Timed Synaptic Inhibition Shapes NMDA Spikes, Influencing Local Dendritic Processing and Global I/O Properties of Cortical 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.

Dendrites and efficiency: Optimizing performance and resource utilization

The brain is a highly efficient system that has evolved to optimize performance under limited resources. In this review, we highlight recent theoretical and experimental studies that support the view that dendrites make information processing and storage in the brain more efficient. This is achieved through the dynamic modulation of integration versus segregation of inputs and activity within a neuron. We argue that under conditions of limited energy and space, dendrites help biological networks to implement complex functions such as processing natural stimuli on behavioral timescales, performing the inference process on those stimuli in a context-specific manner, and storing the information in overlapping populations of neurons. A global picture starts to emerge, in which dendrites help the brain achieve efficiency through a combination of optimization strategies that balance the tradeoff between performance and resource utilization.

A GPU-based computational framework that bridges neuron simulation and artificial intelligence

Biophysically detailed multi-compartment models are powerful tools to explore computational principles of the brain and also serve as a theoretical framework to generate algorithms for artificial intelligence (AI) systems. However, the expensive computational cost severely limits the applications in both the neuroscience and AI fields. The major bottleneck during simulating detailed compartment models is the ability of a simulator to solve large systems of linear equations. Here, we present a novel Dendritic Hierarchical Scheduling (DHS) method to markedly accelerate such a process. We theoretically prove that the DHS implementation is computationally optimal and accurate. This GPU-based method performs with 2-3 orders of magnitude higher speed than that of the classic serial Hines method in the conventional CPU platform. We build a DeepDendrite framework, which integrates the DHS method and the GPU computing engine of the NEURON simulator and demonstrate applications of DeepDendrite in neuroscience tasks. We investigate how spatial patterns of spine inputs affect neuronal excitability in a detailed human pyramidal neuron model with 25,000 spines. Furthermore, we provide a brief discussion on the potential of DeepDendrite for AI, specifically highlighting its ability to enable the efficient training of biophysically detailed models in typical image classification tasks.

Genetically Defined Subtypes of Somatostatin-Containing Cortical Interneurons

Inhibitory interneurons play a crucial role in proper development and function of the mammalian cerebral cortex. Of the different inhibitory subclasses, dendritic-targeting, somatostatin-containing (SOM) interneurons may be the most diverse. Earlier studies used GFP-expressing and recombinase-expressing mouse lines to characterize genetically defined subtypes of SOM interneurons by morphologic, electrophysiological, and neurochemical properties. More recently, large-scale studies classified SOM interneurons into 13 morpho-electric transcriptomic (MET) types. It remains unclear, however, how these various classification schemes relate to each other, and experimental access to MET types has been limited by the scarcity of specific mouse driver lines. To address these issues, we crossed Flp and Cre driver lines with a dual-color intersectional reporter, allowing experimental access to several combinatorially defined SOM subsets. Brains from adult mice of both sexes were retrogradely dye labeled from the pial surface to identify layer 1-projecting neurons and immunostained against several marker proteins, revealing correlations between genetic label, axonal target, and marker protein expression in the same neurons. Lastly, using whole-cell recordings ex vivo, we analyzed and compared electrophysiological properties between different intersectional subsets. We identified two layer 1-targeting subtypes with nonoverlapping marker protein expression and electrophysiological properties, which, together with a previously characterized layer 4-targeting subtype, account for >50% of all layer 5 SOM cells and >40% of all SOM cells, and appear to map onto 5 of the 13 MET types. Genetic access to these subtypes will allow researchers to determine their synaptic inputs and outputs and uncover their roles in cortical computations and animal behavior.

The impact of Hodgkin-Huxley models on dendritic research

For the past seven decades, the Hodgkin-Huxley (HH) formalism has been an invaluable tool in the arsenal of neuroscientists, allowing for robust and reproducible modelling of ionic conductances and the electrophysiological phenomena they underlie. Despite its apparent age, its role as a cornerstone of computational neuroscience has not waned. The discovery of dendritic regenerative events mediated by ionic and synaptic conductances has solidified the importance of HH-based models further, yielding new predictions concerning dendritic integration, synaptic plasticity and neuronal computation. These predictions are often validated through in vivo and in vitro experiments, advancing our understanding of the neuron as a biological system and emphasizing the importance of HH-based detailed computational models as an instrument of dendritic research. In this article, we discuss recent studies in which the HH formalism is used to shed new light on dendritic function and its role in neuronal phenomena.

Optogenetic stimulation reveals a latent tipping point in cortical networks during ictogenesis

Brain-state transitions are readily apparent from changes in brain rhythms,1 but are difficult to predict, suggestive that the underlying cause is latent to passive recording methods. Among the most important transitions, clinically, are the starts of seizures. We here show that an 'active probing' approach may have several important benefits for epileptic management, including by helping predict these transitions. We used mice expressing the optogenetic actuator, channelrhodopsin, in pyramidal cells, allowing this population to be stimulated in isolation. Intermittent stimulation at frequencies as low as 0.033 Hz (period = 30 s) delayed the onset of seizure-like events in an acute brain slice model of ictogenesis, but the effect was lost if stimulation was delivered at even lower frequencies (1/min). Notably, active probing additionally provides advance indication of when seizure-like activity is imminent, revealed by monitoring the postsynaptic response to stimulation. The postsynaptic response, recorded extracellularly, showed an all-or-nothing change in both amplitude and duration, a few hundred seconds before seizure-like activity began-a sufficient length of time to provide a helpful warning of an impending seizure. The change in the postsynaptic response then persisted for the remainder of the recording, indicative of a state change from a pre-epileptic to a pro-epileptic network. This occurred in parallel with a large increase in the stimulation-triggered Ca2+ entry into pyramidal dendrites, and a step increase in the number of evoked postsynaptic action potentials, both consistent with a reduction in the threshold for dendritic action potentials. In 0 Mg2+ bathing media, the reduced threshold was not associated with changes in glutamatergic synaptic function, nor of GABAergic release from either parvalbumin or somatostatin interneurons, but simulations indicate that the step change in the optogenetic response can instead arise from incremental increases in intracellular [Cl-]. The change in the response to stimulation was replicated by artificially raising intracellular [Cl-], using the optogenetic chloride pump, halorhodopsin. By contrast, increases in extracellular [K+] cannot account for the firing patterns in the response to stimulation, although this, and other cellular changes, may contribute to ictal initiation in other circumstances. We describe how these various cellular changes form a synergistic network of positive feedback mechanisms, which may explain the precipitous nature of seizure onset. This model of seizure initiation draws together several major lines of epilepsy research as well as providing an important proof-of-principle regarding the utility of open-loop brain stimulation for clinical management of the condition.

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.

Glutamate spillover drives robust all-or-none dendritic plateau potentials-an in silico investigation using models of striatal projection neurons

Plateau potentials are a critical feature of neuronal excitability, but their all-or-none behavior is not easily captured in modeling. In this study, we investigated models of plateau potentials in multi-compartment neuron models and found that including glutamate spillover provides robust all-or-none behavior. This result arises due to the prolonged duration of extrasynaptic glutamate. When glutamate spillover is not included, the all-or-none behavior is very sensitive to the steepness of the Mg²⁺ block. These results suggest a potentially significant role of glutamate spillover in plateau potential generation, providing a mechanism for robust all-or-none behavior across a wide range of slopes of the Mg²⁺ block curve. We also illustrate the importance of the all-or-none plateau potential behavior for nonlinear computation with regard to the nonlinear feature binding problem.

Mapping thalamic innervation to individual L2/3 pyramidal neurons and modeling their 'readout' of visual input

The thalamus is the main gateway for sensory information from the periphery to the mammalian cerebral cortex. A major conundrum has been the discrepancy between the thalamus's central role as the primary feedforward projection system into the neocortex and the sparseness of thalamocortical synapses. Here we use new methods, combining genetic tools and scalable tissue expansion microscopy for whole-cell synaptic mapping, revealing the number, density and size of thalamic versus cortical excitatory synapses onto individual layer 2/3 (L2/3) pyramidal cells (PCs) of the mouse primary visual cortex. We find that thalamic inputs are not only sparse, but remarkably heterogeneous in number and density across individual dendrites and neurons. Most surprising, despite their sparseness, thalamic synapses onto L2/3 PCs are smaller than their cortical counterparts. Incorporating these findings into fine-scale, anatomically faithful biophysical models of L2/3 PCs reveals how individual neurons with sparse and weak thalamocortical synapses, embedded in small heterogeneous neuronal ensembles, may reliably 'read out' visually driven thalamic input.

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.

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.

Dendritic Excitability and Synaptic Plasticity In Vitro and In Vivo

Much of our understanding of dendritic and synaptic physiology comes from in vitro experimentation, where the afforded mechanical stability and convenience of applying drugs allowed patch-clamping based recording techniques to investigate ion channel distributions, their gating kinetics, and to uncover dendritic integrative and synaptic plasticity rules. However, with current efforts to study these questions in vivo, there is a great need to translate existing knowledge between in vitro and in vivo experimental conditions. In this review, we identify discrepancies between in vitro and in vivo ionic composition of extracellular media and discuss how changes in ionic composition alter dendritic excitability and plasticity induction. Here, we argue that under physiological in vivo ionic conditions, dendrites are expected to be more excitable and the threshold for synaptic plasticity induction to be lowered. Consequently, the plasticity rules described in vitro vary significantly from those implemented in vivo.

The guide to dendritic spikes of the mammalian cortex in vitro and in vivo

Half a century since their discovery by Llinás and colleagues, dendritic spikes have been observed in various neurons in different brain regions, from the neocortex and cerebellum to the basal ganglia. Dendrites exhibit a terrifically diverse but stereotypical repertoire of spikes, sometimes specific to subregions of the dendrite. Despite their prevalence, we only have a glimpse into their role in the behaving animal. This article aims to survey the full range of dendritic spikes found in excitatory and inhibitory neurons, compare them in vivo versus in vitro, and discuss new studies describing dendritic spikes in the human cortex. We focus on dendritic spikes in neocortical and hippocampal neurons and present a roadmap to identify and understand the broader role of dendritic spikes in single-cell computation.

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.

Single cortical neurons as deep artificial neural networks

Utilizing recent advances in machine learning, we introduce a systematic approach to characterize neurons' input/output (I/O) mapping complexity. Deep neural networks (DNNs) were trained to faithfully replicate the I/O function of various biophysical models of cortical neurons at millisecond (spiking) resolution. A temporally convolutional DNN with five to eight layers was required to capture the I/O mapping of a realistic model of a layer 5 cortical pyramidal cell (L5PC). This DNN generalized well when presented with inputs widely outside the training distribution. When NMDA receptors were removed, a much simpler network (fully connected neural network with one hidden layer) was sufficient to fit the model. Analysis of the DNNs' weight matrices revealed that synaptic integration in dendritic branches could be conceptualized as pattern matching from a set of spatiotemporal templates. This study provides a unified characterization of the computational complexity of single neurons and suggests that cortical networks therefore have a unique architecture, potentially supporting their computational power.

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.

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.

Impact of GABAA and GABAB Inhibition on Cortical Dynamics and Perturbational Complexity during Synchronous and Desynchronized States

Quantitative estimations of spatiotemporal complexity of cortical activity patterns are used in the clinic as a measure of consciousness levels, but the cortical mechanisms involved are not fully understood. We used a version of the perturbational complexity index (PCI) adapted to multisite recordings from the ferret (either sex) cerebral cortex in vitro (sPCI) to investigate the role of GABAergic inhibition in cortical complexity. We studied two dynamical states: slow-wave activity (synchronous state) and desynchronized activity, that express low and high causal complexity respectively. Progressive blockade of GABAergic inhibition during both regimes revealed its impact on the emergent cortical activity and on sPCI. Gradual GABAA receptor blockade resulted in higher synchronization, being able to drive the network from a desynchronized to a synchronous state, with a progressive decrease of complexity (sPCI). Blocking GABAB receptors also resulted in a reduced sPCI, in particular when in a synchronous, slow wave state. Our findings demonstrate that physiological levels of inhibition contribute to the generation of dynamical richness and spatiotemporal complexity. However, if inhibition is diminished or enhanced, cortical complexity decreases. Using a computational model, we explored a larger parameter space in this relationship and demonstrate a link between excitatory/inhibitory balance and the complexity expressed by the cortical network.SIGNIFICANCE STATEMENT The spatiotemporal complexity of the activity expressed by the cerebral cortex is a highly revealing feature of the underlying network's state. Complexity varies with physiological brain states: it is higher during awake than during sleep states. But it also informs about pathologic states: in disorders of consciousness, complexity is lower in an unresponsive wakefulness syndrome than in a minimally conscious state. What are the network parameters that modulate complexity? Here we investigate how inhibition, mediated by either GABAA or GABAA receptors, influences cortical complexity. And we do this departing from two extreme functional states: a highly synchronous, slow-wave state, and a desynchronized one that mimics wakefulness. We find that there is an optimal level of inhibition in which complexity is highest.

Sex-Specific Disruption of Distinct mPFC Inhibitory Neurons in Spared-Nerve Injury Model of Neuropathic Pain

The medial prefrontal cortex (mPFC) modulates a range of behaviors, including responses to noxious stimuli. While various pain modalities alter mPFC function, our understanding of changes to specific cell types underlying pain-induced mPFC dysfunction remains incomplete. Proper activity of cortical GABAergic interneurons is essential for normal circuit function. We find that nerve injury increases excitability of layer 5 parvalbumin-expressing neurons in the prelimbic (PL) region of the mPFC from male, but not female, mice. Conversely, nerve injury dampens excitability in somatostatin-expressing neurons in layer 2/3 of the PL region; however, effects are differential between males and females. Nerve injury slightly increases the frequency of spontaneous excitatory post-synaptic currents (sEPSCs) in layer 5 parvalbumin-expressing neurons in males but reduces frequency of sEPSCs in layer 2/3 somatostatin-expressing neurons in females. Our findings provide key insight into how nerve injury drives maladaptive and sex-specific alterations to GABAergic circuits in cortical regions implicated in chronic pain.

Local glutamate-mediated dendritic plateau potentials change the state of the cortical pyramidal neuron

Dendritic spikes in thin dendritic branches (basal and oblique dendrites) are traditionally inferred from spikelets measured in the cell body. Here, we used laser-spot voltage-sensitive dye imaging in cortical pyramidal neurons (rat brain slices) to investigate the voltage waveforms of dendritic potentials occurring in response to spatially restricted glutamatergic inputs. Local dendritic potentials lasted 200-500 ms and propagated to the cell body, where they caused sustained 10- to 20-mV depolarizations. Plateau potentials propagating from dendrite to soma and action potentials propagating from soma to dendrite created complex voltage waveforms in the middle of the thin basal dendrite, comprised of local sodium spikelets, local plateau potentials, and backpropagating action potentials, superimposed on each other. Our model replicated these voltage waveforms across a gradient of glutamatergic stimulation intensities. The model then predicted that somatic input resistance (Rin) and membrane time constant (tau) may be reduced during dendritic plateau potential. We then tested these model predictions in real neurons and found that the model correctly predicted the direction of Rin and tau change but not the magnitude. In summary, dendritic plateau potentials occurring in basal and oblique branches put pyramidal neurons into an activated neuronal state ("prepared state"), characterized by depolarized membrane potential and smaller but faster membrane responses. The prepared state provides a time window of 200-500 ms, during which cortical neurons are particularly excitable and capable of following afferent inputs. At the network level, this predicts that sets of cells with simultaneous plateaus would provide cellular substrate for the formation of functional neuronal ensembles.NEW & NOTEWORTHY In cortical pyramidal neurons, we recorded glutamate-mediated dendritic plateau potentials with voltage imaging and created a computer model that recreated experimental measures from dendrite and cell body. Our model made new predictions, which were then tested in experiments. Plateau potentials profoundly change neuronal state: a plateau potential triggered in one basal dendrite depolarizes the soma and shortens membrane time constant, making the cell more susceptible to firing triggered by other afferent inputs.

The interplay between somatic and dendritic inhibition promotes the emergence and stabilization of place fields

During the exploration of novel environments, place fields are rapidly formed in hippocampal CA1 neurons. Place cell firing rate increases in early stages of exploration of novel environments but returns to baseline levels in familiar environments. Although similar in amplitude and width, place fields in familiar environments are more stable than in novel environments. We propose a computational model of the hippocampal CA1 network, which describes the formation, dynamics and stabilization of place fields. We show that although somatic disinhibition is sufficient to form place fields, dendritic inhibition along with synaptic plasticity is necessary for place field stabilization. Our model suggests that place cell stability can be attributed to strong excitatory synaptic weights and strong dendritic inhibition. We show that the interplay between somatic and dendritic inhibition balances the increased excitatory weights, such that place cells return to their baseline firing rate after exploration. Our model suggests that different types of interneurons are essential to unravel the mechanisms underlying place field plasticity. Finally, we predict that artificially induced dendritic events can shift place fields even after place field stabilization.

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.

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.

Classes of dendritic information processing

Dendrites are much more than passive neuronal components. Mounting experimental evidence and decades of computational work have decisively shown that dendrites leverage a host of nonlinear biophysical phenomena and actively participate in sophisticated computations, at the level of the single neuron and at the level of the network. However, a coherent view of their processing power is still lacking and dendrites are largely neglected in neural network models. Here, we describe four classes of dendritic information processing and delineate their implications at the algorithmic level. We propose that beyond the well-known spatiotemporal filtering of their inputs, dendrites are capable of selecting, routing and multiplexing information. By separating dendritic processing from axonal outputs, neuron networks gain a degree of freedom with implications for perception and learning.

Determination of effective synaptic conductances using somatic voltage clamp

The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance measurement and provides a reliable approach to assess synaptic influence on neuronal computation.

To understand synaptic mechanisms underlying neuronal computations, a fundamental approach is to use voltage clamp to measure the dynamics of excitatory and inhibitory input conductances. Due to the space clamp effect, the measured conductance in general deviates from the local input conductance on the dendrites, hence its biological interpretation is questionable, as we demonstrate in this work. We further propose the concept of effective conductance that is proportional to the local input conductance on the dendrites and reflects directly the synaptic impact on spike generation, and develop a framework to determine the effective conductance reliably. Our work provides a biologically plausible metric for elucidating synaptic influence on neuronal computation under the constraint of the space clamp effect.

Inhibition enhances spatially-specific calcium encoding of synaptic input patterns in a biologically constrained model

Synaptic plasticity, which underlies learning and memory, depends on calcium elevation in neurons, but the precise relationship between calcium and spatiotemporal patterns of synaptic inputs is unclear. Here, we develop a biologically realistic computational model of striatal spiny projection neurons with sophisticated calcium dynamics, based on data from rodents of both sexes, to investigate how spatiotemporally clustered and distributed excitatory and inhibitory inputs affect spine calcium. We demonstrate that coordinated excitatory synaptic inputs evoke enhanced calcium elevation specific to stimulated spines, with lower but physiologically relevant calcium elevation in nearby non-stimulated spines. Results further show a novel and important function of inhibition-to enhance the difference in calcium between stimulated and non-stimulated spines. These findings suggest that spine calcium dynamics encode synaptic input patterns and may serve as a signal for both stimulus-specific potentiation and heterosynaptic depression, maintaining balanced activity in a dendritic branch while inducing pattern-specific plasticity.

Information-Processing Model of Concept Formation – Is First Language Acquisition Universal?

The analysis of child’s speech corpora shows that the process of acquisition of English and French displays identical development of children’s expressions when the speech-utterances are presented as Fibonacci-weighted classes of concepts. A model of concept complexity and information processing based on principles of optimality is proposed to explain this statistical result.

Human Cortical Pyramidal Neurons: From Spines to Spikes via Models

We present detailed models of pyramidal cells from human neocortex, including models on their excitatory synapses, dendritic spines, dendritic NMDA- and somatic/axonal Na⁺ spikes that provided new insights into signal processing and computational capabilities of these principal cells. Six human layer 2 and layer 3 pyramidal cells (HL2/L3 PCs) were modeled, integrating detailed anatomical and physiological data from both fresh and postmortem tissues from human temporal cortex. The models predicted particularly large AMPA- and NMDA-conductances per synaptic contact (0.88 and 1.31 nS, respectively) and a steep dependence of the NMDA-conductance on voltage. These estimates were based on intracellular recordings from synaptically-connected HL2/L3 pairs, combined with extra-cellular current injections and use of synaptic blockers, and the assumption of five contacts per synaptic connection. A large dataset of high-resolution reconstructed HL2/L3 dendritic spines provided estimates for the EPSPs at the spine head (12.7 ± 4.6 mV), spine base (9.7 ± 5.0 mV), and soma (0.3 ± 0.1 mV), and for the spine neck resistance (50–80 MΩ). Matching the shape and firing pattern of experimental somatic Na⁺-spikes provided estimates for the density of the somatic/axonal excitable membrane ion channels, predicting that 134 ± 28 simultaneously activated HL2/L3-HL2/L3 synapses are required for generating (with 50% probability) a somatic Na⁺ spike. Dendritic NMDA spikes were triggered in the model when 20 ± 10 excitatory spinous synapses were simultaneously activated on individual dendritic branches. The particularly large number of basal dendrites in HL2/L3 PCs and the distinctive cable elongation of their terminals imply that ~25 NMDA-spikes could be generated independently and simultaneously in these cells, as compared to ~14 in L2/3 PCs from the rat somatosensory cortex. These multi-sites non-linear signals, together with the large (~30,000) excitatory synapses/cell, equip human L2/L3 PCs with enhanced computational capabilities. Our study provides the most comprehensive model of any human neuron to-date demonstrating the biophysical and computational distinctiveness of human cortical neurons.

Functional implications of inhibitory synapse placement on signal processing in pyramidal neuron dendrites

A rich literature describes inhibitory innervation of pyramidal neurons in terms of the distinct inhibitory cell types that target the soma, axon initial segment, or dendritic arbor. Less attention has been devoted to how localization of inhibition to specific parts of the pyramidal dendritic arbor influences dendritic signal detection and integration. The effect of inhibitory inputs can vary based on their placement on dendritic spines versus shaft, their distance from the soma, and the branch order of the dendrite they inhabit. Inhibitory synapses are also structurally dynamic, and the implications of these dynamics depend on their dendritic location. Here we consider the heterogeneous roles of inhibitory synapses as defined by their strategic placement on the pyramidal cell dendritic arbor.