Biomedical subjects

Benjamin Lindner

Publications and source records attributed to Benjamin Lindner.

11 recordsLinked to original sources

PubMed2006

Superposition of many independent spike trains is generally not a Poisson process.

We study the sum of many independent spike trains and ask whether the resulting spike train has Poisson statistics or not. It is shown that for a non-Poissonian statistics of the single spike train, the resulting sum of spikes has exponential interspike interval (ISI) distributions, vanishing the ISI correlation at a finite lag but exhibits exactly the same power spectrum as the original spike train does. This paradox is resolved by considering what happens to ISI correlations in the limit of an infinite number of superposed trains. Implications of our findings for stochastic models in the neurosciences are briefly discussed.

Action Potentials↗

PubMed2006

Comment on "Characterization of subthreshold voltage fluctuations in neuronal membranes," by M. Rudolph and A. Destexhe.

In two recent articles, Rudolph and Destexhe (2003, 2005) studied a leaky integrator model (an RC-circuit) driven by correlated ("colored") gaussian conductance noise and Gaussian current noise. In the first article, they derived an expression for the stationary probability density of the membrane voltage; in the second, they modified this expression to cover a larger parameter regime. Here we show by standard analysis of solvable limit cases (white noise limit of additive and multiplicative noise sources; only slow multiplicative noise; only additive noise) and by numerical simulations that their first result does not hold for the general colored-noise case and uncover the errors made in the derivation of a Fokker-Planck equation for the probability density. Furthermore, we demonstrate analytically (including an exact integral expression for the time-dependent mean value of the voltage) and by comparison to simulation results that the extended expression for the probability density works much better but still does not exactly solve the full colored-noise problem. We also show that at stronger synaptic input, the stationary mean value of the linear voltage model may diverge and give an exact condition relating the system parameters for which this takes place.

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PubMed2005

Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback.

A network of leaky integrate-and-fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied. We calculate the spectral statistics of the network (power spectrum of the population activity, cross spectrum between spike trains of different neurons) as well as of a single neuron (power spectrum of spike train, cross spectrum between external noise and spike train) within the network. As shown by comparison with numerical simulations, our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise. By means of our analytical results we discuss the quality of the correlation-induced oscillation in a large network as a function of the transmission delay and the internal noise intensity. It is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay (i.e., the delay period is longer than any other time scale in the system). For a neuron with a strong intrinsic frequency, the oscillation becomes strongly anharmonic in the case of a long delay time. We also discuss briefly the kind of synchrony introduced by the feedback-induced oscillation.

Action Potentials↗

PubMed2005

Integrate-and-fire neurons with threshold noise: a tractable model of how interspike interval correlations affect neuronal signal transmission.

Many neurons exhibit interval correlations in the absence of input signals. We study the influence of these intrinsic interval correlations of model neurons on their signal transmission properties. For this purpose, we employ two simple firing models, one of which generates a renewal process, while the other leads to a nonrenewal process with negative interval correlations. Different methods to solve for spectral statistics in the presence of a weak stimulus (spike train power spectra, cross spectra, and coherence functions) are presented, and their range of validity is discussed. Using these analytical results, we explore a lower bound on the mutual information rate between output spike train and input stimulus as a function of the system's parameters. We demonstrate that negative correlations in the baseline activity can lead to enhanced information transfer of a weak signal by means of noise shaping of the background noise spectrum. We also show that an enhancement is not compulsory--for a stimulus with power exclusively at high frequencies, the renewal model can transfer more information than the nonrenewal model does. We discuss the application of our analytical results to other problems in neuroscience. Our results are also relevant to the general problem of how a signal affects the power spectrum of a nonlinear stochastic system.

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PubMed2005

Effect of an exponentially decaying threshold on the firing statistics of a stochastic integrate-and-fire neuron.

We study a white-noise driven integrate-and-fire (IF) neuron with a time-dependent threshold. We give analytical expressions for mean and variance of the interspike interval assuming that the modification of the threshold value is small. It is shown that the variability of the interval can become both smaller or larger than in the case of constant threshold depending on the decay rate of threshold. We also show that the relative variability is minimal for a certain finite decay rate of the threshold. Furthermore, for slow threshold decay the leaky IF model shows a minimum in the coefficient of variation whenever the firing rate of the neuron matches the decay rate of the threshold. This novel effect can be seen if the firing rate is changed by varying the noise intensity or the mean input current.

Animals↗

PubMed2004

Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus.

We present results from a novel experimental paradigm to investigate the influence of spatial correlations of stimuli on electrosensory neural network dynamics. Further, a new theoretical analysis for the dynamics of a model network of stochastic leaky integrate-and-fire neurons with delayed feedback is proposed. Experiment and theory for this system both establish that spatial correlations induce a network oscillation, the strength of which is proportional to the degree of stimulus correlation at constant total stimulus power.

Animals↗

PubMed2004

Interspike interval statistics of neurons driven by colored noise.

A perfect integrate-and-fire model driven by colored noise is studied by means of the interspike interval (ISI) density and the serial correlation coefficient. Exact and approximate expressions for these functions are derived for weak dichotomous or Gaussian noise, respectively. It is shown that correlations in the input result in positive correlations in the ISI sequence and in a reduction of ISI variability. The results also indicate that for weak noise, the noise distribution only shapes the ISI density but not the ISI correlations which are determined by the noise's correlation function.

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PubMed2004

Noise shaping by interval correlations increases information transfer.

The influence of intrinsic firing interspike interval correlations on the noise spectrum and information transfer is studied. This is done through the comparison of two simple firing models, one of which is a renewal process while the other displays interval correlations. These correlations are shown to shape the spike train power spectrum and, in particular, to decrease the noise power at low frequencies. Linear response theory and numerical simulations reveal how this shaping can increase the transmission of information about a time-varying signal. Our results are relevant to the analysis of nonrenewal point processes and signal detection in physics and biology.

Models, Theoretical↗

PubMed2003

Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise.

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Theta neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Theta neuron model is obtained only in the Stratonovich interpretation of the stochastic Theta neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.

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PubMed2002

Noise-induced transport with low randomness.

We study the transport of overdamped Brownian particles in periodic potentials subject to a spatially modulated Gaussian white noise. We derive an analytical expression for the diffusion coefficient of particles. By means of velocity, diffusion coefficient, and their ratio (Péclet number) we discuss (a) symmetric potential and modulation of noise intensity and (b) a ratchet profile with strong noise modulation. It is shown that state dependent fluctuations may not only induce directed transport, but also a pronounced coherence of transport if the potential exhibits a strong asymmetry.

Journal Article↗

PubMed2002

Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model.

We study noise-induced resonance effects in the leaky integrate-and-fire neuron model with absolute refractory period, driven by a Gaussian white noise. It is demonstrated that a finite noise level may either maximize or minimize the regularity of the spike train. We also partition the parameter space into regimes where either or both of these effects occur. It is shown that the coherence minimization at moderate noise results in a flat spectral response with respect to periodic stimulation in contrast to sharp resonances that are observed for both small and large noise intensities.

Journal Article↗