Characterizations of Anti-Alpha-Fetoprotein-Conjugated Magnetic Nanoparticles Associated with Alpha-Fetoprotein for Biomedical Applications

In this work, we report characterizations of biofunctionalized magnetic nanoparticles (BMNPs) associated with alpha-fetoprotein (AFP) for biomedical applications. The example BMNP in this study is anti-alpha-fetoprotein (anti-AFP) conjugated onto dextran-coated Fe3O4 labeled as Fe3O4-anti-AFP, and the target is AFP. We characterize magnetic properties, such as increments of magnetization ΔMH and effective relaxation time Δτeff in the reaction process. It is found that both ΔMH and Δτeff are enhanced when the concentration of AFP, ФAFP, increases. The enhancements are due to magnetic interactions among BMNPs in magnetic clusters, which contribute extra MH after the association with MH and in turn enhance τeff. The screening of patients carrying hepatocellular carcinoma (HCC) is verified via ΔMH/MH. The proposed method can be applied to detect a wide variety of analytes. The scaling characteristics of ΔMH/MH show the potential to develop a vibrating sample magnetometer system with low field strength for clinic applications.


Introduction
Immunoassays are biochemical tests used to detect or quantify a specific substance, such as analytes in samples of blood or bodily fluid, using immunological reactions. Immunoassay methods include the enzyme-linked immunosorbent assay (ELISA) [1], radioimmunoassay (RIA) [2], real-time polymerase chain reaction (real-time PCR) [3], immunonephelometry [4], etc. Some immunoassays, such as ELISA, require two antigens and separation of the unbound antigens, which can be tedious and time-consuming. On the other hand, magnetic immunoassay (MIA) is a novel type of diagnostic technology using magnetic nanoparticles (MNPs) as labels to replace conventional ELISA, RIA, real-time PCR, etc. MNPs are coated with dextran so that they are encapsulated or glued together with polymers in sizes of nanometers or even micrometers. In immunomagnetic tests, MNPs are first biofunctionalized against antibodies to target antigens. Reagents consisting of biofunctionalized magnetic nanoparticles (BMNPs) are then mixed with samples. Due to the molecular interactions among BMNPs and biomarkers, magnetic clusters are conjugated in the reaction process and their magnetic properties change after the association. The magnetic signal due to the changes of magnetic properties is analyzed in order to determine the unknown amount of biomarkers. Magnetic properties (magnetic relaxation [5,6], remanent magnetization [7], Brownian relaxation [8], saturation magnetization [9], spin-spin relaxation of NMR [10], and alternative-current (AC) susceptibility reduction [11][12][13][14][15], etc.) have been developed recently. Magnetic immunoassays can be carried out simply by mixing reagents and tested samples together and taking physical measurements. Additionally, the background noise of magnetic detection is negligible; hence, high detection sensitivity can be achieved.
Based on the increment of saturation magnetization, ∆M S , Chieh et al. [16] recently reported another assay method that used a vibrating sample magnetometer (VSM) to label tumor biomarkers of alpha-fetoprotein (AFP) in clinical studies via the ∆M S /M S -versus-Φ AFP curve at the saturation field H S , where Φ AFP was the concentration of AFP. The authors demonstrated that VSM can be used to screen patients carrying hepatocellular carcinoma (HCC) with sensitivity better than the criterion set in clinics (0.02 µg/mL). It would be interesting to see whether we can screen HCC patients with high detection sensitivity at low magnetic fields (H). Therefore, in this work, we propose a detection method based on the scaling characteristic of the normalized increment of magnetization at low magnetic fields. It is found that M AFP and τ eff are enhanced when Φ AFP increases, where M AFP is the magnetization of the reagent and τ eff is the effective relaxation time. We attribute those results to the molecular interactions among BMNPs in the associated magnetic clusters, which contribute extra magnetization and in turn enhance τ eff . The scaling characteristic of (∆M AFP /M AFP,0 )-versus-Φ AFP curves at low magnetic fields is demonstrated, and the screening of HCC patients via the scaling characteristic is verified in clinical studies.

Experiments
The MNPs in this study were dextran-coated Fe 3 O 4 (MF-DEX-0060, MagQu Co., Ltd., New Taipei City, Taiwan) with a mean core diameter of~35 nm, as detected by x-ray diffraction (D-500, Siemens). The BMNPs were Fe 3 O 4 -anti-AFP (MF-AFP-0060, MagQu Co. Ltd., New Taipei City, Taiwan), and the biotarget was AFP, which is a biomarker for diagnosing HCC. When the AFP level is abnormally high before surgery or other therapy, it is expected to fall to normal levels following the successful removal of all cancer cells.
In performing the AFP tests, the BMNPs consisting of Fe 3 O 4 -anti-AFP were first mixed with AFP. The changes of magnetic properties after the reaction process were then characterized using a VSM (Model Hystermag, MagQu Co., Taiwan) and AC susceptometer. The data of the normalized increments of magnetization ∆M/M were analyzed for a magnetic immunoassay. The AC susceptibility was measured by a highly balanced AC susceptometer in order to monitor the real-time reaction process. The AC susceptibility χ ac (ω) can be expressed as follows: where i = (−1) 1/2 , χ /χ = tanθ = ωτ eff (t), and θ is the phase lag of the time-varying magnetization M(t) with respect to the applied AC magnetic field H(t). Figure 1a shows the detection schematic of the VSM used for characterizing M after the BMNPs had conjugated with AFP. In the measurement of M, the sample vibrated with a frequency of~30 Hz. The magnetic signal was detected with a second-order gradient coil. An electromagnet provided a magnetic field of up to 1.0 Tesla, so that the M-H curves of reagents were characterized. In assaying AFP, a reagent composed of 40 µL Fe 3 O 4 -anti-AFP was mixed with 60 µL AFP. We measured the M-H curves and analyzed the magnetization enhancement (∆M) at low external fields (H) to establish the relationship between ∆M/M and the concentrations of AFP (Φ AFP ). Figure 1b shows the high-T C SQUID-based AC susceptometer for characterizing the AC magnetic susceptibility. The excitation frequency is~16 kHz. The magnetic signal of BMNPs is picked up by a gradient coil that is coupled to a high-T C SQUID via a flux transformer. The detailed design of the pickup coil, gradient coil, and compensation coil in a homemade AC susceptometer that did not use a high-T c SQUID was reported in [17,18]. The reagent was composed of anti-AFP-conjugated Fe3O4 labeled as Fe3O4-anti-AFP. The biotarget was AFP. Figure 2 depicts Fe3O4-anti-AFP, AFP, and a magnetic cluster composed of Fe3O4anti-AFP-AFP.    The reagent was composed of anti-AFP-conjugated Fe3O4 labeled as Fe3O4-anti-AFP. The biotarget was AFP. Figure 2 depicts Fe3O4-anti-AFP, AFP, and a magnetic cluster composed of Fe3O4anti-AFP-AFP.

Results and Discussion
This section addresses and discusses the results from the characterization of magnetic properties when biofunctionalized Fe 3 O 4 -anti-AFPs are associated with AFP. Additionally, we present the results from the real-time association of Fe 3 O 4 -anti-AFP with AFP via the time-dependency studies of τ eff (t) in the reaction process using the technique of AC susceptibility. We also briefly summarize the findings. Finally, we present the clinical research on screening HCC patients via normalized increments of magnetization and address and discuss advances in sensitive bio-sensing. Figure 3 shows ∆M H as a function of Φ AFP at µ 0 H = 0.02 T, 0.06 T, and 0.16 T and ∆M H = M H (Φ AFP ) − M H (Φ AFP = 0). For a fixed magnetic field at µ 0 H = 0.02 T, ∆M H = 0.015 emu/g when Φ AFP = 0.01 µg/mL, and ∆M H increases to ∆M µ0H = 0.02 T = 0.13 emu/g when Φ AFP = 10 µg/mL. For µ 0 H = 0.16 T, ∆M µ0H = 0.16 T = 0.03 emu/g when Φ AFP = 0.01 µg/mL, and ∆M H increases to ∆M µ0H = 0.16 T = 0.23 emu/g when Φ AFP = 10 µg/mL. Hence, we have demonstrated an enhancement of ∆M H when Φ AFP increases at a fixed magnetic field. We attribute those enhancements to the fact that more magnetic clusters are associated and stronger magnetic interactions among BMNPs are present.

Results and Discussion
This section addresses and discusses the results from the characterization of magnetic properties when biofunctionalized Fe3O4-anti-AFPs are associated with AFP. Additionally, we present the results from the real-time association of Fe3O4-anti-AFP with AFP via the time-dependency studies of τeff(t) in the reaction process using the technique of AC susceptibility. We also briefly summarize the findings. Finally, we present the clinical research on screening HCC patients via normalized increments of magnetization and address and discuss advances in sensitive bio-sensing. Figure 3 shows ΔMH as a function of ФAFP at μ0H = 0.02 T, 0.06 T, and 0.16 T and ΔMH = MH(ФAFP) − MH(ФAFP = 0). For a fixed magnetic field at μ0H = 0.02 T, ΔMH = 0.015 emu/g when ФAFP = 0.01 μg/mL, and ΔMH increases to ΔMμ0H = 0.02 T = 0.13 emu/g when ФAFP = 10 μg/mL. For μ0H = 0.16 T, ΔMμ0H = 0.16 T = 0.03 emu/g when ФAFP = 0.01 μg/mL, and ΔMH increases to ΔMμ0H = 0.16 T = 0.23 emu/g when ФAFP = 10 μg/mL. Hence, we have demonstrated an enhancement of ΔMH when ФAFP increases at a fixed magnetic field. We attribute those enhancements to the fact that more magnetic clusters are associated and stronger magnetic interactions among BMNPs are present.  . It is found that ΔMAFP/MAFP,0 as a function of ФAFP in external magnetic fields can be scaled to a universal logistic function described by the following formula [15]: where A and B are dimensionless quantities and Ф0 is dimensionless. The fitting parameters are as follows: A = 0.173, B = 34.2, Φ0 = 3410 μg/mL, and γ = 0.5. We have established a relationship between ΔMAFP/MAFP,0 and ФAFP with ФAFP varied from 0.01 μg/mL to 10 μg/mL. Therefore, the unknown amounts of AFP can be determined via a scaling characteristic of the (ΔMAFP/MAFP,0)-versus-ФAFP curve, which is versatile and can be applied to assay other biomarkers. In assaying other biomarkers, the relationship between ΔMbiomarker/Mbiomarker,0 and Фbiomarker is first established and then ΔMbiomarker/Mbiomarker,0 and the Фbiomarker curve are applied to determine the unknown amount of biomarkers quantitatively.  It is found that ∆M AFP /M AFP,0 as a function of Φ AFP in external magnetic fields can be scaled to a universal logistic function described by the following formula [15]: where A and B are dimensionless quantities and Φ 0 is dimensionless. The fitting parameters are as follows: A = 0.173, B = 34.2, Φ 0 = 3410 µg/mL, and γ = 0.5. We have established a relationship between ∆M AFP /M AFP,0 and Φ AFP with Φ AFP varied from 0.01 µg/mL to 10 µg/mL. Therefore, the unknown amounts of AFP can be determined via a scaling characteristic of the (∆M AFP /M AFP,0 )-versus-Φ AFP curve, which is versatile and can be applied to assay other biomarkers.
In assaying other biomarkers, the relationship between ∆M biomarker /M biomarker,0 and Φ biomarker is first established and then ∆M biomarker /M biomarker,0 and the Φ biomarker curve are applied to determine the unknown amount of biomarkers quantitatively. To observe the real-time association of τeff when Fe3O4-anti-AFPs are associated with AFP directly, we characterize the time-dependent τeff via the following formula: tanθ = ωτeff, where χ''/χ' = tanθ and χ' and χ'' are the real and imaginary parts of AC susceptibility in Equation (1). Figure 5a shows τeff(t) as a function of time in the reaction process. The reagent shows τeff = ~1.3 μs, and τeff is stable to τeff = 1.3 μs at t = 7200 s. It takes approximately 6000 s for the reagent to complete the association and τeff is increased to τeff = ~1.75 μs with ФAFP = 1 μg/mL. Therefore, a detection time of 7200 s is suggested. The real-time association of Fe3O4-anti-AFP with AFP is verified.
The Brownian relaxation time, τB, is a function of the hydrodynamic volume of a magnetic particle, VH, the viscosity of the medium, η, the Boltzmann's constant, k, and the absolute temperature, T, which is expressed as follows [19]: In the reaction process, we assume that the viscosity and temperature are constant. The Brownian relaxation time is proportional to the hydrodynamic volume of the magnetic particle. The ratio of the increase in τeff after the reaction process is 1.35 with an ФAFP value of 1 μg/mL. The effective diameter of the magnetic cluster is 2.4 times larger than a single magnetic particle when ФAFP is 1 μg/mL. It presents the formation of magnetic clusters during the reaction process. Figure 5b shows Δτeff/τeff,0 as a function of ФAFP with ФAFP ranging from ФAFP = 0.001 μg/mL to ФAFP = 1 μg/mL. The reagent shows τeff = 1.3 μs, and τeff is enhanced to τeff = ~1.75 μs when ФAFP = 1 μg/mL. The enhancement of τeff is due to the presence of magnetic clusters in the reaction process. The magnetic interaction among BMNPs enhances M, which in turn increases τeff. The (Δτeff/τeff,0)versus-ФAFP curve follows the characteristic curve [15]: where Δτeff = τeff(7200 s) − τeff(t = 0) and τeff,0 = τeff(t = 0). The curve is fitted to the following parameters: A1 = −0.013 μs, B1 = 0.56 μs, Φ0 = 0.15 μg/mL, and γ = 0.52. Equation (4) reveals the concentration dependency of the characteristic of Δτeff/τeff,0 after the BMNPs have completed the association with AFP. The (Δτeff/τeff,0)-versus-ΦAFP curve shown in Figure 5b can be applied to screening patients carrying HCC. Normalized Δτeff/τeff,0 is analyzed instead of Δτeff for a magnetic immunoassay, because this enables us to eliminate minor differences in magnetic signals due to minor differences in sample amounts used from run to run, which will enhance the detection sensitivity. Detection sensitivity can be defined by the noise level with standard deviations for the detected signal at low concentrations [20]. In this study, the detection sensitivity levels are 0.0024 μg/mL and 0.0177 μg/mL, as determined by measuring Δτeff/τeff,0 and ΔMAFP/MAFP,0 respectively. The reference To observe the real-time association of τ eff when Fe 3 O 4 -anti-AFPs are associated with AFP directly, we characterize the time-dependent τ eff via the following formula: tanθ = ωτ eff , where χ /χ = tanθ and χ and χ are the real and imaginary parts of AC susceptibility in Equation (1). Figure 5a shows τ eff (t) as a function of time in the reaction process. The reagent shows τ eff =~1.3 µs, and τ eff is stable to τ eff = 1.3 µs at t = 7200 s. It takes approximately 6000 s for the reagent to complete the association and τ eff is increased to τ eff =~1.75 µs with Φ AFP = 1 µg/mL. Therefore, a detection time of 7200 s is suggested. The real-time association of Fe 3 O 4 -anti-AFP with AFP is verified.
The Brownian relaxation time, τ B , is a function of the hydrodynamic volume of a magnetic particle, V H , the viscosity of the medium, η, the Boltzmann's constant, k, and the absolute temperature, T, which is expressed as follows [19]: In the reaction process, we assume that the viscosity and temperature are constant. The Brownian relaxation time is proportional to the hydrodynamic volume of the magnetic particle. The ratio of the increase in τ eff after the reaction process is 1.35 with an Φ AFP value of 1 µg/mL. The effective diameter of the magnetic cluster is 2.4 times larger than a single magnetic particle when Φ AFP is 1 µg/mL. It presents the formation of magnetic clusters during the reaction process. Figure 5b shows ∆τ eff /τ eff,0 as a function of Φ AFP with Φ AFP ranging from Φ AFP = 0.001 µg/mL to Φ AFP = 1 µg/mL. The reagent shows τ eff = 1.3 µs, and τ eff is enhanced to τ eff =~1.75 µs when Φ AFP = 1 µg/mL. The enhancement of τ eff is due to the presence of magnetic clusters in the reaction process. The magnetic interaction among BMNPs enhances M, which in turn increases τ eff . The (∆τ eff /τ eff,0 )-versus-Φ AFP curve follows the characteristic curve [15]: where ∆τ eff = τ eff (7200 s) − τ eff (t = 0) and τ eff,0 = τ eff (t = 0). The curve is fitted to the following parameters: A 1 = −0.013 µs, B 1 = 0.56 µs, Φ 0 = 0.15 µg/mL, and γ = 0.52. Equation (4) reveals the concentration dependency of the characteristic of ∆τ eff /τ eff,0 after the BMNPs have completed the association with AFP. The (∆τ eff /τ eff,0 )-versus-Φ AFP curve shown in Figure 5b can be applied to screening patients carrying HCC. Normalized ∆τ eff /τ eff,0 is analyzed instead of ∆τ eff for a magnetic immunoassay, because this enables us to eliminate minor differences in magnetic signals due to minor differences in sample amounts used from run to run, which will enhance the detection sensitivity. Detection sensitivity can be defined by the noise level with standard deviations for the detected signal at low concentrations [20]. In this study, the detection sensitivity levels are 0.0024 µg/mL and 0.0177 µg/mL, as determined by measuring ∆τ eff /τ eff,0 and ∆M AFP /M AFP,0 respectively. The reference criterion of the AFP serum level for HCC is 0.02 µg/mL. The sensitivity of both methods reaches the criteria for a clinical AFP assay. The feasibility of AFP is demonstrated by measuring ∆τ eff /τ eff,0 and ∆M AFP /M AFP,0 .  In this study, we characterized magnetic properties when BMNPs are associated with AFPs for biomedical applications. The findings in the characterization of magnetic properties are briefly summarized as follows. First, M and τeff are enhanced when reagents composed of BMNPs are conjugated with AFP in the reaction process. The magnetic interactions among BMNPs in magnetic clusters enhance M, which in turn increases τeff. Second, the real-time association of BMNPs with AFP was demonstrated in the time-dependent τeff,. Third, bio-detection based on the (Δτeff/τeff,0)-versus-Φbiomarkers curve provided a sensitive methodology for assaying unknown amounts of AFP, and BMNPs could be applied to assay large molecules such as AFP as well as small molecules such as Creactive protein(CRP) [21]. Finally, the proposed detection methodology based on the (Δτeff/τeff,0)versus-Φbiomarkers curve was versatile, and the (ΔMAFP/MAFP,0)-versus-ФAFP curves shown in Figure 4 were scaled to a characteristic function described by Equation (2). The results confirm that both changes in ΔMAFP/MAFP,0 and Δτeff/τeff,0 are caused by the formation of magnetic clusters and can be applied to sense a wide variety of biomarkers.
The sensitivity levels of Δτeff/τeff,0 and ΔMAFP/MAFP,0 reach the criteria for a clinical AFP assay. The cost of a high-TC SQUID-based AC susceptometer is much higher than that of a VSM with a lowstrength magnet. The low-strength VSM has high potential for commercial and clinical applications. Therefore, the screening of HCC patients can be addressed by measuring ΔMH/MH,0. Since the data shown in Figure 4 are scaled to a characteristic function described by Equation (2), it would be interesting to verify whether we can also obtain high detection sensitivity at low magnetic fields via In this study, we characterized magnetic properties when BMNPs are associated with AFPs for biomedical applications. The findings in the characterization of magnetic properties are briefly summarized as follows. First, M and τ eff are enhanced when reagents composed of BMNPs are conjugated with AFP in the reaction process. The magnetic interactions among BMNPs in magnetic clusters enhance M, which in turn increases τ eff . Second, the real-time association of BMNPs with AFP was demonstrated in the time-dependent τ eff, . Third, bio-detection based on the (∆τ eff /τ eff,0 )-versus-Φ biomarkers curve provided a sensitive methodology for assaying unknown amounts of AFP, and BMNPs could be applied to assay large molecules such as AFP as well as small molecules such as C-reactive protein(CRP) [21]. Finally, the proposed detection methodology based on the (∆τ eff /τ eff,0 )-versus-Φ biomarkers curve was versatile, and the (∆M AFP /M AFP,0 )-versus-Φ AFP curves shown in Figure 4 were scaled to a characteristic function described by Equation (2). The results confirm that both changes in ∆M AFP /M AFP,0 and ∆τ eff /τ eff,0 are caused by the formation of magnetic clusters and can be applied to sense a wide variety of biomarkers.
The sensitivity levels of ∆τ eff /τ eff,0 and ∆M AFP /M AFP,0 reach the criteria for a clinical AFP assay. The cost of a high-T C SQUID-based AC susceptometer is much higher than that of a VSM with a low-strength magnet. The low-strength VSM has high potential for commercial and clinical applications. Therefore, the screening of HCC patients can be addressed by measuring ∆M H /M H,0 . Since the data shown in Figure 4 are scaled to a characteristic function described by Equation (2), it would be interesting to verify whether we can also obtain high detection sensitivity at low magnetic fields via Equation (2). Hence, we can apply Equation (2)  The reference criterion of the AFP serum level for HCC is 0.02 µg/mL. We found that the average AFP levels for patients carrying HCC were higher than~0.2 µg/mL, which is significantly higher than the criterion set in clinics (0.02 µg/mL). The average AFP levels for healthy persons were below~0.02 µg/mL, except for one healthy person who showed a false positive (AFP level =~0.03 µg/mL). Figure 6b shows ∆M AFP /M AFP,0 as a function of Φ AFP with data analyzed at 0.16 T. HCC patients showed AFP levels higher than the clinical criterion. Healthy persons showed AFP levels of 0.001 µg/mL, except for one healthy person with a higher AFP level of~0.4 µg/mL. The estimated values of Φ AFP were different between µ 0 H = 0.065 T and 0.16 T. It was probably due to the magnetic clustering effect that induces background magnetic noises. Besides, the ∆M AFP/ ∆M AFP,0 of serum tested at 0.16 T is higher than that at 0.065 T. It leads that the estimated AFP concentration at 0.16 T is higher than that at 0.065 T. The reason may be due to the larger background magnetization of serum than that of the AFP solution. The reference magnetization, M(Φ AFP = 0), in the clinical test may be considered by using the averaging magnetization of healthy persons to reduce the effect in the clinical test. Thus, the feasibility of screening HCC patients by assaying AFP levels in serum was verified. . The reference criterion of the AFP serum level for HCC is 0.02 μg/mL. We found that the average AFP levels for patients carrying HCC were higher than ~0.2 μg/mL, which is significantly higher than the criterion set in clinics (0.02 μg/mL). The average AFP levels for healthy persons were below ~0.02 μg/mL, except for one healthy person who showed a false positive (AFP level = ~0.03 μg/mL). Figure 6b shows ΔMAFP/MAFP,0 as a function of ФAFP with data analyzed at 0.16 T. HCC patients showed AFP levels higher than the clinical criterion. Healthy persons showed AFP levels of 0.001 μg/mL, except for one healthy person with a higher AFP level of ~0.4 μg/mL. The estimated values of ФAFP were different between μ0H = 0.065 T and 0.16 T. It was probably due to the magnetic clustering effect that induces background magnetic noises. Besides, the ΔMAFP/ΔMAFP,0 of serum tested at 0.16 T is higher than that at 0.065 T. It leads that the estimated AFP concentration at 0.16 T is higher than that at 0.065 T. The reason may be due to the larger background magnetization of serum than that of the AFP solution. The reference magnetization, M(ФAFP = 0), in the clinical test may be considered by using the averaging magnetization of healthy persons to reduce the effect in the clinical test. Thus, the feasibility of screening HCC patients by assaying AFP levels in serum was verified.  The AFP level in serum was recently determined via the ∆M S -versus-Φ AFP curve at the saturation field µ 0 H S =~0.4 T [16], where ∆M S is the increment of the saturated magnetization. A clear demarcation between the normal group and the HCC group was verified in the test results, which indicates the feasibility of using ∆M S -versus-Φ AFP at the saturation field as the primary analysis factor for identifying the AFP risk level in patients. In this work, the screening of HCC patients was fulfilled at low magnetic fields, which makes the detection platform simple for biomedical application users.

Conclusions
In summary, we performed measurements of magnetization (M-H curves) and AC susceptibility when reagents consisting of Fe 3 O 4 -anti-AFP were conjugated with AFP. The scaling characteristic of (∆M AFP /M AFP,0 )-versus-Φ AFP curves at low magnetic fields was demonstrated, and bio-sensing using BMNPs via increments of magnetization was proposed. We showed that BMNPs can be applied to assay large as well as small molecules. The screening of HCC patients via the scaling characteristic was verified in clinical studies. The detection mechanism based on the scaling characteristic showed potential to develop a compact VSM with a low magnetic field for biomedical applications.