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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. Using that criterion, I show that none of a set of interactions of weak fields, which I argue is nearly complete on dimensional grounds, can affect biology on the molecular scale. Moreover, I conclude that such weak fields are quite unlikely to generate significant effects in their interactions with larger biological elements such as cells. In the course of that analysis, I examine important special examples of electromagnetic interactions: "direct" interactions where biology is modified simply by the motion of charged elements generated by the electric field; resonance interactions; the effects of electrostrictive forces and induced dipole moments; and modifications of radical pair recombination probabilities. In each case, I show that it is unlikely that low intensity fields can generate significant physiological consequences.

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. However, such microwave excitable resonances are expected to be strongly damped by interaction with their aqueous biological environment. Although those dissipation mechanisms have been studied, the limitations on energy transfers that follow from the limited coupling of these resonances to the electromagnetic field have not generally been considered. We show that this coupling must generally be very small and thus the absorbed energy is so strongly limited that such resonances cannot affect biology significantly even if the systems are much less strongly damped than expected from basic dissipation models.

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. In either case, the initial cation influx causes a small cellular depolarization that further opens Ca 2+ channels, admitting more cations in a positive feedback process that leads to the depolarization of the membrane, thus initiating an action potential pulse. Monte Carlo calculations based on a well defined model of such processes, which include effects of noise, demonstrate quantitative agreement of the model with an extensive body of data.

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. That recombination will generally take place only if the valence electrons in the two radicals are in a singlet state and the effect of the magnetic field is manifest through differential spin precessions that affect the occupation of that state. Because the spin relaxation times are of the order of microseconds, any effects must be largely independent of frequency up to values of a few megahertz. Using exact calculations on an appropriately general model system, we show that one can expect small, but significant, modifications of the recombination rate by a 50 microT field only under a narrow range of circumstances: the cage time during which the two elements are together must be exceptionally long--of the order of 50 ns or longer; the hyperfine field of either radical must not be so great as to generate a precession period greater than the cage containment time; and the characteristic recombination time of the radical pair in the singlet state must be about equal to the containment time. Thus, even under such singularly favorable conditions, fields as small as 5 microT (50 milligauss) cannot change the recombination rate by as much as 1%. Hence, we conclude that environmental magnetic fields much weaker than the earth's field cannot be expected to affect biology significantly by modifying radical pair recombination probabilities.

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. Moreover, molecular shot noise, not thermal voltage noise, is the basis of threshold estimates. Models with and without stochastic resonance are used, with a long exposure time, texp = 10(4) s. We also determined the dependence of the threshold on the basal transport rate. By considering both spherical and elongated cells, we find that the lowest bound for the threshold is Emin approximately 9 x 10(-3) V m-1 (9 x 10(-5) V cm-1). Using a conservative value for the loop radius rloop = 0.3 m for induced current, the corresponding lower bound in the human body for a magnetic field exposure is Bmin approximately 6 x 10(-4) T (6 G). Unless large, organized, and electrically amplifying multicellular systems such as the ampullae of Lorenzini of elasmobranch fish are involved, these results strongly suggest that the biophysical mechanism of voltage-gated macromolecules in the membranes of cells can be ruled out as a basis of possible effects of weak ELF electric and magnetic fields in humans.

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. The firing rate of the afferent neurons that transmit signals from the ampullae has been shown to vary with that potential. We show that those firing rates can be described quantitatively in terms of synchronous firing of the sensory cells that feed the neurons. We demonstrate that such synchronism follows naturally from a hypothetical weak cell-to-cell interaction that results in a self-organization of the sensory cells. Moreover, the pulse rates of those cells-and the neurons that service the cells-can be expected to vary with the imposed electric fields in accord with measured values through actions of voltage gated transmembrane proteins in the apical sector of the cell membranes that admit Ca(++) ions. We also present a more conjectural model of signal processing at the neuron level that could exploit small differences in firing rates of nerve fibers servicing different ampullae to send an unambiguous signal to the central nervous system of the animal. (c) 1998 American Institute of Physics.

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. Also, other objections to the mechanism still stand; hence the model cannot account for any purported biological effects of weak extremely low frequency magnetic fields. Bioelectromagnetics 19:181–191, 1998. © 1998 Wiley-Liss, Inc.

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.

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. A further analysis demonstrates the effects of small signals in the shifting of biologically important chemical equilibria under conditions where stochastic resonance effects are significant.

The effects of 60 Hz magnetic fields of 5 [mu]T (50 mG) or less on biological structures holding magnetite (Fe[sub 3]0[sub 4]) are shown to be much smaller than that from thermal agitation; hence such interactions cannot be expected to be biologically significant. Various species have been shown to manufacture magnetite, which is used in some cases in conjunction with the earth's magnetic field to determine direction ([Frankel, 1986; Kirschvink and Kobayashi-Kirschvink, 1991].) This magnetite is usually found in sets of single domain grains, about 500[angstrom] in diameter, where all grains are magnetized in the same direction. Typically, such grains are enclosed by a membrane and are called magnetosomes. Hence, the possibility that weak ELF magnetic fields may cause biological effects in humans by the interaction of the field with magnetosomes must be considered.

Adair, R. K. Environmental Objections to the PAVE PAWS Radar System: A Scientific Review. Radiat. Res. 159, 128–134 (2003). 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. R. A. Albanese, an applied mathematician at the Air Force Research Laboratory, who has proposed standards by which that PAVE PAWS radiofrequency radiation which is incident on populations should be judged. I discuss those standards that are sufficiently well defined to be subject to analysis and show that they are not based on sound quantitative reasoning.

In their Comment on the paper of Balzano [2002] on the detection of nonlinear responses, Marino and Frilot [2003] state that certain possible biological systems with a response described by ‘‘non linear differential equations’’ can respond (chaotically) to an interaction that is ‘‘arbitrarily small, say kT/10.’’ This is correct but does not lead to the conclusion that significant biological effects can be generated by signals that are much smaller than kT. Indeed voltage gated ion channels, the best understood nonlinear biological system, have long been known to respond to such infinitessimal signals [Koch, 1999], but the biological effects of such channels are still severely limited by thermal noise. Though a very small signal impulse can generate a response, overwhelmingly, those responses will also be generated by noise impulses swamping the responses from the directed signal. I present a specific example: from numerical simulations using the Hodgkins and Huxley [1952] equations to describe ion channel dynamics, I find that a transmembrane pulse of þ6.905 mV applied to an area of a squid giant axon populated by ion channels never generates action pulses while a pulse of þ6.906 mV always does. This change of 0.001 mV represents an energy transfer of about 2.4 10 4 kT in each sodium channel and a little less in the potassium channels. However, the generation of an action pulse follows with equal efficiency from noise impulses and exogenous signals and neither voltage gated channel systems nor the hypothetical systems suggested by Marino and Frilot can discriminate between signal and noise impulses. Hence, when I include the thermally dependent noise chatter of channel openings and closings from MNa&300 000 Na channels and MK&36 000 K channels that occupy an axon area of 1000m, the probability of a channel opening from a signal impulse of&6.9 mV is approximately one-half and the opening probability changes gradually from near zero to near one over a signal impulse range of about 1 mV, or about 0.25 kT per channel. Hence, with thermal noise considered, effects of a signal S kT=ð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MNaþMK p Þ 0:05 mV (a conservative estimate of the noise for signals coherent over M elements) added to an appropriate bias voltage, will not be distinguishable from noise effects. In Balzano’s reply [Balzano, 2003], he says that the nonlinear effects he would investigate can cause ‘‘biological responses that are not limited by the thermal noise level, kT.’’ That statement can be misread to imply that nonlinear systems in general are especially immune to kT noise limitations and that Balzano’s ingenious experiment will be sensitive to all such systems. This is not the case. When voltage gated ion channels are exposed to 900 MHz radiation, those systems will not reradiate 1800 MHz photons at a level detectable by the procedure outlined by Balzano. The voltage sensitive elements of the systems (probably an alpha helix element in the S4 sectors of each of the four domains that largely make up the channel protein), which are accelerated by the 900 MHz incident fields, have masses in excess of 1000 Da. Thus the accelerations of the charged elements are small, they radiate very little, and Balzano’s proposed experiment would not detect that nonlinearity. However, any nonlinearity that led to the reports of rectification of RF radiation that Balzano cited would presumably involve electron currents involving very

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.

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.

I show that Pickard's mathematics cannot properly describe the effects of time-correlated signals in the presence of incoherent noise and cannot, therefore, properly address most signal-to-noise questions. Aside from this objection, I show that Pickard's conclusions follow from an ingenuous definition of “small signals” and do not hold for realistic models of biological processes and more conventional descriptions of “small signals.” © 1995 Wiley-Liss, Inc.