Electromagnetic bioeffects: a multiscale molecular simulation perspective

Abstract

Electromagnetic bioeffects remain an enigma from both the experimental and theoretical perspectives despite the ubiquitous presence of related technologies in contemporary life. Multiscale computational modelling can provide valuable insights into biochemical systems and predict how they will be perturbed by external stimuli. At a microscopic level, it can be used to determine what (sub)molecular scale reactions various stimuli might induce; at a macroscopic level, it can be used to examine how these changes affect dynamic behaviour of essential molecules within the crowded biomolecular milieu in living tissues. In this review, we summarise and evaluate recent computational studies that examined the impact of externally applied electric and electromagnetic fields on biologically relevant molecular systems. First, we briefly outline the various methodological approaches that have been employed to study static and oscillating field effects across different time and length scales. The practical value of such modelling is then illustrated through representative case-studies that showcase the diverse effects of electric and electromagnetic field on the main physiological solvent – water, and the essential biomolecules – DNA, proteins, lipids, as well as some novel biomedically relevant nanomaterials. The implications and relevance of the theoretical multiscale modelling to practical applications in therapeutic medicine are also discussed. Finally, we summarise ongoing challenges and potential opportunities for theoretical modelling to advance the current understanding of electromagnetic bioeffects for their modulation and/or beneficial exploitation in biomedicine and industry.

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Introduction

The interaction of biomaterials with electric fields (EFs) and electromagnetic fields (EMFs) has attracted increasing attention over the last few decades, due to increased recognition of the importance of the external fields in modulating structure and activity of biomolecules^1–8 as well as emerging EF and EMF applications in therapeutic medicine.^9–13 On-going research efforts addressing several important aspects of the EMF health debate including the mechanisms, neurodegenerative diseases, cancer and exposure dosimetry, have been summarised in several reviews.^14–16 In 2015 English and Waldron provided a detailed perspective on the progress and challenges of molecular simulations of external EFs, as well as the potential impact and prospects for exploitation of such simulations for real-world and industrial applications.¹⁷ More generally, the effect of static EFs on chemical reactivity has been discussed in several reviews and perspectives.^18–21 A recently published book on this topic²² provides an excellent and detailed overview of the EM/EMF effects on structure and reactivity, including applications and recent theoretical developments in EF-mediated chemistry.

In this review, we outline how multiscale theoretical methodology can be used to study the impacts of external EF and EMF on the electronic and atomistic structure of biologically relevant molecules and their assemblies in physiological environments. We present a theoretical background of quantum chemical and classical modelling approaches that are used to study the effect of external fields on biomolecular systems. Next, we examine recent literature to highlight how multiscale computational modelling can be used to explore the effects of external EFs (and EMFs) on physiologically relevant biomolecular systems, including aqueous solutions, DNA, proteins and enzymes, membranes and biomedically important nanomaterials.

Sufficiently intense EF and EMF can influence both the structure and reactivity of (bio)molecules. These effects can include altering equilibrium geometries²³ and molecular spectroscopy (e.g. the Stark and Zeeman effect) as well as altering electron^24,25 and H-atom²⁶ transfer and bond cleavage/reformation processes.^27–30 Indeed, the highly specific orientation of charged and polar residues within enzymes naturally creates local EFs that are often necessary for their function.^25,31,32 Given this, it is worth briefly distinguishing between different types of EF and EMF that are encountered within the context of (bio)chemical modelling:

• External static electric fields are uniform with respect to time (and generally space) and are generated by a voltage bias (e.g. within a capacitor, scanning tunnelling microscopy or a charged surface).

• External oscillating electromagnetic fields (electromagnetic radiation) oscillate in both time and space, generally propagating at the speed of light through a given medium. The period of these oscillations (or conversely their wavelength) determines the energy carried by these fields and consequently they are normally categorised as either ionizing or non-ionizing depending on their ability to ionize biomolecules and/or break chemical bonds.

• Local or intrinsic electric fields are generated from orientated dipoles, and ions within molecular systems (e.g. biological membranes, at enzyme active sites) and are essentially inherent. These EFs can fluctuate with time depending on the specific molecular configuration(s) within the system.

As molecules can be viewed as ensembles of charged elementary particles, the molecular systems can be perturbed by external EFs. However, as large intrinsic fields often occur spontaneously within chemical systems, relatively intense external EFs are generally required to observe significant chemical or physical effects. For context, Table 1 compares the peak magnitudes of external EFs that can be generated by various sources to those of intrinsic fields that occur naturally within (bio)chemical systems.

Table 1 Typical exposures from different EF (and EMF) sources and intrinsic EFs encountered within (bio)chemical systems

External fields			Intrinsic fields
Application/source	|[Doublestruck E]| (V nm^−1)	Ref.	System	|[Doublestruck E]| (V nm^−1)	Ref.
Within typical houses	10^−8–10^−7	33	Within liquid water	10	34
Below high voltage transmission lines	10^−6–10^−5	33 and 35	Internal potential within phospholipid membranes	0.1–1	36 and 37
Therapeutic medicine	10^−5–10^−2	38–42	Within DNA	1	19
Electrode surfaces	10^−4–1	19	Transmembrane potential	10^−2	36 and 37
Scanning tunnelling microscopy (STM)	1–10	19, 43 and 44	Within typical proteins	0.1–10	19 and 45
Laser fields	>10	19	Electron charge at 0.53 Å	5.1 × 10^2	19

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As Table 1 outlines, the intrinsic EFs experienced by electrons within a typical molecule are surprisingly large and can easily exceed 10² V nm⁻¹, particularly close to the nucleus. Moreover, many biomolecular structures (e.g. DNA, proteins and membranes) generate significant intrinsic fields on the order of 1 V nm⁻¹. In contrast, external EFs that are generated within houses and offices by consumer electronics are typically of the order 10⁻⁷ V nm⁻¹. However, higher-intensity (typically |E| > 10⁻⁵ V nm⁻¹) and short duration (ranging from microseconds to nanoseconds) pulsed EFs have been utilised for various therapeutic applications. The applications include treating melanoma³⁸ and cutaneous tumours implanted in mice,³⁹ as well wound healing^40,41 and tissue ablation.⁴² In general, these applications operate through the formation of nanoscale defects in the cell membrane (electroporation) that are within the timescale of current modelling capabilities. There has also been substantial interest in the effects of static and time-varying EFs on protein conformation,^{3–8,46–54} as the formation of insoluble aggregates (amyloid fibrils) are thought to contribute to the onset of various neurodegenerative diseases (e.g. Parkinson's and Alzheimer's).^47,55,56 Intriguingly, some evidence has been reported of high-frequency EMFs reducing amyloid fibrils in the brain of Alzheimer's patients.^15,57

Fig. 1 schematically relates the time and length scales accessible to the theoretical modelling techniques associated with various biomolecular systems, physicochemical phenomena and EMF radiation spectrum. Quantum Mechanical (QM) approaches are particularly well suited to the study of bond breaking/forming reactions and are commonly utilised for modelling enzymatic transformations as well as determining chemically accurate interaction energies (e.g. for metal–ligand complexes, molecular recognition, drug binding). QM approaches are well suited for studying enthalpically driven processes, which usually involve significant changes in chemical bonding along a well-defined reaction coordinate. The macroscopic descriptors of the processes in question (e.g. rate coefficients and equilibrium) can be accurately determined by identifying critical points on the potential energy surface that describe motion along these degrees of freedom (see QM approaches below). QM-based approaches are currently only feasible for relatively small molecular systems and so are limited to biomolecules and biochemical processes that occur on the nanometre scale.

Fig. 1 Time and length scales accessible to multiscale modelling associated with various biomolecular systems, physicochemical phenomena, and EMF radiation spectrum, illustrated by exemplar studies of the effect of static EFs on proton-transfer in DNA models^60–62 and hydrogen bond structuring in water,^63,64 the impact of EMFs on peptide conformations⁶⁴ and water permeation of membranes.⁵⁹ Images are not to scale.

Classically propagated systems using molecular mechanics and dynamics (MD) approaches, where atoms are treated as spring connected (bonded) or disconnected (non-bonded) point charges and many-body interactions are represented by inter-atomic interaction potentials, so called force fields (FFs), are significantly larger (100 000+ atoms) and allow for both static and time-dependent (oscillating) EF to be investigated. All-atom inclusive models simulated by MD enable direct insight into the fundamental EF effects on molecular processes, structure, and dynamics of biological molecules (water, DNA, peptides/proteins, lipid membranes) and materials (nanoparticles, organic and inorganic surfaces) in physiological conditions at spatial and temporal resolutions currently inaccessible by laboratory techniques, and as such have proven to be highly complementary to the experimental efforts in this area.^17,58,59 MD is well suited for studying entropically driven processes, which involve significant changes in the configurations of the system (e.g. conformations, solvent orientations) over multiple degrees of freedom. These processes are governed by the probabilities of the system populating different (thermally accessible) microstates, which requires explicit simulation and statistical sampling of these states.

Below we present a theoretical background of quantum chemical and classical modelling approaches and critically review recent literature employing the computational modelling to explore the effect of external EFs (and EMFs) on biomolecular systems. We show how multiscale theoretical approaches can be used to study the impacts of external EF and EMF on the electronic and atomistic structure of biologically relevant molecules and their assemblies in physiological environments of living organisms or within the latest biomedical technologies.

Theoretical background

Quantum mechanical approaches

Quantum mechanical approaches can be categorised depending on how molecular energies/properties are initially calculated (e.g. wavefunction theory, density functional theory) and how these calculations are utilised to predict macroscopic observables (e.g. free-energies, reaction rates). Many references provide detailed summaries on the calculation of molecular energies and properties as well as their use in predicting macroscopic observables.^65–67 Here we focus on key aspects relevant to condensed-phase multiscale modelling, contrasting the strengths and weaknesses of different conceptual approaches for modelling static EFs and oscillating EMFs.

Electronic structure calculations for static EFs and EMF response properties

Electronic structure calculations can be used to infer dynamic behaviour, predicting macroscopic observables (e.g. rate coefficients, equilibrium constants) via critical points on the potential energy surface (PES), the so called ‘potential landscape’ paradigm of chemical reactivity.^68,69 These geometric features can be used to predict how static EFs influence a (bio)molecular system along a predetermined reaction coordinate. Meanwhile, both static and dynamic molecular response properties, which describe how systems are perturbed by EMFs of a given frequency, can be approximated by taking various derivatives of the energy and by using perturbative expansions. Non-ionizing radiation carries insufficient energy to promote electronic excitations in (bio)chemical systems. Instead, this radiation excites vibrational and rotational modes of the underlying nuclei. Thus, the wavelength and intensity of these vibrational transitions will determine how a given system interacts with a dynamic (non-ionizing) EMF.

The standard approach for calculating vibrational (and internal rotational) transitions uses Taylor series expansions to describe the PES and molecular interactions with the EMF.⁷⁰ Under the ‘double harmonic’ approximation, these expansions are truncated at second-order coefficients, though inclusion of additional anharmonic response terms provides better accuracy (at increased computational expense). The double harmonic approximation describes nuclear dynamics via a 3N system of independent quantum harmonic oscillators, in terms of motion along internal degrees of freedom (or normal coordinates), denoted Q₁, Q₂,…,Q_3N ≡ Q.⁷⁰ Within the Born–Oppenheimer approximation, these vibrational states are found by solving the nuclear Schrodinger equation in terms of these normal coordinates:

Here Ψ_s(Q) is the vibrational wavefunction of the sth vibrational state and E_s is its corresponding energy. By neglecting rotational angular momentum and rotational coupling effects, the Hamiltonian operator, , can be written:Here V(Q) is the Born–Oppenheimer PES described in mass-weighted normal coordinates. Because evaluating the full PES across all 3N degrees of freedom is often computationally prohibitive, it is approximated by a second-order Taylor series expansion around the equilibrium nuclear geometry, so-called ‘mechanical harmonicity’:Here ω_k is the fundamental angular frequency of the kth vibrational mode, whose motion is described by Q_k. It should be noted that 6 of these angular frequencies (or 5 for linear molecules) correspond to translations and external rotations, which are removed and treated separately. Having established the energies for these transitions, various terms that are needed to construct a Gibbs free energy surface (e.g. zero-point energies, thermal corrections and vibrational entropy) can be determined.

Calculation of absorption coefficients requires the use of first order time-dependent perturbation theory.⁷¹ The rate of a transition between initial, |ν_i〉, and final quantum states, |ν_f〉, denoted W_f←i, can be written:

Here ρ_N(ν_fi) is the density of photon states per frequency range and is the Hamiltonian describing the interaction of light with the system. The molecular systems that are amenable to QM calculations are typically orders of magnitude smaller in dimensions than the wavelengths of non-ionizing radiation (e.g. IR and microwaves). The so-called ‘long wavelength’ approximation assumes that the EMF can be approximated as spatially uniform (while obviously still varying in time), which greatly simplifies the treatment of light/molecule interactions.⁷¹ The magnetic component of radiation, which is small compared with the electric component, is also normally neglected.⁷¹ The resulting simplified Hamiltonian is:Here μ_fi are elements of the resulting transition dipole matrix, which integrates the dipole operator over the normal coordinates, Q. This dipole operator is approximated via a Taylor series expansion taken around the equilibrium geometry as a function of normal mode coordinates:While this expansion is first order in terms of the normal modes that comprise Q, dipole moments are themselves first-order response properties of V(Q) with respect to an applied EF. Hence the gradient terms used in this expansion are considered ‘electronically harmonic’, and this expansion does not allow for vibrations involving concurrent electronic excitation. Under these assumptions,⁷¹ the absorption coefficient, , is given by:While the ‘double harmonic’ approximation is ubiquitous in QM studies, it has well-documented limitations, particularly for describing very low frequency torsional motion.^72–74 These modes are often strongly anharmonic and more accurately considered hindered internal rotations rather than vibrations.^72–74 When considering far-IR/microwave radiation, mechanical anharmonicity is particularly problematic and additional terms in the Taylor series expansion are often used.^72–74

Explicitly including EFs in electronic structure calculations alters the electronic PES, perturbing both the normal modes Q_k and their corresponding fundamental angular frequencies ω_k. The inclusion of an EF alters the electronic Hamiltonian by introducing an additional term:

Here μ is the dipole moment operator, [Doublestruck E] is the EF vector, r̂_i is the position operator for the ith electron, and Z_j and R_j are the atomic number and position (respectively) of the jth nuclei. The effect of these perturbations can be rationalised via a Taylor series expansion of the potential, V([Doublestruck E]), with respect to the applied field [Doublestruck E]:Here V₀ denotes the potential energy at zero field, μ₀ is the permanent dipole moment of the ground-state, is the polarizability tensor and is the first hyperpolarizability. These terms are defined as progressively higher derivatives of the energy with respect to the applied field. Similar evaluations can be performed on oscillating fields to establish analogous frequency dependent properties (e.g. dynamic polarizabilities). Most popular QM software packages (e.g. Gaussian,⁷⁵ QChem,⁷⁶ Turbomole⁷⁷) can calculate basic EMF response properties (e.g. IR and Raman wavelengths and intensities) and can incorporate static EFs in DFT and wavefunction calculations. More specialised packages, such as TITAN,⁷⁸ can generate various types of external EF and quantify intrinsic electric fields within biological systems.

Modelling static and oscillating EFs with ab initio molecular dynamics

Rather than using static nuclear configurations and derivative information, ab initio molecular dynamics (AIMD) calculates the PES (and forces acting on the nuclei) either in advance, or more commonly, “on the fly” at discrete points at each step of a given trajectory.

The incorporation of EFs in AIMD is discussed extensively in ref. 79, though we provide a brief summary here. For systems within periodic boundary conditions, a metastable state induced by an external field, [Doublestruck E], can be described by the energy functional:

E[{ψ_i}, [Doublestruck E]] = E₀[{ψ_i}] − [Doublestruck E]·P[{ψ_i}] (10)

Here E₀[{ψ_i}] is the standard energy functional in the absence of a field and P[{ψ_i}] is the polarization along the direction of [Doublestruck E]. This polarization can be determined from the periodicity of the cell, L, and the elements of the S[{ψ_i}] matrix:The resulting perturbed eigenstates, |ψ^{[Doublestruck E]}_i〉, are given by:This approach can then be used to calculate atomic forces for implementation molecular dynamics schemes.

Classical molecular dynamics

The presence of externally applied EF in classically propagated molecular systems, whether static or time-varying, renders the classical MD simulations as non-equilibrium, thus appropriately referred to as non-equilibrium molecular dynamics or NEMD.

To represent the EF acting on an atomically represented system, the system's Hamiltonian, H, is perturbed by an additional term H_E.

H_E(t) = −μ_tot·E(t) = −μ_tot,zE(t) (13)

where μ_tot is the total, collective dipole vector, and E represents the field acting along the z-axis. The method of perturbation depends on whether the system is treated as classical point charges or using electronic-structure approaches, the latter explained in the preceding QM section of the review. Here, we described the formulation of EF in classical molecular mechanics using force fields, where the applied electromagnetic forces are added to the Newton's 2nd law of motion as follows:where the force f_i, is due to the force field determined interactions between all particles (V), q_iE is the electric field induced force applied to each partial charge i with charge q_i, and q_iv_i × B(t) is the Lorentz (magnetic) force acting on individual particle traveling at velocity v_i.⁸⁰ The electric and magnetic components can be taken to act along the mutually orthogonal x- and y-directions respectively, represented as:resulting in the plane of polarization being in the x–y coordinate plane, with propagation along the z-axis. The electric- (E) and magnetic- (B) field strengths are related by , where c is the speed of light. Due to the electric-field strength being orders of magnitude greater than that of the magnetic component, common molecular simulation packages such as Gromacs,⁸¹ NAMD⁸² and LAMMPS⁸³ have only embedded the EF component with continuous and time-variant amplitudes in their algorithms. To the best of our current knowledge, DL-POLY⁸⁴ is the only publicly available simulation package through which the magnetic field, albeit separately, can also be applied via an external force. There are also several groups which have made in-house modifications to the NAMD and LAMMPS algorithms to incorporate the stand-alone magnetic field forces.^85,86 The first full-representation of the EMF in simulations was achieved by the English group.⁸⁷ The code was tested for biologically relevant solvated peptide systems and small differences in peptide conformation between EF and EMF simulations have been observed, however, whether this was due to the additional magnetic force or the finite nature of the simulations remains an open question.⁶⁴ Below we review some seminal and most recent (at time of writing) case studies in which molecular modelling of EF/EMF has been employed to better understand the applied field effects on molecules and materials relevant to life systems.

Recent case studies

Water and solutions

Water being one of the most fascinating and important molecules to life plays an important part in many biological and chemical systems. Although water molecule appears quite simple, it possesses an electric dipole and the dynamic behaviour and properties of bulk, surface and interfacial water are controlled by the formation and breaking of orientated hydrogen bonds. As such, the physicochemical properties of liquid water can easily be influenced by EF,⁸⁸ and have, therefore, been extensively studied.^34,89–92

QM studies have mainly focused on quantifying the effect of static EFs on the hydrogen bond structure of molecular water clusters. Kim and co-workers used DFT and wavefunction methodology to investigate the effect of static EFs on the structure, energetics, and transition states of trimer to pentamer water clusters.⁹³ The authors noted transitions from cyclic to linear water structures when EFs of 3 V nm⁻¹ were applied. Pathak and co-workers used similar DFT methodology to investigate the effect of EFs on the structure of water hexamers to octamers.⁹⁴ These authors found that increasing EF strength tended to reduce the number of hydrogen bonds within a cluster, with 4 V nm⁻¹ fields significantly affecting the relative stability of cluster configurations. Ramalho and co-workers investigated the effect of EFs on larger water clusters (H₂O)_n, where n = 2–15, with DFT calculations.⁹⁵ These authors noted changes to the number of hydrogen bonds, a reduction in cluster sizes and an increase in the strength of inter-cluster hydrogen bonds.⁹⁵ Kreuzer and co-workers used DFT to investigate the formation of whiskers in trimer, tetramer, octamer and decamer water clusters.⁹⁶ Interestingly, these authors noted that the HOMO–LUMO gap of the clusters decreased with increasing field strength, approaching zero at the point of structural breakdown of the hydrogen bond networks.⁹⁶

Pathak and co-workers investigated EF responses of larger water clusters, (H₂O)_n, where n = 9–20, with DFT calculations.⁶³ These authors noted similar EF responses, with distortion of clusters by elongation of hydrogen bonding, ultimately breaking down native three-dimensional morphologies to form net-like structures.⁶³ Perhaps unsurprisingly, Pathak noted EF induced hydrogen bond disruption was more pronounced for larger water clusters, though such clusters tended not to undergo breakdown until applied fields of 5–8 V nm⁻¹ were reached.⁶³ Pathak and co-workers later reinvestigated EF responses of large water clusters, specifically examining OH stretching frequencies.⁹⁷ Huang and co-workers used wavefunction theory to investigate the effect of very intense static EFs on the structure of water clusters (H₂O)_n, where n = 2–7.⁹⁸ These authors characterised the unusually strong H-bonding characteristics of the resulting water whiskers that form when a critical EF (∼10 V nm⁻¹) is applied.⁹⁸ They also noted that the critical external EF needed to induce this bonding decreases monotonically with increasing chain length of the water whiskers.⁹⁸ More recently, Lu and co-workers used both DFT and MD to study the formation of water nanowires induced by more modest external EFs (∼3 V nm⁻¹).⁹⁹ These authors noted that nanowires around 10 nm long are rapidly formed when an external EF is applied and is accelerated by increasing the applied field strength.⁹⁹ DFT calculations showed that H-bonding in the resulting structures is highly anisotropic, with notable enhancement of H-bonds along the applied EF direction and weaking of those perpendicular to the EF.⁹⁹

In addition to bulk water structure, several QM studies have investigated how EFs affect substrates solvated in water. Pathak and co-workers investigated the EF responses of CH₃OH, H₂O₂ and CO₂, encapsulated as “guests” within a dodecahedral water cage “host”, (H₂O)₂₀.¹⁰⁰ Consistent with expectations, EFs destabilise the hydrogen bond network, rupturing the host–guest complex. Bresme and co-workers examined the response of model Li⁺(H₂O)₄ and Li⁺(H₂O)₆ water clusters to external EFs, finding disruption of the first solvation shell occurs at field intensities of >1.5 V nm⁻¹.¹⁰¹ Cassone and co-workers used AIMD to study the EF response of NaCl solutions.¹⁰² These authors observed significant changes in the (Na–O and Cl–H) radial distribution functions when a static EF of 2.5 V nm⁻¹ was applied, with noticeable disruption of the first solvation shells. A follow up study by Cassone and co-workers used similar AIMD methodology to compare EF responses of LiCl, NaCl and KCl in aqueous solution.¹⁰² The authors specifically investigated ion diffusivity, noting that EF effects on ion mobility were dependent on the identity of the cation.¹⁰² Another recent AIMD study by Cassone investigated divalent cation responses to EFs, studying the behaviour of aqueous MgCl₂ and CaCl₂ solutions.¹⁰³ A more recent AIMD study by English and co-workers specifically probed the difference between responses to static and dynamic EFs for modest sized water boxes.¹⁰⁴

Similarly, large volume of classical studies has been reported trying to elucidate the effects of EF irradiation of water both in bulk and heterogeneous molecular environments (see ref. 17 and references therein). For example, investigations into the shape and behaviour of water droplets in strong EFs have grown due to their relevance to a variety of applications including electrospinning and inkjet printing.^89,105 All-atom classical MD simulations have proven useful in studying the structural and energetic behaviour of water nanodroplets under the influence of an externally applied static EFs.¹⁰⁵ The study identified the molecular mechanism responsible for shape extension of a nanodroplet from a spheroid to a highly prolate ellipsoid when exposed to 0.9 V nm⁻¹ EF (see Fig. 2) to be due to the propensity of the water dipoles to align with the electric field while simultaneously restructuring to minimize the dipole–dipole interaction energy. The authors were able to develop a quantitative theory that describes the energetic landscape for the nanodroplet shape extension process and to enable predictions of the nanodroplet behaviour based on its initial size and the strength of the applied field.

Fig. 2 (left) Shape evolution of a water droplet with the initial radius r₀ = 2 nm for (a) low electric field strength of E = 0.7 V nm⁻¹ and (b) high electric field strength of E = 0.9 V nm⁻¹. (right) (c) Energy cycle of four representative states of water structuring and dipole alignments. (d) The respective energies of the four water structuring states are shown, where the total potential energy of the system is U_pot = U_LJ + U_elec + U_d–f. U_LJ is the Lennard–Jones interaction energy among water molecules, U_elec is the energy of the electrostatic interaction among water molecules, and U_d–f is the interaction energy between the water dipoles and the applied external electric field. The water dipole–dipole interaction energy U_d–d which is part of U_elec, and the surface energy U_surf, defined as the internal energy change to increase the exposed surface area of the droplet, are also shown. Adapted with permission from ref. 105. Copyright 2021 American Chemical Society.

The effects of static and oscillating EF on liquid water have been simulated by non-equilibrium MD (NEMD) and it was shown that in terms of dipolar and dynamical properties a general linear-response régime is in the vicinity of field intensities up to ∼0.5–0.7 V nm⁻¹, suggesting that the external field forces and torques should be no more than a few percent of those present intrinsically due to electrostatic fields created by local, intramolecular charge distributions.^34,106 NEMD simulations of liquid water in EF nanosecond pulses were used to evaluate the non-thermal field effects in terms of dipolar response of water molecules.¹⁰⁷ The study was able to show that once the EF was removed, the dipoles relaxed, exhibiting no memory or permanent dipolar alignment, debunking the proposition that water may retain (permanent) “memory”¹⁰⁸ of conditions or EF that it has been subjected to. More recently, the effects of static and high frequency 50, 100 and 200 GHz oscillating fields of 0.5 V nm⁻¹ and 1.0 V nm⁻¹ rms intensities on liquid water in supercooled and room temperatures (200 to 310 K) were investigated using NEMD simulations and the rigid potential model TIP4P/2005 of water.¹⁰⁹ The authors showed the application of static fields reduced the self-diffusion of liquid water, due to ‘dipole-locking’, or suppression of rotational motion, whilst diffusivity was enhanced in oscillating fields, especially at high frequencies and outside the supercooled region.

Molecular dynamics simulations have proven useful also in elucidating the dielectric properties, molecular structures, and hydrogen bonding dynamics of glycerol/water mixture exposed to microwave irradiation, due to potential use of glycerol as solvent for nanomaterial synthesis.¹¹⁰ The study showed that dipole–dipole correlation of glycerol is linked to the field intensity of the microwaves, where the glycerol–glycerol hydrogen bond number and lifetime increased with increasing field intensity up to 1 V nm⁻¹. These results indicated with the assistance of the microwave field, glycerol molecules become more concentrated through higher coordination, which explained the nanomaterial synthesis observations. Externally applied EFs have also been used for their inhibitory effect on electro-coalescence of water-in-oil emulsions. To clarify the mechanism of droplet breakup at the microscopic level, MD simulations have been performed to study the deformation and breakup characteristics of a moving droplet at different field strengths.¹¹¹ The results showed that interparticle spacings increased with the growth of the field strength, leading to significantly higher values of the electrostatic potential and van der Waals potential, and hence an increase of the deformation degree. Evidently, there is a critical EF strength, above which droplets undergo a complete coalescence process. An MD study of doubly conducting droplets dissolved in NaCl solution exposed to EF, showed that in presence of EF stronger than the critical field of 0.52 V nm⁻¹, a break-up occurs due to the ion exchange and neutralization in the connecting liquid bridge.¹¹²

Ionic solutions are particularly interesting models for EF irradiation due to their charged states and the ability of EF to manipulate their associations, diffusion, and structuring. Modelling attempts of ionic liquids have been made using more crude (coarse-grained) approaches,¹¹³ and all-atom simulations using fixed charges which were able to demonstrate the ionic association and transport in electrolyte solution.¹¹⁴ However, local interactions in a fluctuating charged environment cannot be easily modelled by static electrostatic parameters, i.e., fixed charges. This is particularly important for highly charged systems such as ionic liquids, enzymes and membranes, thus induced dipoles methods using polarizable force field are needed to model these systems more accurately.¹¹⁵ Furthermore, the polarized interface between two immiscible liquids is crucial for electroanalytical and ion extraction applications, where an EF is typically used to selectively induce the transfer of ionic species across the interfaces. Computational simulations are useful for modelling such processes. However, due to the long-range nature of the electrostatic interactions and the use of periodic boundary conditions, the use of external EF in MD simulations requires special care. A recent study demonstrated the importance of careful simulation design and setup to accurately model the dielectric response of the materials and that it is possible to obtain the correct EF on both sides of a liquid–liquid interface when using standard 3D Ewald summation methods.¹¹⁶

One of the disadvantages of using the constant force/field method for modelling the responses to externally applied fields is its inability to properly capture the propagation of the electric field across the system under study. In experimental setting, the electric field emanates from the anode, penetrating through the sample toward the cathode. The electric field is substantially weakened (shielding) as it penetrates through a liquid sample, due to the high relative dielectric permittivity of water. This is important consideration since physical properties such as mobility exhibit different behaviour at the liquid–vapor interface in comparison to the bulk, where at the interface the coordination number of the hydrated ions and the local field are different from the bulk.¹¹⁷

The Constant Electrode Potential Method (CPM)¹¹⁸ enables an external electric field to be applied on a system, accounting for the shielding effects by water. A recent study employed the CPM method to investigate the effects of an external electric field on the surface tension of water and to compare that to the conventional (constant force) method, in addition to computing the interfacial mobilities of Na⁺ and Cl⁻ ions at a liquid–vapor interface.¹¹⁹ The CPM method was able to predict a weaker variation in the surface tension in comparison to that of the conventional method, with the maximum reported difference being 36% of the surface tension value.

Although the above QM and classical MD studies do not always directly refer to biological systems, the behaviour of water molecules, clusters, droplets and, especially, physiologically relevant salt solutions is crucial for understanding the effects of EMFs on larger scale aqueous biomolecular assemblies.

Proton transfer in DNA

Deoxyribonucleic acid (DNA) stores biological information that is essential for the development, normal functioning, and reproduction of all known organisms. Over 50 years ago, Lowdin proposed that proton transfer reactions between base-pairs could alter DNA's underlying hydrogen bond structure and introduce mutations, the so called ‘rare tautomer’ hypothesis of spontaneous mutagenesis.^120,121 This tautomerisation is thought to be the potential origin of spontaneous DNA errors by introducing point mutations during replication (e.g. GC → AT, see Fig. 3). While the thermodynamic stability of canonical base-pairs minimises the mutagenic potential of these rare tautomers, it is thought that environmental agents could potentially enhance these underlying proton transfer reactions.¹²² For instance, pairing of unnatural nucleobases, ionizing radiation and intercalating agents have been found to influence the stability of these tautomers.^123–125 Guanine–cytosine (G:C) base-pairs are known to be more susceptible to tautomeric induced mutations, with adenine–thymine (A:T) pairs showing greater resistance.^126–128 As different tautomers can possess markedly different electrostatic properties (i.e. partial charge distributions, dipole moments), EFs are likely to alter both their stabilities and rate of interconversion. Relatively intense pulsed EFs (10⁻³ − 10⁻² V nm⁻¹) have been investigated for medical applications, specifically delivery of non-permeable drugs and gene therapy (via electroporation).^42,129–132 Indeed, 0.06 V nm⁻¹ picosecond pulsed EFs have been investigated experimentally for the treatment of tumours.¹³³ Thus, the potential impact of such fields on the structure and stability of DNA is of significant interest.

Fig. 3 The chemical structure of a canonical G:C base-pair, G⁻:CH⁺ (iminium/azanide) zwitterion and G*:C* (enol/imino) rare tautomer. The direction of the EF required to induce these proton transfers is indicated by an orange arrow. Hypothetical point mutations that could arise from these non-canonical base-pairs are given in parenthesis. Solid red circles indicate the deprotonated heteroatom, while solid blue circles indicate the transferring proton.

Computational interest in potential EF effects on double stranded DNA arose following a seminal QM study by Matta and Arabi, which found that external EFs influenced the equilibrium structure and hydrogen transfer kinetics of the formic acid dimer.¹³⁴ Following a detailed QM study of the effect of Mg²⁺ cations on Lowdin tautomerisation,¹³⁵ Jacquemin and Cerón-Carrasco investigated the effect of external EFs on a model G:C base-pair with QM calculations.⁶⁰ These authors found that strong EFs can significantly influence the rate coefficients and mechanism of proton transfer that lead to rare G:C tautomers. EFs on the order of 0.5–4 V nm⁻¹ lowered the barrier leading to the G*:C* tautomer by 20–55 kJ mol⁻¹, though stabilisation of the G*:C* tautomer itself was more minor (≤10 kJ mol⁻¹). Consequently, the G*:C* tautomer had a shallow energy profile in the presence of EFs, with reversion to the canonical base-pairs being essentially barrierless. Moreover, the estimated equilibrium constant for G*:C* tautomer formation across all EF strengths was small (∼10⁻⁶–10⁻⁸). In contrast, at fields of 3–5 V nm⁻¹, the G⁻:C⁺ zwitterion was found to be comparably stable to (or even more stable than) canonical G:C base-pairs. Further to this, in the presence of these fields, G⁻:C⁺ zwitterions were well-defined minima, with substantial equilibrium constants of formation (∼10⁻¹–10⁵) and significant barriers to reversion. The authors concluded that in the presence of EFs, only G⁻:C⁺ zwitterions fit the necessary kinetic criteria to be considered a viable route to mutagenesis (see ref. 127). Following this initial study, Jacquemin and Cerón-Carrasco applied a hybrid ONIOM style (QM/QM′) approach to investigate a more realistic d(5′-GGG-3′):d(3′-CCC-5′) DNA fragment and account for stacking of adjacent nucleobases.⁶¹ These calculations broadly supported their earlier conclusions, though EFs ≤ 1 V nm⁻¹ had no discernible effect on the barrier for G*:C* formation. However, at fields ≥ 2 V nm⁻¹, the double hydrogen transfer to form G*:C* was barrierless, with these rare tautomers possessing very shallow potential energy profiles. At field intensities ≥4 V nm⁻¹, the G⁻:C⁺ zwitterion was again found to be more stable than canonical G:C base-pairs and met the necessary requirements to be considered a potential source of mutagenesis. To ascertain if these EFs would influence the tertiary structure of DNA, Jacquemin and Cerón–Carrasco used classical MD to investigate the dynamic response of a dodecamer duplex dG12:dC12.⁶² These authors found that continuous application of intense EFs (≥3 V nm⁻¹) causes unwinding of double stranded DNA within 10 picoseconds.⁶² However, these authors proposed that external EFs around 3 V nm⁻¹ applied in 5 picosecond pulses could potentially induce selective mutation (via the G⁻:C⁺ zwitterion) while also limiting changes to the tertiary structure of DNA.⁶²

More recently, Matta and Arabi used QM methodology to verify that A:T base-pairs were considerably less susceptible to tautomeric mutation, even in the presence of strong external EFs (up to 5 V nm⁻¹).¹³⁶ Matta and Arabi also used QM methodology to investigate EF effects on the formation of the G*:C* tautomer, accounting for quantum tunnelling effects.¹³⁷ These authors thoroughly characterised the effect of EFs on the order of 1 V nm⁻¹ on the kinetics and thermodynamics of G*:C* tautomerisation. Very recently, Arabi and co-workers used QM/MM and classical MD simulations to study the effects of EF ranging from 10⁻⁵–1 V nm⁻¹ on a dodecamer DNA model.¹³⁸ Consistent with earlier studies, the authors noted the application of large EFs (∼1 V nm⁻¹) increased the thermodynamic population of G*:C* tautomers by up to 1 order of magnitude.¹³⁸ However, in contrast to the previous studies of Cerón-Carrasco and Jacquemin,^60–62 Arabi and co-workers also noted the formation of the G⁻:C⁺ zwitterion at lower EF strengths (∼1 V nm⁻¹).¹³⁸ However, we should note that these studies not only employed different methodologies (e.g. different sized QM models and density functionals) but also investigated a differing configuration of stacking nucleobases. Ultimately, Arabi et al. concluded that at EFs of ≤1 V nm⁻¹, both the G*:C* tautomer and the G⁻:C⁺ zwitterion were too transient to contribute towards mutations, as their lifetimes were on the order of picoseconds compared to the nanosecond timescale for DNA opening during replication.¹³⁸

While double helices are the most common tertiary structures adopted by DNA, other structural motifs have also been identified at lower concentrations. G-quadruplexes are helical G-tetrads formed from DNA sequences rich in G-bases (see Fig. 4). These tertiary structures are much rarer than canonical double helices but are thought to play an important role in cellular function and replication.¹³⁹ Capitalising on insights from their previous studies, Jacquemin and Cerón-Carrasco used QM/MM methodology to study the effect of EFs on a model trimeric G-quadruplex (see Fig. 4, left).¹⁴⁰ As with their previous studies, G-quadruplexes were found to be susceptible to tautomerisation when external EF around 4 V nm⁻¹ were applied.¹⁴⁰ The most favourable rare tautomer identified was an oxonium/azanide zwitterion (Fig. 4b), with the iminium/azanide zwitterion (Fig. 4c) and quadruple enol/pyrimidine tautomer (Fig. 4d) found to be significantly less stable (regardless of field intensity). While the quadruple enol/pyrimidine tautomer was found to be a stable minimum even in the absence of applied EF, neither zwitterionic structure was stable when the applied EF was less than 4 V nm⁻¹. This study concluded that the sensitivity of G-tetrads (within G-quadruplexes) to external EFs is comparable to that of G:C base-pairs (within double stranded DNA), despite the differences in secondary and tertiary structure.

Fig. 4 Left: The trimeric G-quadruplex investigated by Jacquemin and Cerón-Carrasco, with the central quadruplex (depicted atomistically) shown in its G⁺:G⁻:G:G (oxonium/azanide) zwitterion form. Optimised structure taken from ref. 140. Right: Chemical structures of a canonical G-quadruplex, G⁺:G⁻:G:G (oxonium/azanide) and GH′⁺:G′⁻:G:G (iminium/azanide) zwitterion, and a G*:G*:G*:G* (quadruple enol/pyrimidine) rare tautomer. The direction of the EF required to induce these proton transfers is indicated by an orange arrow. Solid red circles indicate the deprotonated heteroatom, while solid blue circles indicate the transferring proton.

Intercalated-motifs (i-motifs) are tetrameric DNA structures that consist of two parallel duplexes combined in an antiparallel manner (see Fig. 5). They are typically formed in C-rich sequences and thus are often encountered on complementary strands of G-rich (G-quadruplex forming) sequences. While the stability of i-motifs is dependent on their environment (e.g. pH),¹⁴¹ it has been postulated that they play a role in gene expression as well as DNA replication and repair.¹⁴² Recently, Jacquemin and Cerón-Carrasco used QM calculations to investigate the effects of external EFs on a hemi-protonated-C:C dimer (CH⁺:C), which is the central moiety of the i-motif (see Fig. 5, left).¹⁴³ Intriguingly, these calculations indicated that this dimer is significantly affected by weaker EFs (∼0.5 V nm⁻¹), which block normal proton exchange between the C nucleobases (see Fig. 5, right).¹⁴³ In the absence of external EF, the CH⁺:C and C:CH⁺ base-pairs are degenerate with the central proton undergoing rapid exchange (k_trans ∼ 10¹¹ s⁻¹).¹⁴³ However, in the presence of a 0.5–2.0 V nm⁻¹ EF, the C:CH⁺ configuration (relative to the applied EF) is 6–27 kJ mol⁻¹ more stable than its CH⁺:C counterpart.¹⁴³ As this exchange process plays a fundamental role in delocalising the cationic character of the CH⁺:C base-pairs, it mitigates the risk of side-reactions with the surrounding molecules (e.g. oxidation by water).¹⁴³ By blocking this exchange process, external EFs effectively localise the cationic character of i-motifs onto a single C base, which may increase the probability of deleterious reactions with the surrounding media.¹⁴³

Fig. 5 Left: A prototypical i-motif, with the two central hemi-protonated base-pairs (CH⁺:C) depicted atomistically. Taken from ref. 141 (PDB ID: 5OGA). (right) Chemical structures of the protonated CH⁺:C base-pair and the functionally equivalent C:CH⁺ base-pair, which is degenerate in the absence of an applied EF. The direction of the EF required to block this proton transfer is indicated by the orange arrow. Red circles indicate the deprotonated heteroatom, while blue circles indicate the transferring proton.

Protein structure and dynamics

Over the last decades there has been tremendous interest for an improved understanding of the effects of EFs on protein structure and dynamics using experimental^3,47 and computational techniques.^144,145 The thermal effects of EF irradiation have been well studied and are easier for interpretation mostly due to the expected inherent denaturation of proteins at increased temperatures.^146–148 The mechanisms of non-thermal EF effects, however, remain poorly understood. This is mostly due to the interconnection of specific EF frequencies and strengths capable of exciting certain vibrational modes of proteins and peptides, causing (sometimes irreversible) structural changes which can affect their structure, behaviour and function.

QM-based studies of EF effects on standard proteins are usually prohibitively expensive, so work has generally focused on prototypical model fragments of relevance to protein structure (e.g. salt bridges) and small peptides. Most of these studies have focused on the computational prediction of Vibrational Circular Dichroism (VCD) and Raman Optical Activity (ROA) spectra, which can be used to characterise the structure of peptides. For instance, Jalkanen and co-workers studied the spectroscopic properties, including in the mid- and far-IR regions, of L-alanine in the gas-phase and in non-polar solvents with DFT.¹⁴⁹ Similarly, Suhai and co-workers used DFT to examine the spectroscopic properties of various amino acids and small peptides.¹⁵⁰ Other studies have used DFT to predict spectroscopic behaviour of, for instance, model 3₁₀- and α-helices,¹⁵¹ β-hairpin structures¹⁵² and γ-turns.¹⁵³ Various other small biomolecules and fragments have also been examined with QM-based approaches.^154–157 However, as the application of VCD and ROA spectroscopy for peptide structural characterisation was recently reviewed by Keiderling,¹⁵⁸ we focus here on studies that explicitly consider the structural effects of relatively intense EFs. Dudev and co-workers examined the effect of static EFs on the secondary structure of a range of model helical peptides.⁴⁵ These authors found that application of intense external fields (>2.5 V nm⁻¹) along the axis of the helix resulted in the loss of helical structure and formation of unusual cyclic/ring peptide conformations.⁴⁵ Dudev and co-workers also examined the impact of external EFs on a model salt-bridge peptide, finding minimal disruption of the underling Lys-Asp pair at the field strengths and orientations studied.⁴⁵ While these authors noted that these EF-induced perturbations of secondary structure were reversible,⁴⁵ we should emphasise the peptides were considered in isolation. Bhattacharyya and co-workers studied EF effects on a Lys-Asp pair as a model salt-bridge, noting some changes in electrostatic properties and interaction energies under intense fields.¹⁵⁹ While intense EF can induce spontaneous proton transfer in ion-pairs, generally fields >2.5 V nm⁻¹ are required.¹⁶⁰

Over the last few decades, numerous QM and QM/MM studies have uncovered the role of internal (or intrinsic) electrostatic interactions in modulating enzyme activity. Enzymes have evolved highly tailored structures that specifically orientate charged and polar residues around bound substrates, creating highly complex and anisotropic electrostatic environments in their active sites. While many QM/MM studies have investigated electrostatic catalysis in enzymes, significant emphasis is usually placed on quantifying and replicating the intrinsic electrostatic environment of the active site. However, a few illustrative studies have examined the effects of simple external EFs on active site catalysis. For instance, pioneering work by Shaik and co-workers examined competing C–H hydroxylation and epoxidation mediated by heme species in the presence of external EFs.¹⁶¹ The heme species possessed no selectivity in the absence of an external EF, however application of EFs on the order of 5 V nm⁻¹ provided high selectivity for each pathway (depending on applied field orientation).¹⁶¹ Another elegant QM/MM study by Shaik and co-workers examined the effect of external EFs on the catalytic cycle of cytochrome P450.¹⁶² External fields influenced the initial gating cycle, rate-determining step, O₂ uptake, resting state geometry and spin-state ordering of various active species, with particularly large effects noted perpendicular to the porphyrin plane.¹⁶² Timerghazin and Talipov used DFT to study external EF effects on the properties and reactivity of S-nitrosothiols, which are ubiquitous carriers of nitric oxide.¹⁶³ They noted that barriers for trans-S-nitrosation and S-thiolation were highly dependent on EF strengths and orientations, with the electrostatic environment controlling the resulting kinetic selectivity.¹⁶³ Dudev and co-workers have also investigated the impact of external EFs on binding selectivity of metalloproteins.¹⁶⁴

Classical MD simulations have shown to be particularly useful in elucidating the dynamics and conformational changes in peptides and protein in the presence of static, time-varying and pulsed EF with varying characteristics. The complementarity of quantum and classical theory simulation methods was recently demonstrated in the possibility to orient gas-phase proteins such as ubiquitin using time-dependent EF.¹⁶⁵ The ab initio simulations were used to estimate the field strength required to break protein bonds, with 45 V nm⁻¹ as a breaking point value while the MD simulations showed the minimal field strength required for orientation within 10 ns to be on the order of 0.5 V nm⁻¹. Although high fields can be destructive for proteins, the structures in these simulations were preserved until orientation was achieved regardless of field strength, a principle the authors denoted as “orientation before destruction.” Following this study, Sinelnikova et al. identified the unfolding pathways of ubiquitin, induced by experimentally achievable external electric fields. Their simulations showed that strong EF in conjunction with short-pulsed X-ray sources such as free-electron lasers provide a means for imaging dynamics of gas-phase proteins at high spatial and temporal resolution.⁵⁸

In an all-atom explicit solvent simulations, Budi et al. found that both static and oscillating fields influence the insulin chain-B conformation, with the latter being more disruptive to the structure compared to static fields of similar effective strength.¹⁶⁶ In a follow up studies, the effects of oscillating fields of different frequencies was explored for the isolated chain B¹⁶⁷ and complete insulin monomer.¹⁶⁶ Their results showed the application of lower-frequency 1.225 GHz oscillating fields allowed the peptide dipole moment to consistently respond to the applied field, via the modulation of conformational changes within each field direction, compared to the peptide dis-orientating high frequency of 4.9 GHz field. Studies of pectin methylesterase (PME) showed EF exert non-thermal effects on both local and global protein structure.¹⁶⁸ The 1 μs simulations demonstrated significant shrinkage of the catalytic domain and shortening of enzyme–water hydrogen bond lifetime due to field strengths of equivalent energy input of 5 × 10⁻⁶ V nm⁻¹ experimental EF. Unwinding of the helical segments, altered intra- and intermolecular hydrogen bond patterns, and increased hydration were also caused by the 5 × 10⁻⁶ V nm⁻¹ EF. This and other similar studies^1,87 have shown that catalytic activity of enzymes can be enhanced or inhibited by manipulating the electric field strength, frequency, and treatment temperature. Furthermore, short (<100 ns) and intense (>0.0007 V nm⁻¹) EMF pulses have also been shown capable of modulating protein structure and function.^2,169

More recently, the potential effects of EF on the structure and function of the spike protein found on the SARS-CoV-2 virus, responsible for the COVID-19 pandemic was explored using MD simulations (Fig. 6).¹⁷⁰ The sub-microsecond simulations showed that on a EFs of much lower intensities (10⁻⁴ – 10⁻² V nm⁻¹) can cause significant damage to the tertiary and secondary structure of the spike protein, affecting its interaction with the virus human host cell membrane receptor angiotensin-converting-enzyme (ACE2) and potentially rendering SARS-CoV-2 less infectious.

Fig. 6 Virus entry into the cell is mediated by the recognition between the spike glycoprotein (S protein) present in the virus envelope and the host cell membrane receptor ACE2. The binding between the S protein and ACE2 can be altered when external electric fields induce drastic conformational changes and damage in the S protein.¹⁷⁰

Changes to the native or physiological/functional conformations can lead to misfolding and the formation of pathogenic structures of proteins, which can self-assemble into insoluble aggregates, known as amyloid fibrils. These fibrous deposits have been linked to systemic and neuro-debilitating diseases, such as atherosclerosis, Alzheimer's, Parkinson's, and others.^171,172 Curiously, on the other hand, experimental studies have suggested that EMFs may be used as a therapeutic tool for the breakdown of fibrils implicated in Alzheimer's disease.^15,57 Therefore, an improved understanding of the effects of radiofrequency radiation on biomolecules and their implications in disease processes at the molecular level has been the goal of several research groups.^7,55,144,173 The multivalent interactions during folding/misfolding and self-assembly, combined with the associated complexities of proteins due to their variability in size and sequence require a systematic simulation approach to reproduce and explain the associated adverse or beneficial effects of EF. For example, a series of explicit solvent MD simulations were applied to investigate the effects of EMFs on the amyloidogenic apoC-II(60–70) peptide, implicated in fibril formation by the ApoC-II lipid transport protein associated with heart disease.⁵⁶ The simulations of varied electric field strength from 0.7  V nm⁻¹ to a relatively low intensity field of 0.0007 V nm^−1 64 showed that field strengths lower than 0.004 V nm⁻¹ had no tangible effects on the peptide conformation. The intermediate field-strength range (0.04–0.004 V nm⁻¹) caused a significant increase in peptide dynamics, which resulted in an increased population of structures with fibril-inhibiting characteristics, such as the separated N- and C-termini and colocation of the aromatic residues at the same peptide face. The high strength (>0.04 V nm⁻¹) field simulations, apoC-II(60–70) experienced peptide dipole alignment along the applied field direction, which resulted in elongated structures and disrupted the inherent β-hairpin conformation known to be the intermediate state for fibril formation. In a follow up study, the role of frequency in the radiofrequency (1.0 and 2.5 GHz) and higher frequency (5.0 GHz) ranges was investigated.¹⁷⁴ The study showed that the EM field induced peptide conformations dependent on the field frequency and strength. At the high field strength (0.7 V nm_rms⁻¹), the peptide explored a wider conformational space as the frequency increased from 1.0 to 5.0 GHz. At the intermediate strength fields (0.07–0.0385 V nm_rms⁻¹), the frequencies of 1.0 and 2.5 GHz resulted in the peptide being trapped in specific conformations, with 1.0 GHz enabling both fibril-forming and fibril-inhibiting conformations, while 2.5 GHz led to formation of mostly fibril-competent conformations. In contrast, the 5.0 GHz frequency caused increased peptide dynamics and more extended conformations with fibril-enabling aromatic side-chain arrangement akin to the structures formed under ambient conditions. All the simulated frequencies at low strength fields (0.007–0.0007 V nm_rms⁻¹) resulted in the formation of amyloid-competent hairpin conformations alike those formed under the weak static EF and ambient conditions. Similarly, Derreumaux et al. used MD simulations to explore the impact of transmembrane EF (0.02 V nm⁻¹) on an Alzheimer's implicated Aβ peptide model in solution¹⁷⁵ and at the membrane.⁴⁸ The study demonstrated rupture of the Aβ supramolecular assembly caused by protein chains rearrangement and increase of dipole moment.¹⁷³ These results suggest that specific ranges of EMF parameters produce peptide/protein conformations unfavourable for formation of amyloid fibrils, a phenomenon that can be exploited in treatment and prevention of amyloid diseases. Alternatively, EMF parameters can be selected to modulate the formation of well-ordered peptide/protein assemblies as a rational design strategy for engineering biocompatible materials.

Membranes

Intense static or pulsed electric fields are known to act at the cell membrane level and are already being exploited in biomedical and biotechnological applications.^16,176 Biological cell membranes have been found to become permeable (electropermeabilisation), either reversibly (at low field strengths), or irreversibly (at higher field strengths). This phenomenon has been found useful in extraction of bioactive compounds, breakdown of cellulosic materials, and inactivation of microorganisms. It is well known that EFs can also create pores in membranes (electroporation) which enable transfer of ions, genetic materials and other small solutes across the membrane. The mechanisms of electropermeabilisation and electroporation remain elusive and difficult to visualise experimentally, thus molecular simulations have become very useful in the study of these processes.¹⁷⁷

Computational approaches have shed light on the local perturbations at the membrane interface upon exposure to external stresses, such as those of applied EF. One such study showed that when transmembrane voltage is higher than a certain threshold, hydrophilic pores were formed and stabilised by the membrane lipid headgroups within the nanosecond time scale.¹⁷⁸ The mechanisms responsible for membrane permeabilisation, and structural or dynamic changes imparted on biomolecules by high-frequency (18 GHz) electromagnetic irradiation were recently explored using experimental and computational techniques.⁵⁹ This work suggested that the EMF-induced oscillations, i.e., vibrations and reorientation of water molecules (dipoles) may be able to induce liposome bilayer permeability without affecting their integrity, thus presenting opportunities in applications of EMF for transporting therapeutics to and across live cell membranes. Specifically, extremely high strength fields (0.21 V nm_rms⁻¹) were able to cause an increase in the interfacial water dynamics characterised by water dipole realignments, in the all-atom POPC membrane modelled by classical MD simulations for 200 ns (Fig. 7). At the lower field strengths (<0.21 V nm_rms⁻¹), high frequency EMF induced changes of the water hydrogen bond network, which may contribute to the mechanisms that facilitate membrane permeabilisation within a longer timeframe.

Fig. 7 Exemplar MD simulated molecular representation of the POPC membrane (shown in licorice) exposed to (A) ambient and (B) 0.21 V nm_rms⁻¹ high frequency electric fields, demonstrating the deeper penetration of water during irradiation (the EF direction shown by arrow). Water molecules within 1.6 Å of the membrane are shown in vdW surface representation, and all other water molecules as blue points. The sodium and chloride ions are shown as their vdW surfaces coloured yellow and green respectively.⁵⁹

In typical electroporation treatments, EF higher than the membrane breakdown potential is usually applied so that transient membrane defects can be formed in advance before delivering extracellular materials. Shimitzu et al. used coarse-grained MD simulations to study the permeation of a cationic gold nanoparticle (AuNP) across zwitterionic and negatively charged phospholipid bilayers under an EF.¹⁷⁹ When an EF that is equal to the membrane breakdown potential (intensity) was applied, a typical NP delivery by electroporation was shown whereby the cationic AuNP directly permeated across a lipid bilayer without membrane wrapping of the AuNP, while a persistent transmembrane pore was formed (Fig. 8). However, when a specific range of the EF that is lower than the membrane breakdown intensity was applied, a unique permeation pathway was exhibited where the generated transmembrane pore immediately resealed after the direct permeation of AuNP. The affinity of the NP for the membrane surface was found to be a key for the self-resealing of the pore.

Fig. 8 Cross-sectional side view and top view during nanoparticle permeation of DPPC/DPPG membrane model under externally applied field (V* = 1.0).¹⁷⁹

More recently, the same group explored the translocation mechanisms of negatively charged NP across negatively charged membrane using coarse-grained MD simulations.¹⁸⁰ The study showed that while it would generally be electrostatically impossible under ambient conditions, in their model the anionic NPs were able to translocate across a negatively charged membrane via a non-disruptive pathway under a weak EF due to an ionic charge imbalance. This is a theoretical demonstration that negatively charged NP can, in fact, be delivered into a cell by combining applied EF with membrane hyperpolarization/depolarization induced by an external stimulus.¹⁸¹

Cell-penetrating peptides have a wide biomedical appeal due to their “designability”, low cytotoxicity and ability to penetrate membranes, the latter being possible mostly at high peptide concentrations or by being attached to various nano-carriers.^182,183 External stimuli, such as EF can also be utilised to enhance cell-permeation by CPPs in controllable ways.¹⁸⁴ The processes of single polyarginine (R8) peptide penetration through planar and vesicle membranes under an external electric field were simulated via coarse-grained MD simulations.¹⁸⁵ The study showed that the EF strength and membrane curvature affect the penetration rate of the charged peptide across the membrane. The peptide penetration time across the planar and curved membranes decreased with increasing amplitude of the EF applied. The membrane curvature allowed for faster translocation of the peptide compared to planar membrane due to the increased surface tension and larger area per lipid for vesicle membranes.

Bionanomaterials

The immense potential of nanomaterials for biomedical and industrial applications can be realised via the ability to control the rotation, translation and cooperativity of intra- and intermolecular dynamics, the key factors for the design and development of stimuli-responsive “smart” materials or artificial molecular machines.¹⁸⁶ Electric fields have been employed to control nanoscale robotic arms,¹⁸⁷ molecular gates,¹⁸⁸ and induce structural changes in metal–organic frameworks (MOFs) to modulate the materials electric properties,¹⁸⁹ and tune the porosity of MOFs for single-gas membrane permeability.¹⁹⁰ MD simulations were employed to investigate intense (0.1 V nm⁻¹) nanosecond-scale EF effects on the structure and dipolar properties of the kinesin nanomotor.¹⁹¹ Kinesin is a biological molecular nanomotor which converts chemical energy into mechanical work. The study showed that the function of biological molecular motors can be altered by external irradiation, providing means for the development of novel electromagnetic methods for nanobiotechnology.

The ability of EF to modulate the dipolar orientation and thus the structure of molecules provides an opportunity to control how molecules bind to different materials. The effect of static EF on the adsorption mechanisms of single amino acids on the bare/unprotected Au(111) surface was explored using MD and free energy calculations with the purposely developed Golp-CHARMM forcefield which represents the image charge interactions important for modelling metallic surfaces.¹⁹² The study showed that adsorption of positively charged AAs (arginine, histidine, and lysine) is more affected by the EF than that of negatively charged (aspartic and glutamic acids) and charge-neutral AAs (alanine, glycine, tryptophan, and asparagine). The difference arises from the role of a charged side chain in the molecule's adsorption on the gold surface. The adsorption via a deprotonated carboxyl group was observed to be less favourable and was facilitated by hydrogen bonding with the adsorbed water, while the positive amines directly interacted with surface gold atoms. This explained the relatively weaker adsorption of negatively charged AAs and their smaller scale response to the EF due to solvent-induced electrostatic screening. These results provide insights into the molecular arrangement at the biointerfaces with gold exposed to EFs, which can be exploited for more controlled design of bionanomaterials.

MD simulations were used to investigate the ability of EFs to modulate the mechanical properties of polyelectrolytes and to understand the governing mechanisms.¹⁹³ Mechanical property modulation by EF was found to be sensitive to the charge distribution—charges must be tightly attached to the polymer backbone, and responsivity is greater if a single backbone contains both positive and negative charges. The dominant mechanisms are reorientation and stretching of the polymer chains, which also elongate the ionic clusters to maintain strong electrostatic interactions throughout deformation. These insights are critical for future experimental realisation of polymers with EF regulated mechanical properties.

Summary and future perspectives

The case studies summarised demonstrate the need for more holistic multiscale computational approaches to properly investigate the enthalpic and entropic effects of applied electric fields on molecular systems in realistic biologically relevant environment, from charge transfers and bond breaking/formations to dynamical phenomena such as protein conformational changes and lipid membrane lability. While most QM studies published on external EFs have examined fields that are uniform and static, increasingly powerful computation resources (and improvement software efficiency) should greatly improve the feasibility of modelling biomolecular systems under dynamic EFs and EMFs. Moreover, the development of specialised software packages specifically tailored for QM-based EF and EMF calculations will also help facilitate new research in this area.

In the classical realm, with the computational power and infrastructure dramatically increased over the last decades, it is now feasible for EMF effects to be modelled on long(er) time and length scales, thus enabling observation and quantitative characterisation of tangible molecular level effects of much lower field intensities than previously possible. Furthermore, the longer simulation times ensure a significant count of EF cycles can be implemented for lower frequency fields to collect statistics sufficient for reliable characterisation of biomolecular dynamics and response kinetics at the physiologically relevant timeframes.

The ongoing development of enhanced sampling methods can address the large separation in time scales between molecular dynamics simulations (usually microseconds or shorter) and the time scales of biological processes (often orders of magnitude longer). However, enhanced sampling techniques such as the family suite of metadynamics methods enable improved exploration of the free energy landscape where time-dependent changes such as those induced by oscillating electric fields are not of essence. Therefore, the spontaneous time evolution of biologically relevant systems under the external EMFs may be necessary to observe structural and dynamic molecular changes for reporting any evidence-based conclusions about the effects of radiation on the biological matter.

While the direct comparisons of the EMF induced perturbations to the electronic and atom-resolved structure of the biomolecules and their assemblies with experiments may not be possible, largely due to the lag of the experimental techniques, it is essential to test the computational methodologies for their ability to reproduce the ambient behaviour of biological molecules and previously experimentally identified changes for future benchmarking of any external EMF effects. Further to this, since in biologically relevant systems EMFs can perturb charged and polarisable particles in polarisable environment, it is important to consider polarisation effects and/or electronic degrees of freedom in the theoretical models, which are not yet accounted for by most common forcefields employed with classical MD simulations. There is, therefore, a need to further explore polarisable forcefields developed for and increasingly applied to polarisable systems (e.g. ion channels), including AMOEBA¹⁹⁴ and Drude forcefields.^195–197 albeit they come with their own challenges and limitations.¹⁹⁸

Overall, with the growing interest in applications of the EMF based technologies in contemporary life, from mobile telecommunication to medical treatments and defence technologies, it is clear that predictive capabilities offered by the multiscale simulations for evaluating effects of the external field parameters on a comprehensive range of molecular responses within the biological matter or biomedical materials and technologies are now more crucial than ever. Most importantly, the theoretical simulations continue to provide insights not accessible through experimental observation and, therefore, represent an indispensable tool for furthering our understanding of the electromagnetic bioeffects in life tissues and novel biomedical and engineering devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors would like to acknowledge the financial support of the National Health and Medical Research Council of Australia (Grant No. CRE1135076).

References

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