Possible Magneto-Mechanical and Magneto-Thermal Mechanisms of Ion Channel Activation by Iron-Loaded Ferritin in Magnetogenetics

The palette of tools for stimulation and regulation of neural activity is continually expanding. One of the new methods being introduced is magnetogenetics, where mechano-sensitive and thermo-sensitive ion channels are genetically engineered to be closely coupled to the iron-storage protein ferritin. Such genetic constructs could provide a powerful new way of non-invasively activating ion channels in-vivo using external magnetic fields that easily penetrate biological tissue. Initial reports that introduced this new technology have sparked a vigorous debate on the plausibility of physical mechanisms of ion channel activation by means of external magnetic fields. I argue that the initial criticisms leveled against magnetogenetics as being physically implausible were possibly based on the overly simplistic and unnecessarily pessimistic assumptions about the magnetic spin configurations of iron in ferritin protein. Additionally, all the possible magnetic-field-based mechanisms of ion channel activation in magnetogenetics might not have been fully considered. I present and propose several new magneto-mechanical and magneto-thermal mechanisms of ion channel activation by iron-loaded ferritin protein that may elucidate and clarify some of the mysteries that presently challenge our understanding of the reported biological experiments. Finally, I present some additional puzzles that will require further theoretical and experimental investigation.


Introduction
Interaction of biological systems with magnetic fields has puzzled and fascinated the scientific community for a long time [1][2][3][4][5][6][7] . While experimental evidence for magnetic sense in animals seems uncontroversial, the mystery of biophysical mechanism of its action remains unresolved. Despite the challenges in deciphering the fundamental operating principles of magnetic control of biological ion channels/cells/organisms, the attraction of influencing biological systems with magnetic fields has remained strong. This is mainly due to the fact that external DC and AC magnetic fields easily penetrate biological tissue, are easily generated by current carrying wires or permanent magnets, and their properties and engineering design tools are well understood.
These features of magnetic fields are commonly used in medical diagnostics applications such as Magnetic Resonance Imaging (MRI) 8 , and there is a strong impetus to apply the same advantages of magnetic fields to control biological function, as is the case in Transcranial Magnetic Stimulation (TMS) 9 .
Coupling modern genetic engineering techniques with the magnetic fields to influence biological activity promises a particularly potent way to combine the strength of both methods in control of cellular function. This is the approach of a recent technique development, commonly termed magnetogenetics, where thermo-sensitive and mechano-sensitive ion channels are genetically engineered to be closely spatially coupled to the iron-storage protein ferritin [10][11][12][13] . Initial reports that introduced this new technology have received significant attention and commentary 14,15 , as well as considerable criticism 16 . The plausibility of presented mechanisms of mechanical and thermal ion channel has been challenged on physical grounds, and the present state of reported experimental observations in magnetogenetics and basic magnetic physics arguments that challenge those observations remain in conflict.
Here, I will present the case that the physical viability of magnetogenetics depends critically on many physical parameters of the basic control construct (iron-loaded ferritin protein coupled to the thermo-sensitive or mechano-sensitive ion channel in the cell membrane) that are presently not well known or understood, and therefore the physical possibility of magnetogenetics cannot yet be discounted and needs to be further explored. These critical parameters include the magnetism and magnetic spin configurations of iron atoms in the ferritin protein, as well as the realistic thermal, mechanical, and diamagnetic properties of ion channels and neural cell membranes coupled to the iron loaded ferritin. Additionally, I will argue that all the possible magnetic-field-based mechanisms of ion channel activation by iron-loaded ferritin in magnetogenetics might not have been fully considered. I will present and propose several new possible mechanisms of ion channel activation based on the magneto-caloric effect, mechanical cell membrane deformation by the diamagnetic force, and mechano-thermal Einstein-de-Haas effect. I will also discuss the fundamental magnetic moment fluctuations of the magnetic particle in ferritin and its presently unknown but potentially relevant effect on the ion channels in cell membranes.

Magnetism of Iron in Ferritin Protein
The fundamental genetically engineered construct in magnetogenetics, as reported by the original articles [10][11][12][13] , is shown diagrammatically in Figure 1. Thermo-sensitive or mechanosensitive ion channels of the TRP family of channels (TRPV1 and TRPV4) were genetically engineered to be closely spatially coupled to the novel chimeric iron-loading protein ferritin.
External DC or AC magnetic fields were applied to this construct in in-vivo experimental settings, and it was preliminarily concluded that thermal or mechanical magnetic effects were likely responsible for the observed biological responses, as was intended by the genetic engineering methods. Meister has argued 16 that the presently known magnetic force, torque, and heating mechanisms are many orders of magnitude smaller than necessary to activate ion channels and that the fundamental thermal energy, kBT, is much larger than the energy of any mechanism of magnetogenetics so far proposed. Meister's criticism is fundamentally based on his assumptions on the number of iron atoms (N=2400) in the ferritin protein and on the magnetic configuration in ferritin protein that assumes iron spins as a collection of independent non-interacting particles (paramagnetic configuration). Here I will explore what the physical consequences are if those assumptions are expanded to include reasonable and experimentally observed larger number of iron atoms in the ferritin protein 17 (N=4500) and spin configurations that allow for more strongly coupled iron spins within the ferritin core (ferromagnetic configuration).
It should first be recognized that magnetic properties of iron are notoriously structure sensitive 18 , and assigning the magnetic moment value to the iron atom between 0μB to 5μB (where μB is the Bohr magneton, μB=9.27x10 -24 Am 2 ) and spin coupling configuration (paramagnetic, ferromagnetic, ferrimagnetic, antiferromagnetic, etc.) is highly variable and chemistry dependent. Along the same lines, it should be pointed out that the systematic and complete analysis of magnetism of the iron loaded ferritin core in all the reported magneto-genetics articles has not been performed, and therefore the magnetism of the fundamental magnetogenetic ferritin construct is not presently known. It is generally believed that iron forms different mineral forms within ferritin (for example, magnetite Fe3O4 or maghemite ɣFe2O3). The original enhanced iron-loading chimeric ferritin, reported by Iordanova et al. 19 , was characterized only by NMR and MRI, and showed that one of the fused heavy H and light L subunits constructs (the L*H chimera) exhibited significantly enhanced iron loading ability. It is not clear from the Iordanova et al. report how many iron atoms are indeed loaded into the L*H chimera construct, what chemical structure iron forms in that construct, what the spin configuration of the iron atoms in that construct is, or if there is any shape or crystalline or other magnetic anisotropy in the L*H ferritin (as the magnetic moment vs. magnetic field or magnetic moment vs. temperature measurements or chemical crystal analysis were not reported). In my analysis I will use the commonly stated maximum possible number of iron atoms in ferritin N=4500 and assume atomic moment of mFe=5μB per iron atom (the highest value reported for iron in oxide from, Table 3.5 in Reference 18), with the understanding that the actual number of iron atoms in ferritin in all the magnetogenetics reports is not presently known. ferritin that I will consider as reasonable possibilities. Figure 2a represents N irons spins in a conventional paramagnetic state where all the spins are magnetically independent from one another and non-interacting. This is the configuration considered by Meister 16 . Figure 2c shows the case of ferromagnetic coupling between N iron spin where all the spins are strongly coupled by the magnetic exchange interaction and magnetically behave as a single macro-spin in what is commonly termed a superparamagnetic state of the magnetic particle 18 . In Figure 2b I consider a state that lays in between these two extremes. In this configuration the N iron spins are separated into n independent clusters of N/n exchange coupled spins, and I will call this spin configuration a clusterparamagnetic state. For simplicity of analysis, I will assume that all of the n magnetic clusters in this spin configuration of the particle have the same number N/n of iron spins, and that the magnetic moments of the clusters within the ferritin particle are magnetically independent (non-interacting). It should be clear that Figure 2b represents the most general spin configuration with n clusters of N/n spins in each cluster, while the paramagnetic state of Figure   2a is a special case with n=N and the superparamagnetic state of Figure 2c is a special case where n=1. I will assume the physiological temperature of T=37°C=310K throughout. The thermal average magnetic moment in external magnetic field B of a single cluster of N/n iron spins in the ferritin particle is classically described by the Langevin function 18 : , and the total thermal average magnetic moment mTOT of the ferritin particle along the field direction is: (2) Figure 3a shows the resulting ferritin particle magnetic moment vs. magnetic field at T=310K as a function of different cluster numbers and for the reasonable range of experimentally attainable laboratory magnetic fields (0 to 2 Tesla) generated by either electro-magnets, superconducting magnets, or permanent magnets.
It is immediately apparent that the assumption about the spin configurations of iron atoms in the ferritin particle has dramatic effects on the total magnetism of the particle. For the paramagnetic ( Figure 2a) spin arrangement of the particle (n=N=4500, light blue curve in Figure 3a) the magnetic susceptibility is low, and as an example, the total magnetic moment of the particle at a representative field of 1 Tesla is m=2.4x10 -22 (Am 2 ), in line with the numbers presented by Meister 16 . However, for the superparamagnetic (Figure 2c) spin arrangement of the particle (n=1, black curve of Figure 3a), the particle moment saturates at relatively low magnetic fields, well below 1 Tesla, where the magnetic moment has the value of m=2x10 -19 (Am 2 ), three orders of magnitude higher than for the paramagnetic state. This is the classic superparamagnetic particle behavior 20 where N=4500 spins are uniformly exchange coupled and act as a giant single paramagnetic spin. The other curves in Figure 3a show the magnetic moment for the clusterparamagnetic spin configurations (Figure 2b Figure 3a). In the present analysis, the saturation magnetic moment of a superparamagnetic particle of 4500 iron atoms with moments of 5μB per atom is mTOT = 22500μB = 2.1x10 -19 (Am 2 ) which is very much in line with the numbers in experiments reported by Bulte et al. 21 and Moskowitz et al. 22 indicating that the superparamagnetic state of iron-loaded ferritin is indeed possible. It is also instructive to consider the saturation magnetization MS of magnetite in my calculation by dividing the particle saturation moment mTOT by the volume V of the 8nm diameter particle (MS=mTOT/V) which results in MS=7.8x10 5 (A/m). Commonly reported bulk magnetite magnetization is slightly lower at MS=4.8X10 5 (A/m) 18 , but it should be noted that several independent experimental reports [23][24][25] indicate that magnetite magnetization increases significantly in the size range below 10nm and reaches the value of MS=1X10 6 (A/m). Therefore, my value of MS=7.8X10 5 (A/m) for 8nm diameter ferritin particle of N=4500 iron spins with 5 μB per iron atom falls well within the experimentally reported range for magnetite.

Force and Torque on Iron-Loaded Ferritin
It is instructive to reconsider the possible forces in magnetogenetics on a superparamagnetic ferritin particle (and therefore on the mechano-sensitive ion channel) and compare it to the paramagnetic ferritin particle case presented by Meister 16 . In the most optimistic case where the particle is for example at the entrance to the bore of a superconducting MRI magnet, where the magnetic field gradient could be on the order of ∇B=50 (T/m), the force on the paramagnetic ferritin would be on the order of ‫ܨ‬ = ݉ • ‫ܤ∇‬ =10 -20 (N), while the force on the superparamagnetic particle would be on the order of F=10 -17 (N). The minimum required force to mechanically activate ion channels 26 is on the order of 1pN=10 -12 N. Therefore, the conclusion by Meister 16 remains valid that the force from an externally applied magnetic field gradient on iron loaded ferritin, even the superparamagnetic one, is too low to be effective.
However, the situation is entirely different when one considers the mutual attractive force between two iron loaded ferritin particles that are both in a superparamagnetic spin configuration, as shown diagrammatically in the inset of Figure 3a. In a reasonable external magnetic field of 1 Tesla, both ferritin particles will be magnetically saturated, as Figure 3a shows.
For 8nm diameter (radius r=4nm) ferritin particle, the maximum magnetic field gradient on the surface of the particle is: and has an enormous value of ∇B=4.9x10 8 (T/m), much larger than anything achievable with external laboratory magnetic field gradients. Such a large magnetic field gradient from one ferritin particle acting on the second ferritin particle (and therefore on the mechanosensitive ion channels coupled to the ferritin particles) results in the maximum possible force on the order of 10 -10 (N)=100(pN), well above the required level for activating an ion channel. Therefore, if the construct reported by Iordanova et al. and used by magnetogenetics reports is similar in its magnetism or even more enhanced than what was reported by other superparamagnetic ferritin results of Bulte et al. 21 and Moskowitz et al. 22 , then there is at least the theoretical plausibility that the two ferritin particles pulling on each other could result in a sufficient force to activate mechano-sensitive ion channels to which the ferritin particles are coupled. Figure 3b shows the interaction energy magnitude (E=m·B) of the iron loaded ferritin configurations of Figure 2 in the external magnetic fields between 0-2 Tesla. On the same semilog plot I indicate the thermal energy level at the physiological temperature of T=310K, kBT=4.28x10 -21 (J). As Meister has pointed out for the paramagnetic ferritin particle 16 (n=4500 light blue curve in the plot) that interaction energy is lower than kBT. However, it is interesting that even for modest clustering of N=4500 iron spins into say n=450 clusters of N/n=10 exchange coupled spins each (n=450 dark blue curve in the plot) the interaction energy of the particle rises above kBT in a reasonable laboratory field of 1 Tesla. The magnetic energy diagram of Figure 3b is interesting in that the maximum theoretically possible torque on an anisotropic ferritin particle, as Meister has pointed out 16 , can easily be evaluated since torque Γ Ԧ = ݉ ሬሬԦܺ‫ܤ‬ ሬԦ . Therefore, there is in principle a theoretical possibility that an external magnetic field can exert a sufficient torque on an anisotropic ferritin particle (on the order of 10 -19 N·m in a 1 Tesla external field) to activate mechano-sensitive ion channels.

Diamagnetic Force on Ion Channel from Iron-Loaded Ferritin
In addition to the external forces on the iron loaded ferritin (and therefore on the coupled mechano-sensitive TRP ion channel) due to externally applied magnetic fields and field gradients, I now consider a case that to my knowledge has not been previously considered: the force due to the magnetic fields and field gradients from the ferritin particle itself on the intrinsically diamagnetic mechano-sensitive ion channel and neural cell membrane. I argue that this diamagnetic repulsive force could be sufficient to mechanically deform the ion channel and affect its function, as I diagrammatically describe in Figure 4.
Diamagnetism is generally considered the feeblest forms of known magnetism 18,27 , but it can have surprising and dramatic mechanical effects on biological materials (most of which are diamagnetic), such as levitation 28,29 or restriction of water flow 30,31 , if the sufficient and necessary conditions of high magnetic fields and field gradients are present. The diamagnetic force per unit volume on a diamagnetic material is 29 : It is apparent that the critical parameter for generating appreciable force on a material with diamagnetic susceptibility χ is the product of the magnetic field and the magnetic field gradient ‫ܤ‬ሺ‫ݎ‬ሻ∇‫ܤ‬ሺ‫ݎ‬ሻ. In laboratory settings at the edge of a superconducting magnet bore this parameter can have values on the order of 10 3 (T 2 /m) 29 .
I now consider what the value of this parameter is at the location of the ion channel/cell membrane that is closely coupled to the superparamagnetic ferritin particle, as shown in Figure   4a. In an externally applied uniform magnetic field of 1 Tesla the superparamagnetic particle magnetic moment will be saturated (as shown in Figure 3a), and the ion channel in cell membrane will experience the total combined magnetic field from the saturated magnetite particle Bparticle and the external magnetic field B. The magnetic field on top of the saturated 8nm diameter magnetite particle in my model is: and the total maximum field seen by the ion channel and cell membrane is 1.65 (T). The ion channel in the cell membrane will also be under the influence of the particle gradient magnetic field of 4.9X10 8 (T/m). This results in the critical parameter in the diamagnetic force calculations of ‫01‪=8.1x‬ܤ∇ܤ‬ 8 (T 2 /m), many orders of magnitude larger than anything available in the common laboratory settings 29 . This combination of magnetic fields and magnetic field gradients from the ferritin particle will generate a repulsive diamagnetic force on the ion channel/cell membrane, as shown diagrammatically in Figure 4b. It is particularly intriguing that the diamagnetic repulsive force from the ferritin particle is exerted on the mechanosensitive ion channel in a neural cell membrane which is mechanically extremely soft 32 . The consensus that is emerging from the mechanical properties of ion channels and cell membranes experiments [33][34][35] is that neural cells appear to have extremely low Young's modulus, E, on the order of E=100 (Pa), the lowest of any known materials. The final parameter in the diamagnetic force equation (4) is the diamagnetic susceptibility χ of the ion channel and the cell membrane. It is reasonable to assume that this number is similar to that of water 18 , on the order of χ=-1x10 -5 , but one should not dismiss the possibility that ordered lipid cell membrane domains could have an order of magnitude higher value of diamagnetic susceptibility 36,37 .
Estimating the resulting deformation of the ion channel and cell membrane, as shown in Figure   4b, due to the diamagnetic force of Equation 4 is extremely difficult, as both the magnetic fields and the magnetic field gradients from the magnetite particle are extremely spatially varying in both direction and magnitude. However, preliminary 3D finite element modeling of the cell membrane deformation using the listed magnetic, mechanical, and diamagnetic parameters for the ferritin construct and the cell membrane in my model gives the estimate that the deformation d in Figure 4b is on the order of ~1nm (I thank Richard Smith for performing the numerical computer finite element modeling of this effect). Such deformation represents a significant volume fraction change of the overall cell membrane thickness of ~5nm, and is highly likely to modify the functional properties of mechano-sensitive ion channel in magnetogenetics.

Magneto-Caloric Effect in Iron-Loaded Ferritin
In addition to the forces and torques that could possibly affect mechano-sensitive ion channels in magnetogenetics, heating of iron loaded ferritin by AC magnetic fields has also been considered as one of the mechanisms for thermo-sensitive ion channel activation and argued by Meister to also be implausible. I now consider a thermal mechanism that to my knowledge has also so far not been considered for the clusterparamagnetic spin arrangement in magnetogenetics: the DC magneto-caloric effect in the iron-loaded ferritin particle on the thermo-sensitive ion channel.
Magneto-caloric effect refers to the heating and cooling of magnetic materials by DC magnetic fields 18 . It is fundamentally based on the physical principle that an ensemble of magnetic spins in zero magnetic field is fluctuating and therefore maximally randomized and in a high entropy state.
Upon application of a polarizing magnetic field the magnetic spins align in the field which lowers the entropy of the spin ensemble. In an adiabatic process where there is no exchange of heat with the environment, this change in spin ensemble entropy has to be compensated for by the exchange of energy between the spin ensemble and the lattice, resulting in the change of temperature of the sample. This process of magnetic adiabatic cooling has been used in low-temperature physics for a long time 38 to obtain milliKelvin temperatures in paramagnetic salt powders and sub-milliKelvin temperatures with nuclear spins in metals 39 . Although such magnetic adiabatic energy transfers are generally performed only at cryogenic temperatures, McMichael et. al. 40 have pointed out that this process can be potentially performed at higher temperatures if the spins are coupled into superparamagnetic clusters (such as I diagrammatically show in Figure 2b). In fact, these authors have shown that, for a given magnetic field B and temperature T, there is an optimum clusterparamagnetic size that will generate maximum entropy change and energy transfer from the spin ensemble to the lattice. This hypothesis seems to have been experimentally confirmed 41,42 . Here I investigate the magneto-caloric energy transfer values for the specific case of clusterparamagnetic iron loaded ferritin ( Figure 2) with N=4500 iron atoms with 5μB atomic moments at a physiological temperature of T=310K and reasonable laboratory magnetic fields.  Figure   6 shows the numerical calculation results for that magneto-caloric energy change in N=4500 iron atom ferritin particle as a function of the number of clusters n in the particle at physiological temperature of T=310K and several reasonable magnetic field values. As McMichael et al. 40 have shown, for a given magnetic field B and temperature T there is an optimum clusterparamagnetic size that will generate maximum entropy change and energy transfer to the lattice. For example, for physiological temperature of 310K and magnetic field change of 1 Tesla (black points in Figure   5), the ferritin particle with N=4500 iron spins that separate into n=15 equal clusters of N/n=300 exchange coupled spins in each cluster will provide the maximum energy transfer to the lattice.
In the same plot I show the thermal energy kBT level that reveals the interesting features in this analysis. For the paramagnetic spin state of the ferritin particle (N=n=4500) no value of magnetic field is sufficient to achieve magneto-caloric particle energy change near the level of kBT. However, if the ferritin particle of N=4500 iron spins clusters into n=100 (or fewer) clusters of N/n exchange coupled spins each, the magneto-caloric energy transfer from the spin ensemble to the lattice at physiological temperatures and reasonable laboratory magnetic fields is higher than the kBT level, including for the superparamagnetic state (Figure 2c, n=1 point in Figure 6). It is not clear how this magneto-caloric energy transfer from the clusterparamagnetic spin ensemble to the thermosensitive or mechano-sensitive ion channel could occur for channel activation, but the energy scales in the magneto-caloric process indicate that it is theoretically feasible.
It might well be, as pointed out by Meister 16 , that this amount of energy transfer localized to the single ferritin particle is not sufficient to locally heat up the thermo-sensitive ion channel.
However, it may also be that, as discussed by Keblinski et al. 43 , a large number of iron-loaded ferritin particles expressed throughout the neural cell membrane generate a global temperature rise (on a longer timescale) that is orders of magnitude larger than the negligible short timescale temperature rise adjacent to a single iron-loaded ferritin protein.

Einstein-de Haas Effect on Iron-Loaded Ferritin
I now present another potential magneto-mechanical mechanism, the Einstein-de Haas effect 44,45 , that appears feasible in iron-loaded ferritin and that to my knowledge has not been previously considered for possible ion channel activation. It is a fundamental tenet of quantum mechanics that magnetic moment m of a particle is proportional to mechanical angular momentum L of that particle: m=ɣL where ɣ is the gyromagnetic ratio ɣ=e/me for spin angular momentum of iron (where e is charge of the electron and me is mass of the electron 18 ). The  , the mass of the 8nm diameter particle is mass=1.4x10 -21 (kg), and the energy transferred to the magnetite particle by the rotational motion imparted by the magnetic moment reversal is ∆E=0.33x10 -21 (J). This rotational kinetic energy of the magnetite particle due to the Einstein-de Haas effect has to eventually transfer to the lattice through friction.
It is important to note that the resulting rotational energy of 0.33x10 -21 (J) by a single magnetite particle moment reversal (one half of the applied AC magnetic field cycle) is a significant fraction of kBT=4.28x10 -21 (J). It is interesting to compare this value to the maximum energy loss per cycle of 1 (J/kg) typically reported for magnetic hyperthermia applications 50,51 . For the Einstein-de Haas effect presented here, this value for a full single cycle is 2·∆‫/ܧ‬mass=0.47(J/kg). Therefore, it would appear that the Einstein-de Haas effect should be considered on par with the typical Brown and Néel relaxation modes in magnetic particle hyperthermia [52][53][54] in contributing to the sample heating. As was the case for the magneto-caloric effect, it is not yet known how this Einstein-de Haas magneto-mechanical process would transfer energy to the thermo-sensitive and mechanosensitive ion channel for activation, but the energy scales in this process are again very close to kBT.
This entire analysis of the Einstein-de Haas magneto-mechanical frictional heating for a magnetite particle inside the ferritin protein was predicated on the assumption that the magnetite particle is free to move inside the protein cage, a condition that to my knowledge is not presently known.
So one should also consider the situation in which the spherical magnetite particle is fixed inside the ferritin protein and cannot freely rotate. In this situation the change in magnetic moment direction of the magnetite particle from +m to -m which results in the change of the mechanical angular momentum L of the particle from +m/ɣ to -m/ɣ now has to impart a torque on the surrounding medium Γ = ∆ ∆௧ , where ‫ݐ∆‬ is the time of reversal of the magnetite particle magnetic moment. A reasonable value to assume for the time of the moment reversal is ‫ݐ∆‬ =1(nsec), which results in the torque of 2m/(ɣ·∆‫ݐ‬ሻ=2.4x10 -21 (N·m) per half cycle of the applied AC magnetic field.
The energy scale of this torque is again in the same range as kBT=4.28x10 -21 (J). How this Einsteinde Haas torque would be transferred to the mechano-sensitive ion channel for activation is unknown and remains to be theoretically and experimentally explored.

Magnetic Moment Fluctuations of Iron-Loaded Ferritin
I finally discuss a topic that also appears not to have been previously considered, which is the effect of superparamagnetic ferritin particle magnetic moment fluctuations and its potential effect on the ion channels. As discussed earlier, for a superparamagnetic spin arrangement ( Figure   2c) of the ferritin particle, the magnetic field near the particle surface (Figure 4a) is relatively large at 0.65 Tesla. This field from the particle is not static, but is in fact fluctuating rapidly in time 55,56 , as I show schematically in Figure 8a. The frequency of this fluctuation at physiological temperature is significant and estimated to be in the GHz frequency range. Such superparamagnetic moment fluctuations have been experimentally observed 57 , even on a single particle scale at low temperatures [58][59][60] . Therefore, the ion channel in the vicinity of the iron loaded ferritin experiences large magnetic field gradients and Tesla-scale magnetic fields at GHz-scale frequencies, as well as the corresponding GHz frequency diamagnetic forces and torques, as       Upon application of external magnetic field in (b), the clusterparamagnetic moments align with the field and have low entropy. In the adiabatic process this change in spin entropy is compensated for by the exchange of energy between the spin ensemble and the lattice. For a given magnetic field B and temperature T, there is an optimum clusterparamagnetic size that will generate maximum entropy change and energy transfer. Figure 6. Magneto-caloric energy change for N=4500 iron atom ferritin particle as a function of the number of clusters n at a physiological temperature T=310K and several applied magnetic field values. For a given applied magnetic field B and temperature T there is an optimum clusterparamagnetic size that will generate maximum entropy change and energy transfer to the lattice. No value of applied magnetic field is sufficient to achieve magneto-caloric energy change above kBT for a paramagnetic ferritin (n=4500). However, grouping of the spins into exchange coupled clusters achieves magneto-caloric energy changes above the kBT level.