Effects of Neural Morphology and Input Distribution on Synaptic Processing by Global and Focal NMDA-Spikes

What makes human cortical pyramidal neurons functionally complex

Humans exhibit unique cognitive abilities within the animal kingdom, but the neural mechanisms driving these advanced capabilities remain poorly understood. Human cortical neurons differ from those of other species, such as rodents, in both their morphological and physiological characteristics. Could the distinct properties of human cortical neurons help explain the superior cognitive capabilities of humans? Understanding this relationship requires a metric to quantify how neuronal properties contribute to the functional complexity of single neurons, yet no such standardized measure currently exists. Here, we propose the Functional Complexity Index (FCI), a generalized, deep learning-based framework to assess the input-output complexity of neurons. By comparing the FCI of cortical pyramidal neurons from different layers in rats and humans, we identified key morpho-electrical factors that underlie functional complexity. Human cortical pyramidal neurons were found to be significantly more functionally complex than their rat counterparts, primarily due to differences in dendritic membrane area and branching pattern, as well as density and nonlinearity of NMDA-mediated synaptic receptors. These findings reveal the structural-biophysical basis for the enhanced functional properties of human neurons.

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.

State-dependent modulation of low-threshold-current-regulated dendritic Ca2+ response in thalamic reticular neurons with extracellular electric fields

Deep brain stimulation (DBS) in thalamic reticular nucleus (TRN) neuron provides a novel treatment for drug-resistant epilepsy via the induced electrical field (EFs). However, the mechanisms underlying EF effects remain unclear. This paper investigated how EFs regulate low-threshold dendritic Ca2+ (dCa) response and thus contribute to the input-output relationship of TRN cell. Our results showed that EFs modulate firing modes differently in a neuronal state-dependent manner. At the depolarized state, EFs only regulate the spike timing of a somatic stimulus-evoked single action potential (AP) with less contribution in the regulation of dCa response but could induce the transition between a dendritic stimulus-evoked single AP and a tonic burst of APs via the moderate regulation of dCa response. At the hyperpolarized state, EFs have significant effects on the dCa response, which modulate the large dCa response-dependent burst discharge and even cause a transition from this type of burst discharge to a single AP with less dCa response. Moreover, EF effects on stimulation threshold of somatic spiking prominently depend on EF-regulated dCa responses and the onset time differences between the stimulus and EF give rise to the distinct effect in the EF regulation of dCa responses. Finally, the larger neuronal axial resistance tends to result in the dendritic stimulus-evoked dCa response independent of somatic state. Interestingly, in this case, the EF application could reproduce the similar somatic state-dependent dCa response to dendritic stimulus which occurs in the case of lower axial resistance. These results suggest that the influence of EF on neuronal activities depends on neuronal intrinsic properties, which provides insight into understanding how DBS in TRN neuron modulates epilepsy from the point of view of biophysics.

Synapse-specific diversity of distinct postsynaptic GluN2 subtypes defines transmission strength in spinal lamina I

The unitary postsynaptic response to presynaptic quantal glutamate release is the fundamental basis of excitatory information transfer between neurons. The view, however, of individual glutamatergic synaptic connections in a population as homogenous, fixed-strength units of neural communication is becoming increasingly scrutinized. Here, we used minimal stimulation of individual glutamatergic afferent axons to evoke single synapse resolution postsynaptic responses from central sensory lamina I neurons in an ex vivo adult rat spinal slice preparation. We detected unitary events exhibiting a NMDA receptor component with distinct kinetic properties across synapses conferred by specific GluN2 subunit composition, indicative of GluN2 subtype-based postsynaptic heterogeneity. GluN2A, 2A and 2B, or 2B and 2D synaptic predominance functioned on distinct lamina I neuron types to narrowly, intermediately, or widely tune, respectively, the duration of evoked unitary depolarization events from resting membrane potential, which enabled individual synapses to grade differentially depolarizing steps during temporally patterned afferent input. Our results lead to a model wherein a core locus of proteomic complexity prevails at this central glutamatergic sensory synapse that involves distinct GluN2 subtype configurations. These findings have major implications for subthreshold integrative capacity and transmission strength in spinal lamina I and other CNS regions.

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.

Reduced expression of the psychiatric risk gene DLG2 (PSD93) impairs hippocampal synaptic integration and plasticity

Copy number variants indicating loss of function in the DLG2 gene have been associated with markedly increased risk for schizophrenia, autism spectrum disorder, and intellectual disability. DLG2 encodes the postsynaptic scaffolding protein DLG2 (PSD93) that interacts with NMDA receptors, potassium channels, and cytoskeletal regulators but the net impact of these interactions on synaptic plasticity, likely underpinning cognitive impairments associated with these conditions, remains unclear. Here, hippocampal CA1 neuronal excitability and synaptic function were investigated in a novel clinically relevant heterozygous Dlg2+/- rat model using ex vivo patch-clamp electrophysiology, pharmacology, and computational modelling. Dlg2+/- rats had reduced supra-linear dendritic integration of synaptic inputs resulting in impaired associative long-term potentiation. This impairment was not caused by a change in synaptic input since NMDA receptor-mediated synaptic currents were, conversely, increased and AMPA receptor-mediated currents were unaffected. Instead, the impairment in associative long-term potentiation resulted from an increase in potassium channel function leading to a decrease in input resistance, which reduced supra-linear dendritic integration. Enhancement of dendritic excitability by blockade of potassium channels or activation of muscarinic M1 receptors with selective allosteric agonist 77-LH-28-1 reduced the threshold for dendritic integration and 77-LH-28-1 rescued the associative long-term potentiation impairment in the Dlg2+/- rats. These findings demonstrate a biological phenotype that can be reversed by compound classes used clinically, such as muscarinic M1 receptor agonists, and is therefore a potential target for therapeutic intervention.

Altered cortical processing of sensory input in Huntington disease mouse models

Huntington disease (HD), a hereditary neurodegenerative disorder, manifests as progressively impaired movement and cognition. Although early abnormalities of neuronal activity in striatum are well established in HD models, there are fewer in vivo studies of the cortex. Here, we record local field potentials (LFPs) in YAC128 HD model mice versus wild-type mice. In multiple cortical areas, limb sensory stimulation evokes a greater change in LFP power in YAC128 mice. Mesoscopic imaging using voltage-sensitive dyes reveals more extensive spread of evoked sensory signals across the cortical surface in YAC128 mice. YAC128 layer 2/3 sensory cortical neurons ex vivo show increased excitatory events, which could contribute to enhanced sensory responses in vivo. Cortical LFP responses to limb stimulation, visual and auditory input are also significantly increased in zQ175 HD mice. Results presented here extend knowledge of HD beyond ex vivo studies of individual neurons to the intact cortical network.

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

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

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.

Unifying Long-Term Plasticity Rules for Excitatory Synapses by Modeling Dendrites of Cortical Pyramidal Neurons

A large number of experiments have indicated that precise spike times, firing rates, and synapse locations crucially determine the dynamics of long-term plasticity induction in excitatory synapses. However, it remains unknown how plasticity mechanisms of synapses distributed along dendritic trees cooperate to produce the wide spectrum of outcomes for various plasticity protocols. Here, we propose a four-pathway plasticity framework that is well grounded in experimental evidence and apply it to a biophysically realistic cortical pyramidal neuron model. We show in computer simulations that several seemingly contradictory experimental landmark studies are consistent with one unifying set of mechanisms when considering the effects of signal propagation in dendritic trees with respect to synapse location. Our model identifies specific spatiotemporal contributions of dendritic and axo-somatic spikes as well as of subthreshold activation of synaptic clusters, providing a unified parsimonious explanation not only for rate and timing dependence but also for location dependence of synaptic changes.

•

A phenomenological synaptic plasticity rule is applied to a pyramidal neuron model

•

Model reproduces rate-, timing-, and location-dependent plasticity results

•

Active dendrites allow plasticity via dendritic spikes and subthreshold events

•

Cooperative plasticity exists across the dendritic tree and within single branches

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.

Modeling Hippocampal CA1 Gabaergic Synapses of Audiogenic Rats

Wistar Audiogenic Rats (WARs) are genetically susceptible to sound-induced seizures that start in the brainstem and, in response to repetitive stimulation, spread to limbic areas, such as hippocampus. Analysis of the distribution of interevent intervals of GABAergic inhibitory postsynaptic currents (IPSCs) in CA1 pyramidal cells showed a monoexponential trend in Wistar rats, suggestive of a homogeneous population of synapses, but a biexponential trend in WARs. Based on this, we hypothesize that there are two populations of GABAergic synaptic release sites in CA1 pyramidal neurons from WARs. To address this hypothesis, we used a well-established neuronal computational model of a CA1 pyramidal neuron previously developed to replicate physiological properties of these cells. Our simulations replicated the biexponential trend only when we decreased the release frequency of synaptic currents by a factor of six in at least 40% of distal synapses. Our results suggest that almost half of the GABAergic synapses of WARs have a drastically reduced spontaneous release frequency. The computational model was able to reproduce the temporal dynamics of GABAergic inhibition that could underlie susceptibility to the spread of seizures.

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

The NMDA spike is a long-lasting nonlinear phenomenon initiated locally in the dendritic branches of a variety of cortical neurons. It plays a key role in synaptic plasticity and in single-neuron computations. Combining dynamic system theory and computational approaches, we now explore how the timing of synaptic inhibition affects the NMDA spike and its associated membrane current. When impinging on its early phase, individual inhibitory synapses strongly, but transiently, dampen the NMDA spike; later inhibition prematurely terminates it. A single inhibitory synapse reduces the NMDA-mediated Ca²⁺ current, a key player in plasticity, by up to 45%. NMDA spikes in distal dendritic branches/spines are longer-lasting and more resilient to inhibition, enhancing synaptic plasticity at these branches. We conclude that NMDA spikes are highly sensitive to dendritic inhibition; sparse weak inhibition can finely tune synaptic plasticity both locally at the dendritic branch level and globally at the level of the neuron's output.

Dendrites Enable a Robust Mechanism for Neuronal Stimulus Selectivity

Hearing, vision, touch: underlying all of these senses is stimulus selectivity, a robust information processing operation in which cortical neurons respond more to some stimuli than to others. Previous models assume that these neurons receive the highest weighted input from an ensemble encoding the preferred stimulus, but dendrites enable other possibilities. Nonlinear dendritic processing can produce stimulus selectivity based on the spatial distribution of synapses, even if the total preferred stimulus weight does not exceed that of nonpreferred stimuli. Using a multi-subunit nonlinear model, we demonstrate that stimulus selectivity can arise from the spatial distribution of synapses. We propose this as a general mechanism for information processing by neurons possessing dendritic trees. Moreover, we show that this implementation of stimulus selectivity increases the neuron's robustness to synaptic and dendritic failure. Importantly, our model can maintain stimulus selectivity for a larger range of loss of synapses or dendrites than an equivalent linear model. We then use a layer 2/3 biophysical neuron model to show that our implementation is consistent with two recent experimental observations: (1) one can observe a mixture of selectivities in dendrites that can differ from the somatic selectivity, and (2) hyperpolarization can broaden somatic tuning without affecting dendritic tuning. Our model predicts that an initially nonselective neuron can become selective when depolarized. In addition to motivating new experiments, the model's increased robustness to synapses and dendrites loss provides a starting point for fault-resistant neuromorphic chip development.