Preserving axosomatic spiking features despite diverse dendritic morphology

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

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

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type. We demonstrate our approach on layer 5 pyramidal cells and study the morpho-electrical variability and in particular, find that morphological variability alone is insufficient to reproduce electrical variability. Overall, this approach provides a strong statistical basis to create detailed models of neurons with controlled variability.

A universal workflow for creation, validation, and generalization of detailed neuronal models

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

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.

Age-dependent increased sag amplitude in human pyramidal neurons dampens baseline cortical activity

Aging involves various neurobiological changes, although their effect on brain function in humans remains poorly understood. The growing availability of human neuronal and circuit data provides opportunities for uncovering age-dependent changes of brain networks and for constraining models to predict consequences on brain activity. Here we found increased sag voltage amplitude in human middle temporal gyrus layer 5 pyramidal neurons from older subjects and captured this effect in biophysical models of younger and older pyramidal neurons. We used these models to simulate detailed layer 5 microcircuits and found lower baseline firing in older pyramidal neuron microcircuits, with minimal effect on response. We then validated the predicted reduced baseline firing using extracellular multielectrode recordings from human brain slices of different ages. Our results thus report changes in human pyramidal neuron input integration properties and provide fundamental insights into the neuronal mechanisms of altered cortical excitability and resting-state activity in human aging.

NeuroGPU: Accelerating multi-compartment, biophysically detailed neuron simulations on GPUs

BACKGROUND

The membrane potential of individual neurons depends on a large number of interacting biophysical processes operating on spatial-temporal scales spanning several orders of magnitude. The multi-scale nature of these processes dictates that accurate prediction of membrane potentials in specific neurons requires the utilization of detailed simulations. Unfortunately, constraining parameters within biologically detailed neuron models can be difficult, leading to poor model fits. This obstacle can be overcome partially by numerical optimization or detailed exploration of parameter space. However, these processes, which currently rely on central processing unit (CPU) computation, often incur orders of magnitude increases in computing time for marginal improvements in model behavior. As a result, model quality is often compromised to accommodate compute resources.

NEW METHOD

Here, we present a simulation environment, NeuroGPU, that takes advantage of the inherent parallelized structure of the graphics processing unit (GPU) to accelerate neuronal simulation.

RESULTS & COMPARISON WITH EXISTING METHODS

NeuroGPU can simulate most biologically detailed models 10-200 times faster than NEURON simulation running on a single core and 5 times faster than GPU simulators (CoreNEURON). NeuroGPU is designed for model parameter tuning and best performs when the GPU is fully utilized by running multiple (> 100) instances of the same model with different parameters. When using multiple GPUs, NeuroGPU can reach to a speed-up of 800 fold compared to single core simulations, especially when simulating the same model morphology with different parameters. We demonstrate the power of NeuoGPU through large-scale parameter exploration to reveal the response landscape of a neuron. Finally, we accelerate numerical optimization of biophysically detailed neuron models to achieve highly accurate fitting of models to simulation and experimental data.

CONCLUSIONS

Thus, NeuroGPU is the fastest available platform that enables rapid simulation of multi-compartment, biophysically detailed neuron models on commonly used computing systems accessible by many scientists.

Reduced inhibition in depression impairs stimulus processing in human cortical microcircuits

Cortical processing depends on finely tuned excitatory and inhibitory connections in neuronal microcircuits. Reduced inhibition by somatostatin-expressing interneurons is a key component of altered inhibition associated with treatment-resistant major depressive disorder (depression), which is implicated in cognitive deficits and rumination, but the link remains to be better established mechanistically in humans. Here we test the effect of reduced somatostatin interneuron-mediated inhibition on cortical processing in human neuronal microcircuits using a data-driven computational approach. We integrate human cellular, circuit, and gene expression data to generate detailed models of human cortical microcircuits in health and depression. We simulate microcircuit baseline and response activity and find a reduced signal-to-noise ratio and increased false/failed detection of stimuli due to a higher baseline activity in depression. We thus apply models of human cortical microcircuits to demonstrate mechanistically how reduced inhibition impairs cortical processing in depression, providing quantitative links between altered inhibition and cognitive deficits.

Block Phenomena During Electric Micro-Stimulation of Pyramidal Cells and Retinal Ganglion Cells

Electric micro-stimulation of the nervous system is a means to restore various body functions. The stimulus amplitude necessary to generate action potentials, the lower threshold (LT), is well characterized for many neuronal populations. However, electric overstimulation above an upper threshold (UT) prevents action potential generation and therefore hinders optimal neuro-rehabilitation. Previous studies demonstrated the impact of the UT in micro-stimulation of retinal ganglion cells (RGCs). The observed phenomenon is mostly explained by (i) reversed sodium ion flow in the soma membrane, and (ii) anodal surround block that hinders spike conduction in strongly hyperpolarized regions of the axon at high stimulus intensities. However, up to now, no detailed study of the nature of these phenomena has been presented, particularly for different cell types. Here, we present computational analyses of LT and UT for layer 5 pyramidal cells (PCs) as well as alpha RGCs. Model neurons were stimulated in close vicinity to the cell body and LTs and UTs as well as the ratio UT/LT were compared. Aside from a simple point source electrode and monophasic stimuli also realistic electrode and pulse configurations were examined. The analysis showed: (i) in RGCs, the soma contributed to action potential initiation and block for small electrode distances, whereas in PCs the soma played no role in LTs or UTs. (ii) In both cell types, action potential always initiated within the axon initial segment at LT. (iii) In contrast to a complete block of spike conductance at UT that occurred in RGCs, an incomplete block of spiking appeared in PC axon collaterals. (iv) PC axon collateral arrangement influenced UTs but had small impact on LTs. (v) Population responses of RGCs change from circular regions of activation to ring-shaped patterns for increasing stimulus amplitude. A better understanding of the stimulation window that can reliably activate target neurons will benefit the future development of neuroprostheses.

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.

GABA B Receptor-Mediated Regulation of Dendro-Somatic Synergy in Layer 5 Pyramidal Neurons

Synergistic interactions between independent synaptic input streams may fundamentally change the action potential (AP) output. Using partial information decomposition, we demonstrate here a substantial contribution of synergy between somatic and apical dendritic inputs to the information in the AP output of L5b pyramidal neurons. Activation of dendritic GABA_B receptors (GABA_BRs), known to decrease APs in vivo, potently decreased synergy and increased somatic control of AP output. Synergy was the result of the voltage-dependence of the transfer resistance between dendrite and soma, which showed a two-fold increase per 28.7 mV dendritic depolarization. GIRK channels activated by dendritic GABA_BRs decreased voltage-dependent transfer resistances and AP output. In contrast, inhibition of dendritic L-type Ca²⁺ channels prevented high-frequency bursts of APs, but did not affect dendro-somatic synergy. Finally, we show that NDNF-positive neurogliaform cells effectively control somatic AP via synaptic activation of dendritic GIRK channels. These results uncover a novel inhibitory mechanism that powerfully gates cellular information flow in the cortex.

Orientation processing by synaptic integration across first-order tactile neurons

Our ability to manipulate objects relies on tactile inputs from first-order tactile neurons that innervate the glabrous skin of the hand. The distal axon of these neurons branches in the skin and innervates many mechanoreceptors, yielding spatially-complex receptive fields. Here we show that synaptic integration across the complex signals from the first-order neuronal population could underlie human ability to accurately (< 3°) and rapidly process the orientation of edges moving across the fingertip. We first derive spiking models of human first-order tactile neurons that fit and predict responses to moving edges with high accuracy. We then use the model neurons in simulating the peripheral neuronal population that innervates a fingertip. We train classifiers performing synaptic integration across the neuronal population activity, and show that synaptic integration across first-order neurons can process edge orientations with high acuity and speed. In particular, our models suggest that integration of fast-decaying (AMPA-like) synaptic inputs within short timescales is critical for discriminating fine orientations, whereas integration of slow-decaying (NMDA-like) synaptic inputs supports discrimination of coarser orientations and maintains robustness over longer timescales. Taken together, our results provide new insight into the computations occurring in the earliest stages of the human tactile processing pathway and how they may be critical for supporting hand function.

Retrieving similar substructures on 3D neuron reconstructions

Since manual tracing is time consuming and the performance of automatic tracing is unstable, it is still a challenging task to generate accurate neuron reconstruction efficiently and effectively. One strategy is generating a reconstruction automatically and then amending its inaccurate parts manually. Aiming at finding inaccurate substructures efficiently, we propose a pipeline to retrieve similar substructures on one or more neuron reconstructions, which are very similar to a marked problematic substructure. The pipeline consists of four steps: getting a marked substructure, constructing a query substructure, generating candidate substructures and retrieving most similar substructures. The retrieval procedure was tested on 163 gold standard reconstructions provided by the BigNeuron project and a reconstruction of a mouse’s large neuron. Experimental results showed that the implementation of the proposed methods is very efficient and all retrieved substructures are very similar to the marked one in numbers of nodes and branches, and degree of curvature.

Experience-Dependent Development of Dendritic Arbors in Mouse Visual Cortex

The dendritic arbor of neurons constrains the pool of available synaptic partners and influences the electrical integration of synaptic currents. Despite these critical functions, our knowledge of the dendritic structure of cortical neurons during early postnatal development and how these dendritic structures are modified by visual experience is incomplete. Here, we present a large-scale dataset of 849 3D reconstructions of the basal arbor of pyramidal neurons collected across early postnatal development in visual cortex of mice of either sex. We found that the basal arbor grew substantially between postnatal day 7 (P7) and P30, undergoing a 45% increase in total length. However, the gross number of primary neurites and dendritic segments was largely determined by P7. Growth from P7 to P30 occurred primarily through extension of dendritic segments. Surprisingly, comparisons of dark-reared and typically reared mice revealed that a net gain of only 15% arbor length could be attributed to visual experience; most growth was independent of experience. To examine molecular contributions, we characterized the role of the activity-regulated small GTPase Rem2 in both arbor development and the maintenance of established basal arbors. We showed that Rem2 is an experience-dependent negative regulator of dendritic segment number during the visual critical period. Acute deletion of Rem2 reduced directionality of dendritic arbors. The data presented here establish a highly detailed, quantitative analysis of basal arbor development that we believe has high utility both in understanding circuit development as well as providing a framework for computationalists wishing to generate anatomically accurate neuronal models.SIGNIFICANCE STATEMENT Dendrites are the sites of the synaptic connections among neurons. Despite their importance for neural circuit function, only a little is known about the postnatal development of dendritic arbors of cortical pyramidal neurons and the influence of experience. Here we show that the number of primary basal dendritic arbors is already established before eye opening, and that these arbors primarily grow through lengthening of dendritic segments and not through addition of dendritic segments. Surprisingly, visual experience has a modest net impact on overall arbor length (15%). Experiments in KO animals revealed that the gene Rem2 is positive regulator of dendritic length and a negative regulator of dendritic segments.

Human in vitro systems for examining synaptic function and plasticity in the brain

The human brain shows remarkable complexity in its cellular makeup and function, which are distinct from nonhuman species, signifying the need for human-based research platforms for the study of human cellular neurophysiology and neuropathology. However, the use of adult human brain tissue for research purposes is hampered by technical, methodological, and accessibility challenges. One of the major problems is the limited number of in vitro systems that, in contrast, are readily available from rodent brain tissue. With recent advances in the optimization of protocols for adult human brain preparations, there is a significant opportunity for neuroscientists to validate their findings in human-based systems. This review addresses the methodological aspects, advantages, and disadvantages of human neuron in vitro systems, focusing on the unique properties of human neurons and synapses in neocortical microcircuits. These in vitro models provide the incomparable advantage of being a direct representation of the neurons that have formed part of the human brain until the point of recording, which cannot be replicated by animal models nor human stem-cell systems. Important distinct cellular mechanisms are observed in human neurons that may underlie the higher order cognitive abilities of the human brain. The use of human brain tissue in neuroscience research also raises important ethical, diversity, and control tissue limitations that need to be considered. Undoubtedly however, these human neuron systems provide critical information to increase the potential of translation of treatments from the laboratory to the clinic in a way animal models are failing to provide.

Diversity of Axonal and Dendritic Contributions to Neuronal Output

Our general understanding of neuronal function is that dendrites receive information that is transmitted to the axon, where action potentials (APs) are initiated and propagated to eventually trigger neurotransmitter release at synaptic terminals. Even though this canonical division of labor is true for a number of neuronal types in the mammalian brain (including neocortical and hippocampal pyramidal neurons or cerebellar Purkinje neurons), many neuronal types do not comply with this classical polarity scheme. In fact, dendrites can be the site of AP initiation and propagation, and even neurotransmitter release. In several interneuron types, all functions are carried out by dendrites as these neurons are devoid of a canonical axon. In this article, we present a few examples of "misbehaving" neurons (with a non-canonical polarity scheme) to highlight the diversity of solutions that are used by mammalian neurons to transmit information. Moreover, we discuss how the contribution of dendrites and axons to neuronal excitability may impose constraints on the morphology of these compartments in specific functional contexts.

Cortical Output Is Gated by Horizontally Projecting Neurons in the Deep Layers

Pyramidal tract neurons (PTs) represent the major output cell type of the mammalian neocortex. Here, we report the origins of the PTs’ ability to respond to a broad range of stimuli with onset latencies that rival or even precede those of their intracortical input neurons. We find that neurons with extensive horizontally projecting axons cluster around the deep-layer terminal fields of primary thalamocortical axons. The strategic location of these corticocortical neurons results in high convergence of thalamocortical inputs, which drive reliable sensory-evoked responses that precede those in other excitatory cell types. The resultant fast and horizontal stream of excitation provides PTs throughout the cortical area with input that acts to amplify additional inputs from thalamocortical and other intracortical populations. The fast onsets and broadly tuned characteristics of PT responses hence reflect a gating mechanism in the deep layers, which assures that sensory-evoked input can be reliably transformed into cortical output.

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Simulations predict in vivo responses for major output cell type of the neocortex

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Simulations reveal strategy how to test the origins of cortical output empirically

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Manipulations confirm that deep-layer corticocortical neurons gate cortical output

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Gating of cortical output originates from deep-layer thalamocortical input stratum

Computational Modeling of Genetic Contributions to Excitability and Neural Coding in Layer V Pyramidal Cells: Applications to Schizophrenia Pathology

Pyramidal cells in layer V of the neocortex are one of the most widely studied neuron types in the mammalian brain. Due to their role as integrators of feedforward and cortical feedback inputs, they are well-positioned to contribute to the symptoms and pathology in mental disorders-such as schizophrenia-that are characterized by a mismatch between the internal perception and external inputs. In this modeling study, we analyze the input/output properties of layer V pyramidal cells and their sensitivity to modeled genetic variants in schizophrenia-associated genes. We show that the excitability of layer V pyramidal cells and the way they integrate inputs in space and time are altered by many types of variants in ion-channel and Ca²⁺ transporter-encoding genes that have been identified as risk genes by recent genome-wide association studies. We also show that the variability in the output patterns of spiking and Ca²⁺ transients in layer V pyramidal cells is altered by these model variants. Importantly, we show that many of the predicted effects are robust to noise and qualitatively similar across different computational models of layer V pyramidal cells. Our modeling framework reveals several aspects of single-neuron excitability that can be linked to known schizophrenia-related phenotypes and existing hypotheses on disease mechanisms. In particular, our models predict that single-cell steady-state firing rate is positively correlated with the coding capacity of the neuron and negatively correlated with the amplitude of a prepulse-mediated adaptation and sensitivity to coincidence of stimuli in the apical dendrite and the perisomatic region of a layer V pyramidal cell. These results help to uncover the voltage-gated ion-channel and Ca²⁺ transporter-associated genetic underpinnings of schizophrenia phenotypes and biomarkers.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

Estimating neuronal conductance model parameters using dynamic action potential clamp

BACKGROUND

Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest.

NEW METHOD

We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well.

RESULTS

Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy.

COMPARISON WITH EXISTING METHODS

Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead.

CONCLUSION

DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Experimentally-constrained biophysical models of tonic and burst firing modes in thalamocortical neurons

Somatosensory thalamocortical (TC) neurons from the ventrobasal (VB) thalamus are central components in the flow of sensory information between the periphery and the cerebral cortex, and participate in the dynamic regulation of thalamocortical states including wakefulness and sleep. This property is reflected at the cellular level by the ability to generate action potentials in two distinct firing modes, called tonic firing and low-threshold bursting. Although the general properties of TC neurons are known, we still lack a detailed characterization of their morphological and electrical properties in the VB thalamus. The aim of this study was to build biophysically-detailed models of VB TC neurons explicitly constrained with experimental data from rats. We recorded the electrical activity of VB neurons (N = 49) and reconstructed morphologies in 3D (N = 50) by applying standardized protocols. After identifying distinct electrical types, we used a multi-objective optimization to fit single neuron electrical models (e-models), which yielded multiple solutions consistent with the experimental data. The models were tested for generalization using electrical stimuli and neuron morphologies not used during fitting. A local sensitivity analysis revealed that the e-models are robust to small parameter changes and that all the parameters were constrained by one or more features. The e-models, when tested in combination with different morphologies, showed that the electrical behavior is substantially preserved when changing dendritic structure and that the e-models were not overfit to a specific morphology. The models and their analysis show that automatic parameter search can be applied to capture complex firing behavior, such as co-existence of tonic firing and low-threshold bursting over a wide range of parameter sets and in combination with different neuron morphologies.

Thalamocortical neurons are one of the main components of the thalamocortical system, which is implicated in key functions including sensory transmission and the transition between brain states. These functions are reflected at the cellular level by the ability to generate action potentials in two distinct modes, called burst and tonic firing. Biophysically-detailed computational modeling of these cells can provide a tool to understand the role of these neurons within thalamocortical circuitry. We started by collecting single cell experimental data by applying standardized experimental procedures in brain slices of the rat. Prior work has demonstrated that biological constraints can be integrated using multi-objective optimization to build biologically realistic models of neurons. Here, we employed similar techniques, but extended them to capture the multiple firing modes of thalamic neurons. We compared the model results with additional experimental data, test their generalization and quantitatively reject those that deviated significantly from the experimental variability. These models can be readily integrated in a data-driven pipeline to reconstruct and simulate circuit activity in the thalamocortical system.

Robustness to Axon Initial Segment Variation Is Explained by Somatodendritic Excitability in Rat Substantia Nigra Dopaminergic Neurons

In many neuronal types, axon initial segment (AIS) geometry critically influences neuronal excitability. Interestingly, the axon of rat SNc dopaminergic (DA) neurons displays a highly variable location and most often arises from an axon-bearing dendrite (ABD). We combined current-clamp somatic and dendritic recordings, outside-out recordings of dendritic sodium and potassium currents, morphological reconstructions and multicompartment modeling on male and female rat SNc DA neurons to determine cell-to-cell variations in AIS and ABD geometry, and their influence on neuronal output (spontaneous pacemaking frequency, action potential [AP] shape). Both AIS and ABD geometries were found to be highly variable from neuron to neuron. Surprisingly, we found that AP shape and pacemaking frequency were independent of AIS geometry. Modeling realistic morphological and biophysical variations helped us clarify this result: in SNc DA neurons, the complexity of the ABD combined with its excitability predominantly define pacemaking frequency and AP shape, such that large variations in AIS geometry negligibly affect neuronal output and are tolerated.SIGNIFICANCE STATEMENT In many neuronal types, axon initial segment (AIS) geometry critically influences neuronal excitability. In the current study, we describe large cell-to-cell variations in AIS length or distance from the soma in rat substantia nigra pars compacta dopaminergic neurons. Using neuronal reconstruction and electrophysiological recordings, we show that this morphological variability does not seem to affect their electrophysiological output, as neither action potential properties nor pacemaking frequency is correlated with AIS morphology. Realistic multicompartment modeling suggests that this robustness to AIS variation is mainly explained by the complexity and excitability of the somatodendritic compartment.

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.

Circuit Robustness to Temperature Perturbation Is Altered by Neuromodulators

In the ocean, the crab Cancer borealis is subject to daily and seasonal temperature changes. Previous work, done in the presence of descending modulatory inputs, had shown that the pyloric rhythm of the crab increases in frequency as temperature increases but maintains its characteristic phase relationships until it "crashes" at extremely high temperatures. To study the interaction between neuromodulators and temperature perturbations, we studied the effects of temperature on preparations from which the descending modulatory inputs were removed. Under these conditions, the pyloric rhythm was destabilized. We then studied the effects of temperature on preparations in the presence of oxotremorine, proctolin, and serotonin. Oxotremorine and proctolin enhanced the robustness of the pyloric rhythm, whereas serotonin made the rhythm less robust. These experiments reveal considerable animal-to-animal diversity in their crash stability, consistent with the interpretation that cryptic differences in many cell and network parameters are revealed by extreme perturbations.

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.

Human Cortical Pyramidal Neurons: From Spines to Spikes via Models

We present detailed models of pyramidal cells from human neocortex, including models on their excitatory synapses, dendritic spines, dendritic NMDA- and somatic/axonal Na⁺ spikes that provided new insights into signal processing and computational capabilities of these principal cells. Six human layer 2 and layer 3 pyramidal cells (HL2/L3 PCs) were modeled, integrating detailed anatomical and physiological data from both fresh and postmortem tissues from human temporal cortex. The models predicted particularly large AMPA- and NMDA-conductances per synaptic contact (0.88 and 1.31 nS, respectively) and a steep dependence of the NMDA-conductance on voltage. These estimates were based on intracellular recordings from synaptically-connected HL2/L3 pairs, combined with extra-cellular current injections and use of synaptic blockers, and the assumption of five contacts per synaptic connection. A large dataset of high-resolution reconstructed HL2/L3 dendritic spines provided estimates for the EPSPs at the spine head (12.7 ± 4.6 mV), spine base (9.7 ± 5.0 mV), and soma (0.3 ± 0.1 mV), and for the spine neck resistance (50–80 MΩ). Matching the shape and firing pattern of experimental somatic Na⁺-spikes provided estimates for the density of the somatic/axonal excitable membrane ion channels, predicting that 134 ± 28 simultaneously activated HL2/L3-HL2/L3 synapses are required for generating (with 50% probability) a somatic Na⁺ spike. Dendritic NMDA spikes were triggered in the model when 20 ± 10 excitatory spinous synapses were simultaneously activated on individual dendritic branches. The particularly large number of basal dendrites in HL2/L3 PCs and the distinctive cable elongation of their terminals imply that ~25 NMDA-spikes could be generated independently and simultaneously in these cells, as compared to ~14 in L2/3 PCs from the rat somatosensory cortex. These multi-sites non-linear signals, together with the large (~30,000) excitatory synapses/cell, equip human L2/L3 PCs with enhanced computational capabilities. Our study provides the most comprehensive model of any human neuron to-date demonstrating the biophysical and computational distinctiveness of human cortical neurons.

Comprehensive Morpho-Electrotonic Analysis Shows 2 Distinct Classes of L2 and L3 Pyramidal Neurons in Human Temporal Cortex

There have been few quantitative characterizations of the morphological, biophysical, and cable properties of neurons in the human neocortex. We employed feature-based statistical methods on a rare data set of 60 3D reconstructed pyramidal neurons from L2 and L3 in the human temporal cortex (HL2/L3 PCs) removed after brain surgery. Of these cells, 25 neurons were also characterized physiologically. Thirty-two morphological features were analyzed (e.g., dendritic surface area, 36 333 ± 18 157 μm²; number of basal trees, 5.55 ± 1.47; dendritic diameter, 0.76 ± 0.28 μm). Eighteen features showed a significant gradual increase with depth from the pia (e.g., dendritic length and soma radius). The other features showed weak or no correlation with depth (e.g., dendritic diameter). The basal dendritic terminals in HL2/L3 PCs are particularly elongated, enabling multiple nonlinear processing units in these dendrites. Unlike the morphological features, the active biophysical features (e.g., spike shapes and rates) and passive/cable features (e.g., somatic input resistance, 47.68 ± 15.26 MΩ, membrane time constant, 12.03 ± 1.79 ms, average dendritic cable length, 0.99 ± 0.24) were depth-independent. A novel descriptor for apical dendritic topology yielded 2 distinct classes, termed hereby as “slim-tufted” and “profuse-tufted” HL2/L3 PCs; the latter class tends to fire at higher rates. Thus, our morpho-electrotonic analysis shows 2 distinct classes of HL2/L3 PCs.

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.

Neural architecture: from cells to circuits

Circuit operations are determined jointly by the properties of the circuit elements and the properties of the connections among these elements. In the nervous system, neurons exhibit diverse morphologies and branching patterns, allowing rich compartmentalization within individual cells and complex synaptic interactions among groups of cells. In this review, we summarize work detailing how neuronal morphology impacts neural circuit function. In particular, we consider example neurons in the retina, cerebral cortex, and the stomatogastric ganglion of crustaceans. We also explore molecular coregulators of morphology and circuit function to begin bridging the gap between molecular and systems approaches. By identifying motifs in different systems, we move closer to understanding the structure-function relationships that are present in neural circuits.

The basis of sharp spike onset in standard biophysical models

In most vertebrate neurons, spikes initiate in the axonal initial segment (AIS). When recorded in the soma, they have a surprisingly sharp onset, as if sodium (Na) channels opened abruptly. The main view stipulates that spikes initiate in a conventional manner at the distal end of the AIS, then progressively sharpen as they backpropagate to the soma. We examined the biophysical models used to substantiate this view, and we found that spikes do not initiate through a local axonal current loop that propagates along the axon, but through a global current loop encompassing the AIS and soma, which forms an electrical dipole. Therefore, the phenomenon is not adequately modeled as the backpropagation of an electrical wave along the axon, since the wavelength would be as large as the entire system. Instead, in these models, we found that spike initiation rather follows the critical resistive coupling model proposed recently, where the Na current entering the AIS is matched by the axial resistive current flowing to the soma. Besides demonstrating it by examining the balance of currents at spike initiation, we show that the observed increase in spike sharpness along the axon is artifactual and disappears when an appropriate measure of rapidness is used; instead, somatic onset rapidness can be predicted from spike shape at initiation site. Finally, we reproduce the phenomenon in a two-compartment model, showing that it does not rely on propagation. In these models, the sharp onset of somatic spikes is therefore not an artifact of observing spikes at the incorrect location, but rather the signature that spikes are initiated through a global soma-AIS current loop forming an electrical dipole.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

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

In the neocortex, inhibitory interneurons of the same subtype are electrically coupled with each other via dendritic gap junctions (GJs). The impact of multiple GJs on the biophysical properties of interneurons and thus on their input processing is unclear. The present experimentally based theoretical study examined GJs in L2/3 large basket cells (L2/3 LBCs) with 3 goals in mind: (1) To evaluate the errors due to GJs in estimating the cable properties of individual L2/3 LBCs and suggest ways to correct these errors when modeling these cells and the networks they form; (2) to bracket the GJ conductance value (0.05-0.25 nS) and membrane resistivity (10 000-40 000 Ω cm(2)) of L2/3 LBCs; these estimates are tightly constrained by in vitro input resistance (131 ± 18.5 MΩ) and the coupling coefficient (1-3.5%) of these cells; and (3) to explore the functional implications of GJs, and show that GJs: (i) dynamically modulate the effective time window for synaptic integration; (ii) improve the axon's capability to encode rapid changes in synaptic inputs; and (iii) reduce the orientation selectivity, linearity index, and phase difference of L2/3 LBCs. Our study provides new insights into the role of GJs and calls for caution when using in vitro measurements for modeling electrically coupled neuronal networks.

Neuron Morphology Influences Axon Initial Segment Plasticity

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels.

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels. It has recently been proposed that neurons use plasticity of AIS length and/or location to regulate their intrinsic excitability. Here we quantify the impact of neuron morphology on AIS plasticity using computational models of simplified and realistic somatodendritic morphologies. In small neurons (e.g., dentate granule neurons), excitability was highest when the AIS was of intermediate length and located adjacent to the soma. Conversely, neurons having larger dendritic trees (e.g., pyramidal neurons) were most excitable when the AIS was longer and/or located away from the soma. For any given somatodendritic morphology, increasing dendritic membrane capacitance and/or conductance favored a longer and more distally located AIS. Overall, changes to AIS length, with corresponding changes in total sodium conductance, were far more effective in regulating neuron excitability than were changes in AIS location, while dendritic capacitance had a larger impact on AIS performance than did dendritic conductance. The somatodendritic influence on AIS performance reflects modest soma-to-AIS voltage attenuation combined with neuron size-dependent changes in AIS input resistance, effective membrane time constant, and isolation from somatodendritic capacitance. We conclude that the impact of AIS plasticity on neuron excitability will depend largely on somatodendritic morphology, and that, in some neurons, a shorter or more distally located AIS may promote, rather than limit, action potential generation.

Functional Effects of Schizophrenia-Linked Genetic Variants on Intrinsic Single-Neuron Excitability: A Modeling Study

BACKGROUND

Recent genome-wide association studies have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior across SCZ-related genes.

METHODS

We applied a biophysically detailed multicompartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used changes in neuron model parameters to represent the effects of these variants.

RESULTS

We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree.

CONCLUSIONS

Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously proposed deficits in synaptic communication and network behavior.

Action potential initiation in a multi-compartmental model with cooperatively gating Na channels in the axon initial segment

Somatic action potentials (AP) of cortical pyramidal neurons have characteristically high onset-rapidness. The onset of the AP waveform is an indirect measure for the ability of a neuron to respond to temporally fast-changing stimuli. Theoretical studies on the pyramidal neuron response usually involves a canonical Hodgkin-Huxley (HH) type ion channel gating model, which assumes statistically independent gating of each individual channel. However, cooperative activity of ion channels are observed for various cell types, meaning that the activity (e.g. opening) of one channel triggers the activity (e.g. opening) of a certain fraction of its neighbors and hence, these groups of channels behave as a unit. In this study, we describe a multi-compartmental conductance-based model with cooperatively gating voltage-gated Na channels in the axon initial segment. Our model successfully reproduced the somatic sharp AP onsets of cortical pyramidal neurons. The onset latencies from the initiation site to the soma and the conduction velocities were also in agreement with the previous experimental studies.

ViSAPy: a Python tool for biophysics-based generation of virtual spiking activity for evaluation of spike-sorting algorithms

BACKGROUND

New, silicon-based multielectrodes comprising hundreds or more electrode contacts offer the possibility to record spike trains from thousands of neurons simultaneously. This potential cannot be realized unless accurate, reliable automated methods for spike sorting are developed, in turn requiring benchmarking data sets with known ground-truth spike times.

NEW METHOD

We here present a general simulation tool for computing benchmarking data for evaluation of spike-sorting algorithms entitled ViSAPy (Virtual Spiking Activity in Python). The tool is based on a well-established biophysical forward-modeling scheme and is implemented as a Python package built on top of the neuronal simulator NEURON and the Python tool LFPy.

RESULTS

ViSAPy allows for arbitrary combinations of multicompartmental neuron models and geometries of recording multielectrodes. Three example benchmarking data sets are generated, i.e., tetrode and polytrode data mimicking in vivo cortical recordings and microelectrode array (MEA) recordings of in vitro activity in salamander retinas. The synthesized example benchmarking data mimics salient features of typical experimental recordings, for example, spike waveforms depending on interspike interval.

COMPARISON WITH EXISTING METHODS

ViSAPy goes beyond existing methods as it includes biologically realistic model noise, synaptic activation by recurrent spiking networks, finite-sized electrode contacts, and allows for inhomogeneous electrical conductivities. ViSAPy is optimized to allow for generation of long time series of benchmarking data, spanning minutes of biological time, by parallel execution on multi-core computers.

CONCLUSION

ViSAPy is an open-ended tool as it can be generalized to produce benchmarking data or arbitrary recording-electrode geometries and with various levels of complexity.

Dendrites impact the encoding capabilities of the axon

This study highlights a new and powerful direct impact of the dendritic tree (the input region of neurons) on the encoding capability of the axon (the output region). We show that the size of the dendritic arbors (its impedance load) strongly modulates the shape of the action potential (AP) onset at the axon initial segment; it is accelerated in neurons with larger dendritic surface area. AP onset rapidness is key in determining the capability of the axonal spikes to encode (phase lock to) rapid changes in synaptic inputs. Hence, our findings imply that neurons with larger dendritic arbors have improved encoding capabilities. This "dendritic size effect" was explored both analytically as well as numerically, in simplified and detailed models of 3D reconstructed layer 2/3 cortical pyramidal cells of rats and humans. The cutoff frequency of spikes phase locking to modulated inputs increased from 100 to 200 Hz in pyramidal cells of young rats to 400-600 Hz in human cells. In the latter case, phase locking reached close to 1 KHz in in vivo-like conditions. This work highlights new and functionally profound cross talk between the dendritic tree and the axon initial segment, providing new understanding of neurons as sophisticated nonlinear input/output devices.

The Green's function formalism as a bridge between single- and multi-compartmental modeling

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks use point-neurons-neurons without a morphological component-as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal computation. In this work, we present an approach to model an artificial synapse that mimics dendritic processing without the need to explicitly simulate dendritic dynamics. The model synapse employs an analytic solution for the cable equation to compute the neuron's membrane potential following dendritic inputs. Green's function formalism is used to derive the closed version of the cable equation. We show that by using this synapse model, point-neurons can achieve results that were previously limited to the realms of multi-compartmental models. Moreover, a computational advantage is achieved when only a small number of simulated synapses impinge on a morphologically elaborate neuron. Opportunities and limitations are discussed.