Physical limits to magnetogenetics
There has been renewed interest recently in the effects of magnetic fields on biological cells . On the one hand we have the old puzzle of magnetosensation: How do organisms sense the Earth’s magnetic field for the purpose of navigation ? The biophysical basis for this ability is for the most part unresolved . On the other hand lies the promise of 'magnetogenetics': the dream of making neurons and other cells responsive to magnetic fields for the purpose of controlling their activity with ease . The two are closely linked , because uncovering Nature’s method for magnetosensation can point the way to effectively engineering magnetogenetics . The physical laws by which magnetic fields act on matter are taught to science students in college ( Feynman et al . , 1963 ) . Obviously those principles impose some constraints on what biological mechanisms are plausible candidates , for both magnetosensation and magnetogenetics . A recent spate of high-profile articles has put forward audacious proposals in this domain without any attempt at such reality checks . My goal here is to offer some calculations as a supplement to those articles , which makes them appear in a rather different light . These arguments should also help in evaluating future hypotheses and in engineering new molecular tools .
Generally speaking , magnetic fields interact only weakly with biological matter . The reason magnetic fields are used for whole-body medical imaging , and why they have such appeal for magnetogenetics , is that they penetrate through tissues essentially undisturbed . The other side of this coin is that evolution had to develop rather special mechanisms to sense a magnetic field at all , especially one as weak as the Earth’s field . This mechanism is well understood in just one case: that of magnetotactic bacteria ( Bazylinski and Frankel , 2004 ) . These organisms are found commonly in ponds , and they prefer to live in the muck at the bottom rather than in open water . When the muck gets stirred up they need to return to the bottom , and they accomplish this by following the magnetic field lines down . For that purpose , the bacterium synthesizes ferrimagnetic crystals of magnetite and arranges them in a chain within the cell . This gives the bacterium a permanent magnetic moment , and allows it to act like a small compass needle . The cell’s long axis aligns with the magnetic field and flagella in the back of the cell propel it along the field lines . It has been suggested that magnetosensation in animals similarly relies on a magnetite mechanism , for example by coupling the movement of a small magnetic crystal to a membrane channel ( Kirschvink et al . , 2001 ) . A competing proposal for magnetosensation suggests that the magnetic field acts on single molecules in certain biochemical reactions ( Ritz et al . , 2010 ) . In this so-called 'radical pair mechanism' the products of an electron transfer reaction depend on the equilibrium between singlet and triplet states of a reaction intermediate , and this equilibrium can be biased by an applied magnetic field . These two hypotheses and their respective predictions for magnetosensation have been reviewed extensively ( Johnsen and Lohmann , 2005; Kirschvink et al . , 2010 ) . On this background , a recent article by Qin et al . ( 2016 ) introduces a new proposal . As for magnetotactic bacteria , the principle is that of a compass needle that aligns with the magnetic field , but here the needle consists of a single macromolecule . This putative magnetic receptor protein was isolated from the fruit fly and forms a rod-shaped multimeric complex that includes 40 iron atoms . The authors imaged individual complexes by electron microscopy on a sample grid . They claim ( 1 ) that each such rod has an intrinsic magnetic moment , and ( 2 ) that this moment is large enough to align the rods with the earth’s magnetic field: “about 45% of the isolated rod-like protein particles oriented with their long axis roughly parallel to the geomagnetic field” . We will see that neither claim is plausible based on first principles: With the goal of controlling the activity of neurons , Wheeler et al . ( 2016 ) reported the design of a molecular system intended to couple magnetic fields to ionic current across the cell membrane . Their single-component protein consists of a putative mechano-sensitive cation channel ( TRPV4 ) fused on the intracellular face to two subunits of ferritin . The hope was that “the paramagnetic protein would enable magnetic torque to tug open the channel to depolarize cells” . Indeed , the report includes experimental results from several preparations suggesting that neural activity can be modulated by static magnetic fields ( There is a similar claim in Stanley et al . ( 2015 ) ; but the evidence is scant and hard to interpret: only 18 of ~2000 cells 'responded' ( their Supplementary Figure 10 ) ) . What could be the underlying biophysical mechanism ? Ferritin is a large protein complex with 24 subunits that forms a spherical shell about 12 nm in diameter . Wheeler et al . ( 2016 ) suppose optimistically that the two subunits of ferritin attached to the channel protein are able to nucleate an entire 24-subunit ferritin complex . The hollow core of this particle can be filled with iron in the form of a ferric hydroxide ( Arosio et al . , 2009 ) . At room temperature ferritin has no permanent magnetization: it is strictly paramagnetic or superparamagnetic ( Papaefthymiou , 2010 ) . Unlike the magnetite particles in magnetotactic bacteria , the iron core of ferritin is too small ( ~5 nm ) to sustain a permanent dipole moment ( blocking temperature ~40 K ) . Instead the direction of the Fe spins in the core fluctuates thermally . An external magnetic field biases these fluctuations , producing a magnetic moment m proportional to the field B of ( 7 ) m= ξB , where ξ is the magnetizability of a ferritin particle . This quantity can be derived from bulk measurements of ferritin magnetic susceptibility ( see Methods ) at ( 8 ) ξ=2 . 4×10−22JT2 . I will consider four scenarios by which such a ferritin particle might be manipulated with an external magnetic field . In the first , the magnetic field has a gradient , and the particle is pulled in the direction of higher field strength . In the second , the force arises from interactions among neighboring ferritins through their induced magnetic moments . In the third , the magnetic field exerts a torque assuming that the ferritin core is anisotropic , with a preferred axis of magnetization . Finally , the collective pull of many ferritins on the cell membrane may induce a stress that opens stretch-activated channels . For a different mode of activating membrane channels , Stanley et al . ( 2015 ) combined the expression of ferritin protein with that of the temperature-sensitive membrane channel TRPV1 . The hope was that a high-frequency magnetic field could be used to heat the iron core of ferritin , leading to a local temperature increase sufficient to open the TRPV1 channels , allowing cations to flow into the cell . Stanley et al . ( 2015 ) compared three different options for interaction between the ion channels in the plasma membrane and the ferritin protein: In one case the ferritin was expressed in the cytoplasm , in another it was targeted to the membrane by a myristoyl tail , and in the third it was tethered directly to the channel protein by a camelid antibody linkage . The direct one-to-one linkage between ferritin and ion channel worked best for generating Ca influx via high-frequency magnetic fields , leading the authors to conclude that “Because temperature decays as the inverse distance from the particle surface , heat transfer is likely to be most efficient for this construct , suggesting that heat transfer from the particle could be limiting the efficiency of the other constructs . ” Here I consider whether heat transfer from the ferritin particle is a likely source of thermal activation for the TRPV1 channel at all . Magnetic heating of nanoparticles is indeed a very active area of research ( Pankhurst et al . , 2003 ) . A sample biomedical application is to inject nanoparticles into cancerous tissue , and then damage the tumor selectively by magnetic heating ( Hergt et al . , 2006; Maier-Hauff et al . , 2011 ) . Typical nanoparticles of interest are made of magnetite or maghemite , sometimes doped with other metals , and measure some tens of nanometers in size ( Hergt et al . , 2006 ) . A typical heating apparatus for small preparations – like in the experiments of Stanley et al . ( 2015 ) – consists of an electric coil with a few windings , several centimeters in diameter , that carries a large oscillating current . The magnetic fields generated inside the coil are on the order of tens of kA/m at frequencies of several 100 kHz ( The literature sometimes refers misleadingly to heating by “radio waves” or “electromagnetic radiation” . At these frequencies the wavelength of a radio wave is about a kilometer , so of no practical relevance to the experiments . There is no radiation involved in the interaction between the solenoid coil and the nanoparticle ) . Owing to the small size of the nanoparticles , the physics of heating are quite different from the processes in our kitchen . A microwave oven heats water primarily by flipping molecular dipoles in an oscillating electric field . And an induction stove works by inducing electric eddy currents in the pot’s bottom with an oscillating magnetic field . Neither of these electric effects plays any role for nanoparticles . Instead the heat is generated purely by magnetic forces ( Hergt et al . , 2006 ) . Part of this comes from reorienting the magnetization of the material at high frequency , which is opposed by the particle’s magnetic anisotropy , causing dissipation and heat . For larger nanoparticles , the oscillating magnetic field may also make the particle move , with resulting dissipation from external friction in the surrounding medium . These physical processes have been modeled in great detail , and there is a large experimental literature to determine the heating rates that can be accomplished with different kinds of nanoparticles . A figure of merit is the “specific loss power ( SLP ) ” , namely the heating power that can be generated per unit mass of the magnetic material ( see Materials and methods ) . What sort of heating rate would we expect for the ferritin particles used by Stanley et al . ( 2015 ) ? Given the long-standing interest in ferritin for medical engineering ( Babincova et al . , 2000 ) , the extensive research on its magnetic properties ( Papaefthymiou , 2010 ) , and the ease with which magnetic heating can be measured , it is surprisingly difficult to find any published evidence for magnetic heating in ferritin . One report on the subject concludes simply that there is none: ferritin shells reconstituted with a magnetite core produced no measurable magnetic heating ( SLP < 0 . 1 W/g ) , whereas doping the iron with varying amounts of cobalt did produce some modest heating rates ( Fantechi et al . , 2014 ) . Why is native ferritin such a poor heater ? Both theory and experiment show that the efficiency of heating magnetic nanoparticles depends strongly on the particle size , and plummets steeply below 10 nm ( Fortin et al . , 2007; Purushotham and Ramanujan , 2010 ) . Magnetite particles smaller than 8 nm are not considered useful for magnetic hyperthermia ( Fantechi et al . , 2015 ) . The iron core of ferritin measures only 5–6 nm in diameter . Furthermore , the ferric hydroxide material in native ferritin has much lower magnetic susceptibility than magnetite ( ~8-fold , Zborowski et al . , 1996 ) . So , based on the literature , the heating rate for ferritin is too low to be measurable . Obviously this casts doubt on the claims of Stanley et al . ( 2015 ) that they activated ion channels through heating ferritin . For the sake of keeping the argument alive , and to evaluate potential future developments , let us instead suppose that ferritin could be engineered to produce a specific heating rate of ( 17 ) P=30Wg of metal This is the highest value obtained by filling the ferritin shell with cobalt-doped magnetite ( Fantechi et al . , 2014 ) and thus a generous estimate of what might be accomplished by future engineering of ferritin complexes inside cells . Assuming this specific heating rate , a single ferritin particle with 2400 iron atoms generates heat at a rate of ( 18 ) Q=7×10−18W This heat flux will produce a temperature gradient in the surrounding medium ( Figure 2 ) . As Stanley et al . ( 2015 ) state , the temperature indeed decays as the inverse distance r from the particle ( Feynman et al . , 1963 , Ch 12 ) , namely ( 19 ) T ( r ) =Q4πκ1r where ( 20 ) κ=0 . 61 Wm⋅K is the thermal conductivity of water . Right at the surface of the ferritin sphere the temperature increase is highest , namely ( 21 ) Tferritin=T ( 6 nm ) =1 . 5×10−10K This is a very tiny increase . Activation of a TRPV1 channel requires about 5 K of increase relative to body temperature ( Cao et al . , 2013 ) . So the temperature increase expected , even from a futuristic optimized ferritin , is more than 10 orders of magnitude too small . 10 . 7554/eLife . 17210 . 004Figure 2 . The steady-state temperature profile around a heated sphere in an infinite bath varies inversely with the distance from the center of the sphere . The same argument applies to a ferritin sphere heated from its magnetic core ( top ) and a spherical cell with a large number of heated ferritins on its surface ( bottom ) . DOI: http://dx . doi . org/10 . 7554/eLife . 17210 . 004 The assumption underlying Equation ( 19 ) is that thermal transport from the magnetic particle to the surrounding medium follows Fourier’s Law , in which the heat flux is proportional to the temperature gradient . This is a good approximation , as long as the length scales of the problem are large compared to the mean free path of the heat carriers , which are phonons in the current problem . In water , the phonon mean free path is ~0 . 3 nm , about the size of a water molecule ( Rabin , 2002 ) . Indeed , all the relevant dimensions are at least 10-fold larger than that , namely the size of the ferritin particle , the size of the ion channel protein , and the distance from ferritin to ion channel . One therefore expects that non-Fourier heat transport will make only small corrections to the above results , on the order of 10% or less ( Chen , 1996 ) . Another effect resulting from thermal physics at small scales is the thermal resistance to heat flow at the boundary between two materials . A given heat flux across the boundary will produce a discontinuous step in temperature between the two materials . How large is this step for heated nanoparticles ? Ge et al . ( 2004 ) followed thermal transfer between a metal nanoparticle with organic coating and the surrounding water , and observed a thermal conductance of ( 22 ) G=2×108Wm2⋅K , largely independent of particle size . With the heat flux produced by our ferritin particle the resulting temperature step would be ( 23 ) ΔTferritin=Q4πR21G=7×10−11K . Again , an exceedingly tiny contribution . It appears that there is no possibility of raising the temperature by several degrees near a single nanoparticle , even if the heating rate were 1000-fold higher . While there have been isolated reports of such magnetic heating effects near synthetic nanoparticles ( Huang et al . , 2010; Riedinger et al . , 2013; Piñol et al . , 2015 ) , they have met a good amount of skepticism . As has been pointed out repeatedly , there is no known physical mechanism for such an effect ( Rabin , 2002; Keblinski et al . , 2006; Gupta et al . , 2010 ) , and it has been suggested that the underlying methods of thermometry should be reevaluated ( Dutz and Hergt , 2013; 2014 ) . Moving on from single-particle heating one may ask whether the many other ferritins expressed on the same cell , though they are at greater distance , might contribute to heating the local environment . Suppose one can express Nferritins=10 , 000 TRPV1-ferritin complexes on the surface of a spherical cell with rcell=5μm radius . That is about 10-fold the natural expression level in sensory neurons . One can treat the heat production of those 10 , 000 ferritins as distributed evenly over the surface of the cell . Then the temperature gradient outside the cell again follows a 1/r profile ( Figure 2 ) . At the surface of the cell the resulting temperature increase will be ( 24 ) Tcell=Q Nferritins4π κ rcell=1 . 7×10−9K Unfortunately this is still too low by 9 orders of magnitude . So one cannot achieve activation of single neurons this way , which is of course a central goal of genetically expressed activators . Suppose now that one expresses this number of ferritin-TRPV1 complexes on every neuron in the brain . Would that perhaps be sufficient to heat the entire organ ? At that density , the heating rate per unit mass of brain will be ( 25 ) Pbrain=Q Nferritins43π rcell31ρbrain=1 . 2×10−4Wg , where ρbrain=1 . 03 g/cm3 is the specific density . For comparison , the resting metabolic rate of brain tissue is ~1 . 2×10−2 W/g , and the resulting heat is carried away and regulated by the processes that keep the organ’s temperature stable . Heating of ferritin throughout the entire brain would therefore contribute only a 1% increase to the heat already being generated from basal activity: this will not overwhelm the homothermic regulation mechanisms sufficiently to open TRPV1 channels . In summary , it seems very unlikely that the effects reported in Stanley et al . ( 2015 ) have anything to do with heating ferritin . The available evidence says that native ferritin produces no measurable magnetic heating at all . Even if we ignore that and assume a generous heating rate , namely the largest reported using a custom metal alloy for the ferritin core , the resulting effects are too small to matter by enormous factors of 1010 ( single-channel activation ) and 109 ( for single-neuron activation ) .
The calculations presented here evaluate the mechanisms that might underlie recent observations on a molecular compass ( Qin et al . , 2016 ) and neural activation with static magnetic fields ( Wheeler et al . , 2016 ) or high-frequency magnetic fields ( Stanley et al . , 2015 ) . These calculations show that none of the biophysical schemes proposed in these articles is even remotely plausible , and a few additional proposals were eliminated along the way . The forces or torques or temperatures they produce are too small by many orders of magnitude for the desired effects on molecular orientation or on membrane channels . If the phenomena occurred as described , they must rely on some entirely different mechanism . Barring dramatic new discoveries about the structure of biological matter , the proposed routes to magnetogenetics , based on either pulling or heating a ferritin/channel complex with magnetic fields , have no chance of success . One does have to ask why none of these authors attempted a back-of-the-envelope estimate to bolster the claims in their papers . Neither , it seems , did the referees who reviewed the manuscripts , nor the authors of three pieces that heralded these articles ( Leibiger and Berggren , 2015; Lewis , 2016; Lohmann , 2016 ) . Why is it important to do so ? First of all , claims that violate the known laws of physics often turn out to be wrong ( Maddox et al . , 1988 ) . There is , of course , always a small chance of discovering new physics , but only if one understands what the old physics predicts and recognizes the discrepancy . If any of the claims in these articles were substantiated – a room-temperature molecular magnet or measurable forces and heating from ferritin – their implications for our basic understanding of nanoscale matter would far outweigh their biological significance . More importantly though , calculations are most useful when done ahead of time , to guide the design of experiments . For example , Stanley et al . ( 2015 ) and Wheeler et al . ( 2016 ) evoke an image in which the magnetic field pulls on the ferritin particles . This is possible only if the magnetic field has a strong gradient ( Figure 1a , Equation 10 ) . None of their experiments on animals were designed to produce a strong gradient , nor do the articles report what it was . It is in fact possible to pull on cells that express lots of ferritin , and this has been exploited for magnetic separation ( Owen and Lindsay , 1983 ) . It requires very high magnetic fields , and separation columns with a meshwork of fine steel fibers that produce strong gradients on a microscopic scale . Inserting such a wire mesh into the brain would of course negate the goal of non-invasive control . Two other hypothetical mechanisms for the ferritin effects require a strong field but no gradient . This would be of great experimental value , because a homogeneous magnetic field could then deliver the same control signal throughout an extended volume , like the brain of a mouse . Among these , the dipole interaction between ferritins ( Figure 1b , Equation 14 ) offers little hope . Even with a 100-fold larger field ( 5 T ) , these forces are still 4 log units too small to open a channel . That field strength represents a practical limit: Small movements of the animal , or switching of the field , will cause inductive eddy currents that activate the brain non-specifically , a phenomenon experienced also by MRI subjects ( Schenck et al . , 1992 ) . On the other hand , exploiting anisotropy of the ferritin particle ( Figure 1c , Equation 15 ) may be within range of utility . A 100-fold larger field could produce torque comparable with the thermal energy , which when applied to thousands of channels might have a noticeable effect on membrane currents . To enhance the shape anisotropy of the magnetic particles , perhaps one could engineer the ferritin shell into an elongated shape . More fundamentally , it is clear that the weak effects computed here are a consequence of ferritin’s paramagnetism . A particle with a permanent magnetic moment , such as the magnetosomes made by bacteria ( Bazylinski and Frankel , 2004 ) , could exert much larger forces , torques , and temperatures ( Hergt et al . , 2006 ) , and may offer a physically realistic route to magnetogenetics . With an eye towards such future developments , it is unfortunate that these three questionable claims were published , especially in high-profile journals , because that discourages further innovation . Now that the prize for magnetogenetics has seemingly been taken , what motivates a young scientist to focus on solving the problem for real ? There is an important function here for post-publication peer review: It can make up for pre-publication failures and thus reopen the claimed intellectual space for future pioneers .
Central to the arguments about magnetogenetics is the proportionality factor ξ between the magnetic moment m of a single ferritin molecule and the magnetic field B , ( 26 ) m= ξB . Experimental measurements are usually performed on bulk samples of ferritin and report the magnetic susceptibility χ , defined by ( 27 ) M= χH=χB/μ0 , where M is the magnetization of the material , namely the magnetic moment per unit volume , and ( 28 ) μ0=4π×10−7NA2 is the vacuum permeability . Therefore ( 29 ) ξ=χρμ0 , where ρ is the number of ferritin particles per unit volume . In practice , we will see that the reported measurements of magnetization are more often normalized by the iron content of the sample or by the mass , rather than by volume . Then the choice of ρ must be adjusted accordingly . Table 1 summarizes some published measurements on magnetic heating of small nanoparticles with diameter below 10 nm . The loss power per unit mass ( SLP ) depends on the apparatus used for heating . Over the range of conditions considered here , a good approximation is that SLP varies proportionally to the frequency of the alternating magnetic field and to the square of the field strength ( Hergt et al . , 2004 ) . The table therefore corrects all the SLP numbers to the conditions used by Stanley et al . ( 2015 ) : field strength H=B/μ0=25 . 5kA/m and frequency f=465kHz . 10 . 7554/eLife . 17210 . 005Table 1 . Published measurements of specific loss power ( SLP ) for various magnetic particles of diameter d , taken at a magnetic field strength H and frequency f . The values in the column “SLP corr” are corrected for the field and frequency used by Stanley et al . ( 2015 ) . DOI: http://dx . doi . org/10 . 7554/eLife . 17210 . 005ReferenceMateriald [nm]H [kA/m]f [kHz]SLP [W/g]SLP corr [W/g]NotesFortin et al . ( 2007 ) Fe2O35 . 324 . 870042 . 8Fortin et al . ( 2007 ) Fe2O36 . 724 . 87001410Fortin et al . ( 2007 ) Fe2O3824 . 87003726Fantechi et al . ( 2015 ) Fe3O48121836 . 575Hergt et al . ( 2004 ) Fe2O37154101549Fantechi et al . ( 2014 ) ferritin with Fe3O4612 . 4183<0 . 01<0 . 1per mass of only the metal ionsFantechi et al . ( 2014 ) ferritin with Co0 . 15Fe2 . 85O46 . 812 . 41832 . 8130per mass of only the metal ions
This is an analysis of how magnetic fields affect biological molecules and cells . It was prompted by a series of prominent reports regarding magnetism in biological systems . The first claims to have identified a protein complex that acts like a compass needle to guide magnetic orientation in animals ( Qin et al . , 2016 ) . Two other articles report magnetic control of membrane conductance by attaching ferritin to an ion channel protein and then tugging the ferritin or heating it with a magnetic field ( Stanley et al . , 2015; Wheeler et al . , 2016 ) . Here I argue that these claims conflict with basic laws of physics . The discrepancies are large: from 5 to 10 log units . If the reported phenomena do in fact occur , they must have causes entirely different from the ones proposed by the authors . The paramagnetic nature of protein complexes is found to seriously limit their utility for engineering magnetically sensitive cells .
How biological systems interact with magnetic fields is of great interest both from a basic science perspective and for technological applications . Certain animal species can sense the Earth’s magnetic field for the purposes of navigation . How that compass sense works is perhaps the last true mystery of sensory biology . If we knew how the magnetic field affects the activity of nerve cells , we could harness that mechanism to create new biomedical tools . One technological goal is to genetically engineer specific cells in the brain or elsewhere so their activity can be controlled using an external magnet . This dream has been called “magnetogenetics” . In recent months a string of reports claimed to have solved both the scientific and the technological challenges of magnetogenetics . They all involved the discovery or the engineering of protein molecules that are sensitive to magnetic fields . Markus Meister has now checked whether those claims were consistent with well-established physical laws . For each case , Meister calculated how strongly the protein in question would link magnetic fields to cellular activity . The results show that the predicted effects are too weak to account for the reported measurements by huge margins: between five and ten orders of magnitude . It therefore appears that none of these reports have hit on a solution to magnetogenetics . All of the proposed proteins use iron atoms to couple to the magnetic field , but Meister concludes that these proteins contain far too few iron atoms . How safe is that conclusion ? There has been enormous technological interest in making tiny magnets; for example , to design the ever-denser data storage drives inside computers . Hence the magnetism of small clusters of atoms is exceedingly well understood . If any of the biological reports of magnetogenetics turned out correct , they would force a revolutionary rethinking of basic physics . With the recognition that magnetogenetics remains unsolved , and that different approaches are needed , Meister hopes that other investigators will feel motivated to continue innovating in this area .