A Possible Inductive Mechanism for Magnetogenetics

13 Reports of genetically conferred sensitivity to magnetic stimuli have preceded plausible mechanistic 14 explanations. Frequently, these experiments rely on a fusion of ferritin with a transient receptor potential 15 vanniloid channel protein, speculating associated mechanical or thermal cues. However, it has been 16 argued compellingly that the small magnetic moment of ferritin precludes these possibilities. Here, we 17 offer an alternative hypothesis based on stochastic resonance that does not require appreciable 18 interaction of ferritin with the applied field. Rather, we suggest that ferritin might act merely as a 19 localized source of high frequency inductive noise on the membrane. When combined with externally 20 applied time-varying fields, this noise might help surmount the activation threshold of endogenous 21 voltage-gated ion channels. To explore this concept, we use the stochastic Landau-Lifshitz-Gilbert 22 equation to model magnetization dynamics and compare the magnetic field noise resulting from ferritin 23 and from a 15 nm magnetite particle. 24

The broadly recognized usefulness of optogenetics and chemogenetics for enabling targeted 2 actuation of neurons has spurred interest in development of an analogous "magnetogenetic" technique. 3 Triggering activity via wireless, invisible, and facile magnetic stimuli in transfected neuronal 4 subpopulations holds obvious appeal, and reports describing conferred sensitivity to magnetic fields TRPV family is known to trigger calcium influx in response to mechanical and thermal cues, magnetic 9 interactions with ferritin have been presumed to be a source of similar effects (Barbic, 2019). However, 10 cogent critique has cast doubt on these speculated mechanisms (Meister, 2016). The interaction of 11 ferritin with attainable magnetic fields is far too weak for mechanical actuation, hysteresis heating of 12 ferritin is demonstrably negligible, and even if extraordinary heat flow were to occur, local temperature 13 increase is not expected (Anikeeva & Jasanoff, 2016;Davis et al., 2020;Keblinski, Cahill, Bodapati, 14 Sullivan, & Taton, 2006). With an identified and tested mechanism, magnetogenetics could become a 15 tool that can be used confidently and further optimized. 16 To help bridge this explanatory gap, here we suggest a potential mechanism applicable to 17 excitable cell types expressing voltage gated ion channels. It accounts for actuation with inductively 18 coupled stochastic resonance, mediated by ferritin localized on the cell membrane. Counterintuitively, 19 ferritin may actually be better suited to this purpose than larger magnetite particles. To show this, we 20 consider how the interaction of ferritin with a neighboring voltage-gated ion channel, in combination 21 with a time-varying magnetic field, could plausibly serve to open these channels. We identify 22 experiments that could test this hypothesis and consider possible implications if it were found to be 23  Nevertheless, magnetic characterization of ferritin spans nearly eight decades and can at least inform 30 reasonable bounds for expected behavior (Michaelis, Coryell, & Granick, 1943). Ferritin consists of a 31 protein shell with an outer diameter of approximately 12 nm that surrounds a biomineralized core with 32 diameter 5.5 to 6.0 nm in humans, ranging up to about 8 nm in mollusks (Chasteen & Harrison, 1999). 33

Results and Discussion
The size and crystallinity of human ferritin is comparable to ferritin derived from horse spleens, which 34 is often studied. The core consists primarily of ferrihydrite with an approximate stoichiometry 35  In the hypothesis offered here, we suggest a mechanistic role for this superparamagnetism that 10 shifts focus away from the thermal and mechanical sensitivities that have dominated the discussion and 11 instead consider interaction with voltage gated ion channels ( Figure 1a). Although voltage 12 responsiveness has been observed in the TRPV family, interaction with endogenous ion channels gated 13 at lower voltages could be more relevant (Nilius et al., 2005). A recent response from Wheeler et al. (1) The key relevant input quantities, and , can be estimated from data collected on various ferritin 33 preparations. In the interest of putting the proposed mechanism on firmer footing, values can be selected 34 from a reasonable range that tend to bound or mitigate the relevant effects.
for superparamagnetic 1 particles typically ranges from 100 fs to 1 ns (Kilcoyne & Cywinski, 1995), and although values on the 2 order of 1 to 10 ps have been fitted for ferritin (Dickson et al., 1993;Kilcoyne & Cywinski, 1995), here 3 we conservatively take 1 ns. Reported blocking temperatures seem to depend on preparation and 4 characterization method. Although a blocking temperature of about 12 K seems most likely and is 5 consistent with low temperature magnetization measurements (Dickson et al., 1993;Kilcoyne & 6 Cywinski, 1995; Makhlouf et al., 1997), we have assumed the higher reported value of 40 K because 7 increased anisotropy should also tend to mitigate the hypothesized effect (Chasteen & Harrison, 1999). tangentially to the membrane would induce transmembrane voltage noise (Figure 1c). Estimating the 12 order of magnitude of this / noise at the center of the ion channel, we find: 13 Figure 1. Conceptual illustrations. a) A transgenic TRPV channel protein incorporating a ferritin unit is expressed in the membrane, perhaps occurring near to any one of a variety of voltage-gated ion channels endogenously present in excitable cells. b) At top, the expected field magnitude versus distance is shown assuming a moment of 300 µB for ferritin. At bottom, the rate of change of the field is mapped for a macrospin model with conservative assumptions for kinetically limited reversal. c) A schematic illustrates why the component of the field changing tangentially to the membrane is most relevant to transmembrane potentials. d) The components that might enable inductively coupled stochastic resonance are represented pictorially. At left, the voltage gated ion channel represents a biphasic system that responds to applied potentials, including those induced by time varying fields. In center, a subthreshold stimulus is provided by an externally applied time-varying field. At right, noise is supplied by the fluctuation or precession of one or more ferritin magnetic moments. high frequency / noise with a magnitude relevant to the typical threshold of actuation (Figure 1d). 20 The most appealing feature of stochastic resonance in this case is that it does not require ferritin to 21 interact with the applied magnetic field at a scale comparable to . Rather, the voltage induced by the 22 applied magnetic stimulus itself could supply energy for reconfiguring the channel, and the noise 23 generated by ferritin could merely aid in surmounting the kinetic barrier setting the threshold of 24 actuation. 25

Modelling Magnetic Fluctuation and Precession in Ferritin and Comparing to Magnetite 26
An intriguing feature of this hypothetical mechanism is its implication that ferritin may have 27 features that make it better suited to magnetogenetic stimulation than magnetic nanoparticles with large 28 magnetic moments. As illustrative examples, we have selected ferritin and a 15 nm magnetite particle 29 with a 2.5 nm polymer or silica shell. Using the stochastic Landau-Lifshitz-Gilbert (sLLG) equation to 30 describe both precession and the influence of thermal agitation (Figure 2a), we model the dynamical 31 behavior of a single particle and infer tangential at various locations near the particle (Figure 2b) 32 (Brown, 1963;Usov, 2010). Notably, this noisy signal has an additional high frequency contribution 33 from precession, and a low pass filter reveals behavior arising from kinetically limited reversal. Full 1 details of this simple model can be found in the supplementary materials. Simplified geometric assumptions for calculating the component of the field tangential to the membrane are shown explicitly for both a ferritin and the 15 nm magnetite particle. d) Standard deviation of tangential / noise for simulations of 6 × 10 steps each are shown for a range of applied quasimagnetostatic fields. The raw noise is dominated by the influence of precession. e) A low pass filter set at 10 GHz for ferritin and 1 GHz for magnetite was applied to the same noise data represented in panel d), and tangential / noise was calculated to show the applied field dependence of noise originating from stochastic reversal. f) The additive effects of noise from two adjacent non-interacting ferritins (bottom) is considered. The fold increase in the standard deviation of the noise signal is shown for two points. The first is at the center of the membrane and equidistant from the two ferritins and the other assumes similar geometry to panel c.)

1
Despite possessing a moment nearly 300 times weaker than the 15 nm magnetite particle, this 2 model predicts that ferritin can nevertheless act as a comparable source of tangential / noise. If 3 channel dynamics or other considerations make the timescale of kinetically limited reversals most 4 relevant to actuation, ferritin may even act as a better source of noise than a 15 nm magnetite particle at 5 applied fields above 100 mT (Figure 2e). Moreover, particles suitable for applying torques to 6 mechanosensitive channels would typically have larger moments or require higher anisotropy, further 7 reducing their capacity for rapid fluctuation. 8 In Figure 2f, we consider additive effects in adjacent sources of tangential / noise. At a 9 point equidistant from each source, both filtered and unfiltered noise increase by a factor approaching 10 √2, an expected result for the addition of two sources of uncorrelated noise with the same amplitude. 11 The effect drops off with distance such that nearest neighbor contributions are most relevant. 12 13

Experiments to Test this Hypothesis 14
Although we have endeavored to frame this hypothesis as realistically as possible, we emphasize 15 the need for further inquiry and direct experimental evidence. In this spirit, we suggest several ideas for 16 experiments that could test various aspects. Observing GCaMP fluorescence to monitor neuronal response, the endogenous threshold of 28 wild type inductive actuation could be determined. By comparing to neurons expressing 29 abundant magnetogenetic proteins, this experiment could measure the extent to which the 30 / threshold is lowered upon transfection. 31 32 3. To probe the mechanistic role of ferritin, it might be feasible to influence its dynamics with 33 fields applied simultaneously with a / stimulus. If the frequency components of the 34 noise arising from stochastic reversal are ultimately most important, then a superimposed 1 magnetostatic field of sufficient magnitude (greater than 2 T, Figure 2e) might be used to 2 suppress inductive noise. If noise arising from precession is more important, the system 3 could instead be driven with a microwave frequency electromagnetic field corresponding to 4 the ferromagnetic resonance frequency of the ferritin. If either of these approaches resulted 5 in quantifiable changes in the / threshold required for magnetogentic actuation, it 6 would not be well explained by other proposed mechanisms (Barbic, 2019). 7

Conclusion 8
Inductively coupled stochastic resonance as a mechanism for stimulation is appealingly Competing interests 26 None to declare. 27 * Although natural occurrences such as lightning strikes can generate strong transient magnetic fields, the evolutionary context of natural magnetoreception seems to be centered on navigation in the weak geomagnetic field.