The voltage across the cell membrane of human T-lymphocyte cell lines was recorded by the whole cell patch clamp technique. We studied how this voltage fluctuated in time and found that these fluctuations have fractal characteristics. We used the Hurst rescaled range analysis and the power spectrum of the increments of the voltage (sampled at 0.01-sec intervals) to characterize the time correlations in these voltage fluctuations. Although there was great variability in the shape of these fluctuations from different cells, they all could be represented by the same fractal form. This form displayed two different regimes. At short lags, the Hurst exponent H = 0.76 +/- 0.05 (SD) and, at long lags, H = 0.26 +/- 0.04 (SD). This finding indicated that, over short time intervals, the correlations were persistent (H > 0.5), that is, increases in the membrane voltage were more likely to be followed by additional increases. However, over long time intervals, the correlations were antipersistent (H < 0.5), that is, increases in the membrane voltage were more likely to be followed by voltage decreases. Within each time regime, the increments in the fluctuations had characteristics that were consistent with those of fractional Gaussian noise (fGn), and the membrane voltage as a function of time had characteristics that were consistent with those of fractional Brownian motion (fBm).

Fourier analysis was employed to determine the amplitudes of spectrum components of small variations of electrical resistance (bioimpedance) in human finger recorded using an original hardware-software complex. It revealed periodic bioimpedance oscillations at the frequencies of heartbeats, respiration, and Mayer wave (0.1 Hz). These periodic variations were observed under normal conditions and during circulation arrest in the arm. It is concluded that the spectrum peaks of bioimpedance variations in the phalanx of human finger reflect periodic blood pressure changes in the major vessels and rhythmic neural control of the regional vascular tone. During normal blood flow, the greatest amplitude of rhythmic changes in bioimpedance was observed at the heart rate; it surpassed by an order of magnitude the amplitudes of respiratory oscillations and Mayer wave. In contrast, the largest amplitude of rhythmical changes of the impedance during circulation arrest corresponded to the oscillations at respiration rate, while the amplitude of variations at the heart rate was the smallest. Under circulation arrest, the maximum frequency of bioimpedance variations was approximately 1.4 Hz (the third respiratory harmonic), which indicates the upper limit of frequency range of neural modulation of vascular tone in human finger. During normal respiration and circulation, two side cardiac peaks were revealed in bioimpedance amplitude spectrum, whose amplitude reflected the depth of the respiratory amplitude modulation of pumping action of the heart. During normal breathing, the second and the third harmonics of the cardiac bioimpedance variations were split reflecting respiratory frequency modulation of the heart rate.

It has been proposed that part of a voltage gated channel is a tethered ball and that inactivation occurs when this wandering ball binds to a site in the channel. In order to be able to quantitatively test this model by comparison to experiments we developed analytical solutions and numerical simulations of the distribution of times it takes the ball to reach the binding site when the motion of the ball is random and when it is also influenced by a directed force. If the motion of the ball is one-dimensional, at long times this distribution is a single exponential with a rate constant that is inversely proportional to the square of the length of the chain and does not depend on the starting position of the ball. This dependence on the chain length is not significantly altered if there are short range electrical forces between the ball and its binding site. These predictions suggest that to confirm the validity of this model additional experiments should be done to more precisely determine the form of this distribution and its dependence on the length of the chain.

The front-end low-noise electronic amplifiers and high-throughput computing systems made it possible to record ECG with a high resolution in the low-frequency range including the respiration and Mayer frequencies and to analyze ECG with digital filtering technique and harmonic analysis. These tools yielded ECG spectra of narcotized rats, which contained the characteristic pulsatile triplets and pentaplets with splitting constant equal to respiration rate, as well as the peaks at respiration and Mayer frequencies. The harmonic analysis of ECG determined the frequency parameters employed to tune the software bandpass filters, which revealed the respiratory (R) and Mayer (M) waves in the time domain with the amplitudes of 20-30 μV amounting to 5% ECG amplitude. The depolarizing myorelaxant succinylcholine chloride capable to trigger various types of arrhythmias, transiently increased R-wave, inhibited M-wave, and provoked a negative U-wave within a heartbeat ECG cycle synchronously with inspiration. It is hypothesized that M-, R-, and U-waves in ECG reflect cardiotropic activity of autonomic nervous system. The respective spectral peaks in ECG can be employed to assess intensity of sympathetic and parasympathetic cardiotropic influences, their balance, and the risk of arrhythmias.

Large molecules such as proteins have many of the properties of neural networks. Hence, neural networks may serve as a natural and thus efficient method to compute the time dependent changes of the structure in large molecules. We describe how to encode the spatial conformation and energy structure of a molecule in a neural network. The dynamics of the molecule can then be computed from the dynamics of the corresponding neural network. As a detailed example, we formulated a Hopfield network to compute the molecular dynamics of a small molecule, cyclohexane. We used this network to determine the distribution of times spent in the twist and chair conformational states as the cyclohexane thermally switches between these two states.