Theoretical Considerations Affecting the Susceptibility of VGCCs to External Electric Fields

In examining whether there are grounds for suspecting that VGCCs may be susceptible to RF fields there are essentially two aspects: coupling of RF to cells and the demodulation of extremely low frequency (ELF: defined as the range 1 Hz–100 kHz) modulations from the RF carrier. With respect to the first, the cell membrane can be modeled as a parallel capacitor-resistor combination, with 10^–2 F/m² and 10^–2 Ω.m² values, respectively (13). Displacement and conduction currents are approximately equal at 1.6 kHz (loss tangent 1/(ωRC) =1), but since the majority of induced current is conduction current via intercellular pathways, the conduction current in bulk tissue tends to predominate up to 0.1 GHz (13). At 5 GHz the displacement current is several orders of magnitude greater than conduction current, but because of the dielectric properties of water, the conduction and displacement currents are about the same in the range 10–100 GHz. However, the induced current through channels is infinitesimally small and continues to fall as frequency rises. The occupational basic restriction on specific absorption rate (SAR) is 0.4 W/kg (3), from which the internal electric field can be deduced using the equation E = √(ρ.SAR/σ. Tissue conductivity ranges from 4–50 S/m for muscle and gray matter over the frequency range 5–50 GHz ( http://niremf.ifac.cnr.it/tissprop/). The value corresponding to 5 GHz is thus 10 V/m. Because of the membrane capacitance short-circuiting the resistance (13), the field appearing across the cell membrane will be essentially the same as this average field. The actual voltage drop across an individual membrane is thus of the order of 100 nV, given that the membrane thickness is approximately 10^–8 m. This is several orders of magnitude below the 25 mV (dc) mentioned previously for channel activation and this voltage is also alternating. With respect to alternating currents, the charge displacement required to activate the channel would only occur at frequencies up to a few kHz (15), which is several orders of magnitude below the frequencies considered here.

Regarding the second aspect (ELF demodulation), since most low-level RF studies claiming to show effects have used some form of modulation (see Table 1), this implies that some non-linear elements within tissue are able to detect and rectify the ELF signals. While it is true that certain ion channels show rectification properties (10), this is in relationship to currents in the ELF range. It is unclear whether these properties would affect RF currents in the GHz range. There have been a number of attempts at demonstrating rectification properties at frequencies relevant to telecommunications, but these have failed (14). The most elaborate experiment involved a very elegant exposure system (15) which attempted to detect signals at twice the frequency of the carrier, which would occur if there were a “square law” type response (16). These issues have been extensively reviewed (17, 18).

TABLE 1

Summary of Literature Relating to RF Ca²⁺ Effects

TABLE 1

Continued.

TABLE 1

Continued.

A Review of the Literature Concerning the Possible Influence on RF Fields on Ca²⁺ Levels

As mentioned at the outset, there has been longstanding concern over possible effects of RF on Ca²⁺ levels in cells, since there are clear links between disruption of cell Ca²⁺ signaling processes and disease, particularly cancer (4).

Studies were initially found by searching the EMF-Portal database ( https://www.emf-portal.org/en) using the search term “calcium channel” and limiting studies to RF fields using EMF-portal search settings. In this search 38 articles were identified, of which 18 were studies on the effects of RF on Ca²⁺ levels. We further searched the reference lists of major reviews published by health authorities on RF and health (19–22) which identified an additional 11 studies. Lastly, we searched the reference list of all the included studies and identified one additional study. Only studies with full articles available in English were included. We have identified 30 papers using these criteria.

In each study the fractional change in a parameter related to cell Ca²⁺ was estimated (usually the difference between exposed (E) and sham (S), divided by sham value) (Table 1). Wherever possible, the Glass effect size (ES) as the difference between the means of the exposed and sham groups divided by the standard deviation of the sham group was also computed (23) (Figs. 3–6).

FIG. 3

Effect size (ES) expressed as the difference between the means of the exposed and sham groups divided by the standard deviation of the sham group [(SD_E – SD_S)/SD_S] as a function of power density, plotted on a logarithmic axis to clearly separate low values. n = 13 studies; an outlying value of ES 60 with a PD of 0.001 W/m² was omitted.

FIG. 6

Effect size (ES) (as in previous figs.) versus year of publication. More recent studies are exclusively reporting effects leading to increases in cell [Ca²⁺]. n = 28 studies; two outliers with ES of 60 and 92 not shown in this graph.

In published studies where several frequencies or intensities were trialed, the largest value of ES was selected. In studies where values were displayed as mean ± SE, the SD was estimated from the reported number of observation for the sham value (SD=SE.√n). The sign of the ES value indicates whether the reported effect would tend to increase or decrease cell [Ca²⁺] or alternatively increases or decreases in the amount of Ca²⁺ associated with the cell, if adsorption to glycocalyx is taken into consideration.

Table 1 summarizes the Ca²⁺-related effects reported (0 represents not significant), along with the frequencies investigated and the modulation scheme used, if any. Wherever possible, the reported exposure, either as a power density (PD: W/m²) or SAR (W/kg) is recorded. The ES as a function of PD or SAR is presented in Figs. 3 and 4, respectively (no study reported both PD and SAR). Following the methodology of (24), a quality score (QS) for each of the studies was assigned on the basis that adequate attention had been given to the following aspects: blinding, dosimetry, use of positive controls and use of shams, with 1 for yes, 0 for no and 0.5 if partial attention had been given. Figure 5 shows ES plotted against QS for 26 of the 30 studies for which estimates of ES could be made. Two studies were excluded as outliers (ES of 60 and 92, respectively). The reason for exclusion is discussed further below. Analyses were also performed on carrier frequency and type of modulation (see Table 1) versus ES (results not shown).

FIG. 4

Effect size (ES), as in Fig. 3, but here exposure is expressed in specific absorption rate (SAR) rather than power density. n = 14 studies; an outlying value of ES 98 at a SAR of 0.1 W/kg was omitted.

FIG. 5

Effect size (ES) (as in Figs. 3 and 4) versus “quality” score, as used in (24). Points with identical values are offset slightly to enable visibility. There is no trend to clearer outcomes as quality increases. n = 28 studies; two outliers with ES of 60 and 92 not shown in this graph.

Over the 45 years of publications of “calcium effects” there have been considerable changes in experimental techniques. This is reflected in Fig. 6, which is a plot of ES versus year of publication.

Are External EMFs Sufficient to Activate VGCCs?

Charge transfer for activation. Voltage gating involves the movement of protein subunits associated with the channel under the influence of imposed voltages across the ends of the channel. This movement constitutes a momentary current, which can be measured experimentally (and has been since the 1970s) (10). Gating phenomena for Ca²⁺ channels are essentially very similar to those of Na⁺ and K⁺ channels (54). Typically, these gating currents are of the order of 10 µA/cm² (0.1 A/m²) of membrane area, with a characteristic time constant of 0.4 ms (54). The essential consideration here is whether these gating currents can be elicited by currents induced in tissue by external fields.

One of the most direct methods of investigating the properties of ion channels, including VGCCs, is the “patch clamp” (10), which is used to measure the conductance of single-ion channels (which are of the order of 10 pS) and observe the opening and shutting of the voltage-controlled gates in real time. Typically, a voltage step is applied to the patch of membrane (around 10 µm² in area) and then the resulting current measured. The early phase of the current represents the gate movement and the later phase the flow of particular ions through the channel (in this case Ca²⁺). The chances of the channel being open increase as the voltage across the channel decreases, in a deterministic manner. The voltage at which T-type VGCCs are most likely to be open is around 0 mV, that is, when the resting membrane potential of –50 to –70 mV is reduced by 60 mV. (the field across the 10^–8-m-thick membrane reduced by 6 MV/m). Of the three studies reviewed employing patch clamping, two (40, 46) showed no evidence of effects of RF on Ca²⁺ fluxes and another (43) measured currents in TRPM2 channels, which are not voltage-gated. As just mentioned, unless electric fields can be applied directly across cell membranes (which normally involves impaling the cell with microelectrodes or the removal of membrane patches using micropipettes with suction), the fields required to cause activation are relatively large. If the field is applied in air, without direct contact with the tissue (as in the case of the sciatic nerve), the field required is far greater [see (55)]. Since many commentators have assumed, in emphasizing the importance of ELF modulations in the possibility of low-level RF being biologically active [see (1)], it is instructive to consider whether, even if demodulation were to occur, the ELF components would be sufficient to cause VGCC activation. Essentially, electric fields within tissue are attenuated by a factor of 10⁵–10⁶ (at ELF), thus, to stimulate nerves within tissue using external fields in the surrounding air, fields of the order of 100 MV/m are required. Whether or not the field will cause effective stimulation also depends on the time-course of the way the fields are applied, usually in the form of a square wave in the case of the sciatic nerve of amphibians, with the shape of the leading edge of the square wave a most important factor. The question of the magnitude of external fields leading to effective stimulation is discussed in many standard textbooks (56, 57). In terms of RF, the question of detection of ELF modulations has already been discussed, but in terms of Fourier components, the ELF amplitudes would be less than the carrier, which for the International Commission for Non-Ionizing Radiation Protection (ICNIRP) general public reference level for 6–300 GHz is 87 V/m (in air), several orders of magnitude short of the fields just mentioned.

Molecular dynamics simulations of ion channels in lipid bilayers have confirmed that there is no basis for the claim that Ca²⁺ channels are in some way extremely sensitive to external fields. Recently reported simulations of Ca²⁺ in particular (58) have shown that reducing the potential by 40 mV leads to the expected conformational changes allowing Ca²⁺ permeation. E-fields across the actual membrane of the order of 120–650 MV/m (as 10 ns pulses) are required (59) to open channels (in this case, aquaporin channels, but Ca²⁺ channels would behave similarly).

Are VGCCs unique?. The information given above is not specific to Ca²⁺ channels; many ion channels consist of α-helical subunits (usually four) with many charges within the pores formed by these subunits. Ions within the pores “hop” from fixed charge to fixed charge, accompanied by varying amounts of “water of hydration”. The mechanism for K⁺ translocation through specific ion channels was elucidated by the MacKinnon group (60), and the translocation of Ca²⁺ has been shown to be similar. As mentioned above, the structure of Ca²⁺ channels is known in surprising detail, mainly from X-ray diffraction and electron microscope studies, (61, 62), the latter reference giving a depth of information on the electrophysiological data on activation and inactivation.

There are two main parts to the Ca²⁺ channel: the selectivity filter and the voltage-sensitive gate. The selectivity filter confers a 400:1 selectivity to Ca²⁺ ions over Na⁺, despite the latter being 70X more abundant in the extracellular environment. The protein which forms this selective filter is almost identical to that in the Na⁺ channel, but with subtle changes in amino acid sequence that attracts Ca²⁺ to the outside surface of the pore. There are then three Ca²⁺ binding sites within the pore, with individual hydrated Ca²⁺ ions shuttling between occupying sites 1 and 3 or just site 2. The channel is composed of protein subunits and the charges are most likely to be within the aqueous channel itself (rather than embedded in lipid); this is certainly the location for the “selectivity filter” described above. The gate itself is associated with the membrane-spanning so-called S4 segment, which contains several positive charges. However, this is not unique to Ca²⁺ channels; much of the same information applies to voltage-gated potassium, proton and sodium channels. It appears that VGCCs are no more susceptible to external EMFs than other voltage-gated channels. The “gating” in question results from a change in shape (“conformation”) when a specific change in transmembrane potential occurs (in the case of T-type channels this is around 25 mV, as has already been mentioned). Catterall et al. (61, 62) have suggested a sliding helix mechanism, which although explaining many phenomena is still not without difficulties (63). This conformational change certainly takes place in a high-field environment as already mentioned, so the addition of external fields several orders of magnitude weaker are not expected to affect this process in any significant way. Hille (10) reviews putative mechanisms for voltage sensing, but more recent research on the structure of Ca²⁺ channels implies that the voltage sensor may consist of several interacting subunits within the channel protein (64). Recently published work has used computational structural dynamics (65) and the study of mutations (66) to further elucidate the most likely mechanisms for voltage sensitivity. The movement of positively charged amino acids, such as arginine and lysine, appears to be central to voltage sensitivity. There is no suggestion of Ca²⁺ channels being especially sensitive in relationship to voltage sensors in other ion channels or in relationship to other biological functions. Indeed, certain organisms, such as fish (67) and monotremes (68), do have “extraordinary sensitivity” to environmental dc and ELF electric fields, which these animals use in the detection of prey. This appears to be achieved via the specific anatomical focusing, modulation and integration over many hundreds of neurons in specialized structures, with subsynaptic membranes “well-poised” to amplify small variations (67) and thus not a general property of membranes or channels. Furthermore, the work referred to above on the change in Ca²⁺ currents due to 1 and 10 Hz electric fields use 1-kV/m fields in the media, which would correspond to fields several orders of magnitude higher if applied to the air surrounding the biological samples. Therefore, claims that VGCCs in some way represent an amplification of forces by several orders of magnitude (1) appear not to be borne out by evidence.

Additional considerations. As we have already seen, there is considerable attenuation between the external fields and the fields induced in bulk tissue. In addition, the proportion of this field which adds to or subtracts from the transmembrane potential is highly dependent on cell architecture. As Reilly has pointed out, excitable cells become influenced by fields in the surrounding tissue fluid only at the ends of long cells or where they bend to be at an angle to the impressed field (56). This again makes the likelihood of ensembles of cells being affected by external fields at the ICNIRP limits unlikely.

Effects Reported: Cell Calcium Levels

Figure 2 summarizes the relative concentrations of Ca²⁺ in the various parts of the cell and surrounding media. The state of calcium is of two types: ionized and sequestered. For example, in the extracellular fluid approximately 50% is ionized. The cell glycocalyx has numerous positive charges with adsorbed Ca²⁺, which is in addition to the approximately 1 mM in the extracellular fluid. Thus, any changes in the dynamics of the ratio of ionized to sequestered could lead to an apparent loss of Ca²⁺ from the cell. Normally, the only route for Ca²⁺ loss would be via stimulation of Ca²⁺ pumps or gross damage to the cell membrane, as occurs in cell death. An early report suggests that pH is a major determinant on the amount of Ca²⁺ adsorbed onto phospholipid bilayers (69). However, there is no clear link between RF exposure and pH changes.

FIG. 2

Schematic diagram showing relative [Ca²⁺] values (in µM) within and surrounding typical cells, including internal stores. ER = endoplasmic reticulum.

Taking the sign of the ES into consideration, the number of reports of increases in cell Ca²⁺ is approximately the same as the number of decreases (and the number of studies reporting no effect). The average ES value (leaving out the two outliers, which will be discussed below) is –0.15 ± 0.17 (SE). In terms of fractional change, the average value is +0.22 ± 0.25.

As shown in the final two right-side columns in Table 1, the outcomes are mixed. In fact, very few of the studies were of Ca²⁺ channels per se; some used channel blockers to implicate specific types of VGCC, but the evidence was not direct. Those studies in which patch clamp techniques were used to directly gauge effects on VGCCs did not show significant effects due to RF, as has been discussed above. The list was compiled using certain keywords. While there may be other relevant studies, especially multiple studies from the same laboratory, which have been omitted, these omissions are unlikely to change the overall conclusions.

The estimation of “exposure” is to be used with caution: often it is not clear from descriptions on how PD has been estimated. Indeed, some estimates may be from quoted output power divided by estimates of aperture, without adjustment for reflections, non-uniformity or absorption by overlying media. The variable nature of the way the biological system was placed in media also makes PD a poor indicator of the actual PD at the cell membrane level. Nevertheless, an increase of ES with PD would be expected and is not observed. In Fig. 4, there are several large ES values, both for Ca²⁺ increases and decreases, but no obvious trend. Again, the SAR values used are those presented in the studies, with the possibility that erroneous assumptions were made. In some cases, SAR estimates were the result of detailed modeling, but in other instances the detailed derivation of SAR was not presented. In both Figs 3 and 4 the highest exposure estimates tend to be associated with lack of effects, with one or two exceptions. There is no consistent evidence of PD or SAR “windows”. The two outliers referred to in the caption, with ES values of 60 and 92, report SD values (for Ca²⁺ release) of approximately 1% of the control. These are an order of magnitude lower than those in comparable studies, and thus the possibility of computational error exists.

Figure 5 indicates that there are studies with good QS values with non-zero ES. However, the bulk of studies with QS ≥ 3 are for no effect. Similarly, the scoring of “quality” is not without considerable error. Only 4/32 (13%) of studies were performed blind and 11/32 (34%) used positive controls. The assessment of “exposure” was adjusted up and down by 0.5 points for greater or lesser attempts at assessing actual SAR within the target tissue. The more recent studies have tended to pay more attention to detailed exposure assessment, including, in some cases, monitoring of temperature changes.

Analyses of ES versus carrier frequency and type of modulation (or lack of modulation) did not reveal any significant relationship. This further weakens arguments that the membrane could act as a detector and rectifier of low frequency modulations.

From Fig. 6, it is apparent that the more recent studies, using techniques concentrating on measuring cell [Ca²⁺] (via fluorescent dyes) or channel currents directly (using patch clamping) report either increases or no effects, whereas the earlier studies, using radioactive tracers, report mostly decreases. Possible sources of artefact in the latter method were discussed near the time the earlier studies were published, including the possible non-viability of the brain tissue and the variability in the sham measurements (70). However, it should be acknowledged that there are potential artefacts with the other methods as well. For example, the fluorescent dye method is susceptible to bleaching effects if a non-ratiometric dye is used. The more recent methods are likely to give a much clearer indication of changes in cell Ca²⁺, but potential artefacts of the three methods are unlikely to explain the apparent change in direction of Ca²⁺ movement reported. In fact, earlier studies concluding increased efflux are perhaps using a misleading nomenclature, since, as mentioned, the percentage of Ca²⁺ associated with surface proteins or interstitial fluid movements could equally well account for the changes reported. Nevertheless, the more recent methods are more specific in measuring Ca²⁺ cellular movement and should be afforded greater weight. Small metabolic changes due to weak local “hot spots” in RF absorption could also stimulate Ca²⁺ transport, which is outward-directed (Fig. 1). On the other hand, VGCCs allow Ca²⁺ into cells if activated. However, since all of the studies reporting SAR values are below 5 W/kg, with many well below this value, thermal effects are expected to be minimal, which would make local RF “hot spots” unlikely as an explanation for significant effects.