Contribution of sublinear and supralinear dendritic integration to neuronal computations

Demonstration that sublinear dendrites enable linearly non-separable computations

Theory predicts that nonlinear summation of synaptic potentials within dendrites allows neurons to perform linearly non-separable computations (LNSCs). Using Boolean analysis approaches, we predicted that both supralinear and sublinear synaptic summation could allow single neurons to implement a type of LNSC, the feature binding problem (FBP), which does not require inhibition contrary to the exclusive-or function (XOR). Notably, sublinear dendritic operations enable LNSCs when scattered synaptic activation generates increased somatic spike output. However, experimental demonstrations of scatter-sensitive neuronal computations have not yet been described. Using glutamate uncaging onto cerebellar molecular layer interneurons, we show that scattered synaptic-like activation of dendrites evoked larger compound EPSPs than clustered synaptic activation, generating a higher output spiking probability. Moreover, we also demonstrate that single interneurons can indeed implement the FBP. Using a biophysical model to explore the conditions in which a neuron might be expected to implement the FBP, we establish that sublinear summation is necessary but not sufficient. Other parameters such as the relative sublinearity, the EPSP size, depolarization amplitude relative to action potential threshold, and voltage fluctuations all influence whether the FBP can be performed. Since sublinear synaptic summation is a property of passive dendrites, we expect that many different neuron types can implement LNSCs.

Equal levels of pre- and postsynaptic potentiation produce unequal outcomes

Which proportion of the long-term potentiation (LTP) expressed in the bulk of excitatory synapses is postsynaptic and which presynaptic remains debatable. To understand better the possible impact of either LTP form, we explored a realistic model of a CA1 pyramidal cell equipped with known membrane mechanisms and multiple, stochastic excitatory axo-spinous synapses. Our simulations were designed to establish an input-output transfer function, the dependence between the frequency of presynaptic action potentials triggering probabilistic synaptic discharges and the average frequency of postsynaptic spiking. We found that, within the typical physiological range, potentiation of the postsynaptic current results in a greater overall output than an equivalent increase in presynaptic release probability. This difference grows stronger at lower input frequencies and lower release probabilities. Simulations with a non-hierarchical circular network of principal neurons indicated that equal increases in either synaptic fidelity or synaptic strength of individual connections also produce distinct changes in network activity, although the network phenomenology is likely to be complex. These observations should help to interpret the machinery of LTP phenomena documented in situ. This article is part of a discussion meeting issue 'Long-term potentiation: 50 years on'.

Probing multiplexed basal dendritic computations using two-photon 3D holographic uncaging

Basal dendrites of layer 5 cortical pyramidal neurons exhibit Na+ and N-methyl-D-aspartate receptor (NMDAR) regenerative spikes and are uniquely poised to influence somatic output. Nevertheless, due to technical limitations, how multibranch basal dendritic integration shapes and enables multiplexed barcoding of synaptic streams remains poorly mapped. Here, we combine 3D two-photon holographic transmitter uncaging, whole-cell dynamic clamp, and biophysical modeling to reveal how synchronously activated synapses (distributed and clustered) across multiple basal dendritic branches are multiplexed under quiescent and in vivo-like conditions. While dendritic regenerative Na+ spikes promote millisecond somatic spike precision, distributed synaptic inputs and NMDAR spikes regulate gain. These concomitantly occurring dendritic nonlinearities enable multiplexed information transfer amid an ongoing noisy background, including under back-propagating voltage resets, by barcoding the axo-somatic spike structure. Our results unveil a multibranch dendritic integration framework in which dendritic nonlinearities are critical for multiplexing different spatial-temporal synaptic input patterns, enabling optimal feature binding.

Excitatory and inhibitory synapses show a tight subcellular correlation that weakens over development

Neurons receive correlated levels of excitation and inhibition, a feature that is important for proper brain function. However, how this relationship between excitatory and inhibitory inputs is established during the dynamic period of circuit wiring remains unexplored. Using multiple techniques, including in utero electroporation, electron microscopy, and electrophysiology, we reveal a tight correlation in the distribution of excitatory and inhibitory synapses along the dendrites of developing CA1 hippocampal neurons. This correlation was present within short dendritic stretches (<20 μm) and, surprisingly, was most pronounced during early development, sharply declining with maturity. The tight matching between excitation and inhibition was unexpected, as inhibitory synapses lacked an active zone when formed and exhibited compromised evoked release. We propose that inhibitory synapses form as a stabilizing scaffold to counterbalance growing excitation levels. This relationship diminishes over time, suggesting a critical role for a subcellular balance in early neuronal function and circuit formation.

Clustered synapses develop in distinct dendritic domains in visual cortex before eye opening

Synaptic inputs to cortical neurons are highly structured in adult sensory systems, such that neighboring synapses along dendrites are activated by similar stimuli. This organization of synaptic inputs, called synaptic clustering, is required for high-fidelity signal processing, and clustered synapses can already be observed before eye opening. However, how clustered inputs emerge during development is unknown. Here, we employed concurrent in vivo whole-cell patch-clamp and dendritic calcium imaging to map spontaneous synaptic inputs to dendrites of layer 2/3 neurons in the mouse primary visual cortex during the second postnatal week until eye opening. We found that the number of functional synapses and the frequency of transmission events increase several fold during this developmental period. At the beginning of the second postnatal week, synapses assemble specifically in confined dendritic segments, whereas other segments are devoid of synapses. By the end of the second postnatal week, just before eye opening, dendrites are almost entirely covered by domains of co-active synapses. Finally, co-activity with their neighbor synapses correlates with synaptic stabilization and potentiation. Thus, clustered synapses form in distinct functional domains presumably to equip dendrites with computational modules for high-capacity sensory processing when the eyes open.

A dendritic substrate for temporal diversity of cortical inhibition

In the mammalian neocortex, GABAergic interneurons (INs) inhibit cortical networks in profoundly different ways. The extent to which this depends on how different INs process excitatory signals along their dendrites is poorly understood. Here, we reveal that the functional specialization of two major populations of cortical INs is determined by the unique association of different dendritic integration modes with distinct synaptic organization motifs. We found that somatostatin (SST)-INs exhibit NMDAR-dependent dendritic integration and uniform synapse density along the dendritic tree. In contrast, dendrites of parvalbumin (PV)-INs exhibit passive synaptic integration coupled with proximally enriched synaptic distributions. Theoretical analysis shows that these two dendritic configurations result in different strategies to optimize synaptic efficacy in thin dendritic structures. Yet, the two configurations lead to distinct temporal engagement of each IN during network activity. We confirmed these predictions with in vivo recordings of IN activity in the visual cortex of awake mice, revealing a rapid and linear recruitment of PV-INs as opposed to a long-lasting integrative activation of SST-INs. Our work reveals the existence of distinct dendritic strategies that confer distinct temporal representations for the two major classes of neocortical INs and thus dynamics of inhibition.

Morphology and synapse topography optimize linear encoding of synapse numbers in Drosophila looming responsive descending neurons

Synapses are often precisely organized on dendritic arbors, yet the role of synaptic topography in dendritic integration remains poorly understood. Utilizing electron microscopy (EM) connectomics we investigate synaptic topography in Drosophila melanogaster looming circuits, focusing on retinotopically tuned visual projection neurons (VPNs) that synapse onto descending neurons (DNs). Synapses of a given VPN type project to non-overlapping regions on DN dendrites. Within these spatially constrained clusters, synapses are not retinotopically organized, but instead adopt near random distributions. To investigate how this organization strategy impacts DN integration, we developed multicompartment models of DNs fitted to experimental data and using precise EM morphologies and synapse locations. We find that DN dendrite morphologies normalize EPSP amplitudes of individual synaptic inputs and that near random distributions of synapses ensure linear encoding of synapse numbers from individual VPNs. These findings illuminate how synaptic topography influences dendritic integration and suggest that linear encoding of synapse numbers may be a default strategy established through connectivity and passive neuron properties, upon which active properties and plasticity can then tune as needed.

Dendritic mGluR2 and perisomatic Kv3 signaling regulate dendritic computation of mouse starburst amacrine cells

Dendritic mechanisms driving input-output transformation in starburst amacrine cells (SACs) are not fully understood. Here, we combine two-photon subcellular voltage and calcium imaging and electrophysiological recording to determine the computational architecture of mouse SAC dendrites. We found that the perisomatic region integrates motion signals over the entire dendritic field, providing a low-pass-filtered global depolarization to dendrites. Dendrites integrate local synaptic inputs with this global signal in a direction-selective manner. Coincidental local synaptic inputs and the global motion signal in the outward motion direction generate local suprathreshold calcium transients. Moreover, metabotropic glutamate receptor 2 (mGluR2) signaling in SACs modulates the initiation of calcium transients in dendrites but not at the soma. In contrast, voltage-gated potassium channel 3 (Kv3) dampens fast voltage transients at the soma. Together, complementary mGluR2 and Kv3 signaling in different subcellular regions leads to dendritic compartmentalization and direction selectivity, highlighting the importance of these mechanisms in dendritic computation.

Electric field effects on neuronal input-output relationship by regulating NMDA spikes

Evidence shows that the dendritic polarization induced by weak electrical field (EF) can affect the neuronal input-output function via modulating dendritic integration of AMPA synapses, indicating that the supralinear dendritic integration of NMDA synapses can also be influenced by dendritic polarization. However, it remains unknown how dendritic polarization affects NMDA-type dendritic integration, and then contributes to neuronal input-output relationship. Here, we used a computational model of pyramidal neuron with inhomogeneous extracellular potentials to characterize the relationship among EF, dendritic integration, and somatic output. Basing on singular perturbation we analyzed the subthreshold dynamics of membrane potentials in response to NMDA synapses, and found that the equilibrium mapping of a fast subsystem can characterize the asymptotic subthreshold input-output (sI/O) relationship for EF-regulated supralinear dendritic integration, allowing us to predict the tendency of EF-regulated dendritic integration by showing the variation of equilibrium mapping under EF stimulation. EF-induced depolarization at distal dendrites receiving synapses plays a crucial role in shifting the steep change of sI/O left by facilitating dendritic NMDA spike generation and in decreasing the plateau of sI/O via reducing driving force. And more effective EF modulation appears at sparsely activated NMDA receptors compared with clustered synaptic inputs. During the action potential (AP) generation, the respective contribution of EF-regulated dendritic integration and EF-induced somatic polarization was identified to show their synergetic or antagonistic effect on AP generation, depending on neuronal excitability. These results provided insight in understanding the modulation effect of EF on neuronal computation, which is important for optimizing noninvasive brain stimulation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09922-y.

Spike desensitisation as a mechanism for high-contrast selectivity in retinal ganglion cells

In the vertebrate retina, several dozens of parallel channels relay information about the visual world to the brain. These channels are represented by the different types of retinal ganglion cells (RGCs), whose responses are rendered selective for distinct sets of visual features by various mechanisms. These mechanisms can be roughly grouped into synaptic interactions and cell-intrinsic mechanisms, with the latter including dendritic morphology as well as ion channel complement and distribution. Here, we investigate how strongly ion channel complement can shape RGC output by comparing two mouse RGC types, the well-described ON alpha cell and a little-studied ON cell that is EGFP-labelled in the Igfbp5 mouse line and displays an unusual selectivity for stimuli with high contrast. Using patch-clamp recordings and computational modelling, we show that a higher activation threshold and a pronounced slow inactivation of the voltage-gated Na+ channels contribute to the distinct contrast tuning and transient responses in ON Igfbp5 RGCs, respectively. In contrast, such a mechanism could not be observed in ON alpha cells. This study provides an example for the powerful role that the last stage of retinal processing can play in shaping RGC responses.

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.

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.

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.

Somatic Integration of Incoherent Dendritic Inputs in the Gerbil Medial Superior Olive

The medial superior olive (MSO) is a binaural nucleus that is specialized in detecting the relative arrival times of sounds at both ears. Excitatory inputs to its neurons originating from either ear are segregated to different dendrites. To study the integration of synaptic inputs both within and between dendrites, we made juxtacellular and whole-cell recordings from the MSO in anesthetized female gerbils, while presenting a "double zwuis" stimulus, in which each ear received its own set of tones, which were chosen in a way that all second-order distortion products (DP2s) could be uniquely identified. MSO neurons phase-locked to multiple tones within the multitone stimulus, and vector strength, a measure for spike phase-locking, generally depended linearly on the size of the average subthreshold response to a tone. Subthreshold responses to tones in one ear depended little on the presence of sound in the other ear, suggesting that inputs from different ears sum linearly without a substantial role for somatic inhibition. The "double zwuis" stimulus also evoked response components in the MSO neuron that were phase-locked to DP2s. Bidendritic subthreshold DP2s were quite rare compared with bidendritic suprathreshold DP2s. We observed that in a small subset of cells, the ability to trigger spikes differed substantially between both ears, which might be explained by a dendritic axonal origin. Some neurons that were driven monaurally by only one of the two ears nevertheless showed decent binaural tuning. We conclude that MSO neurons are remarkably good in finding binaural coincidences even among uncorrelated inputs.SIGNIFICANCE STATEMENT Neurons in the medial superior olive are essential for precisely localizing low-frequency sounds in the horizontal plane. From their soma, only two dendrites emerge, which are innervated by inputs originating from different ears. Using a new sound stimulus, we studied the integration of inputs both within and between these dendrites in unprecedented detail. We found evidence that inputs from different dendrites add linearly at the soma, but that small increases in somatic potentials could lead to large increases in the probability of generating a spike. This basic scheme allowed the MSO neurons to detect the relative arrival time of inputs at both dendrites remarkably efficient, although the relative size of these inputs could differ considerably.

Sub-cellular population imaging tools reveal stable apical dendrites in hippocampal area CA3

Anatomically segregated apical and basal dendrites of pyramidal neurons receive functionally distinct inputs, but it is unknown if this results in compartment-level functional diversity during behavior. Here we imaged calcium signals from apical dendrites, soma, and basal dendrites of pyramidal neurons in area CA3 of mouse hippocampus during head-fixed navigation. To examine dendritic population activity, we developed computational tools to identify dendritic regions of interest and extract accurate fluorescence traces. We identified robust spatial tuning in apical and basal dendrites, similar to soma, though basal dendrites had reduced activity rates and place field widths. Across days, apical dendrites were more stable than soma or basal dendrites, resulting in better decoding of the animal's position. These population-level dendritic differences may reflect functionally distinct input streams leading to different dendritic computations in CA3. These tools will facilitate future studies of signal transformations between cellular compartments and their relation to behavior.

Spatial integration of dendrites in fast-spiking basket cells

Dendrites of fast-spiking basket cells (FS BCs) impact neural circuit functions in brain with both supralinear and sublinear integration strategies. Diverse spatial synaptic inputs and active properties of dendrites lead to distinct neuronal firing patterns. How the FS BCs with this bi-modal dendritic integration respond to different spatial dispersion of synaptic inputs remains unclear. In this study, we construct a multi-compartmental model of FS BC and analyze neuronal firings following simulated synaptic protocols from fully clustered to fully dispersed. Under these stimulation protocols, we find that supralinear dendrites dominate somatic firing of FS BC, while the preference for dispersing is due to sublinear dendrites. Moreover, we find that dendritic diameter and Ca2+-permeable AMPA conductance play an important role in it, while A-type K+ channel and NMDA conductance have little effect. The obtained results may give some implications for understanding dendritic computation.

Bistability and criticality in the stochastic Wilson-Cowan model

We study a stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously. One fixed point is characterized by lower activity and scale-free critical behavior, while the second fixed point corresponds to a higher (supercritical) persistent activity, with small fluctuations around a mean value. When the number of neurons is not too large, the system can switch between these two different states with a probability depending on the parameters of the network. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power-law behavior corresponding to the critical state, and a bump of very large avalanches due to the high-activity supercritical state. The bistability is due to the presence of a first-order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low-activity state becomes unstable (spinodal line).

Pharmacological Signature and Target Specificity of Inhibitory Circuits Formed by Martinotti Cells in the Mouse Barrel Cortex

In the neocortex, fast synaptic inhibition orchestrates both spontaneous and sensory-evoked activity. GABAergic interneurons (INs) inhibit pyramidal neurons (PNs) directly, modulating their output activity and thus contributing to balance cortical networks. Moreover, several IN subtypes also inhibit other INs, forming specific disinhibitory circuits, which play crucial roles in several cognitive functions. Here, we studied a subpopulation of somatostatin-positive INs, the Martinotti cells (MCs) in layer 2/3 of the mouse barrel cortex (both sexes). MCs inhibit the distal portion of PN apical dendrites, thus controlling dendrite electrogenesis and synaptic integration. Yet, it is poorly understood whether MCs inhibit other elements of the cortical circuits, and the connectivity properties with non-PN targets are unknown. We found that MCs have a strong preference for PN dendrites, but they also considerably connect with parvalbumin-positive, vasoactive intestinal peptide-expressing, and layer 1 (L1) INs. Remarkably, GABAergic synapses from MCs exhibited clear cell type-specific short-term plasticity. Moreover, whereas the biophysical properties of MC-PN synapses were consistent with distal dendritic inhibition, MC-IN synapses exhibited characteristics of fast perisomatic inhibition. Finally, MC-PN connections used α5-containing GABA_A receptors (GABA_ARs), but this subunit was not expressed by the other INs targeted by MCs. We reveal a specialized connectivity blueprint of MCs within different elements of superficial cortical layers. In addition, our results identify α5-GABA_ARs as the molecular fingerprint of MC-PN dendritic inhibition. This is of critical importance, given the role of α5-GABA_ARs in cognitive performance and their involvement in several brain diseases.SIGNIFICANCE STATEMENT Martinotti cells (MCs) are a prominent, broad subclass of somatostatin-expressing GABAergic interneurons, specialized in controlling distal dendrites of pyramidal neurons (PNs) and taking part in several cognitive functions. Here we characterize the connectivity pattern of MCs with other interneurons in the superficial layers (L1 and L2/3) of the mouse barrel cortex. We found that the connectivity pattern of MCs with PNs as well as parvalbumin, vasoactive intestinal peptide, and L1 interneurons exhibit target-specific plasticity and biophysical properties. The specificity of α5-GABA_ARs at MC-PN synapses and the lack or functional expression of this subunit by other cell types define the molecular identity of MC-PN connections and the exclusive involvement of this inhibitory circuits in α5-dependent cognitive tasks.

Morphological Features of Human Dendritic Spines

Dendritic spine features in human neurons follow the up-to-date knowledge presented in the previous chapters of this book. Human dendrites are notable for their heterogeneity in branching patterns and spatial distribution. These data relate to circuits and specialized functions. Spines enhance neuronal connectivity, modulate and integrate synaptic inputs, and provide additional plastic functions to microcircuits and large-scale networks. Spines present a continuum of shapes and sizes, whose number and distribution along the dendritic length are diverse in neurons and different areas. Indeed, human neurons vary from aspiny or "relatively aspiny" cells to neurons covered with a high density of intermingled pleomorphic spines on very long dendrites. In this chapter, we discuss the phylogenetic and ontogenetic development of human spines and describe the heterogeneous features of human spiny neurons along the spinal cord, brainstem, cerebellum, thalamus, basal ganglia, amygdala, hippocampal regions, and neocortical areas. Three-dimensional reconstructions of Golgi-impregnated dendritic spines and data from fluorescence microscopy are reviewed with ultrastructural findings to address the complex possibilities for synaptic processing and integration in humans. Pathological changes are also presented, for example, in Alzheimer's disease and schizophrenia. Basic morphological data can be linked to current techniques, and perspectives in this research field include the characterization of spines in human neurons with specific transcriptome features, molecular classification of cellular diversity, and electrophysiological identification of coexisting subpopulations of cells. These data would enlighten how cellular attributes determine neuron type-specific connectivity and brain wiring for our diverse aptitudes and behavior.

Functional coordinates: Modeling interactions between brain regions as points in a function space

Here, we propose a novel technique to investigate nonlinear interactions between brain regions that captures both the strength and type of the functional relationship. Inspired by the field of functional analysis, we propose that the relationship between activity in separate brain areas can be viewed as a point in function space, identified by coordinates along an infinite set of basis functions. Using Hermite polynomials as bases, we estimate a subset of these values that serve as "functional coordinates," characterizing the interaction between BOLD activity across brain areas. We provide a proof of the convergence of the estimates in the limit, and we validate the method with simulations in which the ground truth is known, additionally showing that functional coordinates detect statistical dependence even when correlations ("functional connectivity") approach zero. We then use functional coordinates to examine neural interactions with a chosen seed region: the fusiform face area (FFA). Using k-means clustering across each voxel's functional coordinates, we illustrate that adding nonlinear basis functions allows for the discrimination of interregional interactions that are otherwise grouped together when using only linear dependence. Finally, we show that regions in V5 and medial occipital and temporal lobes exhibit significant nonlinear interactions with the FFA.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Anatomical and Functional Connectivity at the Dendrodendritic Reciprocal Mitral Cell–Granule Cell Synapse: Impact on Recurrent and Lateral Inhibition

In the vertebrate olfactory bulb, reciprocal dendrodendritic interactions between its principal neurons, the mitral and tufted cells, and inhibitory interneurons in the external plexiform layer mediate both recurrent and lateral inhibition, with the most numerous of these interneurons being granule cells. Here, we used recently established anatomical parameters and functional data on unitary synaptic transmission to simulate the strength of recurrent inhibition of mitral cells specifically from the reciprocal spines of rat olfactory bulb granule cells in a quantitative manner. Our functional data allowed us to derive a unitary synaptic conductance on the order of 0.2 nS. The simulations predicted that somatic voltage deflections by even proximal individual granule cell inputs are below the detection threshold and that attenuation with distance is roughly linear, with a passive length constant of 650 μm. However, since recurrent inhibition in the wake of a mitral cell action potential will originate from hundreds of reciprocal spines, the summated recurrent IPSP will be much larger, even though there will be substantial mutual shunting across the many inputs. Next, we updated and refined a preexisting model of connectivity within the entire rat olfactory bulb, first between pairs of mitral and granule cells, to estimate the likelihood and impact of recurrent inhibition depending on the distance between cells. Moreover, to characterize the substrate of lateral inhibition, we estimated the connectivity via granule cells between any two mitral cells or all the mitral cells that belong to a functional glomerular ensemble (i.e., which receive their input from the same glomerulus), again as a function of the distance between mitral cells and/or entire glomerular mitral cell ensembles. Our results predict the extent of the three regimes of anatomical connectivity between glomerular ensembles: high connectivity within a glomerular ensemble and across the first four rings of adjacent glomeruli, substantial connectivity to up to eleven glomeruli away, and negligible connectivity beyond. Finally, in a first attempt to estimate the functional strength of granule-cell mediated lateral inhibition, we combined this anatomical estimate with our above simulation results on attenuation with distance, resulting in slightly narrowed regimes of a functional impact compared to the anatomical connectivity.

A Model of Pattern Separation by Single Neurons

For efficient processing, spatiotemporal spike patterns representing similar input must be able to transform into a less similar output. A new computational model with physiologically plausible parameters shows how the neuronal process referred to as “pattern separation” can be very well achieved by single neurons if the temporal qualities of the output patterns are considered. Spike patterns generated by a varying number of neurons firing with fixed different frequencies within a gamma range are used as input. The temporal and spatial summation of dendritic input combined with theta-oscillating excitability in the output neuron by subthreshold membrane potential oscillations (SMOs) lead to high temporal separation by different delays of output spikes of similar input patterns. A Winner Takes All (WTA) mechanism with backward inhibition suffices to transform the spatial overlap of input patterns to much less temporal overlap of the output patterns. The conversion of spatial patterns input into an output with differently delayed spikes enables high separation effects. Incomplete random connectivity spreads the times up to the first spike across a spatially expanded ensemble of output neurons. With the expansion, random connectivity becomes the spatial distribution mechanism of temporal features. Additionally, a “synfire chain” circuit is proposed to reconvert temporal differences into spatial ones.

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.

Differential dendritic integration of long-range inputs in association cortex via subcellular changes in synaptic AMPA-to-NMDA receptor ratio

Synaptic NMDA receptors can produce powerful dendritic supralinearities that expand the computational repertoire of single neurons and their respective circuits. This form of supralinearity may represent a general principle for synaptic integration in thin dendrites. However, individual cortical neurons receive many diverse classes of input that may require distinct postsynaptic decoding schemes. Here, we show that sensory, motor, and thalamic inputs preferentially target basal, apical oblique, and distal tuft dendrites, respectively, in layer 5b pyramidal neurons of the mouse retrosplenial cortex, a visuospatial association area. These dendritic compartments exhibited differential expression of NMDA receptor-mediated supralinearity due to systematic changes in the AMPA-to-NMDA receptor ratio. Our results reveal a new schema for integration in cortical pyramidal neurons, in which dendrite-specific changes in synaptic receptors support input-localized decoding. This coexistence of multiple modes of dendritic integration in single neurons has important implications for synaptic plasticity and cortical computation.

Spatial regulation of coordinated excitatory and inhibitory synaptic plasticity at dendritic synapses

The induction of synaptic plasticity at an individual dendritic glutamatergic spine can affect neighboring spines. This local modulation generates dendritic plasticity microdomains believed to expand the neuronal computational capacity. Here, we investigate whether local modulation of plasticity can also occur between glutamatergic synapses and adjacent GABAergic synapses. We find that the induction of long-term potentiation at an individual glutamatergic spine causes the depression of nearby GABAergic inhibitory synapses (within 3 μm), whereas more distant ones are potentiated. Notably, L-type calcium channels and calpain are required for this plasticity spreading. Overall, our data support a model whereby input-specific glutamatergic postsynaptic potentiation induces a spatially regulated rearrangement of inhibitory synaptic strength in the surrounding area through short-range heterosynaptic interactions. Such local coordination of excitatory and inhibitory synaptic plasticity is expected to influence dendritic information processing and integration.

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LTP of individual dendritic spines causes iLTD at neighboring GABAergic synapses

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Interaction between single-spine LTP and iLTD occurs in the spatial range of ±3 μm

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This iLTD depends on the local dendritic calcium increase and calpain activation

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iLTD is associated with reduced gephyrin clustering and increased GABAAR mobility

Dendritic synapse geometry optimizes binaural computation in a sound localization circuit

Clustering of synapses allows neurons to overcome attenuation of electrical signals at dendrites. However, we show in avian binaural coincidence detectors computing interaural time difference for sound localization that clustering of synapses rather promotes the dendritic attenuation but augments the intensity tolerance of the binaural computations. Using glutamate uncaging, we found in the neurons that synapses were clustered at distal dendritic branches. Modeling revealed that this strengthened sublinear integration within a dendritic tree but enabled the integration of signals from different trees when inputs grow stronger, preventing monoaural output and maintaining the dynamic range of binaural computation. The extent of this clustering differed according to dendritic length and frequency tuning of neurons, being most prominent for long dendrites and low-frequency tuning. This ensures binaural spatial hearing for wide intensity and frequency ranges, highlighting the importance of coupling of synapse geometry with dendritic morphology and input frequency in sensory signal processing.

GABAergic Interneurons with Nonlinear Dendrites: From Neuronal Computations to Memory Engrams

GABAergic interneurons (INs) are a highly diverse class of neurons in the mammalian brain with a critical role in orchestrating multiple cognitive functions and maintaining the balance of excitation/inhibition across neuronal circuitries. In this perspective, we discuss recent findings regarding the ability of some IN subtypes to integrate incoming inputs in nonlinear ways within their dendritic branches. These recently discovered features may endow the specific INs with advanced computing capabilities, whose breadth and functional contributions remain an open question. Along these lines, we discuss theoretical and experimental evidence regarding the potential role of nonlinear IN dendrites in advancing single neuron computations and contributing to memory formation.

Modelling the spatial and temporal constrains of the GABAergic influence on neuronal excitability

GABA (γ-amino butyric acid) is an inhibitory neurotransmitter in the adult brain that can mediate depolarizing responses during development or after neuropathological insults. Under which conditions GABAergic membrane depolarizations are sufficient to impose excitatory effects is hard to predict, as shunting inhibition and GABAergic effects on spatiotemporal filtering of excitatory inputs must be considered. To evaluate at which reversal potential a net excitatory effect was imposed by GABA (E_GABA^Thr), we performed a detailed in-silico study using simple neuronal topologies and distinct spatiotemporal relations between GABAergic and glutamatergic inputs.

These simulations revealed for GABAergic synapses located at the soma an E_GABA^Thr close to action potential threshold (E_AP^Thr), while with increasing dendritic distance E_GABA^Thr shifted to positive values. The impact of GABA on AMPA-mediated inputs revealed a complex temporal and spatial dependency. E_GABA^Thr depends on the temporal relation between GABA and AMPA inputs, with a striking negative shift in E_GABA^Thr for AMPA inputs appearing after the GABA input. The spatial dependency between GABA and AMPA inputs revealed a complex profile, with E_GABA^Thr being shifted to values negative to E_AP^Thr for AMPA synapses located proximally to the GABA input, while for distally located AMPA synapses the dendritic distance had only a minor effect on E_GABA^Thr. For tonic GABAergic conductances E_GABA^Thr was negative to E_AP^Thr over a wide range of g_GABA^tonic values. In summary, these results demonstrate that for several physiologically relevant situations E_GABA^Thr is negative to E_AP^Thr, suggesting that depolarizing GABAergic responses can mediate excitatory effects even if E_GABA did not reach E_AP^Thr.

The neurotransmitter GABA mediates an inhibitory action in the mature brain, while it was found that GABA provokes depolarizations in the immature brain or after neurological insults. It is, however, not clear to which extend these GABAergic depolarizations can contribute to an excitatory effect. In the present manuscript we approached this question with a computational model of a simplified neurons to determine what amount of a GABAergic depolarizing effect, which we quantified by the so called GABA reversal potential (E_GABA), was required to turn GABAergic inhibition to excitation. The results of our simulations revealed that if GABA was applied alone a GABAergic excitation was induced when E_GABA was around the action potential threshold. When GABA was applied together with additional excitatory inputs, which is the physiological situation in the brain, only for spatially and temporally correlated inputs E_GABA was close to the action potential threshold. For situations in which the additional excitatory inputs appear after the GABA input or are distant to the GABA input, an excitatory effect of GABA could be observed already at E_GABA substantially negative to the action potential threshold. This results indicate that even slightly depolarizing GABA responses, which may be induced during or after neurological insults, can potentially turn GABAergic inhibition into GABAergic excitation.

Developmental emergence of two-stage nonlinear synaptic integration in cerebellar interneurons

Synaptic transmission, connectivity, and dendritic morphology mature in parallel during brain development and are often disrupted in neurodevelopmental disorders. Yet how these changes influence the neuronal computations necessary for normal brain function are not well understood. To identify cellular mechanisms underlying the maturation of synaptic integration in interneurons, we combined patch-clamp recordings of excitatory inputs in mouse cerebellar stellate cells (SCs), three-dimensional reconstruction of SC morphology with excitatory synapse location, and biophysical modeling. We found that postnatal maturation of postsynaptic strength was homogeneously reduced along the somatodendritic axis, but dendritic integration was always sublinear. However, dendritic branching increased without changes in synapse density, leading to a substantial gain in distal inputs. Thus, changes in synapse distribution, rather than dendrite cable properties, are the dominant mechanism underlying the maturation of neuronal computation. These mechanisms favor the emergence of a spatially compartmentalized two-stage integration model promoting location-dependent integration within dendritic subunits.

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.

Multibranch Formal Neuron: An Internally Nonlinear Learning Unit

The transformation of synaptic input into action potential in nerve cells is strongly influenced by the morphology of the dendritic arbor as well as the synaptic efficacy map. The multiplicity of dendritic branches strikingly enables a single cell to act as a highly nonlinear processing element. Studies have also found functional synaptic clustering whereby synapses that encode a common sensory feature are spatially clustered together on the branches. Motivated by these findings, here we introduce a multibranch formal model of the neuron that can integrate synaptic inputs nonlinearly through collective action of its dendritic branches and yields synaptic clustering. An analysis in support of its use as a computational building block is offered. Also offered is an accompanying gradient descent-based learning algorithm. The model unit spans a wide spectrum of nonlinearities, including the parity problem, and can outperform the multilayer perceptron in generalizing to unseen data. The occurrence of synaptic clustering boosts the generalization efficiency of the unit, which may also be the answer for the puzzling ubiquity of synaptic clustering in the real neurons. Our theoretical analysis is backed up by simulations. The study could pave the way to new artificial neural networks.

Leucine-rich repeats and immunoglobulin-like domains 1 deficiency affects hippocampal dendrite complexity and impairs cognitive function

Leucine-rich repeat (LRR) transmembrane proteins have been directly linked to neurodevelopmental and cognitive disorders. We have previously shown that the LRR transmembrane protein, leucine-rich repeats and immunoglobulin-like domains 1 (Lrig1), is a physiological regulator of dendrite complexity of hippocampal pyramidal neurons and social behavior. In this study, we performed a battery of behavioral tests to evaluate spatial memory and cognitive capabilities in Lrig1 mutant mice. The cognitive assessment demonstrated deficits in recognition and spatial memory, evaluated by novel object recognition and object location tests. Moreover, we found that Lrig1-deficient mice present specific impairments in the processing of similar but not dissimilar locations in a spatial pattern separation task, which was correlated with an enhanced dendritic growth and branching of Doublecortin-positive immature granule cells of the dentate gyrus. Altogether, these findings indicate that Lrig1 plays an essential role in controlling morphological and functional plasticity in the hippocampus.

Rethinking Single Neuron Electrical Compartmentalization: Dendritic Contributions to Network Computation In Vivo

Decades of experimental and theoretical work support a now well-established theory that active dendritic processing contributes to the computational power of individual neurons. This theory is based on the high degree of electrical compartmentalization observed in the dendrites of single neurons in ex vivo preparations. Compartmentalization allows dendrites to conduct semi-independent operations on their inputs before final integration and output at the axon, producing a "network-in-a-neuron." However, recent in vivo functional imaging experiments in mouse cortex have reported surprisingly little evidence for strong dendritic compartmentalization. In this review, we contextualize these new findings and discuss their impact on the future of the field. Specifically, we consider how highly coordinated, and thus less compartmentalized, activity in soma and dendrites can contribute to cortical computations including nonlinear mixed selectivity, prediction/expectation, multiplexing, and credit assignment.

The Subcortical-Allocortical- Neocortical continuum for the Emergence and Morphological Heterogeneity of Pyramidal Neurons in the Human Brain

Human cortical and subcortical areas integrate emotion, memory, and cognition when interpreting various environmental stimuli for the elaboration of complex, evolved social behaviors. Pyramidal neurons occur in developed phylogenetic areas advancing along with the allocortex to represent 70-85% of the neocortical gray matter. Here, we illustrate and discuss morphological features of heterogeneous spiny pyramidal neurons emerging from specific amygdaloid nuclei, in CA3 and CA1 hippocampal regions, and in neocortical layers II/III and V of the anterolateral temporal lobe in humans. Three-dimensional images of Golgi-impregnated neurons were obtained using an algorithm for the visualization of the cell body, dendritic length, branching pattern, and pleomorphic dendritic spines, which are specialized plastic postsynaptic units for most excitatory inputs. We demonstrate the emergence and development of human pyramidal neurons in the cortical and basomedial (but not the medial, MeA) nuclei of the amygdala with cells showing a triangular cell body shape, basal branched dendrites, and a short apical shaft with proximal ramifications as "pyramidal-like" neurons. Basomedial neurons also have a long and distally ramified apical dendrite not oriented to the pial surface. These neurons are at the beginning of the allocortex and the limbic lobe. "Pyramidal-like" to "classic" pyramidal neurons with laminar organization advance from the CA3 to the CA1 hippocampal regions. These cells have basal and apical dendrites with specific receptive synaptic domains and several spines. Neocortical pyramidal neurons in layers II/III and V display heterogeneous dendritic branching patterns adapted to the space available and the afferent inputs of each brain area. Dendritic spines vary in their distribution, density, shapes, and sizes (classified as stubby/wide, thin, mushroom-like, ramified, transitional forms, "atypical" or complex forms, such as thorny excrescences in the MeA and CA3 hippocampal region). Spines were found isolated or intermingled, with evident particularities (e.g., an extraordinary density in long, deep CA1 pyramidal neurons), and some showing a spinule. We describe spiny pyramidal neurons considerably improving the connectional and processing complexity of the brain circuits. On the other hand, these cells have some vulnerabilities, as found in neurodegenerative Alzheimer's disease and in temporal lobe epilepsy.

The integration of Gaussian noise by long-range amygdala inputs in frontal circuit promotes fear learning in mice

Survival depends on the ability of animals to select the appropriate behavior in response to threat and safety sensory cues. However, the synaptic and circuit mechanisms by which the brain learns to encode accurate predictors of threat and safety remain largely unexplored. Here, we show that frontal association cortex (FrA) pyramidal neurons of mice integrate auditory cues and basolateral amygdala (BLA) inputs non-linearly in a NMDAR-dependent manner. We found that the response of FrA pyramidal neurons was more pronounced to Gaussian noise than to pure frequency tones, and that the activation of BLA-to-FrA axons was the strongest in between conditioning pairings. Blocking BLA-to-FrA signaling specifically at the time of presentation of Gaussian noise (but not 8 kHz tone) between conditioning trials impaired the formation of auditory fear memories. Taken together, our data reveal a circuit mechanism that facilitates the formation of fear traces in the FrA, thus providing a new framework for probing discriminative learning and related disorders.

Efficient Low-Pass Dendro-Somatic Coupling in the Apical Dendrite of Layer 5 Pyramidal Neurons in the Anterior Cingulate Cortex

Signal propagation in the dendrites of many neurons, including cortical pyramidal neurons in sensory cortex, is characterized by strong attenuation toward the soma. In contrast, using dual whole-cell recordings from the apical dendrite and soma of layer 5 (L5) pyramidal neurons in the anterior cingulate cortex (ACC) of adult male mice we found good coupling, particularly of slow subthreshold potentials like NMDA spikes or trains of EPSPs from dendrite to soma. Only the fastest EPSPs in the ACC were reduced to a similar degree as in primary somatosensory cortex, revealing differential low-pass filtering capabilities. Furthermore, L5 pyramidal neurons in the ACC did not exhibit dendritic Ca2+ spikes as prominently found in the apical dendrite of S1 (somatosensory cortex) pyramidal neurons. Fitting the experimental data to a NEURON model revealed that the specific distribution of Ileak, Iir, Im , and Ih was sufficient to explain the electrotonic dendritic structure causing a leaky distal dendritic compartment with correspondingly low input resistance and a compact perisomatic region, resulting in a decoupling of distal tuft branches from each other while at the same time efficiently connecting them to the soma. Our results give a biophysically plausible explanation of how a class of prefrontal cortical pyramidal neurons achieve efficient integration of subthreshold distal synaptic inputs compared with the same cell type in sensory cortices.SIGNIFICANCE STATEMENT Understanding cortical computation requires the understanding of its fundamental computational subunits. Layer 5 pyramidal neurons are the main output neurons of the cortex, integrating synaptic inputs across different cortical layers. Their elaborate dendritic tree receives, propagates, and transforms synaptic inputs into action potential output. We found good coupling of slow subthreshold potentials like NMDA spikes or trains of EPSPs from the distal apical dendrite to the soma in pyramidal neurons in the ACC, which was significantly better compared with S1. This suggests that frontal pyramidal neurons use a different integration scheme compared with the same cell type in somatosensory cortex, which has important implications for our understanding of information processing across different parts of the neocortex.

Dendritic integration in olfactory bulb granule cells upon simultaneous multispine activation: Low thresholds for nonlocal spiking activity

The inhibitory axonless olfactory bulb granule cells form reciprocal dendrodendritic synapses with mitral and tufted cells via large spines, mediating recurrent and lateral inhibition. As a case in point for dendritic transmitter release, rat granule cell dendrites are highly excitable, featuring local Na+ spine spikes and global Ca2+- and Na+-spikes. To investigate the transition from local to global signaling, we performed holographic, simultaneous 2-photon uncaging of glutamate at up to 12 granule cell spines, along with whole-cell recording and dendritic 2-photon Ca2+ imaging in acute juvenile rat brain slices. Coactivation of less than 10 reciprocal spines was sufficient to generate diverse regenerative signals that included regional dendritic Ca2+-spikes and dendritic Na+-spikes (D-spikes). Global Na+-spikes could be triggered in one third of granule cells. Individual spines and dendritic segments sensed the respective signal transitions as increments in Ca2+ entry. Dendritic integration as monitored by the somatic membrane potential was mostly linear until a threshold number of spines was activated, at which often D-spikes along with supralinear summation set in. As to the mechanisms supporting active integration, NMDA receptors (NMDARs) strongly contributed to all aspects of supralinearity, followed by dendritic voltage-gated Na+- and Ca2+-channels, whereas local Na+ spine spikes, as well as morphological variables, barely mattered. Because of the low numbers of coactive spines required to trigger dendritic Ca2+ signals and thus possibly lateral release of GABA onto mitral and tufted cells, we predict that thresholds for granule cell-mediated bulbar lateral inhibition are low. Moreover, D-spikes could provide a plausible substrate for granule cell-mediated gamma oscillations.

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.

Type-specific dendritic integration in mouse retinal ganglion cells

Neural computation relies on the integration of synaptic inputs across a neuron’s dendritic arbour. However, it is far from understood how different cell types tune this process to establish cell-type specific computations. Here, using two-photon imaging of dendritic Ca²⁺ signals, electrical recordings of somatic voltage and biophysical modelling, we demonstrate that four morphologically distinct types of mouse retinal ganglion cells with overlapping excitatory synaptic input (transient Off alpha, transient Off mini, sustained Off, and F-mini Off) exhibit type-specific dendritic integration profiles: in contrast to the other types, dendrites of transient Off alpha cells were spatially independent, with little receptive field overlap. The temporal correlation of dendritic signals varied also extensively, with the highest and lowest correlation in transient Off mini and transient Off alpha cells, respectively. We show that differences between cell types can likely be explained by differences in backpropagation efficiency, arising from the specific combinations of dendritic morphology and ion channel densities.

Neurons compute by integrating synaptic inputs across their dendritic arbor. Here, the authors show that distinct cell-types of mouse retinal ganglion cells that receive similar excitatory inputs have different biophysical mechanisms of input integration to generate their unique response tuning.

Dynamic input-dependent encoding of individual basal ganglia neurons

Computational models are crucial to studying the encoding of individual neurons. Static models are composed of a fixed set of parameters, thus resulting in static encoding properties that do not change under different inputs. Here, we challenge this basic concept which underlies these models. Using generalized linear models, we quantify the encoding and information processing properties of basal ganglia neurons recorded in-vitro. These properties are highly sensitive to the internal state of the neuron due to factors such as dependency on the baseline firing rate. Verification of these experimental results with simulations provides insights into the mechanisms underlying this input-dependent encoding. Thus, static models, which are not context dependent, represent only part of the neuronal encoding capabilities, and are not sufficient to represent the dynamics of a neuron over varying inputs. Input-dependent encoding is crucial for expanding our understanding of neuronal behavior in health and disease and underscores the need for a new generation of dynamic neuronal models.

Heterosynaptic Plasticity Determines the Set Point for Cortical Excitatory-Inhibitory Balance

Excitation in neural circuits must be carefully controlled by inhibition to regulate information processing and network excitability. During development, cortical inhibitory and excitatory inputs are initially mismatched but become co-tuned or balanced with experience. However, little is known about how excitatory-inhibitory balance is defined at most synapses or about the mechanisms for establishing or maintaining this balance at specific set points. Here we show how coordinated long-term plasticity calibrates populations of excitatory-inhibitory inputs onto mouse auditory cortical pyramidal neurons. Pairing pre- and postsynaptic activity induced plasticity at paired inputs and different forms of heterosynaptic plasticity at the strongest unpaired synapses, which required minutes of activity and dendritic Ca²⁺ signaling to be computed. Theoretical analyses demonstrated how the relative rate of heterosynaptic plasticity could normalize and stabilize synaptic strengths to achieve any possible excitatory-inhibitory correlation. Thus, excitatory-inhibitory balance is dynamic and cell specific, determined by distinct plasticity rules across multiple excitatory and inhibitory synapses.

Reverse engineering human brain evolution using organoid models

Primate brains vary dramatically in size and organization, but the genetic and developmental basis for these differences has been difficult to study due to lack of experimental models. Pluripotent stem cells and brain organoids provide a potential opportunity for comparative and functional studies of evolutionary differences, particularly during the early stages of neurogenesis. However, many challenges remain, including isolating stem cell lines from additional great ape individuals and species to capture the breadth of ape genetic diversity, improving the reproducibility of organoid models to study evolved differences in cell composition and combining multiple brain regions to capture connectivity relationships. Here, we describe strategies for identifying evolved developmental differences between humans and non-human primates and for isolating the underlying cellular and genetic mechanisms using comparative analyses, chimeric organoid culture, and genome engineering. In particular, we focus on how organoid models could ultimately be applied beyond studies of progenitor cell evolution to decode the origin of recent changes in cellular organization, connectivity patterns, myelination, synaptic development, and physiology that have been implicated in human cognition.

Metabolic Cost of Dendritic Ca2+ Action Potentials in Layer 5 Pyramidal Neurons

Pyramidal neurons consume most signaling-related energy to generate action potentials (APs) and perform synaptic integration. Dendritic Ca²⁺ spike is an important integration mechanism for coupling inputs from different cortical layers. Our objective was to quantify the metabolic energy associated with the generation of Ca²⁺ APs in the dendrites. We used morphology-based computational models to simulate the dendritic Ca²⁺ spikes in layer 5 pyramidal neurons. We calculated the energy cost by converting Ca²⁺ influx into the number of ATP required to restore and maintain the homeostasis of intracellular Ca²⁺ concentrations. We quantified the effects of synaptic inputs, dendritic voltage, back-propagating Na⁺ spikes, and Ca²⁺ inactivation on Ca²⁺ spike cost. We showed that much more ATP molecules were required for reversing Ca²⁺ influx in the dendrites than for Na⁺ ion pumping in the soma during a Ca²⁺ AP. Increasing synaptic input increased the rate of dendritic depolarization and underlying Ca²⁺ influx, resulting in higher ATP consumption. Depolarizing dendritic voltage resulted in the inactivation of Ca²⁺ channels and reduced the ATP cost, while dendritic hyperpolarization increased the spike cost by de-inactivating Ca²⁺ channels. A back-propagating Na⁺ AP initiated in the soma increased Ca²⁺ spike cost in the apical dendrite when it coincided with a synaptic input within a time window of several milliseconds. Increasing Ca²⁺ inactivation rate reduced Ca²⁺ spike cost, while slowing Ca²⁺ inactivation increased the spike cost. The results revealed that the energy demand of a Ca²⁺ AP was dynamically dependent on the state of dendritic activity. These findings were important for predicting the energy budget for signaling in pyramidal cells, interpreting functional imaging data, and designing energy-efficient neuromorphic devices.

Single Synapse LTP: A Matter of Context?

The most commonly studied form of synaptic plasticity is long-term potentiation (LTP). Over the last 15 years, it has been possible to induce structural and functional LTP in dendritic spines using two-photon glutamate uncaging, allowing for studying the signaling mechanisms of LTP with single synapse resolution. In this review, we compare different stimulation methods to induce single synapse LTP and discuss how LTP is expressed. We summarize the underlying signaling mechanisms that have been studied with high spatiotemporal resolution. Finally, we discuss how LTP in a single synapse can be affected by excitatory and inhibitory synapses nearby. We argue that single synapse LTP is highly dependent on context: the choice of induction method, the history of the dendritic spine and the dendritic vicinity crucially affect signaling pathways and expression of single synapse LTP.

Can NMDA Spikes Dictate Computations of Local Networks and Behavior?

Intelligence is the ability to learn appropriate responses to stimuli and the capacity to master new skills. Synaptic integration at the dendritic level is thought to be essential for this ability through linear and non-linear processing, by allowing neurons to be tuned to relevant information and to maximize adaptive behavior. Showing that dendrites are able to generate local computations that influence how animals perceive the world, form a new memory or learn a new skill was a break-through in neuroscience, since in the past they were seen as passive elements of the neurons, just funneling information to the soma. Here, we provide an overview of the role of dendritic integration in improving the neuronal network and behavioral performance. We focus on how NMDA spikes are generated and their role in neuronal computation for optimal behavioral output based on recent in vivo studies on rodents.

Interaction of Cortical and Amygdalar Synaptic Input Modulates the Window of Opportunity for Information Processing in the Rhinal Cortices

The perirhinal (PER) and lateral entorhinal (LEC) cortex function as a gateway for information transmission between (sub)cortical areas and the hippocampus. It is hypothesized that the amygdala, a key structure in emotion processing, can modulate PER-LEC neuronal activity before information enters the hippocampal memory pathway. This study determined the integration of synaptic activity evoked by simultaneous neocortical and amygdala electrical stimulation in PER-LEC deep layer principal neurons and parvalbumin (PV) interneurons in mouse brain slices. The data revealed that both deep layer PER-LEC principal neurons and PV interneurons receive synaptic input from the neocortical agranular insular cortex (AiP) and the lateral amygdala (LA). Furthermore, simultaneous stimulation of the AiP and LA never reached the firing threshold in principal neurons of the PER-LEC deep layers. PV interneurons however, mainly showed linear summation of simultaneous AiP and LA inputs and reached their firing threshold earlier. This early PV firing was reflected in the forward shift of the evoked inhibitory conductance in principal neurons, thereby creating a more precise temporal window for coincidence detection, which likely plays a crucial role in information processing.

Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators

Interneurons are critical for the proper functioning of neural circuits. While often morphologically complex, their dendrites have been ignored for decades, treating them as linear point neurons. Exciting new findings reveal complex, non-linear dendritic computations that call for a new theory of interneuron arithmetic. Using detailed biophysical models, we predict that dendrites of FS basket cells in both hippocampus and prefrontal cortex come in two flavors: supralinear, supporting local sodium spikes within large-volume branches and sublinear, in small-volume branches. Synaptic activation of varying sets of these dendrites leads to somatic firing variability that cannot be fully explained by the point neuron reduction. Instead, a 2-stage artificial neural network (ANN), with sub- and supralinear hidden nodes, captures most of the variance. Reduced neuronal circuit modeling suggest that this bi-modal, 2-stage integration in FS basket cells confers substantial resource savings in memory encoding as well as the linking of memories across time.

Enhanced Dendritic Compartmentalization in Human Cortical Neurons

The biophysical features of neurons shape information processing in the brain. Cortical neurons are larger in humans than in other species, but it is unclear how their size affects synaptic integration. Here, we perform direct electrical recordings from human dendrites and report enhanced electrical compartmentalization in layer 5 pyramidal neurons. Compared to rat dendrites, distal human dendrites provide limited excitation to the soma, even in the presence of dendritic spikes. Human somas also exhibit less bursting due to reduced recruitment of dendritic electrogenesis. Finally, we find that decreased ion channel densities result in higher input resistance and underlie the lower coupling of human dendrites. We conclude that the increased length of human neurons alters their input-output properties, which will impact cortical computation. VIDEO ABSTRACT.