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.

Reflections on the past two decades of neuroscience.

The first issue of Nature Reviews Neuroscience was published 20 years ago, in 2000. To mark this anniversary, in this Viewpoint article we asked a selection of researchers from across the field who have authored pieces published in the journal in recent years for their thoughts on notable and interesting developments in neuroscience, and particularly in their areas of the field, over the past two decades. They also provide some thoughts on current lines of research and questions that excite them.

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.

Modeling Dendrites and Spatially-Distributed Neuronal Membrane Properties.

The first step toward understanding the brain is to learn how individual neurons process incoming signals, the vast majority of which arrive in their dendrites. Dendrites were first discovered at the beginning of the twentieth century and were characterized by great anatomical variability, both within and across species. Over the past years, a rich repertoire of active and passive dendritic mechanisms has been unveiled, which greatly influences their integrative power. Yet, our understanding of how dendrites compute remains limited, mainly because technological limitations make it difficult to record from dendrites directly and manipulate them. Computational modeling, on the other hand, is perfectly suited for this task. Biophysical models that account for the morphology as well as passive and active neuronal properties can explain a wide variety of experimental findings, shedding new light on how dendrites contribute to neuronal and circuit computations. This chapter aims to help the interested reader build biophysical models incorporating dendrites by detailing how their electrophysiological properties can be described using simple mathematical frameworks. We start by discussing the passive properties of dendrites and then give an overview of how active conductances can be incorporated, leading to realistic in silico replicas of biological neurons.

Two Distinct Sets of Ca2+ and K+ Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites.

In cerebellar Purkinje neuron dendrites, the transient depolarization associated with a climbing fiber (CF) EPSP activates voltage-gated Ca2+ channels (VGCCs), voltage-gated K+ channels (VGKCs), and Ca2+-activated SK and BK K+ channels. The resulting membrane potential (Vm) and Ca2+ transients play a fundamental role in dendritic integration and synaptic plasticity of parallel fiber inputs. Here we report a detailed investigation of the kinetics of dendritic Ca2+ and K+ channels activated by CF-EPSPs, based on optical measurements of Vm and Ca2+ transients and on a single-compartment NEURON model reproducing experimental data. We first measured Vm and Ca2+ transients associated with CF-EPSPs at different initial Vm, and we analyzed the changes in the Ca2+ transients produced by the block of each individual VGCCs, of A-type VGKCs and of SK and BK channels. Then, we constructed a model that includes six active ion channels to accurately match experimental signals and extract the physiological kinetics of each channel. We found that two different sets of channels are selectively activated. When the dendrite is hyperpolarized, CF-EPSPs mainly activate T-type VGCCs, SK channels, and A-type VGKCs that limit the transient Vm ∼ <0 mV. In contrast, when the dendrite is depolarized, T-type VGCCs and A-type VGKCs are inactivated and CF-EPSPs activate P/Q-type VGCCs, high-voltage activated VGKCs, and BK channels, leading to Ca2+ spikes. Thus, the potentially activity-dependent regulation of A-type VGKCs, controlling the activation of this second set of channels, is likely to play a crucial role in signal integration and plasticity in Purkinje neuron dendrites.SIGNIFICANCE STATEMENT The climbing fiber synaptic input transiently depolarizes the dendrite of cerebellar Purkinje neurons generating a signal that plays a fundamental role in dendritic integration. This signal is mediated by two types of Ca2+ channels and four types of K+ channels. Thus, understanding the kinetics of all of these channels is crucial for understanding PN function. To obtain this information, we used an innovative strategy that merges ultrafast optical membrane potential and Ca2+ measurements, pharmacological analysis, and computational modeling. We found that, according to the initial membrane potential, the climbing fiber depolarizing transient activates two distinct sets of channels. Moreover, A-type K+ channels limit the activation of P/Q-type Ca2+ channels and associated K+ channels, thus preventing the generation of Ca2+ spikes.

Basal tree complexity shapes functional pathways in the prefrontal cortex.

While the morphology of basal dendritic trees in cortical pyramidal neurons varies, the functional implications of this diversity are just starting to emerge. In layer 5 pyramidal neurons of the prefrontal cortex, for example, increased basal tree complexity determines the recruitment of these neurons into functional circuits. Here, we use a modeling approach to investigate whether and how the morphology of the basal tree mediates the functional output of neurons. We implemented 57 basal tree morphologies of layer 5 prefrontal pyramidal neurons of the rat and identified morphological types that were characterized by different response features, forming distinct functional types. These types were robust to a wide range of manipulations (distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, or the number of activated synapses) and supported different temporal coding schemes at both the single neuron and the microcircuit level. We predict that the basal tree morphological diversity among neurons of the same class mediates their segregation into distinct functional pathways. Extension of our approach/findings to other cortical areas and/or layers or under pathological conditions may provide a generalized role of the basal trees for neuronal function.NEW & NOTEWORTHY Our results suggest that the segregation of neurons to different functional types based on their basal tree morphology is in large part independent of the distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, and the number of activated synapses; different functional types support distinct temporal coding schemes. This can be exploited to create networks with diverse coding characteristics, thus contributing to the functional heterogeneity within the same layer and area.

Dendrites of dentate gyrus granule cells contribute to pattern separation by controlling sparsity.

The hippocampus plays a key role in pattern separation, the process of transforming similar incoming information to highly dissimilar, nonverlapping representations. Sparse firing granule cells (GCs) in the dentate gyrus (DG) have been proposed to undertake this computation, but little is known about which of their properties influence pattern separation. Dendritic atrophy has been reported in diseases associated with pattern separation deficits, suggesting a possible role for dendrites in this phenomenon. To investigate whether and how the dendrites of GCs contribute to pattern separation, we build a simplified, biologically relevant, computational model of the DG. Our model suggests that the presence of GC dendrites is associated with high pattern separation efficiency while their atrophy leads to increased excitability and performance impairments. These impairments can be rescued by restoring GC sparsity to control levels through various manipulations. We predict that dendrites contribute to pattern separation as a mechanism for controlling sparsity. © 2016 The Authors Hippocampus Published by Wiley Periodicals, Inc.

Pattern separation in the hippocampus through the eyes of computational modeling.

Pattern separation is a mnemonic process that has been extensively studied over the years. It entails the ability -of primarily hippocampal circuits- to distinguish between highly similar inputs, via generating different neuronal activity (output) patterns. The dentate gyrus (DG) in particular has long been hypothesized to implement pattern separation by detecting and storing similar inputs as distinct representations. The ways in which these distinct representations can be generated have been explored in a number of theoretical and computational modeling studies. Here, we review two categories of pattern separation models: those that address the phenomenon in an abstract mathematical fashion and those that delve into the underlying biological mechanisms by taking into account the anatomy and/or physiology of hippocampal circuits. We summarize the strategies, findings and limitations of these modeling approaches in the light of new experimental findings and propose a unifying framework whereby different network, cellular and sub-cellular mechanisms converge to a common goal: controlling sparsity, the key determinant of pattern separation in the DG.

A computational study on how theta modulated inhibition can account for the long temporal windows in the entorhinal-hippocampal loop.

A recent experimental study (Mizuseki, Sirota, Pastalkova, & Buzsaki, 2009) has shown that the temporal delays between population activities in successive entorhinal and hippocampal anatomical stages are longer (about 70-80ms) than expected from axon conduction velocities and passive synaptic integration of feed-forward excitatory inputs. We investigate via computer simulations the mechanisms that give rise to such long temporal delays in the hippocampus structures. A model of the dentate gyrus (DG), CA3 and CA1 microcircuits is presented that uses biophysical representations of the major cell types including granule cells, CA3 and CA1 pyramidal cells (PCs) and six types of interneurons: basket cells (BCs), axo-axonic cells (AACs), bistratified cells (BSCs), oriens lacunosum-moleculare cells (OLMs), mossy cells (MCs) and hilar perforant path associated cells (HC). Inputs to the network came from the entorhinal cortex (EC) (layers 2 and 3) and the medial septum (MS). The model simulates accurately the timing of firing of different hippocampal cells with respect to the theta rhythm. The model shows that the experimentally reported long temporal delays in the DG, CA3 and CA1 hippocampal regions are due to theta modulated somatic and axonic inhibition. The model further predicts that the phase at which the CA1 PCs fire with respect to the theta rhythm is determined primarily by their increased dendritic excitability caused by the decrease of the axial resistance and the A-type K(+) conductance along their dendritic trunk. The model predicted latencies by which the DG, CA3 and CA1 principal cells fire are inline with the experimental evidence. Finally, the model proposes functional roles for the different inhibitory interneurons in the retrieval of the memory pattern by the DG, CA3 and CA1 networks. The model makes a number of predictions, which can be tested experimentally, thus leading to a better understanding of the biophysical computations in the hippocampus.

Dendritic nonlinearities reduce network size requirements and mediate ON and OFF states of persistent activity in a PFC microcircuit model.

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.

GluA2 mRNA distribution and regulation by miR-124 in hippocampal neurons.

AMPA-type glutamate receptors mediate fast, excitatory neurotransmission in the brain, and their concentrations at synapses are important determinants of synaptic strength. We investigated the post-transcriptional regulation of GluA2, the calcium-impermeable AMPA receptor subunit, by examining the subcellular distribution of its mRNA and evaluating its translational regulation by microRNA in cultured mouse hippocampal neurons. Using computational approaches, we identified a conserved microRNA-124 (miR-124) binding site in the 3'UTR of GluA2 and demonstrated that miR-124 regulated the translation of GluA2 mRNA reporters in a sequence-specific manner in luciferase assays. While we hypothesized that this regulation might occur in dendrites, our biochemical and fluorescent in situ hybridization (FISH) data indicate that GluA2 mRNA does not localize to dendrites or synapses of mouse hippocampal neurons. In contrast, we detected significant concentrations of miR-124 in dendrites. Overexpression of miR-124 in dissociated neurons results in a 30% knockdown of GluA2 protein, as measured by immunoblot and quantitative immunocytochemistry, without producing any changes in GluA2 mRNA concentrations. While total GluA2 concentrations are reduced, we did not detect any changes in the concentration of synaptic GluA2. We conclude from these results that miR-124 interacts with GluA2 mRNA in the cell body to downregulate translation. Our data support a model in which GluA2 is translated in the cell body and subsequently transported to neuronal dendrites and synapses, and suggest that synaptic GluA2 concentrations are modified primarily by regulated protein trafficking rather than by regulated local translation.

Leveraging dendritic properties to advance machine learning and neuro-inspired computing.

The brain is a remarkably capable and efficient system. It can process and store huge amounts of noisy and unstructured information, using minimal energy. In contrast, current artificial intelligence (AI) systems require vast resources for training while still struggling to compete in tasks that are trivial for biological agents. Thus, brain-inspired engineering has emerged as a promising new avenue for designing sustainable, next-generation AI systems. Here, we describe how dendritic mechanisms of biological neurons have inspired innovative solutions for significant AI problems, including credit assignment in multi-layer networks, catastrophic forgetting, and high-power consumption. These findings provide exciting alternatives to existing architectures, showing how dendritic research can pave the way for building more powerful and energy efficient artificial learning systems.

A Generative Neighborhood-Based Deep Autoencoder for Robust Imbalanced Classification.

Deep learning models perform remarkably well on many classification tasks recently. The superior performance of deep neural networks relies on the large number of training data, which at the same time must have an equal class distribution in order to be efficient. However, in most real-world applications, the labeled data may be limited with high imbalance ratios among the classes, and thus, the learning process of most classification algorithms is adversely affected resulting in unstable predictions and low performance. Three main categories of approaches address the problem of imbalanced learning, i.e., data-level, algorithmic level, and hybrid methods, which combine the two aforementioned approaches. Data generative methods are typically based on generative adversarial networks, which require significant amounts of data, while model-level methods entail extensive domain expert knowledge to craft the learning objectives, thereby being less accessible for users without such knowledge. Moreover, the vast majority of these approaches are designed and applied to imaging applications, less to time series, and extremely rare to both of them. To address the above issues, we introduce GENDA, a generative neighborhood-based deep autoencoder, which is simple yet effective in its design and can be successfully applied to both image and time-series data. GENDA is based on learning latent representations that rely on the neighboring embedding space of the samples. Extensive experiments, conducted on a variety of widely-used real datasets demonstrate the efficacy of the proposed method. Impact Statement­: Imbalanced data classification is an actual and important issue in many real-world learning applications hampering most classification tasks. Fraud detection, biomedical imaging categorizing healthy people versus patients, and object detection are some indicative domains with an economic, social and technological impact, which are greatly affected by inherent imbalanced data distribution. However, the majority of the existing algorithms that address the imbalanced classification problem are designed with a particular application in mind, and thus they can be used with specific datasets and even hyperparameters. The generative model introduced in this paper overcomes this limitation and produces improved results for a large class of imaging and time series data even under severe imbalance ratios, making it quite competitive.

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.

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons.

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.

Neurofibromin regulates corticostriatal inhibitory networks during working memory performance.

Neurofibromatosis type I (NF1) is one of the most common single-gene causes of learning disabilities. Here, we use behavioral working memory probes and electrophysiological studies in a mouse model of NF1 (Nf1 heterozygous null mutants; Nf1(+/-)) to demonstrate that (i) Neurofibromin regulates prefrontal and striatal inhibitory networks, specifically activity-dependent GABA release and (ii) is required for working memory performance, with inhibition-dependent working memory deficits seen in Nf1(+/-) mice. We find that increased inhibition in medial prefrontal cortex (mPFC) is sufficient to alter persistent activity in a biophysical model of an mPFC microcircuit, suggesting a possible mechanism for Nf1(+/-) working memory deficits. Accordingly, working memory assays applied during functional MRI (fMRI) studies in human subjects with NF1 reveal hypoactivation of corticostriatal networks, which is associated with impaired working memory performance. Collectively, these integrative mouse and human studies reveal molecular and cellular mechanisms contributing to working memory deficits in NF1.

Dendrites and Efficiency: Optimizing Performance and Resource Utilization.

The brain is a highly efficient system evolved to achieve high performance with limited resources. We propose that dendrites make information processing and storage in the brain more efficient through the segregation of inputs and their conditional integration via nonlinear events, the compartmentalization of activity and plasticity and the binding of information through synapse clustering. In real-world scenarios with limited energy and space, dendrites help biological networks process natural stimuli on behavioral timescales, perform the inference process on those stimuli in a context-specific manner, and store the information in overlapping populations of neurons. A global picture starts to emerge, in which dendrites help the brain achieve efficiency through a combination of optimization strategies balancing the tradeoff between performance and resource utilization.

Leveraging dendritic properties to advance machine learning and neuro-inspired computing.

The brain is a remarkably capable and efficient system. It can process and store huge amounts of noisy and unstructured information using minimal energy. In contrast, current artificial intelligence (AI) systems require vast resources for training while still struggling to compete in tasks that are trivial for biological agents. Thus, brain-inspired engineering has emerged as a promising new avenue for designing sustainable, next-generation AI systems. Here, we describe how dendritic mechanisms of biological neurons have inspired innovative solutions for significant AI problems, including credit assignment in multilayer networks, catastrophic forgetting, and high energy consumption. These findings provide exciting alternatives to existing architectures, showing how dendritic research can pave the way for building more powerful and energy-efficient artificial learning systems.

Introducing the Dendrify framework for incorporating dendrites to spiking neural networks.

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