Spike Onset Dynamics and Response Speed in Neuronal Populations

Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency of the order of average firing rate or the inverse membrane time constant. The biophysical origin of the observed high cutoff frequencies is thus not well understood. Here we introduce a neuron model with dynamical action potential generation, in which the linear response can be analytically calculated for uncorrelated synaptic noise. We find that the cutoff frequencies increase to very large values when the time scale of action potential initiation becomes short

Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons

Motif Statistics and Spike Correlations in Neuronal Networks

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state

A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral statistics (power spectra, cross spectra, and coherence functions) in different dynamical regimes (noise-induced and tonic firing regimes with low or moderate noise). We make the models comparable by tuning parameters such that the mean value and the coefficient of variation of the interspike interval match for all of them. We find that, under these conditions, the power spectrum under white-noise stimulation is often very similar while the response characteristics, described by the cross spectrum between a fraction of the input noise and the output spike train, can differ drastically. We also investigate how the spike trains of two neurons of the same kind (e.g. two leaky IF neurons) correlate if they share a common noise input. We show that, depending on the dynamical regime, either two quadratic IF models or two leaky IFs are more strongly correlated. Our results suggest that, when choosing among simple IF models for network simulations, the details of the model have a strong effect on correlation and regularity of the output.Comment: 12 page

Stabilisation of beta and gamma oscillation frequency in the mammalian olfactory bulb

International audienceThe dynamics of the mammalian olfactory bulb (OB) is characterized by local field potential (LFP) oscillations either slow, in the theta range (2-10Hz, tightly linked to the respiratory rhythm), or fast, in the beta (15-30Hz) or gamma (40-90Hz) range. These fast oscillations are known to be modulated by odorant features and animal experience or state, but both their mechanisms and implication in coding are still not well understood. In this study, we used a double canulation protocol to impose artificial breathing rhythms to anesthetized rats while recording the LFP in the OB. We observed that despite the changes in the input air flow parameters (frequency or flow rate), the main characteristics of fast oscillations (duration, frequency or amplitude) were merely constant. We thus made the hypothesis that fast beta and gamma oscillations dynamics are entirely determined by the OB network properties and that external stimulation was only able put the network in a state which permits the generation of one or the other oscillations (they are never present simultaneously)

A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.Comment: Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures

Finite element analysis of trees in the wind based on terrestrial laser scanning data

Wind damage is an important driver of forest structure and dynamics, but it is poorly understood in natural broadleaf forests. This paper presents a new approach in the study of wind damage: combining terrestrial laser scanning (TLS) data and finite element analysis. Recent advances in tree reconstruction from TLS data allowed us to accurately represent the 3D geometry of a tree in a mechanical simulation, without the need for arduous manual mapping or simplifying assumptions about tree shape. We used this simulation to predict the mechanical strains produced on the trunks of 21 trees in Wytham Woods, UK, and validated it using strain data measured on these same trees. For a subset of five trees near the anemometer, the model predicted a five-minute time-series of strain with a mean cross-correlation coefficient of 0.71, when forced by the locally measured wind speed data. Additionally, the maximum strain associated with a 5 ms−1 or 15 ms-1 wind speed was well predicted by the model (N = 17, R2 = 0.81 and R2 = 0.79, respectively). We also predicted the critical wind speed at which the trees will break from both the field data and models and find a good overall agreement (N = 17, R2 = 0.40). Finally, the model predicted the correct trend in the fundamental frequencies of the trees (N = 20, R2 = 0.38) although there was a systematic underprediction, possibly due to the simplified treatment of material properties in the model. The current approach relies on local wind data, so must be combined with wind flow modelling to be applicable at the landscape-scale or over complex terrain. This approach is applicable at the plot level and could also be applied to open-grown trees, such as in cities or parks

Numerical Solution of Differential Equations by the Parker-Sochacki Method

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a university web site, but has now been cited and praised in one or more refereed journals. I am therefore submitting it to the Cornell arXiv so that it may be read in response to its citations. See "Spiking neural network simulation: numerical integration with the Parker-Sochacki method:" J. Comput Neurosci, Robert D. Stewart & Wyeth Bair and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378

The location of the axon initial segment affects the bandwidth of spike initiation dynamics

The dynamics and the sharp onset of action potential (AP) generation have recently been the subject of intense experimental and theoretical investigations. According to the resistive coupling theory, an electrotonic interplay between the site of AP initiation in the axon and the somato-dendritic load determines the AP waveform. This phenomenon not only alters the shape of AP recorded at the soma, but also determines the dynamics of excitability across a variety of time scales. Supporting this statement, here we generalize a previous numerical study and extend it to the quantification of the input-output gain of the neuronal dynamical response. We consider three classes of multicompartmental mathematical models, ranging from ball-and-stick simplified descriptions of neuronal excitability to 3D-reconstructed biophysical models of excitatory neurons of rodent and human cortical tissue. For each model, we demonstrate that increasing the distance between the axonal site of AP initiation and the soma markedly increases the bandwidth of neuronal response properties. We finally consider the Liquid State Machine paradigm, exploring the impact of altering the site of AP initiation at the level of a neuronal population, and demonstrate that an optimal distance exists to boost the computational performance of the network in a simple classification task. Copyright