CA1 pyramidal neurons, small-amplitude (1 mV) long-lasting (seconds) afterdepolarizations have been reported and are thought to depend on calcium-activated nonselective (CAN) currents recently identified as transient receptor potential (TRP) channels. Continuing our previous experimental and computational work on synaptically metabotropic glutamate receptor (mGluR)-activated TRP currents, we here explore small-amplitude long-lasting depolarizations in a detailed multicompartmental model of a CA1 pyramidal neuron. We confirm a previous hypothesis suggesting that the depolarization results from an interplay of TRP and voltage-gated calcium channels, and contribute to the understanding of the depolarization in several ways. Specifically, we show that: (i) the long-lasting depolarization may be intrinsically stable to weak excitatory and inhibitory input, (ii) the phenomenon is essentially located in distal apical dendrites, (iii) induction is facilitated if simultaneous input arrives at several dendritic branches, and if calcium- and/or mGluR-evoked signals undergo summation, suggesting that both spatial and temporal synaptic summation might be required for the depolarization to occur and (iv) we also show that the integration of inputs to oblique dendrites is strongly modulated by the presence of small-amplitude long-lasting depolarizations in distal tuft dendrites. To conclude, we suggest that small-amplitude long-lasting dendritic depolarizations may contribute to sustaining neural information during behavioural tasks in cases where information is separated in time, as in trace conditioning and delay tasks.

Clustered dynamics of inhibitory synapses and dendritic spines in the adult neocortex

A key feature of the mammalian brain is its capacity to adapt in response to experience, in part by remodeling of synaptic connections between neurons. Excitatory synapse rearrangements have been monitored in vivo by observation of dendritic spine dynamics, but lack of a vital marker for inhibitory synapses has precluded their observation. Here, we simultaneously monitor in vivo inhibitory synapse and dendritic spine dynamics across the entire dendritic arbor of pyramidal neurons in the adult mammalian cortex using large-volume, high-resolution dual-color two-photon microscopy. We find that inhibitory synapses on dendritic shafts and spines differ in their distribution across the arbor and in their remodeling kinetics during normal and altered sensory experience. Further, we find inhibitory synapse and dendritic spine remodeling to be spatially clustered and that clustering is influenced by sensory input. Our findings provide in vivo evidence for local coordination of inhibitory and excitatory synaptic rearrangements.

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.

Probing synaptic function in dendrites with calcium imaging

Calcium imaging has become a widely used technique to probe neuronal activity on the cellular and subcellular levels. In contrast to standard electrophysiological methods, calcium imaging resolves sub- and suprathreshold activation patterns in structures as small as fine dendritic branches and spines. This review highlights recent findings gained on the subcellular level using calcium imaging, with special emphasis on synaptic transmission and plasticity in individual spines. Since imaging allows monitoring activity across populations of synapses, it has recently been adopted to investigate how dendrites integrate information from many synapses. Future experiments, ideally carried out in vivo, will reveal how the dendritic tree integrates and computes afferent signals. For example, it is now possible to directly test the concept that dendritic inputs are clustered and that single dendrites or dendritic stretches act as independent computational units.

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.

Understanding calcium waves and sparks in central neurons

All cells use changes in intracellular calcium concentration ([Ca(2+)](i)) to regulate cell signalling events. In neurons, with their elaborate dendritic and axonal arborizations, there are clear examples of both localized and widespread Ca(2+) signals. [Ca(2+)](i) changes that are generated by Ca(2+) entry through voltage- and ligand-gated channels are the best characterized. In addition, the release of Ca(2+) from intracellular stores can result in increased [Ca(2+)](i); the signals that trigger this release have been less well-studied, in part because they are not usually associated with specific changes in membrane potential. However, recent experiments have revealed dramatic widespread Ca(2+) waves and localized spark-like events, particularly in dendrites. Here we review emerging data on the nature of these signals and their functions.

Glutamate spillover promotes the generation of NMDA spikes

NMDA spikes are prominent in the basal dendrites of cortical pyramidal neurons and greatly expand their ability to integrate synaptic inputs. Calcium (Ca) signals during these spikes are important for synaptic plasticity and fundamentally depend on activation of NMDA receptors. However, the factors that shape the activation of these receptors and the initiation of NMDA spikes remain unclear. Here we examine the properties of NMDA spikes in the basal dendrites of layer 5 pyramidal neurons in the mouse prefrontal cortex. Using two-photon imaging, we demonstrate that NMDA spikes evoke large Ca signals in both postsynaptic spines and nearby dendrites. We find that the dendrite Ca signals depend on NMDA and AMPA receptors but not sodium (Na) or Ca channels. Using voltage-clamp recordings, we show that activation of dendrite NMDA receptors is enhanced by concerted synaptic activity. Blocking glutamate reuptake further increases activation of these receptors and promotes the initiation of NMDA spikes. We conclude that glutamate spillover and recruitment of extrasynaptic receptors contribute to the initiation of NMDA spikes. These results have important implications for how synaptic activity generates both electrical and biochemical signals in dendrites and spines.

Distinguishing Linear vs. Non-Linear Integration in CA1 Radial Oblique Dendrites: It's about Time

It was recently shown that multiple excitatory inputs to CA1 pyramidal neuron dendrites must be activated nearly simultaneously to generate local dendritic spikes and supralinear responses at the soma; even slight input desynchronization prevented local spike initiation (Gasparini and Magee, 2006; Losonczy and Magee, 2006). This led to the conjecture that CA1 pyramidal neurons may only express their non-linear integrative capabilities during the highly synchronized sharp waves and ripples that occur during slow wave sleep and resting/consummatory behavior, whereas during active exploration and REM sleep (theta rhythm), inadequate synchronization of excitation would lead CA1 pyramidal cells to function as essentially linear devices. Using a detailed single neuron model, we replicated the experimentally observed synchronization effect for brief inputs mimicking single synaptic release events. When synapses were driven instead by double pulses, more representative of the bursty inputs that occur in vivo, we found that the tolerance for input desynchronization was increased by more than an order of magnitude. The effect depended mainly on paired-pulse facilitation of NMDA receptor-mediated responses at Schaffer collateral synapses. Our results suggest that CA1 pyramidal cells could function as non-linear integrative units in all major hippocampal states.

Dendritic spines and distributed circuits

Dendritic spines receive most excitatory connections in pyramidal cells and many other principal neurons. But why do neurons use spines, when they could accommodate excitatory contacts directly on their dendritic shafts? One suggestion is that spines serve to connect with passing axons, thus increasing the connectivity of the dendrites. Another hypothesis is that spines are biochemical compartments that enable input-specific synaptic plasticity. A third possibility is that spines have an electrical role, filtering synaptic potentials and electrically isolating inputs from each other. In this review, I argue that, when viewed from the perspective of the circuit function, these three functions dovetail with one another to achieve a single overarching goal: to implement a distributed circuit with widespread connectivity. Spines would endow these circuits with nonsaturating, linear integration and input-specific learning rules, which would enable them to function as neural networks, with emergent encoding and processing of information.

Branch-specific plasticity enables self-organization of nonlinear computation in single neurons

It has been conjectured that nonlinear processing in dendritic branches endows individual neurons with the capability to perform complex computational operations that are needed to solve for example the binding problem. However, it is not clear how single neurons could acquire such functionality in a self-organized manner, because most theoretical studies of synaptic plasticity and learning concentrate on neuron models without nonlinear dendritic properties. In the meantime, a complex picture of information processing with dendritic spikes and a variety of plasticity mechanisms in single neurons has emerged from experiments. In particular, new experimental data on dendritic branch strength potentiation in rat hippocampus have not yet been incorporated into such models. In this article, we investigate how experimentally observed plasticity mechanisms, such as depolarization-dependent spike-timing-dependent plasticity and branch-strength potentiation, could be integrated to self-organize nonlinear neural computations with dendritic spikes. We provide a mathematical proof that, in a simplified setup, these plasticity mechanisms induce a competition between dendritic branches, a novel concept in the analysis of single neuron adaptivity. We show via computer simulations that such dendritic competition enables a single neuron to become member of several neuronal ensembles and to acquire nonlinear computational capabilities, such as the capability to bind multiple input features. Hence, our results suggest that nonlinear neural computation may self-organize in single neurons through the interaction of local synaptic and dendritic plasticity mechanisms.

Dendritic slow dynamics enables localized cortical activity to switch between mobile and immobile modes with noisy background input

Mounting lines of evidence suggest the significant computational ability of a single neuron empowered by active dendritic dynamics. This motivates us to study what functionality can be acquired by a network of such neurons. The present paper studies how such rich single-neuron dendritic dynamics affects the network dynamics, a question which has scarcely been specifically studied to date. We simulate neurons with active dendrites networked locally like cortical pyramidal neurons, and find that naturally arising localized activity--called a bump--can be in two distinct modes, mobile or immobile. The mode can be switched back and forth by transient input to the cortical network. Interestingly, this functionality arises only if each neuron is equipped with the observed slow dendritic dynamics and with in vivo-like noisy background input. If the bump activity is considered to indicate a point of attention in the sensory areas or to indicate a representation of memory in the storage areas of the cortex, this would imply that the flexible mode switching would be of great potential use for the brain as an information processing device. We derive these conclusions using a natural extension of the conventional field model, which is defined by combining two distinct fields, one representing the somatic population and the other representing the dendritic population. With this tool, we analyze the spatial distribution of the degree of after-spike adaptation and explain how we can understand the presence of the two distinct modes and switching between the modes. We also discuss the possible functional impact of this mode-switching ability.

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

Postsynaptic [Ca(2+)](i) changes contribute to several kinds of plasticity in pyramidal neurons. We examined the effects of synaptically activated Ca(2+) waves and NMDA spikes on subsequent Ca(2+) signalling in CA1 pyramidal cell dendrites in hippocampal slices. Tetanic synaptic stimulation evoked a localized Ca(2+) wave in the primary apical dendrites. The [Ca(2+)](i) increase from a backpropagating action potential (bAP) or subthreshold depolarization was reduced if it was generated immediately after the wave. The suppression had a recovery time of 30-60 s. The suppression only occurred where the wave was generated and was not due to a change in bAP amplitude or shape. The suppression also could be generated by Ca(2+) waves evoked by uncaging IP(3), showing that other signalling pathways activated by the synaptic tetanus were not required. The suppression was proportional to the amplitude of the [Ca(2+)](i) change of the Ca(2+) wave and was not blocked by a spectrum of kinase or phosphatase inhibitors, consistent with suppression due to Ca(2+)-dependent inactivation of Ca(2+) channels. The waves also reduced the frequency and amplitude of spontaneous, localized Ca(2+) release events in the dendrites by a different mechanism, probably by depleting the stores at the site of wave generation. The same synaptic tetanus often evoked NMDA spike-mediated [Ca(2+)](i) increases in the oblique dendrites where Ca(2+) waves do not propagate. These NMDA spikes suppressed the [Ca(2+)](i) increase caused by bAPs in those regions. [Ca(2+)](i) increases by Ca(2+) entry through voltage-gated Ca(2+) channels also suppressed the [Ca(2+)](i) increases from subsequent bAPs in regions where the voltage-gated [Ca(2+)](i) increases were largest, showing that all ways of raising [Ca(2+)](i) could cause suppression.

The decade of the dendritic NMDA spike

In the field of cortical cellular physiology, much effort has been invested in understanding thick apical dendrites 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).

GABAB receptor modulation of voltage-sensitive calcium channels in spines and dendrites

Although primarily studied at the cell body, GABA(B) receptors (GABA(B)Rs) are abundant at spines and dendrites of cortical pyramidal neurons, where they are positioned to influence both synaptic and dendritic function. Here, we examine how GABA(B)Rs modulate calcium (Ca) signals evoked by action potentials (APs) in spines and dendrites of layer 2/3 pyramidal neurons in mouse prefrontal cortex. We first use two-photon microscopy to show that GABA(B)Rs inhibit AP Ca signals throughout the entire dendritic arbor of these neurons. We then use local pharmacology and GABA uncaging to show that dendritic GABA(B)Rs also decrease the input resistance, shorten the AP afterdepolarization, and generate inhibitory postsynaptic potentials. However, we find that these electrophysiological effects recorded at the cell body do not correlate with the inhibition of AP Ca signals measured in spines and dendrites. Instead, we use voltage-clamp recordings to show that GABA(B)Rs directly inhibit several subtypes of voltage-sensitive calcium channels (VSCCs) in both spines and dendrites. Given the importance of VSCC-mediated Ca signals for neuronal function, our results have implications for the functional role of dendritic GABA(B)Rs in the prefrontal cortex and throughout the brain.

Synaptic integration gradients in single cortical pyramidal cell dendrites

Cortical pyramidal neurons receive thousands of synaptic inputs arriving at different dendritic locations with varying degrees of temporal synchrony. It is not known if different locations along single cortical dendrites integrate excitatory inputs in different ways. Here we have used two-photon glutamate uncaging and compartmental modeling to reveal a gradient of nonlinear synaptic integration in basal and apical oblique dendrites of cortical pyramidal neurons. Excitatory inputs to the proximal dendrite sum linearly and require precise temporal coincidence for effective summation, whereas distal inputs are amplified with high gain and integrated over broader time windows. This allows distal inputs to overcome their electrotonic disadvantage, and become surprisingly more effective than proximal inputs at influencing action potential output. Thus, single dendritic branches can already exhibit nonuniform synaptic integration, with the computational strategy shifting from temporal coding to rate coding along the dendrite.

Dendritic discrimination of temporal input sequences in cortical neurons

The detection and discrimination of temporal sequences is fundamental to brain function and underlies perception, cognition, and motor output. By applying patterned, two-photon glutamate uncaging, we found that single dendrites of cortical pyramidal neurons exhibit sensitivity to the sequence of synaptic activation. This sensitivity is encoded by both local dendritic calcium signals and somatic depolarization, leading to sequence-selective spike output. The mechanism involves dendritic impedance gradients and nonlinear synaptic N-methyl-D-aspartate receptor activation and is generalizable to dendrites in different neuronal types. This enables discrimination of patterns delivered to a single dendrite, as well as patterns distributed randomly across the dendritic tree. Pyramidal cell dendrites can thus act as processing compartments for the detection of synaptic sequences, thereby implementing a fundamental cortical computation.

Spike timing dependent plasticity: a consequence of more fundamental learning rules

Spike timing dependent plasticity (STDP) is a phenomenon in which the precise timing of spikes affects the sign and magnitude of changes in synaptic strength. STDP is often interpreted as the comprehensive learning rule for a synapse - the "first law" of synaptic plasticity. This interpretation is made explicit in theoretical models in which the total plasticity produced by complex spike patterns results from a superposition of the effects of all spike pairs. Although such models are appealing for their simplicity, they can fail dramatically. For example, the measured single-spike learning rule between hippocampal CA3 and CA1 pyramidal neurons does not predict the existence of long-term potentiation one of the best-known forms of synaptic plasticity. Layers of complexity have been added to the basic STDP model to repair predictive failures, but they have been outstripped by experimental data. We propose an alternate first law: neural activity triggers changes in key biochemical intermediates, which act as a more direct trigger of plasticity mechanisms. One particularly successful model uses intracellular calcium as the intermediate and can account for many observed properties of bidirectional plasticity. In this formulation, STDP is not itself the basis for explaining other forms of plasticity, but is instead a consequence of changes in the biochemical intermediate, calcium. Eventually a mechanism-based framework for learning rules should include other messengers, discrete change at individual synapses, spread of plasticity among neighboring synapses, and priming of hidden processes that change a synapse's susceptibility to future change. Mechanism-based models provide a rich framework for the computational representation of synaptic plasticity.

Neuronal arithmetic

The vast computational power of the brain has traditionally been viewed as arising from the complex connectivity of neural networks, in which an individual neuron acts as a simple linear summation and thresholding device. However, recent studies show that individual neurons utilize a wealth of nonlinear mechanisms to transform synaptic input into output firing. These mechanisms can arise from synaptic plasticity, synaptic noise, and somatic and dendritic conductances. This tool kit of nonlinear mechanisms confers considerable computational power on both morphologically simple and more complex neurons, enabling them to perform a range of arithmetic operations on signals encoded ina variety of different ways.

Dendritic organization of sensory input to cortical neurons in vivo

In sensory cortex regions, neurons are tuned to specific stimulus features. For example, in the visual cortex, many neurons fire predominantly in response to moving objects of a preferred orientation. However, the characteristics of the synaptic input that cortical neurons receive to generate their output firing pattern remain unclear. Here we report a novel approach for the visualization and functional mapping of sensory inputs to the dendrites of cortical neurons in vivo. By combining high-speed two-photon imaging with electrophysiological recordings, we identify local subthreshold calcium signals that correspond to orientation-specific synaptic inputs. We find that even inputs that share the same orientation preference are widely distributed throughout the dendritic tree. At the same time, inputs of different orientation preference are interspersed, so that adjacent dendritic segments are tuned to distinct orientations. Thus, orientation-tuned neurons can compute their characteristic firing pattern by integrating spatially distributed synaptic inputs coding for multiple stimulus orientations.

A coordinated local translational control point at the synapse involving relief from silencing and MOV10 degradation

Persistent changes in synaptic strength are locally regulated by both protein degradation and synthesis; however, the coordination of these opposing limbs is poorly understood. Here, we found that the RISC protein MOV10 was present at synapses and was rapidly degraded by the proteasome in an NMDA-receptor-mediated activity-dependent manner. We designed a translational trap to capture those mRNAs whose spatiotemporal translation is regulated by MOV10. When MOV10 was suppressed, a set of mRNAs--including alpha-CaMKII, Limk1, and the depalmitoylating enzyme lysophospholipase1 (Lypla1)--selectively entered the polysome compartment. We also observed that Lypla1 mRNA is associated with the brain-enriched microRNA miR-138. Using a photoconvertible translation reporter, Kaede, we analyzed the activity-dependent protein synthesis driven by Lypla1 and alpha-CaMKII 3'UTRs. We established this protein synthesis to be MOV10 and proteasome dependent. These results suggest a unifying picture of a local translational regulatory mechanism during synaptic plasticity.

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

Bursts of action potentials are important information-bearing signals in the brain, although the neuronal specializations underlying burst generation and detection are only partially understood. In apical dendrites of neocortical pyramidal neurons, calcium spikes are known to contribute to burst generation, but a comparable understanding of basal dendritic mechanisms is lacking. Here we show that NMDA spikes in basal dendrites mediate both detection and generation of bursts through a postsynaptic mechanism. High-frequency inputs to basal dendrites markedly facilitated NMDA spike initiation compared with low-frequency activation or single inputs. Unlike conventional temporal summation effects based on voltage, however, NMDA spike facilitation depended mainly on residual glutamate bound to NMDA receptors from previous activations. Once triggered by an input burst, we found that NMDA spikes in turn reliably trigger output bursts under in vivo-like stimulus conditions. Through their unique biophysical properties, NMDA spikes are thus ideally suited to promote the propagation of bursts through the cortical network.

Possible dendritic contribution to unimodal numerosity tuning and weber-fechner law-dependent numerical cognition

Humans and animals are known to share an ability to estimate or compare the numerosity of visual stimuli, and this ability is considered to be supported by the cortical neurons that have unimodal tuning for numerosity, referred to as the numerosity detector neurons. How such unimodal numerosity tuning is shaped through plasticity mechanisms is unknown. Here, I propose a testable hypothetical mechanism based on recently revealed features of the neuronal dendrite, namely, cooperative plasticity induction and nonlinear input integration at nearby dendritic sites, on the basis of the existing proposal that individual visual stimuli are represented as similar localized activities regardless of the size or the shape in a cortical region in the dorsal visual pathway. Intriguingly, the proposed mechanism naturally explains a prominent feature of the numerosity detector neurons, namely, the broadening of the tuning curve in proportion to the preferred numerosity, which is considered to underlie the known Weber-Fechner law-dependent accuracy of numerosity estimation and comparison. The simulated tuning curves are less sharp than reality, however, and together with the evidence from human imaging studies that numerical representation is a distributed phenomenon, it may not be likely that the proposed mechanism operates by itself. Rather, the proposed mechanism might facilitate the formation of hierarchical circuitry proposed in the previous studies, which includes neurons with monotonic numerosity tuning as well as those with sharp unimodal tuning, by serving as an efficient initial condition.

Capacity-enhancing synaptic learning rules in a medial temporal lobe online learning model

Medial temporal lobe structures are responsible for recording the continuous stream of autobiographical memories that define our unique personal history. Remarkably, these areas can construct durable memories from brief exposures to the constantly changing activity patterns arriving from antecedent cortical areas. Using a computer model of the hippocampal Schaffer collateral pathway that incorporates evidence for dendritic spikes in CA1 pyramidal neurons, we searched for biologically-plausible long-term potentiation (LTP) and homeostatic depression (HD) rules that maximize "online" learning capacity. We found memory utilization is most efficient when (1) very few synapses are modified to store each pattern, (2) LTP, the learning operation, is dendrite-specific and gated by distinct pre- and postsynaptic thresholds, (3) HD, the forgetting operation, co-occurs with LTP and targets least-recently potentiated synapses, and (4) both LTP and HD are all-or-none, leading de facto to binary-valued synaptic weights. In networks containing up to 40 million synapses, the learning scheme led to order-of-magnitude capacity increases compared to conventional plasticity rules.

Rapid neocortical dynamics: cellular and network mechanisms

The highly interconnected local and large-scale networks of the neocortical sheet rapidly and dynamically modulate their functional connectivity according to behavioral demands. This basic operating principle of the neocortex is mediated by the continuously changing flow of excitatory and inhibitory synaptic barrages that not only control participation of neurons in networks but also define the networks themselves. The rapid control of neuronal responsiveness via synaptic bombardment is a fundamental property of cortical dynamics that may provide the basis of diverse behaviors, including sensory perception, motor integration, working memory, and attention.

Synaptic clustering by dendritic signalling mechanisms

Dendritic signal integration is one of the fundamental building blocks of information processing in the brain. Dendrites are endowed with mechanisms of nonlinear summation of synaptic inputs leading to regenerative dendritic events including local sodium, NMDA and calcium spikes. The generation of these events requires distinct spatio-temporal activation patterns of synaptic inputs. We hypothesise that the recent findings on dendritic spikes and local synaptic plasticity rules suggest clustering of common inputs along a subregion of a dendritic branch. These clusters may enable dendrites to separately threshold groups of functionally similar inputs, thus allowing single neurons to act as a superposition of many separate integrate and fire units. Ultimately, these properties expand our understanding about the computational power of neuronal networks.

Control of neuronal persistent activity by voltage-dependent dendritic properties

Neural integrators and working memory rely on persistent activity, a widespread neural phenomenon potentially involving persistent sodium conductances. Using a unique combination of voltage-clamp, dynamic-clamp, and frequency-domain techniques, we have investigated the role of voltage-dependent conductances on the dendritic electrotonic structure of neurons of the prepositus hypoglossi nucleus (PHN), which is known to be involved in oculomotor integration. The PHN contains two main neuronal populations: type B neurons with a double afterhyperpolarization and type D neurons, which not only are oscillatory but also have a greater electrotonic length than that of type B neurons. The persistent sodium conductance is present in all PHN neurons, although its effect on the dynamic electrotonic structure is shown to significantly differ in the two major cell types present in the nucleus. The electrotonic differences are such that the persistent sodium conductance can be almost perfectly manipulated in a type B neuron using an on-line dynamic clamp to add or subtract virtual sodium ion channels. The dynamic-clamp results are confirmed by data-fitted models, which suggest that the persistent sodium conductance has two different roles depending on its somatic versus dendritic location: perisomatic conductances could play a major role in maintaining action potential discharge and dendritic conductances would be more involved in other computational properties, such as those involving remote synaptic processing or bistable events.