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 l/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. Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 38 “Membranforschung”     

Protein dynamics and 1/f noise.

It has long been recognized that protein dynamical processes occur over a wide temporal range. However, the functionality of this spectrum of events remains unclear. In this work, a generalized noise function analysis is applied to a collection of diverse protein dynamical systems. It is shown that a power law model with an oscillatory component can adequately describe the time course of a variety of processes. These results suggest that under the appropriate conditions, proteins are in a metastable state. A microscopic, chemical kinetic model based on a Poisson distribution of activation energies is presented. From this model specific functional forms for the parameters of the generalized noise model can be derived. Additionally, a model is presented to described kinetic hole burning effects observed at low temperatures. Scaling laws are derived for these models that provide a connection with the generalized noise analysis.     

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.     

Extinction risk and the 1/f family of noise models

In order to predict extinction risk in the presence of reddened, or correlated, environmental variability, fluctuating parameters may be represented by the family of 1/f noises, a series of stochastic models with different levels of variation acting on different timescales. We compare the process of parameter estimation for three 1/f models (white, pink and brown noise) with each other, and with autoregressive noise models (which are not 1/f noises), using data from a model time-series (length, T) of population. We then calculate the expected increase in variance and the expected extinction risk for each model, and we use these to explore the implication of assuming an incorrect noise model. When parameterising these models, it is necessary to do so in terms of the measured ("sample") parameters rather than fundamental ("population") parameters. This is because these models are non-stationary: their parameters need not stabilize on measurement over long periods of time and are uniquely defined only over a specified "window" of timescales defined by a measurement process. We find that extinction forecasts can differ greatly between models, depending on the length, T, and the coefficient of variability, CV, of the time series used to parameterise the models, and on the length of time into the future which is to be projected. For the simplest possible models, ones with population itself the 1/f noise process, it is possible to predict the extinction risk based on CV of the observed time series. Our predictions, based on explicit formulae and on simulations, indicate that (a) for very short projection times relative to T, brown and pink noise models are usually optimistic relative to equivalent white noise model; (b) for projection timescales equal to and substantially greater than T, an equivalent brown or pink noise model usually predicts a greater extinction risk, unless CV is very large; and (c) except for very small values of CV, for timescales very much greater than T, the brown and pink models present a more optimistic picture than the white noise model. In most cases, a pink noise is intermediate between white and brown models. Thus, while reddening of environmental noise may increase the long-term extinction probability for stationary processes, this is not generally true for non-stationary processes, such as pink or brown noises.     

Models for 1/f noise in nerve membranes.

A recently proposed model for 1/f(w-1) noise in nerve membrane (Clay and Schlesinger, 1976; Lundström and McQueen, 1974) is shown to be mathematically inconsistent in several respects. A self-consistent model based on similar membranes lipid orientation fluctuation effects is proposed.     

A mechanism for 1/f noise in diffusing membrane channels.

The diffusion polarization effect is shown to produce 1/f (omega-1) noise in the conductance of membranes containing diffusing ion channels. The magnitude and frequency range of the effect are calculated.     

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/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.Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 38 Membranforschung.     

Active behavior and 1/f noise in shell-changing behavior of the hermit crabs.

Hermit crabs are known to carry a gastropod shell to prevent abdomen from injuring by predators and cannibalism. One can regard the shell as a boundary between inside and outside worlds for hermit crabs. We conducted an experiment in which hermit crabs without shells deal with artificial tubes. The situation without a shell requires a part of experimental setup to be regarded as inside by each hermit crab. We accept the distance of locomotion as the indication of the estimation process performed by an individual on parts of the experimental setup. As a result, behavioral hierarchy was found with respect to the way of constituting the boundary. At each level of hierarchy, active behavior produced 1/f noise in comparison with the passive one. It suggests that finding 1/f noise at each level of hierarchy may lead to a lower level of hierarchy in another situation.     

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.     

Unified theory of 1f and conductance noise in nerve membrane

A theory of $\text{1}\text{f}$ and conductance noise is given for ionic channels in nerve membrane. The theory is based on the assumption that the channels are in constant, stochastically independent, rotational motion within a fluid bilayer membrane. The resulting expression for the current noise power density S contains a conduction noise term consistent withStevens (1972) and Hill & Chen (1972) and a $\text{1}\text{f}$ noise term consistent with Lundstrom & McQueen (1974) and Clay & Shlesinger (1976). The expression for S also contains a third term which is the spectrum of the product of the single channel conduction noise and $\text{1}\text{f}$ noise correlation functions. This term is independent of the number of channels in the membrane, R. Consequently, the expression for S effectively reduces to a sum of $\text{1}\text{f}$ and conduction noise for R 10–100 which is in agreement with noise measurements on squid axon. The theory is applied in detail to potassium squid noise measurements of Conti, DeFelice & Wanke (1975) using the stochastic analysis of single file ion motion developed in our previous paper (Clay & Shlesinger (1976)).     

1/f noise in black lipid membranes induced by ionic channels formed by chemically dimerized gramicidin A

Summary The noise behavior of lipid bilayer membranes, doped with a chemically dimerized gramicidin A, was investigated. In contrast to normal gramicidin A, which generates a Lorentzian type power spectrum due to the formation and disappearance of conducting dimers, the current power spectrum densityS _m (f) obtained with this gramicidin A derivative showed over several orders of magnitude a clear 1/f behavior. The intensity of this 1/f component was analyzed as a function of the membrane-applied voltage, membrane resistance, electrolyte concentration, and composition. The relationship between the meansquare fluctuation in current and the membrane current mean value was found to follow Hooge's equation, i.e., I ²=I _m ² /N f whereN is the number of channels and is a constant equal to 1.0×10^–2. It is suggested that a 1/f type noise was observed because the chemically dimerized form of gramicidin A produces long lasting cation selective channels.     

海马神经元信息传递的1／f涨落

采用元胞自动机建立了脑海马神经元信息传递的计算机仿真模型,发现海马神经元从个体到群体,在时间尺度上均呈现出１／ｆ涨落。分析了模型的动力学特性,认为产生１／ｆ涨落的机制在于脑海马神经元处于自组织临界状态,即在混沌的边缘上进化。     

Interpretation of 1/f fluctuations in ion conducting membranes

The main objective of this work is to resolve some uncertainties associated with the analysis of conductance fluctuations that exhibit 1/f spectral density. To this end, we derive mathematical conditions under which a discrete summation of Lorentzian functions best approximates a strictly 1/f density over a given frequency range. The intrinsic errors associated with spectral density estimates are considered and used as a constraint to determine the smallest number of optimally chosen Lorentzians required to fit a 1/f-like spectrum in a statistically acceptable manner. The results provide criteria concerning the extent to which mechanisms generating a strictly 1/f spectra may be distinguished from those generating sums of Lorentzian spectra. It is found, in particular, that 1/f-like fluctuation spectra observed in a variety of biological and model membranes may well arise from the summation of a few Lorentzian components having appropriate amplitudes and corner frequencies. Consideration of physically realistic models of ion conductive channels indicates that 1/f-like conductance fluctuation spectra could originate naturally as a direct consequence of thermodynamic constraints upon the coefficients of Lorentzian components.     

Integration of embryonic and fetal skeletal myogenic programs at the myosin light chain 1f/3f locus

The genetic control of skeletal muscle differentiation at the onset of myogenesis in the embryo is relatively well understood compared to the formation of muscle during the fetal period giving rise to the bulk of skeletal muscle fibers at birth. The Mlc1f/3f (Myl1) locus encodes two alkali myosin light chains, Mlc1f and Mlc3f, from two promoters that are differentially regulated during development. The Mlc1f promoter is active in embryonic, fetal and adult fast skeletal muscle whereas the Mlc3f promoter is upregulated during fetal development and remains on in adult fast skeletal muscle. Two enhancer elements have been identified at the mammalian Mlc1f/3f locus, a 3′ element active at all developmental stages and an intronic enhancer activated during fetal development. Here, using transgenesis, we demonstrate that these enhancers act combinatorially to confer the spatial, temporal and quantitative expression profile of the endogenous Mlc3f promoter. Using double reporter transgenes we demonstrate that each enhancer can activate both Mlc1f and Mlc3f promoters in vivo, revealing enhancer sharing rather than exclusive enhancer-promoter interactions. Finally, we demonstrate that the fetal activated enhancer contains critical E-box myogenic regulatory factor binding sites and that enhancer activation is impaired in vivo in the absence of myogenin but not in the absence of innervation. Together our observations provide insights into the regulation of fetal myogenesis and the mechanisms by which temporally distinct genetic programs are integrated at a single locus.     

Interaction of renatured histones f3 and f2a1

Ultracentrifuge measurements show that the individual histones f2a1 and f3 interact to form tetramers in solution. The conditions which facilitate renaturation are discussed.     

Diffusion of transcription factors can drastically enhance the noise in gene expression

We study by Green's Function Reaction Dynamics the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels for a gene that is under the control of a repressor. We find that spatial fluctuations due to diffusion can drastically enhance the noise in gene expression. After dissociation from the operator, a repressor can rapidly rebind to the DNA. Our results show that the rebinding trajectories are so short that, on this timescale, the RNA polymerase (RNAP) cannot effectively compete with the repressor for binding to the promoter. As a result, a dissociated repressor molecule will on average rebind many times, before it eventually diffuses away. These rebindings thus lower the effective dissociation rate, and this increases the noise in gene expression. Another consequence of the timescale separation between repressor rebinding and RNAP association is that the effect of spatial fluctuations can be described by a well-stirred, zero-dimensional, model by renormalizing the reaction rates for repressor-DNA (un) binding. Our results thus support the use of well-stirred, zero-dimensional models for describing noise in gene expression. We also show that for a fixed repressor strength, the noise due to diffusion can be minimized by increasing the number of repressors or by decreasing the rate of the open complex formation. Lastly, our results emphasize that power spectra are a highly useful tool for studying the propagation of noise through the different stages of gene expression.     

Counting statistics of 1/f fluctuations in neuronal spike trains

The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the celebral cortex. In this paper, the statistical features of single neuronal activities in MRF of cat during dream sleep are investigated; the neuronal spike train exhibits 1/f fluctuations. Counting statistics is applied to the neuronal spike train giving rise to a variance/mean curve which follows at -law. For an interpretation of these findings, the clustering Poisson process is applied which not only gives rise to at -law but also suggests a generation mechanism. The MRF neuronal activities are closely fitted by the clustering Poisson process and the underlying statistical parameters can be estimated. These findings strongly suggest that neuronal activities can be interpreted as superposition of randomly occuring clusters ( = bursts of spikes).