Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-γ peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-γ peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

Synaptic inhibition is the mechanistic backbone of a suite of cortical functions, not the least of which is maintaining overall network stability as well as modulating neuronal gain. Past cortical models have assumed simplified recurrent networks in which all inhibitory neurons are lumped into a single effective pool. In such models the mechanics of inhibitory stabilization and gain control are tightly linked in opposition to one another -meaning high gain coincides with low stability and vice versa. This tethering of stability and response gain restricts the possible operative regimes of the network. However, it is now well known that cortical inhibition is very diverse, with molecularly distinguished cell classes having distinct positions within the cortical circuit. In this study, we analyze populations of spiking neuron models and associated mean-field theories capturing circuits with pyramidal neurons as well as parvalbumin (PV) and somatostatin (SOM) expressing interneurons. Our study outlines arguments for a division of labor within the full cortical circuit where PV interneurons are ideally positioned to stabilize network activity, whereas SOM interneurons serve to modulate pyramidal cell gain. This segregation of inhibitory function supports stable cortical dynamics over a large range of modulation states. Our study offers a blueprint for how to relate the circuit structure of cortical networks with diverse cell types to the underlying population dynamics and stimulus response.

Table of contentsA1 Functional advantages of cell-type heterogeneity in neural circuitsTatyana O. SharpeeA2 Mesoscopic modeling of propagating waves in visual cortexAlain DestexheA3 Dynamics and biomarkers of mental disordersMitsuo KawatoF1 Precise recruitment of spiking output at theta frequencies requires dendritic h-channels in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneuronsVladislav Sekulić, Frances K. SkinnerF2 Kernel methods in reconstruction of current sources from extracellular potentials for single cells and the whole brainsDaniel K. Wójcik, Chaitanya Chintaluri, Dorottya Cserpán, Zoltán SomogyváriF3 The synchronized periods depend on intracellular transcriptional repression mechanisms in circadian clocks.Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett, Kresimir JosićO1 Assessing irregularity and coordination of spiking-bursting rhythms in central pattern generatorsIrene Elices, David Arroyo, Rafael Levi, Francisco B. Rodriguez, Pablo VaronaO2 Regulation of top-down processing by cortically-projecting parvalbumin positive neurons in basal forebrainEunjin Hwang, Bowon Kim, Hio-Been Han, Tae Kim, James T. McKenna, Ritchie E. Brown, Robert W. McCarley, Jee Hyun ChoiO3 Modeling auditory stream segregation, build-up and bistabilityJames Rankin, Pamela Osborn Popp, John RinzelO4 Strong competition between tonotopic neural ensembles explains pitch-related dynamics of auditory cortex evoked fieldsAlejandro Tabas, André Rupp, Emili Balaguer-BallesterO5 A simple model of retinal response to multi-electrode stimulationMatias I. Maturana, David B. Grayden, Shaun L. Cloherty, Tatiana Kameneva, Michael R. Ibbotson, Hamish MeffinO6 Noise correlations in V4 area correlate with behavioral performance in visual discrimination taskVeronika Koren, Timm Lochmann, Valentin Dragoi, Klaus ObermayerO7 Input-location dependent gain modulation in cerebellar nucleus neuronsMaria Psarrou, Maria Schilstra, Neil Davey, Benjamin Torben-Nielsen, Volker SteuberO8 Analytic solution of cable energy function for cortical axons and dendritesHuiwen Ju, Jiao Yu, Michael L. Hines, Liang Chen, Yuguo YuO9 C. elegans interactome: interactive visualization of Caenorhabditis elegans worm neuronal networkJimin Kim, Will Leahy, Eli ShlizermanO10 Is the model any good? Objective criteria for computational neuroscience model selectionJustas Birgiolas, Richard C. Gerkin, Sharon M. CrookO11 Cooperation and competition of gamma oscillation mechanismsAtthaphon Viriyopase, Raoul-Martin Memmesheimer, Stan GielenO12 A discrete structure of the brain wavesYuri Dabaghian, Justin DeVito, Luca PerottiO13 Direction-specific silencing of the Drosophila gaze stabilization systemAnmo J. Kim, Lisa M. Fenk, Cheng Lyu, Gaby MaimonO14 What does the fruit fly think about values? A model of olfactory associative learningChang Zhao, Yves Widmer, Simon Sprecher,Walter SennO15 Effects of ionic diffusion on power spectra of local field potentials (LFP)Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H. Pettersen,Ole A. Andreassen...

Stimuli that project onto central vision facilitate maintenance of eye position, a phenomenon called the fixation reflex. Endogenous control over this fixation reflex enables one to willfully look away. The current study investigated whether these behaviors, which are important for effective visual orienting, change with advancing age. Previous research established that patients with frontal lobe damage exhibit weaker fixation reflexes and reduced control over this reflex. In light of brain atrophy occurring during healthy aging, we predicted similar but less robust changes in neurologically healthy older relative to young adults. The results generally supported this prediction, which has negative implications for performance of time-sensitive visual-orienting tasks.

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Mean-field theory of neuronal networks has led to numerous advances in our analytical and intuitive understanding of their dynamics during the past decades. In order to make mean-field based analysis tools more accessible, we implemented an extensible, easy-to-use open-source Python toolbox that collects a variety of mean-field methods for the leaky integrate-and-fire neuron model. The Neuronal Network Mean-field Toolbox (NNMT) in its current state allows for estimating properties of large neuronal networks, such as firing rates, power spectra, and dynamical stability in mean-field and linear response approximation, without running simulations. In this article, we describe how the toolbox is implemented, show how it is used to reproduce results of previous studies, and discuss different use-cases, such as parameter space explorations, or mapping different network models. Although the initial version of the toolbox focuses on methods for leaky integrate-and-fire neurons, its structure is designed to be open and extensible. It aims to provide a platform for collecting analytical methods for neuronal network model analysis, such that the neuroscientific community can take maximal advantage of them.

Mean-field theory of spiking neuronal networks has led to numerous advances in our analytical and intuitive understanding of the dynamics of neuronal network models during the past decades. But, the elaborate nature of many of the developed methods, as well as the difficulty of implementing them, may limit the wider neuroscientific community from taking maximal advantage of these tools. In order to make them more accessible, we implemented an extensible, easy-to-use open-source Python toolbox that collects a variety of mean-field methods for the widely used leaky integrate-and-fire neuron model. The Neuronal Network Mean-field Toolbox (NNMT) in its current state allows for estimating properties of large neuronal networks, such as firing rates, power spectra, and dynamical stability in mean-field and linear response approximation, without running simulations on high performance systems. In this article we describe how the toolbox is implemented, show how it is used to calculate neuronal network properties, and discuss different use-cases, such as extraction of network mechanisms, parameter space exploration, or hybrid modeling approaches. Although the initial version of the toolbox focuses on methods that are close to our own past and present research, its structure is designed to be open and extensible. It aims to provide a platform for collecting analytical methods for neuronal network model analysis and we discuss how interested scientists can share their own methods via this platform.