Modulation of the time relation of action potential impulses propagating along an axon

Reproducing asymmetrical spine shape fluctuations in a model of actin dynamics predicts self-organized criticality

Dendritic spines change their size and shape spontaneously, but the function of this remains unclear. Here, we address this in a biophysical model of spine fluctuations, which reproduces experimentally measured spine fluctuations. For this, we characterize size- and shape fluctuations from confocal microscopy image sequences using autoregressive models and a new set of shape descriptors derived from circular statistics. Using the biophysical model, we extrapolate into longer temporal intervals and find the presence of 1/f noise. When investigating its origins, the model predicts that the actin dynamics underlying shape fluctuations self-organizes into a critical state, which creates a fine balance between static actin filaments and free monomers. In a comparison against a non-critical model, we show that this state facilitates spine enlargement, which happens after LTP induction. Thus, ongoing spine shape fluctuations might be necessary to react quickly to plasticity events.

Long-range correlation properties of stationary linear models with mixed periodicities

We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.

1/f Noise in human color vision: the role of S-cone signals

We examine the functional role of S-cone signals on reaction time (RT) variability in human color vision. Stimuli were selected along red-green and blue-yellow cardinal directions and at random directions in the isoluminant plane of the color space. Trial-to-trial RT variability was not statistically independent but correlated across experimental conditions and exhibited 1/f noise spectra with an exponent close to unity in most of the cases. Regarding contrast coding, 1/f noise for random chromatic stimuli at isoluminance was similar to that for achromatic stimuli, thus suggesting that S-cone signals reduce variability of higher order color mechanisms. If we regard spatial coding, the effect of S-cone density in the retina on RT variability was investigated. The magnitude of 1/f noise at 16 min of arc (S-cone free zone) was higher than at 90 min of arc in the blue-yellow channel, and it was similar for the red-green channel. The results suggest that S-cone signals are beneficial and they modulate 1/f noise spectra at postreceptoral stages. The implications related to random multiplicative processes as a possible source of 1/f noise and the optimal information processing in color vision are discussed.

Information transmission in cercal giant interneurons is unaffected by axonal conduction noise

What are the fundamental constraints on the precision and accuracy with which nervous systems can process information? One constraint must reflect the intrinsic “noisiness” of the mechanisms that transmit information between nerve cells. Most neurons transmit information through the probabilistic generation and propagation of spikes along axons, and recent modeling studies suggest that noise from spike propagation might pose a significant constraint on the rate at which information could be transmitted between neurons. However, the magnitude and functional significance of this noise source in actual cells remains poorly understood. We measured variability in conduction time along the axons of identified neurons in the cercal sensory system of the cricket Acheta domesticus, and used information theory to calculate the effects of this variability on sensory coding. We found that the variability in spike propagation speed is not large enough to constrain the accuracy of neural encoding in this system.

Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system

It is fairly well established that the higher-order aberrations of the eye fluctuate over relatively short time periods, but as yet there is no conclusive evidence regarding the origin of these fluctuations. We measured the aberrations and the pulse pressure wave simultaneously for five subjects. The aberrations were measured by using a Shack-Hartmann sensor sampling at 21.2 Hz. We decomposed the aberration data into Zernike coefficients up to and including fifth order and also calculated the rms wave-front error. From the pulse data the heart rate variability signal was also derived. Coherence function analysis showed that for all subjects there was a weak correlation between many of the aberrations and the pulse and the derived heart rate variability. The pulse and the heart rate variability can account for only 11% +/- 2% and 20% +/- 2%, respectively, of the aberration dynamics.

Long-term heart rate fluctuations in postoperative and brain-dead patients

Long-term heart rate fluctuations in postoperative and brain-dead patients were investigated. Heart rates were monitored continuously, and the data were stored, edited, and interpolated to allow for data lost during calibration and disconnection of the sensors for various treatments. Heart rate power spectra were calculated using the fast Fourier transform method. The power spectra of the patients who recovered showed that the heart rate fluctuated and produced a 1/f relationship, termed 1/f fluctuations, whereas those of patients who died in the intensive care unit (ICU) consisted of white-noise-like signals. The power spectra in brain-dead patients showed a 1/f relationship under steady-state conditions, while the power density and variation of the frequency distribution were lower than those in a normal subject. Therefore, 1/f fluctuations appear to be universal and occur independent of the central nervous system.

Assessment of behavioral effects of tetrachloroethylene using a set of time-series analyses

A systematic approach to the analysis of time-series data for spontaneous locomotor activity in the rat was developed to evaluate the behavioral effects of chemical substances. Chronogram, spectral analysis, analysis of the slope of fluctuation, and the cosinor method were used to analyze data obtained by continuously recording spontaneous locomotor activity in the rat. Under synchronized conditions, a circadian period of 24 h was observed and the 1/f fluctuation, in which the power spectral density is inversely proportional to frequency, was confirmed. The 1/f fluctuation was considered to reflect the fractal-like structure of ultradian components of spontaneous locomotor activity. IP administration of 1.0 g/kg body weight of tetrachloroethylene at 0900 h produced a remarkable phase-shift (4.0 +/- 0.9 h) in the activity rhythm and an increase in the slope of fluctuation (0.4 +/- 0.1) in contrast to a relatively smaller decrease in the total amount of spontaneous locomotor activity. These behavioral effects of tetrachloroethylene were dose-dependently lower at lower doses. The present study demonstrated the usefulness of our systematic approach in evaluating the behavioral effects of chemical substances.

Further study on 1/f fluctuations observed in central single neurons during REM sleep

Recently, 1/f fluctuations have been discovered in the single-unit activity of mesencephalic reticular formation (MRF) neurons during REM sleep. In a previous paper, such behavior could satisfyingly be interpreted on the basis of the clustering Poisson process. The question of applicability of this model to other MRF neurons remained unanswered. The present paper reports on 1/f fluctuations in 12 MRF neurons all of which can satisfyingly be modeled by the clustering Poisson process.

Chaos and fractals which 1/f spectrum below 10(-2) Hz demonstrates full-term fetal heart rate changes during active phase

Human fetal heart rate changes were analysed using power spectral density (PSD). The data for analysis were obtained from 25 normal fetuses between the 37th and 40th week of gestation. Pulse interval distribution showed an almost Gaussian distribution. PSD was calculated by first Fourier transform technique, and showed the particular fluctuation below 10(-2) Hz to be inversely proportional to frequency (so called '1/f spectrum') during the active phase after the 37th week of gestation. These results revealed that the 1/f spectrum of the human heart rate had already appeared below 10(-2) Hz in full term of pregnancy.

Impulse patterning and relaxational propagation in excitable media

Wavetrains of impulses in homogeneous excitable media relax during propagation toward constant-speed patterns. Here we present a study of this relaxation process. Starting with the basic reaction-diffusion or cable equations, we derive kinematics for the trajectories of widely spaced impulses in the form of ordinary differential equations for the set of times at which impulses arrive at a given point in space. Stability criteria derived from these equations allow us to determine the possible asymptotic forms of propagating trains. When the recovery after excitation is monotonic, only one stable train exists for a given propagation speed. In the case of an oscillatory recovery, however, many stable trains are possible. This essential difference between monotonic and oscillatory recoveries manifests itself in qualitatively distinct relaxational behaviors.

Time-dependent effects of trichloroethylene on motor activity in rats

Circadian variations in acute and subacute neurobehavioural effects of trichloroethylene (TRI: 1.2g/kg i.p.) were investigated in the rat under a light: dark = 12: 12 hr cycle. An acute effect of TRI evaluated by decreased muscle tone was maximal during the early dark phase (21:00). A subacute effect of TRI was evaluated by a continuous recording of spontaneous locomotor activity in the rat. The circadian rhythm in spontaneous locomotor activity was extensively impaired by the injection of TRI for three consecutive days. Spectral analysis of spontaneous locomotor activity showed that ultradian periods became more dominant than the circadian period, and the 1/f fluctuation of the spectrum disappeared after the injection of TRI. The effect of TRI on the circadian rhythm in spontaneous locomotor activity was circadian-phase dependent, and the treatment of TRI at 09:00 provoked greater circadian rhythm impairment than that at 21:00. The mechanisms of the time-dependent effect of TRI on neurobehaviour are the subject of further investigation.

On a mechanism of cardiac electrical stability. The fractal hypothesis

Electrical activation of the ventricles via the His-Purkinje system is represented on the body surface by a waveform with a broad range of frequency components. We speculate that this process is mediated by current flow through a fractal-like conduction network and therefore that the broadband spectrum of the depolarization waveform should be scaled as a power-law distribution. The prediction is confirmed by Fourier analysis of electrocardiographic data from healthy men. This observation suggests a new dynamical link between nonlinear (fractal) structure and nonlinear function in a stable physiologic system.