An organizing center in a planar model of neuronal excitability

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables

Minimum Number of Probes for Brain Dynamics Observability

In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the model of the brain activity satisfies fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contribution of this paper is to show how to place the minimum number of dedicated sensors, i.e., sensors measuring only a state variable, to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720

Ion channel degeneracy enables robust and tunable neuronal firing rates.

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.This is the author accepted manuscript. The final version is available from National Academy of Sciences via http://dx.doi.org/10.1073/pnas.1516400112

MEG sensor and source measures of visually induced gamma-band oscillations are highly reliable

High frequency brain oscillations are associated with numerous cognitive and behavioral processes. Non-invasive measurements using electro-/magnetoencephalography (EEG/MEG) have revealed that high frequency neural signals are heritable and manifest changes with age as well as in neuropsychiatric illnesses. Despite the extensive use of EEG/MEG-measured neural oscillations in basic and clinical research, studies demonstrating test–retest reliability of power and frequency measures of neural signals remain scarce. Here, we evaluated the test–retest reliability of visually induced gamma (30–100 Hz) oscillations derived from sensor and source signals acquired over two MEG sessions. The study required participants (N = 13) to detect the randomly occurring stimulus acceleration while viewing a moving concentric grating. Sensor and source MEG measures of gamma-band activity yielded comparably strong reliability (average intraclass correlation, ICC = 0.861). Peak stimulus-induced gamma frequency (53–72 Hz) yielded the highest measures of stability (ICCsensor = 0.940; ICCsource = 0.966) followed by spectral signal change (ICCsensor = 0.890; ICCsource = 0.893) and peak frequency bandwidth (ICCsensor = 0.856; ICCsource = 0.622). Furthermore, source-reconstruction significantly improved signal-to-noise for spectral amplitude of gamma activity compared to sensor estimates. Our assessments highlight that both sensor and source derived estimates of visually induced gamma-band oscillations from MEG signals are characterized by high test–retest reliability, with source derived oscillatory measures conferring an improvement in the stability of peak-frequency estimates. Importantly, our finding of high test–retest reliability supports the feasibility of pharma-MEG studies and longitudinal aging or clinical studies

Robust Modulation of Integrate-and-Fire Models.

By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks

Excitable neurons, firing threshold manifolds and canards

We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J. Appl. Dyn. Syst. 11(4):1674-1697, 2012). Propofol modulates the decay time-scale of an inhibitory GABAa synaptic current. Interestingly, this system gives rise to rebound spiking within a specific range of propofol doses. Using techniques from geometric singular perturbation theory, we identify geometric structures, known as canards of folded saddle-type, which form the firing threshold manifolds. We find that the position and orientation of the canard separatrix is propofol dependent. Thus, the speeds of relevant slow synaptic processes are encoded within this geometric structure. We show that this behavior cannot be understood using a static, inhibitory current step protocol, which can provide a single threshold for rebound spiking but cannot explain the observed cessation of spiking for higher propofol doses. We then compare the analyses of dynamic and static synaptic inhibition, showing how the firing threshold manifolds of each relate, and why a current step approach is unable to fully capture the behavior of this model