Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms

Electrical neurostimulation for chronic pain: on selective relay of sensory neural activities in myelinated nerve fibers

Chronic pain affects about 100 million adults in the US. Despite their great need, neuropharmacology and neurostimulation therapies for chronic pain have been associated with suboptimal efficacy and limited long-term success, as their mechanisms of action are unclear. Yet current computational models of pain transmission suffer from several limitations. In particular, dorsal column models do not include the fundamental underlying sensory activity traveling in these nerve fibers. We developed a (simple) simulation test bed of electrical neurostimulation of myelinated nerve fibers with underlying sensory activity. This paper reports our findings so far. Interactions between stimulation-evoked and underlying activities are mainly due to collisions of action potentials and losses of excitability due to the refractory period following an action potential. In addition, intuitively, the reliability of sensory activity decreases as the stimulation frequency increases. This first step opens the door to a better understanding of pain transmission and its modulation by neurostimulation therapies

Kick synchronization versus diffusive synchronization

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling.Peer reviewe

Winning versus losing during gambling and its neural correlates

Humans often make decisions which maximize an internal utility function. For example, humans often maximize their expected reward when gambling and this is considered as a "rational" decision. However, humans tend to change their betting strategies depending on how they "feel". If someone has experienced a losing streak, they may "feel" that they are more likely to win on the next hand even though the odds of the game have not changed. That is, their decisions are driven by their emotional state. In this paper, we investigate how the human brain responds to wins and losses during gambling. Using a combination of local field potential recordings in human subjects performing a financial decision-making task, spectral analyses, and non-parametric cluster statistics, we investigated whether neural responses in different cognitive and limbic brain areas differ between wins and losses after decisions are made. In eleven subjects, the neural activity modulated significantly between win and loss trials in one brain region: the anterior insula ($p=0.01$). In particular, gamma activity (30-70 Hz) increased in the anterior insula when subjects just realized that they won. Modulation of metabolic activity in the anterior insula has been observed previously in functional magnetic resonance imaging studies during decision making and when emotions are elicited. However, our study is able to characterize temporal dynamics of electrical activity in this brain region at the millisecond resolution while decisions are made and after outcomes are revealed

The endogenous nature of bursting leads to homeostatic reset in synaptic weights: a key player to regularize network connectivity during sleep

editorial reviewedLearning and memory rely on the ability of neurons to form new connections, a property called synaptic plasticity. Synaptic connections can be strengthened or weakened via plasticity rules sensitive to neuronal firing. Simultaneously, brain information processing is shaped by fluctuations in neuronal activities, defining brain states. A well-known example of brain state switches is the transition from wakefulness to sleep. It is characterized by a change in population rhythm from active to oscillatory state, while at the cellular level neurons switch from tonic to burst. Altogether, it raises the question of how changes in neuronal activity affect memory formation and more precisely how switches from tonic to burst impact synaptic plasticity. To investigate this question, we used a cortical network built with conductance-based neuron models able to switch between tonic and burst. The synaptic connections within the network are plastic. They are driven either by phenomenological rules, such as pair-based [Pfister,2006] or calcium-based rules [Graupner,2016]. These rules are fitted on experimental data [Sjostrom,2001]. We showed that a switch to burst reminiscent of sleep leads to a homeostatic reset of synaptic weights, meaning that all weights converge towards a basal value. Here, we developed analytical analyses to understand the mechanisms underlying this reset and predict its value. For phenomenological plasticity rules, potentiation and depression balance leading to a converging point for the synaptic weight. The burst induces a homogeneous spike train correlation between pre and postsynaptic firing activity thanks to the stationarity during sleep. By contrast, in wakefulness, the correlation is highly heterogeneous. It comes from the variability in spiking activity used for the quick processing of incoming information such that no equilibrium is reached. A similar analysis is derived for calcium-based rules. The burst of action potential drives homeostatic fluctuations in calcium activity. Once again, the burst generates a balance between potentiation and depression unreached during wakefulness. Altogether, the mechanisms of the synaptic reset are rooted in the endogenous nature of the sleep-like bursting activity. Additionally, we show that the homeostatic reset is robust to neuronal variability and network heterogeneity. The sleep-dependent reset could play a central role in sleep homeostasis and sleep-dependent memory consolidation

Invariant Kalman Filtering with Noise-Free Pseudo-Measurements

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Modeling Responses to Peripheral Nerve Stimulation in the Dorsal Horn

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Switches to rhythmic brain activity lead to a plasticity-induced reset in synaptic weights

AbstractBrain function relies on the ability to quickly process incoming information while being capable of forming memories of past relevant events through the formation of novel synaptic connections. Synaptic connections are functionally strengthened or weakened to form new memories through synaptic plasticity rules that strongly rely on neuronal rhythmic activities. Brain information processing, on the other hand, is shaped by fluctuations in these neuronal rhythmic activities, each defining distinctive brain states, which poses the question of how such fluctuations in brain states affect the outcome of memory formation. This question is particularly relevant in the context of sleep-dependent memory consolidation, wakefulness to sleep transitions being characterized by large modifications in global neuronal activity. By combining computational models of neuronal activity switches and plasticity rules, we show that switches to rhythmic brain activity reminiscent of sleep lead to a reset in synaptic weights towards a basal value. This reset is shown to occur both in phenomenological and biophysical models of synaptic plasticity, and to be robust to neuronal and synaptic variability and network heterogeneity. Analytical analyses further show that the mechanisms of the synaptic reset are rooted in the endogenous nature of the sleep-like rhythmic activity. This sleep-dependent reset in synaptic weights permits regularizing synaptic connections during sleep, which could be a key component of sleep homeostasis and has the potential to play a central role in sleep-dependent memory consolidation