Electrical Compartmentalization in Neurons

Conductance-based dendrites perform Bayes-optimal cue integration

A fundamental function of cortical circuits is the integration of information from different sources to form a reliable basis for behavior. While animals behave as if they optimally integrate information according to Bayesian probability theory, the implementation of the required computations in the biological substrate remains unclear. We propose a novel, Bayesian view on the dynamics of conductance-based neurons and synapses which suggests that they are naturally equipped to optimally perform information integration. In our approach apical dendrites represent prior expectations over somatic potentials, while basal dendrites represent likelihoods of somatic potentials. These are parametrized by local quantities, the effective reversal potentials and membrane conductances. We formally demonstrate that under these assumptions the somatic compartment naturally computes the corresponding posterior. We derive a gradient-based plasticity rule, allowing neurons to learn desired target distributions and weight synaptic inputs by their relative reliabilities. Our theory explains various experimental findings on the system and single-cell level related to multi-sensory integration, which we illustrate with simulations. Furthermore, we make experimentally testable predictions on Bayesian dendritic integration and synaptic plasticity.

Network-neuron interactions underlying sensory responses of layer 5 pyramidal tract neurons in barrel cortex

Neurons in the cerebral cortex receive thousands of synaptic inputs per second from thousands of presynaptic neurons. How the dendritic location of inputs, their timing, strength, and presynaptic origin, in conjunction with complex dendritic physiology, impact the transformation of synaptic input into action potential (AP) output remains generally unknown for in vivo conditions. Here, we introduce a computational approach to reveal which properties of the input causally underlie AP output, and how this neuronal input-output computation is influenced by the morphology and biophysical properties of the dendrites. We demonstrate that this approach allows dissecting of how different input populations drive in vivo observed APs. For this purpose, we focus on fast and broadly tuned responses that pyramidal tract neurons in layer 5 (L5PTs) of the rat barrel cortex elicit upon passive single whisker deflections. By reducing a multi-scale model that we reported previously, we show that three features are sufficient to predict with high accuracy the sensory responses and receptive fields of L5PTs under these specific in vivo conditions: the count of active excitatory versus inhibitory synapses preceding the response, their spatial distribution on the dendrites, and the AP history. Based on these three features, we derive an analytically tractable description of the input-output computation of L5PTs, which enabled us to dissect how synaptic input from thalamus and different cell types in barrel cortex contribute to these responses. We show that the input-output computation is preserved across L5PTs despite morphological and biophysical diversity of their dendrites. We found that trial-to-trial variability in L5PT responses, and cell-to-cell variability in their receptive fields, are sufficiently explained by variability in synaptic input from the network, whereas variability in biophysical and morphological properties have minor contributions. Our approach to derive analytically tractable models of input-output computations in L5PTs provides a roadmap to dissect network-neuron interactions underlying L5PT responses across different in vivo conditions and for other cell types.

Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity

Purkinje cells in the cerebellum are among the largest neurons in the brain and have been extensively investigated in rodents. However, their morphological and physiological properties remain poorly understood in humans. In this study, we utilized high-resolution morphological reconstructions and unique electrophysiological recordings of human Purkinje cells ex vivo to generate computational models and estimate computational capacity. An inter-species comparison showed that human Purkinje cell had similar fractal structures but were larger than those of mouse Purkinje cells. Consequently, given a similar spine density (2/μm), human Purkinje cell hosted approximately 7.5 times more dendritic spines than those of mice. Moreover, human Purkinje cells had a higher dendritic complexity than mouse Purkinje cells and usually emitted 2-3 main dendritic trunks instead of one. Intrinsic electro-responsiveness was similar between the two species, but model simulations revealed that the dendrites could process ~6.5 times (n = 51 vs. n = 8) more input patterns in human Purkinje cells than in mouse Purkinje cells. Thus, while human Purkinje cells maintained spike discharge properties similar to those of rodents during evolution, they developed more complex dendrites, enhancing computational capacity.

Dendrites and efficiency: Optimizing performance and resource utilization

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

Distinctive properties of biological neural networks and recent advances in bottom-up approaches toward a better biologically plausible neural network

Although it may appear infeasible and impractical, building artificial intelligence (AI) using a bottom-up approach based on the understanding of neuroscience is straightforward. The lack of a generalized governing principle for biological neural networks (BNNs) forces us to address this problem by converting piecemeal information on the diverse features of neurons, synapses, and neural circuits into AI. In this review, we described recent attempts to build a biologically plausible neural network by following neuroscientifically similar strategies of neural network optimization or by implanting the outcome of the optimization, such as the properties of single computational units and the characteristics of the network architecture. In addition, we proposed a formalism of the relationship between the set of objectives that neural networks attempt to achieve, and neural network classes categorized by how closely their architectural features resemble those of BNN. This formalism is expected to define the potential roles of top-down and bottom-up approaches for building a biologically plausible neural network and offer a map helping the navigation of the gap between neuroscience and AI engineering.

A Conductance-Based Silicon Synapse Circuit

Neuron, synapse, and learning circuits inspired by the brain comprise the key components of a neuromorphic chip. In this study, we present a conductance-based analog silicon synapse circuit suitable for the implementation of reduced or multi-compartment neuron models. Compartmental models are more bio-realistic. They are implemented in neuromorphic chips aiming to mimic the electrical activities of the neuronal networks in the brain and incorporate biomimetic soma and synapse circuits. Most contemporary low-power analog synapse circuits implement bioinspired "current-based" synaptic models suited for the implementation of single-compartment point neuron models. They emulate the exponential decay profile of the synaptic current, but ignore the effect of the postsynaptic membrane potential on the synaptic current. This dependence is necessary to emulate shunting inhibition, which is thought to play important roles in information processing in the brain. The proposed circuit uses an oscillator-based resistor-type element at its output stage to incorporate this effect. This circuit is used to demonstrate the shunting inhibition phenomenon. Next, to demonstrate that the oscillatory nature of the induced synaptic current has no unforeseen effects, the synapse circuit is employed in a spatiotemporal spike pattern detection task. The task employs the adaptive spike-timing-dependent plasticity (STDP) learning rule, a bio-inspired learning rule introduced in a previous study. The mixed-signal chip is designed in a Taiwan Manufacturing Semiconductor Company 250 nm complementary metal oxide semiconductor technology node. It comprises a biomimetic soma circuit and 256 synapse circuits, along with their learning circuitries.

Control of Ca2+ signals by astrocyte nanoscale morphology at tripartite synapses

Much of the Ca2+ activity in astrocytes is spatially restricted to microdomains and occurs in fine processes that form a complex anatomical meshwork, the so-called spongiform domain. A growing body of literature indicates that those astrocytic Ca2+ signals can influence the activity of neuronal synapses and thus tune the flow of information through neuronal circuits. Because of technical difficulties in accessing the small spatial scale involved, the role of astrocyte morphology on Ca2+ microdomain activity remains poorly understood. Here, we use computational tools and idealized 3D geometries of fine processes based on recent super-resolution microscopy data to investigate the mechanistic link between astrocytic nanoscale morphology and local Ca2+ activity. Simulations demonstrate that the nano-morphology of astrocytic processes powerfully shapes the spatio-temporal properties of Ca2+ signals and promotes local Ca2+ activity. The model predicts that this effect is attenuated upon astrocytic swelling, hallmark of brain diseases, which we confirm experimentally in hypo-osmotic conditions. Upon repeated neurotransmitter release events, the model predicts that swelling hinders astrocytic signal propagation. Overall, this study highlights the influence of the complex morphology of astrocytes at the nanoscale and its remodeling in pathological conditions on neuron-astrocyte communication at so-called tripartite synapses, where astrocytic processes come into close contact with pre- and postsynaptic structures.

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.

Assessing Local and Branch-specific Activity in Dendrites

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

A dynamic clamp protocol to artificially modify cell capacitance

Dynamics of excitable cells and networks depend on the membrane time constant, set by membrane resistance and capacitance. Whereas pharmacological and genetic manipulations of ionic conductances of excitable membranes are routine in electrophysiology, experimental control over capacitance remains a challenge. Here, we present capacitance clamp, an approach that allows electrophysiologists to mimic a modified capacitance in biological neurons via an unconventional application of the dynamic clamp technique. We first demonstrate the feasibility to quantitatively modulate capacitance in a mathematical neuron model and then confirm the functionality of capacitance clamp in in vitro experiments in granule cells of rodent dentate gyrus with up to threefold virtual capacitance changes. Clamping of capacitance thus constitutes a novel technique to probe and decipher mechanisms of neuronal signaling in ways that were so far inaccessible to experimental electrophysiology.

Periodicity Pitch Perception Part III: Sensibility and Pachinko Volatility

Neuromorphic computer models are used to explain sensory perceptions. Auditory models generate cochleagrams, which resemble the spike distributions in the auditory nerve. Neuron ensembles along the auditory pathway transform sensory inputs step by step and at the end pitch is represented in auditory categorical spaces. In two previous articles in the series on periodicity pitch perception an extended auditory model had been successfully used for explaining periodicity pitch proved for various musical instrument generated tones and sung vowels. In this third part in the series the focus is on octopus cells as they are central sensitivity elements in auditory cognition processes. A powerful numerical model had been devised, in which auditory nerve fibers (ANFs) spike events are the inputs, triggering the impulse responses of the octopus cells. Efficient algorithms are developed and demonstrated to explain the behavior of octopus cells with a focus on a simple event-based hardware implementation of a layer of octopus neurons. The main finding is, that an octopus' cell model in a local receptive field fine-tunes to a specific trajectory by a spike-timing-dependent plasticity (STDP) learning rule with synaptic pre-activation and the dendritic back-propagating signal as post condition. Successful learning explains away the teacher and there is thus no need for a temporally precise control of plasticity that distinguishes between learning and retrieval phases. Pitch learning is cascaded: At first octopus cells respond individually by self-adjustment to specific trajectories in their local receptive fields, then unions of octopus cells are collectively learned for pitch discrimination. Pitch estimation by inter-spike intervals is shown exemplary using two input scenarios: a simple sinus tone and a sung vowel. The model evaluation indicates an improvement in pitch estimation on a fixed time-scale.

Parallel processing in active dendrites during periods of intense spiking activity

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

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca²⁺ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models.

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.

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

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

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.

The functional organization of excitation and inhibition in the dendrites of mouse direction-selective ganglion cells

Recent studies indicate that the precise timing and location of excitation and inhibition (E/I) within active dendritic trees can significantly impact neuronal function. How synaptic inputs are functionally organized at the subcellular level in intact circuits remains unclear. To address this issue, we took advantage of the retinal direction-selective ganglion cell circuit, where directionally tuned inhibition is known to shape non-directional excitatory signals. We combined two-photon calcium imaging with genetic, pharmacological, and single-cell ablation methods to examine the extent to which inhibition ‘vetoes’ excitation at the level of individual dendrites of direction-selective ganglion cells. We demonstrate that inhibition shapes direction selectivity independently within small dendritic segments (<10µm) with remarkable accuracy. The data suggest that the parallel processing schemes proposed for direction encoding could be more fine-grained than previously envisioned.