A mean-field model for conductance-based networks of adaptive exponential integrate-and-fire neurons

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at mesoscopic scales. Since VSDi signals report the average membrane potential, it seems natural to use a mean-field formalism to model such signals. Here, we investigate a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. The AdEx model can capture the spiking response of different cell types, such as regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the mean-field model. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model accurately predicts the response time course of the population. One notable exception was that the "tail" of the response at long times was not well predicted, because the mean-field does not include adaptation mechanisms. We conclude that the Master Equation formalism can yield mean-field models that predict well the behavior of nonlinear networks with conductance-based interactions and various electrophysiolgical properties, and should be a good candidate to model VSDi signals where both excitatory and inhibitory neurons contribute.Comment: 21 pages, 7 figure

Gain modulation of synaptic inputs by network state in auditory cortex in vivo

The cortical network recurrent circuitry generates spontaneous activity organized into Up (active) and Down (quiescent) states during slow-wave sleep or anesthesia. These different states of cortical activation gain modulate synaptic transmission. However, the reported modulation that Up states impose on synaptic inputs is disparate in the literature, including both increases and decreases of responsiveness. Here, we tested the hypothesis that such disparate observations may depend on the intensity of the stimulation. By means of intracellular recordings, we studied synaptic transmission during Up and Down states in rat auditory cortex in vivo. Synaptic potentials were evoked either by auditory or electrical (thalamocortical, intracortical) stimulation while randomly varying the intensity of the stimulus. Synaptic potentials evoked by the same stimulus intensity were compared in Up/Down states. Up states had a scaling effect on the stimulus-evoked synaptic responses: the amplitude of weaker responses was potentiated whereas that of larger responses was maintained or decreased with respect to the amplitude during Down states. We used a computational model to explore the potential mechanisms explaining this nontrivial stimulus–response relationship. During Up/Down states, there is different excitability in the network and the neuronal conductance varies. We demonstrate that the competition between presynaptic recruitment and the changing conductance might be the central mechanism explaining the experimentally observed stimulus–response relationships. We conclude that the effect that cortical network activation has on synaptic transmission is not constant but contingent on the strength of the stimulation, with a larger modulation for stimuli involving both thalamic and cortical networks.Fil: Reig, Ramon. Institut d'Investigacions Biomèdiques August Pi i Sunyer; España. Karolinska Huddinge Hospital. Karolinska Institutet; SueciaFil: Zerlaut, Yann. Centre National de la Recherche Scientifique; Francia. Unité de Neurosciences, Information et Complexité; FranciaFil: Vergara, Ramiro Oscar. Institut d'Investigacions Biomèdiques August Pi i Sunyer; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Acústica y Percepción Sonora; ArgentinaFil: Destexhe, Alain. Centre National de la Recherche Scientifique; Francia. Unité de Neurosciences, Information et Complexité; FranciaFil: Sánchez Vives, María V.. Institut d'Investigacions Biomèdiques August Pi i Sunyer; España. Institució Catalana de Recerca i Estudis Avancats; Españ

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions

Dynamiques de population dans les réseaux récurrents : impact des méchanismes biophysiques et propriétés de connectivité

The neocortex of awake animals displays an activated state in whichcortical activity manifests highly complex, seemingly noisybehavior. At the level of single neurons the activity is characterizedby strong subthreshold fluctuations and irregular firing at lowrate. At the network level, the activity is weakly synchronized andexhibits a chaotic dynamics. Yet, it is within this regime thatinformation is processed reliably through neural networks. This regimeis thus crucial to neural computation. In this thesis, we contributeto its understanding by investigating how the biophysical propertiesat the cellular level combined with the properties of the networkarchitecture shapes this asynchronous dynamics.This thesis builds up on the so-called mean-field models of networkdynamics, a theoretical formalism that describes population dynamicsvia a self-consistency approach. At the core of this formalism lie theneuronal transfer function: the input-output description of individualneurons. The first part of this thesis focuses on derivingbiologically-realistic neuronal transfer functions. We firstformulate a two step procedure to incorporate biological details (suchas an extended dendritic structure and the effect of various ionicchannels) into this transfer function based on experimentalcharacterizations.First, we investigated in vitro how layer V pyramidal neocorticalneurons respond to membrane potential fluctuations on a cell-by-cellbasis. We found that, not only individual neurons strongly differ interms of their excitability, but also, and unexpectedly, in theirsensitivities to fluctuations. In addition, using theoreticalmodeling, we attempted to reproduce these results. The model predictsthat heterogeneous levels of biophysical properties such as sodiuminactivation, sharpness of sodium activation and spike frequencyadaptation account for the observed diversity of firing rateresponses.Then, we studied theoretically how dendritic integration in branchedstructures shape the membrane potential fluctuations at the soma. Wefound that, depending on the type of presynaptic activity, variouscomodulations of the membrane potential fluctuations could beachieved. We showed that, when combining this observation with theheterogeneous firing responses found experimentally, individual neuronsdifferentially responded to the different types of presynapticactivities. We thus propose that, because this mechanism offers a wayto produce specific activation as a function of the input properties,biophysical heterogeneity might contribute to the encoding of the stimulusproperties during sensory processing in neural networks.The second part of this thesis investigates how circuit properties,such as recurrent connectivity and lateral connectivity, combine withbiophysical properties to impact sensory responses through effectsmediated by population dynamics.We first investigated what was the effect of a high level of ongoingdynamics (the Up-state compared to the Down-state) on the scaling ofpost-synaptic responses. We found that the competition between therecruitment within the active recurrent network (in favor of highresponses in the Up-state) and the increased conductance level due tobackground activity (in favor of reduced responses in the Up-state)predicted a non trivial stimulus-response relationship as a functionof the intensity of the stimulation. This prediction was shown toaccurately capture measurements of post-synaptic membrane potentialresponses in response to cortical, thalamic or auditory stimulation inrat auditory cortex in vivo.Finally, by taking advantage of the mean-field approach, weconstructed a tractable large-scale model of the layer II-III networkincluding the horizontal fiber network. We investigate thespatio-temporal properties of this large-scale model and we compareits predictions with voltage sensitive dye imaging in awake fixatingmonkey...Le néocortex possède un état activé dans lequel l'activité corticalemanifeste un comportement complexe. Au niveau cellulaire, l'activitéest caractérisée par de fortes fluctuations sous-liminaires dupotential membranaire et une décharge irrégulière à bassefréquence. Au niveau du réseau, l'activité est marquée par un faibleniveau de synchronie et une dynamique chaotique. Néanmoins, c'est dansce régime que l'information est traitée de manière fiable par lesréseaux neuronaux. Ce régime est donc crucial pour le traitement del'information par le cortex. Dans cette thèse, nous contribuons à sacompréhension en examinant comment les propriétés biophysiques auniveau cellulaire combinées avec les propriétés d'architecture desréseaux façonnent cette dynamique asynchrone.Cette thèse repose sur les modèles de dynamique de réseaux appelésmodèles de champ moyen, un formalisme théorique qui décrit ladynamique de population grâce à une approche auto-consistante. Aucoeur de ce formalisme se trouve la fonction de transfertneuronale : la fonction entrée-sortie d'un neurone. La première partiede cette thèse s'attache à dériver des fonctions de transfertbiologiquement réalistes en incorporant des caractérisationsexpérimentales.Dans un premier temps, nous avons examiné in vitro comment lesneurones néocorticaux pyramidaux de la couche V du cortex visuelrépondent à des fluctuations du potentiel membranaire. Nous avonsobservé que les neurones individuels ne diffèrent pas seulement entermes d'excitabilité, mais qu'ils diffèrent aussi par leurssensibilités aux paramètres des fluctuations. Dans un deuxième temps,nous avons étudié de manière théorique comment l'intégrationdendritique dans des structures arborescentes façonne les fluctuationsau soma. Nous avons observé que, en fonction des propriétés del'activité présynaptique, différentes comodulations des paramètres desfluctuations pouvaient être obtenues. En combinant cette observationavec nos mesures expérimentales, nous avons observé que cela induisaitdes couplages différents entre activité synaptique et déchargeneuronale pour chaque neurone. Nous proposons donc que, puisque cemécanisme offre un moyen d'activer spécifiquement certains neurones enfonction des propriétés de l'entrée, l'hétérogénéité biophysiquepourrait contribuer à l'encodage de propriétés des stimuli dans lestraitements de l'information sensorielle.La deuxième partie de cette thèse examine comment les propriétésd'architecture des réseaux neuronaux se combinent avec les propriétésbiophysiques et affectent les réponses sensorielles via des effets dedynamiques de populations.Nous avons tout d'abord examiné de manière théorique comment un hautniveau d'activité spontanée impactait les réponses post-synaptiquesdans le cortex. Nous avons observé que la compétition entre lerecrutement dans le réseau cortical activé et les effets deconductances associés prédisaient une relation non-triviale entrel'intensité des stimuli et l'amplitude des réponses. Cette prédictionfut observée dans des enregistrements de réponses post-synaptiquesdans le cortex auditif du rat in vivo en réponse à des stimulicorticaux, thalamiques et auditifs.Pour finir, en tirant avantage des approches de champ moyen, nousavons construit un modèle grande échelle du réseau des couches II-IIIincluant le réseau des fibres horizontales. Nous avons examiné lespropriétés intégratives spatio-temporelles du modèle et nous les avonscomparées avec des mesures par imagerie optique de l'activitécérébrale chez le singe éveillé. En particulier, nous avonsreconstruit une expérience typique du traitement sensoriel: lemouvement apparent. Le modèle prédit un fort signal suppressif dont leprofil spatio-temporel correspond quantitativement à celui observé invivo..

Enhanced Responsiveness and Low-Level Awareness in Stochastic Network States

International audienceDesynchronized brain states are known to be associated with arousal and increased awareness, but the exact mechanisms are unknown. Here, we show that neuronal networks displaying asynchronous irregular (AI) activity can implement a low-level form of awareness, due to their specific responsiveness properties. We emphasize the importance of the conductance state and stochasticity to explain these properties. We suggest that the purpose of cortical structures is to generate AI states with optimal responsiveness, to be globally aware of external stimuli

Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons

International audienceIn this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of dendritic input activity lead to various impact on the somatic membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity

Calibrating the model on <i>in vitro</i> measurements: The simplified model and its size variations provides an approximation for the somatic input impedance of pyramidal cells and their heterogeneity over the recorded population.

<p><b>(A)</b> Input impedance (left: modulus and right: phase shift) measured at the soma in intracellular recordings with sine-wave protocols in current-clamp (inset). The color code indicates the input resistance and is likely to result from size variations of individual cells. <b>(B</b>) A medium size model accounts for the average data and varying the size of the dendritic tree and soma (according to the sizing rule shown in <b>C</b>) partially reproduces the variability in the individual measurements. Large cells (blue) have a lower modulus and a lower phase shift while small cells (red) have both a higher modulus and phase shift. <b>(C</b>) We obtain a map between input resistance and size of the morphological model. <b>(D)</b> Representation of the medium-size model. <b>(E)</b> Additionally the synaptic weights are rescaled with respect to the cell's somatic input resistance. Because the mean transfer resistance to soma is linked to the input resistance, this rescaling insures that the mean synaptic efficacy at soma is the same for all cells.</p

Examples of the firing response of 4 different cells for the various types of presynaptic activity (color-coded) shown in Fig 4.

<p>The abscissa “increasing synaptic quantity” corresponds to the comodulations of the model variables shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005452#pcbi.1005452.g004" target="_blank">Fig 4A</a> (same color code). As an example, the response to a “proximal activity increase” (blue curve) corresponds to a linear increase of and while keeping , and <i>s</i> to their baseline level. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005452#pcbi.1005452.g004" target="_blank">Fig 4A</a> for the comodulations of the other types of increasing activity.</p

Accuracy of the analytical estimate for the properties of the membrane potential fluctuations at the soma: Comparison between numerical simulations and the analytical approximation.

<p><b>Shown for the medium size model of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005452#pcbi.1005452.g002" target="_blank">Fig 2D</a>. (A)</b> In the numerical simulation, we explicitly simulate the whole dendritic arborescence, we show the membrane potential variations for the three locations shown on the left. <b>(B)</b> Properties of the membrane potential fluctuations (mean <i>μ</i>_<i>V</i>, standard deviation <i>σ</i>_<i>V</i> and autocorrelation time <i>τ</i>_<i>V</i>) for different configuration of presynaptic activity: analytical predictions and output from numerical simulations in <i>NEURON</i>. In each column, one variable is varied while the other variables are fixed to the mean configuration value corresponding to = 0.2Hz, = 1.2Hz and s = 0.05. In the <i>σ</i>_<i>V</i> plots (middle panels, dashed gray lines), we added the prediction of the analytical estimate after a +0.18 correction for the synchrony (found with a Newton method).</p