Multi-modal characterization and simulation of human epileptic circuitry

Temporal lobe epilepsy is the fourth most common neurological disorder with about 40% of patients not responding to pharmacological treatment. Increased cellular loss in the hippocampus is linked to disease severity and pathological phenotypes such as heightened seizure propensity. While the hippocampus is the target of therapeutic interventions such as temporal lobe resection, the impact of the disease at the cellular level remains unclear in humans. Here we show that properties of hippocampal granule cells change with disease progression as measured in living, resected hippocampal tissue excised from epilepsy patients. We show that granule cells increase excitability and shorten response latency while also enlarging in cellular volume, surface area and spine density. Single-cell RNA sequencing combined with simulations ascribe the observed electrophysiological changes to gradual modification in three key ion channel conductances: BK, Cav2.2 and Kir2.1. In a bio-realistic computational network model, we show that the changes related to disease progression bring the circuit into a more excitable state. In turn, we observe that by reversing these changes in the three key conductances produces a less excitable, early disease-like state. These results provide mechanistic understanding of epilepsy in humans and will inform future therapies such as viral gene delivery to reverse the course of the disorder

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

Modélisation de la cellule et des phénomènes de réseaux dans le système nerveux : dynamique des ions au cours des oscillations d'épilepsie et résonance stochastique inverse

In this thesis we used dynamical systems methods and numericalsimulations to study the mechanisms of epileptic oscillations associated with ionconcentration changes and cerebellar Purkinje cell bimodal behavior. The general issue in this work is the interplay between single neuron intrinsicproperties and synaptic input structure controlling the neuronal excitability. In the first part of this thesis we focused on the role of the cellular intrinsicproperties, their control over the cellular excitability and their response to thesynaptic inputs. Specifically we asked the question how the cellular changes ininhibitory synaptic function might lead to the pathological neural activity. We developed a model of seizure initiation in temporal lobe epilepsy. Specifically we focused on the role of KCC2 cotransporter that is responsible for maintaining the baseline extracellular potassium and intracellular chloride levels in neurons. Recent experimental data has shown that this cotransporter is absent in the significant group of pyramidal cells in epileptic patients suggesting its epileptogenic role. We found that addition of the critical amount of KCC2-deficient pyramidal cells to the realistic subiculum network can switch the neural activity from normal to epileptic oscillations qualitatively reproducing the activity recorded in human epileptogenic brain slices. In the second part of this thesis we studied how synaptic noise might control the Purkinje cell excitability. We investigated the effect of spike inhibition caused by noise current injection, so-called inverse stochastic resonance (ISR). This effect has been previously found in single neuron models while we provided its first experimental evidence. We found that Purkinje cells in brain slices could be efficiently inhibited by current noise injections. This effect is well reproduced by the phenomenological model fitted for different cells. Using methods of information theory we showed that ISR supports an efficient information transmission of single Purkinje cells suggesting its role for cerebellar computations.Dans cette thèse nous avons utilisé des méthodes de systèmes dynamiques et des simulations numériques pour étudier les mécanismes d'oscillations d'épilepsie associés à des concentrations d’ions dynamiques et au comportement bimodal des cellules Purkinje du cervelet. Le propos général de ce travail est l'interaction entre les propriétés intrinsèques des neurones simple et la structure d'entrée synaptique contrôlant l'excitabilité neuronale. Dans la première partie de la thèse nous avons développé un modèle de transition de crise épileptique dans le lobe temporal du cerveau. Plus précisément nous nous sommes concentrés sur le rôle du cotransporteur KCC2, qui est responsable de la maintenance du potassium extracellulaire et du chlorure intracellulaire dans les neurones. Des données expérimentales récentes ont montré que cette molécule est absente dans un groupe significatif de cellules pyramidales dans le tissue neuronal de patients épileptiques suggérant son rôle épileptogène. Nous avons trouvé que l'addition d’une quantité critique de cellules pyramidale KCC2 déficient au réseau de subiculum, avec une connectivité réaliste, peut provoquer la génération d’oscillations pathologiques, similaire aux oscillations enregistrées dans des tranches de cerveau épileptogène humaines. Dans la seconde partie de la thèse, nous avons étudié le rôle du bruit synaptique dans les cellules de Purkinje. Nous avons étudié l'effet de l'inhibition de la génération du potentiel d’action provoquée par injection de courant de bruit, un phénomène connu comme résonance stochastique inverse (RSI). Cet effet a déjà été trouvé dans des modèles neuronaux, et nous avons fournis sa première validation expérimentale. Nous avons trouvé que les cellules de Purkinje dans des tranches de cerveau peuvent être efficacement inhibées par des injectionsde bruit de courant. Cet effet est bien reproduit par le modèle phénoménologique adapté pour différentes cellules. En utilisant des méthodes de la théorie de l'information, nous avons montré que RSI prend en charge une transmission efficace de l'information des cellules de Purkinje simples suggérant son rôle pour les calculs du cervelet

Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure

International audiencePharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state

Cerebellar Purkinje cells show inverse stochastic resonance (ISR).

<p>A. Whole-cell patch-clamp recording from a Purkinje cell in a cerebellar slice, showing current injection of 1 s noise waveform periods with increasing amplitude, and recorded membrane potential <i>V</i>_<i>m</i>. Holding current is <i>I</i> = −290 pA. The firing rate of the Purkinje cell (PC) is reduced for intermediary noise amplitude. B. Firing frequency during 1 s noise injection vs. noise amplitude <i>σ</i> corresponding to the trace in A. Error bars indicate standard deviation. The firing rate is minimal for <i>σ</i> = 100 pA. C. ISR is observed in all Purkinje cells tested. Summary of optimal noise amplitude σ = 152.60 ± 64.42 pA (n = 19). D. ISR curve of a different PC, generated with a current injection protocol of continuously changing noise amplitude and for a series of holding currents, exploring the full range of the <i>f-I</i> curve (E). The firing rate is most reduced when the cell is hyperpolarized to the edge of the <i>f-I</i> curve step. The optimal noise amplitude for inhibition of firing is σ = 200 pA. E. Frequency vs. current generated with 1 s step current injections. The color code corresponds to the region explored for the ISR curve in D. F. Membrane potential distributions computed from a somatic whole-cell patch-clamp recording from a Purkinje cell during injection of a stimulus current evoking transitions between spiking and silent states (A).</p

Hysteresis and ISR of the aEIF model.

<p>A Voltage response of the aEIF model to Ornstein-Uhlenbeck current noise injection with increasing amplitude. B. Mean firing rate of the aEIF model in response to current noise stimulation with amplitude <i>σ</i> and mean <i>I</i> (color code). C. Hysteresis of the aEIF model. Top, voltage response to ascending (red) and descending (blue) ramp of current. Bottom, instantaneous firing rate vs. instantaneous injected current. Color code is the same as in B. D. Parameter space of the rescaled aEIF model, white region: type I excitability, gray region: type II excitability. The 7 fitted cells are in the type II region. E, F. Dependence of the hysteresis size Δ<i>I</i> on the parameters <i>T τ</i>_<i>w</i>/<i>τ</i>_<i>m</i> (E) and <i>A</i> = <i>a</i>/<i>g</i>_<i>L</i> (F). G. Membrane potential distribution in the aEIF model during spiking and silent states.</p

aEIF model fitting procedure to Purkinje cell experimental data.

<p>A. Double somatic whole-cell patch-clamp recording from a representative Purkinje cell: one electrode for current injection and one for voltage recording (scale bar, 100 <i>μ</i> m). B. Traces of injected noise current <i>I</i>_<i>in</i>(<i>t</i>), recorded membrane potential <i>V</i>_<i>m</i>(<i>t</i>), in a spontaneously active PC, calculated membrane current <i>I</i>_<i>m</i>(<i>t</i>), and calculated spike-dependent adaptation current <i>w</i>_<i>sp</i>(<i>t</i>). C. <i>I</i>_<i>m</i> vs. <i>V</i>_<i>m</i> and dynamic IV curve as the average over <i>V</i>_<i>m</i>. Error bars indicate SEM. Inset, the distribution of data points at <i>V</i>_<i>m</i> = -52 mV is Gaussian. D. Fitting the dynamic IV curve F(<i>V</i>) = −<i>I</i>_<i>dyn</i>/<i>C</i> with the EIF model function. Parameters are: resting potential <i>E</i>_<i>m</i>, membrane time constant <i>τ</i>_<i>m</i>, threshold potential <i>V</i>_<i>T</i>, and spike slope factor Δ_<i>T</i>. Error bars indicate SD. Inset, capacitance determination by minimizing the variance of <i>I</i>_<i>m</i>. E. Spike triggered adaptation <i>w</i>_<i>sp</i>(<i>t</i>) plotted versus time after the last spike. Error bars indicate SEM. Inset, the distribution of data points at <i>t</i> = 12 ms is Gaussian. F. The spike-triggered adaptation is fitted to a single exponential, with time constant <i>τ</i>_<i>w</i> and <i>w</i>_<i>sp</i> (t = 0) = b. Error bars indicate SD.</p

ISR transforms brief inputs into long-term firing states depending on background noise.

<p>A, B, C. Characteristic voltage traces of the aEIF model in response to a single synaptic excitatory input in the presence of different levels of background noise with amplitude <i>σ</i> = 10 pA, 30 pA and 60 pA. Bottom, corresponding probability of spiking for a range of input amplitudes (color code). D. Maximal probability of state transition vs. synaptic input amplitude for 3 background noise amplitudes, E. Decay time constant for the duration of the spiking state induced by a synaptic input of 100 pA. Remark: two data points corresponding to <i>σ</i> = 0 pA, 100 pA are not shown because for <i>σ</i> = 0 pA the duration of stimulus-induced spiking state is infinite, while for <i>σ</i> = 100 pA the duration of this state could not be distinguished from the firing baseline.</p

Experimental characterization of Purkinje cell bistability.

<p>A. Whole-cell patch-clamp recording from a Purkinje cell, showing a representative hysteresis measurement with slow current ramp injection (0.9 nA/s) ascending (red) and descending (blue), and the resulting PC membrane potential response. B. Instantaneous firing frequency and current for each spike. Linear fits of the ascending ramp (red) and the descending ramp (blue) are averages of 10 trials. C. Characterization of the hysteresis using the difference in frequency between first and last spike Δ<i>f</i> and difference in current Δ<i>I</i>. The color code illustrates the region explored for the ISR curve. Red corresponds to both the hysteresis and the optimal ISR region (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005000#pcbi.1005000.g001" target="_blank">Fig 1D and 1E</a>). D. Distribution of hysteresis parameters across the population of recorded Purkinje cells. E. Correlation between the width of the hysteresis range Δ<i>I</i> and the optimal noise level for ISR <i>σ</i>_<i>opt</i>. Error bars indicate standard deviation, <i>R</i>² = 0.79 (n = 19).</p