Laminar population analysis (LPA) is a method for analysis of electrical data recorded by linear multielectrodes passing through all lamina of cortex. Like principal components analysis (PCA) and independent components analysis (ICA), LPA offers a way to decompose the data into contributions from separate cortical populations. However, instead of using purely mathematical assumptions in the decomposition, LPA is based on physiological constraints, i.e., that the observed LFP (low-frequency part of signal) is driven by action-potential firing as observed in the MUA (multi-unit activity; high-frequency part of the signal). In the presently developed generalized laminar population analysis (gLPA) the set of basis functions accounting for the LFP data is extended compared to the original LPA, thus allowing for a better fit of the model to experimental data. This enhances the risk for overfitting, however, and we therefore tested various versions of gLPA on virtual LFP data in which we knew the ground truth. These synthetic data were generated by biophysical forward-modeling of electrical signals from network activity in the comprehensive, and well-known, thalamocortical network model developed by Traub and coworkers. The results for the Traub model imply that while the laminar components extracted by the original LPA method overall are in fair agreement with the ground-truth laminar components, the results may be improved by use of gLPA method with two (gLPA-2) or even three (gLPA-3) postsynaptic LFP kernels per laminar population.

Educational software (apps) can improve science education by providing an interactive way of learning about complicated topics that are hard to explain with text and static illustrations. However, few educational apps are available for simulation of neural networks. Here, we describe an educational app, Neuronify, allowing the user to easily create and explore neural networks in a plug-and-play simulation environment. The user can pick network elements with adjustable parameters from a menu, i.e., synaptically connected neurons modelled as integrate-and-fire neurons and various stimulators (current sources, spike generators, visual, and touch) and recording devices (voltmeter, spike detector, and loudspeaker). We aim to provide a low entry point to simulation-based neuroscience by allowing students with no programming experience to create and simulate neural networks. To facilitate the use of Neuronify in teaching, a set of premade common network motifs is provided, performing functions such as input summation, gain control by inhibition, and detection of direction of stimulus movement. Neuronify is developed in C++ and QML using the cross-platform application framework Qt and runs on smart phones (Android, iOS) and tablet computers as well personal computers (Windows, Mac, Linux).

Multielectrode array recordings of extracellular electrical field potentials along the depth axis of the cerebral cortex are gaining popularity as an approach for investigating the activity of cortical neuronal circuits. The low-frequency band of extracellular potential, i.e., the local field potential (LFP), is assumed to reflect synaptic activity and can be used to extract the laminar current source density (CSD) profile. However, physiological interpretation of the CSD profile is uncertain because it does not disambiguate synaptic inputs from passive return currents and does not identify population-specific contributions to the signal. These limitations prevent interpretation of the CSD in terms of synaptic functional connectivity in the columnar microcircuit. Here we present a novel anatomically informed model for decomposing the LFP signal into population-specific contributions and for estimating the corresponding activated synaptic projections. This involves a linear forward model, which predicts the population-specific laminar LFP in response to synaptic inputs applied at different positions along each population and a linear inverse model, which reconstructs laminar profiles of synaptic inputs from laminar LFP data based on the forward model. Assuming spatially smooth synaptic inputs within individual populations, the model decomposes the columnar LFP into population-specific contributions and estimates the corresponding laminar profiles of synaptic input as a function of time. It should be noted that constant synaptic currents at all positions along a neuronal population cannot be reconstructed, as this does not result in a change in extracellular potential. However, constraining the solution using a priori knowledge of the spatial distribution of synaptic connectivity provides the further advantage of estimating the strength of active synaptic projections from the columnar LFP profile thus fully specifying synaptic inputs.

Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects.NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

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.

En route from the retina to the cortex, visual information passes through the dorsolateral geniculate nucleus (dLGN) of the thalamus, where extensive corticothalamic (CT) feedback has been suggested to modulate spatial processing. How this modulation arises from direct excitatory and indirect inhibitory CT feedback pathways remains enigmatic. Here, we show that in awake mice, retinotopically organized cortical feedback sharpens receptive fields (RFs) and increases surround suppression in the dLGN. Guided by a network model indicating that widespread inhibitory CT feedback is necessary to reproduce these effects, we targeted the visual sector of the thalamic reticular nucleus (visTRN) for recordings. We found that visTRN neurons have large RFs, show little surround suppression and exhibit strong feedback-dependent responses to large stimuli. These features make them an ideal candidate for mediating feedback-enhanced surround suppression in the dLGN. We conclude that cortical feedback sculpts spatial integration in the dLGN, likely via recruitment of neurons in the visTRN.

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 106 neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials ('spikes') or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin. Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for. The work also constitutes a major advance in computational efficiency of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework.

Voltage imaging and "all-optical electrophysiology" in human induced pluripotent stem cell (hiPSC)-derived neurons have opened unprecedented opportunities for high-throughput phenotyping of activity in neurons possessing unique genetic backgrounds of individual patients. While prior all-optical electrophysiology studies relied on genetically encoded voltage indicators, here, we demonstrate an alternative protocol using a synthetic voltage sensor and genetically encoded optogenetic actuator that generate robust and reproducible results. We demonstrate the functionality of this method by measuring spontaneous and evoked activity in three independent hiPSC-derived neuronal cell lines with distinct genetic backgrounds.

The electroencephalogram (EEG) is a major tool for non-invasively studying brain function and dysfunction. Comparing experimentally recorded EEGs with neural network models is important to better interpret EEGs in terms of neural mechanisms. Most current neural network models use networks of simple point neurons. They capture important properties of cortical dynamics, and are numerically or analytically tractable. However, point neurons cannot generate an EEG, as EEG generation requires spatially separated transmembrane currents. Here, we explored how to compute an accurate approximation of a rodent's EEG with quantities defined in point-neuron network models. We constructed different approximations (or proxies) of the EEG signal that can be computed from networks of leaky integrate-and-fire (LIF) point neurons, such as firing rates, membrane potentials, and combinations of synaptic currents. We then evaluated how well each proxy reconstructed a ground-truth EEG obtained when the synaptic currents of the LIF model network were fed into a three-dimensional network model of multicompartmental neurons with realistic morphologies. Proxies based on linear combinations of AMPA and GABA currents performed better than proxies based on firing rates or membrane potentials. A new class of proxies, based on an optimized linear combination of time-shifted AMPA and GABA currents, provided the most accurate estimate of the EEG over a wide range of network states. The new linear proxies explained 85-95% of the variance of the ground-truth EEG for a wide range of network configurations including different cell morphologies, distributions of presynaptic inputs, positions of the recording electrode, and spatial extensions of the network. Non-linear EEG proxies using a convolutional neural network (CNN) on synaptic currents increased proxy performance by a further 2-8%. Our proxies can be used to easily calculate a biologically realistic EEG signal directly from point-neuron simulations thus facilitating a quantitative comparison between computational models and experimental EEG recordings.

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 key element of the European Union's Human Brain Project (HBP) and other large-scale brain research projects is the simulation of large-scale model networks of neurons. Here, we argue why such simulations will likely be indispensable for bridging the scales between the neuron and system levels in the brain, and why a set of brain simulators based on neuron models at different levels of biological detail should therefore be developed. To allow for systematic refinement of candidate network models by comparison with experiments, the simulations should be multimodal in the sense that they should predict not only action potentials, but also electric, magnetic, and optical signals measured at the population and system levels.

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.

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.

A resurgence has taken place in recent years in the use of the extracellularly recorded local field potential (LFP) to investigate neural network activity. To probe monosynaptic thalamic activation of cortical postsynaptic target cells, so called spike-trigger-averaged LFP (stLFP) signatures have been measured. In these experiments, the cortical LFP is measured by multielectrodes covering several cortical lamina and averaged on spontaneous spikes of thalamocortical (TC) cells. Using a well established forward-modeling scheme, we investigated the biophysical origin of this stLFP signature with simultaneous synaptic activation of cortical layer-4 neurons, mimicking the effect of a single afferent spike from a single TC neuron. Constrained by previously measured intracellular responses of the main postsynaptic target cell types and with biologically plausible assumptions regarding the spatial distribution of thalamic synaptic inputs into layer 4, the model predicted characteristic contributions to monosynaptic stLFP signatures both for the regular-spiking (RS) excitatory neurons and the fast-spiking (FS) inhibitory interneurons. In particular, the FS cells generated stLFP signatures of shorter temporal duration than the RS cells. Added together, a sum of the stLFP signatures of these two principal synaptic targets of TC cells were observed to resemble experimentally measured stLFP signatures. Outside the volume targeted by TC afferents, the resulting postsynaptic LFP signals were found to be sharply attenuated. This implies that such stLFP signatures provide a very local measure of TC synaptic activation, and that newly developed inverse current-source density (CSD)-estimation methods are needed for precise assessment of the underlying spatiotemporal CSD profiles.SIGNIFICANCE STATEMENT Despite its long history and prevalent use, the proper interpretation of the extracellularly recorded local field potential (LFP) is still not fully established. Here we investigate by biophysical modeling the origin of the focal LFP signature of the single-axon monosynaptic thalamocortical connection as measured by spike-trigger-averaging of cortical LFPs on spontaneous spikes of thalamocortical neurons. We find that this LFP signature is well accounted for by a model assuming thalamic projections to two cortical layer-4 cell populations: one excitatory (putatively regular-spiking cells) and one inhibitory (putatively fast-spiking cells). The LFP signature is observed to decay sharply outside the cortical region receiving the thalamocortical projection, implying that it indeed provides a very local measure of thalamocortical synaptic activation.

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.

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.

Firing-rate models provide a practical tool for studying the dynamics of trial- or population-averaged neuronal signals. A wealth of theoretical and experimental studies has been dedicated to the derivation or extraction of such models by investigating the firing-rate response characteristics of ensembles of neurons. The majority of these studies assumes that neurons receive input spikes at a high rate through weak synapses (diffusion approximation). For many biological neural systems, however, this assumption cannot be justified. So far, it is unclear how time-varying presynaptic firing rates are transmitted by a population of neurons if the diffusion assumption is dropped. Here, we numerically investigate the stationary and non-stationary firing-rate response properties of leaky integrate-and-fire neurons receiving input spikes through excitatory synapses with alpha-function shaped postsynaptic currents for strong synaptic weights. Input spike trains are modeled by inhomogeneous Poisson point processes with sinusoidal rate. Average rates, modulation amplitudes, and phases of the period-averaged spike responses are measured for a broad range of stimulus, synapse, and neuron parameters. Across wide parameter regions, the resulting transfer functions can be approximated by a linear first-order low-pass filter. Below a critical synaptic weight, the cutoff frequencies are approximately constant and determined by the synaptic time constants. Only for synapses with unrealistically strong weights are the cutoff frequencies significantly increased. To account for stimuli with larger modulation depths, we combine the measured linear transfer function with the nonlinear response characteristics obtained for stationary inputs. The resulting linear-nonlinear model accurately predicts the population response for a variety of non-sinusoidal stimuli.

Most modeling in systems neuroscience has been descriptive where neural representations such as 'receptive fields', have been found by statistically correlating neural activity to sensory input. In the traditional physics approach to modelling, hypotheses are represented by mechanistic models based on the underlying building blocks of the system, and candidate models are validated by comparing with experiments. Until now validation of mechanistic cortical network models has been based on comparison with neuronal spikes, found from the high-frequency part of extracellular electrical potentials. In this computational study we investigated to what extent the low-frequency part of the signal, the local field potential (LFP), can be used to validate and infer properties of mechanistic cortical network models. In particular, we asked the question whether the LFP can be used to accurately estimate synaptic connection weights in the underlying network. We considered the thoroughly analysed Brunel network comprising an excitatory and an inhibitory population of recurrently connected integrate-and-fire (LIF) neurons. This model exhibits a high diversity of spiking network dynamics depending on the values of only three network parameters. The LFP generated by the network was computed using a hybrid scheme where spikes computed from the point-neuron network were replayed on biophysically detailed multicompartmental neurons. We assessed how accurately the three model parameters could be estimated from power spectra of stationary 'background' LFP signals by application of convolutional neural nets (CNNs). All network parameters could be very accurately estimated, suggesting that LFPs indeed can be used for network model validation.

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

The cerebral cortex is organized in cortical layers that differ in their cellular density, composition, and wiring. Cortical laminar architecture is also readily revealed by staining for cytochrome oxidase-the last enzyme in the respiratory electron transport chain located in the inner mitochondrial membrane. It has been hypothesized that a high-density band of cytochrome oxidase in cortical layer IV reflects higher oxygen consumption under baseline (unstimulated) conditions. Here, we tested the above hypothesis using direct measurements of the partial pressure of O2 (pO2) in cortical tissue by means of 2-photon phosphorescence lifetime microscopy (2PLM). We revisited our previously developed method for extraction of the cerebral metabolic rate of O2 (CMRO2) based on 2-photon pO2 measurements around diving arterioles and applied this method to estimate baseline CMRO2 in awake mice across cortical layers. To our surprise, our results revealed a decrease in baseline CMRO2 from layer I to layer IV. This decrease of CMRO2 with cortical depth was paralleled by an increase in tissue oxygenation. Higher baseline oxygenation and cytochrome density in layer IV may serve as an O2 reserve during surges of neuronal activity or certain metabolically active brain states rather than reflecting baseline energy needs. Our study provides to our knowledge the first quantification of microscopically resolved CMRO2 across cortical layers as a step towards better understanding of brain energy metabolism.