Spectral analysis and interpretation of spectral components of heart rate variability

Requirements for a fragment of a random process taken for spectral analysis are formulated. It has been demonstrated that both the random process and its periodic components should be stationary within the fragment selected. Only in this case will the results of spectral analysis reflect the actual characteristics of the process studied. Variations in the depth of breathing and other factors have been shown to cause modulatory fluctuations of the HF and LF waves of the cardiac rhythm. The modulatory fluctuations are expressed as the VLF peak in the heart rate variability spectrum, the position of the peak on the frequency axis and its amplitude being determined by the frequency and depth of modulation, respectively. Depending on the modulation depth and the ratio between the modulation period and the length of the sample studied, spectral analysis of the same process may yield considerably different results. The ambiguity of the results of spectral analysis is the cause of discrepancy about the nature of individual spectral components of heart rate variability.     

Decreasing motion artifacts in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering

A strategy has been developed for the removal of motion artifact and noise in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering. An analytical model indicates that the spectral removal of motion artifacts is independent of the phase shift of the motion waveform in the frequency domain, and thus to the time shift (or delay) of motion in the time domain. This is based on the "shift theorem" of Fourier analysis, which avoids erroneous correction of motion artifact when using the motion signal obtained using reflectance from the heart. Several major steps are adopted to implement this model for elimination of motion as well as detection noise from the fluorescence transient signals from the calcium-sensitive probe Rhod-2. These include (1) extracting the fluorescence calcium transient signal from the raw data by using power spectrum density (PSD) in the frequency domain by subtracting the motion recorded using the reflectance of excitation light, (2) digitally filtering out the random noise using multiple bandpass filters centralized at harmonic frequencies of the transients, and (3) extracting high frequency noise with a Gaussian Kernel filter method. The processed signal of transients acquired with excessive motion artifact is comparable to transients acquired with minimal motion obtained by immobilizing the heart against the detection window, demonstrating the usefulness of this technique.     

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.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured in zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constant ki for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentration Nt of adsorbed ions may be calculated from the observed spectral intensity of current noise. The values of ki obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentration Nt.     

A Fourier method for the analysis of exponential decay curves.

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.     

The influence of the potential dependence of the amplitude of postsynaptic potentials on rhythmic processes of bioelectric activity of the cerebral cortex

The dependence of the postsynaptic potential amplitude on the membrane potential was entered into the earlier derived integral equations describing the interactions between excitatory and inhibitory populations of neocortical neurons. The influence of the potential dependence on steady states and the stable region of oscillations of the mean membrane potential of neurons were investigated. Encephalograms of humans and animals in different functional states were numerically simulated. The real form of a power spectrum of electroencephalogram was obtained. The occurrence of the nonregular spindle-shaped activity was revealed, which expands the frequency of basic oscillations and widens the spectral peak. In the unsteady region, the existence of a limiting cycle and the possibility of arising of the pathological activity observed upon abnormal brain functioning were shown with the help of the numerical nonlinear analysis.     

Self-phosphorylation modulates the gating of rat liver gap junction channels: a nonstationary noise analysis

The effect of phosphorylation on the gating of rat liver gap junction hemichannels (Cx 32) has been investigated. It has been shown that self-phosphorylation of rat liver Cx 32 protein reduces the permeability of proteoliposomes as well the current flowing through multichannels in lipid bilayer membrane (BLM). The low frequency power spectral density analyses of nonstationary noise evolved due to the gating of Cx 32 multichannels demonstrated that self-phosphorylation modulated the channel functioning. A clear change in the power spectrum slopes (alpha) of the nonstationary noise profiles confirmed the modulation of the channel dynamics due to self-regulation.     

Practical Model Fitting Approaches to the Direct Extraction of NMR Parameters Simultaneously from All Dimensions of Multidimensional NMR Spectra

A maximum likelihood (ML)-based approach has been established for the direct extraction of NMR parameters (e.g., frequency, amplitude, phase, and decay rate) simultaneously from all dimensions of a D-dimensional NMR spectrum. The approach, referred to here as HTFD-ML (hybrid time frequency domain maximum likelihood), constructs a time-domain model composed of a sum of exponentially-decaying sinusoidal signals. The apodized Fourier transform of this time-domain signal is a model spectrum that represents the best fit to the equivalent frequency-domain data spectrum. The desired amplitude and frequency parameters can be extracted directly from the signal model constructed by the HTFD-ML algorithm. The HTFD-ML approach presented here, as embodied in the software package CHIFIT, is designed to meet the challenges posed by model fitting of D-dimensional NMR data sets, where each consists of many data points (108 is not uncommon) encoding information about numerous signals (up to 105 for a protein of moderate size) that exhibit spectral overlap. The suitability of the approach is demonstrated by its application to the concerted analysis of a series of ten 2D 1H-15N HSQC experiments measuring 15N T1 relaxation. In addition to demonstrating the practicality of performing maximum likelihood analysis on large, multidimensional NMR spectra, the results demonstrate that this parametric model-fitting approach provides more accurate amplitude and frequency estimates than those obtained from conventional peak-based analysis of the FT spectrum. The improved performance of the model fitting approach derives from its ability to take into account the simultaneous contributions of all signals in a crowded spectral region (deconvolution) as well as to incorporate prior knowledge in constructing models to fit the data.     

Fluorescence emission spectral shift measurements of membrane potential in single cells.

Previous measurements of transmembrane potential using the electrochromic probe di-8-ANEPPS have used the excitation spectral shift response by alternating excitation between two wavelengths centered at voltage-sensitive portions of the excitation spectrum and recording at a single wavelength near the peak of the emission spectrum. Recently, the emission spectral shift associated with the change in transmembrane potential has been used for continuous membrane potential monitoring. To characterize this form of the electrochromic response from di-8-ANEPPS, we have obtained fluorescence signals from single cells in response to step changes in transmembrane potentials set with a patch electrode, using single wavelength excitation near the peak of the dye absorption spectrum. Fluorescence changes at two wavelengths near voltage-sensitive portions of the emission spectrum and shifts in the complete emission spectrum were determined for emission from plasma membrane and internal membrane. We found that the fluorescence ratio from either dual-wavelength recordings, or from opposite sides of the emission spectrum, varied linearly with the amplitude of the transmembrane potential step between -80 and +60 mV. Voltage dependence of difference spectra exhibit a crossover point near the peak of the emission spectra with approximately equal gain and loss of fluorescence intensity on each side of the spectrum and equal response amplitude for depolarization and hyperpolarization. These results are consistent with an electrochromic mechanism of action and demonstrate how the emission spectral shift response can be used to measure the transmembrane potential in single cells.     

Processing of spectral localization-informative changes in sound signals by neurons of inferior colliculus and auditory cortex of the house mouse Mus musculus

Comparative analysis was performed of sensitivity of three populations of neurons of the inferior colliculus central nucleus and of neurons of the auditory cortex A1 and AAF fields of the house mouse Mus musculus to series of signals of wideband noise with spectral notch shifting along the frequency axis and to series of the band noise signals with shifting band. Sensitivity to spectral notches in noise was estimated from a change of impulse activity depending on notch location on the frequency axis (modulation coefficients were determined as the normalized difference between the maximal and minimal spike number in neuronal responses to all noises with notch exposed in the series). It was shown that the highest modulation coefficient values and accordingly the highest frequency-dependent sensitivity to spectral notches in the noise were peculiar to inhibition-dependent inferior colliculus neurons. Statistical analysis confirmed that distribution of modulation coefficients for the group of the inhibition-dependent neurons differed statistically significantly from the distribution for groups of primary-like and V-shaped inferior colliculus neurons as well as of cortical neurons (U-test, p < 0.0001). The lowest sensitivity to spectral notches was revealed in the V-shaped inferior colliculus neurons and cortical neurons; in these groups, distribution of modulation coefficients did not differed statistically significantly (p > 0.3). Thus, although a part of cortical neurons does have the frequency-dependent selectivity to spectral localizationally informative changes in sound signals, its formation needs participation of the inferior colliculus and its inhibition-dependent neurons. Selectivity to direction of the shift of spectral changes in noise signals in neurons of the inferior colliculus and auditory cortex was similar and was manifested mainly as shift along the frequency axis of dependences of the spike number in the neuronal responses and latent periods on central frequency of notch in noise (the noise band).     

The sensitivity of saturation transfer electron paramagnetic resonance spectra to restricted amplitude uniaxial rotational diffusion.

Computational methods have been developed to model the effects of constrained or restricted amplitude uniaxial rotational diffusion (URD) on saturation transfer electron paramagnetic resonance (ST-EPR) signals observed from nitroxide spin labels. These methods, which have been developed to model the global rotational motion of intrinsic membrane proteins that can interact with the cytoskeleton or other peripheral proteins, are an extension of previous work that described computationally efficient algorithms for calculating ST-EPR spectra for unconstrained URD (Hustedt and Beth, 1995, Biophys. J. 69:1409-1423). Calculations are presented that demonstrate the dependence of the ST-EPR signal (V'(2)) on the width (Delta) of a square-well potential as a function of the microwave frequency, the correlation time for URD, and the orientation of the spin-label with respect to the URD axis. At a correlation time of 10 micros, the V'(2) signal is very sensitive to Delta in the range from 0 to 60 degrees, marginally sensitive from 60 degrees to 90 degrees, and insensitive beyond 90 degrees. Sensitivity to Delta depends on the correlation time for URD with higher sensitivity to large values of Delta at the shorter correlation times, on the microwave frequency, and on the orientation of the spin-label relative to the URD axis. The computational algorithm has been incorporated into a global nonlinear least-squares analysis approach, based upon the Marquardt-Levenberg method (Blackman et al., 2001, Biophys. J. 81:3363-3376). This has permitted determination of the correlation time for URD and the width of the square-well potential by automated fitting of experimental ST-EPR data sets obtained from a spin-labeled membrane protein and provided a new automated method for analysis of data obtained from any system that exhibits restricted amplitude URD.     

Noise analysis of ion current through the open and the sugar-induced closed state of the LamB channel of Escherichia coli outer membrane: evaluation of the sugar binding kinetics to the channel interior.

LamB, a sugar-specific channel of Escherichia coli outer membrane was reconstituted into lipid bilayer membranes and the current noise was investigated using fast Fourier transformation. The current noise through the open channels had a rather small spectral density, which was a function of the inverse frequency up to about 100 Hz. The spectral density of the noise of the open LamB channels was a quadratic function of the applied voltage. Its magnitude was not correlated to the number of channels in the lipid bilayer membrane. Upon addition of sugars to the aqueous phase the current decreased in a dose-dependent manner. Simultaneously, the spectral density of the current noise increased drastically, which indicated interaction of the sugars with the binding site inside the channel. The frequency dependence of the spectral density was of Lorentzian type, although the power of its frequency dependence was not identical to -2. Analysis of the power density spectra using a previously proposed simple model (Benz, R., A. Schmid, and G. H. Vos-Scheperkeuter. 1987. J. Membr. Biol. 100: 12-29), allowed the evaluation of the on- and the off-rate constants for the maltopentaose binding to the binding site inside the LamB channels. This means also that the maltopentaose flux through the LamB channel could be estimated by assuming a simple one-site, two-barrier model for the sugar transport from the results of the noise analysis.     

Autocorrelation analysis of hydrophobic ion current noise in lipid bilayer membranes.

The autocorrelation function of a given process is related to its spectral density by the Wiener-Khintchine theorem, and both expressions contain the same information. We report here a measurement of the current noise produced in a lipid bilayer membrane doped with hydrophobic anions of dipicrylamine. The results are in good agreement both with relaxation measurements on the same membrane and with an analysis of the spectral density of the current noise for this system which has been presented by other workers. Although measurement of the spectral density function is generally more complete for technical reasons, the autocorrelation function provides, for the case studied here, more physical insight into the underlying charge transport mechanism. We find that the measured autocorrelation function is negative at short, but nonzero, times. This is a consequence of the operative conductance mechanism in this case, which cannot carry current continuously in the same direction without compensatory reverse flow.     

Solid-state nuclear magnetic resonance derived model for dynamics in the polypeptide backbone of the gramicidin A channel.

The dynamics of the backbone of the gramicidin A transmembrane cation channel in dimyristoylphosphatidylcholine bilayers have been investigated using solid state 15N nuclear magnetic resonance (n.m.r.) spectroscopy. With the temperature-dependent fluidity of the bilayer, the rates of motions in the helical gramicidin channel can be modulated. It is shown that in the gel phase, all substantial motions of the channel are slow on the timescale of the n.m.r. experiment (3.5 kHz). The use of oriented samples in which the axis of global channel rotation is aligned parallel to the magnetic field enables separation of global and local dynamics. Spectra obtained from oriented bilayer samples containing single-site 15N-labeled gramicidin at 8 degrees C are analyzed to yield a spatial model for local backbone motion. This model includes the axis of motion, the mean orientation, and the maximum amplitude of displacement for individual peptide planes. Specific sites in the first turn of the amino terminus were investigated, with emphasis on the Ala3 and Leu4 linkages, for which the orientation of the 15N chemical shift tensor with respect to the molecular frame has been determined. The effect of two well-characterized bilayer defect structures, parabolic focal conics and oily streaks, is included in the spectral simulations. It is found that only relatively small amplitude motions are possible at the two sites, with amplitudes of not more than +/- 8 degrees and +/- 15 degrees for the Ala3 and Leu4 sites, respectively. Detailed characterization of the bilayer surface geometry in the oriented samples is presently the major limiting factor in the use of this technique for probing the spatial extent of local motions in integral membrane proteins.     

Transport noise in membranes. Current and voltage fluctuations at equilibrium

A formulism is described for the treatment of noise resulting from the transport of ions in channels containing an arbitrary number of activation energy barriers. The analysis is based on Nyquist's theorem and is therefore restricted to fluctuations around the equilibrium state. Within this limit the spectral intensities of current and voltage noise are given by the frequency-dependent admittance, which in turn is closely linked to the relaxation-time spectrum of the transport system. Explicit expressions for the spectral intensity of current noise are derived for channels with two and three energy barriers. The analysis may be used to predict the spectral intensity of noise from the gating system in nerve.     

Temporal organization of the thyroid gland in A/He mice (morphometric investigation)

Biological rhythms of structural elements of the thyroid gland of A/He mice were studied by morphometric methods followed by spectral amplitude and phase analysis on the Minsk-32 computer. The morphological data show that the activity of the organ is maximal at night. The biorhythms have a complex frequency spectrum, including intradian, circadian, and ultradian components.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

Summary In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured at zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constantk _i for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentrationN _t of adsorbed ions may be caluculated from the observed spectral intensity of current noise. The values ofk _i obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentrationN _t .     

Membrane Electrical Noise in Chara corallina: II. Effects of Inhibitors on the Low Frequency Spectral Component

Certain inhibitors have been found to affect the low frequency spectral component of the electrical noise power spectrum in Chara corallina. Application of the ATPase inhibitor N,N′-dicyclohexylcarbodiimide removed the low frequency spectral component, strengthening the case that the component is produced by active proton pumping. Cytocholasin B, which inhibits cyclosis in internodes of C. corallina, removed the low frequency spectral component in a time-dependent fashion which was correlated with the cessation of streaming. The protonophore carbonyl cyanide m-chlorophenylhydrazone did not produce consistent effects on the low frequency spectral component in these cells.     

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.     

Spectral analysis of the effect of inflow noise on a fed-batch fermentation for recombinant β-galactosidase

The fermentative production of β-galactosidase from Escherichia coli CSH50 containing the plasmid pOU140 is mechanistically complex and difficult to model in a nonideal bioreactor. A spectral analysis has been done for a fed-batch fermentation with Gaussian disturbances in the feed stream. Inflow noise converts a smooth operation into aperiodic motion, as observed in some chemical reactions also. The disturbances also cause significant differences in the frequency responses of intra-cellular (plasmid DNA and β-galactosidase) and extra-cellular (concentration and mass fraction of recombinant cells) variables, whose implications are discussed.