Grégory Dumont

Is There a Nonadditive Interaction Between Spontaneous and Evoked Activity? Phase-Dependence and Its Relation to the Temporal Structure of Scale-Free Brain Activity

Abstract The aim of our study was to use functional magnetic resonance imaging to investigate how spontaneous activity interacts with evoked activity, as well as how the temporal structure of spontaneous activity, that is, long‐range temporal correlations, relate to this interaction. Using an extremely sparse event‐related design (intertrial intervals: 52‐60 s), a novel blood oxygen level‐dependent signal correction approach (accounting for spontaneous fluctuations using pseudotrials) and phase analysis, we provided direct evidence for a nonadditive interaction between spontaneous and evoked activity. We demonstrated the discrepancy between the present and previous observations on why a linear superposition between spontaneous and evoked activity can be seen by using co‐occurring signals from homologous brain regions. Importantly, we further demonstrated that the nonadditive interaction can be characterized by phase‐dependent effects of spontaneous activity, which is closely related to the degree of long‐range temporal correlations in spontaneous activity as indexed by both power‐law exponent and phase‐amplitude coupling. Our findings not only contribute to the understanding of spontaneous brain activity and its scale‐free properties, but also bear important implications for our understanding of neural activity in general.

Synchronization of an Excitatory Integrate-and-Fire Neural Network

In this paper, we study the influence of the coupling strength on the synchronization behavior of a population of leaky integrate-and-fire neurons that is self-excitatory with a population density approach. Each neuron of the population is assumed to be stochastically driven by an independent Poisson spike train and the synaptic interaction between neurons is modeled by a potential jump at the reception of an action potential. Neglecting the synaptic delay, we will establish that for a strong enough connectivity between neurons, the solution of the partial differential equation which describes the population density function must blow up in finite time. Furthermore, we will give a mathematical estimate on the average connection per neuron to ensure the occurrence of a burst. Interpreting the blow up of the solution as the presence of a Dirac mass in the firing rate of the population, we will relate the blow up of the solution to the occurrence of the synchronization of neurons. Fully stochastic simulations of a finite size network of leaky integrate-and-fire neurons are performed to illustrate our theoretical results.

Macroscopic phase-resetting curves for spiking neural networks

The study of brain rhythms is an open-ended, and challenging, subject of interest in neuroscience. One of the best tools for the understanding of oscillations at the single neuron level is the phase-resetting curve (PRC). Synchronization in networks of neurons, effects of noise on the rhythms, effects of transient stimuli on the ongoing rhythmic activity, and many other features can be understood by the PRC. However, most macroscopic brain rhythms are generated by large populations of neurons, and so far it has been unclear how the PRC formulation can be extended to these more common rhythms. In this paper, we describe a framework to determine a macroscopic PRC (mPRC) for a network of spiking excitatory and inhibitory neurons that generate a macroscopic rhythm. We take advantage of a thermodynamic approach combined with a reduction method to simplify the network description to a small number of ordinary differential equations. From this simplified but exact reduction, we can compute the mPRC via the standard adjoint method. Our theoretical findings are illustrated with and supported by numerical simulations of the full spiking network. Notably our mPRC framework allows us to predict the difference between effects of transient inputs to the excitatory versus the inhibitory neurons in the network.

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar.

A stochastic model of input effectiveness during irregular gamma rhythms

Gamma-band synchronization has been linked to attention and communication between brain regions, yet the underlying dynamical mechanisms are still unclear. How does the timing and amplitude of inputs to cells that generate an endogenously noisy gamma rhythm affect the network activity and rhythm? How does such ”communication through coherence” (CTC) survive in the face of rhythm and input variability? We present a stochastic modelling approach to this question that yields a very fast computation of the effectiveness of inputs to cells involved in gamma rhythms. Our work is partly motivated by recent optogenetic experiments (Cardin et al. Nature, 459(7247), 663–667 2009) that tested the gamma phase-dependence of network responses by first stabilizing the rhythm with periodic light pulses to the interneurons (I). Our computationally efficient model E-I network of stochastic two-state neurons exhibits finite-size fluctuations. Using the Hilbert transform and Kuramoto index, we study how the stochastic phase of its gamma rhythm is entrained by external pulses. We then compute how this rhythmic inhibition controls the effectiveness of external input onto pyramidal (E) cells, and how variability shapes the window of firing opportunity. For transferring the time variations of an external input to the E cells, we find a tradeoff between the phase selectivity and depth of rate modulation. We also show that the CTC is sensitive to the jitter in the arrival times of spikes to the E cells, and to the degree of I-cell entrainment. We further find that CTC can occur even if the underlying deterministic system does not oscillate; quasicycle-type rhythms induced by the finite-size noise retain the basic CTC properties. Finally a resonance analysis confirms the relative importance of the I cell pacing for rhythm generation. Analysis of whole network behaviour, including computations of synchrony, phase and shifts in excitatory-inhibitory balance, can be further sped up by orders of magnitude using two coupled stochastic differential equations, one for each population. Our work thus yields a fast tool to numerically and analytically investigate CTC in a noisy context. It shows that CTC can be quite vulnerable to rhythm and input variability, which both decrease phase preference.

A Density Model for a Population of Theta Neurons

Population density models that are used to describe the evolution of neural populations in a phase space are closely related to the single neuron model that describes the individual trajectories of the neurons of the population and which give in particular the phase-space where the computations are made. Based on a transformation of the quadratic integrate and fire single neuron model, the so-called theta-neuron model is obtained and we shall introduce in this paper a corresponding population density model for it. Existence and uniqueness of a solution will be proved and some numerical simulations are presented. The results of existence are compared to previous results of existence or nonexistence (burst) for populations of leaky integrate and fire neurons.

Finite size effect induces stochastic gamma oscillation in inhibitory network with conduction delay

Cortical gamma frequency (30-100 Hz) are known to be associated with many cognitive processes. Understanding the dynamics in the gamma band is crucial in neuroscience. Stochastic gamma oscillations due to finite size effects were reported using the stochastic Wilson-Cowan model ([1] and [2]). On the other hand, temporal correlation can be induced by excitation [3] as well as inhibition [4]. Especially, oscillations induced by the conduction delay of the inhibitory feedback is a possible mechanism ([4], [5] and [6]) for gamma rhythms. We investigate the role of both finite size effects and the conduction delay on the emergence of gamma oscillations in an inhibitory all-to-all neural network. To this end, we expand the recently proposed linear noise approximation (LNA) technique to this non-markovian ”delay” case [1]. This allows us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations for a range of parameters. We show in the left part of the Figure ​Figure11 a raster plot depicting the spiking time of each neuron where each neuron follows the stochastic random walk between active and silent state, in red the spike timing of one particular neuron. The second plot is a comparison between the deterministic rate model (black curve) and the stochastic spiking process (blue curve). If the deterministic counterpart reaches a stable fixed point, the stochastic process exhibits self sustained oscillations. In the third plot, the theoretical power spectrum obtained via the LNA method (black curve) and the power spectrum obtained from the numerical simulations (blue curve) are shown to agree nicely. In the last plot we give the phase diagram, showing that the model is under the oscillatory regime. This tells us that gamma oscillations can be caused by the combination of delay and finite size effects in such an inhibitory neural network. Figure 1 The left panel is a raster plot of 200 interneurons. The blue line represents the global activity of the network. The second panel shows a comparison between the stochastic process and its deterministic counterpart. The third panel compares the numerical ...

Dopaminergic Neurons in the Ventral Tegmental Area and Their Dysregulation in Nicotine Addiction

Abstract Nicotine is widely considered the major addictive substance in tobacco. While the receptor mechanisms of nicotine have been identified, the circuit level mechanisms by which it usurps dopamine signaling are still not completely clear. In this chapter we describe two modeling approaches: the first is a receptor-circuit model of the ventral tegmental area (VTA), the second is a more detailed modeling of dopamine neuron spiking. Using the circuit model we show that nicotine-evoked upregulation of receptors on the VTA γ-amino butyric acid neurons is a sufficient mechanism for alterations in dopaminergic signaling. Crucially the model points out how nicotine may act to renormalize the otherwise pathological dopamine circuitry in individuals with substance use disorders. In the second approach we show that nicotine-driven increases in glutamate input synchrony to the dopamine neurons induce bursting and hence increased phasic dopamine release. We discuss open questions and ways for models to delineate the mechanisms of nicotine control over motivational signals in the brain.

A stochastic-field description of finite-size spiking neural networks

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.