M 106

LC-MS instrumentation consisted of a breadboard Evosep One coupled to an LTQ Orbitrap for the more than 2000 HeLa injection experiment, and the Evosep One production version coupled to an Q Exactive HF-X Orbitrap (Thermo Fisher Scientific) for all other experiments. Purified peptides were separated on the HPLC columns with 3 μm Reprosil-Pur C18 beads (Dr. Maisch, Ammerbuch, Germany) and dimensions indicated below in Fig. 6B. On the LTQ Orbitrap MS, data were acquired with a Top6 data dependent shotgun method and with a Top12 method for the Q Exactive HF-X instrument. On the Q Exactive HF-X Orbitrap, the target value for the full scan MS spectra was 3 × 10⁶ charges in the 300–1650 m/z range with a maximum injection time of 50 ms and a resolution of 60,000 at m/z 200. Fragmentation of precursor ions was performed by higher-energy C-trap dissociation (HCD) with a normalized collision energy of 27 eV (24 (link)). MS/MS scans were performed at a resolution of 15,000 at m/z 200 with an ion target value of 5 × 10⁴ and a maximum injection time of 25 ms. Dynamic exclusion was set to 15 s to avoid repeated sequencing of identical peptides.

Twenty 3-4-month-old wild boar piglets were bought in a commercial farm known to be free of mycobacterial lesions at slaughter and with a fully negative ELISA test [35] (link). The animals were housed in class III bio-containment facilities where they had ad libitum food and water. Wild boar piglets were randomly assigned to one of four treatment groups: Group 1, unvaccinated controls; Group 2, parenterally vaccinated with heat-inactivated M. bovis; Group 3, orally vaccinated with heat-inactivated M. bovis; Group 4, orally vaccinated with live BCG. Oral vaccines were delivered in baits designed for wild boar piglets [36] (link). For the challenge, 5 ml of a suspension containing 10⁶ colony forming units (cfu) of an M. bovis field strain were administered by the oropharyngeal route as described in previous experiments [17] (link), [37] (link).
The animals were handled nine times during the experiment, including the vaccination (T1, day 1), the challenge two months after vaccination (T2, day 60), and the necropsy four months after challenge and six months after vaccination (T3, day 189). In addition to T1, T2 and T3, blood samples were taken at days 8, 21, and 49 post-vaccination (p.v), and after challenge at days 74, 83, 104 and 133 p.v.
Handling procedures and sampling frequency were designed to reduce stress and health risks for subjects, according to European (86/609) and Spanish laws (R.D. 223/1988, R.D. 1021/2005). The protocol was approved by the Committee on the Ethics of Animal Experiments of the Regional Agriculture Authority (Diputación Foral de Vizcaya, Permit Number: 2731-2009).

The experiments were conducted as the methods described in our prior studies^{5 (link),16 (link),17 (link)}. The period when the distant primary tumor grew was deemed the pre-metastatic phase. The metastatic phase was defined as the period after the intravenous (i.v.) injection of tumor cells into tumor-bearing mice. Synergistic tumor grafts were generated through subcutaneous (s.c.) or mammary fat pad (m.f.p.) implantation of 5 × 10⁶ tumor cells into 8 to 10-week-old mice. We injected tumor cells into mice with growing primary tumors of the same size (size-matched). For the tumor cell homing assays, 1–2 × 10⁴ fluorescent dye (PKH26, Sigma-Aldrich, St. Louis, MO, USA)-labeled metastatic cells were i.v. infused into the mice. At 24–48 h after tumor cell infusion, the lungs were perfused with phosphate-buffered saline (PBS) under physiological pressure to remove circulating tumor cells and then excised. Four to five randomly selected lung tissue fragments (3 mm in diameter) were chosen, and three 10 μm sections per fragment were evaluated using a confocal microscope (SP8 Leica, LSM-710, Carl Zeiss MicroImaging GmbH, Germany) or a fluorescence microscope (BZ-9000, Keyence, Osaka, Japan). The labeled tumor cell counts were normalized to the total tissue surface area. Age- and sex-matched mice were used for the experiments.

We provide an analytical model to show that disassembling an assembly pair using a large external magnet is very unlikely. We first consider a simple case, and then we generalize the case for more complex configurations.
In the simple case, we fix one NdFeB assembly magnet (1.2 × 1 × 0.5 mm) where its center position is at the origin of the Cartesian coordinate system (x = y = z = 0). Its dipole position points toward the positive x direction ( ${\mathbf{x}}_1={\left[\mathrm{0,\; 0,\; 0}\right]}^T$ with magnetic dipole moment ${\mathbf{m}}_1={\left[m_1,\mathrm{0,\; 0}\right]}^T$ ). Now, we consider placing a dipole magnet on the left in the x coordinate (position: ${\mathbf{x}}_2={\left[-L,\mathrm{0,\; 0}\right]}^T$ , with magnetic dipole moment ${\mathbf{m}}_2={\left[m_2,\mathrm{0,\; 0}\right]}^T$ ), as shown in Supplementary Fig. 7a.
The magnetic force between the two dipole magnets is: ${\mathbf{F}}_{m_1-m_2}=\frac{3{\mu }_0}{4\pi {∣\mathbf{r}∣}^4}\left\{\left(\widehat{\mathbf{r}}\times {\mathbf{m}}_1\right)\times {\mathbf{m}}_2+\left(\widehat{\mathbf{r}}\times {\mathbf{m}}_2\right)\times {\mathbf{m}}_1-2\widehat{\mathbf{r}}\left({\mathbf{m}}_1\cdot {\mathbf{m}}_2\right)\right)\left(+5\widehat{\mathbf{r}}\left[\left(\widehat{\mathbf{r}}\times {\mathbf{m}}_1\right)\cdot \left(\widehat{\mathbf{r}}\times {\mathbf{m}}_2\right)\right]\right\}$ where ${\mu }_0$ is the magnetic permeability in a vacuum and $\mathbf{r}$ is the relative position vector between the centers of the two dipole moments ${\mathbf{m}}_1$ and ${\mathbf{m}}_2$ . $\mathbf{r}={\mathbf{x}}_1-{\mathbf{x}}_2={\left[L,0,0\right]}^{\mathrm{T}}$
After plugging in all the relevant values, the force between two magnets can be expressed as ${\mathbf{F}}_{m_1-m_2}=\frac{3{\mu }_0}{4\pi {∣\mathbf{r}∣}^4}{m}_1{m}_2\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 0\hfill \\ \hfill 0\hfill \end{array}\right]$
Now let us consider that there are two magnets with opposite dipole directions, as shown in Supplementary Fig. 7b. In this case, two magnets ( ${\mathbf{m}}_2$ and ${\mathbf{m}}_3$ ) generate opposite force directions on magnet ${\mathbf{m}}_1$ . We would like to use this case to find the scaling effect of magnet ${\mathbf{m}}_3$ that can destabilize the assembly pair ${\mathbf{m}}_1$ and ${\mathbf{m}}_2$ .
If we consider both $m_1$ and $m_2$ to be NdFeB assembly magnets (1.2 × 1 × 0.5 mm), then we consider the third magnet with an opposite dipole direction with magnetic moment ${\mathbf{m}}_3={\left[{-m}_3,\mathrm{0,\; 0}\right]}^T$ , which provides a repulsion force. If we consider that ${\mathrm{m}}_3$ is sufficiently large that the force can balance the attraction force for ${\mathrm{m}}_2$ , it needs to be balanced; as a result: ${\mathbf{F}}_{m_1-m_2}+{\mathbf{F}}_{m_1-m_3}=0$ $\frac{3{\mu }_0}{4\pi L^4}{m}_1{m}_2-\frac{3{\mu }_0}{4\pi D^4}{m}_1{m}_3=0$
The required ${\mathrm{m}}_3$ needs to be large as $m_3=\frac{D^4}{L^4}{m}_2$ at position ${\mathbf{x}}_3={\left[-D,\mathrm{0,\; 0}\right]}^T$ to balance the magnetic force generated by ${\mathrm{m}}_2$ . Now, if we assume that ${\mathrm{m}}_3$ is a cube magnet with an edge size of a, we can rewrite the equation as $M_{NdFeB}{a}^3=\frac{D^4}{L^4}{m}_2$ where $M_{NdFeB}$ is the magnetization of the NdFeB magnet, which is equal to $1.08\times {10}^6$  A m^(-1). If we now consider D as a variable and consider how a needs to scale with D, we will find $a=\sqrt[3]{\frac{m_2}{M_{NdFeB}{L}^4}}{D}^{\frac{4}{3}}$
It shows that with an increasing distance D, the third magnet needs to increase rapidly in size ( ${~D}^{\frac{4}{3}}$ ) to match the force. This means that the magnet needs to be larger than a to destabilize the assembly pair between ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ . If the ${\mathrm{m}}_2$ magnet is touching ${\mathrm{m}}_1$ , as in the assembly pair, the required size of ${\mathrm{m}}_3$ can be so large that it is physically impossible to fit on the left side. If one changes the ${\mathrm{m}}_3$ direction, it will only decrease the magnetic repulsion force. The above scaling law provides an important insight that the magnetic gradient generated by a nearby permanent magnet is very unlikely to destabilize the magnetic assembly pair. The analysis results also resonate with our experimental observations. Therefore, we can conclude that the assembly will be stable in our envisioned applications regardless of the neighboring NdFeB magnet configurations.

All peptide samples were measured in a single-shot manner in a Q-Exactive HF-X hybrid quadrupole-orbitrap mass spectrometer (Thermo Fisher Scientific) after peptide separation by high-performance liquid chromatography (nanoLC 1200, Thermo Fisher Scientific) using a 50 cm reversed-phase column (made in house, packed with 1.9 µm C18 ReproSil particles). Peptides were eluted over a 90-minute-gradient from 0% to 95% buffer B (0.1% formic acid and 80% ACN) with a flow rate of 300 nL/minute.
Full scans were obtained from 300 to 1650 m/z with a target value of 3 × 10⁶ ions at a resolution of 60,000 at 200 m/z. The fifteen most intense ions (Top15) of each full scan were fragmented with higher-energy collisional dissociation (HCD) (target value 1 × 10⁵ ions, maximum injection time 120 ms, isolation window 1.4 m/z, underfill ratio 1%), and fragments were detected in the Orbitrap mass analyzer at a resolution of 15,000 at 200 m/z.