Cell type- and subcellular position-dependent summation of unitary postsynaptic potentials in neocortical neurons

Physiological features of parvalbumin-expressing GABAergic interneurons contributing to high-frequency oscillations in the cerebral cortex

Parvalbumin-expressing (PV+) inhibitory interneurons drive gamma oscillations (30-80 Hz), which underlie higher cognitive functions. In this review, we discuss two groups/aspects of fundamental properties of PV+ interneurons. In the first group (dubbed Before Axon), we list properties representing optimal synaptic integration in PV+ interneurons designed to support fast oscillations. For example: [i] Information can neither enter nor leave the neocortex without the engagement of fast PV+ -mediated inhibition; [ii] Voltage responses in PV+ interneuron dendrites integrate linearly to reduce impact of the fluctuations in the afferent drive; and [iii] Reversed somatodendritic Rm gradient accelerates the time courses of synaptic potentials arriving at the soma. In the second group (dubbed After Axon), we list morphological and biophysical properties responsible for (a) short synaptic delays, and (b) efficient postsynaptic outcomes. For example: [i] Fast-spiking ability that allows PV+ interneurons to outpace other cortical neurons (pyramidal neurons). [ii] Myelinated axon (which is only found in the PV+ subclass of interneurons) to secure fast-spiking at the initial axon segment; and [iii] Inhibitory autapses - autoinhibition, which assures brief biphasic voltage transients and supports postinhibitory rebounds. Recent advent of scientific tools, such as viral strategies to target PV cells and the ability to monitor PV cells via in vivo imaging during behavior, will aid in defining the role of PV cells in the CNS. Given the link between PV+ interneurons and cognition, in the future, it would be useful to carry out physiological recordings in the PV+ cell type selectively and characterize if and how psychiatric and neurological diseases affect initiation and propagation of electrical signals in this cortical sub-circuit. Voltage imaging may allow fast recordings of electrical signals from many PV+ interneurons simultaneously.

Sharp-wave ripple doublets induce complex dendritic spikes in parvalbumin interneurons in vivo

Neuronal plasticity has been shown to be causally linked to coincidence detection through dendritic spikes (dSpikes). We demonstrate the existence of SPW-R-associated, branch-specific, local dSpikes and their computational role in basal dendrites of hippocampal PV+ interneurons in awake animals. To measure the entire dendritic arbor of long thin dendrites during SPW-Rs, we used fast 3D acousto-optical imaging through an eccentric deep-brain adapter and ipsilateral local field potential recording. The regenerative calcium spike started at variable, NMDA-AMPA-dependent, hot spots and propagated in both direction with a high amplitude beyond a critical distance threshold (~150 µm) involving voltage-gated calcium channels. A supralinear dendritic summation emerged during SPW-R doublets when two successive SPW-R events coincide within a short temporal window (~150 ms), e.g., during more complex association tasks, and generated large dSpikes with an about 2.5-3-fold amplitude increase which propagated down to the soma. Our results suggest that these doublet-associated dSpikes can work as a dendritic-level temporal and spatial coincidence detector during SPW-R-related network computation in awake mice.

Predominantly linear summation of metabotropic postsynaptic potentials follows coactivation of neurogliaform interneurons

Summation of ionotropic receptor-mediated responses is critical in neuronal computation by shaping input-output characteristics of neurons. However, arithmetics of summation for metabotropic signals are not known. We characterized the combined ionotropic and metabotropic output of neocortical neurogliaform cells (NGFCs) using electrophysiological and anatomical methods in the rat cerebral cortex. These experiments revealed that GABA receptors are activated outside release sites and confirmed coactivation of putative NGFCs in superficial cortical layers in vivo. Triple recordings from presynaptic NGFCs converging to a postsynaptic neuron revealed sublinear summation of ionotropic GABA_A responses and linear summation of metabotropic GABA_B responses. Based on a model combining properties of volume transmission and distributions of all NGFC axon terminals, we predict that in 83% of cases one or two NGFCs can provide input to a point in the neuropil. We suggest that interactions of metabotropic GABAergic responses remain linear even if most superficial layer interneurons specialized to recruit GABA_B receptors are simultaneously active.

Dendrites Enable a Robust Mechanism for Neuronal Stimulus Selectivity

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.

Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-γ peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-γ peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

Recordings of brain activity show multiple coexisting oscillations. The generation of these oscillations has so far only been investigated in generic one- and two-population networks, neglecting their embedment into larger systems. We introduce a method that determines the mechanisms and sub-circuits generating oscillations in structured spiking networks. Analyzing a multi-layered model of the cortical microcircuit, we trace back characteristic oscillations to experimentally observed connectivity patterns. The approach exposes the influence of individual connections on frequency and amplitude of these oscillations and therefore reveals locations, where biological mechanisms controlling oscillations and experimental manipulations have the largest impact. The new analytical tool replaces parameter scans in computationally expensive models, guides circuit design, and can be employed to validate connectivity data.

Effects of homeostatic constraints on associative memory storage and synaptic connectivity of cortical circuits

The impact of learning and long-term memory storage on synaptic connectivity is not completely understood. In this study, we examine the effects of associative learning on synaptic connectivity in adult cortical circuits by hypothesizing that these circuits function in a steady-state, in which the memory capacity of a circuit is maximal and learning must be accompanied by forgetting. Steady-state circuits should be characterized by unique connectivity features. To uncover such features we developed a biologically constrained, exactly solvable model of associative memory storage. The model is applicable to networks of multiple excitatory and inhibitory neuron classes and can account for homeostatic constraints on the number and the overall weight of functional connections received by each neuron. The results show that in spite of a large number of neuron classes, functional connections between potentially connected cells are realized with less than 50% probability if the presynaptic cell is excitatory and generally a much greater probability if it is inhibitory. We also find that constraining the overall weight of presynaptic connections leads to Gaussian connection weight distributions that are truncated at zero. In contrast, constraining the total number of functional presynaptic connections leads to non-Gaussian distributions, in which weak connections are absent. These theoretical predictions are compared with a large dataset of published experimental studies reporting amplitudes of unitary postsynaptic potentials and probabilities of connections between various classes of excitatory and inhibitory neurons in the cerebellum, neocortex, and hippocampus.

Input transformation by dendritic spines of pyramidal neurons

In the mammalian brain, most inputs received by a neuron are formed on the dendritic tree. In the neocortex, the dendrites of pyramidal neurons are covered by thousands of tiny protrusions known as dendritic spines, which are the major recipient sites for excitatory synaptic information in the brain. Their peculiar morphology, with a small head connected to the dendritic shaft by a slender neck, has inspired decades of theoretical and more recently experimental work in an attempt to understand how excitatory synaptic inputs are processed, stored and integrated in pyramidal neurons. Advances in electrophysiological, optical and genetic tools are now enabling us to unravel the biophysical and molecular mechanisms controlling spine function in health and disease. Here I highlight relevant findings, challenges and hypotheses on spine function, with an emphasis on the electrical properties of spines and on how these affect the storage and integration of excitatory synaptic inputs in pyramidal neurons. In an attempt to make sense of the published data, I propose that the raison d'etre for dendritic spines lies in their ability to undergo activity-dependent structural and molecular changes that can modify synaptic strength, and hence alter the gain of the linearly integrated sub-threshold depolarizations in pyramidal neuron dendrites before the generation of a dendritic spike.

Frequency-dependent signal processing in apical dendrites of hippocampal CA1 pyramidal cells

Depending on an animal's behavioral state, hippocampal CA1 pyramidal cells receive distinct patterns of excitatory and inhibitory synaptic inputs. The time-dependent changes in the frequencies of these inputs and the nonuniform distribution of voltage-gated channels lead to dynamic fluctuations in membrane conductance. In this study, using a whole-cell patch-clamp method, we attempted to record and analyze the frequency dependencies of membrane responsiveness in Wistar rat hippocampal CA1 pyramidal cells following noise current injection directly into dendrites and somata under pharmacological blockade of all synaptic inputs. To estimate the frequency-dependent properties of membrane potential, membrane impedance was determined from the voltage response divided by the input current in the frequency domain. The cell membrane of most neurons showed low-pass filtering properties in all regions. In particular, the properties were strongly expressed in the somata or proximal dendrites. Moreover, the data revealed nonuniform distribution of dendritic impedance, which was high in the intermediate segment of the apical dendritic shaft (∼220-260μm from the soma). The low-pass filtering properties in the apical dendrites were more enhanced by membrane depolarization than those in the somata. Coherence spectral analysis revealed high coherence between the input signal and the output voltage response in the theta-gamma frequency range, and large lags emerged in the distal dendrites in the gamma frequency range. Our results suggest that apical dendrites of hippocampal CA1 pyramidal cells integrate synaptic inputs according to the frequency components of the input signal along the dendritic segments receiving the inputs.

Canonical Organization of Layer 1 Neuron-Led Cortical Inhibitory and Disinhibitory Interneuronal Circuits

Interneurons play a key role in cortical function and dysfunction, yet organization of cortical interneuronal circuitry remains poorly understood. Cortical Layer 1 (L1) contains 2 general GABAergic interneuron groups, namely single bouquet cells (SBCs) and elongated neurogliaform cells (ENGCs). SBCs predominantly make unidirectional inhibitory connections (SBC→) with L2/3 interneurons, whereas ENGCs frequently form reciprocal inhibitory and electric connections (ENGC↔) with L2/3 interneurons. Here, we describe a systematic investigation of the pyramidal neuron targets of L1 neuron-led interneuronal circuits in the rat barrel cortex with simultaneous octuple whole-cell recordings and report a simple organizational scheme of the interneuronal circuits. Both SBCs→ and ENGC ↔ L2/3 interneuronal circuits connect to L2/3 and L5, but not L6, pyramidal neurons. SBC → L2/3 interneuronal circuits primarily inhibit the entire dendritic-somato-axonal axis of a few L2/3 and L5 pyramidal neurons located within the same column. In contrast, ENGC ↔ L2/3 interneuronal circuits generally inhibit the distal apical dendrite of many L2/3 and L5 pyramidal neurons across multiple columns. Finally, L1 interneuron-led circuits target distinct subcellular compartments of L2/3 and L5 pyramidal neurons in a L2/3 interneuron type-dependent manner. These results suggest that L1 neurons form canonical interneuronal circuits to control information processes in both supra- and infragranular cortical layers.

Axo-dendritic overlap and laminar projection can explain interneuron connectivity to pyramidal cells

Neocortical GABAergic interneurons have important roles in the normal and pathological states of the circuit. Recent work has revealed that somatostatin-positive (SOM) and parvalbumin-positive (PV) interneurons connect promiscuously to pyramidal cells (PCs). We investigated whether Peters' rule, that is, the spatial overlap of axons and dendrites, could explain this unspecific connectivity. We reconstructed the morphologies of P11-17 mouse SOM and PV interneurons and their PC targets, and performed Monte Carlo simulations to build maps of predicted connectivity based on Peters' rule. We then compared the predicted with the real connectivity maps, measured with 2-photon uncaging experiments, and found no statistical differences between them in the probability of connection as a function of distance and in the spatial structure of the maps. Finally, using reconstructions of connected SOM-PCs and PV-PCs, we investigated the subcellular targeting specificity, by analyzing the postsynaptic position of the contacts, and found that their spatial distributions match the distribution of postsynaptic PC surface area, in agreement with Peters' rule. Thus, the spatial profile of the connectivity maps and even the postsynaptic position of interneuron contacts could result from the mere overlap of axonal and dendritic arborizations and their laminar projections patterns.

Directional hearing by linear summation of binaural inputs at the medial superior olive

Neurons in the medial superior olive (MSO) enable sound localization by their remarkable sensitivity to submillisecond interaural time differences (ITDs). Each MSO neuron has its own "best ITD" to which it responds optimally. A difference in physical path length of the excitatory inputs from both ears cannot fully account for the ITD tuning of MSO neurons. As a result, it is still debated how these inputs interact and whether the segregation of inputs to opposite dendrites, well-timed synaptic inhibition, or asymmetries in synaptic potentials or cellular morphology further optimize coincidence detection or ITD tuning. Using in vivo whole-cell and juxtacellular recordings, we show here that ITD tuning of MSO neurons is determined by the timing of their excitatory inputs. The inputs from both ears sum linearly, whereas spike probability depends nonlinearly on the size of synaptic inputs. This simple coincidence detection scheme thus makes accurate sound localization possible.

A cytological and experimental study of the neuropil and primary olfactory afferences to the piriform cortex

The microscopic organization of the piriform cortex (PC) was studied in normal and experimental material from adult albino rats. In rapid-Golgi specimens a set of collaterals from the lateral olfactory tract (i.e., sublayer Ia) to the neuropil of the Layer II (LII) was identified. Specimens from experimental animals that received electrolytic lesion of the main olfactory bulb three days before sacrificing, were further processed for pre-embedding immunocytochemistry to the enzyme glutamic acid decarboxylase 67 (GAD 67). This novel approach permitted a simultaneous visualization at electron microscopy of both synaptic degeneration and GAD67-immunoreactive (GAD-I) sites. Degenerating and GAD-I synapses were separately found in the neuropil of Layers I and II of the PC. Previously overlooked patches of neuropil were featured in sublayer Ia. These areas consisted of dendritic and axonal processes including four synaptic types. Tridimensional reconstructions from serial thin sections from LI revealed the external appearance of the varicose and tubular dendrites as well as the synaptic terminals therein. The putative source(s) of processes to the neuropil of sublayer Ia is discussed in the context of the internal circuitry of the PC and an alternative model is introduced.

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.

The organization of two new cortical interneuronal circuits

Deciphering the interneuronal circuitry is central to understanding brain functions, yet it remains a challenging task in neurobiology. Using simultaneous quadruple-octuple in vitro and dual in vivo whole-cell recordings, we found two previously unknown interneuronal circuits that link cortical layer 1-3 (L1-3) interneurons and L5 pyramidal neurons in the rat neocortex. L1 single-bouquet cells (SBCs) preferentially formed unidirectional inhibitory connections on L2/3 interneurons that inhibited the entire dendritic-somato-axonal axis of ∼1% of L5 pyramidal neurons located in the same column. In contrast, L1 elongated neurogliaform cells (ENGCs) frequently formed mutual inhibitory and electric connections with L2/3 interneurons, and these L1-3 interneurons inhibited the distal apical dendrite of >60% of L5 pyramidal neurons across multiple columns. Functionally, SBC→L2/3 interneuron→L5 pyramidal neuronal circuits disinhibited and ENGC↔L2/3 interneuron→L5 pyramidal neuronal circuits inhibited the initiation of dendritic complex spikes in L5 pyramidal neurons. As dendritic complex spikes can serve coincidence detection, these cortical interneuronal circuits may be essential for salience selection.

Integration of subthreshold and suprathreshold excitatory barrages along the somatodendritic axis of pyramidal neurons

Neurons integrate inputs arriving in different cellular compartments to produce action potentials that are transmitted to other neurons. Because of the voltage- and time-dependent conductances in the dendrites and soma, summation of synaptic inputs is complex. To examine summation of membrane potentials and firing rates, we performed whole-cell recordings from layer 5 cortical pyramidal neurons in acute slices of the rat's somatosensory cortex. We delivered subthreshold and suprathreshold stimuli at the soma and several sites on the apical dendrite, and injected inputs that mimic synaptic barrages at individual or distributed sites. We found that summation of subthreshold potentials differed from that of firing rates. Subthreshold summation was linear when barrages were small but became supralinear as barrages increased. When neurons were discharging repetitively the rules were more diverse. At the soma and proximal apical dendrite summation of the evoked firing rates was predominantly sublinear whereas in the distal dendrite summation ranged from supralinear to sublinear. In addition, the integration of inputs delivered at a single location differed from that of distributed inputs only for suprathreshold responses. These results indicate that convergent inputs onto the apical dendrite and soma do not simply summate linearly, as suggested previously, and that distinct presynaptic afferents that target specific sites on the dendritic tree may perform unique sets of computations.

Thin dendrites of cerebellar interneurons confer sublinear synaptic integration and a gradient of short-term plasticity

Interneurons are critical for neuronal circuit function, but how their dendritic morphologies and membrane properties influence information flow within neuronal circuits is largely unknown. We studied the spatiotemporal profile of synaptic integration and short-term plasticity in dendrites of mature cerebellar stellate cells by combining two-photon guided electrical stimulation, glutamate uncaging, electron microscopy, and modeling. Synaptic activation within thin (0.4 μm) dendrites produced somatic responses that became smaller and slower with increasing distance from the soma, sublinear subthreshold input-output relationships, and a somatodendritic gradient of short-term plasticity. Unlike most studies showing that neurons employ active dendritic mechanisms, we found that passive cable properties of thin dendrites determine the sublinear integration and plasticity gradient, which both result from large dendritic depolarizations that reduce synaptic driving force. These integrative properties allow stellate cells to act as spatiotemporal filters of synaptic input patterns, thereby biasing their output in favor of sparse presynaptic activity.

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.

Multiple clusters of release sites formed by individual thalamic afferents onto cortical interneurons ensure reliable transmission

Thalamic afferents supply the cortex with sensory information by contacting both excitatory neurons and inhibitory interneurons. Interestingly, thalamic contacts with interneurons constitute such a powerful synapse that even one afferent can fire interneurons, thereby driving feedforward inhibition. However, the spatial representation of this potent synapse on interneuron dendrites is poorly understood. Using Ca imaging and electron microscopy we show that an individual thalamic afferent forms multiple contacts with the interneuronal proximal dendritic arbor, preferentially near branch points. More contacts are correlated with larger amplitude synaptic responses. Each contact, consisting of a single bouton, can release up to seven vesicles simultaneously, resulting in graded and reliable Ca transients. Computational modeling indicates that the release of multiple vesicles at each contact minimally reduces the efficiency of the thalamic afferent in exciting the interneuron. This strategy preserves the spatial representation of thalamocortical inputs across the dendritic arbor over a wide range of release conditions.

Area CA3 interneurons receive two spatially segregated mossy fiber inputs

Area CA3 receives two extrinsic excitatory inputs, the mossy fibers (MF), and the perforant path (PP). Interneurons with somata in str. lacunosum moleculare (L-M) of CA3 modulate the influence of the MF and PP on pyramidal cell activity by providing strong feed-forward inhibitory influence to pyramidal cells. Here we report that L-M interneurons receive two separate MF inputs, one to the dorsal dendrites from the suprapyramidal blade of the dentate gyrus (MF(SDG)), and a second to ventral dendrites from the str. lucidum (MF(SL)). Responses elicited from MF(SDG) and MF(SL) stimulation sites have strong paired-pulse facilitation, similar DCG-IV sensitivity, amplitude, and decay kinetics but target spatially segregated domains on the interneuron dendrites. These data demonstrate that certain interneuron subtypes are entrained by two convergent MF inputs to spatially separated regions of the dendritic tree. This anatomical arrangement could make these interneurons considerably more responsive to the excitatory drive from dentate granule cells. Furthermore, temporal summation is linear or slightly sublinear between PP and MF(SL) but supralinear between PP and MF(SDG). This specific boosting of the excitatory drive to interneurons from the SDG location may indicate that L-M interneurons could be specifically involved in the processing of the associational component of the recognition memory.

Roller Coaster Scanning reveals spontaneous triggering of dendritic spikes in CA1 interneurons

Inhibitory interneurons are considered to be the controlling units of neural networks, despite their sparse number and unique morphological characteristics compared with excitatory pyramidal cells. Although pyramidal cell dendrites have been shown to display local regenerative events--dendritic spikes (dSpikes)--evoked by artificially patterned stimulation of synaptic inputs, no such studies exist for interneurons or for spontaneous events. In addition, imaging techniques have yet to attain the required spatial and temporal resolution for the detection of spontaneously occurring events that trigger dSpikes. Here we describe a high-resolution 3D two-photon laser scanning method (Roller Coaster Scanning) capable of imaging long dendritic segments resolving individual spines and inputs with a temporal resolution of a few milliseconds. By using this technique, we found that local, NMDA receptor-dependent dSpikes can be observed in hippocampal CA1 stratum radiatum interneurons during spontaneous network activities in vitro. These NMDA spikes appear when approximately 10 spatially clustered inputs arrive synchronously and trigger supralinear integration in dynamic interaction zones. In contrast to the one-to-one relationship between computational subunits and dendritic branches described in pyramidal cells, here we show that interneurons have relatively small (∼14 μm) sliding interaction zones. Our data suggest a unique principle as to how interneurons integrate synaptic information by local dSpikes.

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.

Maturation of GABAergic inhibition promotes strengthening of temporally coherent inputs among convergent pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.

Evidence suggests that maturation of inhibition is required for the development of plasticity to proceed in the visual cortex. However, the mechanisms by which increased inhibition promotes plasticity are not clear. Here we characterized the maturation of synaptic and intrinsic ionic properties of parvalbumin-positive interneurons, a prominent subtype of inhibitory neuron in the cortex. We used a simple integrate-and-fire model to simulate the influence of maturation of inhibition on associative plasticity rules. We simulated two input pathways that converged onto a single postsynaptic neuron. The temporal pattern of activity was constructed differently for the two pathways: one pathway represented visually-driven activity, while the other pathway represented sensory-deprived activity. In mature circuits it is established that postsynaptic cells can select for sensory-driven inputs over deprived inputs, even in the case that deprived inputs have an initial advantage in synaptic size or number. We demonstrated that maturation of inhibition was required for postsynaptic cells to appropriately select sensory-driven patterns of activity when challenged with an opponent pathway of greater size. These results outline a mechanism by which maturation of inhibition can promote plasticity in the young, a period of development that is characterized by heightened learning.

Intrinsic subthreshold oscillations extend the influence of inhibitory synaptic inputs on cortical pyramidal neurons

Fast inhibitory synaptic inputs, which cause conductance changes that typically last for 10–100 ms, participate in the generation and maintenance of cortical rhythms. We show here that these fast events can have influences that outlast the duration of the synaptic potentials by interacting with subthreshold membrane potential oscillations. Inhibitory postsynaptic potentials (IPSPs) in cortical neurons in vitro shifted the oscillatory phase for several seconds. The phase shift caused by two IPSPs or two current pulses summed non-linearly. Cholinergic neuromodulation increased the power of the oscillations and decreased the magnitude of the phase shifts. These results show that the intrinsic conductances of cortical pyramidal neurons can carry information about inhibitory inputs and can extend the integration window for synaptic input.

An arithmetic rule for spatial summation of excitatory and inhibitory inputs in pyramidal neurons

Dendritic integration of excitatory and inhibitory inputs is critical for neuronal computation, but the underlying rules remain to be elucidated. Based on realistic modeling and experiments in rat hippocampal slices, we derived a simple arithmetic rule for spatial summation of concurrent excitatory glutamatergic inputs (E) and inhibitory GABAergic inputs (I). The somatic response can be well approximated as the sum of the excitatory postsynaptic potential (EPSP), the inhibitory postsynaptic potential (IPSP), and a nonlinear term proportional to their product (k*EPSP*IPSP), where the coefficient k reflects the strength of shunting effect. The k value shows a pronounced asymmetry in its dependence on E and I locations. For I on the dendritic trunk, k decays rapidly with E-I distance for proximal Es, but remains largely constant for distal Es, indicating a uniformly high shunting efficacy for all distal Es. For I on an oblique branch, the shunting effect is restricted mainly within the branch, with the same proximal/distal asymmetry. This asymmetry can be largely attributed to cable properties of the dendrite. Further modeling studies showed that this rule also applies to the integration of multiple coincident Es and Is. Thus, this arithmetic rule offers a simple analytical tool for studying E-I integration in pyramidal neurons that incorporates the location specificity of GABAergic shunting inhibition.

Coincidence detection of convergent perforant path and mossy fibre inputs by CA3 interneurons

We performed whole-cell recordings from CA3 s. radiatum (R) and s. lacunosum-moleculare (L-M) interneurons in hippocampal slices to examine the temporal aspects of summation of converging perforant path (PP) and mossy fibre (MF) inputs. PP EPSPs were evoked from the s. lacunosum-moleculare in area CA1. MF EPSPs were evoked from the medial extent of the suprapyramidal blade of the dentate gyrus. Summation was strongly supralinear when examining PP EPSP with MF EPSP in a heterosynaptic pair at the 10 ms ISI, and linear to sublinear at longer ISIs. This pattern of nonlinearities suggests that R and L-M interneurons act as coincidence detectors for input from PP and MF. Summation at all ISIs was linear in voltage clamp mode demonstrating that nonlinearities were generated by postsynaptic voltage-dependent conductances. Supralinearity was not detected when the first EPSP in the pair was replaced by a simulated EPSP injected into the soma, suggesting that the conductances underlying the EPSP boosting were located in distal dendrites. Supralinearity was selectively eliminated with either Ni2+ (30 microm), mibefradil (10 microm) or nimodipine (15 microm), but was unaffected by QX-314. This pharmacological profile indicates that supralinearity is due to recruitment of dendritic T-type Ca2+channels by the first subthreshold EPSP in the pair. Results with the hyperpolarization-activated (Ih) channel blocker ZD 7288 (50 microm) revealed that Ih restricted the time course of supralinearity for coincidently summed EPSPs, and promoted linear to sublinear summation for asynchronous EPSPs. We conclude that coincidence detection results from the counterbalanced activation of T-type Ca2+ channels and inactivation of Ih.

Dendrite-to-Soma Input/Output Function of Continuous Time-Varying Signals in Hippocampal CA1 Pyramidal Neurons

We examined how hippocamal CA1 neurons process complex time-varying inputs that dendrites are likely to receive in vivo. We propose a functional model of the dendrite-to-soma input/output relationship that combines temporal integration and static-gain control mechanisms. Using simultaneous dual whole cell recordings, we injected 50 s of subthreshold and suprathreshold zero-mean white-noise current into the primary dendritic trunk along the proximal 2/3 of stratum radiatum and measured the membrane potential at the soma. Applying a nonlinear system-identification analysis, we found that a cascade of a linear filter followed by an adapting static-gain term fully accounted for the nonspiking input/output relationship between the dendrite and soma. The estimated filters contained a prominent band-pass region in the 1- to 10-Hz frequency range that remained constant as a function of stimulus variance. The gain of the dendrite-to-soma input/output relationship, in contrast, varied as a function of stimulus variance. When the contribution of the voltage-dependent current Ih was eliminated, the estimated filters lost their band-pass properties and the gain regulation was substantially altered. Our findings suggest that the dendrite-to-soma input/output relationship for proximal apical inputs to CA1 pyramidal neurons is well described as a band-pass filter in the theta frequency range followed by a gain-control nonlinearity that dynamically adapts to the statistics of the input signal.

Dendritic spines linearize the summation of excitatory potentials

In mammalian cortex, most excitatory inputs occur on dendritic spines, avoiding dendritic shafts. Although spines biochemically isolate inputs, nonspiny neurons can also implement biochemical compartmentalization; so, it is possible that spines have an additional function. We have recently shown that the spine neck can filter membrane potentials going into and out of the spine. To investigate the potential function of this electrical filtering, we used two-photon uncaging of glutamate and compared the integration of electrical signals in spines vs. dendritic shafts from basal dendrites of mouse layer 5 pyramidal neurons. Uncaging potentials onto spines summed linearly, whereas potentials on dendritic shafts reduced each other's effect. Linear integration of spines was maintained regardless of the amplitude of the response, distance between spines (as close as < 2 microm), distance of the spines to the soma, dendritic diameter, or spine neck length. Our findings indicate that spines serve as electrical isolators to prevent input interaction, and thus generate a linear arithmetic of excitatory inputs. Linear integration could be an essential feature of cortical and other spine-laden circuits.

Early neuropathology of somatostatin/NPY GABAergic cells in the hippocampus of a PS1×APP transgenic model of Alzheimer's disease

At advanced stages, Alzheimer's disease (AD) is characterized by an extensive neuronal loss. However, the early neurodegenerative deficiencies have not been yet identified. Here we report an extensive, selective and early neurodegeneration of the dendritic inhibitory interneurons (oriens-lacunosum moleculare, O-LM, and hilar perforant path-associated, HIPP, cells) in the hippocampus of a transgenic PS1xAPP AD model. At 6 months of age, from 22 different pre- and postsynaptic mRNA markers tested (including GABAergic, glutamatergic and cholinergic markers), only the expression of somatostatin (SOM) and NPY neuropeptides (O-LM and HIPP markers) displayed a significant decrease. Stereological cell counting demonstrated a profound diminution (50-60%) of SOM-immunopositive neurons, preceding the pyramidal cell loss in this AD model. SOM population co-expressing NPY was the most damaged cell subset. Furthermore, a linear correlation between SOM and/or NPY deficiency and Abeta content was also observed. Though the molecular mechanism of SOM neuronal loss remains to be determined, these findings might represent an early hippocampal neuropathology. Therefore, SOM and NPY neuropeptides could constitute important biomarkers to assess the efficacy of potential early AD treatments.

Inside the brain of a neuron

For many decades, neurons were considered to be the elementary computational units of the brain and were assumed to summate incoming signals and elicit action potentials only in response to suprathreshold stimuli. Although modelling studies predicted that single neurons constitute a much more powerful computational entity, able to perform an array of nonlinear calculations, this possibility was not explored experimentally until the discovery of active mechanisms in the dendrites of most neuron types. Here, we review several modelling studies that have addressed information processing in single neurons, starting with those characterizing the arithmetic of different dendritic components, to those tackling neuronal integration at the cell body and, finally, those analysing the computational abilities of the axon. We present modelling predictions along with supporting experimental data in an effort to highlight the significant contribution of modelling work to enhancing our understanding of single-neuron arithmetic.

Dendritic spines and linear networks

The function of the cortical microcircuitry is still mysterious. Using a bottom-up analysis based on the biophysics and connectivity of cortical neurons, we propose the hypothesis that the neocortex is essentially a linear integrator of inputs. Dendritic spines would slow the neuron and contribute to linearize input summation. Since excitatory axons are relatively straight, they appeared designed to help disperse information to a large number of recipient neurons, generating a distributed circuit. A linear summation regime will ensure the full benefit of a distributed connectivity matrix. Linear integration could also help the neocortex decode the sensory world and may have additional computational advantages. In this view, spines would be the anatomical signature of linear networks.

Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.

Controlling synaptic input patterns in vitro by dynamic photo stimulation

Recent experimental and theoretical work indicates that both the intensity and the temporal structure of synaptic activity strongly modulate the integrative properties of single neurons in the intact brain. However, studying these effects experimentally is complicated by the fact that, in experimental systems, network activity is either absent, as in the acute slice preparation, or difficult to monitor and to control, as in in vivo recordings. Here, we present a new implementation of neurotransmitter uncaging in acute brain slices that uses functional projections to generate tightly controlled, spatio-temporally structured synaptic input patterns in individual neurons. For that, a set of presynaptic neurons is activated in a precisely timed sequence through focal photolytic release of caged glutamate with the help of a fast laser scanning system. Integration of synaptic inputs can be studied in postsynaptic neurons that are not directly stimulated with the laser, but receive input from the targeted neurons through intact axonal projections. Our new approach of dynamic photo stimulation employs functional synapses, accounts for their spatial distribution on the dendrites, and thus allows study of the integrative properties of single neurons with physiologically realistic input. Data obtained with our new technique suggest that, not only the neuronal spike generator, but also synaptic transmission and dendritic integration in neocortical pyramidal cells, can be highly reliable.

Spike-timing-dependent synaptic plasticity depends on dendritic location

In the neocortex, each neuron receives thousands of synaptic inputs distributed across an extensive dendritic tree. Although postsynaptic processing of each input is known to depend on its dendritic location, it is unclear whether activity-dependent synaptic modification is also location-dependent. Here we report that both the magnitude and the temporal specificity of spike-timing-dependent synaptic modification vary along the apical dendrite of rat cortical layer 2/3 pyramidal neurons. At the distal dendrite, the magnitude of long-term potentiation is smaller, and the window of pre-/postsynaptic spike interval for long-term depression (LTD) is broader. The spike-timing window for LTD correlates with the window of action potential-induced suppression of NMDA (N-methyl-D-aspartate) receptors; this correlation applies to both their dendritic location-dependence and pharmacological properties. Presynaptic stimulation with partial blockade of NMDA receptors induced LTD and occluded further induction of spike-timing-dependent LTD, suggesting that NMDA receptor suppression underlies LTD induction. Computer simulation studies showed that the dendritic inhomogeneity of spike-timing-dependent synaptic modification leads to differential input selection at distal and proximal dendrites according to the temporal characteristics of presynaptic spike trains. Such location-dependent tuning of inputs, together with the dendritic heterogeneity of postsynaptic processing, could enhance the computational capacity of cortical pyramidal neurons.

On the fight between excitation and inhibition: location is everything

In the intact brain, neurons are constantly subjected to both excitatory and inhibitory inputs to their dendritic trees. Although it is accepted that the overall response of a neuron--its train of output spikes--depends on the balance of excitation and inhibition, we continue to lack specific knowledge of the rules that govern how excitatory and inhibitory inputs interact in space and time within the confines of individual neurons. In a recent paper, Liu starts by providing evidence that the relative locations and numbers of excitatory and inhibitory synapses are tightly regulated in cultured neurons from the hippocampus. This is consistent with findings in other labs that suggest neurons work hard, and in a variety of different ways, to maintain their inputs in proper balance and their outputs within appropriate ranges. On this backdrop, Liu's most important finding of a functional nature is that inhibition appears to act quite locally; that is, an inhibitory synapse effectively opposes an excitatory synapse only when it is very close by within the same dendritic branch (Fig. 1). This finding provides further support for the view--anticipated by neural theorists more than 20 years ago--that the brain's principal neurons contain a potentially large number of separate computational subunits.

Immunocytochemically defined interneuron populations in the hippocampus of mouse strains used in transgenic technology

Transgenic mice are overtaking the role of model animals in neuroscience. They are used in developmental, anatomical, and physiological as well as experimental neurology. However, most results on the organization of the nervous system derive from the rat. The rat hippocampus and its neuronal elements have been thoroughly investigated, revealing remarkable functional and morphological diversity and specificity among hippocampal interneurons. Our aim was to examine the properties of distinct hippocampal interneuron populations, i.e., those immunoreactive for calcium-binding proteins (parvalbumin, calbindin, and calretinin), neuropeptides (cholecystokinin, neuropeptide Y, somatostatin, vasoactive intestinal polypeptide), and certain receptors (metabotropic glutamate receptor 1alpha, cannabinoid receptor type 1) in four strains of mice widely used in transgenic technology, and to compare their properties to those in the rat. Our data indicate that the distribution as well as the dendritic and axonal arborization of mouse interneurons immunoreactive for the different markers was identical in the examined mouse strains, and in most respects are similar to the features found in the rat. The postsynaptic targets of neurons terminating in the perisomatic (parvalbumin), proximal (calbindin), and distal (somatostatin) dendritic region, as well as on other interneurons (calretinin), also matched those found in the rat. However, a few significant differences could also be observed between the two species in addition to the already described immunoreactivity of mossy cells for calretinin: the absence of spiny calretinin-immunoreactive interneurons in the CA3 region, sparse contacts between calretinin-immunoreactive interneurons, and the axon staining for somatostatin and neuropil labeling for cholecystokinin. We can conclude that the morphofunctional classification of interneurons established in the rat is largely valid for mouse strains used in transgenic procedures.

Computational subunits in thin dendrites of pyramidal cells

The thin basal and oblique dendrites of cortical pyramidal neurons receive most of the synaptic inputs from other cells, but their integrative properties remain uncertain. Previous studies have most often reported global linear or sublinear summation. An alternative view, supported by biophysical modeling studies, holds that thin dendrites provide a layer of independent computational 'subunits' that sigmoidally modulate their inputs prior to global summation. To distinguish these possibilities, we combined confocal imaging and dual-site focal synaptic stimulation of identified thin dendrites in rat neocortical pyramidal neurons. We found that nearby inputs on the same branch summed sigmoidally, whereas widely separated inputs or inputs to different branches summed linearly. This strong spatial compartmentalization effect is incompatible with a global summation rule and provides the first experimental support for a two-layer 'neural network' model of pyramidal neuron thin-branch integration. Our findings could have important implications for the computing and memory-related functions of cortical tissue.

Dendrites: bug or feature?

The integrative properties of dendrites are determined by a complex mixture of factors, including their morphology, the spatio-temporal patterning of synaptic inputs, the balance of excitation and inhibition, and neuromodulatory influences, all of which interact with the many voltage-gated conductances present in the dendritic membrane. Recent efforts to grapple with this complexity have focused on identifying functional compartments in the dendritic tree, the number and size of which depend on the aspect of dendritic function being considered. We discuss how dendritic compartments and the interactions between them help to enhance the computational power of the neuron and define the rules for the induction of synaptic plasticity.

Interpolating between Cellular Biophysics and Computation in Single Neurons

What types of computations are performed on synaptic inputs within the dendritic trees of single neurons? In this issue of Neuron, present a systematic method to reduce complex, biophysically realistic neuron models to more tractable, simplified two-layered neural networks that could shed some light on this issue.