Atomistic insights into the magnetic-field modulation of the adenosine receptor

Abstract

Pulsed electromagnetic fields (PEMFs) are increasingly used in clinical settings for the treatment of inflammatory and degenerative conditions. Among their molecular targets, adenosine receptors () show increased receptor density on the cell membrane upon PEMF exposure, yet the underlying physical mechanism remains uncertain. In this study, atomistic molecular dynamics simulations were used to investigate how an external static magnetic field, used as a simplified representation of the quasi-static magnetic component of PEMF exposure, influences the structure and electrostatics of the . Our simulations revealed that the field predominantly affects the receptor’s extracellular region, resulting in a transition from a closed to a more open conformation of the ligand-entry region. This structural rearrangement was accompanied by widening and increased hydration of the extracellular entrance, indicating enhanced accessibility of the orthosteric binding site. At residue level, Glu169, Ala265, and Pro266 exhibited pronounced dipole reorientation, indicating localized electrostatic adaptation consistent with the structural response. Together, these findings provide an atomistic insight into how magnetic perturbations can influence extracellular dynamics and offer a mechanistic framework compatible with experimental observations of altered function under PEMF exposure.

Introduction

Pulsed electromagnetic fields (PEMFs) have long attracted interest in biomedical research because of their beneficial effects in inflammation control and tissue repair^1,2. Yet, the molecular basis of their biological action remains poorly understood, limiting the rational development of therapeutic protocols.

Among the molecular targets influenced by PEMF exposure, the A adenosine receptors () have emerged as a central mediator of biological responses related to inflammation³, neuroprotection, and vascular regulation. are G protein–coupled receptor (GPCR) predominantly coupled to G proteins, whose activation suppresses immune responses by reducing pro-inflammatory cytokine release⁴ and promotes neuronal protection under oxidative or inflammatory stress⁵. are highly expressed in the central nervous system, particularly in the striatum, where their modulation has been associated with neuroprotective effects and improved motor function in Parkinson’s disease^6,7. Beyond the nervous system, are also involved in the regulation of vascular tone and blood flow through their vasodilatory effects⁸. These combined anti-inflammatory, neuroprotective, and vasoregulatory effects highlight as a promising therapeutic target not only in neurodegenerative disorders, but also in cardiovascular conditions characterized by vascular dysfunction, including hypertension.

Thus, represent a strategic molecular hub where PEMFs may exert clinically relevant effects, linking cellular biophysics to translational outcomes. Experimental evidence has shown that exposure to PEMFs increases density on the cell membrane and their binding availability in several cell types^9,10. This biological observation forms the rationale for the present study and motivates the investigation of the atomistic mechanisms that could explain such macroscopic effects.

As summarized in Fig. 1, a synthesis of published experimental data indicates a consistent increase of the maximal binding capacity () of receptors across different cellular systems. This literature-based quantitative summary supports the involvement of -mediated pathways in the anti-inflammatory and neuroprotective signaling reported in multiple cellular and tissue models¹¹. However, while these data support a functional link between field exposure and the activation of -downstream signaling pathways, they do not clarify mechanistic basis by which electromagnetic fields influence receptor structure and dynamics at the molecular scale.

Fig. 1.

Meta-analysis of adenosine receptor modulation under PEMF exposure. Summary of the reported increases in maximal binding capacity () of  adenosine receptors across multiple cell types (granulocytes, neuronal cells, osteoblasts, and chondrocytes) under control and PEMF conditions. The analysis was specifically compiled for this study based on the experimental dataset from Varani et al.^9,12,13, Vincenzi et al.^10,14, and Ongaro et al.¹⁵. It highlights a consistent rise in receptor density and functional availability, providing the biological rationale for the atomistic simulations presented here.

To bridge this gap, computational modeling offers a powerful means to connect experimental data with molecular-level mechanisms. Atomistic molecular dynamics (MD) simulations enable the investigation of receptor conformational transitions in realistic membrane environments, revealing how external physical stimuli may alter activation pathways^16–18. Previous simulation studies have mapped the allosteric coupling among transmembrane helices (TM3, TM5, TM6, TM7) and the influence of lipids and cholesterol on receptor dynamics and signaling^19,20. Similar approaches have been proposed to explore field-dependent effects at the atomic level, indicating that MD can effectively probe the modulation of GPCRs by electromagnetic fields^21–25. Within these frameworks, MD resolves dynamic allosteric networks and transient interaction sites, capturing subtle rearrangements in hydrogen bonds, salt bridges, and hydrophobic contacts that accompany activation^23–25.

Here, we use atomistic MD simulations to investigate how magnetic fields affect the structure and electrostatics of the . Because PEMF waveforms modulate on millisecond timescales, many orders of magnitude slower than atomic motion, the magnetic component experienced by the receptor can be treated as quasi-static within the MD temporal window. A time-independent magnetic field is therefore employed as an adiabatic approximation of the instantaneous magnetic perturbation, with the goal of identifying residue-level structural and electrostatic susceptibilities of the rather than reproducing the full temporal complexity of PEMF exposure. By bridging electromagnetic biophysics and the molecular response of GPCR, this study aims to provide a mechanistic rationale for the experimentally observed receptor sensitization under PEMF exposure.

Results

Field-induced conformational change of the extracellular gate

To investigate how magnetic-field exposure influences receptor accessibility, we first analyzed the geometry of the extracellular region of the , which constitutes the main entry pathway for ligands. Figure 2 provides a structural overview of the receptor model used in this study, showing the receptor embedded in a lipid bilayer (Fig. 2a,b). The lateral and top views (Fig. 2c,d) highlight the key residues involved in defining the extracellular entrance area and in the water-density analysis (colored in violet and orange, respectively). A detailed view of these residues is shown in Fig. 2e,f, where the dashed lines indicate the areas used for quantitative measurements. Leu267 and Ser67, underlined in the figure, are the only residues included in both analyses, while panels g–h report a simplified top view of the residues relative to the eight transmembrane helices.

Fig. 2.

Structural overview of the model. Lateral and top views of the adenosine (green) embedded in a lipid bilayer (light grey) are shown in panels (a–d). Residues defining the extracellular entrance (violet) and those used for the water-density analysis (orange) are highlighted. Panels (e–f) provide close-up views of these residues, with dashed lines indicating the areas used for quantitative measurements. Leu267 and Ser67, underlined in the figure, are the only residues included in both analyses. Panels (g–h) present simplified top views illustrating the spatial arrangement of the selected residues with respect to the transmembrane helices.

Under control conditions, the structure remained compact, with the extracellular loops and the upper portions of the transmembrane helices forming a partially closed entrance, consistent with the inactive-state conformations previously reported for in structural and simulation studies^16,17,26. Upon magnetic-field application, a clear rearrangement of the extracellular domain occurred. The entrance area progressively expanded during the simulation, indicating a transition toward a more open configuration of the ligand-binding pathway. The most evident displacements involved the second extracellular loop (ECL2) and the upper regions of helices TM1 and TM2, whereas the transmembrane core preserved its overall architecture.

Figure 3 illustrates this change in more detail, comparing the extracellular entrance area between control (0 T, blue) and field-exposed (1 T, red) conditions. The entrance area defined by the residues forming the extracellular gate is used as a quantitative descriptor of its degree of opening, allowing direct comparison between the 0 T and 1 T conditions. In the lateral and top views (Fig. 3a–c), the main extracellular residues forming the entrance are highlighted, and a simplified area is drawn with dashed circles to visualize the relative expansion. The time evolution of the entrance area (Fig. 3d) shows that field-exposed trajectories (red) consistently sample larger values than control simulations (blue). The time evolution is reported for individual trajectories to capture the intrinsic dynamical variability and to highlight transitions that are not evident in averaged profiles. The corresponding probability-density function (PDF) at the bottom of the panel quantifies this shift, revealing two preferential regions centered around approximately and . While control trajectories occasionally displayed spontaneous transitions between the two states (around 90 ns and 150 ns), field-exposed trajectories preferentially sampled configurations with larger entrance areas.

Fig. 3.

Field-dependent conformational change of the extracellular entrance. Comparison between control (0 T, blue) and field-exposed (1 T, red) configurations of the adenosine receptor. (a–c) Lateral and top views showing the residues that define the extracellular entrance; dashed circles mark the area used for quantitative analysis. (d) Temporal evolution of the entrance area over 270 ns for all trajectories. The field-exposed system shows a larger and more variable profile, corresponding to a shift from the closed (0.7 ) to the open (1.4 ) state. The probability-density function (PDF, bottom panel) quantifies the distribution of these states. Control trajectories show occasional transitions between the two conformations (90 ns and 150 ns), whereas the exposed system remains stably open.

The structural snapshots in Fig. 3 further confirm that this field-induced widening of the entrance occurs without perturbing the overall architecture of the transmembrane bundle, as supported by Root-mean-square-deviation (RMSD) analysis of both the full receptor and the transmembrane domain, as well as secondary-structure and pore-radius analyses in Supplementary Material (Fig. S3–S7).

To assess whether this structural opening translated into altered solvent accessibility, water density was analyzed along the receptor axis (Fig. 4). In Fig. 4a, the receptor is shown embedded in the lipid bilayer and surrounded by water molecules, with the subset used for density analysis indicated in dark blue. The corresponding profiles in Fig. 4b display the average number of water molecules per along the z-axis of the simulation box for the control (blue) and exposed (red) trajectories. A pronounced difference emerged near z = 9 nm, where the mean densities reached approximately ∼ 7.5 and ∼ 15 molecules for the control and exposed conditions, respectively. As one moves toward the receptor interior, the number of water molecules decreases and nearly vanishes between z = 6−7 nm before increasing again toward the cytoplasmic side. Below z = 6 nm, corresponding to the intracellular domain, the two conditions overlap, indicating that the magnetic field selectively affects the extracellular portion of the protein. The color map in Fig. 4c shows the temporal evolution of water density inside the protein: under magnetic exposure, a persistent high-density region appears near the entrance, indicating stable water infiltration and greater solvent accessibility. Quantitatively, the mean water density increased from ∼ 7.5 to in the extracellular region, consistent with a two-fold enhancement of hydration. These results demonstrate that magnetic induction promotes both a geometrical expansion of the extracellular gate and enhanced hydration at the entrance region, jointly favouring ligand access. Additional structural analyses reported in the Supplementary Material further confirm that these effects are localized at the extracellular region (Fig. S7) and do not involve destabilization of the transmembrane core (Fig. S4). This interpretation is further supported by a hydrogen bond analysis showing a tendency toward increased protein–water contacts under magnetic-field exposure (median: 318 for 0 T vs. 327 for 1 T), while protein–protein hydrogen bonds remain essentially unchanged (median: 244 for 0 T vs. 243 for 1 T), consistent with a localized increase in solvent accessibility at the extracellular interface without significant perturbation of the receptor core (Fig. S8 and Table S2).

Fig. 4.

Water-density distribution within the under control and field exposure. (a) Lateral view of the receptor embedded in a lipid bilayer and surrounded by water molecules (blue), with those included in the analysis shown in dark blue. (b) Mean water-density profiles along the z-axis for control (blue) and exposed (red) systems. A pronounced difference appears near z = 9 nm, with densities of ≈ 7.5 and 15 molecules·nm for the control and field conditions, respectively. (c) Time–space map of water density inside the protein, showing persistent high-density regions near the extracellular entrance under magnetic-field exposure, consistent with stable hydration and increased solvent accessibility.

Together, these results demonstrate that magnetic-field exposure biases the toward a more open and hydrated extracellular configuration without perturbing the transmembrane bundle. This field-induced conformational shift represents the initial step in a mechanistic pathway by which magnetic perturbations may enhance ligand accessibility and modulate receptor function.

Electrostatic rearrangements and local field response

The structural changes observed in the extracellular region under magnetic-field exposure suggest an accompanying reorganization of the local electrostatic environment. To characterize this response, we analyzed the residue-level dipole moments of the , which report on the orientation and distribution of atomic charges within the protein.

Figure 5a shows a residue-level profile providing a global quantitative view of the x- and y-components of the dipole moment for all 306 residues of under control (0 T) and field-exposed (1 T) conditions over 270 ns. This panel identifies the residues most responsive to the applied field. Distinct peaks, ranging from 4 to 8 Debye, appear for charged residues (Glu, Asp, Arg, Lys), indicating enhanced sensitivity of these side chains to the magnetic field in the x–y plane. Notably, Glu169, marked by the black bar in the y-component plot, shows a difference of up to approximately 6 D between conditions, suggesting a relevant contribution to the extracellular entrance rearrangement described in the previous section. The largest variations occur in the extracellular and intracellular loops and in helix VIII, consistent with the higher charge density and conformational mobility of these domains.

Fig. 5.

Electrostatic response of A adenosine receptor residues under magnetic-field exposure. (a) Residue-level profiles of the x- and y-components of the dipole moment for all 306 residues under control (0 T) and exposed (1 T) conditions. Distinct peaks (4–8 D) identify residues most sensitive to the magnetic field, with Glu169 (black bar) showing the largest variation. (b) Probability-density functions (PDFs) of the y-component of the dipole moment for the six extracellular residues defining the entrance region. Ser67 shows minimal variation, whereas Glu169, His264, Pro266, and Leu267 display clear field-dependent redistributions. (c) Three-dimensional representation of representative residues, including those most affected in panels a–b, showing dipole-moment vectors under 0 T (blue) and 1 T (red). Vectors are normalized and scaled as described in the Methods.

Based on this global screening, six residues defining the extracellular entrance were selected for detailed statistical analysis. Figure 5b focuses on this restricted set of residues, revealing how magnetic-field exposure modifies dipole-orientation distributions and highlighting the difference between stable and responsive sites. This analysis quantifies how the dipole orientations of the selected residues redistribute under magnetic-field exposure, highlighting differences in their sensitivity to the applied field (see Table S1 in Supplementary Material for the statistical characterization). While Ser67 shows minimal changes, four residues – Glu169, His264, Pro266, and Leu267 – display clear field-dependent redistributions. Glu169 exhibits a noticeable redistribution of its dipole-moment distribution under magnetic-field exposure, with a shift toward lower values and a reduction in variability. This behavior is supported by the statistical analysis (Supplementary Material Table S1), which shows a median decrease () and a narrower IQR, indicating a more constrained dipole orientation under the applied field. This is consistent with the large amplitude variation (up to 6 Debye) highlighted in Fig. 5a. Pro266 and Leu267 display a clear shift toward higher dipole values under field exposure, with distributions that move toward larger positive values, whereas His264 shows a comparatively narrower and more localized distribution, with a shift toward lower dipole values under field exposure, indicating a more ordered electrostatic response. In this way, Fig. 5b provides a quantitative layer to the interpretation, showing how dipole orientations redistribute rather than simply change magnitude, thus bridging the residue-level trends of Fig. 5a with the spatial representation shown in Fig. 5c. To visualise how these statistical differences manifest structurally, Fig. 5c provides a three-dimensional representation of selected residues, including those most affected in panels a–b, and shows their dipole-moment vectors within the receptor structure. Vectors are normalized and scaled as described in the Methods, allowing direct comparison between 0 T (blue) and 1 T (red) orientations. Glu169, Ala265, and Pro266 display changes in dipole orientation under the applied field. Among them, Ala265 and Pro266 show the largest angular deviations, whereas Glu169 exhibits a consistent reorientation with reduced variability under magnetic-field exposure, suggesting complementary roles in the receptor’s adaptive electrostatic response.

To further examine how local electrostatics translate into positional rearrangements, three residues (Pro266, Ala265, Glu169) were analyzed through combined three-dimensional spatial mapping and two-dimensional elliptical projections (Fig. 6). These residues were chosen because they showed the largest dipole-moment differences in the global screening.

Fig. 6.

Positional analysis of residues Pro266, Ala265, and Glu169 under control and field-exposed conditions. The left panels show the three-dimensional spatial distribution of atomic positions, while the right panels report the corresponding two-dimensional projections (XY, XZ, YZ) with 95% confidence ellipses illustrating positional dispersion and relative displacement between the two conditions. Pro266 exhibits the most pronounced difference between 0 T and 1 T, with minimal overlap between the blue and red ellipses and a broader, shifted distribution under exposure. Ala265 displays an intermediate behaviour, with partial overlap yet visible shifts in centroid and orientation. Glu169 shows the smallest variation, with strongly overlapping ellipses and comparable spatial dispersion. Together, these patterns reveal residue-specific sensitivity to magnetic exposure, with Pro266 and Ala265 contributing most to the observed rearrangements at the extracellular entrance.

Pro266 displayed the clearest field-dependent response. The three-dimensional point clouds for 0 T and 1 T occupy distinct regions of space, and the two-dimensional projections show almost non-overlapping confidence ellipses, indicating a robust positional shift and increased dispersion under magnetic exposure. This behaviour is consistent with the large dipole reorientation measured for this residue and suggests a strong coupling between its local electrostatics and its conformational freedom. Ala265 showed an intermediate pattern: the two spatial distributions partially overlap, yet their centroids and orientations differ noticeably. The broader ellipse under 1 T suggests a modest increase in local mobility, in line with the moderate dipole variations observed in Fig. 5. In contrast, Glu169 exhibited minimal positional difference between the two conditions. The spatial clouds are highly superimposed, and the corresponding ellipses nearly coincide, indicating that despite its strong dipole-moment response, the residue remains geometrically constrained within its local environment.

Together, this combined geometric–electrostatic analysis demonstrates that magnetic exposure does not elicit a uniform shift across the extracellular region of the , but instead selectively targets residues such as Pro266 and Ala265. Owing to their side-chain flexibility, these residues are particularly susceptible to dipole-driven perturbations, which may contribute to modulating the accessibility of the ligand-entry pathway.

Functional interpretation of the field effect

The combined geometrical and electrostatic analyses suggest that magnetic-field exposure primarily influences the extracellular gate of the by modulating residue-level dipoles in regions of enhanced structural flexibility. The field interacts with polar and charged residues, particularly Glu169, Ala265, and Pro266, whose dipole reorientation under exposure suggests a redistribution of the local electrostatic potential. These changes may extend to the surrounding residues, potentially influencing hydrogen-bond networks and intra-loop interactions. This local electrostatic rearrangement is associated with the extracellular loops toward geometries that favour hydration and a more open gate configuration. In this context, the observed bias toward more open loop geometries and increased hydration is consistent with an electrostatic contribution to the modulation of the extracellular gate. Overall, the results support a coherent interpretation in which magnetic interaction with residue dipoles is associated with changes in the local electrostatic environment and with a modulation of extracellular loops conformations, leading to a more hydrated and accessible entrance to the orthosteric binding site. Importantly, this conformational adaptation remains comparable with the overall fold of the receptor and does not perturb the transmembrane core. The stabilization of an open and hydrated entrance provides a plausible atomistic rationale for the experimentally observed enhancement of adenosine receptor accessibility and functional responsiveness under PEMF exposure. The proposed cascade is illustrated schematically in Fig. 7. These observations support a mechanistic interpretation in which electrostatic rearrangements contribute to the modulation of ligand accessibility at the extracellular entrance.

Fig. 7.

Proposed mechanistic model of the field-induced adenosine receptor response. Schematic representation of the molecular cascade inferred from the simulations. In the control condition (0 T, left), the extracellular gate is narrow and poorly hydrated, with locally disordered dipoles. Under magnetic-field exposure (1 T, right), key residues (Glu169, Ala265, Pro266) display reoriented dipoles and a redistributed electrostatic environment that favour relaxation of the extracellular loops and water entry. The combined effect stabilizes a hydrated, open configuration consistent with enhanced receptor accessibility and provides a plausible atomistic basis for the experimentally observed increase in receptor responsiveness under PEMF exposure.

Discussion

This study provides an atomistic description of the response of the to an external time-independent magnetic field, exploring a possible link between electromagnetic exposure and receptor conformational dynamics. By combining equilibrium and non-equilibrium molecular dynamics simulations, the results indicate that the magnetic field predominantly affects the extracellular region of the receptor, inducing subtle changes in geometry, hydration, and local electrostatics while preserving the integrity of the transmembrane core.

Analysis of the extracellular entrance revealed the presence of two predominant conformational states of the extracellular entrance, which can be described as “less accessible” and “more accessible” configurations. Under control conditions, the receptor remained mainly in the less accessible state, whereas magnetic-field exposure increased the probability of the more accessible configuration. This shift suggests that the field may bias conformations more open to ligand interaction, in agreement with experimental reports of enhanced responsiveness under PEMF exposure^8,9,12,27.

The observed increase in water density within the extracellular cavity further supports this interpretation. Enhanced hydration and cavity expansion are recognized features linked to ligand accessibility and early activation processes in GPCR^28,29. The effect was limited to the extracellular region, while the cytoplasmic portion and G-protein interface remained stable, suggesting that the magnetic field modifies local electrostatics and hydration rather than producing large-scale structural perturbations. A hydrogen bond analysis further reveals a tendency toward increased protein–water contacts under magnetic-field exposure, while protein–protein hydrogen bonds remain essentially unchanged, consistent with a localized increase in solvent accessibility at the extracellular interface without significant perturbation of the receptor core.

At the residue level, Ala265 and Pro266, located at the extracellular ends of helices VI and VII, showed the strongest field sensitivity, displaying dipole reorientation and local charge redistribution. These residues correspond to sites previously implicated in extracellular gating and TM6–TM7 rearrangements preceding GPCR activation^16,17,28. Notably, the meta-binding site defined by these and neighboring residues has been identified as a key determinant of ligand accessibility to the orthosteric pocket²⁸, suggesting that the field-induced perturbation observed here may influence ligand recognition and receptor conformational flexibility in functionally relevant ways. Together, these observations support a model in which magnetic exposure selectively perturbs the electrostatic landscape experienced by flexible extracellular residues, facilitating local conformational adjustments that bias the entrance region toward increased accessibility.

From a methodological perspective, this work employed an extended Velocity–Verlet algorithm capable of integrating the Lorentz force^30,31, ensuring accurate particle motion under magnetic perturbations. Validation against the analytical solution for cyclotron motion confirmed the stability and precision of the modified integrator, providing a reliable computational framework for the study of field–protein interactions.

It should be noted that the time-independent magnetic field employed here represents an adiabatic approximation of the full PEMF waveform. While this choice is physically justified by the separation of timescales between field modulation and atomic motions, and by the instantaneous nature of the Lorentz force, it does not capture possible effects associated with the temporal modulation of the field. The present results should therefore be interpreted as identifying residue-level susceptibilities to magnetic perturbation, providing a molecular-level framework that future studies employing time-varying field protocols or multiscale approaches could build upon.

In addition, the field strength employed (1 T) is higher than the millitesla range typically used in PEMF experiments. At the molecular scale, magnetic interactions are typically much smaller than thermal fluctuations, making their direct effects difficult to resolve within the timescales accessible to MD simulations. In this framework, the applied field acts as a sensitivity-enhancing perturbation that enables the identification of residue-level structural and electrostatic responses, following an approach analogous to that commonly adopted in MD studies of electric-field effects on biological membranes and proteins^32–35, and consistent with recent MD studies employing field strengths in the range of 1–10 T to probe magnetic field effects on biological systems³⁶. Overall, these results support a scenario in which residue-level electrostatic perturbations represent the earliest detectable signatures of the magnetic-field effect, while increased receptor accessibility emerges as a collective, higher-order consequence of these local responses. Although the induced rearrangements are modest in magnitude, they appear sufficient to bias the extracellular gate toward more accessible conformational states.

In conclusion, static magnetic fields appear to induce limited but measurable rearrangements in the extracellular region of the . The combination of geometrical expansion, increased hydration, and residue-specific dipole changes suggests that magnetic exposure may bias the receptor towards configurations with greater solvent accessibility. These atomistic observations offer a plausible physical interpretation of previously reported increases in the activation of signaling cascade under PEMF exposure^8,9,12,13 delivering a direct mechanistic rationale at the molecular level that complements the macroscopic biological evidence, and provide a basis for further studies on electromagnetic modulation of GPCRs.

Future developments could extend this approach to different field strengths or orientations and employ enhanced-sampling or multiscale models to explore the coupling between electromagnetic fields and receptor dynamics. Overall, the methodology described here may support broader investigations into the molecular mechanisms underlying electromagnetic interactions with biological systems.

Materials and methods

Model construction

A ligand-free three-dimensional model of the human adenosine receptor was selected as the starting configuration. The structure was obtained from the Adenosiland repository³⁷, which provides homology models for all human adenosine receptor subtypes based on the UniProtKB entry P11617. The chosen model, originally derived from the canine sequence, shares 96.1 sequence identity with the crystallographic structure of the human receptor (PDB ID: 3EML)³⁸, supporting its suitability for the present study. The receptor was embedded in a pre-equilibrated lipid bilayer and solvated in a rectangular box of TIP3P water molecules with neutralizing counterions (Fig. 2a–b), in order to reproduce a realistic membrane environment suitable for atomistic MD simulations. The complete system comprised 154154 atoms in total, including 4902 protein atoms, 272 lipid molecules (36448 atoms), 37558 water molecules (112674 atoms), 60 and 70 ions with a simulation box of 10 × 10 × 14 . All titratable residues were assigned protonation states consistent with standard physiological conditions: Asp and Glu residues were kept deprotonated, Lys and Arg residues protonated, cysteine residues in the neutral thiol form, and histidine residues in the HIE (\varepsilon-protonated) state. A complete summary of the system composition is provided in Table 1.

Table 1.

Summary of the simulated system composition.

Component	Number
Total atoms	154154
Protein atoms	4902
Water molecules	37558
Water atoms	112674
Lipid molecules	272
Lipid atoms	36448
Na+ ions	60
Cl− ions	70

The comprises seven transmembrane α-helices (H1–H7) spanning the lipid bilayer and an additional short helix VIII lying parallel to the cytoplasmic surface. These helices are connected by three extracellular and three intracellular loops (ECLs and ICLs, respectively). The transmembrane bundle encloses an internal cavity acting as the primary orthosteric binding site, whose conformation modulates G-protein activation. The extracellular region also includes a meta-binding site located at the entrance of the orthosteric pocket, defined by six residues (Ser67, Glu169, His264, Ala265, Pro266 and Leu267) previously identified as key determinants of ligand accessibility^28,29. The spatial distribution of these residues is shown in Fig. 2c–h, where panels (e–h) illustrate both detailed and schematic representations of their arrangement relative to the transmembrane helices. Among them, four residues (His264, Ala265, Pro266, Leu267) connect transmembrane helices VI and VII and are positioned at the extracellular apex of the receptor, where they remain highly flexible. Additionally, seven residues (Trp7, Ser67, Cys74, Leu141, Asn175, Phe258 and Leu267) were used to define the boundaries of the extracellular entrance for the water-density analysis. These regions were visualized as reference points for the hydration calculations described in the Results Section.

Magnetic field implementation and validation

Although GROMACS is a highly reliable tool for MD simulations and includes built-in functionalities for applying uniform electric fields, it does not provide a native routine for introducing an external magnetic field. Therefore, a custom implementation was developed to apply a static magnetic field and the corresponding Lorentz force to each atom. This feature was incorporated into the GROMACS source code following the algorithmic framework proposed by Spreiter and Walter³¹ and extended by Della Valle et al.³⁰. The static field employed here represents an adiabatic approximation of the magnetic component of PEMF exposure. Because PEMF waveforms typically vary on millisecond timescales ( s), several orders of magnitude slower than atomic motions ( s), the receptor effectively experiences the magnetic perturbation as quasi-static within the temporal window accessible to atomistic MD simulations. Furthermore, the Lorentz force acting on each atom at any given instant depends solely on the instantaneous field value and particle velocity, carrying no memory of the waveform’s temporal profile. The structural and electrostatic observables probed here therefore reflect the receptor’s instantaneous response to the magnetic perturbation, independently of the full temporal structure of PEMF exposure. A uniform induction magnetic field B (specified in Tesla) was passed to the integrator and converted into GROMACS internal units through a constant scaling factor (Eq. 1):

1

according to (Eq. 2):

2

where is the field strength in Tesla.

The action of the external magnetic field on charged atoms was introduced by explicitly adding a Lorentz-force term to the Newtonian equation of motion (Eq. 3):

3

where , , and denote the mass, charge, and velocity of atom i; represents the sum of bonded and non-bonded forces acting on the particle; and is the magnetic-field vector.

The external magnetic field enters the equations of motion exclusively through the Lorentz force term and does not modify the underlying potential energy function or the parametrization of the force field: bonded and non-bonded interaction terms remain unchanged, as reflected in Eq. (3), where retains its standard form. This formulation is consistent with classical electrodynamics, in which a magnetic field does not perform work on charged particles and therefore does not contribute to the potential energy surface, but rather modifies particle trajectories through velocity-dependent forces. As a consequence, the observed structural and electrostatic effects arise from the direct coupling between the Lorentz force and the dynamics of charged atoms and residues, rather than from modifications of the underlying force field parametrization. The physical consistency of this approach is further supported by the validation described below, and is consistent with previously established approaches for magnetic molecular dynamics simulations of biological systems^30,36,39.

Time integration was performed using an extended Velocity–Verlet scheme^30,31,36, in which the magnetic contribution is introduced through the Larmor frequency component into the velocity and position update equations. Specifically, we adopted the inversion algorithm described in³¹, in which the strength of the magnetic field enters through the Larmor frequency Ω = qB/m, where q is the particle charge, B the magnetic field intensity, and m the particle mass. The magnetic field was applied along the z-direction, introducing the Lorentz force along the x and y axes. The resulting update equations for positions and velocities are (Eqs. 4 and 5):

4

5

where is the unit vector in the z-direction, represents the accelerations independent of atom velocities (i.e., arising from bonded and non-bonded interactions), and Ω = qB/m is the Larmor frequency. This formulation ensures that the magnitude of the velocity vector is conserved at each integration step, consistent with the non-working nature of the magnetic force, and provides numerical stability for the time steps used in the present simulations ().

A uniform magnetic induction of was applied along the z-axis of the simulation box, perpendicular to the membrane plane and parallel to the receptor’s main transmembrane axis. This configuration was chosen to maximize the coupling between the magnetic field and the dipole components of the extracellular residues, while allowing a direct comparison between exposed (1 T) and control (0 T) simulations.

The implementation was validated by reproducing the analytical solution for a single charged particle moving in a uniform magnetic field. The simulated trajectory followed the expected cyclotron motion, characterized by (Eq. 6):

6

where is the cyclotron radius and the angular frequency. The numerical trajectories matched the analytical predictions with deviations below 0.01% over integration steps, confirming both the accuracy and long-term stability of the modified integration algorithm.

Additional validation and stability checks were performed on the full receptor–membrane system. Energy conservation was monitored throughout the trajectories under both 0 T and 1 T conditions, showing total-energy drifts below per steps. Temperature and pressure profiles remained stable and indistinguishable between control and exposed simulations, confirming that inclusion of the Lorentz term does not perturb the thermodynamic equilibrium of the NPT ensemble. The time evolution of total energy, temperature, and pressure for representative control (0 T) and field-exposed (1 T) trajectories is reported in Supplementary Material Figs. S1, S2.

Together with the single-particle benchmark, these tests validate the numerical implementation and ensure that the modified code reproduces the correct magnetic dynamics without introducing artificial heating or structural bias. The verified implementation was then incorporated into the production version of GROMACS used in this study, enabling atomistic computation of both interatomic and Lorentz forces. This extension allowed the direct coupling between the applied magnetic field and molecular dynamics, providing a physically consistent framework for the analysis of the field-induced rearrangements described in the Results.

Simulation setup and data generation

The system preparation followed a standard multi-step protocol. After system construction, an initial energy minimization step was performed to remove steric clashes and optimize local geometry. This was followed by an equilibration phase under NPT conditions (310 K,1 bar), allowing the lipid bilayer and solvent environment to relax around the protein. The equilibration phase was followed by an additional unrestrained pre-production simulation (∼50 ns) to ensure full stabilization of the system prior to data collection. Following this preparation, a series of all-atom molecular dynamics simulations were performed under both control and field-exposed conditions.

All simulations were carried out using the GROMACS package⁴⁰ with the CHARMM27 force field⁴¹. A modified version of the code, including the Lorentz-force term described in the previous Section, was employed. A total of 11 independent simulations were generated, consisting of 5 trajectories for the 0 T condition and 6 trajectories for the 1 T condition, each with durations up to 270 ns, corresponding to an aggregate sampling of approximately 1.5  for each condition.

An external magnetic induction field of was applied along the z-axis, orthogonal to the membrane and parallel to the receptor’s transmembrane bundle. Periodic boundary conditions were used in all three spatial directions. Long-range electrostatic interactions were treated with the Particle Mesh Ewald (PME) method, and Lennard–Jones interactions were truncated at 1.2 nm.

Temperature was maintained at 310 K using a Berendsen thermostat⁴² with a coupling constant of 0.1 ps, while pressure was controlled semi-isotropically at 1 bar using a coupling constant of 1 ps. The time step was set to 2 fs. All covalent bonds involving hydrogen atoms were constrained using the LINCS algorithm.

RMSD analysis, secondary-structure analysis using DSSP⁴³, and pore-radius profiles along the receptor axis⁴⁴, and hydrogen bond counts for protein–water and protein–protein interactions were used to monitor the global stability of the receptor throughout the simulations and to verify preservation of the overall fold under both conditions. These analyses are reported in the Supplementary Material. Each trajectory was visually inspected to confirm the absence of artifacts related to periodic imaging or boundary effects.

This protocol yielded a statistically consistent ensemble of equilibrated configurations for both the control and field-exposed systems, forming the basis for the structural and electrostatic analyses described in the Results Sections.

Trajectory analysis

Three complementary analyses were performed on the molecular dynamics trajectories to quantify the effects of magnetic-field exposure on the receptor: (i) extracellular entrance area, (ii) water density distribution, and (iii) residue dipole moments. These analyses were performed using custom C++ routines, whose mathematical formulations are described in detail in the following subsections. Post-processing, statistical analyses, and figure generation were carried out in MATLAB (MathWorks).

Extracellular entrance area

To assess the conformational dynamics of the extracellular gate, we defined an entrance region based on six residues (Ser67, Glu169, His264, Ala265, Pro266, and Leu267) which delineate the meta-binding site and the access path to the orthosteric pocket²⁸. For each simulation frame, the positions of these residues were projected onto the xy plane, and the covariance matrix of their coordinates was computed. The area of the best-fitting ellipse was then calculated as (Eq. 7):

7

where and are the eigenvalues of the positional covariance matrix. This metric captures both the amplitude and orientation of conformational fluctuations at the receptor entrance. The entrance area is therefore used as a quantitative descriptor of the degree of opening of the extracellular gate.

The temporal evolution of the extracellular area was monitored over 270 ns for each trajectory and analyzed independently in order to capture the intrinsic dynamical variability and to highlight transitions that may not be evident in averaged profiles. The corresponding probability density function (PDF) was computed to characterize the distribution of entrance-area values. The distributions reveal two preferential regions centered around approximately and corresponding to configurations with smaller and larger entrance areas, respectively.

Control trajectories displayed occasional spontaneous transitions between configurations characterized by smaller and larger entrance areas (around 90 ns and 150 ns), whereas the magnetic-field–exposed systems preferentially sampled configurations with larger entrance areas. The shift of the distribution toward larger entrance-area values under magnetic-field exposure indicates an increased sampling of more open configurations, consistent with enhanced accessibility of the ligand-binding site.

Water density analysis

To evaluate hydration dynamics within the receptor, the number of water molecules was quantified inside a cylindrical volume spanning the extracellular and intracellular regions and centered on the receptor z-axis. The spatial density ρ (z) was computed as Eq. 8:

8

where N(z) is the number of water molecules in a slice of thickness Δ z, and V(z) is the corresponding cylindrical volume. Mean profiles and standard errors were calculated for both control (0 T) and field-exposed (1 T) conditions.

A marked increase in hydration was observed in the extracellular region (around ), with mean densities of approximately 7.5 and for 0 T and 1 T, respectively, corresponding to a maximum difference of about . In the receptor interior (6–), the water content approached zero in both conditions, while the intracellular region () showed no significant difference.

A small variation in water density was also detected around , likely reflecting the flexibility of the extracellular loops.

To visualize the temporal evolution of hydration, water-density maps ρ (z,t) were constructed over the 270 ns trajectories. The field-exposed system displayed a persistent high-density band near the extracellular gate, confirming a stable hydration enhancement, consistent with the structural expansion described in Results Section.

Dipole moment analysis

Local electrostatic changes were investigated by computing the dipole moment vector for each residue i as Eq. 9:

9

where and denote the partial charge and position of atom j belonging to residue i. The Cartesian components and were averaged over the 270 ns trajectories and compared between control (0 T) and exposed (1 T) conditions. The differences and were used to identify residues exhibiting the strongest field-induced alterations.

Subsequently, probability density functions (PDFs) of the y-component were computed for the six key residues that define the extracellular gate. Those showing the largest dipole reorientations–Glu169, His264, Pro266, and Leu267–were further analyzed through 3D vector mapping within the receptor structure, highlighting orientation shifts and magnitude variations under magnetic-field exposure.

Together, these analyses quantify the local electrostatic and mechanical contributions to the receptor’s conformational response and support the structural interpretation discussed in Results Section.

Supplementary Information

Supplementary Information. ^{(1.4MB, pdf)}

Author contributions

C.P. contributed to manuscript writing (original draft), data curation, visualization, and interpretation of the results. F.D.S. performed the molecular dynamics simulations and data generation. P.M. contributed to study conceptualization, methodology development, simulations, data analysis, and interpretation of the results. I.P. contributed to data analysis and visualization. D.C. contributed to the conceptualization of the study. E.D.V. contributed to methodology development and software implementation related to magnetic-field modeling. S.S. and R.C. contributed to the study’s conceptualization and interpretation of the results. M.L. and F.A. coordinated and supervised the study and contributed to conceptualization. All authors reviewed the manuscript.

Data availability

 The GROMACS input files (.mdp), receptor model files, and representative trajectory files (.xtc) used in this study are publicly available at https://doi.org/10.5281/zenodo.19488863.

Declarations

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-026-55027-5.