Biological cell as a soft magnetoelectric material: Elucidating the physical mechanisms underpinning the detection of magnetic fields by animals

Sharks, birds, bats, turtles, and many other animals can detect magnetic fields. Aside from using this remarkable ability to exploit the terrestrial magnetic field map to sense direction, a subset is also able to implement a version of the so-called geophysical positioning system. How do these animals detect magnetic fields? The answer to this rather deceptively simple question has proven to be quite elusive. The currently prevalent theories, while providing interesting insights, fall short of explaining several aspects of magnetoreception. For example, minute magnetic particles have been detected in magnetically sensitive animals. However, how is the detected magnetic field converted into electrical signals given any lack of experimental evidence for relevant electroreceptors? In principle, a magnetoelectric material is capable of converting magnetic signals into electricity (and vice versa). This property, however, is rare and restricted to a rather small set of exotic hard crystalline materials. Indeed, such elements have never been detected in the animals studied so far. In this work we quantitatively outline the conditions under which a biological cell may detect a magnetic field and convert it into electrical signals detectable by biological cells. Specifically, we prove the existence of an overlooked strain-mediated mechanism and show that most biological cells can act as nontrivial magnetoelectric materials provided that the magnetic permeability constant is only slightly more than that of a vacuum. The enhanced magnetic permeability is easily achieved by small amounts of magnetic particles that have been experimentally detected in magnetosensitive animals. Our proposed mechanism appears to explain most of the experimental observations related to the physical basis of magnetoreception.

Figure 1

Magnetosensitive animals. Shown on top are European robins, which have an avian magnetic compass that has been extensively researched. Shown on the bottom are sharks, which are among the numerous marine animals that can perceive the Earth's magnetic field.

Figure 2

Conceptual schematic of the magnetosensitive biological cell. The cell is enclosed by a soft homogeneous dielectric thin membrane of dielectric permittivity ${\epsilon }_r$ and we will assume that the permeability of the membrane and its surrounding is about the same as in a vacuum $\left({\mu }_r=1\right)$. However, the interior of the cell may have a different magnetic permeability ${\mu }_r>1$. (a) The state where the cell is perfectly spherical is hypothetical but useful as a reference to explain the mechanism outlined in the text. (b) As is well known, we consider the cell membrane to possess a preexisting (or resting) voltage across its thickness. The electrical field due to the resting voltage leads to the so-called electrical Maxwell stress and polarizes the membrane. We assume that our starting configuration is a nearly spherical ellipsoid as discussed in the text. The magnetic field is now switched on. The magnetic Maxwell stress causes further deformation and consequently alters the preexisting electric field across the membrane.

Figure 3

Variation of the electric field within a cell membrane with respect to the relative permeability for different magnitudes of the Earth's magnetic field. To make quantitative estimates, we consider a cell subjected to a magnetic field and plot the ensuing change in the electrical field $\mathrm{\Delta }E$ as a function of the magnetic permeability of its interior. For example, a neuron can sense a variation in electric field as low as 0.1 V/m; the dashed line shows this threshold. These calculations are done using (14) under the assumption that the thickness across the membrane remains uniform.

Figure 4

Schematic of a magnetic map. The isolines represent isodynamics (lines of equal magnetic field intensity) with a contour interval equal to 4 A/m.

Figure 5

Variation of the electric field within a cell membrane for a fixed value of the Earth's magnetic field. We consider $|h^e|=50\mathrm{A}/\mathrm{m}$ and plot the change in the electrical field as a function of the polar angle $\theta$ for several values of the magnetic permeability. Evidently, a local change in the animal position by a simple rotation produces a change in the resulting electric field. These calculations are done using (14) under the assumption (13).

Figure 6

Variation of the electric field within a cell membrane for a fixed value of the relative permeability of its interior. We consider ${\mu }_r=5$ and plot the ensuing change in the electrical field as a function of the polar angle $\theta$ for several values of the geomagnetic field. As is evident, the animal captures the intensity of the magnetic field and recognizes locally a sense of its direction. These calculations are done using (14) under the assumption (13).

Figure 7

Schematic of the possible ways to include the compass ability in the presented mechanism. (a) Adding a correction mode to the thickness (the inclination angle $I$ is the angle measured between the Earth's surface and the geomagnetic lines and $\theta$ is the polar angle within the spheroidal coordinates system and belongs to $[0,\pi ])$. (b) Introduction of a nonuniformly distributed relative permeability inside the cell caused by the concentration of magnetites in a specific region.

Figure 8

Key ingredients of the mechanism underlying the conversion of magnetic signal into a change in electrical field and its relation to thickness and $\theta$.

Figure 9

Deformation of the ellipsoid's equator and polar semiaxis $(a$ and $c)$ with respect to the relative magnetic permeability of the interior of the cell. As is evident, if the relative permeability ${\mu }_r=1$ then there is no effect of the magnetic field on the biological cell. In that case, only the transmembrane voltage will deform its shape. The data points corresponding to ${\mu }_r=1$ show the equilibrium state of the cell when the magnetic field is switched off. However, when ${\mu }_r>1$, the cell becomes magnetosensitive and deforms further. $(|h^e|=50\mathrm{kA}/\mathrm{m}$.)

Figure 10

Magnetoelectric coupling constants at high external magnetic field. The colored lines show the coupling constant of a biological membrane. The data points displays the magnetoelectric coefficient of the NCZF-PZT-PZN-NCZF composite.

Figure 11

Dependence of the membrane's uniform thickness on the external magnetic field intensity. At a high external magnetic field intensity, the thinning on the membrane is more important. It becomes more pronounced as we keep increasing the intensity.