*2.8. Electronics*

The electronics is battery supplied to avoid 50 Hz noise. The sensors are biased at voltages between 1 to 2 V and the output signal is amplified 500 times by a low noise preamplifier and filtered at 15 kHz with an additional gain of 20. The signal is then oversampled at 200 kHz using a Data Translation-R acquisition card controlled by a homemade software. A schematic view of this set-up is presented in Figure 1a. Then, a homemade software identifies the signals from the total recording and discriminate them from noise artifacts. Numerical parameters were evaluated on a cohort of several thousands of examples from different experiments. For each spotted point above the threshold, the local minimum and maximum are determined by repeatedly incrementing the interval of interest by 15 points until the maximum (*imax*, *Vmax*) and minimum (*imin*, *Vmin*) determined are more than 20 points from each edge of the interval. The user determines the direction of signals (*k* = 1 if *imax* − *imin* < 0 and *k* = −1 if *imax* − *imin* > 0) and the detection threshold (*Vthr*). Several checks are then carried out to validate the recording of this peak in the processed file. They must be bipolar (|*Vmin*| > 1/3*Vthr* and |*Vmax*| > 1/3*Vthr*) with the right orientation (*k*(*imax* − *imin*) < 0), their width (*imax* − *imin*) must be coherent with the flow velocity (between 25 μs and 2.5 ms) and they must be sufficiently symmetric (| *Vmax*−*Vmin Vmax*+*Vmin* | < 0.4). This last criteria was added to better discriminate signals from radiotelegraphic noise occurring in some experiments. Experimental data before and after treatment are presented respectively in Figure 2a,b.

**Figure 2.** Experimental data. (**a**) Raw experimental recording. (**b**) Recording of the software-selected portions (the same 3 signals are shown).

#### *2.9. Comparative ELISA Tests*

96 wells plates were coated with anti-CD138 antibody. In each well, 100 μL of a suspension of 10 μg/mL of antibodies in potassium phosphate buffer at 50 mM, pH 7.4 were deposited and incubated overnight at 20 ◦C. The following day, wells were emptied and filled with 300 μL of EIA buffer (100 mM potassium phosphate buffer pH 7.4 containing 0.1% bovine serum albumin, 0.15 M NaCl and 0.01% sodium azide). The plates were sealed and stored at 4 ◦C until use.

The day of the experiment, the coated plate was washed once in a washing buffer (50 mM potassium phosphate buffer pH 7.4), 100 μL of serial dilutions of NS1 cells (3 106; 106; 3 105; 105; 3 104; 104; 3 103; 10<sup>3</sup> cells/mL) in PBS were added per well and incubated under agitation at room temperature for 2 h. Then, the plate was washed three times in the washing buffer and 100 μL of a suspension of biotinylated antibody anti-CD138 at 200 ng/mL in EIA buffer without sodium azide were added per well for a 2h-incubation step under agitation at room temperature. The plate was then washed three times in the washing buffer and 100 μL of a solution of streptavidin conjugated with polymers of horseradish peroxidase (Thermofisher Scientific, Waltham, MA, USA) diluted 15,000 fold in EIA buffer without azide was added into the wells. Finally, after 30 min of incubation under agitation at room temperature, the plate was washed 5 times in the washing buffer and 100 μL of 3,3 ,5,5 -Tetramethylbenzidine (TMB, Thermofisher Scientific) were added per well. After 30 min at room temperature under agitation, 100 μL of 2 M sulfuric acid were added per well and the absorbance

of each well was measured at 450 nm (wavelength of absorption of the reaction product) and 620 nm (noise measurement).

The substraction of these two measurements yields the specific signal directly proportional to NS1 cell concentration. The theoretical limit of detection is defined as the lowest cell concentration giving a signal greater than the non-specific binding (mean of eight measurements of EIA buffer) + 3 standard deviations (99.7% confidence). The theoretical limit of quantification is defined as the lowest cell concentration giving a signal greater than the non-specific binding (mean of eight measurements of EIA buffer) + 10 standard deviations (99.9% confidence).

#### *2.10. Comparative Flow Cytometry Tests*

For flow cytometry analysis, NS1 cells were washed once with PBS/0.5% BSA and 200 μL of serial dilutions of cells (105; 3 104; 104; 3 103; 10<sup>3</sup> cells/mL) were incubated for 2 h at 4 ◦C with anti-mouse CD138 labeled with Phycoerythrin (BD Biosciences). After incubation, cells were washed twice with PBS/0.5% BSA and resuspended in 200 μL of PBS/0.5%BSA. The fluorescence was finally assayed for the total volume of 200 μL using a Novocyte flow cytometer (ACEA) and the number of stained cells was evaluated by comparison with cells incubated with buffer alone. Results were analysed using NovoExpress software.

#### **3. Results and Discussion**

#### *3.1. Simulations of Single Magnetic Beads and MP-Labeled Cells*

A GMR sensor is composed of two ferromagnetic metallic layers separated by a nonmagnetic one as shown in Figure 3a. The magnetization of one of these layers is pinned in one direction while the magnetization of the other one is free to rotate in its plane. As the speed of propagation of electrons in a metal strongly depends on the relative orientation of its spin and the magnetization of the metal, this spintronic device will have different properties for spin up and spin down electrons. Depending on the angle between the magnetizations of the two ferromagnetic layers, the overall resistance of the sensor varies as shown in Figure 3b. During the detection process, the MPs themselves are magnetized perpendicularly to the sensor plane by a field created with a permanent magne<sup>t</sup> and emit a dipolar field. Only the in-plane component of the dipolar field created by the beads is detected by the magnetic sensor since thin-film GMR sensors are insensitive to out-of-plane field variations (z direction) below a critical value. The sensor yoke geometry, designed especially to have just one magnetic domain [59], is shown in Figure 3d and presents a high aspect ratio. This strong asymmetry between the length and width of the device will tend to align all the moments from the free layer according to its length to reduce the magnetostatic energy by moving the two poles created as far as possible from each other. The free layer magnetization is thus along the x axis at zero field, while the other layer is pinned along the y axis. The device is in its most sensitive configuration at zero field and is sensitive only to the y component of the field. Moreover, improving the alignment of moments from the free layer results in a more linear behavior of the sensor. GMR sensors response to small magnetic fields variations are linear on a range of about ±2 mT around zero field (see Figure 3b), which includes the whole range of fields needed for this application.

The situation to be modeled is presented in Figure 3c. Magnetized objects circulate above the sensor in a laminar flow in a microchannel and induce magnetic field variations that are detected by the sensor. Three types of magnetic objects are modeled: single magnetic beads, aggregates of beads and MPs-labeled cells.

**Figure 3.** Giant magnetoresistance (GMR) sensor. (**a**) Scheme of the main components of a GMR stack. Free and pinned layers are ferromagnetic and their magnetization are represented by arrows. The spacer is a diamagnetic conductor. (**b**) Experimental sensitivity curve with schematic representation of the relative orientations of the two ferromagnetic layers. This sensor shows a sensitivity of 2 %.mT−<sup>1</sup> and no hysteresis on its linear portion. (**c**) Schematic of the experiment: Labeled objects are moved by the laminar flow at a given height crossing the sensor at constant speed. The sensor detects variations of the magnetic field due to the induced dipolar field of the beads. The beads are magnetized by a field normal to the sensor plane created by a permanent magnet. (**d**) Photograph and scheme of a processed GMR sensor in yoke shape. The sensor measures 120 μm along the x axis and 4 μm along the y axis.

The signal corresponding to a single bead moving above the sensor is proportional to the integral over the whole sensor surface of the y-componen<sup>t</sup> of the local dipolar field induced at each successive position. For a MP in position (*xB*, *yB*, *zB*) with a moment *μ* making an angle *θ* with*z* and *φ* with *x* and moving above a sensor of length *L* and width *l*, it is given by the Formula (1) [60].

$$\begin{split} H\_{\mathcal{Y}} &= \frac{\mu}{Ll} ( (\frac{y\_l}{q\_2^2} (\frac{x\_r}{r\_2} - \frac{x\_l}{r\_1}) + \frac{y\_r}{q\_4^2} (\frac{x\_l}{r\_4} - \frac{x\_r}{r\_3}) ) \sin \theta \sin \psi \\ &+ (\frac{1}{r\_1} - \frac{1}{r\_2} + \frac{1}{r\_3} - \frac{1}{r\_4}) \sin \theta \cos \psi \\ &+ (\frac{h}{q\_2^2} (\frac{x\_l}{r\_1} - \frac{x\_r}{r\_2}) + \frac{h}{q\_4^2} (\frac{x\_r}{r\_3} - \frac{x\_l}{r\_4}) ) \cos \theta) \end{split} \tag{1}$$

where *xr*, *xl*, *yr*, *yl*, *h*,*r*1,*r*2,*r*3,*r*4, *q*2 and *q*4 are defined as follows.

$$\begin{aligned} \mathbf{x}\_{r} &= \frac{L}{2} - \mathbf{x}\_{B} \\ \mathbf{y}\_{r} &= \frac{l}{2} - \mathbf{y}\_{B} \\ \mathbf{h} &= \mathbf{z}\_{B} - \mathbf{z}\_{C} \\ \mathbf{r}\_{1} &= \sqrt{\mathbf{x}\_{r}^{2} + \mathbf{y}\_{r}^{2} + h^{2}} \\ \mathbf{r}\_{3} &= \sqrt{\mathbf{x}\_{r}^{2} + \mathbf{y}\_{r}^{2} + h^{2}} \\ \mathbf{q}\_{2} &= \sqrt{\mathbf{y}\_{l}^{2} + h^{2}} \end{aligned} \qquad \begin{aligned} \mathbf{x}\_{l} &= -\frac{L}{2} - \mathbf{x}\_{B} \\ \mathbf{y}\_{l} &= -\frac{l}{2} - \mathbf{y}\_{B} \\ \mathbf{r}\_{2} &= \sqrt{\mathbf{x}\_{r}^{2} + \mathbf{y}\_{l}^{2} + h^{2}} \\ \mathbf{r}\_{4} &= \sqrt{\mathbf{x}\_{l}^{2} + \mathbf{y}\_{r}^{2} + h^{2}} \\ \mathbf{q}\_{4} &= \sqrt{\mathbf{y}\_{r}^{2} + h^{2}} \end{aligned} \end{aligned}$$

After several simulation tests (data not shown), it has been concluded that the influence of the spatial distribution of the moments in the aggregates was negligible. Signals from aggregates of N beads are simulated as N times the signals coming from a single bead with the same parameters.

On the contrary, the distribution of MPs on the cell surface was proven to have an influence on the generated signals, as presented in Figure 4b. Cells are thus simulated as spheres with several magnetic beads distributed randomly on their surfaces and with a random angle *θ* between the direction of their moment and the vertical axis with the constraint of a total magnetization equal to the experimentally measured one (see Section 3.2). This observation leads to the conclusion that detecting one passage with one single sensor cannot be sufficient to deduce precisely the nature and the details of the detected object.

**Figure 4.** (**a**) Simulation results of the magnetic object detection demonstrating the influence of the three main parameters: distance between object and sensor (Z), number of magnetic particles (MPs) (N) and moment orientation (*θ*). Curves are labeled by the triplet (Z,N,*θ*). (**b**) Simulation results for a 6 μm diameter cell at 6 μm height covered by 10 MPs, with four sets of random positions of the beads on the cell surface.

However, our objective is to discriminate the MP-labeled cells from the aggregates of magnetic beads. Three experimental parameters must be chosen together to optimize the discrimination: (i) the chip design, (ii) the permanent magnet, (iii) the magnetic particles. Indeed, with fixed values for these three settings, the values of the two parameters determining the signal shape (the height of the magnetic object and its magnetic moment) are framed. The object distance from the sensor has the largest importance on the amplitude of the signal as shown on Figure 4a. As a consequence, to increase the impact of the number of MPs per object on the resulting signal (value correlated to the nature of this object), the object distance from the sensor needs to be the most homogeneous as possible, hence, the channel must be the smallest possible. This parameter was set to 25 μm, the lowest value at which the channel would not clog after 2 h of use. The permanent magne<sup>t</sup> must be chosen so that its field is sufficient to have a small average angle *θ* between the beads magnetic moments and the vertical axis but must be low enough not to pull the pinned layer of the sensor out of plane. This value was set at 90 mT as it was a good compromise knowing the MPs magnetization curves. The choice of the magnetic beads and of the chip design are explained in the following paragraphs.

#### *3.2. Deduction of Best Experimental Conditions*

The chip design was optimized by testing different configurations of the sensor and microchannel geometries on simulated samples. The main idea was to make some static changes that would not complicate the use of the device but would enhance the discrimination between "positive" and "negative" samples. Samples are called "positive" if they are supposed to contain MPs-labeled cells (they contain a specific complex mAbs-coated beads/cells possessing antigens targeted by the mAbs) and "negative" if they are not, see Table 1.

## 3.2.1. Sample Characterization

The two kinds of samples had thus to be experimentally characterized to make a proper model. Five sorts of commercial magnetic beads ranging from 200 nm to 2.8 μm in diameter from three companies were tested for the preparation of these samples. Indeed, the choice of MPs is important. Ideal beads should have a magnetic moment sufficiently high to be attracted by a permanent magne<sup>t</sup> within few minutes to enable simple and quick washing steps (required for mAbs functionalization of MPs before performing the test). They should also have a low saturation field so that a permanent magne<sup>t</sup> of 90 mT is enough to reach quasi-saturation and, above all, they must present the lowest propensity to aggregation. All these properties were investigated as follows.

First, the magnetic moment of 50 μL of each of the MPs suspensions has been measured using a Vibrating Sample Magnetometer (VSM) and, using the manufacturer number of beads information, the saturation magnetic moment of a single bead has been calculated and the saturation field was determined.

Then, each type of beads was functionalized with antibodies. After this step, their kinetics of cell labeling and their aggregation were studied in parallel. Different concentrations of each type of MPs have been mixed in PBS and with 10<sup>5</sup> NS1/mL in PBS. For 2 to 3 h, regularly, 100 μL of these suspensions were poured into a well and let to sediment for 15 min. Pictures were then taken under optical microscope. For each cell-containing sample, the distribution of the number of beads per cell was evaluated by visual counting. For the samples without cells, hundreds of these photographs were analyzed with the ImageJ software. They were binarized before the software counted the number of pixels in each aggregate. From these data, the distribution of beads in aggregates was deduced.

Finally, Dynabeads MyOne Streptavidin T1 superparamagnetic have been chosen for the present study (Figure 5, results for the 4 other investigated types of beads can be found in Appendix A). They are 1 μm polymer beads containing maghemite clusters and have a sufficiently high moment that they can be attracted by a permanent magne<sup>t</sup> within 2 min, thus washing steps (required for mAbs functionalization of MPs) are extremely simple and quick. The saturation magnetic moment of a single bead has been calculated to be 2.1 10−<sup>11</sup> emu per bead and reached at a field of 700 mT but at 90 mT these beads already have an average magnetic moment of 1.6 10−<sup>11</sup> emu per bead (data not shown). They are easily functionalized with any kind of purified biotinylated antibodies with high efficiency, with the protocol described in Section 2.5. Moreover the number and size of bead aggregates in the commercial suspension were the lowest of the 5 studied MP types (93% of the objects in the suspension are composed of less than 7 beads, 99% less than 15 beads, the complete curve is presented on Figure 5f) and the distribution of beads per cell was satisfying with an average of roughly 50 MPs per cell (the distribution and the 100 magnification photographs are shown on Figure 5).

## 3.2.2. Chip Design

The objective is to find the most favorable conditions to discriminate labeled cells from aggregates. As described in details in the Section 3.1, the signals are determined by the dipolar field created by the detected object which depends mainly on the magnetic moment of the object and its height from the sensor. The expression of the dipolar field *Hdip* created in B and sensed in C is given by Equation (2) where *μ* is the magnetic moment of a bead and *N* is the number of beads of the detected object.

$$H\_{dip}^{\vec{\tau}} = 3\vec{BC} . \frac{\vec{BC}.N\vec{\mu}}{||\vec{BC}||^5} - \frac{N\vec{\mu}}{||\vec{BC}||^3} \tag{2}$$

On the Figure 5f, the distributions of beads in cells and in aggregates are given for our system. By using Equation (2), it can be calculated that, between the smallest object in negative samples (1 bead) and the most labeled cell (around 100 beads), the signal is multiplied by 100. Between a height of 1 μm from the sensor and of 10 μm from the sensor, the signal is divided by 1000. Thus, when the channel is directly placed at the top of the sensor, even a signal from a single bead (at 1 μm height) cannot be

discriminated from a signal coming from a labeled cell further away from the sensor in the channel, independently of the detection threshold.

**Figure 5.** Labeling and aggregation study. Four sample photographs (magnification 100) were taken under optical microscope and illustrate beads repartition. (The scale bars represent 5 μm.) (**a**) Group of two NS1 cells labeled with Dynabeads MyOne functionalized with anti-CD138 mAbs. (**b**) Group of two NS1 cells after two hours-contact with Dynabeads MyOne functionalized with control IpaD-315 mAbs. (**c**) CHO cell after two hours-contact with Dynabeads MyOne functionalized with anti-CD138 mAb (**d**) Dynabeads MyOne functionalized with anti-CD138 mAbs in Phosphate Buffer Saline (PBS). (**e**) Adapted spacer layer thickness estimation. In this illustration, the detectivity is set to 2.2 μT. Relation between the number of beads covering an object and the maximum height at which it can be detected. Objects below the red curve are detectable while objects above are not. (**f**) Corresponding detectable population of cells and aggregates. Graph of the observed cumulative frequency of the number of MPs per NS1 cell and per aggregate in decreasing order. Estimation based on the study of 309 cells in a solution containing 10<sup>5</sup> NS1/mL and 23 μg/mL anti-CD138 functionalized MPs/mL after 2h-contact and of 18,630 aggregates in a suspension containing 23 μg/mL anti-CD138 in PBS.

Knowing the detectivity of the sensor (experimental characterizations are given on Table 2), the maximal distance from the sensor at which an object composed of N beads can be detected is deduced and plotted in the Figure 5. Above this distance, all the aggregates containing less than N MPs are undetectable. While 98% of NS1 are labeled with more than 7 beads, only 7% of aggregates are composed of more than 7 beads. This minimum number of beads seems to be a good discrimination factor. The Figure 5e shows that objects of 7 beads are undetectable from 6 μm above the sensor.

Adding a separation layer between the sensor and the bottom of the channel eliminates most of the nonspecific signals (from small aggregates and single beads) and improves the discrimination on the number of beads by reducing the importance of the height parameter. Indeed, between 7 and 16 μm height, the signal is divided by approximately 12 only. Without this supplementary layer, objects of small magnetization could still induce large amplitude signals that could be mistaken for labeled cells.

This study leads to the conclusion that the best configuration for our system is the addition of a 6 μm thick separation layer between the sensor and the channel. The thickness of the separation layer needs to be optimized for each couple bead/biological target, because it depends strongly on the expected moment per target and thus on the number of antigens expressed by the target.

#### *3.3. Performance of the GMR Chip Test*

Seven experiments (See Table 2 and Figure 6a) were realized on six days using 4 similar chips with different sample volumes ranging from 200 to 400 μL and the number of events was normalized to a volume of 1 mL. To avoid biased results, samples have been injected in the chip in different orders at each experiment and between two samples the chip was washed with deionized water and dried. For each experiment, the sensitivity and the noise level of the sensor have been measured and the detection thresholds were deduced (given in Table 2). In order to coherently treat data from these seven experiments, only signals above the highest detection threshold (2.2 μT) were considered.

**Table 2.** Experimental conditions of the seven experiments. The threshold of each experiment is defined as the lowest detectable signal (with a signal to noise ratio at 3). Results are given as a number of events above 2.2 μT detected per milliliter of sample. The average count is given with its standard deviation (SD) for each sample. Control samples are presented at the bottom of the table, separated from positive samples. The highest count in negative samples, in bold, is obtained for anti-CD138 beads in PBS for which the average value added to three standard deviations gives 3.6 10<sup>3</sup> counts.


Between 60 and 2200 counts per milliliter were found in each type of negative control samples in PBS (14 measurements in total). Studying these results allow us to determine a count threshold characterizing the test. The count threshold above which the sample can be considered positive (the detection threshold) is calculated as the average of the values obtained for the negative test having the most counts (thus, the anti-CD138 beads) added to three times their standard deviation. This method concludes to an average non-specific count of 1.1 10<sup>3</sup> counts per milliliter and a detection count threshold of 3.6 10<sup>3</sup> counts per milliliter.

Looking at the positive sample results, this threshold corresponds to a concentration between 1 and 3 10<sup>4</sup> NS1 per milliliter.

#### *3.4. ELISA Test Sensitivity*

The ELISA test was repeated in three independent experiments in order to compare its detection limit to the one of the GMR sensor. Results are presented in Figure 6b. For this 5 h-test in PBS suspensions, the detection limit (the lowest concentration at which the test can determine positivity of the sample) was found equal to 2.0 10<sup>4</sup> NS1/mL ± 1.8 10<sup>4</sup> while the quantification limit (the lowest concentration at which the test can give a correct estimation of the sample concentration) was found at 6.7 10<sup>4</sup> NS1/mL ± 2.9 104.

#### *3.5. Flow Cytometry Results*

The number of NS1 cells was evaluated by flow cytometry using a specific monoclonal antibody against the CD138 surface molecule. The living cells were selected by size and cell granularity and the number of CD138+ cells in each sample was evaluated by comparison with cells incubated with buffer alone. As can be seen in Figure 6c, the evaluation of the number of positive cells for the CD138 marker is possible up to a cell concentration in the sample equal to 3 10<sup>3</sup> cells/mL.

**Figure 6.** Experimental results of the three tests. All were performed in different days, thus the same samples were not tested with the three techniques. (**a**) Experimental results of the GMR test. Red dashes represent the mean of the experiments. Error bars represent standard deviations from the experiments. (**b**) Experimental results of the ELISA tests. Different concentrations of NS1 cells in PBS were detected using the homologous sandwich ELISA involving anti-CD138 mAb as capture and tracer antibody in a 5 h sequential format. The signal to noise ratio was calculated from the mean of eight measurements of PBS alone. Red dashes represent the mean of the three independent experiments, each performed in duplicate. Error bars represent standard deviations from the three experiments. The insert shows the low concentration part of the curve. (**c**) Experimental results of flow cytometry presented as counts per milliliter for each concentration. Red dashes represent the mean of the three independent experiments. Error bars represent standard deviations from the three experiments.
