Stochastic contributions to global temperature changes.

Records of the mean annual global surface temperatures from 1850 to 1970 show annual temperatures that are correlated with temperatures of the previous years as a one-dimensional random walk with a limiting feedback. This description accounts for the variation in those temperatures observed until the present by assuming that the base temperature is proportional to the increase in carbon dioxide concentration over the level in 1890. Climate models that better fit the observed variations are shown to be statistically improbable and thus likely to be artifacts.

Essay: Physical Review Letters; Sam Goudsmit's Vision.

Sam Goudsmit implemented his vision of converting the Letters section of Physical Review into a distinct journal fifty years ago. Physical Review Letters was designed to publish "only papers that really deserve rapid communication." The new journal became so successful with physicists throughout the world that Physical Review Letters now publishes 3500 Letters per year.

Comment: analyses of models of ion actions under the combined action of AC and DC magnetic fields.

I show that the interaction of weak DC and ELF magnetic fields with contained ions cannot generate significant biological effects through changing the character of the ion orbits.

Optimum ion channel properties in the squid giant axon.

Evolutionary pressures are presumed to act so as to maximize the efficiency of biological systems. However, the utility of that premise is marred by the difficulties in defining and evaluating both the efficiency of systems and the character of the available variation space. Following Hodgkin and Adrian, we examine the character of voltage gated ion channels in the nonmyelinated giant axons of the squid and find that both the channel densities and channel transition rates have values that nearly optimize signal sensitivity as well as signal velocity.

Noise and stochastic resonance in voltage-gated ion channels.

Using Monte Carlo techniques, I calculate the effects of internally generated noise on information transfer through the passage of action potential spikes along unmyelinated axons in a simple nervous system. I take the Hodgkin-Huxley (HH) description of Na and K channels in squid giant axons as the basis of the calculations and find that most signal transmission noise is generated by fluctuations in the channel open and closed populations. To bring the model closer to conventional descriptions in terms of thermal noise energy, kT, and to determine gating currents, I express the HH equations in the form of simple relations from statistical mechanics where the states are separated by a Gibbs energy that is modified by the action of the transmembrane potential on dipole moments held by the domains.

Detection of weak electric fields by sharks, rays, and skates.

The elasmobranchs-sharks, rays, and skates-can detect very weak electric fields in their aqueous environment through a complex sensory system, the ampullae of Lorenzini. The ampullae are conducting tubes that connect the surface of the animal to its interior. In the presence of an electric field, the potential of the surface of the animal will differ from that of the interior and that potential is applied across the apical membrane of the special sensory cells that line the ampullae.

Environmental objections to the PAVE PAWS radar system: a scientific review.

As part of our continental defense system, the United States Air Force has operated a radar system, known generally by the label PAVE PAWS, off of Cape Cod, MA since 1978. Some populated areas in the vicinity of the system are subject to a low level of background radiofrequency radiation from the system, and local citizens' groups have expressed concern that this radiofrequency radiation may affect their health. These concerns have been fueled by presentations and letters by Dr.

Biophysical limits on athermal effects of RF and microwave radiation.

Using biophysical criteria, I show that continuous radiofrequency (RF) and microwave radiation with intensity less than 10 mW/cm(2) are unlikely to affect physiology significantly through athermal mechanisms. Biological systems are fundamentally noisy on the molecular scale as a consequence of thermal agitation and are noisy macroscopically as a consequence of physiological functions and animal behavior. If electromagnetic fields are to significantly affect physiology, their direct physical effect must be greater than that from the ubiquitous endogenous noise.

Vibrational resonances in biological systems at microwave frequencies.

Many biological systems can be expected to exhibit resonance behavior involving the mechanical vibration of system elements. The natural frequencies of such resonances will, generally, be in the microwave frequency range. Some of these systems will be coupled to the electromagnetic field by the charge distributions they carry, thus admitting the possibility that microwave exposures may generate physiological effects in man and other species.

Simple neural networks for the amplification and utilization of small changes in neuron firing rates.

I describe physiologically plausible "voter-coincidence" neural networks such that secondary "coincidence" neurons fire on the simultaneous receipt of sufficiently large sets of input pulses from primary sets of neurons. The networks operate such that the firing rate of the secondary, output neurons increases (or decreases) sharply when the mean firing rate of primary neurons increases (or decreases) to a much smaller degree. In certain sensory systems, signals that are generally smaller than the noise levels of individual primary detectors, are manifest in very small increases in the firing rates of sets of afferent neurons.

A model of the detection of warmth and cold by cutaneous sensors through effects on voltage-gated membrane channels.

Warmth and cold sensations are known to derive from separate warm and cold cutaneous thermoreceptors in the form of differentiated afferent nerves. The firing rate of warm-sensing nerves increases as the temperature increases; the firing rate of cold-sensing nerves increases if the temperature is reduced. I postulate that the primary sensitivity of the warm sensors derives from voltage-gated Ca(2+) membrane channels configured such that an increase in temperature opens channels and increases the ion influx while a reduction in temperature increases the ion influx through voltage-gated Na(+) channels in the cold sensory nerve ends.

Effects of very weak magnetic fields on radical pair reformation.

We can expect that biological responses to very weak ELF electromagnetic fields will be masked by thermal noise. However, the spin of electrons bound to biologically important molecules is not strongly coupled to the thermal bath, and the effects of the precession of those spins by external magnetic fields is not bounded by thermal noise. Hence, the known role of spin orientation in the recombination of radical pairs (RP) may constitute a mechanism for the biological effects of very weak fields.

Theoretical limits on the threshold for the response of long cells to weak extremely low frequency electric fields due to ionic and molecular flux rectification.

Understanding exposure thresholds for the response of biological systems to extremely low frequency (ELF) electric and magnetic fields is a fundamental problem of long-standing interest. We consider a two-state model for voltage-gated channels in the membrane of an isolated elongated cell (Lcell = 1 mm; rcell = 25 micron) and use a previously described process of ionic and molecular flux rectification to set lower bounds for a threshold exposure. A key assumption is that it is the ability of weak physical fields to alter biochemistry that is limiting, not the ability of a small number of molecules to alter biological systems.

A physical analysis of the ion parametric resonance model.

We show, in elementary terms, using for the most part only elementary mathematics, the physical bases for the ion parametric resonance model so as to clarify the assumptions and consequences of the model. The analysis shows why, contrary to earlier conclusions, no combination of weak DC and AC magnetic fields can modify the transition rate to the ground state of excited ions. Although reinterpretations of the biological consequences of the motion of the excited ions circumvent that particular objection to the model, those changes introduce other difficulties.

Extremely low frequency electromagnetic fields do not interact directly with DNA.

Blank and Goodman [(1997): Bioelectromagnetics 18:111-115] suggest that weak extremely low frequency (ELF) electric and magnetic fields affect intracellular DNA directly. We show that such a conclusion is not in accord with physical principles.

Measurements described in a paper by Blackman, Blanchard, Benane, and House are statistically invalid.

Blackman et al. [1994] describe an experiment that purports to show that weak 45 Hz magnetic fields inhibit the growth of neurites from PC-12 cells treated with a growth stimulation factor. I present a statistical analysis of the data in that paper that shows that the data were corrupted in some way; hence, the results are invalid.

Didactic discussion of stochastic resonance effects and weak signals.

A simple, paradigmatic, model is used to illustrate some general properties of effects subsumed under the label "stochastic resonance." In particular, analyses of the transparent model show that 1) a small amount of noise added to a much larger signal can greatly increase the response to the signal, but 2) a weak signal added to much larger noise will not generate a substantial added response. The conclusions drawn from the model illustrate the general result that stochastic resonance effects do not provide an avenue for signals that are much smaller than noise to affect biology.

Ultrashort microwave signals: a didactic discussion.

As a consequence of the variation with frequency of the attenuation and phase velocity of electromagnetic waves in tissue, the shape (variation of the electric field with time) of short electromagnetic pulses incident on tissue changes with depth of penetration. We show that a conjecture that such well-known and long understood changes in pulse shape may generate harmful biological effects is not credible. We also consider the suggestion that such pulses may be useful in medical imaging and the mapping of the electrical properties of complex tissues and show that such use is impracticably difficult for fundamental reasons.

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity.

Biological responses to weak 60-Hz electric and magnetic fields must vary as the square of the field strength.

Under quite general conditions, the biological response j(G) to a very weak continuous 60-Hz electric or magnetic field G is shown to be proportional to the square of the field strength. This conclusion follows from the continuity of the function j(G) and the first three derivatives of j(G) with respect to G over the amplitude of G. That continuity is ensured in nominally discontinuous systems by the presence of thermal noise.