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Section: New Results

Neuronal modelling

Linear response in neuronal networks: from neurons dynamics to collective responses

Participant : Bruno Cessac.

We have reviewed two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitly, including network parameters dependence. This is done in a statistical physics-like approach where one associates to the spontaneous dynamics of the model a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. These two examples are the Amari-Wilson-Cowan mode and a conductance based Integrate and Fire model

This work has been published in [13], [31], [18].

On the role of Nav1.7 sodium channels in chronic pain: an experimental and computational study

Participants : Lyle Armstrong [Institute of Neuroscience (ION), Newcastle, UK] , Alberto Capurro [Institute of Neuroscience (ION), Newcastle, UK] , Bruno Cessac, Jack Thornton [Institute of Neuroscience (ION), Newcastle, UK] , Evelyne Sernagor [Institute of Neuroscience (ION), Newcastle, UK] .

Chronic pain is a global healthcare problem with a huge societal impact. Its management remains generally unsatisfactory, with no single treatment clinically approved in most cases. In this study we use an in vitro model of erythromelalgia consisting of dorsal root ganglion neurons derived from human induced pluripotent stem cells obtained from a patient (carrying the mutation F1449V) and a control subject. We combine neurophysiology and computational modelling to focus on the Nav1.7 voltage gated sodium channel, which acts as an amplifier of the receptor potential in nociceptive neurons and plays a critical role in erythromelalgia due to gain of function mutations causing the channel to open with smaller depolarisations. Using extracellular recordings, we found that the scorpion toxin OD1 (a Nav1.7 channel opener) increases dorsal root ganglion cell excitability in cultures obtained from the control donor, evidenced by an increase in spontaneous discharges, firing rate and spike amplitude. In addition, we confirmed previous reports of voltage clamp experiments concerning an increase in spontaneous discharge in the patient cell cultures and the analgesic effects of the Nav1.7 blocker PF-05089771. Our findings are explained with a conductance-based model of the dorsal root ganglion neuron, exploring its behaviour for different values of half activation voltage and inactivation removal rate of the Nav1.7 current. Erythromelalgia was simulated through a decrease of the Nav1.7 half activation voltage, turning previously subthreshold stimuli to pain-inducing, and successfully counteracted with the channel blocker. The painful effects of OD1 were simulated through a quicker removal of Nav1.7 inactivation that reproduced the effects of the toxin not only on the spike frequency but also on its amplitude. This work has been submitted to J. Neuroscience. [30].

Ghost attractors in spontaneous brain activity: wandering in a repertoire of functionally relevant BOLD phaselocking solutions

Participants : Joana Cabral [Department of Psychiatry, Medical Sciences Division, University of Oxford,UK ] , Bruno Cessac, Gustavo Deco [Catalan Institute for Research and Advance Studies (ICREA), Spain] , Morten L. Kringelbach [University of Oxford, UK] , Jakube Vohryzek [Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Denmark] .

Functionally relevant network patterns form transiently in brain activity during rest, where a given subset of brain areas exhibits temporally synchronized BOLD signals. To adequately assess the biophysical mechanisms governing intrinsic brain activity, a detailed characterization of the dynamical features of functional networks is needed from the experimental side to inform theoretical models. In this work, we use an open-source fMRI dataset from 100 unrelated participants from the Human Connectome Project and analyse whole-brain activity using Leading Eigenvector Dynamics Analysis, which focuses on the detection of recurrent phase-locking patterns in the BOLD signal. Borrowing tools from dynamical systems theory, we characterise spontaneous brain activity in the form of trajectories within a low-dimensional phase space. Decomposing the phase space into Voronoi-like cells using k-means clustering algorithm, we demonstrate that the cluster centroids (representing recurrent BOLD phase-locking patterns) closely overlap with previously identified resting-state networks. We further demonstrate that the metric associated with the phase-locking patterns shows moderate reliability across recordings indicating potential existence of subject specific dynamical landscapes. Our results point to the hypothesis that functional brain networks behave as ghost attractor states in a low-dimensional phase space, providing insights into the evolutionary rules governing brain activity in the spontaneous state and reinforcing the importance of addressing brain function within the framework of dynamical systems theory. This work has been submitted to Frontiers in Systems Neuroscience.