Neural manifolds in V1 change with top-down signals from V4 targeting the foveal region.

High-dimensional brain activity is often organized into lower-dimensional neural manifolds. However, the neural manifolds of the visual cortex remain understudied. Here, we study large-scale multi-electrode electrophysiological recordings of macaque (Macaca mulatta) areas V1, V4, and DP with a high spatiotemporal resolution. We find that the population activity of V1 contains two separate neural manifolds, which correlate strongly with eye closure (eyes open/closed) and have distinct dimensionalities. Moreover, we find strong top-down signals from V4 to V1, particularly to the foveal region of V1, which are significantly stronger during the eyes-open periods. Finally, in silico simulations of a balanced spiking neuron network qualitatively reproduce the experimental findings. Taken together, our analyses and simulations suggest that top-down signals modulate the population activity of V1. We postulate that the top-down modulation during the eyes-open periods prepares V1 for fast and efficient visual responses, resulting in a type of visual stand-by state.

Modular-integrative modeling: a new framework for building brain models that blend biological realism and functional performance.

This Perspective presents the Modular-Integrative Modeling approach, a novel framework in neuroscience for developing brain models that blend biological realism with functional performance to provide a holistic view on brain function in interaction with the body and environment.

Ubiquitous lognormal distribution of neuron densities in mammalian cerebral cortex.

Numbers of neurons and their spatial variation are fundamental organizational features of the brain. Despite the large corpus of cytoarchitectonic data available in the literature, the statistical distributions of neuron densities within and across brain areas remain largely uncharacterized. Here, we show that neuron densities are compatible with a lognormal distribution across cortical areas in several mammalian species, and find that this also holds true within cortical areas. A minimal model of noisy cell division, in combination with distributed proliferation times, can account for the coexistence of lognormal distributions within and across cortical areas. Our findings uncover a new organizational principle of cortical cytoarchitecture: the ubiquitous lognormal distribution of neuron densities, which adds to a long list of lognormal variables in the brain.

Connectivity concepts in neuronal network modeling.

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Fast Simulation of a Multi-Area Spiking Network Model of Macaque Cortex on an MPI-GPU Cluster.

Spiking neural network models are increasingly establishing themselves as an effective tool for simulating the dynamics of neuronal populations and for understanding the relationship between these dynamics and brain function. Furthermore, the continuous development of parallel computing technologies and the growing availability of computational resources are leading to an era of large-scale simulations capable of describing regions of the brain of ever larger dimensions at increasing detail. Recently, the possibility to use MPI-based parallel codes on GPU-equipped clusters to run such complex simulations has emerged, opening up novel paths to further speed-ups. NEST GPU is a GPU library written in CUDA-C/C++ for large-scale simulations of spiking neural networks, which was recently extended with a novel algorithm for remote spike communication through MPI on a GPU cluster. In this work we evaluate its performance on the simulation of a multi-area model of macaque vision-related cortex, made up of about 4 million neurons and 24 billion synapses and representing 32 mm2 surface area of the macaque cortex. The outcome of the simulations is compared against that obtained using the well-known CPU-based spiking neural network simulator NEST on a high-performance computing cluster. The results show not only an optimal match with the NEST statistical measures of the neural activity in terms of three informative distributions, but also remarkable achievements in terms of simulation time per second of biological activity. Indeed, NEST GPU was able to simulate a second of biological time of the full-scale macaque cortex model in its metastable state 3.1× faster than NEST using 32 compute nodes equipped with an NVIDIA V100 GPU each. Using the same configuration, the ground state of the full-scale macaque cortex model was simulated 2.4× faster than NEST.

1024-channel electrophysiological recordings in macaque V1 and V4 during resting state.

Co-variations in resting state activity are thought to arise from a variety of correlated inputs to neurons, such as bottom-up activity from lower areas, feedback from higher areas, recurrent processing in local circuits, and fluctuations in neuromodulatory systems. Most studies have examined resting state activity throughout the brain using MRI scans, or observed local co-variations in activity by recording from a small number of electrodes. We carried out electrophysiological recordings from over a thousand chronically implanted electrodes in the visual cortex of non-human primates, yielding a resting state dataset with unprecedentedly high channel counts and spatiotemporal resolution. Such signals could be used to observe brain waves across larger regions of cortex, offering a temporally detailed picture of brain activity. In this paper, we provide the dataset, describe the raw and processed data formats and data acquisition methods, and indicate how the data can be used to yield new insights into the 'background' activity that influences the processing of visual information in our brain.

Cortical oscillations support sampling-based computations in spiking neural networks.

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.

Correction to: Multi-scale account of the network structure of macaque visual cortex.

Unfortunately, some errors slipped into the manuscript, which we correct here.

An architectonic type principle integrates macroscopic cortico-cortical connections with intrinsic cortical circuits of the primate brain.

The connections linking neurons within and between cerebral cortical areas form a multiscale network for communication. We review recent work relating essential features of cortico-cortical connections, such as their existence and laminar origins and terminations, to fundamental structural parameters of cortical areas, such as their distance, similarity in cytoarchitecture, defined by lamination or neuronal density, and other macroscopic and microscopic structural features. These analyses demonstrate the presence of an architectonic type principle. Across species and cortices, the essential features of cortico-cortical connections vary consistently and strongly with the cytoarchitectonic similarity of cortical areas. By contrast, in multivariate analyses such relations were not found consistently for distance, similarity of cortical thickness, or cellular morphology. Gradients of laminar cortical differentiation, as reflected in overall neuronal density, also correspond to regional variations of cellular features, forming a spatially ordered natural axis of concerted architectonic and connectional changes across the cortical sheet. The robustness of findings across mammalian brains allows cross-species predictions of the existence and laminar patterns of projections, including estimates for the human brain that are not yet available experimentally. The architectonic type principle integrates cortical connectivity and architecture across scales, with implications for computational explorations of cortical physiology and developmental mechanisms.

Open Source Brain: A Collaborative Resource for Visualizing, Analyzing, Simulating, and Developing Standardized Models of Neurons and Circuits.

Computational models are powerful tools for exploring the properties of complex biological systems. In neuroscience, data-driven models of neural circuits that span multiple scales are increasingly being used to understand brain function in health and disease. But their adoption and reuse has been limited by the specialist knowledge required to evaluate and use them. To address this, we have developed Open Source Brain, a platform for sharing, viewing, analyzing, and simulating standardized models from different brain regions and species. Model structure and parameters can be automatically visualized and their dynamical properties explored through browser-based simulations. Infrastructure and tools for collaborative interaction, development, and testing are also provided. We demonstrate how existing components can be reused by constructing new models of inhibition-stabilized cortical networks that match recent experimental results. These features of Open Source Brain improve the accessibility, transparency, and reproducibility of models and facilitate their reuse by the wider community.

A multi-scale layer-resolved spiking network model of resting-state dynamics in macaque visual cortical areas.

Cortical activity has distinct features across scales, from the spiking statistics of individual cells to global resting-state networks. We here describe the first full-density multi-area spiking network model of cortex, using macaque visual cortex as a test system. The model represents each area by a microcircuit with area-specific architecture and features layer- and population-resolved connectivity between areas. Simulations reveal a structured asynchronous irregular ground state. In a metastable regime, the network reproduces spiking statistics from electrophysiological recordings and cortico-cortical interaction patterns in fMRI functional connectivity under resting-state conditions. Stable inter-area propagation is supported by cortico-cortical synapses that are moderately strong onto excitatory neurons and stronger onto inhibitory neurons. Causal interactions depend on both cortical structure and the dynamical state of populations. Activity propagates mainly in the feedback direction, similar to experimental results associated with visual imagery and sleep. The model unifies local and large-scale accounts of cortex, and clarifies how the detailed connectivity of cortex shapes its dynamics on multiple scales. Based on our simulations, we hypothesize that in the spontaneous condition the brain operates in a metastable regime where cortico-cortical projections target excitatory and inhibitory populations in a balanced manner that produces substantial inter-area interactions while maintaining global stability.

Criteria on Balance, Stability, and Excitability in Cortical Networks for Constraining Computational Models.

During ongoing and Up state activity, cortical circuits manifest a set of dynamical features that are conserved across these states. The present work systematizes these phenomena by three notions: excitability, the ability to sustain activity without external input; balance, precise coordination of excitatory and inhibitory neuronal inputs; and stability, maintenance of activity at a steady level. Slice preparations exhibiting Up states demonstrate that balanced activity can be maintained by small local circuits. While computational models of cortical circuits have included different combinations of excitability, balance, and stability, they have done so without a systematic quantitative comparison with experimental data. Our study provides quantitative criteria for this purpose, by analyzing in-vitro and in-vivo neuronal activity and characterizing the dynamics on the neuronal and population levels. The criteria are defined with a tolerance that allows for differences between experiments, yet are sufficient to capture commonalities between persistently depolarized cortical network states and to help validate computational models of cortex. As test cases for the derived set of criteria, we analyze three widely used models of cortical circuits and find that each model possesses some of the experimentally observed features, but none satisfies all criteria simultaneously, showing that the criteria are able to identify weak spots in computational models. The criteria described here form a starting point for the systematic validation of cortical neuronal network models, which will help improve the reliability of future models, and render them better building blocks for larger models of the brain.

Performance Comparison of the Digital Neuromorphic Hardware SpiNNaker and the Neural Network Simulation Software NEST for a Full-Scale Cortical Microcircuit Model.

The digital neuromorphic hardware SpiNNaker has been developed with the aim of enabling large-scale neural network simulations in real time and with low power consumption. Real-time performance is achieved with 1 ms integration time steps, and thus applies to neural networks for which faster time scales of the dynamics can be neglected. By slowing down the simulation, shorter integration time steps and hence faster time scales, which are often biologically relevant, can be incorporated. We here describe the first full-scale simulations of a cortical microcircuit with biological time scales on SpiNNaker. Since about half the synapses onto the neurons arise within the microcircuit, larger cortical circuits have only moderately more synapses per neuron. Therefore, the full-scale microcircuit paves the way for simulating cortical circuits of arbitrary size. With approximately 80, 000 neurons and 0.3 billion synapses, this model is the largest simulated on SpiNNaker to date. The scale-up is enabled by recent developments in the SpiNNaker software stack that allow simulations to be spread across multiple boards. Comparison with simulations using the NEST software on a high-performance cluster shows that both simulators can reach a similar accuracy, despite the fixed-point arithmetic of SpiNNaker, demonstrating the usability of SpiNNaker for computational neuroscience applications with biological time scales and large network size. The runtime and power consumption are also assessed for both simulators on the example of the cortical microcircuit model. To obtain an accuracy similar to that of NEST with 0.1 ms time steps, SpiNNaker requires a slowdown factor of around 20 compared to real time. The runtime for NEST saturates around 3 times real time using hybrid parallelization with MPI and multi-threading. However, achieving this runtime comes at the cost of increased power and energy consumption. The lowest total energy consumption for NEST is reached at around 144 parallel threads and 4.6 times slowdown. At this setting, NEST and SpiNNaker have a comparable energy consumption per synaptic event. Our results widen the application domain of SpiNNaker and help guide its development, showing that further optimizations such as synapse-centric network representation are necessary to enable real-time simulation of large biological neural networks.

Multi-scale account of the network structure of macaque visual cortex.

Cortical network structure has been extensively characterized at the level of local circuits and in terms of long-range connectivity, but seldom in a manner that integrates both of these scales. Furthermore, while the connectivity of cortex is known to be related to its architecture, this knowledge has not been used to derive a comprehensive cortical connectivity map. In this study, we integrate data on cortical architecture and axonal tracing data into a consistent multi-scale framework of the structure of one hemisphere of macaque vision-related cortex. The connectivity model predicts the connection probability between any two neurons based on their types and locations within areas and layers. Our analysis reveals regularities of cortical structure. We confirm that cortical thickness decays with cell density. A gradual reduction in neuron density together with the relative constancy of the volume density of synapses across cortical areas yields denser connectivity in visual areas more remote from sensory inputs and of lower structural differentiation. Further, we find a systematic relation between laminar patterns on source and target sides of cortical projections, extending previous findings from combined anterograde and retrograde tracing experiments. Going beyond the classical schemes, we statistically assign synapses to target neurons based on anatomical reconstructions, which suggests that layer 4 neurons receive substantial feedback input. Our derived connectivity exhibits a community structure that corresponds more closely with known functional groupings than previous connectivity maps and identifies layer-specific directional differences in cortico-cortical pathways. The resulting network can form the basis for studies relating structure to neural dynamics in mammalian cortex at multiple scales.

Fundamental Activity Constraints Lead to Specific Interpretations of the Connectome.

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks.

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm2 patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.

Pronounced Surface Band Bending of Thin-Film Silicon Revealed by Modeling Core Levels Probed with Hard X-rays.

Enhancing the probing depth of photoemission studies by using hard X-rays allows the investigation of buried interfaces of real-world device structures. However, it also requires the consideration of photoelectron-signal attenuation when evaluating surface effects. Here, we employ a computational model incorporating surface band bending and exponential photoelectron-signal attenuation to model depth-dependent spectral changes of Si 1s and Si 2s core level lines. The data were acquired from hydrogenated boron-doped microcrystalline thin-film silicon, which is applied in silicon-based solar cells. The core level spectra, measured by hard X-ray photoelectron spectroscopy using different excitation energies, reveal the presence of a 0.29 nm thick surface oxide layer. In the silicon film a downward surface band bending of eVbb = -0.65 eV over ∼6 nm obtained via inverse modeling explains the observed core level shifts and line broadening. Moreover, the computational model allows the extraction of the "real" Si 1s and Si 2s bulk core level binding energies as 1839.13 and 150.39 eV, and their natural Lorentzian line widths as 496 and 859 meV, respectively. These values significantly differ from those directly extracted from the measured spectra. Because band bending usually occurs at material surfaces we highly recommend the detailed consideration of signal integration over depth for quantitative statements from depth-dependent measurements.

Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations.

Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics are conserved, here we show that limitations already arise if also second-order statistics are to be maintained. The temporal structure of pairwise averaged correlations in the activity of recurrent networks is determined by the effective population-level connectivity. We first show that in general the converse is also true and explicitly mention degenerate cases when this one-to-one relationship does not hold. The one-to-one correspondence between effective connectivity and the temporal structure of pairwise averaged correlations implies that network scalings should preserve the effective connectivity if pairwise averaged correlations are to be held constant. Changes in effective connectivity can even push a network from a linearly stable to an unstable, oscillatory regime and vice versa. On this basis, we derive conditions for the preservation of both mean population-averaged activities and pairwise averaged correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. We find that mean activities and correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a range of numbers of synapses that is limited by the variance of external inputs to the network. Our results therefore show that the reducibility of asynchronous networks is fundamentally limited.

Cortical information flow in Parkinson's disease: a composite network/field model.

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main "input" layer of the cortex (layer 4) to the main "output" layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.