Correlations and Population Dynamics in Cortical Networks

2008 ◽  
Vol 20 (9) ◽  
pp. 2185-2226 ◽  
Author(s):  
Birgit Kriener ◽  
Tom Tetzlaff ◽  
Ad Aertsen ◽  
Markus Diesmann ◽  
Stefan Rotter
Keyword(s):  
Mean Field ◽  
Power Spectra ◽  
Membrane Potentials ◽  
Network Activity ◽  
Inhibitory Neurons ◽  
Connectivity Matrix ◽  
Cortical Networks ◽  
Population Activity ◽  
Neuronal Populations ◽  
Experimental Findings

The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

scholarly journals Untangling stability and gain modulation in cortical circuits with multiple interneuron classes

2020 ◽  
Author(s):  
Hannah Bos ◽  
Anne-Marie Oswald ◽  
Brent Doiron
Keyword(s):  
Pyramidal Neurons ◽  
Mean Field ◽  
Gain Control ◽  
Cell Types ◽  
High Gain ◽  
Cortical Inhibition ◽  
Network Activity ◽  
Inhibitory Neurons ◽  
Neuron Models ◽  
Cortical Circuit

AbstractSynaptic 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.

scholarly journals Hierarchical Timescales in the Neocortex: Mathematical Mechanism and Biological Insights

2021 ◽  
Author(s):  
Songting Li ◽  
Xiao-Jing Wang
Keyword(s):  
Large Scale ◽  
Detailed Balance ◽  
Receptive Fields ◽  
Spatial Summation ◽  
Progressive Increase ◽  
Connectivity Matrix ◽  
Electrophysiological Properties ◽  
Neuronal Populations ◽  
Sensory Neural ◽  
Experimental Findings

A cardinal feature of the neocortex is the progressive increase of the spatial receptive fields along the cortical hierarchy. Recently, theoretical and experimental findings have shown that the temporal response windows also gradually enlarge, so that early sensory neural circuits operate on short-time scales whereas higher association areas are capable of integrating information over a long period of time. While an increased receptive field is accounted for by spatial summation of inputs from neurons in an upstream area, the emergence of timescale hierarchy cannot be readily explained, especially given the dense inter-areal cortical connectivity known in modern connectome. To uncover the required neurobiological properties, we carried out a rigorous analysis of an anatomically-based large-scale cortex model of macaque monkeys. Using a perturbation method, we show that the segregation of disparate timescales is defined in terms of the localization of eigenvectors of the connectivity matrix, which depends on three circuit properties: (1) a macroscopic gradient of synaptic excitation, (2) distinct electrophysiological properties between excitatory and inhibitory neuronal populations, and (3) a detailed balance between long-range excitatory inputs and local inhibitory inputs for each area-to-area pathway. Our work thus provides a quantitative understanding of the mechanism underlying the emergence of timescale hierarchy in large-scale primate cortical networks.

scholarly journals Feedforward inhibition allows input summation to vary in recurrent cortical networks

2017 ◽  
Author(s):  
Mark H. Histed
Keyword(s):  
Cortical Network ◽  
Network Activity ◽  
Inhibitory Neurons ◽  
Input Output ◽  
Cortical Networks ◽  
Sensory Stimuli ◽  
Cortical Input ◽  
V1 Neurons ◽  
Internal Network ◽  
Feedforward Inhibition

AbstractBrain computations depend on how neurons transform inputs to spike outputs. Here, to understand input-output transformations in cortical networks, we recorded spiking responses from visual cortex (V1) of awake mice of either sex while pairing sensory stimuli with optogenetic perturbation of excitatory and parvalbumin-positive inhibitory neurons. We found V1 neurons’ average responses were primarily additive (linear). We used a recurrent cortical network model to determine if these data, as well as past observations of nonlinearity, could be described by a common circuit architecture. The model showed cortical input-output transformations can be changed from linear to sublinear with moderate (∼20%) strengthening of connections between inhibitory neurons, but this change depends on the presence of feedforward inhibition. Thus, feedforward inhibition, a common feature of cortical circuitry, enables networks to flexibly change their spiking responses via changes in recurrent connectivity.Significance statementBrains are made up of neural networks that process information by receiving input activity and transforming those inputs into output activity. We use optogenetic manipulations in awake mice to expose how a transformation in a cortical network depends on internal network activity. Combining numerical simulations with our observations uncovers that transformation depend critically on feedforward inhibition – the fact that inputs to the cortex often make strong connections on both excitatory and inhibitory neurons.

scholarly journals OFF-periods reduce the complexity of neocortical activity during sleep

2021 ◽  
Author(s):  
Joaquin Gonzalez ◽  
Matias Cavelli ◽  
Adriano BL Tort ◽  
Pablo Torterolo ◽  
Nicolás Rubido
Keyword(s):  
Rem Sleep ◽  
Slow Wave Sleep ◽  
Neural Mechanism ◽  
Population Activity ◽  
Temporal Complexity ◽  
Field Recordings ◽  
Neuronal Populations ◽  
Branching Model ◽  
Experimental Findings

Field recordings decrease their temporal complexity during slow-wave sleep (SWS), however, the neural mechanism for this decrease remains elusive. Here, we show that this complexity reduction is caused by synchronous neuronal OFF-periods by analysing in-vivo recordings from neocortical neuronal populations. We find that OFF-periods trap cortical dynamics, disrupting causal interactions and making the population activity more recurrent, deterministic, and less chaotic than during REM sleep or Wakefulness. Moreover, when we exclude OFF-periods, SWS becomes indistinguishable from Wakefulness or REM sleep. In fact, for all states, we show that the spiking activity has a universal scaling compatible with critical phenomena. We complement these results by analysing a critical branching model that replicates the experimental findings, where we show that forcing OFF-periods into a percentage of neurons suffices to generate a decrease in complexity that replicates SWS.

scholarly journals Network instability dynamics drive a transient bursting period in the developing hippocampus in vivo

2021 ◽  
Author(s):  
Jürgen Graf ◽  
Vahid Rahmati ◽  
Myrtill Majoros ◽  
Otto W. Witte ◽  
Christian Geis ◽  
...  
Keyword(s):  
Developmental Trajectories ◽  
Local Population ◽  
Pyramidal Cells ◽  
Network Activity ◽  
Functional Coupling ◽  
Population Activity ◽  
Neuronal Synchrony ◽  
Underlying Network ◽  
Experimental Findings

Spontaneous correlated activity is a universal hallmark of immature neural circuits. However, the cellular dynamics and intrinsic mechanisms underlying neuronal synchrony in the intact developing brain are largely unknown. Here, we use two-photon Ca2+ imaging to comprehensively map the developmental trajectories of spontaneous network activity in hippocampal area CA1 in vivo. We unexpectedly find that synchronized activity peaks after the developmental emergence of effective synaptic inhibition in the second postnatal week. We demonstrate that the enhanced network synchrony reflects an increased functional coupling of individual neurons to local population activity. However, pairwise neuronal correlations are low, and network bursts recruit CA1 pyramidal cells in a virtually random manner. Using a dynamic systems modeling approach, we reconcile these experimental findings and identify network bi-stability as a potential regime underlying network burstiness at this age. Our analyses reveal an important role of synaptic input characteristics and network instability dynamics for the emergence of neuronal synchrony. Collectively, our data suggest a mechanism, whereby developing CA1 performs extensive input-discrimination learning prior to the onset of environmental exploration.

scholarly journals Equations governing dynamics of excitation and inhibition in the mouse corticothalamic network

2020 ◽  
Author(s):  
I-Chun Lin ◽  
Michael Okun ◽  
Matteo Carandini ◽  
Kenneth D. Harris
Keyword(s):  
Cortical Neurons ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Cortical Circuits ◽  
Mean Field Model ◽  
Population Activity ◽  
Cortical Dynamics ◽  
Mean Field Models ◽  
Cortical Responses ◽  
Mouse Visual Cortex

Although cortical circuits are complex and interconnected with the rest of the brain, their macroscopic dynamics are often approximated by modeling the averaged activities of excitatory and inhibitory cortical neurons, without interactions with other brain circuits. To verify the validity of such mean-field models, we optogenetically stimulated populations of excitatory and parvalbumin-expressing inhibitory neurons in awake mouse visual cortex, while recording population activity in cortex and in its thalamic correspondent, the lateral geniculate nucleus. The cortical responses to brief test pulses could not be explained by a mean-field model including only cortical excitatory and inhibitory populations. However, these responses could be predicted by extending the model to include thalamic interactions that cause net cortical suppression following activation of cortical excitatory neurons. We conclude that mean-field models can accurately summarize cortical dynamics, but only when the cortex is considered as part of a dynamic corticothalamic network.

scholarly journals Robust associative learning is sufficient to explain structural and dynamical properties of local cortical circuits

2018 ◽  
Author(s):  
Danke Zhang ◽  
Chi Zhang ◽  
Armen Stepanyants
Keyword(s):  
Associative Learning ◽  
Network Activity ◽  
Inhibitory Neurons ◽  
Cortical Circuits ◽  
Cortical Networks ◽  
Connection Weight ◽  
Postsynaptic Potential ◽  
Weight Distributions ◽  
Network Properties ◽  
Dynamical Properties

ABSTRACTThe ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memory sequences of varying lengths and compared network properties to those observed experimentally. We show that when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overrepresentations of specific 3-neuron motifs, distributions of connection numbers in clusters of 3–8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. What is more, memories loaded into the network can be retrieved even in the presence of noise comparable to the baseline variations in the postsynaptic potential. Confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning.

scholarly journals Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Hamidreza Abbaspourazad ◽  
Mahdi Choudhury ◽  
Yan T. Wong ◽  
Bijan Pesaran ◽  
Maryam M. Shanechi
Keyword(s):  
Neural Control ◽  
Multiple Scales ◽  
Network Activity ◽  
Neural Dynamics ◽  
Population Activity ◽  
Reach And Grasp ◽  
Spatiotemporal Scales ◽  
Motor Cortical ◽  
Low Dimensional ◽  
Low Dimensional Dynamics

AbstractMotor function depends on neural dynamics spanning multiple spatiotemporal scales of population activity, from spiking of neurons to larger-scale local field potentials (LFP). How multiple scales of low-dimensional population dynamics are related in control of movements remains unknown. Multiscale neural dynamics are especially important to study in naturalistic reach-and-grasp movements, which are relatively under-explored. We learn novel multiscale dynamical models for spike-LFP network activity in monkeys performing naturalistic reach-and-grasps. We show low-dimensional dynamics of spiking and LFP activity exhibited several principal modes, each with a unique decay-frequency characteristic. One principal mode dominantly predicted movements. Despite distinct principal modes existing at the two scales, this predictive mode was multiscale and shared between scales, and was shared across sessions and monkeys, yet did not simply replicate behavioral modes. Further, this multiscale mode’s decay-frequency explained behavior. We propose that multiscale, low-dimensional motor cortical state dynamics reflect the neural control of naturalistic reach-and-grasp behaviors.

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