Transmembrane potential induced on the internal organelle by a time-varying magnetic field: a model study

Abstract

Background: When a cell is exposed to a time-varying magnetic field, this leads to an induced voltage on the cytoplasmic membrane, as well as on the membranes of the internal organelles, such as mitochondria. These potential changes in the organelles could have a significant impact on their functionality. However, a quantitative analysis on the magnetically-induced membrane potential on the internal organelles has not been performed.

Methods: Using a two-shell model, we provided the first analytical solution for the transmembrane potential in the organelle membrane induced by a time-varying magnetic field. We then analyzed factors that impact on the polarization of the organelle, including the frequency of the magnetic field, the presence of the outer cytoplasmic membrane, and electrical and geometrical parameters of the cytoplasmic membrane and the organelle membrane.

Results: The amount of polarization in the organelle was less than its counterpart in the cytoplasmic membrane. This was largely due to the presence of the cell membrane, which "shielded" the internal organelle from excessive polarization by the field. Organelle polarization was largely dependent on the frequency of the magnetic field, and its polarization was not significant under the low frequency band used for transcranial magnetic stimulation (TMS). Both the properties of the cytoplasmic and the organelle membranes affect the polarization of the internal organelle in a frequency-dependent manner.

Conclusions: The work provided a theoretical framework and insights into factors affecting mitochondrial function under time-varying magnetic stimulation, and provided evidence that TMS does not affect normal mitochondrial functionality by altering its membrane potential.

Figure 1

The model of a spherical cell with a concentric spherical internal organelle. A. Relative coil and the targeted cell location, and the direction of the magnetically-induced electrical field in the brain. The current flowing in the coil generated a sinusoidally alternating magnetic field, which in turn induced an electric current in the tissue, in the opposite direction. The small circle represented a single neuron in the brain. B. The cell and its internal organelle represented in a spherical coordinates (r, θ, ϕ). The cell includes five homogenous, isotropic regions: the extracellular medium, the cytoplasmic membrane, the cytoplasm, the organelle membrane and the organelle interior The externally applied magnetic field was in cylindrical coordinates (r', ϕ', z'). The axis of the magnetic field overlapped with the O' Z' axis. The distance between the center of the cell and the axis of the coil was C.

Figure 2

Regional polarization of the cytoplasmic membrane and the organelle membrane by the time-varying magnetic field. The plot demonstrated an instant polarization pattern on both membranes. A cleft was made to illustrate the internal structure. The orientation of the cell to the coil was the same as that shown in Figure 1B. The color map represented the amount of polarization (in mV) calculated with the standard values listed in table 1. A. Field frequency was 10 KHz. B. Field frequency was 100 KHz.

Figure 3

The frequency dependency of ψ_cell and ψ_org. A. Maximal amplitudes of ψ_cell (large circle) and ψ_org plotted as a function of field frequency. B. Ratio of the two membrane polarizations as a function of the field frequency. C. Phases of ψ_cell (large circle) and ψ_org plotted as a function of field frequency. D. Phase difference between the two membrane polarizations.

Figure 4

"Shielding" effects of cytoplasmic membrane on the internal membrane. A. Amplitude of ψ_org with and without the presence of the cytoplasmic membrane. Presence of the cytoplasmic membrane reduced ψ_org. B. Phase of ψ_org with and without the presence of the cytoplasmic membrane.

Figure 5

Impact of the presence of internal organelle on ψ_cell. Amplitude (A) and phase (B) of ψ_cell with the presence of the internal organelle (cycle) or after the organelle was removed from the cell (line).

Figure 6

Dependency of ψ_org on the cytoplasmic membrane properties. Effects of cell diameter (A), cell membrane thickness (B), cell membrane conductivity (C) and cell membrane di-electricity (D) on the amplitude and phase of ψ_org.

Figure 7

Dependency of ψ_org on its own membrane properties. Effects of organelle diameter (A), thickness (B), membrane conductivity (C) and membrane di-electricity (D) on the amplitude and phase of ψ_org.