Can noise induce chaos?

An important component of the mathematical definition of chaos is sensitivity to initial conditions. Sensitivity to initial conditions is usually measured in a deterministic model by the dominant Lyapunov exponent (LE), with chaos indicated by a positive LE. The sensitivity measure has been extended to stochastic models; however, it is possible for the stochastic Lyapunov exponent (SLE) to be positive when the LE of the underlying deterministic model is negative, and vice versa. This occurs because the LE is a long-term average over the deterministic attractor while the SLE is the long-term average over the stationary probability distribution. The property of sensitivity to initial conditions, uniquely associated with chaotic dynamics in deterministic systems, is widespread in stochastic systems because of time spent near repelling invariant sets (such as unstable equilibria and unstable cycles). Such sensitivity is due to a mechanism fundamentally different from deterministic chaos. Positive SLE's should therefore not be viewed as a hallmark of chaos. We develop examples of ecological population models in which contradictory LE and SLE values lead to confusion about whether or not the population fluctuations are primarily the result of chaotic dynamics. We suggest that "chaos" should retain its deterministic definition in light of the origins and spirit of the topic in ecology. While a stochastic system cannot then strictly be chaotic, chaotic dynamics can be revealed in stochastic systems through the strong influence of underlying deterministic chaotic invariant sets.     

What's all the noise about developmental stochasticity?

In October 2010, researchers from diverse backgrounds collided at the historic Cumberland Lodge (Windsor, UK) to discuss the role of randomness in cell and developmental biology. Organized by James Briscoe and Alfonso Marinez-Arias, The Company of Biologists' workshop was the latest in a series of meetings aimed at encouraging interdisciplinary interactions between biologists. This aim was reflected in talks at this workshop that ranged from the tissue to the cellular scale, and that integrated experimental and theoretical approaches to examining stochastic behavior in diverse systems.     

Can a synaptic signal arise from noise?

The spontaneous fusion of vesicles at nerve terminals produces random miniature postsynaptic potentials (quantal responses) that are thought to have little functional significance. In this issue of Neuron, Sharma and Vijayaraghavan provide evidence that exogenous signals can accelerate and synchronize the occurrence of quanta strongly enough to activate postsynaptic neurons in what may be a new way to transfer information across synapses.     

Neuronal variability: noise or part of the signal?

Sensory, motor and cortical neurons fire impulses or spikes at a regular, but slowly declining, rate in response to a constant current stimulus. Yet, the intervals between spikes often vary randomly during behaviour. Is this variation an unavoidable effect of generating spikes by sensory or synaptic processes ('neural noise') or is it an important part of the 'signal' that is transmitted to other neurons? Here, we mainly discuss this question in relation to sensory and motor processes, as the signals are best identified in such systems, although we also touch on central processes.     

Do birds differentiate between white noise and deterministic chaos?

Noisy, unpredictable sounds are often present in the vocalizations of fearful and stressed animals across many taxa. A variety of structural characteristics, called nonlinear acoustic phenomena, that include subharmonics, rapid frequency modulations, and deterministic chaos are responsible for the harsh sound quality of these vocalizations. Exposure to nonlinear sound can elicit increased arousal in birds and mammals. Past experiments have used white noise to test for effects of deterministic chaos on perceivers. However, deterministic chaos differs structurally from white noise (i.e., random signal with equal energy at all frequencies), and unlike white noise, may differ dramatically depending on how it is produced. In addition, the subtle structural variation of chaos may not be distinguishable in the environment due to the attenuation and degradation of sound over distance and different habitat types. We designed two experiments to clarify whether American robins (Turdus migratorius) and warbling vireos (Vireo gilvus) discriminate between white noise and deterministic chaos. We broadcast and re‐recorded white noise and two exemplars of deterministic chaos—one generated with a Chua oscillator and the other generated using a logistic equation—at 1, 10, 20, 30, 40, and 80 m across open and forested habitat and used spectrogram correlations to compare stimuli along this degradational gradient. We found that sounds degraded similarly in both habitats when compared to a reference distance of 1 m. Comparing pairs of stimuli across distances suggested that Chua chaos was more easily distinguishable from noise and logistic chaos. In addition, all stimuli became more distinctive over increased distance. The second experiment tested behavioral responses of robins and warbling vireos to control sounds of tropical kingbird (Quiscalus mexicanus), white noise, and two exemplars of deterministic chaos (Chua and logistic). Neither American robins nor warbling vireos responded differently to at least two types of deterministic chaos and white noise, validating previous playback studies that used white noise as a surrogate for deterministic chaos. Uniform responses to a variety of nonlinear features in these birds possibly reflect error management in alarm signal detection.     

What is signal and what is noise in the brain?

The response of a cortical neuron to a stimulus can show a very large variability when repeatedly stimulated by exactly the same stimulus. This has been quantified in terms of inter-spike-interval (ISI) statistics by several researchers (e.g., [Softky, W., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13(1), 334-350.]). The common view is that this variability reflects noisy information processing based on redundant representation in large neuron populations. This view has been challenged by the idea that the apparent noise inherent in brain activity that is not strictly related or temporally coupled to the experiment could be functionally significant. In this work we examine the ISI statistics and discuss these views in a recently published model of interacting cortical areas [Knoblauch, A., Palm, G., 2002. Scene segmentation by spike synchronization in reciprocally connected visual areas. I. Local effects of cortical feedback. Biol. Cybernet. 87(3), 151-167.]. From the results of further single neuron simulations we can isolate temporally modulated synaptic input as a main contributor for high ISI variability in our model and possibly in real neurons. In contrast to alternative mechanisms, our model suggests a function of the temporal modulations for short-term binding and segmentation of figures from background. Moreover, we show that temporally modulated inputs lead to ISI statistics which fit better to the neurophysiological data than alternative mechanisms.     

How high is the level of technical noise in microarray data?

Background  

Microarray gene expression data are commonly perceived as being extremely noisy because of many imperfections inherent in the current technology. A recent study conducted by the MicroArray Quality Control (MAQC) Consortium and published in Nature Biotechnology provides a unique opportunity to probe into the true level of technical noise in such data.     

Crosstalk in cellular signaling: background noise or the real thing?

During the past two decades, molecular biologists and geneticists have deconstructed intracellular signaling pathways in individual cells, revealing a great deal of crosstalk among key signaling pathways in the animal kingdom. Fewer examples have been reported in plants, which appear to integrate multiple signals on the promoters of target genes or to use gene family members to convey signal-specific output. For both plants and animals, the question now is whether the "crosstalk" is biologically relevant or simply noise in the experimental system. To minimize such noise, we suggest studying signaling pathways in the context of intact organisms with minimal perturbation from the experimenter.     

Effects of α lipoic acid on noise induced oxidative stress in rats

This study was conducted to identify how exposure to ambient noise that is over 75 dB affects the oxidant-antioxidant profile using hematological and biochemical indicators, and to investigate the effects of a strong and current antioxidant, $\alpha$ lipoic acid, on rats that were subjected to noise stress. For this purpose, five groups of eight rats were formed as follows: Control (K), Noise Exposure (GK), Lipoic Acid (LA), Noise Pollution + $\alpha$Lipoic Acid (GK + LA) and Oil (Y). The blood samples collected from rats were analyzed and MDA (malondialdehyde), GSH (glutathione), SOD (superoxide dismutase), CAT (catalase), NO (nitrit oxide), GPx (glutathione peroxidase), leukocytes, monocytes, lymphocytes, erythrocytes, hemoglobin, hematocrit, glucose, cholesterol, total protein, triglycerides, HDL (high density lipoprotein), LDL (low density lipoprotein), and urea-N levels were measured. The physical factory environment in a textile factory was preferred to simulate the noise exposure. Ambient noise was measured to be 75 dB. Exposure to physical ambient noise was sustained for 30 days. MDA level was measured at the lowest level in the LA and GKLA groups while it was statistically significantly higher in other groups than it was in the control group. It was observed that GSH reached its lowest level in the group that was exposed to noisy environment, the 100 mg/kg/day $\alpha$lipoic acid administered on the experimental model increased this level to that of the control group and this change was statistically significant (p < 0.05). Considering the urea levels, the increases in GK and GKLA groups and the decreases in LA and Y groups were observed to be statistically significant. When glucose levels were compared to the control group, they were found to be statistically significantly lower in all groups. As a result, it was observed that exposure to noise for 30 days was likely to lead to leukocyte-based immune deficiency and using $\alpha$ lipoic acid as an antioxidant might provide a significant protection against the noise stress.     

Influence of noise on the function of a “physiological” neural network

A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless autoassociative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.     

The role of noise in a predator–prey model with Allee effect

The existence and implications of alternative stable states in ecological systems have been investigated extensively within deterministic models. However, it is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. Thus, in this paper, we study the role of noise on the pattern formation of a spatial predator–prey model with Allee effect. The obtained results show that the spatially extended system exhibits rich dynamic behavior. More specifically, the stationary pattern can be induced to be a stable target wave when the noise intensity is small. As the noise intensity is increased, patchy invasion emerges. These results indicate that the dynamic behavior of predator–prey models may be partly due to stochastic factors instead of deterministic factors, which may also help us to understand the effects arising from the undeniable susceptibility to random fluctuations of real ecosystems.     

Increased noise sensitivity and altered inner ear MENA distribution in VASP−/− mice

Vasodilator-stimulated phosphoprotein (VASP) and mammalian-enabled protein (MENA) share similar cellular localisation and functions (signal transduction pathways, regulation of actin cytoskeleton dynamics). Functional substitution and compensation among Ena/VASP proteins have been proposed as the reason for the absence of major morphological and functional deficits in VASP–/– mice. The aim of this study was to investigate VASP expression in the mouse cochlea, to analyse cochlear function in VASP–/– mice compared with wildtype mice, and to analyse cochlear MENA distribution taking into account that MENA protein might compensate VASP loss in the cochlea of VASP–/– mice. We confirmed specific VASP expression in the pillar cells of the mice organ of Corti as previously reported for rat cochlea. By analysing the hearing function in VASP–/– mice, we found no differences in auditory brainstem responses and distortion product otoacoustic emissions from those of wildtype mice but evidence for an increased noise sensitivity at lower frequencies. When MENA protein levels in cochlea tissue were tested in mutant and wildtype mice by Western blot analysis, no significant differences were found, as was also seen with regard to MENA mRNA levels in laser-microdissected single pillar cells. Most surprisingly, however, MENA protein was absent in pillar cells of VASP–/– mice, whereas it was detected in other cochlear cells. The finding of a cell-specific, and not organ-specific, redundancy of MENA protein expression noted for the first time in VASP–/– mice is proposed as the reason for the observed distinct cochlear phenotype.     

Inner ear: Ca(2+)n you feel the noise?

The death of hair cells in the inner ear as a result of exposure to loud noise can lead to irreversible deafness. New work shows that the mammalian cochlea can sense noxious sounds and use Ca(2+) waves to rapidly propagate hair cell damage signals.     

Is the impact of environmental noise visible in the dynamics of age-structured populations?

Climate change has ignited lively research into its impact on various population-level processes. The research agenda in ecology says that some of the fluctuations in population size are accountable for by the external noise (e.g. weather) modulating the dynamics of populations. We obeyed the agenda by assuming population growth after a resource-limited Leslie matrix model in an age-structured population. The renewal process was disturbed by superimposing noise on the development of numbers in one or several age groups. We constructed models for iteroparous and semelparous breeders so that, for both categories, the population growth rate was matching. We analysed how the modulated population dynamics correlates with the noise signal with different time-lags. No significant correlations were observed for semelparous breeders, whereas for iteroparous breeders high correlations were frequently observed with time-lags of 71 year or longer. However, the latter occurs under red-coloured noise and for low growth rates when the disturbance is on the youngest age group only. It is laborious to find any clear signs of the (red) noise- and age group-specific fluctuations if the disturbance influences older age groups only. These results cast doubts on the possibility of detecting the signature of external disturbance after it has modulated temporal fluctuations in age-structured populations.     

Skeletons, noise and population growth: the end of an old debate?

Population dynamics models remain largely deterministic, although the presence of random fluctuations in nature is well recognized. This deterministic approach is based on the implicit assumption that systems can be separated into a deterministic part that captures the essential features of the system and a random part that can be neglected. But is it possible, in general, to understand population dynamics without the explicit consideration of random fluctuations? Here, we suggest perhaps not, and argue that the dynamics of many systems are a result of interactions between the deterministic nonlinear skeleton and noise.     

Studying molecular motor-based cargo transport: what is real and what is noise?

Noise is a major problem in analyzing tracking data of cargos moved by molecular motors. We use Bayesian statistics to incorporate what is known about the noise in parsing the trajectory of a cargo into a series of constant velocity segments. Tracks with just noise and no underlying motion are fit with constant velocity segments to produce a calibration curve of fit quality versus average segment duration. Fits to tracks of moving cargos are compared to the calibration curves with similar noise. The fit with the optimum number of constant velocity states has the least number of segments needed to match the fit quality of the calibration curve. We have tested this approach using tracks with known underlying motion generated by computer simulations and with a specially designed in vitro experiment. We present the results of using this parsing approach to analyze transport of lipid droplets in Drosophila embryos.