A quantitative description of dendritic conductances and its application to dendritic excitation in layer 5 pyramidal neurons

A Multimodal Fitting Approach to Construct Single-Neuron Models With Patch Clamp and High-Density Microelectrode Arrays

In computational neuroscience, multicompartment models are among the most biophysically realistic representations of single neurons. Constructing such models usually involves the use of the patch-clamp technique to record somatic voltage signals under different experimental conditions. The experimental data are then used to fit the many parameters of the model. While patching of the soma is currently the gold-standard approach to build multicompartment models, several studies have also evidenced a richness of dynamics in dendritic and axonal sections. Recording from the soma alone makes it hard to observe and correctly parameterize the activity of nonsomatic compartments. In order to provide a richer set of data as input to multicompartment models, we here investigate the combination of somatic patch-clamp recordings with recordings of high-density microelectrode arrays (HD-MEAs). HD-MEAs enable the observation of extracellular potentials and neural activity of neuronal compartments at subcellular resolution. In this work, we introduce a novel framework to combine patch-clamp and HD-MEA data to construct multicompartment models. We first validate our method on a ground-truth model with known parameters and show that the use of features extracted from extracellular signals, in addition to intracellular ones, yields models enabling better fits than using intracellular features alone. We also demonstrate our procedure using experimental data by constructing cell models from in vitro cell cultures. The proposed multimodal fitting procedure has the potential to augment the modeling efforts of the computational neuroscience community and provide the field with neuronal models that are more realistic and can be better validated.

Kinetics and functional consequences of BK channels activation by N-type Ca2+ channels in the dendrite of mouse neocortical layer-5 pyramidal neurons

The back-propagation of an action potential (AP) from the axon/soma to the dendrites plays a central role in dendritic integration. This process involves an intricate orchestration of various ion channels, but a comprehensive understanding of the contribution of each channel type remains elusive. In this study, we leverage ultrafast membrane potential recordings (Vm) and Ca2+ imaging techniques to shed light on the involvement of N-type voltage-gated Ca2+ channels (VGCCs) in layer-5 neocortical pyramidal neurons' apical dendrites. We found a selective interaction between N-type VGCCs and large-conductance Ca2+-activated K+ channels (BK CAKCs). Remarkably, we observe that BK CAKCs are activated within a mere 500 μs after the AP peak, preceding the peak of the Ca2+ current triggered by the AP. Consequently, when N-type VGCCs are inhibited, the early broadening of the AP shape amplifies the activity of other VGCCs, leading to an augmented total Ca2+ influx. A NEURON model, constructed to replicate and support these experimental results, reveals the critical coupling between N-type and BK channels. This study not only redefines the conventional role of N-type VGCCs as primarily involved in presynaptic neurotransmitter release but also establishes their distinct and essential function as activators of BK CAKCs in neuronal dendrites. Furthermore, our results provide original functional validation of a physical interaction between Ca2+ and K+ channels, elucidated through ultrafast kinetic reconstruction. This insight enhances our understanding of the intricate mechanisms governing neuronal signaling and may have far-reaching implications in the field.

Toward a holographic brain paradigm: a lipid-centric model of brain functioning

Due to the stimulation of neuronal membrane dipoles by action potentials, under suitable conditions coherent dipole oscillations can be formed. We argue that these dipole oscillations satisfy the weak Bose-Einstein condensate criteria of the Froehlich model of biological coherence. They can subsequently generate electromagnetic fields (EMFs) propagating in the inter-neuronal space. When neighboring neurons fire synchronously, EMFs can create interference patterns and hence form holographic images containing analog information about the sensory inputs that trigger neuronal activity. The mirror pattern projected by EMFs inside the neuron can encode information in the neuronal cytoskeleton. We outline an experimental verification of our hypothesis and its consequences for anesthesia, neurodegenerative diseases, and psychiatric states.

Hyperpolarization-Activated Cation Channels Shape the Spiking Frequency Preference of Human Cortical Layer 5 Pyramidal Neurons

Discerning the contribution of specific ionic currents to complex neuronal dynamics is a difficult, but important, task. This challenge is exacerbated in the human setting, although the widely characterized uniqueness of the human brain compared with preclinical models necessitates the direct study of human neurons. Neuronal spiking frequency preference is of particular interest given its role in rhythm generation and signal transmission in cortical circuits. Here, we combine the frequency-dependent gain (FDG), a measure of spiking frequency preference, and novel in silico analyses to dissect the contributions of individual ionic currents to the suprathreshold features of human layer 5 (L5) neurons captured by the FDG. We confirm that a contemporary model of such a neuron, primarily constrained to capture subthreshold activity driven by the hyperpolarization-activated cyclic nucleotide gated (h-) current, replicates key features of the in vitro FDG both with and without h-current activity. With the model confirmed as a viable approximation of the biophysical features of interest, we applied new analysis techniques to quantify the activity of each modeled ionic current in the moments before spiking, revealing unique dynamics of the h-current. These findings motivated patch-clamp recordings in analogous rodent neurons to characterize their FDG, which confirmed that a biophysically detailed model of these neurons captures key interspecies differences in the FDG. These differences are correlated with distinct contributions of the h-current to neuronal activity. Together, this interdisciplinary and multispecies study provides new insights directly relating the dynamics of the h-current to suprathreshold spiking frequency preference in human L5 neurons.

A biophysical and statistical modeling paradigm for connecting neural physiology and function

To understand single neuron computation, it is necessary to know how specific physiological parameters affect neural spiking patterns that emerge in response to specific stimuli. Here we present a computational pipeline combining biophysical and statistical models that provides a link between variation in functional ion channel expression and changes in single neuron stimulus encoding. More specifically, we create a mapping from biophysical model parameters to stimulus encoding statistical model parameters. Biophysical models provide mechanistic insight, whereas statistical models can identify associations between spiking patterns and the stimuli they encode. We used public biophysical models of two morphologically and functionally distinct projection neuron cell types: mitral cells (MCs) of the main olfactory bulb, and layer V cortical pyramidal cells (PCs). We first simulated sequences of action potentials according to certain stimuli while scaling individual ion channel conductances. We then fitted point process generalized linear models (PP-GLMs), and we constructed a mapping between the parameters in the two types of models. This framework lets us detect effects on stimulus encoding of changing an ion channel conductance. The computational pipeline combines models across scales and can be applied as a screen of channels, in any cell type of interest, to identify ways that channel properties influence single neuron computation.

Morphological Features of Human Dendritic Spines

Dendritic spine features in human neurons follow the up-to-date knowledge presented in the previous chapters of this book. Human dendrites are notable for their heterogeneity in branching patterns and spatial distribution. These data relate to circuits and specialized functions. Spines enhance neuronal connectivity, modulate and integrate synaptic inputs, and provide additional plastic functions to microcircuits and large-scale networks. Spines present a continuum of shapes and sizes, whose number and distribution along the dendritic length are diverse in neurons and different areas. Indeed, human neurons vary from aspiny or "relatively aspiny" cells to neurons covered with a high density of intermingled pleomorphic spines on very long dendrites. In this chapter, we discuss the phylogenetic and ontogenetic development of human spines and describe the heterogeneous features of human spiny neurons along the spinal cord, brainstem, cerebellum, thalamus, basal ganglia, amygdala, hippocampal regions, and neocortical areas. Three-dimensional reconstructions of Golgi-impregnated dendritic spines and data from fluorescence microscopy are reviewed with ultrastructural findings to address the complex possibilities for synaptic processing and integration in humans. Pathological changes are also presented, for example, in Alzheimer's disease and schizophrenia. Basic morphological data can be linked to current techniques, and perspectives in this research field include the characterization of spines in human neurons with specific transcriptome features, molecular classification of cellular diversity, and electrophysiological identification of coexisting subpopulations of cells. These data would enlighten how cellular attributes determine neuron type-specific connectivity and brain wiring for our diverse aptitudes and behavior.

The effect of alterations of schizophrenia-associated genes on gamma band oscillations

Abnormalities in the synchronized oscillatory activity of neurons in general and, specifically in the gamma band, might play a crucial role in the pathophysiology of schizophrenia. While these changes in oscillatory activity have traditionally been linked to alterations at the synaptic level, we demonstrate here, using computational modeling, that common genetic variants of ion channels can contribute strongly to this effect. Our model of primary auditory cortex highlights multiple schizophrenia-associated genetic variants that reduce gamma power in an auditory steady-state response task. Furthermore, we show that combinations of several of these schizophrenia-associated variants can produce similar effects as the more traditionally considered synaptic changes. Overall, our study provides a mechanistic link between schizophrenia-associated common genetic variants, as identified by genome-wide association studies, and one of the most robust neurophysiological endophenotypes of schizophrenia.

Excitatory and inhibitory effects of HCN channel modulation on excitability of layer V pyramidal cells

Dendrites of cortical pyramidal cells are densely populated by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, a.k.a. Ih channels. Ih channels are targeted by multiple neuromodulatory pathways, and thus are one of the key ion-channel populations regulating the pyramidal cell activity. Previous observations and theories attribute opposing effects of the Ih channels on neuronal excitability due to their mildly hyperpolarized reversal potential. These effects are difficult to measure experimentally due to the fine spatiotemporal landscape of the Ih activity in the dendrites, but computational models provide an efficient tool for studying this question in a reduced but generalizable setting. In this work, we build upon existing biophysically detailed models of thick-tufted layer V pyramidal cells and model the effects of over- and under-expression of Ih channels as well as their neuromodulation. We show that Ih channels facilitate the action potentials of layer V pyramidal cells in response to proximal dendritic stimulus while they hinder the action potentials in response to distal dendritic stimulus at the apical dendrite. We also show that the inhibitory action of the Ih channels in layer V pyramidal cells is due to the interactions between Ih channels and a hot zone of low voltage-activated Ca2+ channels at the apical dendrite. Our simulations suggest that a combination of Ih-enhancing neuromodulation at the proximal part of the apical dendrite and Ih-inhibiting modulation at the distal part of the apical dendrite can increase the layer V pyramidal excitability more than either of the two alone. Our analyses uncover the effects of Ih-channel neuromodulation of layer V pyramidal cells at a single-cell level and shed light on how these neurons integrate information and enable higher-order functions of the brain.

Layer-specific pyramidal neuron properties underlie diverse anterior cingulate cortical motor and limbic networks

The laminar cellular and circuit mechanisms by which the anterior cingulate cortex (ACC) exerts flexible control of motor and affective information for goal-directed behavior have not been elucidated. Using multimodal tract-tracing, in vitro patch-clamp recording and computational approaches in rhesus monkeys (M. mulatta), we provide evidence that specialized motor and affective network dynamics can be conferred by layer-specific biophysical and structural properties of ACC pyramidal neurons targeting two key downstream structures -the dorsal premotor cortex (PMd) and the amygdala (AMY). AMY-targeting neurons exhibited significant laminar differences, with L5 more excitable (higher input resistance and action potential firing rates) than L3 neurons. Between-pathway differences were found within L5, with AMY-targeting neurons exhibiting greater excitability, apical dendritic complexity, spine densities, and diversity of inhibitory inputs than PMd-targeting neurons. Simulations using a pyramidal-interneuron network model predict that these layer- and pathway-specific single-cell differences contribute to distinct network oscillatory dynamics. L5 AMY-targeting networks are more tuned to slow oscillations well-suited for affective and contextual processing timescales, while PMd-targeting networks showed strong beta/gamma synchrony implicated in rapid sensorimotor processing. These findings are fundamental to our broad understanding of how layer-specific cellular and circuit properties can drive diverse laminar activity found in flexible behavior.

Kinetic and thermodynamic modeling of a voltage-gated sodium channel

Like all biological and chemical reactions, ion channel kinetics are highly sensitive to changes in temperature. Therefore, it is prudent to investigate channel dynamics at physiological temperatures. However, most ion channel investigations are performed at room temperature due to practical considerations, such as recording stability and technical limitations. This problem is especially severe for the fast voltage-gated sodium channel, whose activation kinetics are faster than the time constant of the standard patch-clamp amplifier at physiological temperatures. Thus, biologically detailed simulations of the action potential generation evenly scale the kinetic models of voltage-gated channels acquired at room temperature. To quantitatively study voltage-gated sodium channels' temperature sensitivity, we recorded sodium currents from nucleated patches extracted from the rat's layer five neocortical pyramidal neurons at several temperatures from 13.5 to 30 °C. We use these recordings to model the kinetics of the voltage-gated sodium channel as a function of temperature. We show that the temperature dependence of activation differs from that of inactivation. Furthermore, the data indicate that the sustained current has a different temperature dependence than the fast current. Our kinetic and thermodynamic analysis of the current provided a numerical model spanning the entire temperature range. This model reproduced vital features of channel activation and inactivation. Furthermore, the model also reproduced action potential dependence on temperature. Thus, we provide an essential building block for the generation of biologically detailed models of cortical neurons.

(-)-Naringenin 4',7-dimethyl Ether Isolated from Nardostachys jatamansi Relieves Pain through Inhibition of Multiple Channels

(−)-Naringenin 4′,7-dimethyl ether ((−)-NRG-DM) was isolated for the first time by our lab from Nardostachys jatamansi DC, a traditional medicinal plant frequently used to attenuate pain in Asia. As a natural derivative of analgesic, the current study was designed to test the potential analgesic activity of (−)-NRG-DM and its implicated mechanism. The analgesic activity of (−)-NRG-DM was assessed in a formalin-induced mouse inflammatory pain model and mustard oil-induced mouse colorectal pain model, in which the mice were intraperitoneally administrated with vehicle or (−)-NRG-DM (30 or 50 mg/kg) (n = 10 for each group). Our data showed that (−)-NRG-DM can dose dependently (30~50 mg/kg) relieve the pain behaviors. Notably, (−)-NRG-DM did not affect motor coordination in mice evaluated by the rotarod test, in which the animals were intraperitoneally injected with vehicle or (−)-NRG-DM (100, 200, or 400 mg/kg) (n = 10 for each group). In acutely isolated mouse dorsal root ganglion neurons, (−)-NRG-DM (1~30 μM) potently dampened the stimulated firing, reduced the action potential threshold and amplitude. In addition, the neuronal delayed rectifier potassium currents (I_K) and voltage-gated sodium currents (I_Na) were significantly suppressed. Consistently, (−)-NRG-DM dramatically inhibited heterologously expressed Kv2.1 and Nav1.8 channels which represent the major components of the endogenous I_K and I_Na. A pharmacokinetic study revealed the plasma concentration of (−)-NRG-DM is around 7 µM, which was higher than the effective concentrations for the I_K and I_Na. Taken together, our study showed that (−)-NRG-DM is a potential analgesic candidate with inhibition of multiple neuronal channels (mediating I_K and I_Na).

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.

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.

Unique properties of dually innervated dendritic spines in pyramidal neurons of the somatosensory cortex uncovered by 3D correlative light and electron microscopy

Pyramidal neurons (PNs) are covered by thousands of dendritic spines receiving excitatory synaptic inputs. The ultrastructure of dendritic spines shapes signal compartmentalization, but ultrastructural diversity is rarely taken into account in computational models of synaptic integration. Here, we developed a 3D correlative light-electron microscopy (3D-CLEM) approach allowing the analysis of specific populations of synapses in genetically defined neuronal types in intact brain circuits. We used it to reconstruct segments of basal dendrites of layer 2/3 PNs of adult mouse somatosensory cortex and quantify spine ultrastructural diversity. We found that 10% of spines were dually innervated and 38% of inhibitory synapses localized to spines. Using our morphometric data to constrain a model of synaptic signal compartmentalization, we assessed the impact of spinous versus dendritic shaft inhibition. Our results indicate that spinous inhibition is locally more efficient than shaft inhibition and that it can decouple voltage and calcium signaling, potentially impacting synaptic plasticity.

The Subcortical-Allocortical- Neocortical continuum for the Emergence and Morphological Heterogeneity of Pyramidal Neurons in the Human Brain

Human cortical and subcortical areas integrate emotion, memory, and cognition when interpreting various environmental stimuli for the elaboration of complex, evolved social behaviors. Pyramidal neurons occur in developed phylogenetic areas advancing along with the allocortex to represent 70-85% of the neocortical gray matter. Here, we illustrate and discuss morphological features of heterogeneous spiny pyramidal neurons emerging from specific amygdaloid nuclei, in CA3 and CA1 hippocampal regions, and in neocortical layers II/III and V of the anterolateral temporal lobe in humans. Three-dimensional images of Golgi-impregnated neurons were obtained using an algorithm for the visualization of the cell body, dendritic length, branching pattern, and pleomorphic dendritic spines, which are specialized plastic postsynaptic units for most excitatory inputs. We demonstrate the emergence and development of human pyramidal neurons in the cortical and basomedial (but not the medial, MeA) nuclei of the amygdala with cells showing a triangular cell body shape, basal branched dendrites, and a short apical shaft with proximal ramifications as "pyramidal-like" neurons. Basomedial neurons also have a long and distally ramified apical dendrite not oriented to the pial surface. These neurons are at the beginning of the allocortex and the limbic lobe. "Pyramidal-like" to "classic" pyramidal neurons with laminar organization advance from the CA3 to the CA1 hippocampal regions. These cells have basal and apical dendrites with specific receptive synaptic domains and several spines. Neocortical pyramidal neurons in layers II/III and V display heterogeneous dendritic branching patterns adapted to the space available and the afferent inputs of each brain area. Dendritic spines vary in their distribution, density, shapes, and sizes (classified as stubby/wide, thin, mushroom-like, ramified, transitional forms, "atypical" or complex forms, such as thorny excrescences in the MeA and CA3 hippocampal region). Spines were found isolated or intermingled, with evident particularities (e.g., an extraordinary density in long, deep CA1 pyramidal neurons), and some showing a spinule. We describe spiny pyramidal neurons considerably improving the connectional and processing complexity of the brain circuits. On the other hand, these cells have some vulnerabilities, as found in neurodegenerative Alzheimer's disease and in temporal lobe epilepsy.

HippoUnit: A software tool for the automated testing and systematic comparison of detailed models of hippocampal neurons based on electrophysiological data

Anatomically and biophysically detailed data-driven neuronal models have become widely used tools for understanding and predicting the behavior and function of neurons. Due to the increasing availability of experimental data from anatomical and electrophysiological measurements as well as the growing number of computational and software tools that enable accurate neuronal modeling, there are now a large number of different models of many cell types available in the literature. These models were usually built to capture a few important or interesting properties of the given neuron type, and it is often unknown how they would behave outside their original context. In addition, there is currently no simple way of quantitatively comparing different models regarding how closely they match specific experimental observations. This limits the evaluation, re-use and further development of the existing models. Further, the development of new models could also be significantly facilitated by the ability to rapidly test the behavior of model candidates against the relevant collection of experimental data. We address these problems for the representative case of the CA1 pyramidal cell of the rat hippocampus by developing an open-source Python test suite, which makes it possible to automatically and systematically test multiple properties of models by making quantitative comparisons between the models and electrophysiological data. The tests cover various aspects of somatic behavior, and signal propagation and integration in apical dendrites. To demonstrate the utility of our approach, we applied our tests to compare the behavior of several different rat hippocampal CA1 pyramidal cell models from the ModelDB database against electrophysiological data available in the literature, and evaluated how well these models match experimental observations in different domains. We also show how we employed the test suite to aid the development of models within the European Human Brain Project (HBP), and describe the integration of the tests into the validation framework developed in the HBP, with the aim of facilitating more reproducible and transparent model building in the neuroscience community.

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

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

Modeling Reveals Human-Rodent Differences in H-Current Kinetics Influencing Resonance in Cortical Layer 5 Neurons

While our understanding of human neurons is often inferred from rodent data, inter-species differences between neurons can be captured by building cellular models specifically from human data. This includes understanding differences at the level of ion channels and their implications for human brain function. Thus, we here present a full spiking, biophysically detailed multi-compartment model of a human layer 5 (L5) cortical pyramidal cell. Model development was primarily based on morphological and electrophysiological data from the same human L5 neuron, avoiding confounds of experimental variability. Focus was placed on describing the behavior of the hyperpolarization-activated cation (h-) channel, given increasing interest in this channel due to its role in pacemaking and differentiating cell types. We ensured that the model exhibited post-inhibitory rebound spiking considering its relationship with the h-current, along with other general spiking characteristics. The model was validated against data not used in its development, which highlighted distinctly slower kinetics of the human h-current relative to the rodent setting. We linked the lack of subthreshold resonance observed in human L5 neurons to these human-specific h-current kinetics. This work shows that it is possible and necessary to build human-specific biophysical neuron models in order to understand human brain dynamics.

A Minimal Biophysical Model of Neocortical Pyramidal Cells: Implications for Frontal Cortex Microcircuitry and Field Potential Generation

Ca²⁺ spikes initiated in the distal trunk of layer 5 pyramidal cells (PCs) underlie nonlinear dynamic changes in the gain of cellular response, critical for top-down control of cortical processing. Detailed models with many compartments and dozens of ionic channels can account for this Ca²⁺ spike-dependent gain and associated critical frequency. However, current models do not account for all known Ca²⁺-dependent features. Previous attempts to include more features have required increasing complexity, limiting their interpretability and utility for studying large population dynamics. We overcome these limitations in a minimal two-compartment biophysical model. In our model, a basal-dendrites/somatic compartment included fast-inactivating Na⁺ and delayed-rectifier K⁺ conductances, while an apical-dendrites/trunk compartment included persistent Na⁺, hyperpolarization-activated cation (I _h ), slow-inactivating K⁺, muscarinic K⁺, and Ca²⁺ L-type. The model replicated the Ca²⁺ spike morphology and its critical frequency plus three other defining features of layer 5 PC synaptic integration: linear frequency-current relationships, back-propagation-activated Ca²⁺ spike firing, and a shift in the critical frequency by blocking I _h Simulating 1000 synchronized layer 5 PCs, we reproduced the current source density patterns evoked by Ca²⁺ spikes and describe resulting medial-frontal EEG on a male macaque monkey. We reproduced changes in the current source density when I _h was blocked. Thus, a two-compartment model with five crucial ionic currents in the apical dendrites reproduces all features of these neurons. We discuss the utility of this minimal model to study the microcircuitry of agranular areas of the frontal lobe involved in cognitive control and responsible for event-related potentials, such as the error-related negativity.SIGNIFICANCE STATEMENT A minimal model of layer 5 pyramidal cells replicates all known features crucial for distal synaptic integration in these neurons. By redistributing voltage-gated and returning transmembrane currents in the model, we establish a theoretical framework for the investigation of cortical microcircuit contribution to intracranial local field potentials and EEG. This tractable model will enable biophysical evaluation of multiscale electrophysiological signatures and computational investigation of cortical processing.

An efficient analytical reduction of detailed nonlinear neuron models

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

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.

Alterations in Schizophrenia-Associated Genes Can Lead to Increased Power in Delta Oscillations

Genome-wide association studies have implicated many ion channels in schizophrenia pathophysiology. Although the functions of these channels are relatively well characterized by single-cell studies, the contributions of common variation in these channels to neurophysiological biomarkers and symptoms of schizophrenia remain elusive. Here, using computational modeling, we show that a common biomarker of schizophrenia, namely, an increase in delta-oscillation power, may be a direct consequence of altered expression or kinetics of voltage-gated ion channels or calcium transporters. Our model of a circuit of layer V pyramidal cells highlights multiple types of schizophrenia-related variants that contribute to altered dynamics in the delta-frequency band. Moreover, our model predicts that the same membrane mechanisms that increase the layer V pyramidal cell network gain and response to delta-frequency oscillations may also cause a deficit in a single-cell correlate of the prepulse inhibition, which is a behavioral biomarker highly associated with schizophrenia.

Biophysical Psychiatry-How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders

The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a "biophysical psychiatry," an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.

A Dendritic Substrate for the Cholinergic Control of Neocortical Output Neurons

The ascending cholinergic system dynamically regulates sensory perception and cognitive function, but it remains unclear how this modulation is executed in neocortical circuits. Here, we demonstrate that the cholinergic system controls the integrative operations of neocortical principal neurons by modulating dendritic excitability. Direct dendritic recordings revealed that the optogenetic-evoked release of acetylcholine (ACh) transformed the pattern of dendritic integration in layer 5B pyramidal neurons, leading to the generation of dendritic plateau potentials which powerfully drove repetitive action potential output. In contrast, the synaptic release of ACh did not positively modulate axo-somatic excitability. Mechanistically, the transformation of dendritic integration was mediated by the muscarinic ACh receptor-dependent enhancement of dendritic R-type calcium channel activity, a compartment-dependent modulation which decisively controlled the associative computations executed by layer 5B pyramidal neurons. Our findings therefore reveal a biophysical mechanism by which the cholinergic system controls dendritic computations causally linked to perceptual detection.

Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0

Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Pleiotropic effects of schizophrenia-associated genetic variants in neuron firing and cardiac pacemaking revealed by computational modeling

Schizophrenia patients have an increased risk of cardiac dysfunction. A possible factor underlying this comorbidity are the common variants in the large set of genes that have recently been discovered in genome-wide association studies (GWASs) as risk genes of schizophrenia. Many of these genes control the cell electrogenesis and calcium homeostasis. We applied biophysically detailed models of layer V pyramidal cells and sinoatrial node cells to study the contribution of schizophrenia-associated genes on cellular excitability. By including data from functional genomics literature to simulate the effects of common variants of these genes, we showed that variants of voltage-gated Na⁺ channel or hyperpolarization-activated cation channel-encoding genes cause qualitatively similar effects on layer V pyramidal cell and sinoatrial node cell excitability. By contrast, variants of Ca²⁺ channel or transporter-encoding genes mostly have opposite effects on cellular excitability in the two cell types. We also show that the variants may crucially affect the propagation of the cardiac action potential in the sinus node. These results may help explain some of the cardiac comorbidity in schizophrenia, and may facilitate generation of effective antipsychotic medications without cardiac side-effects such as arrhythmia.

A stepwise neuron model fitting procedure designed for recordings with high spatial resolution: Application to layer 5 pyramidal cells

BACKGROUND

Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level.

NEW METHOD

In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca²⁺ imaging.

RESULT

We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model.

COMPARISON WITH EXISTING METHODS

Our approach combines features from several previously applied model-fitting strategies. The reduced-morphology neuron model obtained using our approach reliably reproduces the membrane-potential dynamics across the dendrites as predicted by the full-morphology model.

CONCLUSIONS

The network models produced using our method are cost-efficient and predict that interconnected L5PCs are able to amplify delta-range oscillatory inputs across a large range of network sizes and topologies, largely due to the medium after hyperpolarization mediated by the Ca²⁺-activated SK current.

Differential Somatic Ca2+ Channel Profile in Midbrain Dopaminergic Neurons

Dopaminergic (DA) neurons located in the ventral midbrain continuously generate a slow endogenous pacemaker activity, the mechanism of which is still debated. It has been suggested that, in the substantia nigra pars compacta (SNc), the pacemaking relies more on Ca(2+) channels and that the density of L-type Ca(2+) channels is higher in these DA neurons than in those located in the ventral tegmental area (VTA). This might lead to a higher Ca(2+) load in SNc DA neurons and explain their higher susceptibility to degeneration. However, direct evidence for this hypothesis is lacking. We found that the L-type current and channel density are indeed higher in the somata of rat SNc DA neurons and that this current undergoes less inactivation in this region. Nonstationary fluctuation analysis measurements showed a much higher number of L-type channels in the soma of SNc DA neurons, as well as a smaller single-channel conductance, pointing to a possible different molecular identity of L-type channels in DA neurons from the two areas. A major consequence of this is that pacemaking and, even more so, bursting are associated with a larger Ca(2+) entry through L-type channels in SNc DA neurons than in their VTA counterparts. Our results establish a molecular and functional difference between two populations of midbrain DA neurons that may contribute to their differential sensitivity to neurodegeneration.

SIGNIFICANCE STATEMENT

Dopamine neurons from the substantia nigra pars compacta (SNc) and ventral tegmental area (VTA) are involved in various brain functions, such as movement initiation and goal directed behavior, respectively. This work shows that, although both neurons fire in a similar regular and slow pacemaker mode, this firing activity is supported by different calcium channel landscapes. Indeed, the L-type calcium current is larger in the soma of dopamine neurons of the SNc, leading to a higher charge transfer through L-type channels during pacemaking and bursting. Therefore, these neurons may be physiologically exposed to a larger stress than their neighbors from the VTA.

Optimizing computer models of corticospinal neurons to replicate in vitro dynamics

Corticospinal neurons (SPI), thick-tufted pyramidal neurons in motor cortex layer 5B that project caudally via the medullary pyramids, display distinct class-specific electrophysiological properties in vitro: strong sag with hyperpolarization, lack of adaptation, and a nearly linear frequency-current (F-I) relationship. We used our electrophysiological data to produce a pair of large archives of SPI neuron computer models in two model classes: 1) detailed models with full reconstruction; and 2) simplified models with six compartments. We used a PRAXIS and an evolutionary multiobjective optimization (EMO) in sequence to determine ion channel conductances. EMO selected good models from each of the two model classes to form the two model archives. Archived models showed tradeoffs across fitness functions. For example, parameters that produced excellent F-I fit produced a less-optimal fit for interspike voltage trajectory. Because of these tradeoffs, there was no single best model but rather models that would be best for particular usages for either single neuron or network explorations. Further exploration of exemplar models with strong F-I fit demonstrated that both the detailed and simple models produced excellent matches to the experimental data. Although dendritic ion identities and densities cannot yet be fully determined experimentally, we explored the consequences of a demonstrated proximal to distal density gradient of I_h, demonstrating that this would lead to a gradient of resonance properties with increased resonant frequencies more distally. We suggest that this dynamical feature could serve to make the cell particularly responsive to major frequency bands that differ by cortical layer.

NEW & NOTEWORTHY

We developed models of motor cortex corticospinal neurons that replicate in vitro dynamics, including hyperpolarization-induced sag and realistic firing patterns. Models demonstrated resonance in response to synaptic stimulation, with resonance frequency increasing in apical dendrites with increasing distance from soma, matching the increasing oscillation frequencies spanning deep to superficial cortical layers. This gradient may enable specific corticospinal neuron dendrites to entrain to relevant oscillations in different cortical layers, contributing to appropriate motor output commands.

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.

Effects of Calcium Spikes in the Layer 5 Pyramidal Neuron on Coincidence Detection and Activity Propagation

The role of dendritic spiking mechanisms in neural processing is so far poorly understood. To investigate the role of calcium spikes in the functional properties of the single neuron and recurrent networks, we investigated a three compartment neuron model of the layer 5 pyramidal neuron with calcium dynamics in the distal compartment. By performing single neuron simulations with noisy synaptic input and occasional large coincident input at either just the distal compartment or at both somatic and distal compartments, we show that the presence of calcium spikes confers a substantial advantage for coincidence detection in the former case and a lesser advantage in the latter. We further show that the experimentally observed critical frequency phenomenon, in which action potentials triggered by stimuli near the soma above a certain frequency trigger a calcium spike at distal dendrites, leading to further somatic depolarization, is not exhibited by a neuron receiving realistically noisy synaptic input, and so is unlikely to be a necessary component of coincidence detection. We next investigate the effect of calcium spikes in propagation of spiking activities in a feed-forward network (FFN) embedded in a balanced recurrent network. The excitatory neurons in the network are again connected to either just the distal, or both somatic and distal compartments. With purely distal connectivity, activity propagation is stable and distinguishable for a large range of recurrent synaptic strengths if the feed-forward connections are sufficiently strong, but propagation does not occur in the absence of calcium spikes. When connections are made to both the somatic and the distal compartments, activity propagation is achieved for neurons with active calcium dynamics at a much smaller number of neurons per pool, compared to a network of passive neurons, but quickly becomes unstable as the strength of recurrent synapses increases. Activity propagation at higher scaling factors can be stabilized by increasing network inhibition or introducing short term depression in the excitatory synapses, but the signal to noise ratio remains low. Our results demonstrate that the interaction of synchrony with dendritic spiking mechanisms can have profound consequences for the dynamics on the single neuron and network level.

Active subthreshold dendritic conductances shape the local field potential

Key points

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Abstract

The main contribution to the local field potential (LFP) is thought to stem from synaptic input to neurons and the ensuing subthreshold dendritic processing. The role of active dendritic conductances in shaping the LFP has received little attention, even though such ion channels are known to affect the subthreshold neuron dynamics. Here we used a modelling approach to investigate the effects of subthreshold dendritic conductances on the LFP. Using a biophysically detailed, experimentally constrained model of a cortical pyramidal neuron, we identified conditions under which subthreshold active conductances are a major factor in shaping the LFP. We found that, in particular, the hyperpolarization‐activated inward current, I_h, can have a sizable effect and cause a resonance in the LFP power spectral density. To get a general, qualitative understanding of how any subthreshold active dendritic conductance and its cellular distribution can affect the LFP, we next performed a systematic study with a simplified model. We found that the effect on the LFP is most pronounced when (1) the synaptic drive to the cell is asymmetrically distributed (i.e. either basal or apical), (2) the active conductances are distributed non‐uniformly with the highest channel densities near the synaptic input and (3) when the LFP is measured at the opposite pole of the cell relative to the synaptic input. In summary, we show that subthreshold active conductances can be strongly reflected in LFP signals, opening up the possibility that the LFP can be used to characterize the properties and cellular distributions of active conductances.

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance

Despite advances in experimental and theoretical neuroscience, we are still trying to identify key biophysical details that are important for characterizing the operation of brain circuits. Biological mechanisms at the level of single neurons and synapses can be combined as 'building blocks' to generate circuit function. We focus on the importance of capturing multiple timescales when describing these intrinsic and synaptic components. Whether inherent in the ionic currents, the neuron's complex morphology, or the neurotransmitter composition of synapses, these multiple timescales prove crucial for capturing the variability and richness of circuit output and enhancing the information-carrying capacity observed across nervous systems.

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.

Modeling the calcium spike as a threshold triggered fixed waveform for synchronous inputs in the fluctuation regime

Modeling the layer 5 pyramidal neuron as a system of three connected isopotential compartments, the soma, proximal, and distal compartment, with calcium spike dynamics in the distal compartment following first order kinetics, we are able to reproduce in-vitro experimental results which demonstrate the involvement of calcium spikes in action potentials generation. To explore how calcium spikes affect the neuronal output in-vivo, we emulate in-vivo like conditions by embedding the neuron model in a regime of low background fluctuations with occasional large synchronous inputs. In such a regime, a full calcium spike is only triggered by the synchronous events in a threshold like manner and has a stereotypical waveform. Hence, in such a regime, we are able to replace the calcium dynamics with a simpler threshold triggered current of fixed waveform, which is amenable to analytical treatment. We obtain analytically the mean somatic membrane potential excursion due to a calcium spike being triggered while in the fluctuating regime. Our analytical form that accounts for the covariance between conductances and the membrane potential shows a better agreement with simulation results than a naive first order approximation.

Branch specific and spike-order specific action potential invasion in basal, oblique, and apical dendrites of cortical pyramidal neurons

In neocortical pyramidal neurons, action potentials (APs) propagate from the axon into the dendritic tree to influence distal synapses. Traditionally, AP backpropagation was studied in the thick apical trunk. Here, we used the principles of optical imaging developed by Cohen to investigate AP invasion into thin dendritic branches (basal, oblique, and tuft) of prefrontal cortical L5 pyramidal neurons. Multisite optical recordings from neighboring dendrites revealed a clear dichotomy between two seemingly equal dendritic branches belonging to the same cell ("sister branches"). We documented the variable efficacy of AP invasion in basal and oblique branches by revealing their AP voltage waveforms. Using fast multisite calcium imaging, we found that trains of APs are filtered differently between two apical tuft branches. Although one dendritic branch passes all spikes in an AP train, another branch belonging to the same neuron, same cortical layer, and same path distance from the cell body, experiences only one spike. Our data indicate that the vast differences in dendritic voltage and calcium transients, detected in dendrites of pyramidal neurons, arise from a nonuniform distribution of A-type [Formula: see text] conductance, an aggregate number of branch points in the path of the AP propagation and minute differences in dendritic diameter.

Computational models in the age of large datasets

Technological advances in experimental neuroscience are generating vast quantities of data, from the dynamics of single molecules to the structure and activity patterns of large networks of neurons. How do we make sense of these voluminous, complex, disparate and often incomplete data? How do we find general principles in the morass of detail? Computational models are invaluable and necessary in this task and yield insights that cannot otherwise be obtained. However, building and interpreting good computational models is a substantial challenge, especially so in the era of large datasets. Fitting detailed models to experimental data is difficult and often requires onerous assumptions, while more loosely constrained conceptual models that explore broad hypotheses and principles can yield more useful insights.

Glutamate-bound NMDARs arising from in vivo-like network activity extend spatio-temporal integration in a L5 cortical pyramidal cell model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such 'background' synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a 'balanced' background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.