Self-Organized Criticality in Developing Neuronal Networks

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro

Order without design

Experimental reality in molecular and cell biology, as revealed by advanced research technologies and methods, is manifestly inconsistent with the design perspective on the cell, thus creating an apparent paradox: where do order and reproducibility in living systems come from if not from design

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. Herein, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis the influence of nonequilibrium fluctuations and periodic electrical fields on quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres

Order in Spontaneous Behavior

Brains are usually described as input/output systems: they transform sensory input into motor output. However, the motor output of brains (behavior) is notoriously variable, even under identical sensory conditions. The question of whether this behavioral variability merely reflects residual deviations due to extrinsic random noise in such otherwise deterministic systems or an intrinsic, adaptive indeterminacy trait is central for the basic understanding of brain function. Instead of random noise, we find a fractal order (resembling Lévy flights) in the temporal structure of spontaneous flight maneuvers in tethered Drosophila fruit flies. Lévy-like probabilistic behavior patterns are evolutionarily conserved, suggesting a general neural mechanism underlying spontaneous behavior. Drosophila can produce these patterns endogenously, without any external cues. The fly's behavior is controlled by brain circuits which operate as a nonlinear system with unstable dynamics far from equilibrium. These findings suggest that both general models of brain function and autonomous agents ought to include biologically relevant nonlinear, endogenous behavior-initiating mechanisms if they strive to realistically simulate biological brains or out-compete other agents

Exploring the Fundamental Dynamics of Error-Based Motor Learning Using a Stationary Predictive-Saccade Task

The maintenance of movement accuracy uses prior performance errors to correct future motor plans; this motor-learning process ensures that movements remain quick and accurate. The control of predictive saccades, in which anticipatory movements are made to future targets before visual stimulus information becomes available, serves as an ideal paradigm to analyze how the motor system utilizes prior errors to drive movements to a desired goal. Predictive saccades constitute a stationary process (the mean and to a rough approximation the variability of the data do not vary over time, unlike a typical motor adaptation paradigm). This enables us to study inter-trial correlations, both on a trial-by-trial basis and across long blocks of trials. Saccade errors are found to be corrected on a trial-by-trial basis in a direction-specific manner (the next saccade made in the same direction will reflect a correction for errors made on the current saccade). Additionally, there is evidence for a second, modulating process that exhibits long memory. That is, performance information, as measured via inter-trial correlations, is strongly retained across a large number of saccades (about 100 trials). Together, this evidence indicates that the dynamics of motor learning exhibit complexities that must be carefully considered, as they cannot be fully described with current state-space (ARMA) modeling efforts

How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics

Persistent regimes and extreme events of the North Atlantic atmospheric circulation

Society is increasingly impacted by natural hazards which cause significant damage in economic and human terms. Many of these natural hazards are weather and climate related. Here, we show that North Atlantic atmospheric circulation regimes affect the propensity of extreme wind speeds in Europe. We also show evidence that extreme wind speeds are long-range dependent, follow a generalized Pareto distribution and are serially clustered. Serial clustering means that storms come in bunches and, hence, do not occur independently. We discuss the use of waiting time distributions for extreme event recurrence estimation in serially dependent time series

The Spontaneous-Rate Histogram of the Auditory Nerve Can Be Explained by Only Two or Three Spontaneous Rates and Long-Range Dependence

Estimates of the spontaneous discharge rate (SR) of auditory-nerve (AN) fibers are often based on measurements of the average rate over a long (e.g., 30 s) interval. These measurements are important because SR is apparently correlated with other AN properties, such as threshold to acoustic stimuli, shape of rate-level function, recovery from prior stimulation, and certain anatomical characteristics. Furthermore, histograms of SR estimates from large numbers of fibers suggest that they can be divided into two (i.e., low and high) or three (i.e., low, medium, and high) SR classes. Yet, even “simple” statistical estimates, such as average rate, can behave surprisingly poorly for processes with long-range dependence (LRD), which has been found in the spontaneous activity of AN fibers. In particular, LRD greatly increases the variability of estimates of mean discharge rate. We investigated the implications of this effect of LRD for our understanding of the SRs of AN fibers. The fractional-Gaussian-noise-driven Poisson process (fGnDP) was originally developed to model the LRD action-potential trains of AN fibers. Using rate estimates computed from this model, we were able to reproduce the shape of published histograms of SR using only three fixed SR values. Moreover, by using a Poisson-equivalent integrate-and-fire (IF) model in place of the inhomogeneous Poisson process in the fGnDP model, we were able to reproduce SR histograms using only two fixed SR values. These results suggest that AN fibers may have only two or three possible values for their long-term average spontaneous discharge rates. In other words, all “high-SR” neurons may actually have the same underlying SR. Furthermore, both “low-SR” and “medium-SR” neurons may have a single “true” SR value, or these two classes may have two different “true” SR values. Furthermore, the Poisson-equivalent IF model may prove useful in other applications involving the modeling of trains of action potentials