Principles governing the operation of synaptic inhibition in dendrites

Multidimensional analysis of cortical interneuron synaptic features reveals underlying synaptic heterogeneity

Cortical interneurons represent a diverse set of neuronal subtypes characterized in part by their striking degree of synaptic specificity. However, little is known about the extent of synaptic diversity because of the lack of unbiased methods to extract synaptic features among interneuron subtypes. Here, we develop an approach to aggregate image features from fluorescent confocal images of interneuron synapses and their post-synaptic targets, in order to characterize the heterogeneity of synapses at fine scale. We started by training a model that recognizes pre- and post-synaptic compartments and then determines the target of each genetically-identified interneuron synapse in vitro and in vivo. Our model extracts hundreds of spatial and intensity features from each analyzed synapse, constructing a multidimensional data set, consisting of millions of synapses, which allowed us to perform an unsupervised analysis on this dataset, uncovering novel synaptic subgroups. The subgroups were spatially distributed in a highly structured manner that revealed the local underlying topology of the postsynaptic environment. Dendrite-targeting subgroups were clustered onto subdomains of the dendrite along the proximal to distal axis. Soma-targeting subgroups were enriched onto different postsynaptic cell types. We also find that the two main subclasses of interneurons, basket cells and somatostatin interneurons, utilize distinct strategies to enact inhibitory coverage. Thus, our analysis of multidimensional synaptic features establishes a conceptual framework for studying interneuron synaptic diversity.

Physical and functional convergence of the autism risk genes Scn2a and Ank2 in neocortical pyramidal cell dendrites

Dysfunction in sodium channels and their ankyrin scaffolding partners have both been implicated in neurodevelopmental disorders, including autism spectrum disorder (ASD). In particular, the genes SCN2A, which encodes the sodium channel NaV1.2, and ANK2, which encodes ankyrin-B, have strong ASD association. Recent studies indicate that ASD-associated haploinsufficiency in Scn2a impairs dendritic excitability and synaptic function in neocortical pyramidal cells, but how NaV1.2 is anchored within dendritic regions is unknown. Here, we show that ankyrin-B is essential for scaffolding NaV1.2 to the dendritic membrane of mouse neocortical neurons and that haploinsufficiency of Ank2 phenocopies intrinsic dendritic excitability and synaptic deficits observed in Scn2a+/- conditions. These results establish a direct, convergent link between two major ASD risk genes and reinforce an emerging framework suggesting that neocortical pyramidal cell dendritic dysfunction can contribute to neurodevelopmental disorder pathophysiology.

Bidirectional Neuronal Actuation by Uncaging with Violet and Green Light

We have developed a photochemical protecting group that enables wavelength selective uncaging using green versus violet light. Change of the exocyclic oxygen of the laser dye coumarin-102 to sulfur, gave thio-coumarin-102, a new chromophore with an absorption ratio at 503/402 nm of 37. Photolysis of thio-coumarin-102 caged γ-aminobutyric acid was found to be highly wavelength selective on neurons, with normalized electrical responses >100-fold higher in the green versus violet channel. When partnered with coumarin-102 caged glutamate, we could use whole cell violet and green irradiation to fire and block neuronal action potentials with complete orthogonality. Localized irradiation of different dendritic segments, each connected to a neuronal cell body, in concert with 3-dimenional Ca2+ imaging, revealed that such inputs could function independently. Chemical signaling in living cells always involves a complex balance of multiple pathways, use of (thio)-coumarin-102 caged compounds will enable arbitrarily timed flashes of green and violet light to interrogate two independent pathways simultaneously.

An Anatomical and Physiological Basis for Coincidence Detection Across Time Scales in the Auditory System

Coincidence detection is a common neural computation that identifies co-occurring stimuli by integration of inputs. In the auditory system, octopus cells act as coincidence detectors for complex sounds that include both synchronous and sequenced combinations of frequencies. Octopus cells must detect coincidence on both the millisecond and submillisecond time scale, unlike the average neuron, which integrates inputs over time on the order of tens of milliseconds. Here, we show that octopus cell computations in the cell body are shaped by inhibition in the dendrites, which adjusts the strength and timing of incoming signals to achieve submillisecond acuity. This mechanism is crucial for the fundamental process of integrating the synchronized frequencies of natural auditory signals over time.

Genetic context drives age-related disparities in synaptic maintenance and structure across cortical and hippocampal neuronal circuits

The disconnection of neuronal circuitry through synaptic loss is presumed to be a major driver of age-related cognitive decline. Age-related cognitive decline is heterogeneous, yet whether genetic mechanisms differentiate successful from unsuccessful cognitive decline through maintenance or vulnerability of synaptic connections remains unknown. Previous work using rodent and primate models leveraged various techniques to imply that age-related synaptic loss is widespread on pyramidal cells in prefrontal cortex (PFC) circuits but absent on those in area CA1 of the hippocampus. Here, we examined the effect of aging on synapses on projection neurons forming a hippocampal-cortico-thalamic circuit important for spatial working memory tasks from two genetically distinct mouse strains that exhibit susceptibility (C57BL/6J) or resistance (PWK/PhJ) to cognitive decline during aging. Across both strains, synapse density on CA1-to-PFC projection neurons appeared completely intact with age. In contrast, we found synapse loss on PFC-to-nucleus reuniens (RE) projection neurons from aged C57BL/6J but not PWK/PhJ mice. Moreover, synapses from aged PWK/PhJ mice but not from C57BL/6J exhibited altered morphologies that suggest increased efficiency to drive depolarization in the parent dendrite. Our findings suggest resistance to age-related cognitive decline results in part by age-related synaptic adaptations, and identification of these mechanisms in PWK/PhJ mice could uncover new therapeutic targets for promoting successful cognitive aging and extending human health span.

Layer 1 neocortex: Gating and integrating multidimensional signals

Layer 1 (L1) of the neocortex acts as a nexus for the collection and processing of widespread information. By integrating ascending inputs with extensive top-down activity, this layer likely provides critical information regulating how the perception of sensory inputs is reconciled with expectation. This is accomplished by sorting, directing, and integrating the complex network of excitatory inputs that converge onto L1. These signals are combined with neuromodulatory afferents and gated by the wealth of inhibitory interneurons that either are embedded within L1 or send axons from other cortical layers. Together, these interactions dynamically calibrate information flow throughout the neocortex. This review will primarily focus on L1 within the primary sensory cortex and will use these insights to understand L1 in other cortical areas.

GABAergic regulation of striatal spiny projection neurons depends upon their activity state

Synaptic transmission mediated by GABAA receptors (GABAARs) in adult, principal striatal spiny projection neurons (SPNs) can suppress ongoing spiking, but its effect on synaptic integration at subthreshold membrane potentials is less well characterized, particularly those near the resting down-state. To fill this gap, a combination of molecular, optogenetic, optical, and electrophysiological approaches were used to study SPNs in mouse ex vivo brain slices, and computational tools were used to model somatodendritic synaptic integration. In perforated patch recordings, activation of GABAARs, either by uncaging of GABA or by optogenetic stimulation of GABAergic synapses, evoked currents with a reversal potential near -60 mV in both juvenile and adult SPNs. Transcriptomic analysis and pharmacological work suggested that this relatively positive GABAAR reversal potential was not attributable to NKCC1 expression, but rather to HCO3- permeability. Regardless, from down-state potentials, optogenetic activation of dendritic GABAergic synapses depolarized SPNs. This GABAAR-mediated depolarization summed with trailing ionotropic glutamate receptor (iGluR) stimulation, promoting dendritic spikes and increasing somatic depolarization. Simulations revealed that a diffuse dendritic GABAergic input to SPNs effectively enhanced the response to dendritic iGluR signaling and promoted dendritic spikes. Taken together, our results demonstrate that GABAARs can work in concert with iGluRs to excite adult SPNs when they are in the resting down-state, suggesting that their inhibitory role is limited to brief periods near spike threshold. This state-dependence calls for a reformulation for the role of intrastriatal GABAergic circuits.

Lateral inhibition in V1 controls neural & perceptual contrast sensitivity

Lateral inhibition is a central principle for sensory system function. It is thought to operate by the activation of inhibitory neurons that restrict the spatial spread of sensory excitation. Much work on the role of inhibition in sensory systems has focused on visual cortex; however, the neurons, computations, and mechanisms underlying cortical lateral inhibition remain debated, and its importance for visual perception remains unknown. Here, we tested how lateral inhibition from PV or SST neurons in mouse primary visual cortex (V1) modulates neural and perceptual sensitivity to stimulus contrast. Lateral inhibition from PV neurons reduced neural and perceptual sensitivity to visual contrast in a uniform subtractive manner, whereas lateral inhibition from SST neurons more effectively changed the slope (or gain) of neural and perceptual contrast sensitivity. A neural circuit model identified spatially extensive lateral projections from SST neurons as the key factor, and we confirmed this with direct subthreshold measurements of a larger spatial footprint for SST versus PV lateral inhibition. Together, these results define cell-type specific computational roles for lateral inhibition in V1, and establish their unique consequences on sensitivity to contrast, a fundamental aspect of the visual world.

Local and long-range GABAergic circuits in hippocampal area CA1 and their link to Alzheimer's disease

GABAergic inhibitory neurons are the principal source of inhibition in the brain. Traditionally, their role in maintaining the balance of excitation-inhibition has been emphasized. Beyond homeostatic functions, recent circuit mapping and functional manipulation studies have revealed a wide range of specific roles that GABAergic circuits play in dynamically tilting excitation-inhibition coupling across spatio-temporal scales. These span from gating of compartment- and input-specific signaling, gain modulation, shaping input-output functions and synaptic plasticity, to generating signal-to-noise contrast, defining temporal windows for integration and rate codes, as well as organizing neural assemblies, and coordinating inter-regional synchrony. GABAergic circuits are thus instrumental in controlling single-neuron computations and behaviorally-linked network activity. The activity dependent modulation of sensory and mnemonic information processing by GABAergic circuits is pivotal for the formation and maintenance of episodic memories in the hippocampus. Here, we present an overview of the local and long-range GABAergic circuits that modulate the dynamics of excitation-inhibition and disinhibition in the main output area of the hippocampus CA1, which is crucial for episodic memory. Specifically, we link recent findings pertaining to GABAergic neuron molecular markers, electrophysiological properties, and synaptic wiring with their function at the circuit level. Lastly, given that area CA1 is particularly impaired during early stages of Alzheimer's disease, we emphasize how these GABAergic circuits may contribute to and be involved in the pathophysiology.

The computational power of the human brain

At the end of the 20th century, analog systems in computer science have been widely replaced by digital systems due to their higher computing power. Nevertheless, the question keeps being intriguing until now: is the brain analog or digital? Initially, the latter has been favored, considering it as a Turing machine that works like a digital computer. However, more recently, digital and analog processes have been combined to implant human behavior in robots, endowing them with artificial intelligence (AI). Therefore, we think it is timely to compare mathematical models with the biology of computation in the brain. To this end, digital and analog processes clearly identified in cellular and molecular interactions in the Central Nervous System are highlighted. But above that, we try to pinpoint reasons distinguishing in silico computation from salient features of biological computation. First, genuinely analog information processing has been observed in electrical synapses and through gap junctions, the latter both in neurons and astrocytes. Apparently opposed to that, neuronal action potentials (APs) or spikes represent clearly digital events, like the yes/no or 1/0 of a Turing machine. However, spikes are rarely uniform, but can vary in amplitude and widths, which has significant, differential effects on transmitter release at the presynaptic terminal, where notwithstanding the quantal (vesicular) release itself is digital. Conversely, at the dendritic site of the postsynaptic neuron, there are numerous analog events of computation. Moreover, synaptic transmission of information is not only neuronal, but heavily influenced by astrocytes tightly ensheathing the majority of synapses in brain (tripartite synapse). At least at this point, LTP and LTD modifying synaptic plasticity and believed to induce short and long-term memory processes including consolidation (equivalent to RAM and ROM in electronic devices) have to be discussed. The present knowledge of how the brain stores and retrieves memories includes a variety of options (e.g., neuronal network oscillations, engram cells, astrocytic syncytium). Also epigenetic features play crucial roles in memory formation and its consolidation, which necessarily guides to molecular events like gene transcription and translation. In conclusion, brain computation is not only digital or analog, or a combination of both, but encompasses features in parallel, and of higher orders of complexity.

Synaptic weights that correlate with presynaptic selectivity increase decoding performance

The activity of neurons in the visual cortex is often characterized by tuning curves, which are thought to be shaped by Hebbian plasticity during development and sensory experience. This leads to the prediction that neural circuits should be organized such that neurons with similar functional preference are connected with stronger weights. In support of this idea, previous experimental and theoretical work have provided evidence for a model of the visual cortex characterized by such functional subnetworks. A recent experimental study, however, have found that the postsynaptic preferred stimulus was defined by the total number of spines activated by a given stimulus and independent of their individual strength. While this result might seem to contradict previous literature, there are many factors that define how a given synaptic input influences postsynaptic selectivity. Here, we designed a computational model in which postsynaptic functional preference is defined by the number of inputs activated by a given stimulus. Using a plasticity rule where synaptic weights tend to correlate with presynaptic selectivity, and is independent of functional-similarity between pre- and postsynaptic activity, we find that this model can be used to decode presented stimuli in a manner that is comparable to maximum likelihood inference.

The dendritic engram

Accumulating evidence from a wide range of studies, including behavioral, cellular, molecular and computational findings, support a key role of dendrites in the encoding and recall of new memories. Dendrites can integrate synaptic inputs in non-linear ways, provide the substrate for local protein synthesis and facilitate the orchestration of signaling pathways that regulate local synaptic plasticity. These capabilities allow them to act as a second layer of computation within the neuron and serve as the fundamental unit of plasticity. As such, dendrites are integral parts of the memory engram, namely the physical representation of memories in the brain and are increasingly studied during learning tasks. Here, we review experimental and computational studies that support a novel, dendritic view of the memory engram that is centered on non-linear dendritic branches as elementary memory units. We highlight the potential implications of dendritic engrams for the learning and memory field and discuss future research directions.

Asymmetric Voltage Attenuation in Dendrites Can Enable Hierarchical Heterosynaptic Plasticity

Long-term synaptic plasticity is mediated via cytosolic calcium concentrations ([Ca2+]). Using a synaptic model that implements calcium-based long-term plasticity via two sources of Ca2+ - NMDA receptors and voltage-gated calcium channels (VGCCs) - we show in dendritic cable simulations that the interplay between these two calcium sources can result in a diverse array of heterosynaptic effects. When spatially clustered synaptic input produces a local NMDA spike, the resulting dendritic depolarization can activate VGCCs at nonactivated spines, resulting in heterosynaptic plasticity. NMDA spike activation at a given dendritic location will tend to depolarize dendritic regions that are located distally to the input site more than dendritic sites that are proximal to it. This asymmetry can produce a hierarchical effect in branching dendrites, where an NMDA spike at a proximal branch can induce heterosynaptic plasticity primarily at branches that are distal to it. We also explored how simultaneously activated synaptic clusters located at different dendritic locations synergistically affect the plasticity at the active synapses, as well as the heterosynaptic plasticity of an inactive synapse "sandwiched" between them. We conclude that the inherent electrical asymmetry of dendritic trees enables sophisticated schemes for spatially targeted supervision of heterosynaptic plasticity.

Diverse role of NMDA receptors for dendritic integration of neural dynamics

Neurons, represented as a tree structure of morphology, have various distinguished branches of dendrites. Different types of synaptic receptors distributed over dendrites are responsible for receiving inputs from other neurons. NMDA receptors (NMDARs) are expressed as excitatory units, and play a key physiological role in synaptic function. Although NMDARs are widely expressed in most types of neurons, they play a different role in the cerebellar Purkinje cells (PCs). Utilizing a computational PC model with detailed dendritic morphology, we explored the role of NMDARs at different parts of dendritic branches and regions. We found somatic responses can switch from silent, to simple spikes and complex spikes, depending on specific dendritic branches. Detailed examination of the dendrites regarding their diameters and distance to soma revealed diverse response patterns, yet explain two firing modes, simple and complex spike. Taken together, these results suggest that NMDARs play an important role in controlling excitability sensitivity while taking into account the factor of dendritic properties. Given the complexity of neural morphology varying in cell types, our work suggests that the functional role of NMDARs is not stereotyped but highly interwoven with local properties of neuronal structure.

State-dependent GABAergic regulation of striatal spiny projection neuron excitability

Synaptic transmission mediated by GABA A receptors (GABA A Rs) in adult, principal striatal spiny projection neurons (SPNs) can suppress ongoing spiking, but its effect on synaptic integration at sub-threshold membrane potentials is less well characterized, particularly those near the resting down-state. To fill this gap, a combination of molecular, optogenetic, optical and electrophysiological approaches were used to study SPNs in mouse ex vivo brain slices, and computational tools were used to model somatodendritic synaptic integration. Activation of GABA A Rs, either by uncaging of GABA or by optogenetic stimulation of GABAergic synapses, evoked currents with a reversal potential near -60 mV in perforated patch recordings from both juvenile and adult SPNs. Molecular profiling of SPNs suggested that this relatively positive reversal potential was not attributable to NKCC1 expression, but rather to a dynamic equilibrium between KCC2 and Cl-/HCO3-cotransporters. Regardless, from down-state potentials, optogenetic activation of dendritic GABAergic synapses depolarized SPNs. This GABAAR-mediated depolarization summed with trailing ionotropic glutamate receptor (iGluR) stimulation, promoting dendritic spikes and increasing somatic depolarization. Simulations revealed that a diffuse dendritic GABAergic input to SPNs effectively enhanced the response to coincident glutamatergic input. Taken together, our results demonstrate that GABA A Rs can work in concert with iGluRs to excite adult SPNs when they are in the resting down-state, suggesting that their inhibitory role is limited to brief periods near spike threshold. This state-dependence calls for a reformulation of the role intrastriatal GABAergic circuits.

Differential effects of group III metabotropic glutamate receptors on spontaneous inhibitory synaptic currents in spine-innervating double bouquet and parvalbumin-expressing dendrite-targeting GABAergic interneurons in human neocortex

Diverse neocortical GABAergic neurons specialize in synaptic targeting and their effects are modulated by presynaptic metabotropic glutamate receptors (mGluRs) suppressing neurotransmitter release in rodents, but their effects in human neocortex are unknown. We tested whether activation of group III mGluRs by L-AP4 changes GABAA receptor-mediated spontaneous inhibitory postsynaptic currents (sIPSCs) in 2 distinct dendritic spine-innervating GABAergic interneurons recorded in vitro in human neocortex. Calbindin-positive double bouquet cells (DBCs) had columnar "horsetail" axons descending through layers II-V innervating dendritic spines (48%) and shafts, but not somata of pyramidal and nonpyramidal neurons. Parvalbumin-expressing dendrite-targeting cell (PV-DTC) axons extended in all directions innervating dendritic spines (22%), shafts (65%), and somata (13%). As measured, 20% of GABAergic neuropil synapses innervate spines, hence DBCs, but not PV-DTCs, preferentially select spine targets. Group III mGluR activation paradoxically increased the frequency of sIPSCs in DBCs (to median 137% of baseline) but suppressed it in PV-DTCs (median 92%), leaving the amplitude unchanged. The facilitation of sIPSCs in DBCs may result from their unique GABAergic input being disinhibited via network effect. We conclude that dendritic spines receive specialized, diverse GABAergic inputs, and group III mGluRs differentially regulate GABAergic synaptic transmission to distinct GABAergic cell types in human cortex.

Circadian time- and sleep-dependent modulation of cortical parvalbumin-positive inhibitory neurons

Parvalbumin-positive neurons (PVs) are the main class of inhibitory neurons in the mammalian central nervous system. By examining diurnal changes in synaptic and neuronal activity of PVs in the supragranular layer of the mouse primary visual cortex (V1), we found that both PV input and output are modulated in a time- and sleep-dependent manner throughout the 24-h day. We first show that PV-evoked inhibition is stronger by the end of the light cycle (ZT12) relative to the end of the dark cycle (ZT0), which is in line with the lower inhibitory input of PV neurons at ZT12 than at ZT0. Interestingly, PV inhibitory and excitatory synaptic transmission slowly oscillate in opposite directions during the light/dark cycle. Although excitatory synapses are predominantly regulated by experience, inhibitory synapses are regulated by sleep, via acetylcholine activating M1 receptors. Consistent with synaptic regulation of PVs, we further show in vivo that spontaneous PV activity displays daily rhythm mainly determined by visual experience, which negatively correlates with the activity cycle of surrounding pyramidal neurons and the dorsal lateral geniculate nucleus-evoked responses in V1. These findings underscore the physiological significance of PV's daily modulation.

Lateral entorhinal cortex inputs modulate hippocampal dendritic excitability by recruiting a local disinhibitory microcircuit

The lateral entorhinal cortex (LEC) provides multisensory information to the hippocampus, directly to the distal dendrites of CA1 pyramidal neurons. LEC neurons perform important functions for episodic memory processing, coding for contextually salient elements of an environment or experience. However, we know little about the functional circuit interactions between the LEC and the hippocampus. We combine functional circuit mapping and computational modeling to examine how long-range glutamatergic LEC projections modulate compartment-specific excitation-inhibition dynamics in hippocampal area CA1. We demonstrate that glutamatergic LEC inputs can drive local dendritic spikes in CA1 pyramidal neurons, aided by the recruitment of a disinhibitory VIP interneuron microcircuit. Our circuit mapping and modeling further reveal that LEC inputs also recruit CCK interneurons that may act as strong suppressors of dendritic spikes. These results highlight a cortically driven GABAergic microcircuit mechanism that gates nonlinear dendritic computations, which may support compartment-specific coding of multisensory contextual features within the hippocampus.

Introducing the Dendrify framework for incorporating dendrites to spiking neural networks

Computational modeling has been indispensable for understanding how subcellular neuronal features influence circuit processing. However, the role of dendritic computations in network-level operations remains largely unexplored. This is partly because existing tools do not allow the development of realistic and efficient network models that account for dendrites. Current spiking neural networks, although efficient, are usually quite simplistic, overlooking essential dendritic properties. Conversely, circuit models with morphologically detailed neuron models are computationally costly, thus impractical for large-network simulations. To bridge the gap between these two extremes and facilitate the adoption of dendritic features in spiking neural networks, we introduce Dendrify, an open-source Python package based on Brian 2. Dendrify, through simple commands, automatically generates reduced compartmental neuron models with simplified yet biologically relevant dendritic and synaptic integrative properties. Such models strike a good balance between flexibility, performance, and biological accuracy, allowing us to explore dendritic contributions to network-level functions while paving the way for developing more powerful neuromorphic systems.

Functional architecture of executive control and associated event-related potentials in macaques

The medial frontal cortex (MFC) enables executive control by monitoring relevant information and using it to adapt behavior. In macaques performing a saccade countermanding (stop-signal) task, we simultaneously recorded electrical potentials over MFC and neural spiking across all layers of the supplementary eye field (SEF). We report the laminar organization of neurons enabling executive control by monitoring the conflict between incompatible responses, the timing of events, and sustaining goal maintenance. These neurons were a mix of narrow-spiking and broad-spiking found in all layers, but those predicting the duration of control and sustaining the task goal until the release of operant control were more commonly narrow-spiking neurons confined to layers 2 and 3 (L2/3). We complement these results with evidence for a monkey homolog of the N2/P3 event-related potential (ERP) complex associated with response inhibition. N2 polarization varied with error-likelihood and P3 polarization varied with the duration of expected control. The amplitude of the N2 and P3 were predicted by the spike rate of different classes of neurons located in L2/3 but not L5/6. These findings reveal features of the cortical microcircuitry supporting executive control and producing associated ERPs.

Computational models reveal how chloride dynamics determine the optimal distribution of inhibitory synapses to minimise dendritic excitability

Many neurons in the mammalian central nervous system have complex dendritic arborisations and active dendritic conductances that enable these cells to perform sophisticated computations. How dendritically targeted inhibition affects local dendritic excitability is not fully understood. Here we use computational models of branched dendrites to investigate where GABAergic synapses should be placed to minimise dendritic excitability over time. To do so, we formulate a metric we term the “Inhibitory Level” (IL), which quantifies the effectiveness of synaptic inhibition for reducing the depolarising effect of nearby excitatory input. GABAergic synaptic inhibition is dependent on the reversal potential for GABA_A receptors (EGABA), which is primarily set by the transmembrane chloride ion (Cl^-) concentration gradient. We, therefore, investigated how variable EGABA and dynamic chloride affects dendritic inhibition. We found that the inhibitory effectiveness of dendritic GABAergic synapses combines at an encircled branch junction. The extent of this inhibitory accumulation is dependent on the number of branches and location of synapses but is independent of EGABA. This inhibitory accumulation occurs even for very distally placed inhibitory synapses when they are hyperpolarising–but not when they are shunting. When accounting for Cl^- fluxes and dynamics in Cl^- concentration, we observed that Cl^- loading is detrimental to inhibitory effectiveness. This enabled us to determine the most inhibitory distribution of GABAergic synapses which is close to–but not at–a shared branch junction. This distribution balances a trade-off between a stronger combined inhibitory influence when synapses closely encircle a branch junction with the deleterious effects of increased Cl^- by loading that occurs when inhibitory synapses are co-located.

Dendritic branches allow for a rich repertoire of computational capabilities for neurons within the brain. Inhibitory synaptic inputs, which utilise the neurotransmitter GABA, refine and enhance dendritic computations. They are traditionally viewed with regards to their inhibitory effect on action potential generation at the neuronal cell body. Here, we studied the local effects of inhibitory synapses on excitability in dendrites. We also considered the dynamic nature of inhibition that deteriorates the longer it is active due to intracellular chloride ion loading. The central goal of our investigation was to find the best locations for multiple inhibitory synapses to maximise their combined inhibitory effectiveness on nearby excitation in the dendritic tree. We found that the optimal distribution is when inhibitory synapses closely encircle a branch junction, without being co-located at the junction itself. This maximises how their inhibitory influence combines whilst minimising the deleterious effects of chloride loading.

Functionally distinct NPAS4-expressing somatostatin interneuron ensembles critical for motor skill learning

During motor learning, dendritic spines on pyramidal neurons (PNs) in the primary motor cortex (M1) undergo reorganization. Intriguingly, the inhibition from local somatostatin-expressing inhibitory neurons (SST-INs) plays an important role in regulating the PN plasticity and thus new motor skill acquisition. However, the molecular mechanisms underlying this process remain unclear. Here, we identified that the early-response transcription factor, NPAS4, is selectively expressed in SST-INs during motor learning. By utilizing in vivo two-photon imaging in mice, we found that cell-type-specific deletion of Npas4 in M1 disrupted learning-induced spine reorganization among PNs and impaired motor learning. In addition, NPAS4-expressing SST-INs exhibited lower neuronal activity during task-related movements, and chemogenetically increasing the activity of NPAS4-expressing ensembles was sufficient to mimic the effects of Npas4 deletion. Together, our results reveal an instructive role of NPAS4-expressing SST-INs in modulating the inhibition to downstream task-related PNs to allow proper spine reorganization that is critical for motor learning.

Non-monotonic effects of GABAergic synaptic inputs on neuronal firing

GABA is generally known as the principal inhibitory neurotransmitter in the nervous system, usually acting by hyperpolarizing membrane potential. However, GABAergic currents sometimes exhibit non-inhibitory effects, depending on the brain region, developmental stage or pathological condition. Here, we investigate the diverse effects of GABA on the firing rate of several single neuron models, using both analytical calculations and numerical simulations. We find that GABAergic synaptic conductance and output firing rate exhibit three qualitatively different regimes as a function of GABA reversal potential, EGABA: monotonically decreasing for sufficiently low EGABA (inhibitory), monotonically increasing for EGABA above firing threshold (excitatory); and a non-monotonic region for intermediate values of EGABA. In the non-monotonic regime, small GABA conductances have an excitatory effect while large GABA conductances show an inhibitory effect. We provide a phase diagram of different GABAergic effects as a function of GABA reversal potential and glutamate conductance. We find that noisy inputs increase the range of EGABA for which the non-monotonic effect can be observed. We also construct a micro-circuit model of striatum to explain observed effects of GABAergic fast spiking interneurons on spiny projection neurons, including non-monotonicity, as well as the heterogeneity of the effects. Our work provides a mechanistic explanation of paradoxical effects of GABAergic synaptic inputs, with implications for understanding the effects of GABA in neural computation and development.

Assessing Local and Branch-specific Activity in Dendrites

Dendrites are elaborate neural processes which integrate inputs from various sources in space and time. While decades of work have suggested an independent role for dendrites in driving nonlinear computations for the cell, only recently have technological advances enabled us to capture the variety of activity in dendrites and their coupling dynamics with the soma. Under certain circumstances, activity generated in a given dendritic branch remains isolated, such that the soma or even sister dendrites are not privy to these localized signals. Such branch-specific activity could radically increase the capacity and flexibility of coding for the cell as a whole. Here, we discuss these forms of localized and branch-specific activity, their functional relevance in plasticity and behavior, and their supporting biophysical and circuit-level mechanisms. We conclude by showcasing electrical and optical approaches in hippocampal area CA3, using original experimental data to discuss experimental and analytical methodology and key considerations to take when investigating the functional relevance of independent dendritic activity.

Classical-Contextual Interactions in V1 May Rely on Dendritic Computations

A signature feature of the neocortex is the dense network of horizontal connections (HCs) through which pyramidal neurons (PNs) exchange "contextual" information. In primary visual cortex (V1), HCs are thought to facilitate boundary detection, a crucial operation for object recognition, but how HCs modulate PN responses to boundary cues within their classical receptive fields (CRF) remains unknown. We began by "asking" natural images, through a structured data collection and ground truth labeling process, what function a V1 cell should use to compute boundary probability from aligned edge cues within and outside its CRF. The "answer" was an asymmetric 2-D sigmoidal function, whose nonlinear form provides the first normative account for the "multiplicative" center-flanker interactions previously reported in V1 neurons (Kapadia et al., 1995, 2000; Polat et al., 1998). Using a detailed compartmental model, we then show that this boundary-detecting classical-contextual interaction function can be computed by NMDAR-dependent spatial synaptic interactions within PN dendrites - the site where classical and contextual inputs first converge in the cortex. In additional simulations, we show that local interneuron circuitry activated by HCs can powerfully leverage the nonlinear spatial computing capabilities of PN dendrites, providing the cortex with a highly flexible substrate for integration of classical and contextual information.

Parallel processing in active dendrites during periods of intense spiking activity

A neuron's ability to perform parallel computations throughout its dendritic arbor substantially improves its computational capacity. However, during natural patterns of activity, the degree to which computations remain compartmentalized, especially in neurons with active dendritic trees, is not clear. Here, we examine how the direction of moving objects is computed across the bistratified dendritic arbors of ON-OFF direction-selective ganglion cells (DSGCs) in the mouse retina. We find that although local synaptic signals propagate efficiently throughout their dendritic trees, direction-selective computations in one part of the dendritic arbor have little effect on those being made elsewhere. Independent dendritic processing allows DSGCs to compute the direction of moving objects multiple times as they traverse their receptive fields, enabling them to rapidly detect changes in motion direction on a sub-receptive-field basis. These results demonstrate that the parallel processing capacity of neurons can be maintained even during periods of intense synaptic activity.

Input rate encoding and gain control in dendrites of neocortical pyramidal neurons

Elucidating how neurons encode network activity is essential to understanding how the brain processes information. Neocortical pyramidal cells receive excitatory input onto spines distributed along dendritic branches. Local dendritic branch nonlinearities can boost the response to spatially clustered and synchronous input, but how this translates into the integration of patterns of ongoing activity remains unclear. To examine dendritic integration under naturalistic stimulus regimes, we use two-photon glutamate uncaging to repeatedly activate multiple dendritic spines at random intervals. In the proximal dendrites of two populations of layer 5 pyramidal neurons in the mouse motor cortex, spatially restricted synchrony is not a prerequisite for dendritic boosting. Branches encode afferent inputs with distinct rate sensitivities depending upon cell and branch type. Thus, inputs distributed along a dendritic branch can recruit supralinear boosting and the window of this nonlinearity may provide a mechanism by which dendrites can preferentially amplify slow-frequency network oscillations.

When Are Depolarizing GABAergic Responses Excitatory?

The membrane responses upon activation of GABA(A) receptors critically depend on the intracellular Cl⁻ concentration ([Cl⁻]_i), which is maintained by a set of transmembrane transporters for Cl⁻. During neuronal development, but also under several pathophysiological conditions, the prevailing expression of the Cl⁻ loader NKCC1 and the low expression of the Cl⁻ extruder KCC2 causes elevated [Cl⁻]_i, which result in depolarizing GABAergic membrane responses. However, depolarizing GABAergic responses are not necessarily excitatory, as GABA(A) receptors also reduces the input resistance of neurons and thereby shunt excitatory inputs. To summarize our knowledge on the effect of depolarizing GABA responses on neuronal excitability, this review discusses theoretical considerations and experimental studies illustrating the relation between GABA conductances, GABA reversal potential and neuronal excitability. In addition, evidences for the complex spatiotemporal interaction between depolarizing GABAergic and glutamatergic inputs are described. Moreover, mechanisms that influence [Cl⁻]_i beyond the expression of Cl⁻ transporters are presented. And finally, several in vitro and in vivo studies that directly investigated whether GABA mediates excitation or inhibition during early developmental stages are summarized. In summary, these theoretical considerations and experimental evidences suggest that GABA can act as inhibitory neurotransmitter even under conditions that maintain substantial depolarizing membrane responses.

A general principle of dendritic constancy: A neuron's size- and shape-invariant excitability

Reducing neuronal size results in less membrane and therefore lower input conductance. Smaller neurons are thus more excitable, as seen in their responses to somatic current injections. However, the impact of a neuron's size and shape on its voltage responses to dendritic synaptic activation is much less understood. Here we use analytical cable theory to predict voltage responses to distributed synaptic inputs in unbranched cables, showing that these are entirely independent of dendritic length. For a given synaptic density, neuronal responses depend only on the average dendritic diameter and intrinsic conductivity. This remains valid for a wide range of morphologies irrespective of their arborization complexity. Spiking models indicate that morphology-invariant numbers of spikes approximate the percentage of active synapses. In contrast to spike rate, spike times do depend on dendrite morphology. In summary, neuronal excitability in response to distributed synaptic inputs is largely unaffected by dendrite length or complexity.

Burst control: Synaptic conditions for burst generation in cortical layer 5 pyramidal neurons

The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na+, Ca2+, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron's dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na+, Ca2+, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity.

A synaptic learning rule for exploiting nonlinear dendritic computation

Information processing in the brain depends on the integration of synaptic input distributed throughout neuronal dendrites. Dendritic integration is a hierarchical process, proposed to be equivalent to integration by a multilayer network, potentially endowing single neurons with substantial computational power. However, whether neurons can learn to harness dendritic properties to realize this potential is unknown. Here, we develop a learning rule from dendritic cable theory and use it to investigate the processing capacity of a detailed pyramidal neuron model. We show that computations using spatial or temporal features of synaptic input patterns can be learned, and even synergistically combined, to solve a canonical nonlinear feature-binding problem. The voltage dependence of the learning rule drives coactive synapses to engage dendritic nonlinearities, whereas spike-timing dependence shapes the time course of subthreshold potentials. Dendritic input-output relationships can therefore be flexibly tuned through synaptic plasticity, allowing optimal implementation of nonlinear functions by single neurons.

Dendritic Branch-constrained N-Methyl-d-Aspartate Receptor-mediated Spikes Drive Synaptic Plasticity in Hippocampal CA3 Pyramidal Cells

N-methyl-d-aspartate receptor-mediated ( spikes can be causally linked to the induction of synaptic long-term potentiation (LTP) in hippocampal and cortical pyramidal cells. However, it is unclear if they regulate plasticity at a local or global scale in the dendritic tree. Here, we used dendritic patch-clamp recordings and calcium imaging to investigate the integrative properties of single dendrites of hippocampal CA3 cells. We show that local hyperpolarization of a single dendritic segment prevents NMDA spikes, their associated calcium transients, as well as LTP in a branch-specific manner. This result provides direct, causal evidence that the single dendritic branch can operate as a functional unit in regulating CA3 pyramidal cell plasticity.

The Impact of SST and PV Interneurons on Nonlinear Synaptic Integration in the Neocortex

Excitatory synaptic inputs arriving at the dendrites of a neuron can engage active mechanisms that nonlinearly amplify the depolarizing currents. This supralinear synaptic integration is subject to modulation by inhibition. However, the specific rules by which different subtypes of interneurons affect the modulation have remained largely elusive. To examine how inhibition influences active synaptic integration, we optogenetically manipulated the activity of the following two subtypes of interneurons: dendrite-targeting somatostatin-expressing (SST) interneurons; and perisomatic-targeting parvalbumin-expressing (PV) interneurons. In acute slices of mouse primary visual cortex, electrical stimulation evoked nonlinear synaptic integration that depended on NMDA receptors. Optogenetic activation of SST interneurons in conjunction with electrical stimulation resulted in predominantly divisive inhibitory gain control, reducing the magnitude of the supralinear response without affecting its threshold. PV interneuron activation, on the other hand, had a minimal effect on the supralinear response. Together, these results delineate the roles for SST and PV neurons in active synaptic integration. Differential effects of inhibition by SST and PV interneurons likely increase the computational capacity of the pyramidal neurons in modulating the nonlinear integration of synaptic output.

Unique properties of dually innervated dendritic spines in pyramidal neurons of the somatosensory cortex uncovered by 3D correlative light and electron microscopy

Pyramidal neurons (PNs) are covered by thousands of dendritic spines receiving excitatory synaptic inputs. The ultrastructure of dendritic spines shapes signal compartmentalization, but ultrastructural diversity is rarely taken into account in computational models of synaptic integration. Here, we developed a 3D correlative light-electron microscopy (3D-CLEM) approach allowing the analysis of specific populations of synapses in genetically defined neuronal types in intact brain circuits. We used it to reconstruct segments of basal dendrites of layer 2/3 PNs of adult mouse somatosensory cortex and quantify spine ultrastructural diversity. We found that 10% of spines were dually innervated and 38% of inhibitory synapses localized to spines. Using our morphometric data to constrain a model of synaptic signal compartmentalization, we assessed the impact of spinous versus dendritic shaft inhibition. Our results indicate that spinous inhibition is locally more efficient than shaft inhibition and that it can decouple voltage and calcium signaling, potentially impacting synaptic plasticity.

Dendritic normalisation improves learning in sparsely connected artificial neural networks

Artificial neural networks, taking inspiration from biological neurons, have become an invaluable tool for machine learning applications. Recent studies have developed techniques to effectively tune the connectivity of sparsely-connected artificial neural networks, which have the potential to be more computationally efficient than their fully-connected counterparts and more closely resemble the architectures of biological systems. We here present a normalisation, based on the biophysical behaviour of neuronal dendrites receiving distributed synaptic inputs, that divides the weight of an artificial neuron's afferent contacts by their number. We apply this dendritic normalisation to various sparsely-connected feedforward network architectures, as well as simple recurrent and self-organised networks with spatially extended units. The learning performance is significantly increased, providing an improvement over other widely-used normalisations in sparse networks. The results are two-fold, being both a practical advance in machine learning and an insight into how the structure of neuronal dendritic arbours may contribute to computation.

Active dendrites enable strong but sparse inputs to determine orientation selectivity

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

Multidimensional population activity in an electrically coupled inhibitory circuit in the cerebellar cortex

Inhibitory neurons orchestrate the activity of excitatory neurons and play key roles in circuit function. Although individual interneurons have been studied extensively, little is known about their properties at the population level. Using random-access 3D two-photon microscopy, we imaged local populations of cerebellar Golgi cells (GoCs), which deliver inhibition to granule cells. We show that population activity is organized into multiple modes during spontaneous behaviors. A slow, network-wide common modulation of GoC activity correlates with the level of whisking and locomotion, while faster (<1 s) differential population activity, arising from spatially mixed heterogeneous GoC responses, encodes more precise information. A biologically detailed GoC circuit model reproduced the common population mode and the dimensionality observed experimentally, but these properties disappeared when electrical coupling was removed. Our results establish that local GoC circuits exhibit multidimensional activity patterns that could be used for inhibition-mediated adaptive gain control and spatiotemporal patterning of downstream granule cells.

Short-Term Synaptic Plasticity Makes Neurons Sensitive to the Distribution of Presynaptic Population Firing Rates

The ability to discriminate spikes that encode a particular stimulus from spikes produced by background activity is essential for reliable information processing in the brain. We describe how synaptic short-term plasticity (STP) modulates the output of presynaptic populations as a function of the distribution of the spiking activity and find a strong relationship between STP features and sparseness of the population code, which could solve this problem. Furthermore, we show that feedforward excitation followed by inhibition (FF-EI), combined with target-dependent STP, promote substantial increase in the signal gain even for considerable deviations from the optimal conditions, granting robustness to this mechanism. A simulated neuron driven by a spiking FF-EI network is reliably modulated as predicted by a rate analysis and inherits the ability to differentiate sparse signals from dense background activity changes of the same magnitude, even at very low signal-to-noise conditions. We propose that the STP-based distribution discrimination is likely a latent function in several regions such as the cerebellum and the hippocampus.

How auditory selectivity for sound timing arises: The diverse roles of GABAergic inhibition in shaping the excitation to interval-selective midbrain neurons

Across sensory systems, temporal frequency information is progressively transformed along ascending central pathways. Despite considerable effort to elucidate the mechanistic basis of these transformations, they remain poorly understood. Here we used a novel constellation of approaches, including whole-cell recordings and focal pharmacological manipulation, in vivo, and new computational algorithms that identify conductances resulting from excitation, inhibition and active membrane properties, to elucidate the mechanisms underlying the selectivity of midbrain auditory neurons for long temporal intervals. Surprisingly, we found that stimulus-driven excitation can be increased and its selectivity decreased following attenuation of inhibition with gabazine or intracellular delivery of fluoride. We propose that this nonlinear interaction is due to shunting inhibition. The rate-dependence of this inhibition results in the illusion that excitation to a cell shows greater temporal selectivity than is actually the case. We also show that rate-dependent depression of excitation, an important component of long-interval selectivity, can be decreased after attenuating inhibition. These novel findings indicate that nonlinear shunting inhibition plays a key role in shaping the amplitude and interval selectivity of excitation. Our findings provide a major advance in understanding how the brain decodes intervals and may explain paradoxical temporal selectivity of excitation to midbrain neurons reported previously.

The Input-Output Relation of Primary Nociceptive Neurons is Determined by the Morphology of the Peripheral Nociceptive Terminals

The output from the peripheral terminals of primary nociceptive neurons, which detect and encode the information regarding noxious stimuli, is crucial in determining pain sensation. The nociceptive terminal endings are morphologically complex structures assembled from multiple branches of different geometry, which converge in a variety of forms to create the terminal tree. The output of a single terminal is defined by the properties of the transducer channels producing the generation potentials and voltage-gated channels, translating the generation potentials into action potential (AP) firing. However, in the majority of cases, noxious stimuli activate multiple terminals; thus, the output of the nociceptive neuron is defined by the integration and computation of the inputs of the individual terminals. Here, we used a computational model of nociceptive terminal tree to study how the architecture of the terminal tree affects the input-output relation of the primary nociceptive neurons. We show that the input-output properties of the nociceptive neurons depend on the length, the axial resistance (Ra), and location of individual terminals. Moreover, we show that activation of multiple terminals by a capsaicin-like current allows summation of the responses from individual terminals, thus leading to increased nociceptive output. Stimulation of the terminals in simulated models of inflammatory or neuropathic hyperexcitability led to a change in the temporal pattern of AP firing, emphasizing the role of temporal code in conveying key information about changes in nociceptive output in pathologic conditions, leading to pain hypersensitivity.SIGNIFICANCE STATEMENT Noxious stimuli are detected by terminal endings of primary nociceptive neurons, which are organized into morphologically complex terminal trees. The information from multiple terminals is integrated along the terminal tree, computing the neuronal output, which propagates toward the CNS, thus shaping the pain sensation. Here, we revealed that the structure of the nociceptive terminal tree determines the output of nociceptive neurons. We show that the integration of noxious information depends on the morphology of the terminal trees and how this integration and, consequently, the neuronal output change under pathologic conditions. Our findings help to predict how nociceptive neurons encode noxious stimuli and how this encoding changes in pathologic conditions, leading to pain.

Excess Neuronal Branching Allows for Local Innervation of Specific Dendritic Compartments in Mature Cortex

The connectivity of cortical microcircuits is a major determinant of brain function; defining how activity propagates between different cell types is key to scaling our understanding of individual neuronal behavior to encompass functional networks. Furthermore, the integration of synaptic currents within a dendrite depends on the spatial organization of inputs, both excitatory and inhibitory. We identify a simple equation to estimate the number of potential anatomical contacts between neurons; finding a linear increase in potential connectivity with cable length and maximum spine length, and a decrease with overlapping volume. This enables us to predict the mean number of candidate synapses for reconstructed cells, including those realistically arranged. We identify an excess of potential local connections in mature cortical data, with densities of neurite higher than is necessary to reliably ensure the possible implementation of any given axo-dendritic connection. We show that the number of local potential contacts allows specific innervation of distinct dendritic compartments.

Ultrastructural, Molecular and Functional Mapping of GABAergic Synapses on Dendritic Spines and Shafts of Neocortical Pyramidal Neurons

The location of GABAergic synapses on dendrites is likely key for neuronal integration. In particular, inhibitory inputs on dendritic spines could serve to selectively veto or modulate individual excitatory inputs, greatly expanding the computational power of individual neurons. To investigate this, we have undertaken a combined functional, molecular, and ultrastructural mapping of the location of GABAergic inputs onto dendrites of pyramidal neurons from upper layers of juvenile mouse somatosensory cortex. Using two-photon uncaging of GABA, intracellular labeling with gerphyrin intrabodies, and focused ion beam milling with scanning electron microscopy, we find that most (96-98%) spines lack GABAergic synapses, although they still display GABAergic responses, potentially due to extrasynaptic GABA receptors. We conclude that GABAergic inputs, in practice, contact dendritic shafts and likely control clusters of excitatory inputs, defining functional zones on dendrites.

Measurements of neuronal morphological variation across the rat neocortex

Neuron morphology is highly variable across the mammalian brain. It is thought that these attributes of neuronal cell shape, such as soma surface area and branching frequency, are determined by biological function and information processing. In this study, a large data set of neurons across the rat neocortex were clustered by their anatomical characters for evidence of distinctiveness among neocortical regions and the somatosensory layers. This data set of neuronal morphologies was compiled from 31 different lab sources with a validation procedure so that data records are potentially comparable across research studies. With this large set of heterogeneous data and by clustering analysis, this study shows that neuronal morphological traits overlap among neocortical and somatosensory regions. In the context of past neuroanatomical studies, this result is not congruent with tissue level analysis and strongly suggests further sampling of neuronal data to lessen the effect of confounding factors, such as the influence of different methodologies from use of heterogeneous samples of neuronal data.

Illuminating dendritic function with computational models

Dendrites have always fascinated researchers: from the artistic drawings by Ramon y Cajal to the beautiful recordings of today, neuroscientists have been striving to unravel the mysteries of these structures. Theoretical work in the 1960s predicted important dendritic effects on neuronal processing, establishing computational modelling as a powerful technique for their investigation. Since then, modelling of dendrites has been instrumental in driving neuroscience research in a targeted manner, providing experimentally testable predictions that range from the subcellular level to the systems level, and their relevance extends to fields beyond neuroscience, such as machine learning and artificial intelligence. Validation of modelling predictions often requires - and drives - new technological advances, thus closing the loop with theory-driven experimentation that moves the field forward. This Review features the most important, to our understanding, contributions of modelling of dendritic computations, including those pending experimental verification, and highlights studies of successful interactions between the modelling and experimental neuroscience communities.

Distinct subtypes of inhibitory interneurons differentially promote the propagation of rate and temporal codes in the feedforward neural network

Sensory information is believed to be encoded in neuronal spikes using two different neural codes, the rate code (spike firing rate) and the temporal code (precisely-timed spikes). Since the sensory cortex has a highly hierarchical feedforward structure, sensory information-carrying neural codes should reliably propagate across the feedforward network (FFN) of the cortex. Experimental evidence suggests that inhibitory interneurons, such as the parvalbumin-positive (PV) and somatostatin-positive (SST) interneurons, that have distinctively different electrophysiological and synaptic properties, modulate the neural codes during sensory information processing in the cortex. However, how PV and SST interneurons impact on the neural code propagation in the cortical FFN is unknown. We address this question by building a five-layer FFN model consisting of a physiologically realistic Hodgkin-Huxley-type models of excitatory neurons and PV/SST interneurons at different ratios. In response to different firing rate inputs (20-80 Hz), a higher ratio of PV over SST interneurons promoted a reliable propagation of all ranges of firing rate inputs. In contrast, in response to a range of precisely-timed spikes in the form of pulse-packets [with a different number of spikes (α, 40-400 spikes) and degree of dispersion (σ, 0-20 ms)], a higher ratio of SST over PV interneurons promoted a reliable propagation of pulse-packets. Our simulation results show that PV and SST interneurons differentially promote a reliable propagation of the rate and temporal codes, respectively, indicating that the dynamic recruitment of PV and SST interneurons may play critical roles in a reliable propagation of sensory information-carrying neural codes in the cortical FFN.

Perceptron Learning and Classification in a Modeled Cortical Pyramidal Cell

The perceptron learning algorithm and its multiple-layer extension, the backpropagation algorithm, are the foundations of the present-day machine learning revolution. However, these algorithms utilize a highly simplified mathematical abstraction of a neuron; it is not clear to what extent real biophysical neurons with morphologically-extended non-linear dendritic trees and conductance-based synapses can realize perceptron-like learning. Here we implemented the perceptron learning algorithm in a realistic biophysical model of a layer 5 cortical pyramidal cell with a full complement of non-linear dendritic channels. We tested this biophysical perceptron (BP) on a classification task, where it needed to correctly binarily classify 100, 1,000, or 2,000 patterns, and a generalization task, where it was required to discriminate between two "noisy" patterns. We show that the BP performs these tasks with an accuracy comparable to that of the original perceptron, though the classification capacity of the apical tuft is somewhat limited. We concluded that cortical pyramidal neurons can act as powerful classification devices.

Electrical Compartmentalization in Neurons

The dendritic tree of neurons plays an important role in information processing in the brain. While it is thought that dendrites require independent subunits to perform most of their computations, it is still not understood how they compartmentalize into functional subunits. Here, we show how these subunits can be deduced from the properties of dendrites. We devised a formalism that links the dendritic arborization to an impedance-based tree graph and show how the topology of this graph reveals independent subunits. This analysis reveals that cooperativity between synapses decreases slowly with increasing electrical separation and thus that few independent subunits coexist. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of the subunits in a context-dependent manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features. Analysis of dendritic patch-clamp recording experiments confirmed our theoretical predictions.

Whole-Neuron Synaptic Mapping Reveals Spatially Precise Excitatory/Inhibitory Balance Limiting Dendritic and Somatic Spiking

The balance between excitatory and inhibitory (E and I) synapses is thought to be critical for information processing in neural circuits. However, little is known about the spatial principles of E and I synaptic organization across the entire dendritic tree of mammalian neurons. We developed a new open-source reconstruction platform for mapping the size and spatial distribution of E and I synapses received by individual genetically-labeled layer 2/3 (L2/3) cortical pyramidal neurons (PNs) in vivo. We mapped over 90,000 E and I synapses across twelve L2/3 PNs and uncovered structured organization of E and I synapses across dendritic domains as well as within individual dendritic segments. Despite significant domain-specific variation in the absolute density of E and I synapses, their ratio is strikingly balanced locally across dendritic segments. Computational modeling indicates that this spatially precise E/I balance dampens dendritic voltage fluctuations and strongly impacts neuronal firing output.

Cell-type specific innervation of cortical pyramidal cells at their apical dendrites

We investigated the synaptic innervation of apical dendrites of cortical pyramidal cells in a region between layers (L) 1 and 2 using 3-D electron microscopy applied to four cortical regions in mouse. We found the relative inhibitory input at the apical dendrite's main bifurcation to be more than 2-fold larger for L2 than L3 and L5 thick-tufted pyramidal cells. Towards the distal tuft dendrites in upper L1, the relative inhibitory input was at least about 2-fold larger for L5 pyramidal cells than for all others. Only L3 pyramidal cells showed homogeneous inhibitory input fraction. The inhibitory-to-excitatory synaptic ratio is thus specific for the types of pyramidal cells. Inhibitory axons preferentially innervated either L2 or L3/5 apical dendrites, but not both. These findings describe connectomic principles for the control of pyramidal cells at their apical dendrites and support differential computational properties of L2, L3 and subtypes of L5 pyramidal cells in cortex.

Dendritic action potentials and computation in human layer 2/3 cortical neurons

The active electrical properties of dendrites shape neuronal input and output and are fundamental to brain function. However, our knowledge of active dendrites has been almost entirely acquired from studies of rodents. In this work, we investigated the dendrites of layer 2 and 3 (L2/3) pyramidal neurons of the human cerebral cortex ex vivo. In these neurons, we discovered a class of calcium-mediated dendritic action potentials (dCaAPs) whose waveform and effects on neuronal output have not been previously described. In contrast to typical all-or-none action potentials, dCaAPs were graded; their amplitudes were maximal for threshold-level stimuli but dampened for stronger stimuli. These dCaAPs enabled the dendrites of individual human neocortical pyramidal neurons to classify linearly nonseparable inputs—a computation conventionally thought to require multilayered networks.