Paul C. Gailey

DETECTING DYNAMICAL CHANGE IN NONLINEAR TIME SERIES

Abstract We present a robust, model-independent technique for measuring changes in the dynamics underlying nonlinear time-serial data. After constructing discrete density distributions of phase-space points on the attractor for time-windowed data sets, we measure the dissimilarity between density distributions via L 1 -distance and χ 2 statistics. The discriminating power of the new measures is first tested on the Lorenz model and then applied to EEG data to detect the transition between non-seizure and epileptic activity. We find a clear superiority of the new measures in comparison to traditional nonlinear measures as discriminators of changing dynamics.

Membrane potential and time requirements for detection of weak signals by voltage-gated ion channels †

The question of minimum detection limits for biological processes sensitive to membrane potential perturbations has arisen in various contexts. Of special interest are the prediction of theoretical limits for sensory perception processes and for possible biological effects of environmental or therapeutic electric and magnetic fields. A new method is presented here, addressing the particular case in which perturbations of membrane potential affect the gating rate probability of voltage-sensitive ion channels. Using a two-state model for channel gating, the influence of the perturbing potential on the mean fraction of open channels is approximated by a Boltzmann distribution, and integrated over time to obtain a quantity proportional to the net change in expected charge transfer through the membrane. This change in net charge transfer (the signal, S) is compared to the expected root mean variance in charge transfer (the noise, N) due to random channel gating. Using a nominal criterion of S/N = 1, a model is developed for predicting the minimum time and number of ion channels necessary to detect a given membrane potential. Example calculations, carried out for a gating charge of 6, indicate that a 1 microV induced membrane potential can be detected after 10 ms by an ensemble of less than 10(8) ion channels.

Distribution of the ratio of gamma variates

The distribution of the ratio of independent gamma variates x and y each with shape parameters unity is studied, the ratio being t=x/(x+y). The problem arises from a model of ionic current fluctuations in biological membranes. Moments of the distribution are found, and an algorithm relating the fundamental parameter to the mean. This is used to set up percentage points. The moment estimator of the fundamental ratio parameter is defined as a series using Faa di Brunos formulas for derivatives of a composite function (function of a function). Terms to order four in the sample size are given for mean and variance and compared to assessment using Pearson-Tukey transformations.

Power frequency magnetic field exposure and gap junctional communication in Clone 9 cells.

Exposure to a power-frequency magnetic field has been reported to produce a statistically significant inhibition of gap junctional communication (GJC) in Clone 9 cells that have been pre-stressed by treatment with low concentrations of chloral hydrate (CH) [C.F. Blackman, J.P. Blanchard, S.G. Benane, D.E. House, J.A. Elder, Double blind test of magnetic field effects on neurite outgrowth, Bioelectromagnetics, 19 (1998) 204-209]. This observation might provide mechanistic insight into the possible role of electromagnetic fields (EMFs) in the carcinogenic process, since cancer cells frequently show decreased or absent GJC, and tumor promoting chemicals have been observed to inhibit GJC. Magnetic field exposure conditions were 45 Hz, 23.8 microT rms + parallel DC 36.6 microT, for 30 min of exposure. The responses of Clone 9 cells to the GJC-inhibiting effects of the tumor promoter 12-O-tetradecanoylphorbol 13-acetate and the chemical CH were evaluated and compared to reported results [S.G. Benane, C.F. Blackman, D.E. House, Effects of perchloroethylene and its metabolites on intercellular communication in Clone 9 rat liver cells, J. Toxicol. Environ. Health, 48 (1996) 427-437]. Before magnetic field exposure, cells were exposed for 24 h to either 3 (nine experiments) or 5 mM (11 experiments) CH to produce GJC of 67% or 50%, respectively, relative to unexposed controls. GJC was assessed microscopically using the scrape-loading technique and a blinded protocol. No statistically significant effect was observed due to magnetic field exposure with either CH concentration.

Cellular communication in clone 9 cells exposed to magnetic fields.

Abstract Griffin, G. D., Williams, M. W. and Gailey, P. C. Cellular Communication in Clone 9 Cells Exposed to Magnetic Fields. Magnetic-field exposure (45 Hz Ba.c. over a flux density range of 7.7 to 49.9 μT r.m.s. with parallel Bd.c. of 36.6 μT) has been reported by Blackman and coworkers to inhibit gap junction intercellular communication in Clone 9 cells treated with chloral hydrate for 24 h prior to field exposure in accord with predictions of the ion parametric resonance model. The study reported here is an attempt to reproduce this effect. Baseline experiments showed that growth in culture and state of confluence at time of addition of chloral hydrate were comparable in both laboratories. PMA inhibited cell–cell communication in a dose-dependent manner, similar to the results of Blackman and coworkers, whereas cells in the present study were somewhat more sensitive to chloral hydrate than reported by Blackman and coworkers. A total of 38 exposure experiments were undertaken using a 45 Hz magnetic field with a flux density of 23.8 μT r.m.s., in parallel with a 36.6-μT static magnetic field for 40 to 45 min, after pretreatment with 2.5 mM chloral hydrate for 24 h. In 14 unblinded experiments, a small but statistically significant effect of magnetic-field exposure was observed, but due to the subjective nature of the assay, it was deemed essential to carry out blinded experiments. The remaining 24 experiments were blinded. In 15 blinded experiments, cells purchased from the American Type Culture Collection and grown only in this laboratory were used, while in 9 experiments, the cells had originally been grown in Blackmans laboratory and were subsequently sent to this laboratory. There was no statistically significant effect of magnetic-field exposure on gap junction intercellular communication in these blinded experiments using either cell line.

ROBUST DETECTION OF DYNAMICAL CHANGE IN SCALP EEG

We present a robust, model-independent technique for measuring changes in the dynamics underlying nonlinear time-serial data. We define indicators of dynamical change by comparing distribution functions on the attractor via L{sub 1}-distance and X{sup 2} statistics. We apply the measures to scalp EEG data with the objective of capturing the transition between non-seizure and epileptic brain activity in a timely, accurate, and non-invasive manner. We find a clear superiority of the new metrics in comparison to traditional nonlinear measures as discriminators of dynamical change.

Correlation of Thermal Electrical Noise in Ion Channel Arrays

The question of minimum detection limits of biological systems to weak external signals occurs in several contexts, especially sensory perception. Ability to detect weak signals is generally limited by stochastic fluctuations or noise associated with the detection or processing system. In the simplest approach to theoretical prediction of detection limits, the signal is compared to the noise in the form of a signal-to-noise ratio (SNR). An SNR of unity has long served as a nominal requirement for detection, although recent developments in the area of stochastic resonance have indicated that noise may actually enhance signal detection in certain systems. However, the relevance of the SNR (=1) criterion may also depend on the configuration of the sensing system. While direct signal-to-noise comparisons are often sufficient for a single sensor, they may be inappropriate for the case of an array of sensors where the sensors are experiencing correlated, partially correlated, or uncorrelated noise.