COMPASS – rapid and highly sensitive medical point-of-care diagnostic

In the last decade Magnetic nanoparticles (MNPs) have gained an enormous interest in specialized areas such as medicine, cancer theranostics, biosensing, catalysis, agriculture, and the environmental protection. By controlled engineering of speci�c surface properties, named functionalization, MNPs are gaining special features for desired applications, e.g., bioassays for the detection of biomolecules or biomarkers such as antibodies. The characterization as well as a highly speci�c measurement of such binding states is of high interest and limited to highly sensitive techniques such as ELISA (Enzyme-linked Immunosorbent Assay) or �ow cytometry, which are relatively in�exible, di�cult to handle, expensive and time-consuming. Novel upcoming methods, such as ACS (AC susceptometry) or MPS (Magnetic Particle Spectroscopy), exploit the magnetization response of functionalized MNP ensembles to assess speci�c information about the MNP mobility within their environment as well as the conjugations of chemical or biological compounds on their surface. Both methods have shown promising results reaching similar sensitivities within short measurement times but showing di�culties in data interpretation. Here, we report a novel method, COMPASS (Critical Offset Magnetic PArticle SpectroScopy), which is based on a critical offset magnetic �eld of MNPs, which enables sensitive detection to minimal changes in mobility of MNP ensembles, e.g., resulting from SARS-CoV-2 antibodies binding to the S antigen on the surface of functionalized MNPs. With a validated sensitivity of 0.85 fmole/50 µl sample volume ( ≙ 33 pM) SARS-CoV-2-S1 antibodies, measured with a low-cost portable COMPASS device, the proposed technique is not only competitive with the sensitivity of commonly used ELISA or �ow cytometry methods but provides more �exibility, robustness and rapid measurement withinwell below a minute per sample, including sample conjugation, mixing and incubation times. The underlying physical effect is based on an offset magnetic �eld induced suppression of a higher harmonic in the nonlinear magnetization response of the MNP to a time varying magnetic �eld resulting in a highly sensitive response of the signal phase to minimal changes in particle mobility. Since this effect is independent of

exploit the magnetization response of functionalized MNP ensembles to assess speci c information about the MNP mobility within their environment as well as the conjugations of chemical or biological compounds on their surface. Both methods have shown promising results reaching similar sensitivities within short measurement times but showing di culties in data interpretation.
Here, we report a novel method, COMPASS (Critical Offset Magnetic PArticle SpectroScopy), which is based on a critical offset magnetic eld of MNPs, which enables sensitive detection to minimal changes in mobility of MNP ensembles, e.g., resulting from SARS-CoV-2 antibodies binding to the S antigen on the surface of functionalized MNPs. With a validated sensitivity of 0.85 fmole/50 µl sample volume ( ≙ 33 pM) SARS-CoV-2-S1 antibodies, measured with a low-cost portable COMPASS device, the proposed technique is not only competitive with the sensitivity of commonly used ELISA or ow cytometry methods but provides more exibility, robustness and rapid measurement withinwell below a minute per sample, including sample conjugation, mixing and incubation times.
The underlying physical effect is based on an offset magnetic eld induced suppression of a higher harmonic in the nonlinear magnetization response of the MNP to a time varying magnetic eld resulting in a highly sensitive response of the signal phase to minimal changes in particle mobility. Since this effect is independent of MNP concentration, the sample handling is much simpler and robust.
Our method thus may pave the way for deeper insights into complex and rapid binding dynamics of functionalization chemistry and can lead to a huge step forwards in point-of-care diagnostics as well as impacts other elds in research and industries.

Full Text
The characterization of ensembles of magnetic nanoparticles (MNP) is a dynamically developing eld and found various applications in many elds of research such as medicine, cancer theranostics, biosensing, catalysis, agriculture, and the environment [1][2][3]. Thus, a huge portfolio of different methods and techniques is available today to investigate the complex dynamics of MNP ensembles [4,5].
Magnetic particle spectroscopy (MPS) is a quite young technology for the characterization of MNPs. It uses an oscillating magnetic eld of su cient eld strength to drive the MNP ensemble periodically into their non-linear magnetization response [6]. This reveals speci c information for each MNP type in form of higher harmonics of the excitation frequency and can be used to measure parameters such as hydrodynamic diameter or viscosity and temperature of the surrounding solution as well as the conjugations of chemical or biological compounds on the surface of the MNPs. In short, MPS is able to investigate the mobility of MNPs [7].
Due to the fact, that MPS directly measures the analytical signals from the entire sample volume is making bioassays simple and fast [8-10]. E.g., functionalization of the surface of the MNPs by anchoring linkers, such as speci c antibodies, allows detecting viral proteins by binding speci c epitopes. Crosslinking between the MNPs in uences their mobility resulting in a minimal signal change. This offers the detection of, e.g., 44 nM H1N1 nucleoprotein or 1.56 nM SARS-CoV-2 spike protein within a measurement time of about 10 seconds [8, 10]. However, since the sensitivity of MPS is mainly based on the particle core composition and not on the environmental serum, the signal change in the experiments between binding and non-binding samples is quite small. In addition, the signal as well as its change strongly depends on MNP and the analyte concentration, which requires sophisticated sample handling and data processing to robustly detect the relevant signal changes.
Similar modalities using MNPs, such as AC-susceptometry (ACS) measurement [11][12][13][14] provide a more sensitive technique to investigate and determine parameters of the environmental serum, e.g., rapid detection of 84 pM mimic SARS-CoV-2 in 36 s [11]. But ACS is complicated by long acquisition times, the complexity of handling of those devices as well as the data processing, which require sophisticated hardware and experienced personnel.
Common MPS devices are working with a strong time varying magnetic eld H AC , while ACS devices are working with weak excitation elds H AC below 2 mT and multiple frequencies f AC and sometimes with additional strong offset magnetic elds H DC (static or with low frequency ≪f AC ).
We combined a strong excitation eld H AC with a strong offset magnetic eld H DC and expand the parameter space with COMPASS (Critical Offset Magnetic PArticle SpectroScopy) as indicated in Fig. 1. This allowed extremely sensitive and robust investigation of MNP dynamics and surface chemistry at critical offset elds which to our knowledge was not exploited before and allows for measurements with higher sensitivities than MPS or ACS. Furthermore, COMPASS reaches a detection limit of SARS-CoV-2-S1 antibodies binding to the S antigen on a functionalized surface of MNPs, which is comparable with the gold-standard methods ELISA (Enzyme-linked Immunosorbent Assay) [15] and ow cytometry [16]. While both techniques are limited by their in exibility, the complex handling, and the long measurement time, COMPASS provides a robust and easy-to-use testing environment.

Physical background of critical points
The magnetization of a superparamagnetic sample depends on the surrounding magnetic eld H=H AC +H DC consisting of dynamic H AC and static H DC magnetic elds. Particles, which usually exhibiting superparamagnetic properties, consist of a single magnetic domain and can be seen as tiny permanent magnets (single domain particles). In absence of an external magnetic eld, all nanoparticles of such an ensemble (sample) are statistically oriented, which causes the magnetization of the sample to be zero. Increasing the external magnetic eld strength leads to more and more particles aligning along the external magnetic eld resulting in an increase of the magnetization. At a speci c magnetic eld strength M sat , all particles are aligned and the magnetization of the sample is saturated (saturation magnetization M sat ). The dependency of the sample magnetization M on the external magnetic eld strength H can be described by the Langevin function L(ξ): with m as the magnetic moment of a particle, μ 0 as the vacuum permeability, k B as the Boltzmann constant and T as temperature. The Langevin parameter ξ describes the different regimes of the magnetization response: |ξ|≪1 describes the linear regime for small external magnetic elds and |ξ|≥1 describes the non-linear regime (Fig. 2 a). However, it is important to note that Eq. (1) is only an approximation to real particles. Especially the assumption that the magnetization follows the external eld instantaneous is not ful lled (see supplementary S2) MPS devices are using time-varying magnetic excitation elds H AC (t)=H 0 ·sin(2π·f 1 ·t)), which are su ciently high to drive the magnetization M of a sample periodically with frequency f 1 into their nonlinear response. In contrast, the magnetic eld strength of ACS devices is much smaller (H 0,ACS < 2 mT < H 0,MPS ). That means, ACS investigates the behavior of the sample in the linear regime (|ξ|≪1) determining the susceptibility or slope (χ=dM/dH) of the magnetization curve while MPS is more focused on the non-linear response of the magnetization (|ξ|≥1).
The magnetization response M(t) over time of a sample during continuous magnetic eld excitation H AC (t) larger than 5 mT (MPS) approximates a mostly rectangular shape depending on the amplitude H 0 of the excitation eld. An analysis of the time signal using a Fourier transformation reveals odd higher harmonics (2n-1)·f 1 (n∈ℕ) of the excitation frequency f 1 in the spectrum due to the symmetric behavior of the signal over one period 1/f 1 . These higher harmonics are speci c for the MNP type and encode information of its magnetic response and, hence, on the properties of the particle or its surrounding.
During ACS experiments, only the fundamental frequency f 1 is usually studied at different frequencies in the linear regime to get a frequency-dependent characterization of the MNPs [11][12][13][14].
For both ACS and MPS the application of static offset magnetic eld H DC parallel to the excitation eld (H AC (t)||H DC ) extends both methods and allows for a closer investigation of the magnetization curve in the non-linear regime.
During MPS experiments in the presence of an offset magnetic eld H DC the magnetization response M(t) becomes asymmetric, which introduces higher even harmonics 2n·f 1 (n∈ℕ) of the excitation frequency f 1 in the Fourier spectrum (Fig. 2 a&b).
Investigating the spectral components A n of each higher harmonic n in dependence of the offset magnetic eld strengths H DC , the real and imaginary part of A n (H DC ) show an interesting behavior. For H DC <H AC a wavelike functional dependence on H DC with zeroes, also called nodes, at offset elds speci c for each harmonic n is observed (Fig. 2 c&d) (see gif-animations). This behavior can be described by a convolution of Chebyshev polynomials of second kind U n with the derivative of the magnetization curve M'=dM/dH (see supplementary S1) [17]. With increasing harmonic number n, the spectral component A n (H DC ) shows an increasing number of nodes. The corresponding phase plot φ n (H DC ) of the harmonic signal shows a steep slope of the phase near such nodes or 'dips'. Hence, minimal changes in the magnetization response curve due to changes in particle or environmental parameters, e.g., hydrodynamic diameter, lead to a strong detectable phase difference dφ=φ res =φ 1 -φ 2 between two experiments with two different samples (see supplementary S2). This implies a high sensitivity on changes of the sample parameters at these distinct offset eld induced nodes which are, hence, called critical points (CPs) in the following.

Critical points sensitivity evaluation
To evaluate the novel COMPASS method, we hypothesized that we can exploit COMPASS to detect SARS-2 speci c antibodies as these bind to MNP ensembles with sensitivities competing with ELISA and ow cytometry. Furthermore, decreasing the serum conjugation time down to several seconds provides a real rapid testing protocol (see supplementary S8).
Multiple samples with slightly different hydrodynamic diameters were prepared and measured in-vitro with the aim of detecting commercially available SARS-CoV-2 speci c antibodies. For the binding sample (S+) SARS-CoV-2-S1 protein was covalently bound to the surface of MNPs functionalized with (3-Aminopropyl)tiethoxysilan (APTES) using a protocol modi ed from [18] and resulting in MNP-APTES-S1. The preparation of the samples for the measurements were the following (see supplementary S3): antibodies were diluted 1:2,000…200,000 (3.3 pM…33 pM) in a buffer (PBS with 0.1% BSA). For each measurement, 25 µl antibody dilution or reference sample (dilution buffer) were added to 25 µl of MNP-APTES-S1 dispersions (100 µg Fe/ml) in an 0.5 ml Eppendorf cap. After adding the antibody dilution or buffer (reference sample), the samples were mixed shortly by pipetting and directly measured without any further incubation time. The reference sample (ref) contained the MNP-APTES-S1 and a buffer solution.
In Fig. 3 Fig. 3 b) while subtle was clearly detectable. In Fig. 3 c, the differences between both experiments are indicated (amplitude differences and phase differences). Two prominent results became evident: rst, the difference in the peak height and width of the phase differences (solid line) between both experiments. The phase difference between a reference and binding sample measurement is by a factor f dφ ≈17 increased compared to the phase difference of two reference The phase difference for the ref 1 & ref 1 ' measurement also showed a clearly visible peak, which lay, as expected, at the highest phase sensitivity of the system (critical point). This effect is dominated by noise and slightly by systematic errors such as sample positioning between the successively performed measurements. This re ects an intrinsic sensitivity limit of the used device.
The initial result in Fig. 3 revealed not only a high sensitivity on minimal changes of particle diameters (mobility) in the vicinity of each CP for each higher harmonic but also indicated a high robustness on hardware requirements or magnetic eld parameters due to the width of the peak.

Mobile COMPASS device
Many measuring techniques are based on physical effects and their sensitivity commonly correlates with the complexity of the underlying measurement hardware. With increasing demand on sensitivity, the requirements for sophisticated hardware to guarantee the necessary speci city and robustness increase signi cantly. Thus, depending on the desired application, such methods may become non-feasible.
The observed results suggest design parameters and design speci cations for a highly exible and robust device allowing very sensitive and speci c measurements. The device presented in the following is based on common MPS technology running at a base-frequency f 1 =20 kHz and comes with a robust hardware design and easy-to-handle experiments [6]. Based on the results shown above, an important hardware modi cation was introduced. By adding a strong permanent magnet, which generates a strong magnetic eld gradient G along the measurement area providing a range of offset magnetic elds H DC within the sample volume. Under the right condition between excitation eld H AC and offset magnetic elds covering one or more CPs, the sensitivity of MPS experiments against minimal changes in mobility was improved signi cantly (see supplementary S2).
In Fig. 4 a, the proposed modi ed MPS device is shown. As a mobile and highly exible stand-alone device, it consists of the main control device with all required electronic parts, such as transmit/receive (tx/rx) module for generating the required magnetic elds and measuring the sample signals as well as a battery pack as power supply. The sketch in Fig. 4 b of the tx/rx module shows a cross-section through the tx/rx module indicating the position of the sample in the eld of view (FOV) in the center of one of the receive coil pair (rx) wired as gradiometer, the transmit solenoid (tx) and the permanent magnet. The offset magnetic eld H DC (x) generated by the permanent magnet creates a strong magnetic eld gradient G within the FOV (see supplementary S5), which in uences the inductively measured signal signi cantly.
In Fig. 5 a, the rst results of the proposed mobile modi ed MPS device measuring the binding state of MNP-APTES-S1 particles are shown (for data processing details see supplementary S6). Each measurement was performed 5 times without averaging. The sequence of samples was reference sample (ref) containing buffer, binding sample (S+) containing a S1 binding antibody (SARS-CoV-2-S1 antibody) and non-binding-sample (S-) containing a non-binding antibody (MERS-CoV-S1 antibody) and was repeated 2 times resulting in 30 individual measurements. The acquisition time for each experiment was 10 ms with a minimum repetition time of 1 s. The graph shows the phase difference dφ n on selected higher harmonic (n=2 nd to 9 th ) against the reference sample. A signi cant phase difference on each harmonic was observed for the binding sample (S+) but not for the non-binding sample (S-). Here, the 9 th harmonic showed the highest difference. But also other harmonics revealed signi cant phase differences since the applied gradient (permanent magnet) ensured a broad range of offset magnetic elds acquiring signals from multiple critical points.
For comparison, a series of experiments were performed to demonstrate the in uence of the magnetic offset elds and magnetic eld gradient on the signal (Fig. 5 b). For that, the same experiment sequence was performed for three different cases: (1) with permanent magnet in described position, (2) with permanent magnet in a rotated position (90° degrees against the tx/rx orientation) and (3) without permanent magnet. It became evident, that in case (1) and (2) (with permanent magnets) the desired signal (phase difference) was more prominent than without (case (3)). The signals with permanent magnets differed depending on the gradient strength generated by the permanent magnet within the FOV. This variation depended on the range of offset elds (gradient G) mentioned above.
Can COMPASS be an alternative to ELISA and ow cytometry?
The results in Fig. 5 with the modi ed MPS device represent the signal not only at one speci c position H DC of the Chebyshev-like polynomial (Fig. 3) but the integration of signals over a range of offset magnetic elds (supplementary S2). The sensitivity strongly depends on the chosen gradient eld G as indicated in Fig. S2-2. As shown in Fig. 3, the sensitivity of the method for speci c harmonics increased further by adjusting the gradient eld around a very small and speci c range covering the area of a speci c critical point CP i,j (see S5-4) but potentially at the cost of reduced robustness.
More important, the handling of COMPASS experiments and measurements are more exible and requires no complicated sample preparation and the results are robustly available in shorter protocol time (seconds Vs. hours) including conjugation time. Furthermore, a quanti cation of the amount of bindings on the surface of the functionalized particles was observed with COMPASS at a high speci city (supplementary S7).
Our method can be used as a robust, fast and easy-to-handle and cheap testing method for sensitive and speci c antigen or antibody determination. It thus offers a wide variety of applications in clinical chemistry and biomedical analytics.
COMPASS also allows the measurement of intermolecular interactions of different compartments on functionalized magnetic particles. This opens a wide eld in physics, medicine, biology and chemistry [10,20].
Since In Addition, the differential measurement (sample Vs reference) of the phases can overcome issues in signal interpretation occurring in MPS or ACS experiments due to concentration dependencies. This provides a huge list of particle parameters accessible with high accuracy, which can be seen in the Langevin equation (EquS. 2-1) consisting of multiple parameters such as the magnetic moment of the particle m, the Temperature T and the friction ζ, where the latter is the product of viscosity η of the surrounding medium, the hydrodynamic particle radius R H and the particle shape κ. The advantage of this method is the direct access to particle parameters, which are of high interest for understanding the complex dynamics of MNP ensembles. Furthermore, fast and easy access to these parameters allows a robust MNP characterization during synthetization and hence gives immediate feedback of improving the quality of magnetic particles, e.g., for medical applications or environmental treatment [21,22].
Beyond the aforementioned, many more applications in different elds of research are conceivable, and COMPASS will pave the way for their realization.   consists not only of the fundamental frequency but also odd (and even) higher harmonics (f n =n·f 1 ) depending on the presence of an offset magnetic eld H DC , which can be visualized in the Fourier spectrum.
(c) Visualizing the dependency of the harmonic A n for the n-th higher harmonic for increasing offset magnetic eld H DC (with H DC <H AC ). The speci c shape for varying H DC with nodes (green arrow) depends on the harmonic number n. As an example, the real part of the 3 rd harmonic of simulated data is indicated to show the connection between a 'dip' in the Fourier spectrum and a 'node' in the A n (H DC ) plot: this point is called critical point (CP).

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