A model of spike initiation in neocortical pyramidal neurons

A spatial model of autophosphorylation of Ca 2+ /calmodulin-dependent protein kinase II in a glutamatergic spine reveals dynamics of kinase activation in the first several seconds after a complex synaptic stimulus

Long-term potentiation (LTP) is a biochemical process in excitatory glutamatergic synapses in the Central Nervous System (CNS). It is initiated by a bout of synaptic activation that is strong enough to contribute to production of an action potential in the axon of the postsynaptic neuron, and it results in an increase in the size of postsynaptic depolarization during subsequent activity. The first step leading to LTP is activation and autophosphorylation of an abundant postsynaptic enzyme, Ca 2+ /calmodulin-dependent protein kinase II (CaMKII). We use simulation of activation of CaMKII holoenzymes in a realistic spatial model of a spine synapse, created in MCell4, to test three hypotheses about how the autophosphorylation response of CaMKII is shaped during a repeated high-frequency stimulus. First, the simulation results indicate that autophosphorylation of CaMKII does not constitute a bistable switch under biologically realistic conditions. Instead, prolonged autophosphorylation of CaMKII may contribute to a biochemical "kinetic proof-reading" mechanism that controls induction of synaptic plasticity. Second, concentration of CaMKII near the postsynaptic membrane increases the local concentration of kinase activity. However, neither localization nor "Ca 2+ -calmodulin-trapping (CaM-trapping)" increase the proportion of autophosphorylated subunits in holoenzymes after a complex stimulus, as previously hypothesized. Finally, we show that, as hypothesized, the amplitude of autophosphorylation in the first 30 seconds after a stimulus is extremely sensitive to the level and location of PP1 activity when PP1 is present in biologically accurate amounts. We further show that prolonged steric hindrance of dephosphorylation of CaMKII, caused by CaM-trapping, can increase the amplitude of autophosphorylation after a complex stimulus. These simulation results sharpen our quantitative understanding of the early events leading to LTP at excitatory synapses.

Author Summary

Neurons in the brain are interconnected in an organized fashion by synapses that transmit neuronal activity from one neuron to another. Most of the billions of neurons in the brain have about 10,000 synapses spread over the neuronal membrane. Information is stored in the brain when the ability of specific synapses to pass along neuronal activity is strengthened resulting in formation of new networks. The increase in strength of a synapse is tightly controlled by the frequency and amplitude of its activity, and by neurohormonal signals, which, in combination, can cause long-lasting biochemical changes at the synapse that underlie learning and memory. Defects in these biochemical pathways cause mental and neurological diseases. To develop treatments, we need to understand the precise choreography of these critical biochemical changes. However, the tiny size of the synaptic compartment makes precise measurements of the biochemical reactions impossible. We have used computer simulation techniques and information gathered from experiments on purified synaptic proteins to simulate, within a single synapse, the choreography of the first biochemical step in synaptic strengthening: activation of the enzyme Ca 2+ / calmodulin-dependent protein kinase II. Our results provide insights that can be used in future studies to develop treatments for neuronal diseases.

Model-based analysis of the acute effects of transcutaneous magnetic spinal cord stimulation on micturition after spinal cord injury in humans

AIM

After spinal cord injuries (SCIs), patients may develop either detrusor-sphincter dyssynergia (DSD) or urinary incontinence, depending on the level of the spinal injury. DSD and incontinence reflect the loss of coordinated neural control among the detrusor muscle, which increases bladder pressure to facilitate urination, and urethral sphincters and pelvic floor muscles, which control the bladder outlet to restrict or permit bladder emptying. Transcutaneous magnetic stimulation (TMS) applied to the spinal cord after SCI reduced DSD and incontinence. We defined, within a mathematical model, the minimum neuronal elements necessary to replicate neurogenic dysfunction of the bladder after a SCI and incorporated into this model the minimum additional neurophysiological features sufficient to replicate the improvements in bladder function associated with lumbar TMS of the spine in patients with SCI.

METHODS

We created a computational model of the neural circuit of micturition based on Hodgkin-Huxley equations that replicated normal bladder function. We added interneurons and increased network complexity to reproduce dysfunctional micturition after SCI, and we increased the density and complexity of interactions of both inhibitory and excitatory lumbar spinal interneurons responsive to TMS to provide a more diverse set of spinal responses to intrinsic and extrinsic activation of spinal interneurons that remains after SCI.

RESULTS

The model reproduced the re-emergence of a spinal voiding reflex after SCI. When we investigated the effect of monophasic and biphasic TMS at two frequencies applied at or below T10, the model replicated the improved coordination between detrusor and external urethral sphincter activity that has been observed clinically: low-frequency TMS (1 Hz) within the model normalized control of voiding after SCI, whereas high-frequency TMS (30 Hz) enhanced urine storage.

CONCLUSION

Neuroplasticity and increased complexity of interactions among lumbar interneurons, beyond what is necessary to simulate normal bladder function, must be present in order to replicate the effects of SCI on control of micturition, and both neuronal and network modifications of lumbar interneurons are essential to understand the mechanisms whereby TMS reduced bladder dysfunction after SCI.

Is the Papez circuit the location of the elusive episodic memory engram?

All of the brain structures and white matter that make up Papez' circuit, as well as the circuit as a whole, are implicated in the literature in episodic memory formation and recall. This paper shows that Papez' circuit has the detailed structure and connectivity that is evidently required to support the episodic memory engram, and that identifying Papez' circuit as the location of the engram answers a number of long-standing questions regarding the role of medial temporal lobe structures in episodic memory. The paper then shows that the process by which the episodic memory engram may be formed is a network-wide Hebbian potentiation termed "racetrack potentiation", whose frequency corresponds to that observed in vivo in humans for memory functions. Further, by considering the microcircuits observed in the medial temporal lobe structures forming Papez' circuit, the paper establishes the neural mechanisms behind the required functions of sensory information storage and recall, pattern completion, pattern separation, and memory consolidation. The paper shows that Papez' circuit has the necessary connectivity to gather the various elements of an episodic memory occurring within Pöppel's experienced time or "quantum of experience". Finally, the paper shows how the memory engram located in Papez' circuit might be central to the formation of a duplicate engram in the cortex enabling consolidation and long-term storage of episodic memories.

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.

Impact on backpropagation of the spatial heterogeneity of sodium channel kinetics in the axon initial segment

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (NaVs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of NaVs with gating properties that are "right-shifted" to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of NaV subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of NaV subtypes in the AIS. We implemented a range of hypothetical NaV distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of NaV subtypes is varied. With axonal stimulation, proximal NaV availability dominates, such that concentrating right-shifted NaVs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted NaVs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of NaV1.2 and NaV1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these NaV subtypes.

Human voltage-gated Na+ and K+ channel properties underlie sustained fast AP signaling

Human cortical pyramidal neurons are large, have extensive dendritic trees, and yet have unexpectedly fast input-output properties: Rapid subthreshold synaptic membrane potential changes are reliably encoded in timing of action potentials (APs). Here, we tested whether biophysical properties of voltage-gated sodium (Na+) and potassium (K+) currents in human pyramidal neurons can explain their fast input-output properties. Human Na+ and K+ currents exhibited more depolarized voltage dependence, slower inactivation, and faster recovery from inactivation compared with their mouse counterparts. Computational modeling showed that despite lower Na+ channel densities in human neurons, the biophysical properties of Na+ channels resulted in higher channel availability and contributed to fast AP kinetics stability. Last, human Na+ channel properties also resulted in a larger dynamic range for encoding of subthreshold membrane potential changes. Thus, biophysical adaptations of voltage-gated Na+ and K+ channels enable fast input-output properties of large human pyramidal neurons.

Compartment-specific dendritic information processing in striatal cholinergic interneurons is reconfigured by peptide neuromodulation

Cholinergic interneurons are central hubs of the striatal neuronal network, controlling information processing in a behavioral-state-dependent manner. It remains unknown, however, how such state transitions influence the integrative properties of these neurons. To address this, we made simultaneous somato-dendritic recordings from identified rodent cholinergic interneurons, revealing that action potentials are initiated at dendritic sites because of a dendritic axonal origin. Functionally, this anatomical arrangement ensured that the action potential initiation threshold was lowest at axon-bearing dendritic sites, a privilege efficacy powerfully accentuated at the hyperpolarized membrane potentials achieved in cholinergic interneurons following salient behavioral stimuli. Experimental analysis revealed the voltage-dependent attenuation of the efficacy of non-axon-bearing dendritic excitatory input was mediated by the recruitment of dendritic potassium channels, a regulatory mechanism that, in turn, was controlled by the pharmacological activation of neurokinin receptors. Together, these results indicate that the neuropeptide microenvironment dynamically controls state- and compartment-dependent dendritic information processing in striatal cholinergic interneurons.

Optimized monophasic pulses with equivalent electric field for rapid-rate transcranial magnetic stimulation

Objective.Transcranial magnetic stimulation (TMS) with monophasic pulses achieves greater changes in neuronal excitability but requires higher energy and generates more coil heating than TMS with biphasic pulses, and this limits the use of monophasic pulses in rapid-rate protocols. We sought to design a stimulation waveform that retains the characteristics of monophasic TMS but significantly reduces coil heating, thereby enabling higher pulse rates and increased neuromodulation effectiveness.Approach.A two-step optimization method was developed that uses the temporal relationship between the electric field (E-field) and coil current waveforms. The model-free optimization step reduced the ohmic losses of the coil current and constrained the error of the E-field waveform compared to a template monophasic pulse, with pulse duration as a second constraint. The second, amplitude adjustment step scaled the candidate waveforms based on simulated neural activation to account for differences in stimulation thresholds. The optimized waveforms were implemented to validate the changes in coil heating.Main results.Depending on the pulse duration and E-field matching constraints, the optimized waveforms produced 12%-75% less heating than the original monophasic pulse. The reduction in coil heating was robust across a range of neural models. The changes in the measured ohmic losses of the optimized pulses compared to the original pulse agreed with numeric predictions.Significance.The first step of the optimization approach was independent of any potentially inaccurate or incorrect model and exhibited robust performance by avoiding the highly nonlinear behavior of neural responses, whereas neural simulations were only run once for amplitude scaling in the second step. This significantly reduced computational cost compared to iterative methods using large populations of candidate solutions and more importantly reduced the sensitivity to the choice of neural model. The reduced coil heating and power losses of the optimized pulses can enable rapid-rate monophasic TMS protocols.

Heterogeneity of voltage gated sodium current density between neurons decorrelates spiking and suppresses network synchronization in Scn1b null mouse models

Voltage gated sodium channels (VGSCs) are required for action potential initiation and propagation in mammalian neurons. As with other ion channel families, VGSC density varies between neurons. Importantly, sodium current (INa) density variability is reduced in pyramidal neurons of Scn1b null mice. Scn1b encodes the VGSC β1/ β1B subunits, which regulate channel expression, trafficking, and voltage dependent properties. Here, we investigate how variable INa density in cortical layer 6 and subicular pyramidal neurons affects spike patterning and network synchronization. Constitutive or inducible Scn1b deletion enhances spike timing correlations between pyramidal neurons in response to fluctuating stimuli and impairs spike-triggered average current pattern diversity while preserving spike reliability. Inhibiting INa with a low concentration of tetrodotoxin similarly alters patterning without impairing reliability, with modest effects on firing rate. Computational modeling shows that broad INa density ranges confer a similarly broad spectrum of spike patterning in response to fluctuating synaptic conductances. Network coupling of neurons with high INa density variability displaces the coupling requirements for synchronization and broadens the dynamic range of activity when varying synaptic strength and network topology. Our results show that INa heterogeneity between neurons potently regulates spike pattern diversity and network synchronization, expanding VGSC roles in the nervous system.

Modeling extracellular stimulation of retinal ganglion cells: theoretical and practical aspects

Objective.Retinal prostheses use electric current to activate inner retinal neurons, providing artificial vision for blind people. Epiretinal stimulation primarily targets retinal ganglion cells (RGCs), which can be modeled with cable equations. Computational models provide a tool to investigate the mechanisms of retinal activation, and improve stimulation paradigms. However, documentation of RGC model structure and parameters is limited, and model implementation can influence model predictions.Approach.We created a functional guide for building a mammalian RGC multi-compartment cable model and applying extracellular stimuli. Next, we investigated how the neuron's three-dimensional shape will influence model predictions. Finally, we tested several strategies to maximize computational efficiency.Main results.We conducted sensitivity analyses to examine how dendrite representation, axon trajectory, and axon diameter influence membrane dynamics and corresponding activation thresholds. We optimized the spatial and temporal discretization of our multi-compartment cable model. We also implemented several simplified threshold prediction theories based on activating function, but these did not match the prediction accuracy achieved by the cable equations.Significance.Through this work, we provide practical guidance for modeling the extracellular stimulation of RGCs to produce reliable and meaningful predictions. Robust computational models lay the groundwork for improving the performance of retinal prostheses.

Ultrafast simulation of large-scale neocortical microcircuitry with biophysically realistic neurons

Understanding the activity of the mammalian brain requires an integrative knowledge of circuits at distinct scales, ranging from ion channel gating to circuit connectomics. Computational models are regularly employed to understand how multiple parameters contribute synergistically to circuit behavior. However, traditional models of anatomically and biophysically realistic neurons are computationally demanding, especially when scaled to model local circuits. To overcome this limitation, we trained several artificial neural network (ANN) architectures to model the activity of realistic multicompartmental cortical neurons. We identified an ANN architecture that accurately predicted subthreshold activity and action potential firing. The ANN could correctly generalize to previously unobserved synaptic input, including in models containing nonlinear dendritic properties. When scaled, processing times were orders of magnitude faster compared with traditional approaches, allowing for rapid parameter-space mapping in a circuit model of Rett syndrome. Thus, we present a novel ANN approach allowing for rapid, detailed network experiments using inexpensive and commonly available computational resources.

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin-Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

Characteristic columnar connectivity caters to cortical computation: Replication, simulation, and evaluation of a microcircuit model

The neocortex, and with it the mammalian brain, achieves a level of computational efficiency like no other existing computational engine. A deeper understanding of its building blocks (cortical microcircuits), and their underlying computational principles is thus of paramount interest. To this end, we need reproducible computational models that can be analyzed, modified, extended and quantitatively compared. In this study, we further that aim by providing a replication of a seminal cortical column model. This model consists of noisy Hodgkin-Huxley neurons connected by dynamic synapses, whose connectivity scheme is based on empirical findings from intracellular recordings. Our analysis confirms the key original finding that the specific, data-based connectivity structure enhances the computational performance compared to a variety of alternatively structured control circuits. For this comparison, we use tasks based on spike patterns and rates that require the systems not only to have simple classification capabilities, but also to retain information over time and to be able to compute nonlinear functions. Going beyond the scope of the original study, we demonstrate that this finding is independent of the complexity of the neuron model, which further strengthens the argument that it is the connectivity which is crucial. Finally, a detailed analysis of the memory capabilities of the circuits reveals a stereotypical memory profile common across all circuit variants. Notably, the circuit with laminar structure does not retain stimulus any longer than any other circuit type. We therefore conclude that the model's computational advantage lies in a sharper representation of the stimuli.

Motor learning drives dynamic patterns of intermittent myelination on learning-activated axons

Myelin plasticity occurs when newly formed and pre-existing oligodendrocytes remodel existing patterns of myelination. Myelin remodeling occurs in response to changes in neuronal activity and is required for learning and memory. However, the link between behavior-induced neuronal activity and circuit-specific changes in myelination remains unclear. Using longitudinal in vivo two-photon imaging and targeted labeling of learning-activated neurons in mice, we explore how the pattern of intermittent myelination is altered on individual cortical axons during learning of a dexterous reach task. We show that behavior-induced myelin plasticity is targeted to learning-activated axons and occurs in a staged response across cortical layers in the mouse primary motor cortex. During learning, myelin sheaths retract, which results in lengthening of nodes of Ranvier. Following motor learning, addition of newly formed myelin sheaths increases the number of continuous stretches of myelination. Computational modeling suggests that motor learning-induced myelin plasticity initially slows and subsequently increases axonal conduction speed. Finally, we show that both the magnitude and timing of nodal and myelin dynamics correlate with improvement of behavioral performance during motor learning. Thus, learning-induced and circuit-specific myelination changes may contribute to information encoding in neural circuits during motor learning.

Quantitative analysis of the GABAergic innervation of the soma and axon initial segment of pyramidal cells in the human and mouse neocortex

Perisomatic GABAergic innervation in the cerebral cortex is carried out mostly by basket and chandelier cells, which differentially participate in the control of pyramidal cell action potential output and synchronization. These cells establish multiple synapses with the cell body (and proximal dendrites) and the axon initial segment (AIS) of pyramidal neurons, respectively. Using multiple immunofluorescence, confocal microscopy and 3D quantification techniques, we have estimated the number and density of GABAergic boutons on the cell body and AIS of pyramidal neurons located through cortical layers of the human and mouse neocortex. The results revealed, in both species, that there is clear variability across layers regarding the density and number of perisomatic GABAergic boutons. We found a positive linear correlation between the surface area of the soma, or the AIS, and the number of GABAergic terminals in apposition to these 2 neuronal domains. Furthermore, the density of perisomatic GABAergic boutons was higher in the human cortex than in the mouse. These results suggest a selectivity for the GABAergic innervation of the cell body and AIS that might be related to the different functional attributes of the microcircuits in which neurons from different layers are involved in both human and mouse.

Dendritic Morphology Affects the Velocity and Amplitude of Back-propagating Action Potentials

The back-propagating action potential (bpAP) is crucial for neuronal signal integration and synaptic plasticity in dendritic trees. Its properties (velocity and amplitude) can be affected by dendritic morphology. Due to limited spatial resolution, it has been difficult to explore the specific propagation process of bpAPs along dendrites and examine the influence of dendritic morphology, such as the dendrite diameter and branching pattern, using patch-clamp recording. By taking advantage of Optopatch, an all-optical electrophysiological method, we made detailed recordings of the real-time propagation of bpAPs in dendritic trees. We found that the velocity of bpAPs was not uniform in a single dendrite, and the bpAP velocity differed among distinct dendrites of the same neuron. The velocity of a bpAP was positively correlated with the diameter of the dendrite on which it propagated. In addition, when bpAPs passed through a dendritic branch point, their velocity decreased significantly. Similar to velocity, the amplitude of bpAPs was also positively correlated with dendritic diameter, and the attenuation patterns of bpAPs differed among different dendrites. Simulation results from neuron models with different dendritic morphology corresponded well with the experimental results. These findings indicate that the dendritic diameter and branching pattern significantly influence the properties of bpAPs. The diversity among the bpAPs recorded in different neurons was mainly due to differences in dendritic morphology. These results may inspire the construction of neuronal models to predict the propagation of bpAPs in dendrites with enormous variation in morphology, to further illuminate the role of bpAPs in neuronal communication.

Single-neuron models linking electrophysiology, morphology, and transcriptomics across cortical cell types

Which cell types constitute brain circuits is a fundamental question, but establishing the correspondence across cellular data modalities is challenging. Bio-realistic models allow probing cause-and-effect and linking seemingly disparate modalities. Here, we introduce a computational optimization workflow to generate 9,200 single-neuron models with active conductances. These models are based on 230 in vitro electrophysiological experiments followed by morphological reconstruction from the mouse visual cortex. We show that, in contrast to current belief, the generated models are robust representations of individual experiments and cortical cell types as defined via cellular electrophysiology or transcriptomics. Next, we show that differences in specific conductances predicted from the models reflect differences in gene expression supported by single-cell transcriptomics. The differences in model conductances, in turn, explain electrophysiological differences observed between the cortical subclasses. Our computational effort reconciles single-cell modalities that define cell types and enables causal relationships to be examined.

Scaling and Benchmarking an Evolutionary Algorithm for Constructing Biophysical Neuronal Models

Single neuron models are fundamental for computational modeling of the brain's neuronal networks, and understanding how ion channel dynamics mediate neural function. A challenge in defining such models is determining biophysically realistic channel distributions. Here, we present an efficient, highly parallel evolutionary algorithm for developing such models, named NeuroGPU-EA. NeuroGPU-EA uses CPUs and GPUs concurrently to simulate and evaluate neuron membrane potentials with respect to multiple stimuli. We demonstrate a logarithmic cost for scaling the stimuli used in the fitting procedure. NeuroGPU-EA outperforms the typically used CPU based evolutionary algorithm by a factor of 10 on a series of scaling benchmarks. We report observed performance bottlenecks and propose mitigation strategies. Finally, we also discuss the potential of this method for efficient simulation and evaluation of electrophysiological waveforms.

Controlling synchronization of gamma oscillations by astrocytic modulation in a model hippocampal neural network

Recent in vitro and in vivo experiments demonstrate that astrocytes participate in the maintenance of cortical gamma oscillations and recognition memory. However, the mathematical understanding of the underlying dynamical mechanisms remains largely incomplete. Here we investigate how the interplay of slow modulatory astrocytic signaling with fast synaptic transmission controls coherent oscillations in the network of hippocampal interneurons that receive inputs from pyramidal cells. We show that the astrocytic regulation of signal transmission between neurons improves the firing synchrony and extends the region of coherent oscillations in the biologically relevant values of synaptic conductance. Astrocyte-mediated potentiation of inhibitory synaptic transmission markedly enhances the coherence of network oscillations over a broad range of model parameters. Astrocytic regulation of excitatory synaptic input improves the robustness of interneuron network gamma oscillations induced by physiologically relevant excitatory model drive. These findings suggest a mechanism, by which the astrocytes become involved in cognitive function and information processing through modulating fast neural network dynamics.

Evolution of the Wilson-Cowan equations

The Wilson-Cowan equations were developed to provide a simplified yet powerful description of neural network dynamics. As such, they embraced nonlinear dynamics, but in an interpretable form. Most importantly, it was the first mathematical formulation to emphasize the significance of interactions between excitatory and inhibitory neural populations, thereby incorporating both cooperation and competition. Subsequent research by many has documented the Wilson-Cowan significance in such diverse fields as visual hallucinations, memory, binocular rivalry, and epilepsy. The fact that these equations are still being used to elucidate a wide range of phenomena attests to their validity as a dynamical approximation to more detailed descriptions of complex neural computations.

A general principle of dendritic constancy: A neuron's size- and shape-invariant excitability

Reducing neuronal size results in less membrane and therefore lower input conductance. Smaller neurons are thus more excitable, as seen in their responses to somatic current injections. However, the impact of a neuron's size and shape on its voltage responses to dendritic synaptic activation is much less understood. Here we use analytical cable theory to predict voltage responses to distributed synaptic inputs in unbranched cables, showing that these are entirely independent of dendritic length. For a given synaptic density, neuronal responses depend only on the average dendritic diameter and intrinsic conductivity. This remains valid for a wide range of morphologies irrespective of their arborization complexity. Spiking models indicate that morphology-invariant numbers of spikes approximate the percentage of active synapses. In contrast to spike rate, spike times do depend on dendrite morphology. In summary, neuronal excitability in response to distributed synaptic inputs is largely unaffected by dendrite length or complexity.

Neural excitability increases with axonal resistance between soma and axon initial segment

The position of the axon initial segment (AIS) is thought to play a critical role in neuronal excitability. Previous experimental studies have found that a distal shift in AIS position correlates with a reduction in excitability. Yet theoretical work has suggested the opposite, because of increased electrical isolation. A distal shift in AIS position corresponds to an elevation of axial resistance R _a We therefore examined how changes in R _a at the axon hillock impact the voltage threshold (V_th) of the somatic action potential in L5 pyramidal neurons. Increasing R _a by mechanically pinching the axon between the soma and the AIS was found to lower V_th by ∼6 mV. Conversely, decreasing R _a by substituting internal ions with higher mobility elevated V_th All R _a -dependent changes in V_th could be reproduced in a Hodgkin-Huxley compartmental model. We conclude that in L5 pyramidal neurons, excitability increases with axial resistance and therefore with a distal shift of the AIS.

The dendrite arbor of Purkinje cells is altered following to tail regeneration in the leopard gecko

Purkinje cells of the cerebellum have a complex arborized arrangement of dendrites and are amongst the most distinctive cell types of the nervous system. Although the neuromorphology of Purkinje cells has been well described for some mammals and teleost fish, for most vertebrates less is known. Here we used a modified Golgi-Cox method to investigate the neuromorphology of Purkinje cells from the lizard Eublepharis macularius, the leopard gecko. Using Sholl and Branch Structure Analyses, we sought to investigate whether the neuromorphology of gecko Purkinje cells was altered is response to tail loss and regeneration. Tail loss is an evolved mechanism commonly used by geckos to escape predation. Loss of the tail represents a significant and sudden change in body length and mass, which is only partially recovered as the tail is regenerated. We predicted that tail loss and regeneration would induce a quantifiable change in Purkinje cell dendrite arborization. Post hoc comparisons of Sholl analyses data showed that geckos with regenerated tails have significant changes in dendrite diameter and the number of dendrite intersections in regions corresponding to the position of parallel fiber synapses. We propose that the neuromorphological alterations observed in gecko Purkinje cells represent a compensatory response to tail regrowth, and perhaps a role in motor learning.

Influence of Neuronal Morphology on the Shape of Extracellular Recordings With Microelectrode Arrays: A Finite Element Analysis

OBJECTIVE

Measuring neuronal cell activity using microelectrode arrays reveals a great variety of derived signal shapes within extracellular recordings. However, possible mechanisms responsible for this variety have not yet been entirely determined, which might hamper any subsequent analysis of the recorded neuronal data.

METHODS

To investigate this issue, we propose a computational model based on the finite element method describing the electrical coupling between an electrically active neuron and an extracellular recording electrode in detail. This allows for a systematic study of possible parameters that may play an essential role in defining or altering the shape of the measured electrode potential.

RESULTS

Our results indicate that neuronal geometry, neurite structure, as well as the actual pathways of input potentials that evoke action potential generation, have a significant impact on the shape of the resulting extracellular electrode recording and explain most of the known variations of signal shapes.

CONCLUSION

The presented models offer a comprehensive insight into the effect of geometrical and morphological factors on the resulting electrode signal.

SIGNIFICANCE

Computational modeling complemented with experimental measurements shows much promise to yield meaningful insights into the electrical activity of a neuronal network.

Asynchronous release sites align with NMDA receptors in mouse hippocampal synapses

Neurotransmitter is released synchronously and asynchronously following an action potential. Our recent study indicates that the release sites of these two phases are segregated within an active zone, with asynchronous release sites enriched near the center in mouse hippocampal synapses. Here we demonstrate that synchronous and asynchronous release sites are aligned with AMPA receptor and NMDA receptor clusters, respectively. Computational simulations indicate that this spatial and temporal arrangement of release can lead to maximal membrane depolarization through AMPA receptors, alleviating the pore-blocking magnesium leading to greater activation of NMDA receptors. Together, these results suggest that release sites are likely organized to activate NMDA receptors efficiently.

Drosophila Voltage-Gated Sodium Channels Are Only Expressed in Active Neurons and Are Localized to Distal Axonal Initial Segment-like Domains

In multipolar vertebrate neurons, action potentials (APs) initiate close to the soma, at the axonal initial segment. Invertebrate neurons are typically unipolar with dendrites integrating directly into the axon. Where APs are initiated in the axons of invertebrate neurons is unclear. Voltage-gated sodium (NaV) channels are a functional hallmark of the axonal initial segment in vertebrates. We used an intronic Minos-Mediated Integration Cassette to determine the endogenous gene expression and subcellular localization of the sole NaV channel in both male and female Drosophila, para Despite being the only NaV channel in the fly, we show that only 23 ± 1% of neurons in the embryonic and larval CNS express para, while in the adult CNS para is broadly expressed. We generated a single-cell transcriptomic atlas of the whole third instar larval brain to identify para expressing neurons and show that it positively correlates with markers of differentiated, actively firing neurons. Therefore, only 23 ± 1% of larval neurons may be capable of firing NaV-dependent APs. We then show that Para is enriched in an axonal segment, distal to the site of dendritic integration into the axon, which we named the distal axonal segment (DAS). The DAS is present in multiple neuron classes in both the third instar larval and adult CNS. Whole cell patch clamp electrophysiological recordings of adult CNS fly neurons are consistent with the interpretation that Nav-dependent APs originate in the DAS. Identification of the distal NaV localization in fly neurons will enable more accurate interpretation of electrophysiological recordings in invertebrates.SIGNIFICANCE STATEMENT The site of action potential (AP) initiation in invertebrates is unknown. We tagged the sole voltage-gated sodium (NaV) channel in the fly, para, and identified that Para is enriched at a distal axonal segment. The distal axonal segment is located distal to where dendrites impinge on axons and is the likely site of AP initiation. Understanding where APs are initiated improves our ability to model neuronal activity and our interpretation of electrophysiological data. Additionally, para is only expressed in 23 ± 1% of third instar larval neurons but is broadly expressed in adults. Single-cell RNA sequencing of the third instar larval brain shows that para expression correlates with the expression of active, differentiated neuronal markers. Therefore, only 23 ± 1% of third instar larval neurons may be able to actively fire NaV-dependent APs.

Capturing Multiple Timescales of Adaptation to Second-Order Statistics With Generalized Linear Models: Gain Scaling and Fractional Differentiation

Single neurons can dynamically change the gain of their spiking responses to take into account shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), to account for these adaptive effects. The GLM describes spiking as a Poisson process whose rate depends on a linear combination of the stimulus and recent spike history. The GLM successfully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs when the ratio of spike-generating potassium and sodium conductances approaches one. Gain scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus envelope, which has been observed in neurons that include long timescale afterhyperpolarization conductances. Fractional differentiation in GLMs requires long spike history that span several seconds. Together, these results demonstrate that the GLM provides a tractable statistical approach for examining single-neuron adaptive computations in response to changes in stimulus variance.

Tailoring of the axon initial segment shapes the conversion of synaptic inputs into spiking output in OFF-α T retinal ganglion cells

Recently, mouse OFF-α transient (OFF-α T) retinal ganglion cells (RGCs) were shown to display a gradient of light responses as a function of position along the dorsal-ventral axis; response differences were correlated to differences in the level of excitatory presynaptic input. Here, we show that postsynaptic differences between cells also make a strong contribution to response differences. Cells in the dorsal retina had longer axon initial segments (AISs)-the greater number of Na_v1.6 channels in longer AISs directly mediates higher rates of spiking and helps avoid depolarization block that terminates spiking in ventral cells with shorter AISs. The pre- and postsynaptic specializations that shape the output of OFF-α T RGCs interact in different ways: In dorsal cells, strong inputs and the long AISs are both necessary to generate their strong, sustained spiking outputs, while in ventral cells, weak inputs or the short AISs are both sufficient to limit the spiking signal.

Axonal Na+ channels detect and transmit levels of input synchrony in local brain circuits

Sensory processing requires mechanisms of fast coincidence detection to discriminate synchronous from asynchronous inputs. Spike threshold adaptation enables such a discrimination but is ineffective in transmitting this information to the network. We show here that presynaptic axonal sodium channels read and transmit precise levels of input synchrony to the postsynaptic cell by modulating the presynaptic action potential (AP) amplitude. As a consequence, synaptic transmission is facilitated at cortical synapses when the presynaptic spike is produced by synchronous inputs. Using dual soma-axon recordings, imaging, and modeling, we show that this facilitation results from enhanced AP amplitude in the axon due to minimized inactivation of axonal sodium channels. Quantifying local circuit activity and using network modeling, we found that spikes induced by synchronous inputs produced a larger effect on network activity than spikes induced by asynchronous inputs. Therefore, this input synchrony-dependent facilitation may constitute a powerful mechanism, regulating synaptic transmission at proximal synapses.

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na⁺, K⁺, Ca²⁺, and Cl⁻), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

Cooperative Phase Adaptation and Amplitude Amplification of Neuronal Activity in the Vagal Complex: An Interplay Between Microcircuits and Macrocircuits

Clusters of neurons can communicate with others through the cross-frequency coupling mechanism of oscillatory synchrony. We addressed the hypothesis that neuronal networks at various levels from micro- to macrocircuits implement this communication strategy. An abundance of local recurrent axons of vagal complex (VC) cells establish dense local microcircuits and seem to generate high-frequency noise-causing stochastic resonance (reverberation) and coherence resonance, even in in vitro slice preparations. These phenomena were observed in vitro as the generation of episodes of higher-frequency noise after an external stimulation and as stimulus-induced or spontaneous high-amplitude signals (postsynaptic activities). The in vitro microcircuit networks rarely sustained the stochastic resonance and coherence resonance cooperatively; however, in vivo networks involving additional intrabulbar mesocircuits and large-scale macrocircuits were able to sustain them cooperatively. This gave rise to large-scale oscillatory synchrony leading to robust power and coherence of signals with high amplitudes, reaching several millivolts in amplitude from a noise level of ~100 microV through cardiorespiratory frequency coupling. A regenerative mechanism of neuronal circuits might work for the generation of large-scale oscillatory synchrony. The amplitude and phase of neuronal activity in vivo may interact cooperatively to give rise to varying degrees of power and coherence of robust rhythmic activity for distinct physiological roles. The cooperative interaction between phase adaptation and amplitude amplification of neuronal activity may provide diverse nervous systems with both robustness and resilience.

Biophysical reconstruction of the signal conduction underlying short-latency cortical evoked potentials generated by subthalamic deep brain stimulation

OBJECTIVE

Direct activation of the hyperdirect (HD) pathway has been linked to therapeutic benefit from subthalamic deep brain stimulation (DBS) for the treatment of Parkinson's disease (PD). We sought to quantify the axonal conduction biophysics of corticofugal axons directly stimulated by subthalamic DBS and reconcile those findings with short-latency cortical evoked potential (EP) results.

METHODS

We used a detailed computational model of human subthalamic DBS to quantify axonal activation and conduction. Signal propagation to cortex was evaluated for medium (5.7 µm), large (10.0 µm), and exceptionally large (15.0 µm) diameter corticofugal axons associated with either internal capsule (IC) fibers of passage or the HD pathway. We then compared the modeling results to human cortical EP measurements that have described an exceptionally fast component (EP0) occurring ~1 ms after the stimulus pulse, a fast component (EP1) at ~3 ms, and a slower component (EP2) at ~5 ms.

RESULTS

Subthalamic stimulation of the HD pathway with large and medium diameter axons propagated action potentials to cortex with timings that coincide with the EP1 and EP2 signals, respectively. Only direct activation of exceptionally large diameter fibers in the IC generated signals that could approach the EP0 timing. However, the action potential biophysics do not generally support the existence of a cortical EP less than 1.5 ms after DBS onset.

CONCLUSIONS

The EP1 and EP2 signals can be biophysically linked to antidromic activation of the HD pathway.

SIGNIFICANCE

Theoretical reconstruction of cortical EPs from subthalamic DBS demonstrate a convergence of anatomical, biophysical, and electrophysiological results.

Scaling of the AIS and Somatodendritic Compartments in α S RGCs

The anatomical properties of the axon initial segment (AIS) are tailored in certain types of CNS neurons to help optimize different aspects of neuronal function. Here, we questioned whether the AISs of retinal ganglion cells (RGC) were similarly customized, and if so, whether they supported specific RGC functions. To explore this, we measured the AIS properties in alpha sustained RGCs (α S RGCs) of mouse; α S RGCs sizes vary systematically along the nasal temporal axis of the retina, making these cells an attractive population with which to study potential correlations between AIS properties and cell size. Measurements of AIS length as well as distance from the soma revealed that both were scaled to cell size, i.e., cells with large dendritic fields had long AISs that were relatively far from the soma. Within the AIS, the percentage of Na v 1.6 voltage-gated sodium channels remained highly consistent, regardless of cell size or other AIS properties. Although ON RGCs were slightly larger than OFF cells at any given location of the retina, the level of scaling and relative distribution of voltage-gated sodium channels were highly similar. Computational modeling revealed that AIS scaling influenced spiking thresholds, spike rate as well as the kinetics of individual action potentials, Interestingly, the effect of individual features of the AIS varied for different neuronal functions, e.g., AIS length had a larger effect on the efficacy by which the AIS initiated spike triggered the somatic spike than it did on repetitive spiking. The polarity of the effect varied for different properties, i.e., increases to soma size increased spike threshold while increases to AIS length decreased threshold. Thus, variations in the relative level of scaling for individual components could fine tune threshold or other neuronal functions. Light responses were highly consistent across the full range of cell sizes suggesting that scaling may post-synaptically shape response stability, e.g., in addition to several well-known pre-synaptic contributors.

The Impact of Frequency Scale on the Response Sensitivity and Reliability of Cortical Neurons to 1/fβ Input Signals

What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f0 power spectrum, pink noise 1/f, and brown noises 1/f2) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f0 with short-term correlations for a broad frequency range, and also higher than 1/f2 for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f0 white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.

Analysis of upper threshold mechanisms of spherical neurons during extracellular stimulation

Exceeding a certain stimulation strength can prevent the generation of somatic action potentials, as has been demonstrated in vitro with extracellularly stimulated dorsal root ganglion cells as well as retinal ganglion cells. This phenomenon, termed upper threshold, is currently thought to be a consequence of sodium current reversal in strongly depolarized regions. Here we analyze the contribution of membrane kinetics, using spherical model neurons that are stimulated externally with a microelectrode, in more detail. During extracellular pulse application, the electric field depolarizes one part and hyperpolarizes the other part of the cell. Strong transmembrane currents are generated only in the active depolarized region, changing the overall polarization level. The asymmetric membrane voltage distribution caused by the stimulus strongly influences the cell's behavior during and even after the stimulus. Effects on membrane voltage and transmembrane currents during and after the stimulus are shown and discussed in detail. Aside from the sodium current reversal, two more key mechanisms were identified in causing the upper threshold: strong potassium currents and inactivation of sodium channels. The contributions of the mechanisms involved strongly depend on cell properties, stimulus parameters, and other factors such as temperature. The conclusions presented here are based on several retinal ganglion cell models of the Fohlmeister group, a model with original Hodgkin-Huxley membrane, and a pyramidal cell model. NEW & NOTEWORTHY The upper threshold phenomenon in extracellular stimulation is analyzed in detail for spherical cells. Three main mechanisms were identified that prevent the generation of action potentials at high stimulation strengths: 1) strong potassium currents, 2) inactivating sodium ion channels, and 3) sodium current reversal. Ion channel kinetics in retinal ganglion cells, pyramidal cells, and the original Hodgkin-Huxley model were investigated under the influence of an extracellular stimulus.

The Axon Initial Segment is the Dominant Contributor to the Neuron's Extracellular Electrical Potential Landscape

Extracellular voltage fields, produced by a neuron's action potentials, provide a widely used means for studying neuronal and neuronal-network function. The neuron's soma and dendrites are thought to drive the extracellular action potential (EAP) landscape, while the axon's contribution is usually considered less important. However, by recording voltages of single neurons in dissociated rat cortical cultures and Purkinje cells in acute mouse cerebellar slices through hundreds of densely packed electrodes, it is found, instead, that the axon initial segment dominates the measured EAP landscape, and, surprisingly, the soma only contributes to a minor extent. As expected, the recorded dominant signal has negative polarity (charge entering the cell) and initiates at the distal end. Interestingly, signals with positive polarity (charge exiting the cell) occur near some but not all dendritic branches and occur after a delay. Such basic knowledge about which neuronal compartments contribute to the extracellular voltage landscape is important for interpreting results from all electrical readout schemes. Finally, initiation of the electrical activity at the distal end of the axon initial segment (AIS) and subsequent spreading into the axon proper and backward through the proximal AIS toward the soma are confirmed. The corresponding extracellular waveforms across different neuronal compartments could be tracked.

How does the presence of neural probes affect extracellular potentials?

OBJECTIVE

Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them.

APPROACH

We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes' presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials.

MAIN RESULTS

Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation.

SIGNIFICANCE

Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.

Stimulus dynamics-dependent information transfer of olfactory and vomeronasal sensory neurons in mice

The parallel processing of chemical signals by the main olfactory system and the vomeronasal system has been known to control animal behavior. The physiological significance of peripheral parallel pathways consisting of olfactory sensory neurons and vomeronasal sensory neurons is not well understood. Here, we show complementary characteristics of the information transfer of the olfactory sensory neurons and vomeronasal sensory neurons. A difference in excitability between the sensory neurons was revealed by patch-clamp experiments. The olfactory and vomeronasal sensory neurons showed phasic and tonic firing, respectively. Intrinsic channel kinetics determining firing patterns was demonstrated by a Hodgkin-Huxley-style computation. Our estimation of the information carried by action potentials during one cycle of sinusoidal stimulation with variable durations revealed distinct characteristics of information transfer between the sensory neurons. Phasic firing of the olfactory sensory neurons was suitable to carry information about rapid changes in a shorter cycle (<200 ms). In contrast, tonic firing of the vomeronasal sensory neurons was able to convey information about smaller stimuli changing slowly with longer cycles (>500 ms). Thus, the parallel pathways of the two types of sensory neurons can convey information about a wide range of dynamic stimuli. A combination of complementary characteristics of olfactory information transfer may enhance the synergy of the interaction between the main olfactory system and the vomeronasal system.

Biophysically realistic neuron models for simulation of cortical stimulation

OBJECTIVE

We implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.

APPROACH

We adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.

MAIN RESULTS

The strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.

SIGNIFICANCE

These results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

An axon initial segment is required for temporal precision in action potential encoding by neuronal populations

Central neurons initiate action potentials (APs) in the axon initial segment (AIS), a compartment characterized by a high concentration of voltage-dependent ion channels and specialized cytoskeletal anchoring proteins arranged in a regular nanoscale pattern. Although the AIS was a key evolutionary innovation in neurons, the functional benefits it confers are not clear. Using a mutation of the AIS cytoskeletal protein βIV-spectrin, we here establish an in vitro model of neurons with a perturbed AIS architecture that retains nanoscale order but loses the ability to maintain a high Na_V density. Combining experiments and simulations, we show that a high Na_V density in the AIS is not required for axonal AP initiation; it is, however, crucial for a high bandwidth of information encoding and AP timing precision. Our results provide the first experimental demonstration of axonal AP initiation without high axonal channel density and suggest that increasing the bandwidth of the neuronal code and, hence, the computational efficiency of network function, was a major benefit of the evolution of the AIS.

Role of sodium channel subtype in action potential generation by neocortical pyramidal neurons

Neocortical pyramidal neurons express several distinct subtypes of voltage-gated Na⁺ channels. In mature cells, Na_v1.6 is the dominant channel subtype in the axon initial segment (AIS) as well as in the nodes of Ranvier. Action potentials (APs) are initiated in the AIS, and it has been proposed that the high excitability of this region is related to the unique characteristics of the Na_v1.6 channel. Knockout or loss-of-function mutation of the Scn8a gene is generally lethal early in life because of the importance of this subtype in noncortical regions of the nervous system. Using the Cre/loxP system, we selectively deleted Na_v1.6 in excitatory neurons of the forebrain and characterized the excitability of Na_v1.6-deficient layer 5 pyramidal neurons by patch-clamp and Na⁺ and Ca²⁺ imaging recordings. We now report that, in the absence of Na_v1.6 expression, the AIS is occupied by Na_v1.2 channels. However, APs are generated in the AIS, and differences in AP propagation to soma and dendrites are minimal. Moreover, the channels that are expressed in the AIS still show a clear hyperpolarizing shift in voltage dependence of activation, compared with somatic channels. The only major difference between Na_v1.6-null and wild-type neurons was a strong reduction in persistent sodium current. We propose that the molecular environment of the AIS confers properties on whatever Na channel subtype is present and that some other benefit must be conferred by the selective axonal presence of the Na_v1.6 channel.

Simulation of electromyographic recordings following transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that enables noninvasive manipulation of neural activity and holds promise in both clinical and basic research settings. The effect of TMS on the motor cortex is often measured by electromyography (EMG) recordings from a small hand muscle. However, the details of how TMS generates responses measured with EMG are not completely understood. We aim to develop a biophysically detailed computational model to study the potential mechanisms underlying the generation of EMG signals following TMS. Our model comprises a feed-forward network of cortical layer 2/3 cells, which drive morphologically detailed layer 5 corticomotoneuronal cells, which in turn project to a pool of motoneurons. EMG signals are modeled as the sum of motor unit action potentials. EMG recordings from the first dorsal interosseous muscle were performed in four subjects and compared with simulated EMG signals. Our model successfully reproduces several characteristics of the experimental data. The simulated EMG signals match experimental EMG recordings in shape and size, and change with stimulus intensity and contraction level as in experimental recordings. They exhibit cortical silent periods that are close to the biological values and reveal an interesting dependence on inhibitory synaptic transmission properties. Our model predicts several characteristics of the firing patterns of neurons along the entire pathway from cortical layer 2/3 cells down to spinal motoneurons and should be considered as a viable tool for explaining and analyzing EMG signals following TMS. NEW & NOTEWORTHY A biophysically detailed model of EMG signal generation following transcranial magnetic stimulation (TMS) is proposed. Simulated EMG signals match experimental EMG recordings in shape and amplitude. Motor-evoked potential and cortical silent period properties match experimental data. The model is a viable tool to analyze, explain, and predict EMG signals following TMS.

Quantitative simulation of extracellular single unit recording from the surface of cortex

OBJECTIVE

Neural recording is important for a wide variety of clinical applications. Until recently, recording from the surface of the brain, even when using micro-electrocorticography (μECoG) arrays, was not thought to enable recording from individual neurons. Recent results suggest that when the surface electrode contact size is sufficiently small, it may be possible to record single neurons from the brain's surface. In this study, we use computational techniques to investigate the ability of surface electrodes to record the activity of single neurons.

APPROACH

The computational model included the rat head, μECoG electrode, two existing multi-compartmental neuron models, and a novel multi-compartmental neuron model derived from patch clamp experiments in layer 1 of the cortex.

MAIN RESULTS

Using these models, we reproduced single neuron recordings from μECoG arrays, and elucidated their possible source. The model resembles the experimental data when spikes originate from layer 1 neurons that are less than 60 μm from the cortical surface. We further used the model to explore the design space for surface electrodes. Although this model does not include biological or thermal noise, the results indicate the electrode contact area should be 100 μm² or smaller to maintain a detectable waveform amplitude. Furthermore, the model shows the width of lateral insulation could be reduced, which may reduce scar formation, while retaining 95% of signal amplitude.

SIGNIFICANCE

Overall, the model suggests single-unit surface recording is limited to neurons in layer 1 and further improvement in electrode design is needed.

Action potential initiation, propagation, and cortical invasion in the hyperdirect pathway during subthalamic deep brain stimulation

BACKGROUND

High frequency (∼130 Hz) deep brain stimulation (DBS) of the subthalamic region is an established clinical therapy for the treatment of late stage Parkinson's disease (PD). Direct modulation of the hyperdirect pathway, defined as cortical layer V pyramidal neurons that send an axon collateral to the subthalamic nucleus (STN), has emerged as a possible component of the therapeutic mechanisms. However, numerous questions remain to be addressed on the basic biophysics of hyperdirect pathway stimulation.

OBJECTIVE

Quantify action potential (AP) initiation, propagation, and cortical invasion in hyperdirect neurons during subthalamic stimulation.

METHODS

We developed an anatomically and electrically detailed computational model of hyperdirect neuron stimulation with explicit representation of the stimulating electric field, axonal response, AP propagation, and synaptic transmission.

RESULTS

We found robust AP propagation throughout the complex axonal arbor of the hyperdirect neuron. Even at therapeutic DBS frequencies, stimulation induced APs could reach all of the intracortical axon terminals with ∼100% fidelity. The functional result of this high frequency axonal driving of the thousands of synaptic connections made by each directly stimulated hyperdirect neuron is a profound synaptic suppression that would effectively disconnect the neuron from the cortical circuitry.

CONCLUSIONS

The synaptic suppression hypothesis integrates the fundamental biophysics of electrical stimulation, axonal transmission, and synaptic physiology to explain a generic mechanism of DBS.

Single synaptic inputs drive high-precision action potentials in parvalbumin expressing GABA-ergic cortical neurons in vivo

A defining feature of cortical layer 2/3 excitatory neurons is their sparse activity, often firing in singlets of action potentials. Local inhibitory neurons are thought to play a major role in regulating sparseness, but which cell types are recruited by single excitatory synaptic inputs is unknown. Using multiple, targeted, in vivo whole-cell recordings, we show that single _uEPSPs have little effect on the firing rates of excitatory neurons and somatostatin-expressing GABA-ergic inhibitory neurons but evoke precisely timed action potentials in parvalbumin-expressing inhibitory neurons. Despite a _uEPSP decay time of 7.8 ms, the evoked action potentials were almost completely restricted to the _uEPSP rising phase (~0.5 ms). Evoked parvalbumin-expressing neuron action potentials go on to inhibit the local excitatory network, thus providing a pathway for single spike evoked disynaptic inhibition which may enforce sparse and precisely timed cortical signaling.

Action potential propagation recorded from single axonal arbors using multielectrode arrays

We report the presence of co-occurring extracellular action potentials (eAPs) from cultured mouse hippocampal neurons among groups of planar electrodes on multielectrode arrays (MEAs). The invariant sequences of eAPs among coactive electrode groups, repeated co-occurrences, and short interelectrode latencies are consistent with action potential propagation in unmyelinated axons. Repeated eAP codetection by multiple electrodes was widespread in all our data records. Codetection of eAPs confirms they result from the same neuron and allows these eAPs to be isolated from all other spikes independently of spike sorting algorithms. We averaged co-occurring events and revealed additional electrodes with eAPs that would otherwise be below detection threshold. We used these eAP cohorts to explore the temperature sensitivity of action potential propagation and the relationship between voltage-gated sodium channel density and propagation velocity. The sequence of eAPs among coactive electrodes "fingerprints" neurons giving rise to these events and identifies them within neuronal ensembles. We used this property and the noninvasive nature of extracellular recording to monitor changes in excitability at multiple points in single axonal arbors simultaneously over several hours, demonstrating independence of axonal segments. Over several weeks, we recorded changes in interelectrode propagation latencies and ongoing changes in excitability in different regions of single axonal arbors. Our work illustrates how repeated eAP co-occurrences can be used to extract physiological data from single axons with low-density MEAs. However, repeated eAP co-occurrences lead to oversampling spikes from single neurons and thus can confound traditional spike-train analysis. NEW & NOTEWORTHY We studied action potential propagation in single axons using low-density multielectrode arrays. We unambiguously identified the neuronal sources of propagating action potentials and recorded extracellular action potentials from several positions within single axonal arbors. We found a surprisingly high density of axonal voltage-gated sodium channels responsible for a high propagation safety factor. Our experiments also demonstrate that excitability in different segments of single axons is regulated independently on timescales from hours to weeks.

Selective Modulation of Axonal Sodium Channel Subtypes by 5-HT1A Receptor in Cortical Pyramidal Neuron

Serotonergic innervation of the prefrontal cortex (PFC) modulates neuronal activity and PFC functions. However, the cellular mechanism for serotonergic modulation of neuronal excitability remains unclear. We performed patch-clamp recording at the axon of layer-5 pyramidal neurons in rodent PFC slices. We found surprisingly that the activation of 5-HT1A receptors selectively inhibits Na+ currents obtained at the axon initial segment (AIS) but not those at the axon trunk. In addition, Na+ channel subtype NaV1.2 but not NaV1.6 at the AIS is selectively modulated by 5-HT1A receptors. Further experiments revealed that the inhibitory effect is attributable to a depolarizing shift of the activation curve and a facilitation of slow inactivation of AIS Na+ currents. Consistently, dual somatic and axonal recording and simulation results demonstrate that the activation of 5-HT1A receptors could decrease the success rate of action potential (AP) backpropagation toward the somatodendritic compartments, enhancing the segregation of axonal and dendritic activities. Together, our results reveal a selective modulation of NaV1.2 distributed at the proximal AIS region and AP backpropagation by 5-HT1A receptors, suggesting a potential mechanism for serotonergic regulation of functional polarization in the dendro-axonal axis, synaptic plasticity and PFC functions.

New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics

During slow-wave sleep, brain electrical activity is dominated by the slow (< 1 Hz) electroencephalogram (EEG) oscillations characterized by the periodic transitions between active (or Up) and silent (or Down) states in the membrane voltage of the cortical and thalamic neurons. Sleep slow oscillation is believed to play critical role in consolidation of recent memories. Past computational studies, based on the Hodgkin-Huxley type neuronal models, revealed possible intracellular and network mechanisms of the neuronal activity during sleep, however, they failed to explore the large-scale cortical network dynamics depending on collective behavior in the large populations of neurons. In this new study, we developed a novel class of reduced discrete time spiking neuron models for large-scale network simulations of wake and sleep dynamics. In addition to the spiking mechanism, the new model implemented nonlinearities capturing effects of the leak current, the Ca²⁺ dependent K⁺ current and the persistent Na⁺ current that were found to be critical for transitions between Up and Down states of the slow oscillation. We applied the new model to study large-scale two-dimensional cortical network activity during slow-wave sleep. Our study explained traveling wave dynamics and characteristic synchronization properties of transitions between Up and Down states of the slow oscillation as observed in vivo in recordings from cats. We further predict a critical role of synaptic noise and slow adaptive currents for spike sequence replay as found during sleep related memory consolidation.