Date Published: March 14, 2019
Publisher: Public Library of Science
Author(s): Claus Nielsen, Ron Hui, Wing-Yee Lui, Ilia A. Solov’yov, Zhongliang Zu.
Recent experiments have reported an effect of weak radiofrequency magnetic fields in the MHz-range on the concentrations of reactive oxygen species (ROS) in living cells. Since the energy that could possibly be deposited by the radiation is orders of magnitude smaller than the energy of molecular thermal motion, it was suggested that the effect was caused by the interaction of RF magnetic fields with transient radical pairs within the cells, affecting the ROS formation rates through the radical pair mechanism. It is, however, at present not entirely clear how to predict RF magnetic field effects at certain field frequency and intensity in nanoscale biomolecular systems. We suggest a possible recipe for interpreting the radiofrequency effects in cells by presenting a general workflow for calculation of the reactive perturbations inside a cell as a function of RF magnetic field strength and frequency. To justify the workflow, we discuss the effects of radiofrequency magnetic fields on generic spin systems to particularly illustrate how the reactive radicals could be affected by specific parameters of the experiment. We finally argue that the suggested workflow can be used to predict effects of radiofrequency magnetic fields on radical pairs in biological cells, which is specially important for wireless recharging technologies where one has to know of any harmful effects that exposure to such radiation might cause.
Weak radiofrequency (RF) magnetic fields in the MHz-range was shown to influence the concentrations of reactive oxygen species (ROS) in living cells [1–4]. Remarkably, the energy that could possibly be deposited by such radiation is orders of magnitude smaller than the energy of molecular thermal motion. A plausible explanation to the observed effect relies on the interaction of RF magnetic fields with transient radicals within the cells, affecting the ROS formation rates through the radical pair mechanism [5–9]. Prediction of the RF magnetic field effects in biomolecular systems is, however, not straightforward, as it relies on multiple interlinked scales ranging from electrons to the whole cell. This gap in our understanding of RF field effects on biological systems is, however, important and needs special attention because wireless charging has already been commercialized in various sectors such as portable consumer electronics  and manufacturing facilities . While the World’s first wireless charging standard “Qi” launched by the Wireless Power Consortium focuses on short-range wireless charging which has no danger of human exposure to electromagnetic radiation, mid-range wireless charging (with possible human exposure to electromagnetic radiation) has been suggested recently by a group of companies through the AirFuel Alliance.
Interpretation of RF field effects in real biological systems involves a significant effort, but the workflow outlined in Fig 1 breaks it down into smaller manageable tasks, which are discussed in detail below. All steps in this workflow are essentially relying on a computational approach which should be closely coupled to experiment in terms of defining the variable parameters of RF magnetic fields and of the key observables.
To employ the generic workflow in Fig 1, it is illuminating to consider simple generic radical pair models. An example of a simple radical pair model is illustrated in Fig 2A, consisting of two magnetic nuclei (red arrows) and two unpaired electrons (blue arrows), such that each radical has a single magnetic nucleus. The unpaired electrons in the radical pair posses a property called spin , which permits them to be affected by external magnetic fields, such as RF magnetic fields. The external magnetic fields, as well as other magnetic interactions of the unpaired electronic spins, result in the singlet-triplet mixing of the radical pair, which is an interconversion between two different types of quantum mechanical states that the spins of the unpaired electrons can reside in, called singlet and triplet states, and occuring with a characteristic rate constant kmix. More details about the quantum states of a radical pair can be found in the Supporting Information (SI). The significance of the singlet and triplet states is illustrated in Fig 2B, and note also the presence of two spin-dependent processes occuring with rate constants kS and kT from the singlet and triplet state, respectively. These processes could, for example, be electron transfer processes, and will (possibly together with kmix) determine the lifetime of the radical pair, τ0. The oversimplified radical pair model system in Fig 2 is expected to be more complex in reality and include more nuclei [15, 48, 51], and, therefore, more local magnetic interactions, that will add a specific signature to how a radical pair will respond to external magnetic fields. A more complex model including more magnetic nuclei is, therefore, also considered below. The minimal model, however, is supposed to illuminate in an intuitive fashion the principal effects that are expected to arise in a radical pair system, once it is subject to RF magnetic fields.
In order to characterize an ensemble of radical pairs, one should first consider how a single radical pair is described. The results of such a description are the so-called quantum yields, which determine the probability for reaction pathways for the single radical pair. Since most of the radical pairs in an experiment are expected to be similarly prepared, they are assumed to be spawned in the same quantum state, and experience the same internal interactions as the molecular structures of the radical pairs are thought identical. The calculated probabilities for the various reaction products in a single radical pair could then be generalized for every radical pair in the experimental system. There are two potential problems with this approach: (i) the radical pairs in the experimental setup have different orientation relative to external static and RF magnetic fields, and (ii) the inherent randomness of the thermal motion present in the radicals will lead to different molecular motions for each of the radical pairs in the ensemble. The first problem is solved by averaging the yield obtained for a single radical pair over all possible orientations of this radical pair. The second problem can be handled through the Redfield theory [18, 45, 47, 48], which has been developed to take spin relaxation into account.
Determining whether radical pairs residing in a biological environment are susceptible to RF magnetic field effects is no simple matter, but the presented workflow outlines the steps necessary to produce a realistic computational model of ensembles of such radical pairs, as well as the interpretation of calculation results in terms of physical observables. Such a computational approach has the predictive power necessary to evaluate the possible health effects of RF magnetic fields.