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

2020 ◽  
Vol 123 (3) ◽  
pp. 1042-1051 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
The Brain ◽  
Powerful Mathematical Tool

Population 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 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 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.

Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

2001 ◽  
Vol 13 (11) ◽  
pp. 2495-2516 ◽  
Author(s):  
Francisco B. Rodríguez ◽  
Alberto Suárez ◽  
Vicente López
Keyword(s):  
Population Dynamics ◽  
Detailed Analysis ◽  
Field Model ◽  
Dominant Role ◽  
Mean Field ◽  
Progressive Decrease ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
The Individual ◽  
Firing Period

The population dynamics of an ensemble of nonleaky integrate-and-fire stochastic neurons is studied. The model selected allows for a detailed analysis of situations where noise plays a dominant role. Simulations in a regime with weak to moderate interactions show that a mechanism of excitatory message interchange among the neurons leads to a decrease in the firing period dispersion of the individual units. The dispersion reduction observed is larger than what would be expected from the decrease in the period. This ‘period focusing’ is explained using a mean-field model. It is a dynamical effect that arises from the progressive decrease of the effective firing threshold as a result of the messages received by each unit from the rest of the population. A back-of-the-envelope formula to calculate this nontrivial dispersion reduction and a simple geometrical description of the effect are also provided.

scholarly journals Dynamics of Populations of Integrate-and-Fire Neurons, Partial Synchronization and Memory

1993 ◽  
Vol 5 (4) ◽  
pp. 570-586 ◽  
Author(s):  
Marius Usher ◽  
Heinz Georg Schuster ◽  
Ernst Niebur
Keyword(s):  
Functional Role ◽  
Temporal Dynamics ◽  
Mean Field ◽  
External Input ◽  
Field Potentials ◽  
Field Approach ◽  
Integrate And Fire ◽  
Delay Times ◽  
Dynamics Of Populations ◽  
Global Activity

We study the dynamics of completely connected populations of refractory integrate-and-fire neurons in the presence of noise. Solving the master equation based on a mean-field approach, and by computer simulations, we find sustained states of activity that correspond to fixed points and show that for the same value of external input, the system has one or two attractors. The dynamic behavior of the population under the influence of external input and noise manifests hysteresis effects that might have a functional role for memory. The temporal dynamics at higher temporal resolution, finer than the transmission delay times and the refractory period, are characterized by synchronized activity of subpopulations. The global activity of the population shows aperiodic oscillations analogous to experimentally found field potentials.

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 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 Computational Study of a Spatiotemporal Mean Field Model Capturing the Emergence of Alpha and Gamma Rhythmic Activity in the Neocortex

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 568
Author(s):  
Wassim Haddad
Keyword(s):  
Finite Element ◽  
Bifurcation Analysis ◽  
Field Model ◽  
Computational Study ◽  
Mean Field ◽  
Rhythmic Activity ◽  
Dynamic Equations ◽  
Mean Field Model ◽  
Pharmacological Agents ◽  
The Brain

In this paper, we analyze the spatiotemporal mean field model developed by Liley et al. in order to advance our understanding of the wide effects of pharmacological agents and anesthetics. Specifically, we use the spatiotemporal mean field model for capturing the electrical activity in the neocortex to computationally study the emergence of α - and γ -band rhythmic activity in the brain. We show that α oscillations in the solutions of the model appear globally across the neocortex, whereas γ oscillations can emerge locally as a result of a bifurcation in the dynamics of the model. We solve the dynamic equations of the model using a finite element solver package and show that our results verify the predictions made by bifurcation analysis.

scholarly journals Assembly formation is stabilized by Parvalbumin neurons and accelerated by Somatostatin neurons

2021 ◽  
Author(s):  
Fereshteh Lagzi ◽  
Martha Canto Bustos ◽  
Anne-Marie Oswald ◽  
Brent Doiron
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Spike Timing ◽  
Excitatory Synapses ◽  
Mean Field Models ◽  
Stdp Rule ◽  
Somatostatin Neurons ◽  
Large Scale Simulations ◽  
The Brain ◽  
Parvalbumin Neurons

AbstractLearning entails preserving the features of the external world in the neuronal representations of the brain, and manifests itself in the form of strengthened interactions between neurons within assemblies. Hebbian synaptic plasticity is thought to be one mechanism by which correlations in spiking promote assembly formation during learning. While spike timing dependent plasticity (STDP) rules for excitatory synapses have been well characterized, inhibitory STDP rules remain incomplete, particularly with respect to sub-classes of inhibitory interneurons. Here, we report that in layer 2/3 of the orbitofrontal cortex of mice, inhibition from parvalbumin (PV) interneurons onto excitatory (E) neurons follows a symmetric STDP function and mediates homeostasis in E-neuron firing rates. However, inhibition from somatostatin (SOM) interneurons follows an asymmetric, Hebbian STDP rule. We incorporate these findings in both large scale simulations and mean-field models to investigate how these differences in plasticity impact network dynamics and assembly formation. We find that plasticity of SOM inhibition builds lateral inhibitory connections and increases competition between assemblies. This is reflected in amplified correlations between neurons within assembly and anti-correlations between assemblies. An additional finding is that the emergence of tuned PV inhibition depends on the interaction between SOM and PV STDP rules. Altogether, we show that incorporation of differential inhibitory STDP rules promotes assembly formation through competition, while enhanced inhibition both within and between assemblies protects new representations from degradation after the training input is removed.

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