Magnetically induced behaviour of ferritin corpuscles in avian ears: can cuticulosomes function as magnetosomes?

Abstract

Magnetoreception is an enigmatic, poorly understood sensory ability, described mainly on the basis of behavioural studies in animals of diverse taxa. Recently, corpuscles containing superparamagnetic iron-storage protein ferritin were found in the inner ear hair cells of birds, a predominantly single ferritin corpuscle per cell. It was suggested that these corpuscles might represent magnetosomes and function as magnetosensors. Here we determine ferritin low-field paramagnetic susceptibility to estimate its magnetically induced intracellular behaviour. Physical simulations show that ferritin corpuscles cannot be deformed or rotate in weak geomagnetic fields, and thus cannot provide magnetoreception via deformation of the cuticular plate. Furthermore, we reached an alternative hypothesis that ferritin corpuscle in avian ears may function as an intracellular electromagnetic oscillator. Such an oscillator would generate additional cellular electric potential related to normal cell conditions. Though the phenomenon seems to be weak, this effect deserves further analyses.

1. Introduction

According to new experiments, the orientation ability of birds can be disrupted by megahertz electromagnetic waves having magnetic and electric components only of the order of B ≈ 0.1–100 nT and ɛ ≈ 0.1–10 V m⁻¹, and also by microtesla long-term exposure [1,2]. Therefore, we may assume the existence of innervated magnetically sensitive sensors for detection of geomagnetic field strength or direction in diverse animal species. Such sensor/sensors may serve as a compass or a navigational map tool depending whether they detect direction or strength of the geomagnetic field [3]. However, the location, biological form and functional principle of such sensors are still unknown [4,5]. Although currently the radical pair/cryptochrome hypothesis [6–8] seems to dominate theoretical considerations on biological magnetoreception, the hypothesis of magnetite-based magnetoreception is still alive and has recently been given new impetus through discovery of spherical ferritin corpuscles found in hair cells of the avian inner ear [9].

Previously, magnetite structures were described in a pigeon upper beak [10–12], but their mode of operation and role remain unclear, and their existence has been seriously challenged on histological grounds [13,14]. While behavioural studies support the existence of a trigeminally innervated magnetic sensor [15,16], physical simulations of the structures reported in Jandacka et al. [17] do not support the conclusion they are involved in magnetosensation. Nevertheless, not all the physical processes that might be involved in magnetoreception have been tested, including, for example, the Hall effect on thin beak platelets, as these crystals were described in the original histological papers [11].

The avian ear is another organ where magnetoreception could be mediated. Iron-containing otoliths were detected in the bird lagena [18]. An association between magnetoreception and the avian inner ear has been implicated by neurobiological studies [19,20]. Although the role of electromagnetic induction, a phenomenon generated by quick change or switch-on of the artificial magnetic field, was not discussed in these papers, the results indicate that avian magnetoreception sensor may be actually seated in the ear.

Recently, magnetic ferritin corpuscles were found in the avian ear receptor hair cells. Spherical ferritin-containing corpuscles (diameter 300–600 nm), predominantly a single corpuscle per cell, were discovered in the cuticular plates of these cells, in basilar papilla, lagena, utricle and saccule, in several species of birds [9]. About 28% of hair cells in the basilar papilla, i.e. the actual hearing organ, contain such structures. The corpuscles contained ferrihydrite crystals 3–11 nm in size, identified by electron diffraction analysis. With regard to the location in the cuticular plate of the hair cells, the authors called the corpuscles ‘cuticulosomes’ and suggested three hypotheses with respect to their role: iron storage, a stabilizer of stereocilia and, referring to magnetic properties of ferrihydrite, mediator of magnetic detection.

Ferritin is an iron-storage protein composed of a non-magnetic shell and magnetic core. The size of ferritin molecules is approximately 11–12 nm [21–23]. The magnetic core contains magnetite/maghemite, hematite and ferrihydrite crystals in a narrow size range of 3–8 nm and ratio between these minerals changing according to Fe concentration in the molecule. Under conditions of extremely low Fe concentration, 70 ± 20% of magnetite/maghemite crystals were detected [24]. Physicists expect superparamagnetic behaviour of ferritin molecules as bigger crystals of maghemite and magnetite are ferrimagnetic, while hematite is weakly ferromagnetic and ferrihydrite antiferromagnetic at room temperature [25]. Magnetization of ferrihydrite exhibits ferromagnetic hysteresis, which is attributed to uncompensated electron spins on the material surface [25,26]. In previous studies, magnetic properties of ferritin were analysed under lower temperatures than physiological ones [27–29].

The goal of this paper is to determine the magnetic properties of superparamagnetic ferritin at physiological temperatures of around 37°C (normal body temperature of birds ranges from 37 to 42°C). Subsequently, physical simulations were used to describe the behaviour of ferritin inside the avian hair receptor cells under an external magnetic field, whereas equine spleen ferritin and putative magnetite-rich ferritin were selected as model substances. We address the question whether cuticulosome-containing cells might function as magnetosensors.

2. Material and methods

Throughout the paper the SI unit system has been used (table 1). The standard uncertainties of quantities are presented. Accuracy of simulations presented is estimated to be ±10%. Goodness of fits is evaluated according to the R² number.

Table 1.

Nomenclature.

a	major axis of ellipsoid (a ↑↑ B)	(m)
a0	radius of spherical corpuscle	(m)
A	surface area of membrane: sphere → prolate ellipsoid A = 2π[b2 + ab · asin(e)/e]	(m2)
A0	surface area of sphere	(m2)
ΔA	increase of the surface area: ΔA = A−A0	(m2)
b	minor axis of ellipsoid: b = [3V/(4πa)]0.5 = (a03/a)0.5	(m)
B	external magnetic induction	(T)
Bi	induced magnetic induction or internal magnetic induction	(T)
Bgeo	induction of geomagnetic field, in computations 50 μT	(T)
c	concentration of ferritin/magnetite in solution	(mg ml−1)
e	eccentricity of ellipsoid: e2 = 1 − b2/a2	(−)
E	energy of corpuscle	(J)
f	oscillation frequency	(Hz)
f0	original oscillation frequency (system without corpuscle)	(Hz)
h1, h2	theoretical fit constants
k1, k2, k3, k4	theoretical fit constants
q1, q2, q3, q4	theoretical fit constants
kB	Boltzmann constant (1.38 × 10−23 J K−1)	(J K−1)
qp	charge of proton (1.602 × 10−19 C)	(C)
H	intensity of magnetic field in vacuum	(A m−1)
K	elastic area expansion modulus of the membrane	(J m−2, N m−1)
L	demagnetization factor: sphere → prolate ellipsoid	(−)
	L = 4π[1/(p2 − 1)] · [p/{2(p2 − 1)0.5} · ln{(p + (p2 − 1)0.5)/(p − (p2 − 1)0.5)} − 1], p = a/b, a > b
m	mass	(kg)
m0	mass of vibration system without Fe-rich corpuscle	(kg)
m1	mass of magnetite in sample	(kg)
Δm	mass of Fe-rich corpuscle	(kg)
M	magnetization	(A m−1, A m2 kg−1)
MS	saturation magnetization	(A m−1)
P	packing factor P = 0.7 (maximum packing for spheres is 0.74)	(−)
t, T	temperature	(°C, K)
u	normal electric potential	(V)
ui	induced electric potential—influence of magnetic corpuscle	(V)
V	volume	(ml, m3)
w	magnetic moment of corpuscle	(A m2)
x	size of crystals (side of a cube)	(m)
xV	size of crystal with the average volume	(m)
γ	interface tension	(N m−1)
Φ	magnetic flux	(Wb)
μ	magnetic moment	(A m2)
μdia	diamagnetic moment	(A m2)
μpar	paramagnetic moment	(A m2)
μB	Bohr magneton (1 μB= 9.27 × 10−24 J T−1)	(−)
μ0	permeability of vacuum, 4π × 10−7 H m−1	(H m−1)
χi	intrinsic low-field susceptibility, χi = χ/(1 − χL)	(A m2 mg−1 T−1, dim-less, m3 kg−1, μB T−1)
χ	low-field susceptibility, χ = χi/(1 + χiL)	(A m2 mg−1 T−1, dim-less, m3 kg−1, μB T−1)
σ	stress of membrane, σ = KΔA/A0	(N m−1)
σ0	pre-stress of membrane	(N m−1)
τ	time	(s)

Fresh equine spleen ferritin (c = 53 ± 3 mg ml⁻¹ of saline solution, less than 0.9% of NaCl, product number: F4503) and superparamagnetic magnetite (c = 5.0 ± 0.3 mg ml⁻¹ of toluene, product no. 700320) provided by Sigma Aldrich were magnetized using a vibrating sample magnetometer (Microsense EV9, magnetic moment resolution 10⁻¹⁰ A m² and generated field resolution 10⁻⁴ T) to find the magnetic low-field susceptibility at physiological temperatures. The size distribution of magnetite crystals was first presented in Jandacka et al. [17] and has a range of 5–18 nm, while the size of the crystal with average volume is x_V = 8.4 nm using cubic approximation. In toluene, the magnetite crystals aggregate to micrometric spherules.

The ferritin was magnetized in liquid form to preserve its chemical stability. No drying processes were used. With regard to a very weak magnetic moment of ferritin samples, we had to prepare a diamagnetic sample holder, which was composed of a glass holder and small cylindrical container, where liquid was sealed by paraffin (figure 1). Without ferritin these components exhibit a diamagnetic moment independent of temperature.

Figure 1.

Schematic representation of the method selected for magnetic measurements of ferritin. (Online version in colour.)

Prior to the magnetization of magnetite an adhesive paper was affixed on the top of a glass sample holder. The top of the holder was dipped into the suspension with the superparamagnetic magnetite. The mass difference between the holder plus the adhesive paper with and without absorbed magnetite suspension was found to be m = 16 ± 1 mg. Toluene evaporated during several minutes. After the mass measurement, a second adhesive paper was affixed on the dry sample to prevent loss of crystals during temperature measurements. The magnetic moment of the glass holder and the adhesive paper, measured separately without magnetite, was subtracted from the total magnetic moment.

The temperature measurements were performed using temperature regulation of N₂ gas flow. In the case of constant changes of temperature (increasing) during measurement very slow regimes were chosen, i.e. 2°C min⁻¹ or 1°C min⁻¹, to ensure the smallest difference possible between temperatures of the sensor and the ferritin solution. Temperature measurements of ferritin were limited by a range of 2–40°C. Uncertainties of temperature measurements are ±1°C.

Theoretical simulations were undertaken using Matlab and Origin software. Physical interaction between magnetic field and magnetic structures was analysed considering their most probable arrangement and composition as described in histological studies.

3. Results and discussion

3.1. Magnetic susceptibility of equine spleen ferritin and superparamagnetic magnetite

Magnetization of ferritin solution exhibits a mixed signal composed of diamagnetic and paramagnetic components, μ = μ_par + μ_dia (figure 2). Paramagnetic moment μ_par may be extracted from experimental data using physical Langevin equation or mathematical asymptotic function (we found that atan function appropriately fits the superparamagnetic curve), as simple Langevin equation describes only one mineral component, where there could be three in reality (magnetite/maghemite, hematite and ferrihydrite) [24,27]. Both equations are completed with diamagnetic signal μ_dia from glass, paraffin, Cl ions and water. The paramagnetic moment of Na ions of saline solution was neglected, because its tabulated susceptibility is approximately 8.5 × 10⁻⁹ m³ kg⁻¹. The parameters found after fits are presented in figure 2. Determined low-field susceptibilities χ = V⁻¹c⁻¹ · lim_B→0(dμ_par/dB) are χ = k₁q₁/(cV) = (2.5 ± 0.9) × 10⁻⁷ A m² mg⁻¹ T⁻¹ and χ = k₂q₂/(3cV) = (2.2 ± 0.7) × 10⁻⁷ A m² mg⁻¹ T⁻¹, both values valid for 20°C. To check validity of our results, we graphically processed the magnetization curve of ferritin, presented in fig. 4b of [27]. Estimation of low-field susceptibility at 27°C from that paper gives M/B = 3.8 × 10⁻⁷ A m² mg⁻¹ T⁻¹, adding a slope to the initial dependency. The small numerical difference between our two values and the value in [27] indicates that both measurements are correct.

Figure 2.

Magnetization of ferritin solution at 20°C. The experimental data are fit by two equations (note: atan = arctangent). The measured signal is graphically decomposed to magnetic and non-magnetic components (using more accurate ‘atan’ fit). The fit parameters are k₁ = (1.51 ± 0.27) × 10⁻⁸ A m², q₁ = 49.7 ± 12.9 T⁻¹, h₁ = (8.47 ± 0.32) × 10⁻⁷ A m² T⁻¹, R² = 0.997 and k₂ = (2.34 ± 0.39) × 10⁻⁸ A m², q₂ = 84.2 ± 17.7 T⁻¹, h₂ = (8.48 ± 0.32) × 10⁻⁷ A m² T⁻¹, R² = 0.995, where saturation magnetic moments are 2k₁/π and k₂. Volume of the sample was V = 0.058 ± 0.010 ml.

In parallel, a temperature measurement on ferritin solution was performed (figure 3). The constant external magnetic fields were set to 0.02, 0.05 and 0.1 T. With regard to paramagnetic moment depending on term 1/T, as described by the Curie law [30], and temperature independence of diamagnetic moment, the data measured were fitted by function displayed in the figure. Eventually, it was discovered that only measurement under 0.02 T contains information about low-field susceptibility, because 0.05 and 0.1 T are out of linear magnetization according to figure 2 and results presented in Brem [27]. Derived magnetic susceptibility is generally χ = k₃/(BcVT) and equals (2.5 ± 0.5) × 10⁻⁷ A m² mg⁻¹ T⁻¹ for 20°C and (2.3 ± 0.5) × 10⁻⁷ A m² mg⁻¹ T⁻¹ for 37°C.

Figure 3.

Temperature magnetization of ferritin solution. The experimental data are fit using Curie law, μ_par ∼ 1/T, and considering the temperature independence of diamagnetic moment. The parameters found are: k₃ = (4.39 ± 0.57) × 10⁻⁶ A m² K and q₃ = (3.17 ± 0.19) × 10⁻⁸ A m², R² = 0.18 for 0.02 T, k₃ = (1.31 ± 0.07) × 10⁻⁵ A m² K and q₃ = (7.02 ± 0.24) × 10⁻⁸ A m², R² = 0.42 for 0.05 T, k₃ = (2.29 ± 0.06) × 10⁻⁵ A m² K and q₃ = (1.40 ± 0.02) × 10⁻⁷ A m², R² = 0.74 for 0.1 T. Volumes of samples V are 0.058 ± 0.010 ml, 0.067 ± 0.010 ml and 0.063 ± 0.010 ml, respectively.

The superparamagnetic magnetite exhibits a relatively strong magnetic moment, so we derived its low-field susceptibility from magnetization of dry magnetite sample at five temperature points (figure 4) above the Verwey transition, which is typically less than 123 K [31,32]. The low-field susceptibility is χ = q₄/(m₁T) and equals (3.7 ± 0.3) × 10⁻⁴ A m² mg⁻¹ T⁻¹ for 20°C and (3.5 ± 0.3) × 10⁻⁴ A m² mg⁻¹ T⁻¹ for 37°C, where m₁ = cm/ρ · (1 + c/ρ − c/ρ₁)⁻¹ ≈ cm ρ⁻¹ is mass of magnetite, where ρ = 867 kg m⁻³ is density of toluene and ρ₁ = 5175 kg m⁻³ density of magnetite at room temperature.

Figure 4.

Magnetization of superparamagnetic magnetite (x_V = 8.4 nm) at selected temperature points: −150°C, −100°C, −50°C, 0°C and 50°C. The low-field dependencies with corresponding theoretical fits are displayed in the main frame and the dependence of parameter k₄ on temperature with fit based on Curie law is in the subplot. The parameters found are: k₄(−150°C) = (8.28 ± 0.09) × 10⁻⁵ A m² T⁻¹, k₄(−100°C) = (5.96 ± 0.07) × 10⁻⁵ A m² T⁻¹, k₄(−50°C) = (4.51 ± 0.06) × 10⁻⁵ A m² T⁻¹, k₄(0°C) = (3.21 ± 0.04) × 10⁻⁵ A m² T⁻¹, k₄(50°C) = (2.46 ± 0.02) × 10⁻⁵ A m² T⁻¹, all R² in k₄ fits higher than 0.997, and q₄ = (9.92 ± 0.48) × 10⁻³ A m² K T⁻¹, R² = 0.969. Mass of the magnetite solution (magnetite plus toluene) adhered to adhesive paper was m = 16 ± 1 mg and mass of dry magnetite was computed to be m₁ = 0.092 ± 0.007 mg.

The above-presented susceptibilities for 20°C and 37°C are not significantly different and may be transformed to various units. Estimations for 20°C are χ = 2.5 × 10⁻⁷ A m² mg⁻¹ T⁻¹ = 2.6 × 10⁻⁴ (SI, dim-less) = 0.31 × 10⁻⁶ m³ kg⁻¹ = 6.3 μ_B T⁻¹ per molecule for ferritin and χ = 3.7 × 10⁻⁴ A m² mg⁻¹ T⁻¹ = 1.7 (SI, dim-less) for magnetite (x_V = 8.4 nm), using the density of ferritin molecules of 1200 kg m⁻³ [33], mass of a single molecule is 2.4 × 10⁻¹⁶ mg [33] and their packing in corpuscles characterized by factor P = 0.7. The determined ferritin susceptibility is one order lower than that of the ferrihydrite as given in Pannalal et al. [25], which probably induces the diamagnetic effect of apoferritin, while susceptibility of magnetite coincides with the results previously presented, and is consistent with the theory. The intrinsic susceptibility of the superparamagnetic substance is theoretically χ_i = constant · x_V³ [17]. (Link to data files is presented in the Data accessibility section).

3.2. Magnetoreception hypotheses

Presence of ferritin cuticulosomes in the basilar papilla is of particular interest. The authors of a biological study suggested that they might be involved in magnetoreception and thus represent magnetosomes interacting with geomagnetic field [9]. This hypothesis is strongly supported by neurobiological studies on inner ear neurons [19,20]. Accordingly, some theoretical simulations with stable single domain magnetic crystals rotating under magnetic forces were done [4].

Based on histological data revealing magnetic corpuscles in cuticular plates of hair cells in avian inner ears, predominantly a single corpuscle per cell, two physical principles might explain the function of these hypothetic magnetosensors. The first is deformation of a cuticular plate via magnetically induced rotation/deformation of the corpuscles and the second is a corpuscle functioning as an intracellular electromagnetic oscillator.

Specifically, activation of magnetosomes of a certain region of a given (left or right) ear might, due to the frequency specialization of hair cells, the tonotopic principle, influence hearing by modifying activation, excitation or inhibition of hair cells in different regions of the basilar papilla. As a result of this phenomenon, the animal might perceive polarity of the magnetic field as a sound in a frequency-dependent tinnitus-like manner, or deviation from a certain compass direction might be perceived as disharmony in ‘magnetic tinnitus’ between both ears, or as a modification of a familiar sound perception. Thus, for instance sound of wings during flight might be subjectively perceived as being of different hearing colour depending on geomagnetic point or flight direction.

Composition of model corpuscles used in simulations. In subsequent simulations, the first model substance is ferritin, having the same magnetic properties as equine spleen ferritin experimentally described in this paper, containing a large amount of ferrihydrite. The second model substance is magnetite-rich ferritin designated as magnetite in figures. The corpuscles composed of magnetite-rich ferritin have magnetic properties as superparamagnetic magnetite presented in the experimental section. The possibility that corpuscles are magnetite-rich should not be excluded from our considerations, in spite of the fact that in bird hair cells only ferrihydrite corpuscles were observed. These magnetosensorically active magnetite-rich corpuscles might be present in ear hair cells in statistically hardly detectable frequency.

3.2.1. Simulations of magnetically induced rotation/deformation of corpuscles

It was assessed that forces exerted upon hair cell stereocilia of approximately 0.1 pN might already result in neuronal excitation [34]. Consequently, we may assume that if magnetosomes were able to develop such a force on cuticular plate, they could influence hearing sensation, and in this way provide the brain with information about direction or intensity of the geomagnetic field. In the first step of the hypothesis testing, the magnetically induced motion of isolated ferritin corpuscles should be simulated. In the literature, such magnetosomes are proposed to be connected with mechano-sensitive ion channels [35]. Alternative mode of action would be deformation of the cuticular plate mediating thus deflection of stereocilia. Thus, any marked motion reaction of cuticulosomes to geomagnetic field would indicate that these structures may function as magnetosensors and would call for advanced force-based analyses.

As mentioned above, in most cases a single ferritin cuticulosome per hair cell was observed in avian inner ears. Therefore, two modes of response of putative magnetosomes to the geomagnetic field should be considered: rotation and shape deformation. The translation motion through the cell is excluded since such motion depends on a magnetic field gradient [17]. Below, simulations of those motions are presented on the basis of the published histological data [9].

Rotation. Magnetic corpuscles composed of superparamagnetic ferritin molecules exhibiting paramagnetic magnetization cannot rotate in an external magnetic field since they have no remanent magnetization—they cannot serve as a component of a torque magnetoreceptor [36]. The remanence is demonstrated as hysteresis during magnetization. The mentioned rotation is typical of stable single domain magnetite organelles, such as those existing in magnetotactic bacteria [37–39]. The amplitude of force coming from rotation of a stable single magnetic domain crystal is F = 2M_S · x²B taking into account that mechanical moment equals magnetic moment. The least force on ear hair cell stereocilia that induces stimulation of ear neurons is at the level of 0.1 pN [34]. The geomagnetic field is sufficiently strong to generate such force acting on 20–120 nm sized magnetite in a stable single domain form. However, such crystals have not been observed in avian ears, in the ferritin corpuscles. Such rotations were indeed observed in the case of Fe-rich cells from trout olfactory epithelium [40]. In the case of superparamagnetic corpuscles only pseudo-rotation depending on level of their deformation can be expected, induced by relative rotation of a magnetic field around them.

Deformation. Although the cuticular plate is generally considered as a rigid plate, considering the ideally fluidic inner environment in cuticulosomes and their anchorage to the cuticular plate, their magnetically induced shape deformations can be computed. About 22% of cuticulosomes were membrane-bound, and therefore two kinds of their behaviour should be analysed: (i) corpuscle enclosed in isotropic lipid membrane and (ii) corpuscle without a membrane, where molecules are aggregated by interface tension between cell plasma and molecules in the corpuscle. The level of shape deformation can be determined from energetic minima of corpuscles, considering the volume V of the corpuscle as a constant for simplicity.

The energy components of a corpuscle are magnetic energy, interface energy γA for membrane/cell plasma or ferritin/cell plasma interfaces that are membrane-bound and non-bound cases, elastic energy of lipid membrane [41,42] and a pre-stress energy σ₀A₀ saved in membrane when corpuscle has a spherical shape, which is neglected in subsequent simulations (σ₀ ∼ 10⁻⁹–10⁻⁸ N m⁻¹) [43]. The magnetic energy of the corpuscle depends on the value of demagnetization factor L [44] and is derived from a well-known equation for the total magnetic energy of space E_space =−0.5∫_V B_tH dV [45], where B_t = B + B_i = μ₀(H + M) is the total magnetic induction, B_i = μ₀M is the internal (substance) magnetic induction and H (A m⁻¹) is the intensity of the external magnetic field. The extraction of paramagnetic substance energy results in E =−0.5 B_iHV =−0.5μ₀MHV, see Flament et al. [46], and leads to the forms displayed below in equations (3.1) and (3.2), since M = χH = χB/μ₀ and χ = χ_i/(1 + χ_iL). The elastic energy of isotropic lipid membrane may be derived as _A0∫^Aσ· dA = _A0∫^A(KΔA/A₀) · dA = 0.5 K(ΔA)²/A₀, where ΔA = A − A₀. Viscosity of the cell plasma does not influence the final deformation of a cuticulosome. However, it influences the speed of its deformation.

Similar analyses focused on magnetoreception were undertaken in a more general form in Winklhofer et al. [47], where the authors described magnetically induced deformations of superparamagnetic magnetite clusters in membrane-bound and non-membrane-bound corpuscles in elastic matrices, whereas Shcherbakov & Winklhofer [48] analysed osmotic effect and thermal fluctuations during such deformations, considering again corpuscles to be composed of superparamagnetic magnetite.

Deformation: membrane-bound corpuscles. The minimal elastic area expansion modulus of lipid bilayers presented in the literature is K ≈ 60 dyne cm⁻¹ = 0.06 N m⁻¹ [41]. Neglecting the interface energy, in the literature estimated to be of zero value for lipid bilayer/cell plasma interface [49], the energetic equation has the following form:

3.1

The simulations presented in figure 5 demonstrated that an induction of 0.02 T, which is a boundary value of a linear region in ferritin magnetization, slightly deforms the magnetite-rich ferritin. However, a magnetic field strength of 0.2 T, which is the boundary of a linear region in superparamagnetic magnetite magnetization, significantly deforms structures composed of magnetite-rich ferritin. The results show that geomagnetic field (50 µT) is very weak to cause corpuscle deformation.

Figure 5.

Simulations according to equation (3.1) of magnetically induced shape deformation of membrane-bound magnetic corpuscles, diameter of spherical corpuscles 600 nm, P = 0.7, membrane parameter K = 60 mN m⁻¹. The SI dimensionless intrinsic susceptibilities χ_i derived from above determined ones are 2.4 × 10⁻⁴ (ferritin) and 3.3 (magnetite). Under 0.02 T, 400 times stronger magnetic field than geomagnetic field, the deformation is a/b ≈ 1.15 for magnetite-rich ferritin and a/b ≈ 1 for equine spleen ferritin. The magnetite-rich corpuscles deform significantly under 0.2 T, energetic minimum being at a/b ≈ 2.2. (Online version in colour.)

Validity of equation (3.1) was evaluated according to measurement presented in Bacri et al. [50] (figure 6). The difference in energy minima between theory and experiment could be explained by variability in density of ferrofluid substance inside the membrane affecting the value of susceptibility, which results from notes in the study [50]. A small quantitative difference shows that equation (3.1) is likely to be valid. Similar magnetically induced shape deformations of membrane-bound magnetic ferrofluid were presented in Petrichenko et al. [43].

Figure 6.

Validity of equation (3.1) evaluated according to its comparison with experiment presented in Bacri et al. [50]. Parameters presented in the experimental paper are: determined susceptibility is χ(CGS) = 0.1, which we transformed to SI value χ_i = 2.2 for simulations using relations χ(SI) = 4 · π · χ(CGS) and χ_i = χ/(1 − χ/3), radius of spherical corpuscle is 9 µm and magnetic field equals 4 mT. Membrane parameter K is set to the lowest value of 60 mN m⁻¹ in order to match the experiment value as closely as possible. (Online version in colour.)

Deformation: corpuscles without membranes. Energetic equation for ferritin molecules aggregated by interface tension has the following form:

3.2

In simulations displayed in figure 7, the interface tension between ferritin and cell plasma was set to be 5 mN m⁻¹, which lies on the minimal boundary of generally known values for interface tensions, as no information about interface energy of such indeterminate systems is available. The magnetic field of 0.02 T is not able to deform ferritin corpuscles. The induction of 0.2 T, however, deforms the magnetite-rich ferritin markedly. The results show that geomagnetic field is very weak to cause corpuscle deformation.

Figure 7.

Simulations according to equation (3.2) of magnetically induced shape deformations of magnetic corpuscles without lipid membrane, formed by interface tension, sphere diameter of 600 nm. A very low model value of interface tension of 5 mN m⁻¹, see Flament et al. [46], was used to reach extreme deformation. The ferritin and magnetite-rich ferritin corpuscles are not deformed significantly under 0.02 T. The deformation of magnetite-rich ferritin under 0.2 T is a/b ≈ 2.5.

Validity of equation (3.2) was evaluated according to the measurement presented in Flament et al. [46] (figure 8). The results show small differences between the measurement and the theoretical calculation, which indicates that the simulations performed in this study are valid.

Figure 8.

Validity of equation (3.2) evaluated according to the experiment presented in Flament et al. [46]. In the experiment, the shape deformations of CoFe₂O₄ water-based ferrofluid droplets in oil were observed, non-membrane-bound clusters, interface tension 3.07 mN m⁻¹, χ_i = 2.2, at room temperature. The diameter of the spherical droplet is approximately 1.7 mm. (Online version in colour.)

3.2.2. Intracellular electromagnetic oscillator

Magnetic corpuscles are embedded in the cuticular plate and thus have to follow vibration motion together with the reticular lamina. Such effect is discussed in Lauwers et al. [9]. Primarily, presence of this iron-rich corpuscle can change normal vibration frequency of the system composed of tectorial membrane, stereocilia and cuticular plate, as Fe has relative atomic number 56. The new frequency is f = f₀(1 − Δm/m₀) as derived in the electronic supplementary material. This vibration of magnetized corpuscle having a magnetic moment w = χB_geoV/μ₀ has to generate electromagnetic induction and therefore induce additional AC electric potential on hair cell membrane, between its internal and external surface, or alternatively via eddy currents around cuticular plate and stereocilia, as presented in figure 9. The additional AC component, described by the Faraday law of electromagnetic induction by the relation u_i = −dΦ/dτ, is generated by non-stationary magnetic flux Φ flowing via hair cell wall. This effect must exist and its significance should be evaluated in spite of the fact that we do not know nanometric biological structures on the cell membrane where charges are distributed. This additional AC component of electric potential in afferent neurons may provide the brain with information about direction/intensity of the geomagnetic field, in a statistically significant manner. This hypothesis can be considered in the sense of experiments where mammalian cochlear hair cell potentials were measured [51]. These records show that inner hair cells stimulated by sinusoidal mechanical forces have sinusoidal AC potential during low frequency stimulation, and mixed DC/AC potential when exposed to high frequency stimulation. Physical analysis is presented in the electronic supplementary material. Simulation results show that a vibrating magnetite-rich corpuscle may really induce additional AC electric component in receptor cells and subsequently in auditory neurons, but its amplitude is only about 10 fV or 0.1 pV, where parameters are optimized to simulate the strongest electromagnetic effect (figure 10; electronic supplementary material).

Figure 9.

Intracellular electromagnetic oscillator. Normal rest potential of receptor cells is negative and amounts to several tens of mV. Hypothetic magnetosensor (ferritin corpuscle) modulates normal electric energy of receptor cell via electromagnetic induction generated by vibration motion of the cuticular plate. (Online version in colour.)

Figure 10.

Simulation of induced AC component of ear cell receptor electric potential for the four selected combinations of length parameters that are related to the position and vibration behaviour of corpuscles in the cells. In all simulations w = 7.6 × 10⁻¹⁸ A m² (corpuscle size 600 nm under geomagnetic field 50 µT) and external sound frequency is 10 kHz. (a) Z₀ = 4 µm, Δz = 4 µm and R = 3 µm, (b) Z₀ = 2 µm, Δz = 2 µm and R = 3 µm, (c) Z₀ = 0.5 μm, Δz = 0.4 μm and R = 3 μm, (d) Z₀ = 0.4 μm, Δz = 0.2 µm and R = 0.4 µm (optimized situation to simulate the strongest electromagnetic effect). (Online version in colour.)

Such electric energy u_iq_p related to single ion is significantly lower than Brownian noise k_BT. Therefore, it may hardly provide the magnetic map or compass information directly. Only an unknown intracellular amplifying mechanism could increase the u_i amplitude, and to be the missing mediator of such hypothetic magnetosensor. On the other hand, this principle working on the basis of sound energy modulated by electromagnetic energy seems to be simple and logical since the magnetic energy is directly transformed to the electric one in the nerve cell. For example, the existence of magnetite magnetosensors in the beak is considered to be connected with mechano-sensitive ion channels, where filaments connect the magnetic corpuscles with ion gates. However, this means that the elasticity of the filaments and ion gates has to consume a certain part of the magnetic energy. Owing to a very weak geomagnetic flux, nature may have preferred choosing the electromagnetic effect, not mechano-magnetic interaction, to provide magnetoreception more effectively. We are not able to understand whether the avian neuronal system is really connected to vibrating magnetic corpuscles via electromagnetic induction. However, our hypothesis is that magnetic compass/map information may be decoded from alternating u_i value, i.e. via colour of total electric auditory receptor potential u + u_i. This implies that birds might perceive the geomagnetic field via coloured hearing of a well-known sound generated by their own body.

4. Conclusion

The low-field magnetic susceptibility at physiological temperature of 37°C was determined to be (2.3 ± 0.5) × 10⁻⁷ A m² mg⁻¹ T⁻¹ for equine spleen ferritin and (3.5 ± 0.3) × 10⁻⁴ A m² mg⁻¹ T⁻¹ for superparamagnetic magnetite. These values are not significantly different from those under ambient laboratory temperature conditions, i.e. 20°C. Such ferritin magnetic corpuscles, as observed in avian inner ears [9], may function as magnetosensors. Two hypotheses describing their intracellular behaviour were discussed in the paper. The first one considers magnetically induced deformation of the cuticular plate, and the second one deals with a corpuscle functioning as an electromagnetic oscillator. Based on numerical modelling, using histological data, we conclude that ferritin corpuscles do not change their shape and orientation under a geomagnetic field, and therefore a mechano-magnetic function of cuticulosomes could be excluded. The hypothesis of an intracellular electromagnetic oscillator, composed of magnetite-rich ferritin located in the cuticular plate, seems to be more appropriate for subsequent considerations, in spite of the fact that such oscillators may generate maximal additional AC cell electric potential of only approximately 0.1 pV. This new hypothesis is analogous to older radical pair/cryptochrome hypothesis. Within radical pair/cryptochrome hypothesis the birds are able ‘to see’ the geomagnetic field. The energy from electromagnetic waves interacts via cryptochromes with the geomagnetic field. Within the hypothesis of ear electromagnetic oscillator the mechanical waves (sound) mediate the main source of energy and the additional electric potential from oscillator modulates the normal sound information. Do birds hear the magnetic field? We cannot answer this question based on the physical simulation presented in this paper. Only neurobiological or behavioural measurements could confirm or deny such a hypothesis.

Data accessibility

(1) zf.nazory.cz/ESM1.xls: figures 2, 3 and 4 (data, xls file). (2) zf.nazory.cz/ESM2.doc: corpuscle deformations (Matlab script, doc file)—adjustable simulation. (3) zf.nazory.cz/ESM3.doc: figure 10 (Matlab script, doc file)—simulation of u_i (AC). (4) zf.nazory.cz/ESM4.xls: additional file (MS Excel script)—simulation of effective u_i.

Funding statement

H.B. acknowledges support by the Grant Agency of the Czech Republic (project no. 506/11/2121).