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.     

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.     

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 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.     

Diffusion and 1/f noise

Summary The noise associated with ion transport through porous membranes is considered as a diffusion process. This is confirmed experimentally by measuring the noise spectra associated with pores of known dimension. It is then shown that one dimensional diffusion through pores of variable length can produce approximate 1/f noise spectra, if the distribution of lengths is proportional to (length)^–1.     

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 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.     

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.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

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.     

A new analysis for membrane noise. The integral spectrum.

A new method of random data analysis has been developed with special implications for membrane noise. The integral spectrometer uses overlapping broad-band filters of simple design, whose bandwidth increases linearly with center frequency. A random two-state process, which has a Lorentzian-shaped spectral density, results in an integral spectrum whose maximum value occurs at the mean frequency of the events, and which is symmetric about that frequency on a semilog plot. 1/f noise is flat and does not distort the symmetry on the frequency axis. The integral spectrum exchanges resolution on the frequency axis for accuracy in the amplitude. The expected statistical error in amplitude has been calculated for three types of membrane noise assuming finite data. The integral spectrum compares favorably with conventional spectral densities and may be a reasonable alternative for random data analysis.     

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.     

A proposed 1-f noise mechanism in nerve cell membranes

A model is presented which can be used to understand the observed 1/f electrical noise in nerve cell membranes. It is based on recent theories of normal mode vibrations in liquid crystals.     

From membrane tension to channel gating: A principal energy transfer mechanism for mechanosensitive channels

Mechanosensitive (MS) channels are evolutionarily conserved membrane proteins that play essential roles in multiple cellular processes, including sensing mechanical forces and regulating osmotic pressure. Bacterial MscL and MscS are two prototypes of MS channels. Numerous structural studies, in combination with biochemical and cellular data, provide valuable insights into the mechanism of energy transfer from membrane tension to gating of the channel. We discuss these data in a unified two‐state model of thermodynamics. In addition, we propose a lipid diffusion‐mediated mechanism to explain the adaptation phenomenon of MscS.     

A molecular model for ion selectivity in membrane channels

In this article, the three-dimensional motion of an ion within a molecular channel is discussed for the first time; escape rates from binding sites are calculated using the transition state method. For a given ligand configuration and a particular pore radius the rates depend upon ion size and mass. It is found that the activation energies depend strongly on the ion size, i.e., they increase with decreasing ion radius. In contrast to the rates obtained from the mass dependence alone, the rates depending on both mass and size of the alkali ions yield the completely inverted sequence, namely the Eisenman sequence I.