Patterns of interval correlations in neural oscillators with adaptation

Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of noisy neural oscillators with spike-triggered adaptation of arbitrary strength and time scale. Our weak-noise theory provides a general relation between the correlations and the phase-response curve (PRC) of the oscillator, proves anti-correlations between neighboring intervals for adapting neurons with type I PRC and identifies a single order parameter that determines the qualitative pattern of correlations. Monotonically decaying or oscillating correlation structures can be related to qualitatively different voltage traces after spiking, which can be explained by the phase plane geometry. A thigh firing rates, the long-term variability of the spike train associated with the cumulative interval correlations becomes small, independent of model details. Our results are verified by comparison with stochastic simulations of the exponential, leaky, and generalized integrate-and-fire models with adaptation

Made-to-Order Spiking Neuron Model Equipped with a Multi-Timescale Adaptive Threshold

Information is transmitted in the brain through various kinds of neurons that respond differently to the same signal. Full characteristics including cognitive functions of the brain should ultimately be comprehended by building simulators capable of precisely mirroring spike responses of a variety of neurons. Neuronal modeling that had remained on a qualitative level has recently advanced to a quantitative level, but is still incapable of accurately predicting biological data and requires high computational cost. In this study, we devised a simple, fast computational model that can be tailored to any cortical neuron not only for reproducing but also for predicting a variety of spike responses to greatly fluctuating currents. The key features of this model are a multi-timescale adaptive threshold predictor and a nonresetting leaky integrator. This model is capable of reproducing a rich variety of neuronal spike responses, including regular spiking, intrinsic bursting, fast spiking, and chattering, by adjusting only three adaptive threshold parameters. This model can express a continuous variety of the firing characteristics in a three-dimensional parameter space rather than just those identified in the conventional discrete categorization. Both high flexibility and low computational cost would help to model the real brain function faithfully and examine how network properties may be influenced by the distributed characteristics of component neurons

Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue

Neuronal adaptation as well as interdischarge interval correlations havebeen shown to be functionally important properties of physiological neurons.We explore the dynamics of a modified leaky integrate-and-fire (LIF)neuron, referred to as the LIF with threshold fatigue, and show that itreproduces these properties. In this model, the postdischarge thresholdreset depends on the preceding sequence of discharge times. We showthat in response to various classes of stimuli, namely, constant currents,step currents, white gaussian noise, and sinusoidal currents, the modelexhibits new behavior compared with the standard LIF neuron. More precisely,(1) step currents lead to adaptation, that is, a progressive decreaseof the discharge rate following the stimulus onset, while in the standardLIF, no such patterns are possible; (2) a saturation in the firing rate occursin certain regimes, a behavior not seen in the LIF neuron; (3) interspikeintervals of the noise-driven modified LIF under constant current are correlatedin a way reminiscent of experimental observations, while thoseof the standard LIF are independent of one another; (4) the magnitude ofthe correlation coefficients decreases as a function of noise intensity; and(5) the dynamics of the sinusoidally forced modified LIF are describedby iterates of an annulus map, an extension to the circle map dynamicsdisplayed by the LIF model. Under certain conditions, this map can giverise to sensitivity to initial conditions and thus chaotic behavior

Deterministic and stochastic dynamics of multi-variable neuron models : resonance, filtered fluctuations and sodium-current inactivation

Neurons are the basic elements of the networks that constitute the computational units of the brain. They dynamically transform input information into sequences of electrical pulses. To conceive the complex function of the brain, it is crucial to understand this transformation and identify simple neuron models which accurately reproduce the known features of biological neurons. This thesis addresses three different features of neurons. We start by exploring the effect of subthreshold resonance on the response of a periodically forced neuron using a simple threshold model. The response is studied in terms of an implicit one-dimensional time map that corresponds to the Poincar´e map of the forced system. Qualitatively distinct responses are found, including mode locking and chaos. We analytically find the stability regions of mode-locking solutions, and identify the transition to chaos through period-adding bifurcations. We show that the response becomes chaotic when the forcing frequency is close to the resonant frequency. Then we will consider an experimentally verified model with realistic spikegenerating mechanism and study the effect of filtered synaptic fluctuations on the firing-rate response of the neuron. Using a population density method as well as an efficient numerical method, we find the steady-state firing rate in two limits of fast and slow synaptic inputs and present the linear response theory for the firing rate of the model in response to both time-dependent mean inputs and time-dependent noise intensity. Finally, a novel model is introduced that incorporates threshold variability of neurons. We determine the modulation of the input-output properties of the model due to oscillatory inputs and in the presence of filtered synaptic fluctuations.EThOS - Electronic Theses Online ServiceUniversity of WarwickOverseas Research Students Awards Scheme (ORSAS)GBUnited Kingdo

Neues Konzept zur Bewegungsanalyse und -synthese für Humanoide Roboter basierend auf Vorbildern aus der Biologie

Es werden neue Methoden zur Bewegungsgenerierung und -analyse von humanoiden Robotern vorgestellt und zur Anwendung gebracht. Als Vorbild dienen zum Einen menschliche Reflexe, zum Anderen zentrale neuronale Mustergeneratoren (CPG) für zyklische Bewegungen. Mit Leaky Integrate-and-Fire Neuronen wird ein generisches Reflexmodell erstellt und für konkrete Reflexe realisiert. Die erstellten CPGs dienen sowohl der Bewegungsanalyse als auch der -generierung für einen zweibeinigen Demonstrator

Experimentally verified reduced models of neocortical pyramidal cells

Reduced neuron models are essential tools in computational neuroscience to aid understanding from the single cell to network level. In this thesis I use these models to address two key challenges: introducing experimentally verifi�ed heterogeneity into neocortical network models, and furthering understanding of post-spike refractory mechanisms. Neocortical network models are increasingly including cell class diversity. However, within these classes significant heterogeneity is displayed, an aspect often neglected in modelling studies due to the lack of empirical constraints on the variance and covariance of neuronal parameters. To address this I quantified the response of pyramidal cells in neocortical layers 2/3-5 to square-pulse and naturalistic current stimuli. I used standard and dynamic I-V protocols to measure electrophysiological parameters, a byproduct of which is the straightforward extraction of reduced neuron models. I examined the between- and within-class heterogeneity, culminating in an algorithm to generate populations of exponential integrate-and-�re (EIF) neurons adhering to the empirical marginal distributions and covariance structure. This provides a novel tool for investigating heterogeneity in neocortical network models. Spike threshold is dynamic and, on spike initiation, displays a jump and subsequent exponential decay back to baseline. I examine extensions to the EIF model that include these dynamics, fi�nding that a simple renewal process model well captures the cell's response. It has been previously noted that a two-variable EIF model describing the voltage and threshold dynamics can be reduced to a single-variable system when the membrane and threshold time constants are similar. I examine the response properties of networks of these models by taking a perturbative approach to solving the corresponding Fokker-Planck equation, �finding the results in agreement with simulations over the physiological range of the membrane to threshold time constant ratio. Finally, I found that the observed threshold dynamics are not fully described by the inclusion of slow sodium-channel inactivation

The Dynamics of Adapting Neurons

How do neurons dynamically encode and treat information? Each neuron communicates with its distinctive language made of long silences intermitted by occasional spikes. The spikes are prompted by the pooled effect of a population of pre-synaptic neurons. To understand the operation made by single neurons is to create a quantitative description of their dynamics. The results presented in this thesis describe the necessary elements for a quantitative description of single neurons. Almost all chapters can be unified under the theme of adaptation. Neuronal adaptation plays an important role in the transduction of a given stimulation into a spike train. The work described here shows how adaptation is brought by every spike in a stereotypical fashion. The spike-triggered adaptation is then measured in three main types of cortical neurons. I analyze in detail how the different adaptation profiles can reproduce the diversity of firing patterns observed in real neurons. I also summarize the most recent results concerning the spike-time prediction in real neurons, resulting in a well-founded single-neuron model. This model is then analyzed to understand how populations can encode time-dependent signals and how time-dependent signals can be decoded from the activity of populations. Finally, two lines of investigation in progress are described, the first expands the study of spike-triggered adaptation on longer time scales and the second extends the quantitative neuron models to models with active dendrites