Controling Switching between Birhythmic States in a New Conductance-based Bursting Neuronal Model

A birhythmic conductance-based neuronal model with fast and slow variables is proposed to generate and control the coexistence of two different attracting modes in amplitudes and frequencies. However, periodic bursting, chaotic spiking and bursting haven’t been clearly observed there. The control of bistability is investigated in a three-dimensional birhythmic conductance-based neuronal model. We consider slow processes in neuron materialized by an adaptation variable coupled to system in the presence of an externalinusoidal current applied. By using the harmonic balance method, we obtain the frequency-response curve in which membrane potential resonance with his corresponding frequency are control by varying a specific parameter. At the resonance frequency, bifurcation and lyapunov exponent diagrams versus a control parameter are obtained. They reveal, a coexistence of two different complex attractors namely periodic and chaotic spiking, periodic and chaotic bursting. By using the control parameter as the slow variable, the system can switch from bistable to monostable behavior. This is done by destroying subthreshold (small) oscillation of the neuron. The role of adaptation variable in neuron system is then to filtered many existing electrical processes and permit to adapt the system by the multiple transitions states in the chosen electrical mode. A fairly good agreement is observed between analytical and numerical results.

Evidence for Multiple Teosinte Hybrid Zones in Central Mexico

1SummaryHybrid zones provide an excellent opportunity for studying population dynamics and whether hybrid genetic architectures are locally adaptive. The genus Zea contains many diverse wild taxa collectively called teosinte. Zea mays ssp. parviglumis, the lowland progenitor of maize (Zea mays ssp. mays), and its highland relative Zea mays ssp. mexicana live parapatrically and, while putative hybrids have been identified in regions of range overlap, these have never been deeply explored.Here we use a broadly sampled SNP data set to identify and confirm 112 hybrids between Zea mays ssp. parviglumis and Zea mays ssp. mexicana, mostly clustered in three genetically and geographically distinct hybrid groups in Central Mexico.These hybrid groups inhabit intermediate environments relative to parental taxa. We demonstrate that these individuals are true hybrids and not products of isolation by distance or ancestral to parviglumis and mexicana. This work expands on previous studies, clearly identifying hybrid zones in Zea, genetically characterizing hybrid groups, and showing what appear to be unique genetic architectures of hybridization in distinct hybrid groups.With the potential for local adaptation, variable hybrid zone dynamics, and differential architectures of hybridization, we present these teosinte hybrids and parental taxa as a promising model system for studying hybridization and hybrid zones.

Enhanced Signal Detection by Adaptive Decorrelation of Interspike Intervals

Spike trains with negative interspike interval (ISI) correlations, in which long/short ISIs are more likely followed by short/long ISIs, are common in many neurons. They can be described by stochastic models with a spike-triggered adaptation variable. We analyze a phenomenon in these models where such statistically dependent ISI sequences arise in tandem with quasi-statistically independent and identically distributed (quasi-IID) adaptation variable sequences. The sequences of adaptation states and resulting ISIs are linked by a nonlinear decorrelating transformation. We establish general conditions on a family of stochastic spiking models that guarantee this quasi-IID property and establish bounds on the resulting baseline ISI correlations. Inputs that elicit weak firing rate changes in samples with many spikes are known to be more detectible when negative ISI correlations are present because they reduce spike count variance; this defines a variance-reduced firing rate coding benchmark. We performed a Fisher information analysis on these adapting models exhibiting ISI correlations to show that a spike pattern code based on the quasi-IID property achieves the upper bound of detection performance, surpassing rate codes with the same mean rate—including the variance-reduced rate code benchmark—by 20% to 30%. The information loss in rate codes arises because the benefits of reduced spike count variance cannot compensate for the lower firing rate gain due to adaptation. Since adaptation states have similar dynamics to synaptic responses, the quasi-IID decorrelation transformation of the spike train is plausibly implemented by downstream neurons through matched postsynaptic kinetics. This provides an explanation for observed coding performance in sensory systems that cannot be accounted for by rate coding, for example, at the detection threshold where rate changes can be insignificant.

On the Simulation of Nonlinear Bidimensional Spiking Neuron Models

Bidimensional spiking models are garnering a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons and are used particularly for large network simulations. These models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. Spikes are emitted when the membrane potential blows up or reaches a cutoff θ. The precise simulation of the spike times and of the adaptation variable is critical, for it governs the spike pattern produced and is hard to compute accurately because of the exploding nature of the system at the spike times. We thoroughly study the precision of fixed time-step integration schemes for this type of model and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time. Precise evaluation of these quantities therefore involves very small time steps and long simulation times. In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time-step Euler scheme and other more accurate simulation algorithms.

Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value Vc or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing Vc can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.