Abstract There is an urgent need for better treatment options for many neurological conditions, including Alzheimer’s disease, Parkinson’s disease, depression, and epilepsy. Transcranial electrical stimulation (tES) is a non-invasive, safe, inexpensive, and promising method that could address some of this unmet need. The therapeutic value of tES has been well demonstrated, but the effect is highly variable. To enable tES to reach its full potential requires a better understanding of how tES modulates neural activity so that tES treatments can be tailored to specific neurological conditions and individual patients. The neural response to tES is, however, highly complex, and the parameter space involved in optimizing tES treatments is daunting. This has made it difficult to obtain general insights into how tES modulates neural activity, and a central challenge lies in the cell-type-specific and frequency-dependent nature of these responses. In this study, we investigate cell-type-specific neuronal responses to tES over a broad frequency range, using a large database of biophysically detailed neuron models. We find that pyramidal cells respond strongly to low-frequency tES, but their responses drop sharply with frequency. In contrast, inhibitory neurons show a smaller reduction and, on average, become more responsive than pyramidal cells above ∼ 60 Hz. By leveraging a reciprocity theorem we demonstrate that the effect of tES on a given cell-type is proportional to the frequency-dependent current-dipole moment that determines the EEG-signal contribution of this cell-type. We further identified the dendritic asymmetry as key in determining tES responses across the frequency spectrum. Counterintuitively, we also found that while total cell length increases tES sensitivity at low frequencies, it can have the opposite effect at high frequencies. Furthermore, we derived an analytical formula for idealized neuron models which can approximately predict the tES sensitivity of different cell types at any given frequency. By characterizing the role of morphology and stimulation frequency in determining tES responses of single cells, this is an important step towards a better understanding of tES at the fundamental level. These results also provide an efficient and accurate method for characterizing and comparing the tES responses of different neural populations across the frequency spectrum, which facilitates optimizing tES for cell-type specific targeting. Author summary

The human auditory system rapidly distinguishes between novel and familiar sounds, a process reflected in mismatch negativity (MMN), an electroencephalogram (EEG)-based biomarker of auditory novelty detection. MMN is impaired in psychiatric conditions, most notably schizophrenia (SCZ), yet the neuronal mechanisms underlying this deficit remain unclear. Here, we combined computational modelling and genetic analyses to investigate how SCZ-associated cellular abnormalities affect auditory novelty detection. We developed an integrate-and-fire spiking network model capable of detecting four types of auditory novelty, including stimulus omission. Based on assumptions of short-term depressing synapses between the subpopulations of the network and the existence of neuronal inputs that are phase-locked to the rhythm of the recently experienced stimulus sequence, we showed that the model reliably reproduced MMN-like novelty detection and allowed systematic testing of SCZ-related cellular alterations. We also demonstrated that the required phase locking can theoretically be achieved in a synfire chain network exhibiting spike-timing dependent plasticity (STDP) in its feedback synapses that becomes entrained to the rhythmic stimulus. Simulations of our novelty-detecting network revealed that both reduced pyramidal cell excitability, linked to ion channel dysfunction, and decreased spine density impaired novelty detection, with the latter producing stronger deficits. Our work provides a flexible spiking network model of auditory novelty detection that can link cellular-level abnormalities to measurable MMN deficits, improving their mechanistic interpretation and helping to explain the heterogeneity of SCZ.

Abstract Neuronal activity alters extracellular ion concentrations and electric potentials. Ephaptic effects refer to the feedback influence that these extracellular changes can have on neuronal activity. While electric ephaptic effects occur on a fast timescale due to extracellular potential perturbations, ionic ephaptic effects are driven by slower, accumulative changes in ion concentrations. Among the previous computational studies of ephaptic effects, the vast majority have focused exclusively on electric effects, while ionic ephaptic effects have largely been neglected. In this work, we present an electrodiffusive computational framework consisting of two-compartment neurons that interact via a shared extracellular space. By accounting for both electric potentials and ion-concentration dynamics in a self-consistent manner, our framework enables us to explore the relative roles of electric and ionic ephaptic effects. Through numerical experiments, we demonstrate that ionic and electric ephaptic interactions play very different roles. While ionic ephaptic interactions increase population firing rates, electric ephaptic interactions primarily drive subtle shifts in spike timing. Furthermore, we show that these spike shifts cause the phase difference (the distance in spike times between a small collection of neurons) to converge to a stable, unique phase difference, which we coin the ephaptic intrinsic phase preference . Author summary Neurons predominantly communicate through synapses: specialized contact points where a brief electrical signal, known as a spike or action potential, in one neuron influences another. Neurons generate these spikes by exchanging ions with the surrounding extracellular space. This way, spiking neurons alter extracellular ion concentrations and electric potentials. Since neurons are sensitive to such changes in their environment, they can also influence one another indirectly through the shared extracellular medium. This form of non-synaptic interaction is known as ephaptic coupling . Most computational models of neuronal activity neglect ephaptic interactions, and those that include them typically consider only electric effects while ignoring ionic contributions. As a result, the relative roles of electric and ionic ephaptic effects remain poorly understood. Here, we introduce a computational framework that accounts for both mechanisms in a self-consistent way. Our results show a functional distinction: ionic ephaptic effects act slowly, regulating population firing rates, whereas electric ephaptic effects act on millisecond timescales and subtly shift spike timing. These shifts cause spike-time differences between neurons to converge to a stable value, a phenomenon we call ephaptic intrinsic phase preference .

Simulations of large-scale neural activity are an increasingly important tool for investigating neural network activity. Calculating measurable brain signals, like the local field potential (LFP) from such simulations is crucial because it bridges the gap between model predictions and experimental observations and helps us better understand the information content of such signals. Accurately simulating LFPs from large-scale neural network models has, however, required highly biologically detailed models, which pose significant computational challenges, and have limited their practical application. In this study, we demonstrate that a kernel-based method can accurately and efficiently estimate the LFPs simulated in a highly detailed multicompartmental network model of the mouse primary visual cortex (V1), in response to both drifting gratings and full-field flashes of light. Beyond enabling computationally efficient and accurate LFP estimation, the kernel method also aids analysis by disentangling the contributions of individual neuronal populations to the LFP. Leveraging this capability, we found that the LFP in the mouse V1 model was dominated by external synaptic inputs: feedback from lateromedial visual areas in the upper visual layers, and thalamic afferents in layer 4. In contrast, local synaptic activity from V1 neuronal families contributed only marginally to the LFP. We further demonstrated how correlations between external and local neural activity could mask this insight in experimental data. Our findings demonstrate the kernel method as an accurate tool for LFP estimation in state-of-the-art large-scale network models. Moreover, we highlight its potential to reveal novel insights into the neural mechanisms that shape measurable brain signals.

Neural activity at the population level is commonly studied experimentally through measurements of electric brain signals like local field potentials (LFPs), or electroencephalography (EEG) signals. To allow for comparison between observed and simulated neural activity it is therefore important that simulations of neural activity can accurately predict these brain signals. Simulations of neural activity at the population level often rely on point-neuron network models or firing-rate models. While these simplified representations of neural activity are computationally efficient, they lack the explicit spatial information needed for calculating LFP/EEG signals. Different heuristic approaches have been suggested for overcoming this limitation, but the accuracy of these approaches has not fully been assessed. One such heuristic approach, the so-called kernel method, has previously been applied with promising results and has the additional advantage of being well-grounded in the biophysics underlying electric brain signal generation. It is based on calculating rate-to-LFP/EEG kernels for each synaptic pathway in a network model, after which LFP/EEG signals can be obtained directly from population firing rates. This amounts to a massive reduction in the computational effort of calculating brain signals because the brain signals are calculated for each population instead of for each neuron. Here, we investigate how and when the kernel method can be expected to work, and present a theoretical framework for predicting its accuracy. We show that the relative error of the brain signal predictions is a function of the single-cell kernel heterogeneity and the spike-train correlations. Finally, we demonstrate that the kernel method is most accurate for contributions which are also dominating the brain signals: spatially clustered and correlated synaptic input to large populations of pyramidal cells. We thereby further establish the kernel method as a promising approach for calculating electric brain signals from large-scale neural simulations.

GABAB receptors (GABABRs) are an important building block in neural activity. Despite their widely hypothesized role in many basic neuronal functions and mental disorder symptomatology, there is a lack of biophysically and biochemically detailed models of these receptors and the way they mediate neuronal inhibition. Here, we developed a computational model for the activation of GABABRs and its effects on the activation of G protein-coupled inwardly rectifying potassium (GIRK) channels as well as inhibition of voltage-gated Ca2+ channels. To ensure the generality of our modeling framework, we fit our model to electrophysiological data including patch-clamp and intracellular recordings that described both pre- and postsynaptic effects of the receptor activation. We validated our model using data on postsynaptic effects of GABABRs on layer V pyramidal cell firing activity ex vivo and in vivo and confirmed the strong impact of dendritic GIRK channel activation on the neuron output. Finally, we reproduced and dissected the effects of a knockout of RGS7 (a G protein signaling protein) on CA1 pyramidal cell electrophysiological properties, which shows the potential of our model in generating insights on genetic manipulations of the GABABR system and related genetic variants. Our model thus provides a flexible tool for biochemically and biophysically detailed simulations of different aspects of GABABR activation that can reveal both foundational principles of neuronal dynamics and brain disorder-associated traits and treatment options.

To understand the neural basis of behavior, it is essential to sensitively and accurately measure neural activity at single-neuron and single-spike resolution. Extracellular electrophysiology delivers this, but it has biases in the neurons it detects and it imperfectly resolves their action potentials. To minimize these limitations, we developed a silicon probe with much smaller and denser recording sites than previous designs, called Neuropixels Ultra (NP Ultra). Using NP Ultra, neuronal yield in mouse visual cortex recordings increased by more than 2-fold. With ultra-high spatial resolution, we discovered that a feature of extracellular waveforms, the spatial extent or “footprint,” distinguished axonal from somatic recordings. In addition, three genetically identified cortical cell types could be discriminated from one another with ∼80% accuracy and from other neurons with ∼85% accuracy. NP Ultra improves yield, detection of subcellular compartments, and cell type identification to enable a more powerful dissection of neural circuit activity during behavior.

Electrical stimulation of nervous tissue is grounded in well-established biophysical principles, yet understanding its precise effect on neural activity remains challenging. This represents a major obstacle to both scientific and clinical applications of electrical brain stimulation. We here show that the reciprocity theorem of electromagnetism can be applied more broadly than previously acknowledged, providing a framework for elucidating the effects of electrical brain stimulation on neurons. Through this new perspective, we account for the observed weak frequency-dependence of extracellular electrical stimulation-induced membrane potential changes, and demonstrate a 1/r falloff for nearby and 1/r2 falloff for distant neurons. We also show that for transcranial electrical stimulation, the susceptibility of a neuron to the stimulation is directly proportional to the size of the current dipole moment resulting from somatic current input. The induced somatic membrane potential changes are small and exhibit weak spatial but strong orientation dependency across human neocortex. The reciprocity-based approach to electrical stimulation reproduces a large body of previous experimental data, and provides new insights into how ES affects neurons.

The human brain operates at multiple levels, from molecules to circuits, and understanding these complex processes requires integrated research efforts. Simulating biophysically-detailed neuron models is a computationally expensive but effective method for studying local neural circuits. Recent innovations have shown that artificial neural networks (ANNs) can accurately predict the behavior of these detailed models in terms of spikes, electrical potentials, and optical readouts. While these methods have the potential to accelerate large network simulations by several orders of magnitude compared to conventional differential equation based modelling, they currently only predict voltage outputs for the soma or a select few neuron compartments. Our novel approach, based on enhanced state-of-the-art architectures for multitask learning (MTL), allows for the simultaneous prediction of membrane potentials in each compartment of a neuron model, at a speed of up to two orders of magnitude faster than classical simulation methods. By predicting all membrane potentials together, our approach not only allows for comparison of model output with a wider range of experimental recordings (patch-electrode, voltage-sensitive dye imaging), it also provides the first stepping stone towards predicting local field potentials (LFPs), electroencephalogram (EEG) signals, and magnetoencephalography (MEG) signals from ANN-based simulations. While LFP and EEG are an important downstream application, the main focus of this paper lies in predicting dendritic voltages within each compartment to capture the entire electrophysiology of a biophysically-detailed neuron model. It further presents a challenging benchmark for MTL architectures due to the large amount of data involved, the presence of correlations between neighbouring compartments, and the non-Gaussian distribution of membrane potentials.

To understand the neural basis of behavior, it is essential to sensitively and accurately measure neural activity at single neuron and single spike resolution. Extracellular electrophysiology delivers this, but it has biases in the neurons it detects and it imperfectly resolves their action potentials. To minimize these limitations, we developed a silicon probe with much smaller and denser recording sites than previous designs, called Neuropixels Ultra (NP Ultra). This device samples neuronal activity at ultra-high spatial density (~10 times higher than previous probes) with low noise levels, while trading off recording span. NP Ultra is effectively an implantable voltage-sensing camera that captures a planar image of a neuron's electrical field. We use a spike sorting algorithm optimized for these probes to demonstrate that the yield of visually-responsive neurons in recordings from mouse visual cortex improves up to ~3-fold. We show that NP Ultra can record from small neuronal structures including axons and dendrites. Recordings across multiple brain regions and four species revealed a subset of extracellular action potentials with unexpectedly small spatial spread and axon-like features. We share a large-scale dataset of these brain-wide recordings in mice as a resource for studies of neuronal biophysics. Finally, using ground-truth identification of three major inhibitory cortical cell types, we found that these cell types were discriminable with approximately 75% success, a significant improvement over lower-resolution recordings. NP Ultra improves spike sorting performance, detection of subcellular compartments, and cell type classification to enable more powerful dissection of neural circuit activity during behavior.

The primary visual cortex is one of the most well understood regions supporting the processing involved in sensory computation. Following the popularization of high-density neural recordings, it has been observed that the activity of large neural populations is often constrained to low dimensional manifolds. In this work, we quantify the structure of such neural manifolds in the visual cortex. We do this by analyzing publicly available two-photon optical recordings of mouse primary visual cortex in response to visual stimuli with a densely sampled rotation angle. Using a geodesic metric along with persistent homology, we discover that population activity in response to such stimuli generates a circular manifold, encoding the angle of rotation. Furthermore, we observe that this circular manifold is expressed differently in subpopulations of neurons with differing orientation and direction selectivity. Finally, we discuss some of the obstacles to reliably retrieving the truthful topology generated by a neural population.

Lee et al. recently reported robust, frequency-independent subthreshold membrane coupling to extracellular current stimulation across cell classes and brain regions, in both human and mice cortical slices. Specifically, small extracellular sinusoidal electrical stimulations (ES) at frequencies between 1-140 Hz induced a local oscillation in the extracellular potential, leading to sub-threshold (< 0.5 mV) sinusoidal potentials across the cell membrane of nearby cell bodies. Surprisingly, these induced changes in Vm did not decrease with frequency. This seems to imply that ES is a fundamentally different stimulus than equivalent intracellular stimulation that results in strong membrane filtering, caused by the frequency-dependent membrane capacitance. Here we would like to draw attention to the reciprocity theorem as a powerful and (to the best of our knowledge) as-of-yet-unused tool for understanding the effects of ES on neural dynamics, and this counterintuitive result in particular. ### Competing Interest Statement The authors have declared no competing interest.

Schizophrenia phenotypes are suggestive of impaired cortical plasticity in the disease, but the mechanisms of these deficits are unknown. Genomic association studies have implicated a large number of genes that regulate neuromodulation and plasticity, indicating that the plasticity deficits have a genetic origin. Here, we used biochemically detailed computational modeling of postsynaptic plasticity to investigate how schizophrenia-associated genes regulate long-term potentiation (LTP) and depression (LTD). We combined our model with data from postmortem RNA expression studies (CommonMind gene-expression datasets) to assess the consequences of altered expression of plasticity-regulating genes for the amplitude of LTP and LTD. Our results show that the expression alterations observed post mortem, especially those in the anterior cingulate cortex, lead to impaired protein kinase A (PKA)-pathway-mediated LTP in synapses containing GluR1 receptors. We validated these findings using a genotyped electroencephalogram (EEG) dataset where polygenic risk scores for synaptic and ion channel-encoding genes as well as modulation of visual evoked potentials were determined for 286 healthy controls. Our results provide a possible genetic mechanism for plasticity impairments in schizophrenia, which can lead to improved understanding and, ultimately, treatment of the disorder.

In recent years, brain research has indisputably entered a new epoch, driven by substantial methodological advances and digitally enabled data integration and modelling at multiple scales—from molecules to the whole brain. Major advances are emerging at the intersection of neuroscience with technology and computing. This new science of the brain combines high-quality research, data integration across multiple scales, a new culture of multidisciplinary large-scale collaboration, and translation into applications. As pioneered in Europe’s Human Brain Project (HBP), a systematic approach will be essential for meeting the coming decade’s pressing medical and technological challenges. The aims of this paper are to: develop a concept for the coming decade of digital brain research, discuss this new concept with the research community at large, identify points of convergence, and derive therefrom scientific common goals; provide a scientific framework for the current and future development of EBRAINS, a research infrastructure resulting from the HBP’s work; inform and engage stakeholders, funding organisations and research institutions regarding future digital brain research; identify and address the transformational potential of comprehensive brain models for artificial intelligence, including machine learning and deep learning; outline a collaborative approach that integrates reflection, dialogues, and societal engagement on ethical and societal opportunities and challenges as part of future neuroscience research.

Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic mappings for optimal solutions, such as classification problems. In this work, we leverage the fact that neural networks are equivalent to continuous piecewise-affine maps, whose rank can be used to pinpoint regions in the input space that undergo non-homeomorphic transformations, leading to alterations in the topological structure of the input dataset. Our approach enables us to make use of the relative homology sequence, with which one can study the homology groups of the quotient of a manifold ℳ and a subset A, assuming some minimal properties on these spaces. As a proof of principle, we empirically investigate the presence of low-rank (topology-changing) affine maps as a function of network width and mean weight. We show that in randomly initialized narrow networks, there will be regions in which the (co)homology groups of a data manifold can change. As the width increases, the homology groups of the input manifold become more likely to be preserved. We end this part of our work by constructing highly non-random wide networks that do not have this property and relating this non-random regime to Dale's principle, which is a defining characteristic of biological neural networks. Finally, we study simple feedforward networks trained on MNIST, as well as on toy classification and regression tasks, and show that networks manipulate the topology of data differently depending on the continuity of the task they are trained on.