Tuning to natural stimulus dynamics in primary auditory cortex

The amplitude and pitch fluctuations of natural soundscapes often exhibit "1/f spectra", which means that large, abrupt changes in pitch or loudness occur proportionally less frequently in nature than gentle, gradual fluctuations. Furthermore, human listeners reportedly prefer 1/f distributed random melodies to melodies with faster (1/f0) or slower (1/f2) dynamics. One might therefore suspect that neurons in the central auditory system may be tuned to 1/f dynamics, particularly given that recent reports provide evidence for tuning to 1/f dynamics in primary visual cortex. To test whether neurons in primary auditory cortex (A1) are tuned to 1/f dynamics, we recorded responses to random tone complexes in which the fundamental frequency and the envelope were determined by statistically independent "1/f(gamma) random walks," with gamma set to values between 0.5 and 4. Many A1 neurons showed clear evidence of tuning and responded with higher firing rates to stimuli with gamma between 1 and 1.5. Response patterns elicited by 1/f(gamma) stimuli were more reproducible for values of gamma close to 1. These findings indicate that auditory cortex is indeed tuned to the 1/f dynamics commonly found in the statistical distributions of natural soundscapes.     

Viability in a pink environment: why "white noise" models can be dangerous

Analysis of long time series suggests that environmental fluctuations may be accurately represented by 1/ f   noise (pink noise), where temporal correlation is found at several scales, and the range of fluctuations increases over time. Previous studies on the effects of coloured noise on population dynamics used first or second order autoregressive noise. I examined the importance of coloured noise for extinction risk using true 1/ f   noise. I also considered the problem of estimating extinction risk with a limited sample of environmental variation. Pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate. However, pink noise environments decreased extinction risk in the Ricker model where environmental variation modified the carrying capacity. Underestimation of environmental variance almost always yielded underestimation of extinction risk. For either population viability analysis or management, we should carefully consider the long-term behaviour of the environment as well as how we include environmental noise in population models.     

Toroidal inhomogeneity of plasma density fluctuations during ECR plasma heating in the L-2M stellarator

Correlation between short-wavelength (k_⊥ ≈ 20–30 cm^–1) and long-wavelength (k_⊥ ≈ 1–2 cm^–1) plasma density fluctuations in two poloidal cross sections of the stellarator chamber separated by 1/14 or 5/14 of the torus perimeter was studied using collective scattering of radiation of two 75-GHz gyrotrons and radiation of a 37-GHz Doppler reflectometer at an ECR heating power density of 1.6–3.2 MW/m³. It is found that excitation of turbulent fluctuations is bursty in character and that fluctuations excited in different L-2M cross sections are uncorrelated. It is shown that the energy of turbulent fluctuations is modulated by a low frequency of 5–20 kHz. An idea is put forward that anomalous transport is toroidally inhomogeneous.     

A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.     

1/f Membrane noise generated by diffusion processes in unstirred solution layers.

A mathematical treatment is given for 1/f noise observed in the ion transport through membranes. It is shown that this noise can be generated by current or voltage fluctuations which occur after step changes of the membrane permeability. Due to diffusion polarization in the unstirred solution layers near the membrane these fluctuations exhibit a 1 square root of t time course which produces noise with a 1/f frequency dependence. The spectral density of 1/f noise is calculated for porous membranes with random switches between a finite and zero pore permeability. A wide frequency range and a magnitude of 1/f noise are obtained which are compatible with experimental data of 1/f noise reported for nerve membranes.     

Noise-driven stem cell and progenitor population dynamics

Background

The balance between maintenance of the stem cell state and terminal differentiation is influenced by the cellular environment. The switching between these states has long been understood as a transition between attractor states of a molecular network. Herein, stochastic fluctuations are either suppressed or can trigger the transition, but they do not actually determine the attractor states.

Methodology/Principal Findings

We present a novel mathematical concept in which stem cell and progenitor population dynamics are described as a probabilistic process that arises from cell proliferation and small fluctuations in the state of differentiation. These state fluctuations reflect random transitions between different activation patterns of the underlying regulatory network. Importantly, the associated noise amplitudes are state-dependent and set by the environment. Their variability determines the attractor states, and thus actually governs population dynamics. This model quantitatively reproduces the observed dynamics of differentiation and dedifferentiation in promyelocytic precursor cells.

Conclusions/Significance

Consequently, state-specific noise modulation by external signals can be instrumental in controlling stem cell and progenitor population dynamics. We propose follow-up experiments for quantifying the imprinting influence of the environment on cellular noise regulation.     

Population dynamics and the colour of environmental noise.

The effect of red, white and blue environmental noise on discrete-time population dynamics is analyzed. The coloured noise is superimposed on Moran-Ricker and Maynard Smith dynamics, the resulting power spectra are less than examined. Time series dominated by short- and long-term fluctuations are said to be blue and red, respectively. In the stable range of the Moran-Ricker dynamics, environmental noise of any colour will make population dynamics red or blue depending the intrinsic growth rate. Thus, telling apart the colour of the noise from the colour of the population dynamics may not be possible. Population dynamics subjected to red and blue environmental noises show, respectively, more red or blue power spectra than those subjected to white noise. The sensitivity to differences in the noise colours decreases with increasing complexity and ultimately disappears in the chaotic range of the population dynamics. These findings are duplicated with the Maynard Smith model for high growth rates when the strength of density dependence changes. However, for low growth rates the power spectra of the population dynamics with noise are red in stable, periodic and aperiodic ranges irrespective of the noise colour. Since chaotic population fluctuations may show blue spectra in the deterministic case, this implies that blue deterministic chaos may become red under any colour of the noise.     

Bursty Communication Patterns Facilitate Spreading in a Threshold-Based Epidemic Dynamics

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.     

Partial Least-Squares Functional Mode Analysis: Application to the Membrane Proteins AQP1, Aqy1, and CLC-ec1

We introduce an approach based on the recently introduced functional mode analysis to identify collective modes of internal dynamics that maximally correlate to an external order parameter of functional interest. Input structural data can be either experimentally determined structure ensembles or simulated ensembles, such as molecular dynamics trajectories. Partial least-squares regression is shown to yield a robust solution to the multidimensional optimization problem, with a minimal and controllable risk of overfitting, as shown by extensive cross-validation. Several examples illustrate that the partial least-squares-based functional mode analysis successfully reveals the collective dynamics underlying the fluctuations in selected functional order parameters. Applications to T4 lysozyme, the Trp-cage, the aquaporin channels Aqy1 and hAQP1, and the CLC-ec1 chloride antiporter are presented in which the active site geometry, the hydrophobic solvent-accessible surface, channel gating dynamics, water permeability (p(f)), and a dihedral angle are defined as functional order parameters. The Aqy1 case reveals a gating mechanism that connects the inner channel gating residues with the protein surface, thereby providing an explanation of how the membrane may affect the channel. hAQP1 shows how the p(f) correlates with structural changes around the aromatic/arginine region of the pore. The CLC-ec1 application shows how local motions of the gating Glu(148) couple to a collective motion that affects ion affinity in the pore.     

Bistable cell fate specification as a result of stochastic fluctuations and collective spatial cell behaviour

Background

In culture, isogenic mammalian cells typically display enduring phenotypic heterogeneity that arises from fluctuations of gene expression and other intracellular processes. This diversity is not just simple noise but has biological relevance by generating plasticity. Noise driven plasticity was suggested to be a stem cell-specific feature.

Results

Here we show that the phenotypes of proliferating tissue progenitor cells such as primary mononuclear muscle cells can also spontaneously fluctuate between different states characterized by the either high or low expression of the muscle-specific cell surface molecule CD56 and by the corresponding high or low capacity to form myotubes. Although this capacity is a cell-intrinsic property, the cells switch their phenotype under the constraints imposed by the highly heterogeneous microenvironment created by their own collective movement. The resulting heterogeneous cell population is characterized by a dynamic equilibrium between “high CD56” and “low CD56” phenotype cells with distinct spatial distribution. Computer simulations reveal that this complex dynamic is consistent with a context-dependent noise driven bistable model where local microenvironment acts on the cellular state by encouraging the cell to fluctuate between the phenotypes until the low noise state is found.

Conclusions

These observations suggest that phenotypic fluctuations may be a general feature of any non-terminally differentiated cell. The cellular microenvironment created by the cells themselves contributes actively and continuously to the generation of fluctuations depending on their phenotype. As a result, the cell phenotype is determined by the joint action of the cell-intrinsic fluctuations and by collective cell-to-cell interactions.     

Visibility of the environmental noise modulating population dynamics

Characterizing population fluctuations and their causes is a major theme in population ecology. The debate is on the relative merits of density-dependent and density-independent effects. One paradigm (revived by the research on global warming and its relation to long-term population data) states that fluctuations in population densities can often be accounted for by external noise. Several empirical models have been suggested to support this view. We followed this by assuming a given population skeleton dynamics (Ricker dynamics and second-order autoregressive dynamics) topped off with noise composed of low- and high-frequency components. Our aim was to determine to what extent the modulated population dynamics correlate with the noise signal. High correlations (with time-lag -1) were observed with both model categories in the region of stable dynamics, but not in the region of periodic or complex dynamics. This finding is not very sensitive to low-frequency noise. High correlations throughout the entire range of dynamics are only achievable when the impact of the noise is very high. Fitted parameter values of skeleton dynamics modulated with noise are prone to err substantially. This casts doubt as to what degree the underlying dynamics are any more recognizable after being modulated by the external noise.     

Overcompensatory population dynamic responses to environmental stochasticity

1. To quantify the interactions between density-dependent, population regulation and density-independent limitation, we studied the time-series dynamics of an experimental laboratory insect microcosm system in which both environmental noise and resource limitation were manipulated. 2. A hierarchical Bayesian state-space approach is presented through which it is feasible to capture all sources of uncertainty, including observation error to accurately quantify the density dependence operating on the dynamics. 3. The regulatory processes underpinning the dynamics of two different bruchid beetles (Callosobruchus maculatus and Callosobruchus chinensis) are principally determined by environmental conditions, with fluctuations in abundance explained in terms of changes in overcompensatory dynamics and stochastic processes. 4. A general, stochastic population model is developed to explore the link between abundance fluctuations and the interaction between density dependence and noise. Taking account of time-lags in population regulation can substantially increase predicted population fluctuations resulting from underlying noise processes.     

Noise-reduction through interaction in gene expression and biochemical reaction processes

We demonstrate that interaction in gene expression and biochemical reaction processes has a significant influence on reducing fluctuations. Especially, we have found that the interaction between synthesized proteins and background molecules can reduce the fluctuation level in gene expression, which is a counter example to the intuition that background factors disturb information processing in genetic networks by increasing the noise level. This fact also indicates that the macromolecular crowding observed in actual cells can contribute to reduce the noise level. In addition, the noise-reduction phenomenon is not limited to the interaction between the proteins and background molecules, but can be applied to other reactions such as a dimerization process and the coupling of reactions with large fluctuations by intrinsic noise. Finally, on the basis of these results, we propose a new and plausible method for reducing the fluctuations generated in synthesized genetic networks, and also discuss the applicability of this method to the stabilization of system dynamics by using a toggle switch model.     

Unraveling the finding of 1/<Emphasis Type="Italic">f</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript> noise in self-paced and synchronized tapping: a unifying mechanistic model

1/f ( beta ) noise has been revealed in both self-paced and synchronized tapping sequences, without being consistently taken into consideration for the modeling of underlying timing mechanisms. In this study we characterize variability, short-range, and long-range correlation properties of asynchronies and inter-tap intervals collected in a synchronization tapping experiment, attesting statistically the presence of 1/f ( beta ) noise in asynchronies. We verify that the linear phase correction model of synchronization tapping in its original formulation cannot account for the empirical long-range correlation properties. On the basis of previous accounts of 1/f ( beta ) noise in the literature on self-paced tapping, we propose an extension of the original synchronization model by modeling the timekeeping process as a source of 1/f ( beta ) fluctuations. Simulations show that this '1/f-AR synchronization model' accounts for the statistical properties of empirical series, including long-range correlations, and provides an unifying mechanistic account of 1/f ( beta ) noise in self-paced and synchronization tapping. This account opens the original synchronization framework to further investigations of timing mechanisms with regard to the serial correlation properties in performed time intervals.     

Open channel noise. V. Fluctuating barriers to ion entry in gramicidin A channels.

We have measured the fluctuations in the current through gramicidin A (GA) channels in symmetrical solutions of monovalent cations of various concentrations, and compared the spectral density values with those computed using E. Frehland's theory for noise in discrete transport systems (Frehland, E. 1978. Biophys. Chem. 8:255-265). The noise for the transport of NH4+ and Na+ ions in glycerol-monooleate/squalene membranes could be accounted for entirely by "shot noise" in the process of transport through a single-filing pore with two ion binding sites. However, in confirmation of results in a previous paper (Sigworth, F. J., D. W. Urry, and K. U. Prasad. 1987. Biophys. J. 52:1055-1064) currents of Cs+ showed a substantial excess noise at low ion concentrations, as did currents of K+ and Rb+. The excess noise was increased in thicker membranes. The observations are accounted for by a theory that postulates fluctuations of the entry rates of ions into the channel on a time scale of approximately 1 microsecond. These fluctuations occur preferentially when the channel is empty; the presence of bound ions stabilizes the "high conductance" conformation of the channel. The fluctuations are sensed to different degrees by the various ion species, and their kinetics depend on membrane thickness.     

You name it--memory and delay govern first name dynamics

The adoption and abandonment of first names through time is a fascinating phenomenon that may shed light on social dynamics and the forces that determine cultural taste in general. Here we show that baby name dynamics is governed almost solely by deterministic forces, even though the emerging abundance statistics resembles the one obtained from a pure drift model. Exogenous events are shown to affect the name dynamics very rarely, and most of the year-to-year fluctuations around the deterministic trend may be attributed solely to demographic noise. We suggest that the rise and fall of a name reflect an "infection" process with delay and memory. The symmetry between adoption and abandonment speed emerges from our model without further assumptions.     

1/f noise in membranes.

The present situation of 1/f noise in the passage of ions across membranes is examined. A survey of biological and synthetic membranes is given at which a 1/f frequency dependence has been observed in the spectrum of voltage or current fluctuations. Empirical relations and theories of 1/f noise in membranes are critically discussed.     

Biodiversity enhancement induced by environmental noise

Recent research in ecology has concentrated on the effect of environmental changes on ecosystem structure and function. In most cases the focus has been on how ecosystems respond to changes in the mean values of environmental parameters, while the impact of changes in the variance has seldom been studied. However, changes in environmental variability may be important. For example, recent climate change predictions indicate that, in addition to trends in the mean values of climate variables, an increase in interannual variability is expected to occur in the near future. How will this increase in the variance of environmental parameters affect the dynamics of terrestrial and aquatic ecosystems? Environmental fluctuations are usually believed to play a "destructive role" in ecosystem dynamics and to act as a source of disturbance, which perturbs the state of a system. However, noise is also known for its "constructive role", i.e., for the ability to create new ordered states in dynamical systems. Here we show that environmental noise may also enhance biodiversity. To this end we develop a conceptual model to show how random environmental fluctuations may favor biodiversity. Noise-induced biodiversity is observed for moderate levels of noise intensity, while it disappears with stronger environmental fluctuations, consistently with the notion underlying the "intermediate disturbance hypothesis".