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J. Phys. Chem. C 2011, 115, 18–22
Heat Production by Bacterial Magnetosomes Exposed to an Oscillating Magnetic Field E. Alphande´ry,*,† S. Faure,‡ L. Raison,§ E. Duguet,§ P. A. Howse,| and D. A. Bazylinski| Institut de Mine´ralogie et de physique de la matie`re condense´e (IMPMC), UniVersite´ Pierre et Marie-Curie, UMR 7590, CNRS, 140 rue de Lourmel, 75015 Paris, Nanobacterie, SARL, 36 bouleVard Flandrin, 75016 Paris, and ICMB, UniVersite´ Bordeaux, CNRS, 87 aVenue du Docteur Albert Schweitzer, F-33 608 Pessac Cedex, France, and School of Life Sciences, UniVersity of NeVada at Las Vegas, 4505 Maryland Parkway, Las Vegas, NeVada 89154-4004, United States ReceiVed: May 19, 2010; ReVised Manuscript ReceiVed: NoVember 19, 2010
In this work, we examined mechanisms of heat production by whole intact cells of the magnetotactic bacterium Magnetospirillum magneticum strain AMB-1, as well as by their extracted chains of magnetosomes or extracted individual magnetosomes when exposed to an oscillating magnetic field of frequency 108 kHz and field amplitudes 23 and 88 mT. In this study, magnetosomes did not contain magnetite as the magnetite oxidized to maghemite. For intact bacterial cells that contain chains of magnetosomes, heat is generated through hysteresis losses, yielding specific absorption rates (SARs) of 115 ( 12 W/gFe at 23 mT and 864 ( 9 W/gFe at 88 mT. When the chains of magnetosomes are extracted from the bacterial cells and exposed to the same magnetic field, the heat-producing mechanism includes an additional contribution that is due to their rotation in the magnetic field. This contribution appeared to result in higher observed SARs of 864 ( 13 W/gFe at 23 mT and 1242 ( 24 W/gFe at 88 mT. SAR values of 529 ( 14 W/gFe at 23 mT and 950 ( 18 W/gFe at 88 mT were obtained with individual magnetosomes whose membranes had been removed. Introduction Magnetotactic bacteria are a unique group of mainly aquatic bacteria that biomineralize intracellular, membrane-bound, nanometer-sized, single-magnetic-domain crystals of the iron oxide magnetite (Fe3O4) and/or iron sulfide greigite (FeS4).1 These structures, called magnetosomes, are most often arranged as a chain within the cells. The bacteria appear to use the magnetosomes to navigate in the Earth’s geomagnetic field and help them to locate and maintain optimal conditions for their growth and survival.1 Over time, the magnetite in freeze-dried and frozen wet cells oxidizes to maghemite.2,3 Magnetosomes and magnetosome magnetite crystals have been shown to be useful in a number of scientific, commercial, and clinical applications.4 Recently, great efforts have been devoted to synthesizing magnetic nanoparticles for these reasons and because they can be easily manipulated using magnetic fields. Another interesting feature of magnetic nanoparticles is that they are able to induce the production of heat when an oscillating magnetic field is applied to them.5 These features have led to the idea that magnetic nanoparticles may be helpful in the destruction or elimination of tumors through hyperthermia or thermoablation or that they can be used to release drugs at specific localized regions of the body.5-10 Although significant progress has been made in this area, concerns have been raised regarding the toxicity induced by the presence of magnetic nanoparticles in the body.11 To minimize the potential side effects of magnetic nanoparticle-based clinical treatments, the quantity of nanoparticles administered needs to be as small as possible while still retaining their desired effect. For that, * To whom correspondence should be addressed. Email: edouardalphandery@ hotmail.com. † Universite´ Pierre et Marie-Curie. ‡ Nanobacterie, SARL. § Universite´ Bordeaux. | University of Nevada at Las Vegas.
magnetic nanoparticles have to generate a sufficiently large amount of heat, i.e., a significant specific absorption rate (SAR). This can be achieved by using magnetic materials with either large volumes or high magnetocrystalline anisotropy.12 Magnetosomes are among the largest single-magnetic-domain ferrite nanoparticles, making them good candidates for the applications mentioned above. Although magnetosomes have been shown to produce a large amount of heat when they are subjected to an oscillating magnetic field,13-15 this property has not been fully explained. In this paper, we provide a detailed study of the mechanisms of heat production by magnetosomes biomineralized by magnetotactic bacteria. The values of the magnetic field frequency (108 kHz) and magnetic field amplitude (23-88 mT) used to heat the different samples lie within the range of the magnetic field parameters used to carry out high-frequency, highamplitude AMF (alternative magnetic field) hyperthermia.16-18 For AMF hyperthermia, recommended magnetic field frequencies lie between 50 kHz and 1 MHz while the magnetic field amplitude needs to remain below 100 mT.19 We compare the heat-producing properties of three different types of magnetosome arrangements:2,20 (1) magnetosome chains within intact cells; (2) chains of magnetosomes that retained their magnetosome membranes extracted from cells; (3) individual magnetosome crystals whose magnetosome membranes have been removed. It is known that, for large ferromagnetic nanoparticles, there are two main heat-producing mechanisms. The first one is due to the physical rotation of magnetic nanoparticles in a magnetic field, and the second one is a result of hysteresis losses.21 To determine which of these mechanisms is responsible for heat production by the three different types of magnetosome arrangements mentioned above, we compare the heating rates of the samples in water, in which rotation of the cells and extracted magnetosomes is possible, with those present in a gel, where rotation is inhibited. In this way, the amount of heat
10.1021/jp104580t 2011 American Chemical Society Published on Web 12/13/2010
Heat Production by Bacterial Magnetosomes
J. Phys. Chem. C, Vol. 115, No. 1, 2011 19
Figure 1. Magnetic properties of intact cells of the magnetotactic bacterium M. magneticum strain AMB-1 containing chains of magnetosomes. (a) TEM of two cells of M. magneticum strain AMB-1 containing chains of magnetosomes. (b) Variation of the temperature of a suspension of intact magnetotactic bacterial cells as a function of time when the suspension is subjected to an oscillating magnetic field of frequency 108 kHz and magnetic field amplitude 23 mT. The black and red lines correspond to the suspension of cells in water (suspension) and in a 2% agarose gel (gel), respectively. (c) Minor hysteresis loops of the whole bacteria measured at 23 mT (squares) or 88 mT (line). (d) SAR of the intact cells measured at 23 and 88 mT (column bars). The blue box represents the contribution to the observed increases in temperature due to hysteresis losses.
generated by the rotation of the bacteria or extracted magnetosomes and that arising from hysteresis losses can be determined. To verify that heat produced in the gel is due to hysteresis losses, we measure hysteresis losses independently using magnetic measurements.
contribution to heat production (Supporting Information Figure 1b). For the measurements of the bacteria in the gel, there has been a loss of some of the bacterial cells during the preparation of the gel, yielding a lower concentration of magnetosomes (by a factor of 2.4) than in the other samples as verified by magnetic measurements. This loss has been taken into account to measure the SAR (Supporting Information Figure 1b). The values of the hysteresis losses have been further confirmed by measuring the areas of the minor hysteresis loops of the whole intact cells (Figure 1c). Using the method of Hergt et al.,14 we deduced from the areas of the minor hysteresis loops shown in Figure 1d that the hysteresis losses of the intact cells increased from 54 ( 6 W/gFe at 23 mT to 810 ( 17 W/gFe at 88 mT (Figure 1d). The estimates of the hysteresis losses deduced by the two methods described above were similar for most of the magnetic field amplitudes tested (88, 66, and 36 mT, Supporting Information table). They are only different at 23 mT. This difference can be explained by the fact that hysteresis losses cannot always be estimated by simply using continuous magnetic measurement as pointed out by other authors.22 Another possible explanation comes from the difficulty in estimating the slope ∆T/δT for such a small temperature increase as that observed for the bacteria in the gel and an applied magnetic field of 23 mT. This possibly yields an overestimate of the SAR for the bacteria in the gel at 23 mT. From these results, we conclude that the rotation of intact bacterial cells does not contribute to the production of heat in this case. Due to their large volume, intact cells of M. magneticum are not able to rotate sufficiently well under the application of an external magnetic field to generate heat. The absence of a contribution of the rotation can be confirmed by estimating the SAR due to the rotation of the bacterial cells, SARrot. The latter is estimated using the following equation:21,23
Results and Discussion Figure 1a depicts a transmission electron micrograph (TEM) of cells of Magnetospirillum magneticum strain AMB-1 showing typical chains of magnetosomes. The volume occupied by magnetosomes in a whole cell is rather small, typically ∼0.02%. An aqueous suspension containing intact whole cells of M. magneticum was subjected to an oscillating magnetic field of frequency ν ) 108 kHz and field amplitudes H ) 23 and 88 mT. The heating rates of cells suspended in liquid increased when the magnetic field strength was increased from 23 to 88 mT (Figure 1b and Supporting Information Figure 1a). From the slopes of the variations with time of the temperature measured at 22 °C (∆T/δT), we estimated the SAR of the intact cells suspended in liquid using the following equation:19
SAR ) Cwater
( ∆Tδt ) x1
(1)
m
where Cwater is the specific heat capacity of water (Cwater ) 4.184 J/(g · K)) and xm is the concentration of iron (g/mL of solvent (water)). Using the above formula, we deduced that the SAR of the whole bacterial suspension increased from 110 ( 6 to 864 ( 11 W/gFe when the magnetic field amplitude was increased from 23 to 88 mT. To determine whether the amount of heat (SAR) generated by the whole magnetotactic bacteria arises from the rotation of the whole bacteria, from hysteresis losses, or from both of these mechanisms, we measured the SAR of the cells fixed in agarose gel, which provide good estimates of hysteresis losses. These SARs are similar to those measured in solution, suggesting that hysteresis loss is the dominating
SARrot )
2 2 1 (MsHV) 1 1 (ωτb) 2 KbT FV τb 1 + (ωτ )2 b
(2)
In eq 2, ω ) 2πf, where f ) 108 kHz is the frequency of the oscillating magnetic field, Ms is the saturating magnetization of maghemite (Ms ) 390 emu/cm3), H is the amplitude of the applied magnetic field (23 mT < H < 88 mT), V ≈ 20 × 10-17 cm3 is the volume of a typical chain of magnetosomes,24 F ≈ 5 g/cm3 is the specific weight of maghemite, Kb ≈ 1.38 × 10-23 J/K is the Boltzmann constant, and τb ≈ 0.3 s is the Brownian relaxation time of an intact bacterial cell in water.23,24 Using these values, we find that SARrot lies between ∼1 and ∼20 W/gFe for values of H lying between 23 and 88 mT. These values are much smaller than the measured hysteresis losses, which are 115 ( 12 W/gFe at 23 mT and 864 ( 9 W/gFe at 88 mT (Supporting Information Figure 1b), where these SAR are averages between the SAR deduced from the heating rates of the bacteria in the gel and the SAR deduced from the heating rates of the bacteria in the solution. Thus, rotation of the whole bacterial cells can be neglected. Indeed, it does not appear to contribute by more than 3% to the observed increase in temperature. As indicated in Figure 1d, the SAR appears to be completely due to hysteresis losses. These losses become much more significant at higher magnetic field amplitudes (SAR ≈ 864 ( 9 W/gFe at 88 mT) than at 23 mT (SAR ≈ 115 ( 12 W/gFe). This finding, increased hysteresis losses with increasing magnetic field amplitude, has been previously observed for chemically synthesized magnetite nanoparticles.21 The SAR per cycle of the whole cells in suspension, which is defined as the
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Figure 2. Properties of the extracted chains of magnetosomes from cells of M. magneticum strain AMB-1. (a) TEM of extracted chains of magnetosomes. (b) Increase in temperature of the extracted chains of magnetosomes as a function of time in the presence of an oscillating magnetic field of frequency 108 kHz and field amplitude 23 mT. The black and red lines indicate the heating rate of the extracted chains of magnetosomes suspended in water (solution) or in a 2% agarose gel (gel), respectively. (c) Minor hysteresis loops of extracted chains of magnetosomes at 23 mT (squares) and 88 mT (line). (d) SAR of the extracted chains of magnetosomes measured at 23 and 88 mT (column bars). Blue and green boxes represent the contribution to the observed increases in temperature resulting from hysteresis losses and rotation of the chains of magnetosomes, respectively.
SAR divided by the frequency of the oscillating magnetic field, lies between 1.1 ( 0.1 and 8 ( 0.1 J/kgFe. These values are higher than most of those obtained with chemically synthesized magnetic nanoparticles, which typically lie between 0.001and 1.2 J/kgFe for a wide range of magnetic nanoparticle sizes and compositions as well as for a large choice of magnetic field frequencies and amplitudes.8,25-28 We conclude that the suspensions of whole magnetotactic bacteria produce a larger amount of heat than most of the chemically synthesized magnetic nanoparticles under our experimental conditions. Chains of magnetosomes were extracted from bacterial cells to presumably enhance their rotation in the magnetic field without the cell structure interfering with rotation. To verify that the magnetosomes were actually extracted from the bacteria and that they remained as chains, we used electron microscopy. Figure 2a shows typical assemblies of chains of magnetosomes2,20 which do not aggregate into clumps but are sufficiently close one to another as chains to be interacting magnetically. Heat production rates of the extracted chains of magnetosomes are shown in Figure 2b and Supporting Information Figure 2a for magnetic field amplitudes of 23 and 88 mT, respectively. In solution, they are characterized by a ∼43 °C increase over a time period of 1500 s at 23 mT (Figure 2b) and by a ∼48 °C increase over the same period of time at 88 mT (Supporting Information Figure 2a). These heating rates are much larger than those obtained with the whole cells (Figure 1b and Supporting Information Figure 1a). This suggests either that the extracted chains of magnetosomes produce larger hysteresis losses than intact bacteria cells or that their rotation in the oscillating magnetic field contributes to heat production or both. To discern which, if any, of these explanations is responsible for the greater heat production rates, hysteresis losses of the extracted chains of magnetosomes were determined. Figure 2c shows the minor hysteresis loops of the chains at 23 and 88 mT. The areas of the minor hysteresis loops for the extracted magnetosome chains were less than those obtained with the intact bacteria cells (Figure 1c). This decrease is likely due to magnetic interactions
Alphande´ry et al. between the chains of magnetosomes,2 and thus, we conclude that the higher heat production rate observed for the extracted chains of magnetosomes compared to the intact bacterial cells suspended in liquid is not due to an increase of hysteresis losses but to the rotation of the chains. The contribution of the rotation to heat production by the extracted chains of magnetosomes can be further confirmed by estimating the SAR of the extracted chains of magnetosomes suspended in liquid. We find that the latter increased from ∼864 ( 13 W/gFe at 23 mT to ∼1242 ( 24 W/gFe at 88 mT. These SAR values are larger than the hysteresis losses deduced from the SAR of the extracted chains in the gel (SAR ≈ 54 ( 5 W/gFe at 23 mT and SAR ≈ 487 ( 21 W/gFe at 88 mT). To confirm the contribution of rotation to the heat-producing mechanism of the chains of magnetosomes, we determined SARrot using eq 2, which factors in the Brownian relaxation time. This formula is only applicable below the saturating region, where the SAR shows a strong dependence on the field amplitude.21 Since saturation occurs above ∼36 mT (Supporting Information Figure 2b), we only measured the SAR at 23 mT. Using a Brownian relaxation time τB ≈ 1.5 × 10-4 s,20 we find that SARrot ≈ 2600 W/gFe at 23 mT, which is larger than the SAR of 810 ( 18 W/gFe we measured experimentally by measuring the difference between the SAR of magnetosome chains suspended in liquid (864 ( 13 W/gFe) and the SAR of magnetosome chains blocked within the gel (54 ( 5 W/gFe). The difference between the theoretical prediction and the experimental observation may be explained by the partial aggregation of the chains of magnetosomes. We conclude that the rotation contributes to the heating mechanism of the extracted chains of magnetosomes and that this contribution decreases from 93 ( 4% of the SAR at 23 mT to 60 ( 5% of the same SAR at 88 mT (Figure 2d). This decrease could be explained by the stronger enhancement with increasing magnetic field amplitude of the hysteresis losses than of the SAR due to the rotation of the chains of magnetosomes in the magnetic field.21 The last sample we tested was a suspension of extracted magnetosomes whose membranes had been removed using a combination of heat and a detergent that dissolved lipids, sodium deodecyl sulfate (SDS). These crystals do not remain in chains as shown in Figure 3a. These nanocrystals interact and organize within compact assemblies of individual nanocrystals,2,20,29 unlike the magnetosomes with membranes shown in Figure 2a. The heating rates of the liquid suspension containing these magnetosomes are shown in Figure 3b and Supporting Information Figure 3a for magnetic field amplitudes of 23 and 88 mT, respectively. They are lower than those observed for the extracted chains of magnetosomes suspended in liquid at both 23 and 88 mT (Figures 2b and 3b and Supporting Information Figures 2a and 3a). The difference in the solution heating rates observed between the chains of magnetosomes and the individual magnetosomes can be due to a difference in the contribution of the magnetosome rotation or hysteresis losses to the SAR or a combination of both. The hysteresis losses were estimated from the heating rates of the individual magnetosomes in the gel (Figure 3b), yielding SAR values lying between 270 ( 9 W/gFe at 23 mT and 427 ( 17 W/gFe at 88 mT. As for the intact bacterial cells and extracted chains of magnetosomes, the accuracy of these estimates is confirmed by the good agreement existing between the hysteresis losses deduced from the heating rates in the gel and those deduced from the area of the minor hysteresis loops (Figure 3c and Supporting Information Figure 3b). The hysteresis losses estimated above (Figure 3d, Supporting Information Figure 3b) are similar to those estimated for the
Heat Production by Bacterial Magnetosomes
Figure 3. Properties of extracted individual magnetosomes from cells of M. magneticum strain AMB-1. (a) TEM of an assembly of extracted individual magnetosomes. (b) Increase in temperature of the extracted individual magnetosomes as a function of time when an oscillating magnetic field of frequency 108 kHz and amplitude 23 mT is applied. The black and red lines indicate the variations in temperature of the individual magnetosomes suspended in water (solution) or in a 2% agarose gel (gel), respectively. (c) Minor hysteresis loops of the individual magnetosomes measured at 23 mT (squares) and 88 mT (line). (d) SAR of the individual magnetosomes measured at 23 and 88 mT (column bars). Blue and green boxes represent the contributions to the observed increases in temperature due to hysteresis losses and rotation of the chains of magnetosomes, respectively.
extracted chains of magnetosomes (Figure 2d, Supporting Information Figure 2b). Therefore, the difference in SAR observed between the extracted chains of magnetosomes and the individual magnetosomes suspended in liquid must result from a difference in the ability of the structures to rotate in the magnetic field. Conclusion In this study, we studied heat production by intact whole magnetotactic bacterial cells, extracted chains of magnetosomes, and extracted individual magnetosomes without membranes exposed to an oscillating magnetic field. The SAR of each of these three magnetic samples is larger than that reported for smaller superparamagnetic nanoparticles.8,25-28 The predominant contribution to heat production by the intact bacterial cells appears to be hysteresis losses, while physical rotation and hysteresis losses are both responsible for the generation of heat for the extracted chains of magnetosomes and individual magnetosomes. Experimental Section Preparation of the Samples. M. magneticum strain AMB-1 was purchased from the ATCC (ATCC 700274). Cells were grown anaerobically at room temperature (∼25 °C) in liquid culture under N2 gas in revised MSGM medium (ATCC medium 1653). Cells were harvested as described below at the stationary phase. The stationary phase occurred when the medium became completely reduced as indicated by a change in the coloration of the growth medium from pink to colorless. Three different types of samples were prepared from intact whole cells of M. magneticum. Cells were harvested at the stationary phase by centrifugation at 8000 rpm for 15 min. The supernatant (spent growth medium) was discarded, and the cells were resuspended in 3 mL of deionized water. For suspensions of whole intact cells, this sample was not treated further. To
J. Phys. Chem. C, Vol. 115, No. 1, 2011 21 extract the chains of magnetosomes, 1 mL of the cell suspension was recentrifuged and resuspended in 10 mM Tris · HCl buffer (pH 7.4) and then sonicated for 60 min at 30 W to lyse the cells, releasing the chains of magnetosomes. After sonication, the suspension of extracted chains of magnetosomes was magnetically separated by placing a strong magnet next to the tube, where the magnetic material collected as a pellet. The supernatant containing cell debris and other organic material was removed. The magnetosome chains were washed 10 times with 10 mM Tris · HCl buffer (pH 7.4) in this way and were finally resuspended in deionized water. Individual magnetosomes (not in chains) were obtained by heating the suspension of magnetosome chains for 5 h at 90 °C in the presence of 1% SDS in deionized water to remove the magnetosome membranes. Individual magnetosomes were washed as described for magnetosome chains and resuspended in deionized water. Characterization of the Samples. Samples were examined using a JEOL model JEM 1011 transmission electron microscope (JEOL Ltd., Tokyo) operating at 100 kV. A 5 µL volume of a solution containing 2 × 10-4% (by weight) magnetosomes was deposited on a carbon-coated copper grid, and the grids were allowed to dry before examination. The same relative quantity of magnetosomes was used to prepare all samples; thus, aggregation in a particular sample was not a result of a difference in the concentration of the magnetosomes. Magnetic measurements were carried out using a vibrating sample magnetometer (VSM; Quantum Design, San Diego, CA). For magnetic measurements, 25 µL of a liquid suspension of magnetotactic bacterial cells, extracted chains of magnetosomes, or extracted individual magnetosomes containing 2 × 10-3% (by weight) magnetosomes was deposited on top of a silica substrate. The samples were then positioned inside a capsule made of hard gelatin in a direction parallel to that of the magnetic field. Three types of magnetic measurements were performed, those of the saturating isothermal remanent magnetization (SIRM) and major or minor hysteresis loops. SIRM measurements were used to determine the composition of the magnetosomes following a method similar to that previously described2 and showed that the magnetite in the magnetosomes had been almost completely oxidized to maghemite. This result was not unexpected as our suspensions of magnetic material were not freshly prepared and magnetite in magnetosomes has been known to oxidize to maghemite over time.2,3 The fact that the magnetosome magnetite had transformed to maghemite does not substantially change the conclusions drawn in this paper since maghemite and magnetite have very similar magnetic properties at room temperature.2 Major hysteresis loop measurements were carried out at 300 K to determine the amount of maghemite contained within the samples. The latter is determined by dividing the saturating magnetization of the samples by the saturating magnetization of maghemite. For nanoparticles as large as the magnetosome crystals, the saturating magnetization is that of the bulk material (in this case bulk maghemite). Finally, measurements of minor hysteresis loops were also carried out by recording the magnetization of the samples as a function of a continuous magnetic field, which is applied between -H0 and +H0, where H0 is 23, 36, 66, or 88 mT. Heating Experiments. These experiments were carried out with the whole bacteria, extracted chains of magnetosomes, and extracted individual magnetosomes suspended either in ultrapure deionized water (18.6 MΩ) or in aqueous agarose gel (2% by weight). The concentration of maghemite was 457 µg mL-1 for the liquid suspension containing the whole cells, 435 µg mL-1 for that containing the extracted chains of magnetosomes, and
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380 µg mL-1 for that containing the extracted individual magnetosomes. A 250 µL volume of each of these three suspensions was poured into polypropylene tubes and positioned at the center of a coil producing an oscillating magnetic field of frequency 108 kHz, the field amplitude being fixed at 23, 36, 66, or 88 mT. To generate the alternating current, the coil was connected to a generator (Celes inductor C97104) and the temperature was measured using an optical fiber probe (Luxtron STF-2, BFi OPTiLAS SAS). Acknowledgment. We thank the French biotechtechnology company Nanobacterie, SARL, for its participation in this study. S.F. experimentally verified some of the results. E.A. designed all the protocols of the experiments and also carried out all the analyses of the data presented. D.A.B. showed E.A. how to cultivate magnetotactic bacteria. D.A.B. is supported by U.S. National Science Foundation (NSF) grant EAR-0920718. P.A.H. was the recipient of an award from the NSF Research Experience for Undergraduates (REU) program A Broad View of Environmental Microbiology at the University of Nevada at Las Vegas (Award NSF-0649267). Supporting Information Available: Figures showing the magnetic properties of intact cells of the magnetotactic bacterium M. magneticum strain AMB-1 containing chains of magnetosomes, the extracted chains of magnetosomes from cells of M. magneticum strain AMB-1, and extracted individual magnetosomes from cells of M. magneticum strain AMB-1 and a table giving the SAR values deduced for the different samples. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) For a comprehensive review on magnetotactic bacteria, see: Bazylinski, D. A.; Frankel, R. B. Nat. ReV. Microbiol. 2004, 2, 217–230. (2) Alphande´ry, E.; Ngo, A. T.; Lefe`vre, C.; Lisiecki, I.; Wu, L. F.; Pileni, M. P. J. Phys. Chem. C 2008, 112, 12304–12309. (3) Chen, T.; Xu, H.; Xie, X.; Chen, J.; Ji, J.; Lu, H. Earth Planet. Sci. Lett. 2005, 240, 790–802. (4) Arakaki, A.; Nakazawa, H.; Nemoto, M.; Mori, T.; Matsunaga, T. J. R. Soc. Interface 2005, 5, 977–999. (5) Duguet, E.; Mornet, S.; Vasseur, S.; Devoisselle, J. M. Nanomedicine 2006, 1, 157–168. (6) Ito, A.; Honda, H.; Kobayahi, T. Cancer Immunol. Immunother. 2006, 55, 320–328. (7) Ciofani, G.; Riggio, C.; Raffa, V.; Menciassi, A.; Cuschieri, A. Med. Hypotheses 2009, 73, 80–82. (8) Dutz, S.; Hergt, R.; Mu¨rbe, J.; Mu¨ller, R.; Zeisberger, M.; Andra¨, W.; To¨pfer, J.; Bellemann, M. E. J. Magn. Magn. Mater. 2007, 308, 305– 312. (9) Bae, Y.; Buresh, R. A.; Williamson, T. P.; Chen, T-H. H.; Furgeson, D. Y. J. Controlled Release 2007, 122, 16–23. (10) Hilger, I.; Wilfried, A.; Hergt, R.; Hiergeist, R.; Schubert, H.; Kaiser, A. K. Radiology 2001, 218, 570–575. (11) See, for example: Oberdo¨rster, G.; Oberdo¨rster, E.; Oberdo¨rster, J. EnViron. Health Perspect. 2005, 113, 823–839.
Alphande´ry et al. (12) Habib, A. H.; Ondeck, C. L.; Chaudhary, P.; Bockstaller, M. R.; McHenry, M. E. J. Appl. Phys. 2008, 103, 07A307-1-07A307-3. (13) Hergt, R.; Dutz, S.; Mu¨ller, R.; Zeisberger, M. J. Phys.: Condens. Matter 2006, 18, S2919–S2934. (14) Hergt, R.; Hiergeist, R.; Zeisberger, M.; Schu¨ler, D.; Heyen, U.; Higler, I.; Kaiser, W. A. J. Magn. Magn. Mater. 2005, 293, 80–86. (15) Timko, M.; Dzarova, A.; Kovac, J.; Skumiel, A.; Jozefczak, A.; Hornowski, T.; Gojzewsi, H.; Zavisova, V.; Koneracka, M.; Sprincova, A.; Stbak, O.; Kopcansky, P.; Tomasovicova, N. J. Magn. Magn. Mater. 2009, 321, 1521–1524. (16) Ivkov, R.; DeNardo, S. J.; Daum, W.; Foreman, A. R.; Goldstein, R. C.; Nemkov, V. S.; DeNardo, G. L. Clin. Cancer Res. 2005, 11, 7093s– 7103s. (17) DeNardo, S. J.; DeNardo, G. L.; Miers, L. A.; Natarajan, A.; Foremann, A. R.; Gruettner, C.; Adamson, G. N.; Ivkov, R. Clin. Cancer Res. 2005, 11, 7087s–7092s. (18) DeNardo, S. J.; DeNardo, G. L.; Natarjan, A.; Miers, L. A.; Foreman, A. R.; Gruettner, C.; Adamson, G. N.; Ivkov, R. J. Nucl. Med. 2007, 48, 437–444. (19) Mornet, S.; Vasseur, S.; Grasset, F.; Duguet, E. J. Mater. Chem. 2004, 14, 2161–2175. (20) Alphande´ry, E.; Ding, Y.; Ngo, A. T.; Wang, Z. L.; Wu, L. F.; Pileni, M. P. ACS Nano 2009, 3, 1539–1547. (21) Hergt, R.; Andra¨, W.; d’Ambly, C. G.; Higler, I.; Kaiser, W. A.; Richter, U.; Schmidt, H.-G. IEEE Trans. Magn. 1998, 34, 3745–3754. (22) Hergt, R.; Dutz, S.; Zeisberger, M. Nanotechnology 2010, 21, 015706. (23) In eq 2, we have assumed that the Brownian relaxation time, τb, is much smaller than the Ne´el relaxation time, τn, where τb ) 3ηV/KbT and τn ) τ0 exp(Ea/KbT). For the different samples, τb lies between 2.5 × 10-5 and 0.3 s (see ref 19). Given that τ0 ≈ 10-9 s and the ratio between the anisotropy energy of a chain of magnetosomes and the thermal energy, Ea/KbT, is ∼480 (see ref 2), we find that τn ≈ 3 × 1038 s and hence τb/τn ≈ ,1. This justifies the use of eq 2 to measure the SAR. (24) The Brownian relaxation times are estimated using the formula τb ) 3ηVh/KbT, where Vh is the hydrodynamic volume. For the whole magnetotactic bacteria, we estimate that Vh ≈ 0.4 × 10-18 m3 using Vh ) lr2, where l is the typical length of a bacterium (1.5 µm) and r is the typical width of a bacterium (0.5 µm). The flagella were not taken into account in this estimate since the bacteria are dead and are therefore not thought to take an important role in the movement of the bacteria in this case. For the chains of magnetosomes, the hydrodynamic volume is estimated as being the volume of a typical chain of magnetosomes, Vh ) NVmag ≈ 20 × 10-23 m3, where N ≈ 6 is the number of magnetosomes in a typical chain and Vmag ≈ 3.3 × 10-23 m3 is the typical volume of a magnetosome. For the individual magnetosomes, the hydrodynamic volume is estimated as being the volume of a typical magnetosome, Vh ≈ Vmag ≈ 3.3 × 10-23 m3. Using η ) 10-3 Pa · s and T ≈ 295 K, this yields τb ≈ 0.3 s for a whole bacterium, τb ≈ 1.5 × 10-4 s for an extracted chain of magnetosomes, and τb ≈ 2.5 × 10-5 s for an individual magnetosome. (25) Ma, M.; Wu, Y.; Zhou, J.; Sun, Y.; Zhang, Y.; Gu, N. J. Magn. Magn. Mater. 2004, 268, 33–39. (26) Jordan, A.; Rheinla¨nder, T.; Waldo¨fner, N.; Scholz, R. J. Nanopart. Res. 2003, 5, 597–600. (27) Brusentsov, N. A.; Gogosov, V. V.; Brusentsova, T. N.; Sergeev, A. V.; Jurchenko, N. Y.; Kuznetsov, A. A.; Kuznetsov, O. A.; Shumakov, L. I. J. Magn. Magn. Mater. 2001, 225, 113–117. (28) Chan, D. C. F.; Kirpotin, D. B.; Bunn, P. A. In Scientific and Clinical Applications of Magnetic Carriers; Ha¨feli, U., Schu¨tt, W., Teller, J., Zborowski, M., Eds.; Plenum Press: New York, 1997; pp 607-618. (29) Kobayashi, A.; Kirschvink, J. L.; Nash, C. Z.; Kopp, R. E.; Sauer, D. A.; Bertani, L. E.; Voorhout, W. F.; Taguchi, T. Earth Planet. Sci. Lett. 2006, 245, 538–5550.
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