3.1 Basics
Advantages and basic principles of using magnetic fields
In order to control E. coli remotely, we decided to use magnetic fields because of a few key reasons. First, magnetic fields allow to control the cells by an external force field which means that cells do not have to be directly treated or media conditions have to be changed as it is the case in many chemotaxis assays. Second, magnets are widely spread and electro magnets easily built as you can see in this video: https://www.youtube.com/watch?v=wzXRFp0DDrU The accessibility and safety of magnetic fields opens up the field for new innovation and ideas using remote controlled bacteria. Third, magnetic fields do have a high energy density and are way more viable to transfer energy than other energy fields like electrical fields. However, the magnetic moment of an atom is the product of of the atoms orbital angular momentum and its electron spins. Atomic magnetism is based on unfilled electron orbits. Nobel gases and alkyl halogenide are non-magnetic or “diamagnetic”. Other elements like metals may have an increased magnetic moment as long as their electron orbit are unfilled, meaning they are unbound. Mn2+, Fe3+ have a magnetic moment of about 5 µB, Cr2+, Mn3+, Fe2+ and Co3+ have a magnetic moment of 3 µB. [http://www.diss.fu-berlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivate_000000000626/2_f-Kapitel1.pdf?hosts=]
Because of the variety of atomar magnetic properties, magnetism can be divided into different forms by looking at apparent forces and effects. There is diamagnetism, antiferromagnetism, paramagnetism, ferrimagnetism, superparamagnetism and Ferromagnetism. Ferromagnetic forced are about 1000 times stronger than super paramagnetic forces. However, it turns out that creating ferromagnetic particels or residues is very difficult (see magnetite formation in magnetospirrilium bacteria). Also note that in a lot of biological papers, people tend to mix e.g. super paramagnetism with ferromagnetism [Various magnetic Nanoparticles Paper].
Magnetic properties are depended on the crystal structure of a metall particle. The magnetic moment is proportional to the aligment of the electron spins within an component. If electron spins are alignt magnetism can be observed. However on a nanoscale real ferromagnetism can only be noted after a critical particle size of 128 nm.[An-Hui Lu, An-Hui; E. L. Salabas; Ferdi Schüth (2007). "Magnetic Nanoparticles: Synthesis, Protection, Functionalization, and Application". Angew. Chem. Int. Ed. 46 (8): 1222–1244] This is due to thermal fluctations that prevent the alignment of electron spins and therefore prevent the development of sufficient magnetic moments. Because of this phenomena all meassurements for magnetism are usually conducted at very low temperatures.
All magnetic effects that are observed for particles between 1 nm to 100 nm are considered superparamagnetic. Superparamagnetic nanoparticles only show magnetic effects when an external magentic field is applied. This field aligns the electron spins in the particle resulting in an magnetic moment mediated by an external magnetic field. [Picture Atomarer Magnetismus]

3.2 Iron Homeostasis, E. coli Nissle and Knockouts
As an essential element for almost all life iron is often necessary for the activity of certain proteins but can also be problematic because of its toxicity and poor solubility. Organisms have evolved to regulate their iron effectively and as iron in an organism is usually supplied in a limited condition pathogens evolved iron aquisation systems to outcompete other microorganism. A very efficient iron aquisition system, which bacteria inlcuding E. coli use are siderophore mediated transport pathways. [Simon C. Andrews, Andrea K. Robinson, Francisco Rodriguez-Quinones; School of Animal and Microbial Sciences, University of Reading, Reading RG6 6AJ, UK; 2003] Iron E.coli Link

3.3 Ferritin Strategy
Ferritins as scaffolds for magnetic nanoparticle synthesis
In order to protect themselves against radical stress as well as the lack of co-factors, organisms evolved a high regulated and stable iron acquisition system, also known as iron homeostasis. [Iron Homeostasis of E. coli] To put it in a nutshell iron is taken up by iron transporters or siderophore mediated mechanism and is transporters through the outer membrane into the periplasm, in the periplasm it “changes” transporters and is transported through the inner membrane into the cytoplasm. It always gets released as Fe2+ into the cytoplasm. In order to protect themselves against superoxide formation by the Fenton-Reaction a lot of organisms evolved iron storage proteins. One of the superfamily of these proteins is called ferritin. These ferritins are highly symmertrical protein nanocages synthesizing iron concentrates required for cells to make cofactors of iron proteins. Through their ability to cage in biominerals they were the first and most obvious scaffolds for the synthesis of magnetic nanoparticles. These natural metal storage homomers form solid particles inside of their protein shell. Ferritins are ubiquitous in nature and protect the cell from redox stress through iron overload and from iron deficiency. They consist of 24 protein subunits which can consists of a heavy (catalytical active) and light chain (catalytical inactive but stabilizing). Caged ferritin minerals can have diameters as larg as 8-12 nm with thousands of iron and oxygen atoms. Between species ferritins have different affinity for phosphate. Phosphate is low in animal ferritin iron minerals (Fe:P = 8:1) whereas in bacterial and plant ferritins iron minerals are usually occurring in higher relations (Fe:P = 1:1).[1] Mössbauer studies on the superparamagnetic character of bacterioferritins (bfr) revealed that the phosphate concentration in a ferritin iron mineral reduces superparamegntic effects heavily due to replacement of the iron bridges between the iron atoms with phosphate. As these bridges have a lower exchange constant the order temperature is reduced further. [2] The hollow ferritin nanocages are used in the chemical industry as scaffolds for synthesis of magnetite particles as well as for delivery of magnetic resonance imaging (MRI) contrast agents, drug delivery and catalysis.
[1]
Ferritins for Chemistry and for Life.
Elizabeth C Theil, Rabindra K Behera, Takehiko Tosha Children's Hospital Oakland Research Institute, University of California, Berkeley ; Department of Nutritional Science and Toxicology, University of California, Berkeley. Coordination Chemistry Reviews (Impact Factor: 11.02). 01/2013; 257(2):579-586. DOI: 10.1016/j.ccr.2012.05.013
[2] Mössbauer studies of superparamagnetism in E. coli; Hawkins, C.; Williams, J. M. Journal of Magnetism and Magnetic Materials, Volume 104, p. 1549-1550

iGEM Berlin Ferritin Library
During our summer we collected a variety of ferritin-coding sequences from bacterial and mammalian sources. As ferritins are common among all organisms we categorized our ferritins in three major groups. (Table)

3.4 Inclusion body Strategy
By talking to the Fussenegger group from the ETH Zurich, who published the superparamagnetism paper about ferritins we got the tip to look for another strategy as they experienced the limitations of ferritins. [1] For this reason, we came up with a different strategy. Park et al came up with a different strategy for the synthesis of biogenic nanoparticles in E. coli. [2] A strategy where they produced impressive results showing one strategy to synthesize a whole array of diverse nanoparticles with E. coli. (See Figure 1) Two heavy metal binging proteins were combined and co-expressed on one plasmid. Peptides called phytochelatins are produced in fungus and plants to detoxify the cell from harmful heavy metals. Structurally phytochelatins are (gamma-Glu-Cys)n-Gly (n=2-7) peptides and function as metal ion accumulators through formation of peptide-metal conjugates. In this study the phytochelatin synthase from Arabidopsis thaliana (Columbia leave) was used (ATPCS). The other peptid that was used in combination with ATPCS was a metallothionein from Pseudomonas Putida KT2240 strain (PPMT). Metallothioneins are low-molecular proteins with a high content of cysteine and bind well cadmium, zinc, nickel and copper. For expression of ATPCS a trc promotor was used while PPMT was expressed using a T5 promotor. After co expressing both proteins in an standard E. coli strain(DH5alpha) for 4 h the culture broth was centrifuged and fresh metal rich LB media added. (1 – 5 mM of corresponding final metal concentration (see table 1.). After further incubation at 37°C for about 6 - 12 hours the cultures and the biogenic synthesized nanoparticles can be harvested. Park et al reported further that by incubating these ATPCS and PPMT co-expressing in 1.0 mM FeSO4 and MnCl2 magnetic nanoparticles where obtained and cell moved by high magnetic fields (see figure 2).

[1] Kim T, Moore D, Fussenegger M. Genetically programmed superparamagnetic behavior of mammalian cells. J Biotechnol. 2012 Dec 31;162(2-3):237-45. doi: 10.1016/j.jbiotec.2012.09.019. Epub 2012 Oct 2. PubMed PMID: 23036923.
[2] Park, T. J., Lee, S. Y., Heo, N. S. and Seo, T. S. (2010), In Vivo Synthesis of Diverse Metal Nanoparticles by Recombinant Escherichia coli. Angew. Chem. Int. Ed., 49: 7019–7024. doi: 10.1002/anie.201001524
[3] Wu CM, Lin LY. Immobilization of metallothionein as a sensitive biosensor chip for the detection of metal ions by surface plasmon resonance. Biosens Bioelectron. 2004 Nov 1;20(4):864-71. PubMed PMID: 15522603.

3.5 Magnetic modelleing
To test the supermagnetic behavior of our E.Coli containing iron-loaded ferritin, we placed strong permanent neodym-magnets N45 (1.32-1.37 T) under the petriglass and observed under light microscope the movement of the cells towards the magnets. After excluding contamination of magnetized particles outside the cell, we could conclude that our E.Coli. were successfully magnetized. In order to achieve the maneuverability of the cells, by controlling the magnetic fields, different geometries of electromagnets were tried. These consisted in the iron core of a microwave, metal rods and nails with different permeability with a corresponding coil. Pure iron is difficult to find. The magnetic force acting on the cells is proportional to its magnetic moment $\backslash mu$ and\; the\; gradient\; of\; the\; magnetic\; field$ \backslash nabla\; B$:$$
\pi=\frac{3}{4} \sqrt{3}+24 \int_0^{1/4}{\sqrt{x-x^2}dx}
\pi=\frac{3}{4} \sqrt{3}+24 \int_0^{1/4}{\sqrt{x-x^2}dx} Already with a magnetic field of 0.5T, the native ferritin is saturated (Gossuin et., 2009) and its magnetic moment is reported to be between 250 and 400<math>\mu_B<math> (Brem et al., 2006). Doing a Finite Element Analysis with the software Ansoft Maxwell for the gradient of the magnetic field of a simple electromagnet, rectangle with coil, we made the qualitative and already intuitive observation that the gradient was stronger at the edges. This was confirmed by the paper (Hoke, C. Dahmani et al., 2008) in which multiple possible magnet forms were simulated in order to maximize a high field Gradient. The simulation was performed with COMSOL. It was found that the best configuration for a higher gradient was a loop with a tipat one end and a flat surface at the other end. So the best and easiest option for our application should be a curved nail. The relevant equestions for the simulation were <math>\nabla x H=J<math> and <math>\nabla B=0<math> with the relation <math>B=\mu_0 \mu_r H <math>. The magnetic vector potential A produces the governing equation of the magnetostatics mode <math>\nabla x(\mu^{-1}\lambda x A-M)=J. It follows that the basic input parameters are the relative permeability of the magnet and the external current density. For the Comsol simulation in this paper an external current density of J of1.9e6 A/m^2 and a relative permeability of 4e3 (iron) were chosen. As a result, a B-field of 1.43T and a magnetic flux density directly under the magnet tip of 588mT could be reached. But this flux density drops rapidly with the distance. The field gradient for a distance of 1mm amounts 27.08T/m and for a distance of 2cm, only 10.37T/m. Because of this result we came to the idea of having many electromagnets under the petri glass in order to have a high gradient and consequently stronger magnetic forces over the whole area. In order to have an idea of the speed the cells can reach, we follow the derivation of the paper of Martin Fusseneger but use as upper boundary, the field gradient simulated in the paper above for 1mm, meaning 27.08T/m. The net force
<math>F_{net}=ma=F_{mag}-F_{drag}<math>
<math>F_{drag}=6\pi \nu R v<math> Where

(Hoke, C. Dahmani et al., 2008) Design of a High Field Gradient Electromagnet for Magnetic Drug Delivery to a Mouse Brain)