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 Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

scholarly journals A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

2019 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Inhibitory Neurons ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
Field Formalism

AbstractWe present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the populations response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHYPopulation models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

scholarly journals Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

2019 ◽  
Vol 31 (4) ◽  
pp. 653-680 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

scholarly journals Flux-transport and mean-field dynamo theories of solar cycles

2012 ◽  
Vol 8 (S294) ◽  
pp. 37-47
Author(s):  
Arnab Rai Choudhuri
Keyword(s):  
Solar Cycle ◽  
Meridional Circulation ◽  
Mean Field ◽  
Dynamo Model ◽  
Solar Cycles ◽  
Poloidal Field ◽  
Flux Transport ◽  
Mean Field Model ◽  
Mean Field Models ◽  
Mean Field Dynamo

AbstractWe point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in detail. The most promising kinematic mean-field model is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. Depending on whether the diffusivity is high or low, either the diffusivity or the meridional circulation provides the main transport mechanism for the poloidal field to reach the bottom of the convection zone from the top. We point out that the high-diffusivity flux transport dynamo model is consistent with various aspects of observational data. The irregularities of the solar cycle are primarily produced by fluctuations in the Babcock–Leighton mechanism and in the meridional circulation. We summarize recent work on the fluctuations of meridional circulation in the flux transport dynamo, leading to explanations of such things as the Waldmeier effect.

scholarly journals Learning shapes cortical dynamics to enhance integration of relevant sensory input

2021 ◽  
Author(s):  
Angus Chadwick ◽  
Adil Khan ◽  
Jasper Poort ◽  
Antonin Blot ◽  
Sonja Hofer ◽  
...  
Keyword(s):  
Neural Coding ◽  
Sensory Input ◽  
Temporal Dynamics ◽  
Network Dynamics ◽  
Sensory Information ◽  
Neural Population ◽  
Cortical Circuits ◽  
Population Activity ◽  
Cortical Dynamics ◽  
Network Output

Adaptive sensory behavior is thought to depend on processing in recurrent cortical circuits, but how dynamics in these circuits shapes the integration and transmission of sensory information is not well understood. Here, we study neural coding in recurrently connected networks of neurons driven by sensory input. We show analytically how information available in the network output varies with the alignment between feedforward input and the integrating modes of the circuit dynamics. In light of this theory, we analyzed neural population activity in the visual cortex of mice that learned to discriminate visual features. We found that over learning, slow patterns of network dynamics realigned to better integrate input relevant to the discrimination task. This realignment of network dynamics could be explained by changes in excitatory-inhibitory connectivity amongst neurons tuned to relevant features. These results suggest that learning tunes the temporal dynamics of cortical circuits to optimally integrate relevant sensory input.

scholarly journals Spatiotemporal constraints on optogenetic inactivation in cortical circuits

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
Nuo Li ◽  
Susu Chen ◽  
Zengcai V Guo ◽  
Han Chen ◽  
Yan Huo ◽  
...  
Keyword(s):  
Cortical Neurons ◽  
Pyramidal Neurons ◽  
Inhibitory Neurons ◽  
Dependent Manner ◽  
Cortical Circuits ◽  
Neuronal Populations ◽  
Multiple Length Scales ◽  
Dose Dependent ◽  
Reduced Activity

Optogenetics allows manipulations of genetically and spatially defined neuronal populations with excellent temporal control. However, neurons are coupled with other neurons over multiple length scales, and the effects of localized manipulations thus spread beyond the targeted neurons. We benchmarked several optogenetic methods to inactivate small regions of neocortex. Optogenetic excitation of GABAergic neurons produced more effective inactivation than light-gated ion pumps. Transgenic mice expressing the light-dependent chloride channel GtACR1 produced the most potent inactivation. Generally, inactivation spread substantially beyond the photostimulation light, caused by strong coupling between cortical neurons. Over some range of light intensity, optogenetic excitation of inhibitory neurons reduced activity in these neurons, together with pyramidal neurons, a signature of inhibition-stabilized neural networks ('paradoxical effect'). The offset of optogenetic inactivation was followed by rebound excitation in a light dose-dependent manner, limiting temporal resolution. Our data offer guidance for the design of in vivo optogenetics experiments.

scholarly journals Inhibition-Dominated Rich-Club Shapes Dynamics in Cortical Microcircuits of Awake Behaving Mice

2021 ◽  
Author(s):  
Hadi Hafizi ◽  
Sunny Nigam ◽  
Josh Barnathan ◽  
Ian Stevenson ◽  
Sotiris C Masmanidis ◽  
...  
Keyword(s):  
Cortical Neurons ◽  
Large Scale ◽  
Population Level ◽  
Inhibitory Neurons ◽  
Population Activity ◽  
Rich Club ◽  
Large Scale Network ◽  
Type Composition ◽  
Scale Network ◽  
The Rich

Functional networks of cortical neurons contain highly interconnected hubs, forming a rich-club structure. However, the cell type composition within this distinct subnetwork and how it influences large-scale network dynamics is unclear. Using spontaneous activity recorded from hundreds of cortical neurons in orbitofrontal cortex of awake behaving mice we show that the rich-club is disproportionately composed of inhibitory neurons, and that inhibitory neurons within the rich-club are significantly more synchronous than other neurons. At the population level, Granger causality showed that neurons in the rich-club are the dominant drivers of overall population activity and do so in a frequency-specific manner. Moreover, early activity ofinhibitory neurons, along with excitatory neurons within the rich-club, synergistically predicts the duration of neuronal cascades. Together, these results reveal an unexpected role of a highly connected core of inhibitory neurons in driving and sustaining activity in local cortical networks.

scholarly journals Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns

2021 ◽  
Author(s):  
Lyndsay Kerr ◽  
Duncan Sproul ◽  
Ramon Grima
Keyword(s):  
Dna Methylation ◽  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Statistical Properties ◽  
Stochastic Simulations ◽  
Model Parameters ◽  
Mean Field Model ◽  
Mean Field Models ◽  
Methylation Patterns

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Mega-base scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here we test the utility of three different mean-field models to predict large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.

scholarly journals Spontaneous behaviors drive multidimensional, brain-wide activity

2018 ◽  
Author(s):  
Carsen Stringer ◽  
Marius Pachitariu ◽  
Nicholas Steinmetz ◽  
Charu Bai Reddy ◽  
Matteo Carandini ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Spontaneous Activity ◽  
Random Noise ◽  
Population Activity ◽  
Sensory Stimuli ◽  
Cortical Responses ◽  
Ongoing Behavior ◽  
Visual Cortical ◽  
Mouse Visual Cortex ◽  
Behavioral Information

Cortical responses to sensory stimuli are highly variable, and sensory cortex exhibits intricate spontaneous activity even without external sensory input. Cortical variability and spontaneous activity have been variously proposed to represent random noise, recall of prior experience, or encoding of ongoing behavioral and cognitive variables. Here, by recording over 10,000 neurons in mouse visual cortex, we show that spontaneous activity reliably encodes a high-dimensional latent state, which is partially related to the mouse’s ongoing behavior and is represented not just in visual cortex but across the forebrain. Sensory inputs do not interrupt this ongoing signal, but add onto it a representation of visual stimuli in orthogonal dimensions. Thus, visual cortical population activity, despite its apparently noisy structure, reliably encodes an orthogonal fusion of sensory and multidimensional behavioral information.

Sign in / Sign up

Export Citation Format

Share Document