Abstract
Halgamuge and Abeyrathne's study (2011) is important because it shows by numbers set in an appropriate computer program that the first two theories cannot work under realistic viscosity conditions within biological tissue, but there is no limitation for the third theory. The study indicates that a free ion's resonant response as predicted by ICR and IPR theories would be possible only in an unrealistically low viscosity environment. Indeed, in both the first two theories, viscosity of the ion motion within the proteins was not taken into account (Liboff, 1985; Liboff and McLeod, 1988; Lednev, 1991), in contrast to the third theory in which viscosity was accounted for and an appropriate factor, defined as the “attenuation coefficient” for the free ion motion, was calculated based on the latest available molecular data. Halgamuge and Abeyrathne (2011) verify the result of an older numerical study (Galt et al., 1993) in regard to the ICR theory, which had also concluded that the ICR model cannot work in realistic viscosity conditions. In regard to the IPR and the IFV theories, however, there was no numerical test until now. Therefore, this numerical study by Halgamuge and Abeyrathne (2011) is an important contribution to the debate concerning one of the most important issues in the area of the biological effects of EMFs: the mechanism by which even very weak natural or man-made EMFs act on cells and alter their function resulting in health effects in animals (including humans) as indicated by a large number of experimental, epidemiological, and clinical studies (Panagopoulos and Margaritis, 2008; Panagopoulos, 2011) but not explained theoretically so far due to the lack of a commonly accepted mechanism.
Indeed, in spite of the numerous data during the last four decades indicating that even very weak external electric or magnetic fields—mainly oscillating ones—can alter cellular functions and produce biological effects leading to health effects, there is still no generally accepted mechanism to explain these data. Since this numerical test (Halgamuge and Abeyrathne, 2011) disproves the ICR and IPR theories but verifies the IFV theory, it seems an explanation of the mechanism is imminent and the IFV theory should be accepted by the scientific community as a realistic mechanism by which EMFs may act on living tissue.
This study by Halgamuge and Abeyrathne (2011) also corrects an older review study by Halgamuge et al. (2009), which compared theoretically the validity of the IFV, ICR, and IPR theories and incorrectly concluded that the IFV theory would be the least effective of the three theories. In that study (Halgamuge et al., 2009) the reviewed theories were not described correctly and several mistakes were made, leading to wrong conclusions. Although the matter is now clarified by the latest study (Halgamuge and Abeyrathne, 2011), we would like to point out several mistakes made in the earlier one (Halgamuge et al., 2009) in order to avoid possible future confusion.
In Figs. 1 and 4 of Halgamuge et al. (2009), the depiction of the channel is not correct according to the latest available molecular data. The inner walls of the channels are known to be constructed by several parallel symmetrically arranged α-helices. The voltage sensors of the electro-sensitive channels are a set number (four in sodium and potassium channels) of positively charged α-helices that are also symmetrically arranged around the pore of the channel, called S4 helices. The so-called pore is the narrowest part of the channel; therefore, the diameter of the channel is not the same along its length. Close to the sensors and to the pore there are several (at least three) ion binding sites occupied by ions ready to pass through the channel when it opens. The channel opens and closes not by any kind of cover, as it is depicted by the authors, but by rotational outward/inward movement of the S4 helices once their uncoupled positive charges—voltage sensors—sense a minimum necessary change in the cell membrane potential (Stuhmer et al., 1989; Tytgat et al., 1993; Miller, 2000; Panagopoulos et al., 2002). Therefore, the depiction of the voltage-gated ion channels by the authors is incorrect, and this may lead to incorrect considerations about the mechanism of channel irregular gating.
The authors claimed that according to the IFV model, for a frequency of 50 Hz, an external electric field of at least 10 mV/m would be necessary to produce biological effects (Halgamuge et al., 2009), but their calculation was incorrect. According to their Fig. 2, and more precisely according to Equation 11 in Panagopoulos et al. (2002): Eoqe/λω ≥ 0.25×10−12 m (where ω is in Hz, Eo is in V/m), the necessary electric field strength to produce biological effects ranges from 0.49 to 3.14 mV/m depending on λ (the attenuation coefficient for the ion movement), which is calculated to be about 10−12 kg/s for ions moving outside channels, or λ≅ 6.4×10−12 kg/s (in the case of Na+ ions) for ions moving within channels. Thus, the authors' calculation was wrong by a factor of more than 20.
The authors claimed that induced electric fields in the human body are produced by much stronger external electric fields. Such a claim is not supported by experimental evidence. Even if such a hypothesis was realistic for the inner cells of the body, it is certainly not valid for the skin cells, the eyes, the blood cells, vessels, or nerve cells that end on the skin. Therefore, there are millions of cells on the human body that directly sense external electric fields. Thus, the conclusion of Panagopoulos et al., that external 50-Hz electric fields of less than 1 mV/m can produce biological effects, is not wrong. Moreover, it is known that even relatively weak extremely low frequency (ELF) magnetic fields can induce detectable electric fields within biological tissue. For example, a simple calculation based on Maxwell's third equation for the magnitude of a 50-Hz magnetic field necessary to induce an electric field of 1 mV/m, conservatively gives an RMS value of about 1 G=10−4 T or 10−5 T (=10 μT) under certain conditions. Therefore, the authors' interpretation of Panagopoulos et al. that electric fields of 1000 kV/m or magnetic fields above 1 mT (= 10 G) are necessary in order to produce biological effects, was incorrect.
In the same article (Halgamuge et al., 2009) the authors disregarded the possibility that electric fields can directly affect cell function, without sufficient explanation. The theory of Panagopoulos et al. (2000, 2002) refers mainly to direct action of electric fields on cells, while the other two theories refer exclusively to the action of magnetic fields. The problem of which field is actually responsible for the biological and health effects of weak ELF electromagnetic fields (e.g., the cause of cancer near to power transmission lines) is not yet clarified. It is possible that electric fields of about 1 V/m or lower are more responsible than magnetic ones of several milligauss.
The Panagopoulos et al. theory presents calculations for two ions interacting simultaneously with the channel's voltage sensor, and it is clearly stated that several ions can interact together in phase with the channel's sensors. It is also explained that IFV is a coherent motion of several ions in the same direction, resulting in additive forces on the channel's sensors and for this it can be more effective than thermal motion, which is a random motion in every possible direction, resulting in mutually extinguishing forces on the channel sensors (Panagopoulos et al., 2002). Thus, the authors' statement (Halgamuge et al., 2009:1474) that this theory “was developed by considering only one ion in the vicinity of the voltage sensor” is also not correct.
In the Panagopoulos et al. theory, the forces exerted by an oscillating magnetic field were calculated for ions moving through an open channel parallel to the channel's direction (Panagopoulos et al., 2002). Such moving charges constitute detectable electric currents that can be measured by the patch-clamp technique (Neher and Sakmann, 1992; Terlau and Stuhmer, 1998). Therefore, the authors' criticism that in the IFV theory the Lorentz force was considered to be acting on ions moving in any possible direction was also not correct.
The facts indicated in Halgamuge et al. (2009) in regard to the induced electric field, are not omitted in Panagopoulos' theory as the authors claimed. The value of 1 V/m for the induced electric field in the Panagopoulos et al. theory was not introduced arbitrarily; rather, it was adopted as a typical mean value for electric fields induced by external oscillating magnetic fields according to the literature (Panagopoulos et al., 2002).
The authors' conclusion in the last sentence of the abstract that the IFV model cannot be applied for amplitude-modulated microwaves and also their conclusion that “it is unlikely that microwave exposure might have the ability to open ion channels by the mechanism described” (Halgamuge et al., 2009:1475) is not correct since microwaves are always pulsed or modulated by ELFs in order to be able to carry information. No model is suggested for nonmodulated microwaves, since that would be useless.
The authors' opinion in the Halgamuge et al. (2009:1473) study that, in most biological studies “unrealistically high amplitudes were used for exposure” is a generalization that it is not correct; it should refer to certain studies only. In addition, the authors' opinion that “a crucial problem that any interaction model must deal with is how a large enough signal-to-noise ratio can be obtained to enable the living cell to detect the signal” is again a not correct generalization since a weak but polarized signal can be more detectable than stronger stochastic noise.
At the end of the Introduction, Halgamuge et al. (2009:1474) wrote, “as the use of wireless communications is expanding.…it should be considered whether proposed theoretical models…might also be applicable to amplitude modulated radiofrequency electromagnetic radiation.” The radiation used currently in wireless communications, such as the digital mobile telephony radiation, is not amplitude modulated but uses a type of phase modulation called Gaussian minimum shift keying modulation (Panagopoulos and Margaritis, 2008).
In the same article (Halgamuge et al., 2009), the restrictions of the ion cyclotron resonance, were not well explained (e.g., that the radius of an ion cyclotron motion would be too large for any reasonable value of ion speed; Zhadin, 1998). Also, Equation 1 in the description of the IPR model was not explained correctly because ω is not the cyclotron frequency (q/m)Bdc, but instead the frequencies of an alternating magnetic field, at which the transition probabilities increase. Further, Bstat is the static field (Lednev, 1991) and not a “combination of static and alternating” as the authors wrote. Accordingly, the restrictions of the IPR model were not analyzed. This model assumes emission/absorption of photons at the cyclotron frequency (on the order of 30 Hz or quantum energy on the order of 10−13 eV). Such photons are not known to exist in nature, and even if they existed they would correspond to quantum states of 1011 times lower energy than the background of thermal noise (Zhadin, 1998). Therefore the authors' conclusion that “in this model the signal to noise ratio is highly improved” (Halgamuge et al., 2009:1477) was not correct. The authors' statement that “Engstrom showed that criticisms on Lednev's theory were not valid” was also not correct. Engstrom states about this theory: “I cannot provide satisfying answers or justifications to all issues raised” (Engstrom, 1996:59).
Lednev's IPR model refers to Ca2+-binding proteins such as calmodulin (Lednev, 1991). This protein is not a channel, or even a transmembrane protein as incorrectly depicted in Fig. 4 of Halgamuge et al. (2009), but an intracellular protein that binds to different enzymes, modifying their activities. Lednev's theory does not concern channel proteins or irregular channel gating, but changes in enzymatic activity of proteins like calmodulin. The basic fact that the IPR theory (Lednev, 1991) refers to possible changes in the activity of enzymes like calmodulin, in contrast to the IFV theory, which refers to irregular channel gating, was not evident in Halgamuge et al. (2009). In contrast, calmodulin was confused with the channel proteins. There are indeed some experimental results on the activity of transport proteins that seem to be explained by IPR models (Bauréus Koch et al., 2003), but these results could be at least partly explained by the IFV theory also, since the AC magnetic fields used (25 μT) could most likely induce electric fields of the order of 1 mV/m. Unfortunately, in Bauréus Koch et al. (2003), as in many other articles that utilized magnetic fields, there were no measurements or calculations for the induced electric field.
In conclusion, the theoretical discussion in Halgamuge et al. (2009) was based on incorrect assumptions and interpretations by its authors, and for this, it is actually disproved by the recent numerical test by Halgamuge and Abeyrathne (2011). As the authors of the latest study conclude themselves, this study showed that “resonance as proposed by ICR and IPR theories is not possible under realistic conditions. This result verifies the previous result by Galt et al. 1993 in regards to the ICR theory. The recorded biological effects must be due to another mechanism as is probably the Ion Forced-Vibration mechanism by its own” (Halgamuge and Abeyranthe, 2011:8).
Therefore, as we strongly believed since the first publication of our theory (Panagopoulos et al., 2000, 2002), it seems that finally, after decades of research, science in this area now has a strong tool to explain theoretically the recorded biological and health effects of environmental EMFs, and that is the IFV theory.