From Neuron Biophysics to Orientation Selectivity in Electrically Coupled Networks of Neocortical L2/3 Large Basket Cells

Sub-threshold neuronal activity and the dynamical regime of cerebral cortex

Cortical neurons exhibit temporally irregular spiking patterns and heterogeneous firing rates. These features arise in model circuits operating in a 'fluctuation-driven regime', in which fluctuations in membrane potentials emerge from the network dynamics. However, it is still debated whether the cortex operates in such a regime. We evaluated the fluctuation-driven hypothesis by analyzing spiking and sub-threshold membrane potentials of neurons in the frontal cortex of mice performing a decision-making task. We showed that while standard fluctuation-driven models successfully account for spiking statistics, they fall short in capturing the heterogeneity in sub-threshold activity. This limitation is an inevitable outcome of bombarding single-compartment neurons with a large number of pre-synaptic inputs, thereby clamping the voltage of all neurons to more or less the same average voltage. To address this, we effectively incorporated dendritic morphology into the standard models. Inclusion of dendritic morphology in the neuronal models increased neuronal selectivity and reduced error trials, suggesting a functional role for dendrites during decision-making. Our work suggests that, during decision-making, cortical neurons in high-order cortical areas operate in a fluctuation-driven regime.

The Anterolateral Barrel Subfield Differs from the Posteromedial Barrel Subfield in the Morphology and Cell Density of Parvalbumin-Positive GABAergic Interneurons

Layer 4 of the rodent somatosensory cortex has unitary structures called barrels that receive tactile information from individual vibrissae. Barrels in the anterolateral barrel subfield (ALBSF) are much smaller and have gained less attention than larger barrels in the posteromedial barrel subfield (PMBSF), though the former outnumber the latter. We compared the morphological features of barrels between the ALBSF and PMBSF in male mice using deformation-free tangential sections and confocal optical slice-based, precise reconstructions of barrels. The average volume of a single barrel in the ALBSF was 34.7% of that in the PMBSF, but the numerical density of parvalbumin (PV)-positive interneurons in the former was 1.49 times higher than that in the latter. Moreover, PV neuron density in septa was 2.08 times higher in the ALBSF than that in the PMBSF. The proportions of PV neuron number to both all neuron number and all GABAergic neuron number in the ALBSF were also higher than those in the PMBSF. Somata of PV neurons in barrels and septa in the ALBSF received 1.64 and 1.50 times more vesicular glutamate transporter Type 2-labeled boutons than those in the PMBSF, suggesting more potent feedforward inhibitory circuits in the ALBSF. The mode of connectivity through dendritic gap junctions among PV neurons also differed between the ALBSF and PMBSF. Clusters of smaller unitary structures containing a higher density of representative GABAergic interneurons with differential morphological features in the ALBSF suggest a division of functional roles in the two vibrissa-barrel systems, as has been demonstrated by behavioral studies.

Simulations of cortical networks using spatially extended conductance-based neuronal models

The Hodgkin-Huxley model of action potential generation and propagation, published in the Journal of Physiology in 1952, initiated the field of biophysically detailed computational modelling in neuroscience, which has expanded to encompass a variety of species and components of the nervous system. Here we review the developments in this area with a focus on efforts in the community towards modelling the mammalian neocortex using spatially extended conductance-based neuronal models. The Hodgkin-Huxley formalism and related foundational contributions, such as Rall's cable theory, remain widely used in these efforts to the current day. We argue that at present the field is undergoing a qualitative change due to new very rich datasets describing the composition, connectivity and functional activity of cortical circuits, which are being integrated systematically into large-scale network models. This trend, combined with the accelerating development of convenient software tools supporting such complex modelling projects, is giving rise to highly detailed models of the cortex that are extensively constrained by the data, enabling computational investigation of a multitude of questions about cortical structure and function.

On the Diverse Functions of Electrical Synapses

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Statistical Emulation of Neural Simulators: Application to Neocortical L2/3 Large Basket Cells

Many scientific systems are studied using computer codes that simulate the phenomena of interest. Computer simulation enables scientists to study a broad range of possible conditions, generating large quantities of data at a faster rate than the laboratory. Computer models are widespread in neuroscience, where they are used to mimic brain function at different levels. These models offer a variety of new possibilities for the neuroscientist, but also numerous challenges, such as: where to sample the input space for the simulator, how to make sense of the data that is generated, and how to estimate unknown parameters in the model. Statistical emulation can be a valuable complement to simulator-based research. Emulators are able to mimic the simulator, often with a much smaller computational burden and they are especially valuable for parameter estimation, which may require many simulator evaluations. This work compares different statistical models that address these challenges, and applies them to simulations of neocortical L2/3 large basket cells, created and run with the NEURON simulator in the context of the European Human Brain Project. The novelty of our approach is the use of fast empirical emulators, which have the ability to accelerate the optimization process for the simulator and to identify which inputs (in this case, different membrane ion channels) are most influential in affecting simulated features. These contributions are complementary, as knowledge of the important features can further improve the optimization process. Subsequent research, conducted after the process is completed, will gain efficiency by focusing on these inputs.

Intrinsic Sources and Functional Impacts of Asymmetry at Electrical Synapses

Electrical synapses couple inhibitory neurons across the brain, underlying a variety of functions that are modifiable by activity. Despite recent advances, many functions and contributions of electrical synapses within neural circuitry remain underappreciated. Among these are the sources and impacts of electrical synapse asymmetry. Using multi-compartmental models of neurons coupled through dendritic electrical synapses, we investigated intrinsic factors that contribute to effective synaptic asymmetry and that result in modulation of spike timing and synchrony between coupled cells. We show that electrical synapse location along a dendrite, input resistance, internal dendritic resistance, or directional conduction of the electrical synapse itself each alter asymmetry as measured by coupling between cell somas. Conversely, we note that asymmetrical gap junction (GJ) conductance can be masked by each of these properties. Furthermore, we show that asymmetry modulates spike timing and latency of coupled cells by up to tens of milliseconds, depending on direction of conduction or dendritic location of the electrical synapse. Coordination of rhythmic activity between two cells also depends on asymmetry. These simulations illustrate that causes of asymmetry are diverse, may not be apparent in somatic measurements of electrical coupling, influence dendritic processing, and produce a variety of outcomes on spiking and synchrony of coupled cells. Our findings highlight aspects of electrical synapses that should always be included in experimental demonstrations of coupling, and when assembling simulated networks containing electrical synapses.

The Role of Hub Neurons in Modulating Cortical Dynamics

Many neurodegenerative diseases are associated with the death of specific neuron types in particular brain regions. What makes the death of specific neuron types particularly harmful for the integrity and dynamics of the respective network is not well understood. To start addressing this question we used the most up-to-date biologically realistic dense neocortical microcircuit (NMC) of the rodent, which has reconstructed a volume of 0.3 mm³ and containing 31,000 neurons, ∼37 million synapses, and 55 morphological cell types arranged in six cortical layers. Using modern network science tools, we identified hub neurons in the NMC, that are connected synaptically to a large number of their neighbors and systematically examined the impact of abolishing these cells. In general, the structural integrity of the network is robust to cells’ attack; yet, attacking hub neurons strongly impacted the small-world topology of the network, whereas similar attacks on random neurons have a negligible effect. Such hub-specific attacks are also impactful on the network dynamics, both when the network is at its spontaneous synchronous state and when it was presented with synchronized thalamo-cortical visual-like input. We found that attacking layer 5 hub neurons is most harmful to the structural and functional integrity of the NMC. The significance of our results for understanding the role of specific neuron types and cortical layers for disease manifestation is discussed.

Feed-forward recruitment of electrical synapses enhances synchronous spiking in the mouse cerebellar cortex

In the cerebellar cortex, molecular layer interneurons use chemical and electrical synapses to form subnetworks that fine-tune the spiking output of the cerebellum. Although electrical synapses can entrain activity within neuronal assemblies, their role in feed-forward circuits is less well explored. By combining whole-cell patch-clamp and 2-photon laser scanning microscopy of basket cells (BCs), we found that classical excitatory postsynaptic currents (EPSCs) are followed by GABA_A receptor-independent outward currents, reflecting the hyperpolarization component of spikelets (a synapse-evoked action potential passively propagating from electrically coupled neighbors). FF recruitment of the spikelet-mediated inhibition curtails the integration time window of concomitant excitatory postsynaptic potentials (EPSPs) and dampens their temporal integration. In contrast with GABAergic-mediated feed-forward inhibition, the depolarizing component of spikelets transiently increases the peak amplitude of EPSPs, and thus postsynaptic spiking probability. Therefore, spikelet transmission can propagate within the BC network to generate synchronous inhibition of Purkinje cells, which can entrain cerebellar output for driving temporally precise behaviors.

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.

Network Analysis of Murine Cortical Dynamics Implicates Untuned Neurons in Visual Stimulus Coding

Unbiased and dense sampling of large populations of layer 2/3 pyramidal neurons in mouse primary visual cortex (V1) reveals two functional sub-populations: neurons tuned and untuned to drifting gratings. Whether functional interactions between these two groups contribute to the representation of visual stimuli is unclear. To examine these interactions, we summarize the population partial pairwise correlation structure as a directed and weighted graph. We find that tuned and untuned neurons have distinct topological properties, with untuned neurons occupying central positions in functional networks (FNs). Implementation of a decoder that utilizes the topology of these FNs yields accurate decoding of visual stimuli. We further show that decoding performance degrades comparably following manipulations of either tuned or untuned neurons. Our results demonstrate that untuned neurons are an integral component of V1 FNs and suggest that network interactions contain information about the stimulus that is accessible to downstream elements.

Coupled sensory interneurons mediate escape neural circuit processing in an aquatic annelid worm, Lumbriculus variegatus

The interneurons associated with rapid escape circuits are adapted for fast pathway activation and rapid conduction. An essential aspect of fast activation is the processing of sensory information with limited delays. Although aquatic annelid worms have some of the fastest escape responses in nature, the sensory networks that mediate their escape behavior are not well defined. Here, we demonstrate that the escape circuit of the mud worm, Lumbriculus variegatus, is a segmentally arranged network of sensory interneurons electrically coupled to the central medial giant fiber (MGF), the command-like interneuron for head withdrawal. Electrical stimulation of the body wall evoked fast, short-duration spikelets in the MGF, which we suggest are the product of intermediate giant fiber activation coupled to MGF collateral dendrites. Since these contact sites have immunoreactivity with a glutamate receptor antibody, and the glutamate receptor antagonist 6-cyano-7-nitroquinoxaline-2,3-dion abolishes evoked MGF responses, we conclude that the afferent pathway for MGF-mediated escape is glutamatergic. This electrically coupled sensory network may facilitate rapid escape activation by enhancing the amplitude of giant axon depolarization.

Using subthreshold events to characterize the functional architecture of the electrically coupled inferior olive network

The electrical connectivity in the inferior olive (IO) nucleus plays an important role in generating well-timed spiking activity. Here we combined electrophysiological and computational approaches to assess the functional organization of the IO nucleus in mice. Spontaneous fast and slow subthreshold events were commonly encountered during in vitro recordings. We show that whereas the fast events represent intrinsic regenerative activity, the slow events reflect the electrical connectivity between neurons (‘spikelets’). Recordings from cell pairs revealed the synchronized occurrence of distinct groups of spikelets; their rate and distribution enabled an accurate estimation of the number of connected cells and is suggestive of a clustered organization. This study thus provides a new perspective on the functional and structural organization of the olivary nucleus and a novel experimental and theoretical approach to study electrically coupled networks.

An efficient analytical reduction of detailed nonlinear neuron models

Detailed conductance-based nonlinear neuron models consisting of thousands of synapses are key for understanding of the computational properties of single neurons and large neuronal networks, and for interpreting experimental results. Simulations of these models are computationally expensive, considerably curtailing their utility. Neuron_Reduce is a new analytical approach to reduce the morphological complexity and computational time of nonlinear neuron models. Synapses and active membrane channels are mapped to the reduced model preserving their transfer impedance to the soma; synapses with identical transfer impedance are merged into one NEURON process still retaining their individual activation times. Neuron_Reduce accelerates the simulations by 40-250 folds for a variety of cell types and realistic number (10,000-100,000) of synapses while closely replicating voltage dynamics and specific dendritic computations. The reduced neuron-models will enable realistic simulations of neural networks at unprecedented scale, including networks emerging from micro-connectomics efforts and biologically-inspired "deep networks". Neuron_Reduce is publicly available and is straightforward to implement.

Axonal Computations

Axons functionally link the somato-dendritic compartment to synaptic terminals. Structurally and functionally diverse, they accomplish a central role in determining the delays and reliability with which neuronal ensembles communicate. By combining their active and passive biophysical properties, they ensure a plethora of physiological computations. In this review, we revisit the biophysics of generation and propagation of electrical signals in the axon and their dynamics. We further place the computational abilities of axons in the context of intracellular and intercellular coupling. We discuss how, by means of sophisticated biophysical mechanisms, axons expand the repertoire of axonal computation, and thereby, of neural computation.

Beyond plasticity: the dynamic impact of electrical synapses on neural circuits

Electrical synapses are found in vertebrate and invertebrate nervous systems. The cellular basis of these synapses is the gap junction, a group of intercellular channels that mediate direct communication between adjacent neurons. Similar to chemical synapses, electrical connections are modifiable and their variations in strength provide a mechanism for reconfiguring neural circuits. In addition, electrical synapses dynamically regulate neural circuits through properties without equivalence in chemical transmission. Because of their continuous nature and bidirectionality, electrical synapses allow electrical currents underlying changes in membrane potential to leak to 'coupled' partners, dampening neuronal excitability and altering their integrative properties. Remarkably, this effect can be transiently alleviated when comparable changes in membrane potential simultaneously occur in each of the coupled neurons, a phenomenon that is dynamically dictated by the timing of arriving signals such as synaptic potentials. By way of this mechanism, electrical synapses influence synaptic integration and action potential generation, imparting an additional layer of dynamic complexity to neural circuits.

Electrical Synapses Enhance and Accelerate Interneuron Recruitment in Response to Coincident and Sequential Excitation

Electrical synapses are ubiquitous in interneuron networks. They form intercellular pathways, allowing electrical currents to leak between coupled interneurons. I explored the impact of electrical coupling on the integration of excitatory signals and on the coincidence detection abilities of electrically-coupled cerebellar basket cells (BCs). In order to do so, I quantified the influence of electrical coupling on the rate, the probability and the latency at which BCs generate action potentials when stimulated. The long-lasting simultaneous suprathreshold depolarization of a coupled cell evoked an increase in firing rate and a shortening of action potential latency in a reference basket cell, compared to its depolarization alone. Likewise, the action potential probability of coupled cells was strongly increased when they were simultaneously stimulated with trains of short-duration near-threshold current pulses (mimicking the activation of presynaptic granule cells) at 10 Hz, and to a lesser extent at 50 Hz, an effect that was absent in non-coupled cells. Moreover, action potential probability was increased and action potential latency was shortened in response to synaptic stimulations in mice lacking the protein that forms gap junctions between BCs, connexin36, relative to wild-type (WT) controls. These results suggest that electrical synapses between BCs decrease the probability and increase the latency of stimulus-triggered action potentials, both effects being reverted upon simultaneous excitation of coupled cells. Interestingly, varying the delay at which coupled cells are stimulated revealed that the probability and the speed of action potential generation are facilitated maximally when a basket cell is stimulated shortly after a coupled cell. These findings suggest that electrically-coupled interneurons behave as coincidence and sequence detectors that dynamically regulate the latency and the strength of inhibition onto postsynaptic targets depending on the degree of input synchrony in the coupled interneuron network.

Efficient encoding of motion is mediated by gap junctions in the fly visual system

Understanding the computational implications of specific synaptic connectivity patterns is a fundamental goal in neuroscience. In particular, the computational role of ubiquitous electrical synapses operating via gap junctions remains elusive. In the fly visual system, the cells in the vertical-system network, which play a key role in visual processing, primarily connect to each other via axonal gap junctions. This network therefore provides a unique opportunity to explore the functional role of gap junctions in sensory information processing. Our information theoretical analysis of a realistic VS network model shows that within 10 ms following the onset of the visual input, the presence of axonal gap junctions enables the VS system to efficiently encode the axis of rotation, θ, of the fly’s ego motion. This encoding efficiency, measured in bits, is near-optimal with respect to the physical limits of performance determined by the statistical structure of the visual input itself. The VS network is known to be connected to downstream pathways via a subset of triplets of the vertical system cells; we found that because of the axonal gap junctions, the efficiency of this subpopulation in encoding θ is superior to that of the whole vertical system network and is robust to a wide range of signal to noise ratios. We further demonstrate that this efficient encoding of motion by this subpopulation is necessary for the fly's visually guided behavior, such as banked turns in evasive maneuvers. Because gap junctions are formed among the axons of the vertical system cells, they only impact the system’s readout, while maintaining the dendritic input intact, suggesting that the computational principles implemented by neural circuitries may be much richer than previously appreciated based on point neuron models. Our study provides new insights as to how specific network connectivity leads to efficient encoding of sensory stimuli.

Understanding sensory stimuli from the environment and deciding how best to respond to it behaviorally is essential for survival. What makes organisms efficient in encoding these sensory stimuli? This study provides a novel view on this unresolved issue using the visual system of the fly. We show that a specific synaptic connectivity manifested via gap junctions (GJs) among axons in the Vertical System (VS) network leads to particularly high encoding efficiency of the axis of rotation of the fly’s ego motion. Due to these GJs, triplets of VS neurons (the VS5-6-7 triplet), which connect to a downstream motor system, encode motion stimuli at an efficiency close to the physical limit; this efficient encoding is necessary for evasive maneuvers that are critical for the fly to escape predators. We then suggest why GJs in the VS network enable such high encoding efficiency.

Does layer 4 in the barrel cortex function as a balanced circuit when responding to whisker movements?

Neurons in one barrel in layer 4 (L4) in the mouse vibrissa somatosensory cortex are innervated mostly by neurons from the VPM nucleus and by other neurons within the same barrel. During quiet wakefulness or whisking in air, thalamic inputs vary slowly in time, and excitatory neurons rarely fire. A barrel in L4 contains a modest amount of neurons; the synaptic conductances are not very strong and connections are not sparse. Are the dynamical properties of the L4 circuit similar to those expected from fluctuation-dominated, balanced networks observed for large, strongly coupled and sparse cortical circuits? To resolve this question, we analyze a network of 150 inhibitory parvalbumin-expressing fast-spiking inhibitory interneurons innervated by the VPM thalamus with random connectivity, without or with 1600 low-firing excitatory neurons. Above threshold, the population-average firing rate of inhibitory cortical neurons increases linearly with the thalamic firing rate. The coefficient of variation CV is somewhat less than 1. Moderate levels of synchrony are induced by converging VPM inputs and by inhibitory interaction among neurons. The strengths of excitatory and inhibitory currents during whisking are about three times larger than threshold. We identify values of numbers of presynaptic neurons, synaptic delays between inhibitory neurons, and electrical coupling within the experimentally plausible ranges for which spike synchrony levels are low. Heterogeneity in in-degrees increases the width of the firing rate distribution to the experimentally observed value. We conclude that an L4 circuit in the low-synchrony regime exhibits qualitative dynamical properties similar to those of balanced networks.

Synaptic integration in cortical inhibitory neuron dendrites

Cortical inhibitory interneurons have a wide range of important functions, including balancing network excitation, enhancing spike-time precision of principal neurons, and synchronizing neural activity within and across brain regions. All these functions critically depend on the integration of synaptic inputs in their dendrites. But the sparse number of inhibitory cells, their small caliber dendrites, and the problem of cell-type identification, have prevented fast progress in analyzing their dendritic properties. Despite these challenges, recent advancements in electrophysiological, optical and molecular tools have opened the door for studying synaptic integration and dendritic computations in molecularly defined inhibitory interneurons. Accumulating evidence indicates that the biophysical properties of inhibitory neuron dendrites differ substantially from those of pyramidal neurons. In addition to the supralinear dendritic integration commonly observed in pyramidal neurons, interneuron dendrites can also integrate synaptic inputs in a linear or sublinear fashion. In this comprehensive review, we compare the dendritic biophysical properties of the three major classes of cortical inhibitory neurons and discuss how these cell type-specific properties may support their functions in the cortex.

Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity

Rhythmic neuronal activity of multiple frequency bands has been described in many brain areas and attributed to numerous brain functions. Among these, little is known about the mechanism and role of infra-slow oscillations, which have been demonstrated recently in the mouse accessory olfactory bulb (AOB). Along with prolonged responses to stimuli and distinct network connectivity, they inexplicably affect the AOB processing of social relevant stimuli. Here, we show that assemblies of AOB mitral cells are synchronized by lateral interactions through chemical and electrical synapses. Using a network model, we demonstrate that the synchronous oscillations in these assemblies emerge from interplay between intrinsic membrane properties and network connectivity. As a consequence, the AOB network topology, in which each mitral cell receives input from multiple glomeruli, enables integration of chemosensory stimuli over extended time scales by interglomerular synchrony of infra-slow bursting. These results provide a possible functional significance for the distinct AOB physiology and topology. Beyond the AOB, this study presents a general model for synchronous infra-slow bursting in neuronal networks.SIGNIFICANCE STATEMENT Infra-slow rhythmic neuronal activity with a very long (>10 s) duration has been described in many brain areas, but little is known about the role of this activity and the mechanisms that produce it. Here, we combine experimental and computational methods to show that synchronous infra-slow bursting activity in mitral cells of the mouse accessory olfactory bulb (AOB) emerges from interplay between intracellular dynamics and network connectivity. In this novel mechanism, slow intracellular Na⁺ dynamics endow AOB mitral cells with a weak tendency to burst, which is further enhanced and stabilized by chemical and electrical synapses between them. Combined with the unique topology of the AOB network, infra-slow bursting enables integration and binding of multiple chemosensory stimuli over a prolonged time scale.