Assaying Biomarkers via Real-Time Measurements of the Effective Relaxation Time of Biofunctionalized Magnetic Nanoparticles Associated with Biotargets

Abstract

An assay of biomarkers consisting of alpha-fetoprotein (AFP) is reported. Real-time measurements of the effective relaxation time [subscript]τeff[/subscript] , when the biofunctionalized magnetic nanoparticles (BMNs) were conjugating with biotargets, were made. The BMNs are anti-alpha-fetoprotein (antiAFP) coated onto dextran-coated iron oxide nanoparticles labeled as Fe3O4-antiAFP. It was found that the effective relaxation time, [subscript]τeff[/subscript] , increases as the association of AFP and Fe3O4-antiAFP evolves. We attribute this to the enhanced Brownian motion of BMNs when magnetic clusters are present during the conjugation. We found that saturation magnetization, [subscript]Ms[/subscript] , increases when the concentration of AFP increases. This is due to the fact that more magnetic clusters are associated in the reagent, and therefore the [subscript]Ms[/subscript] increases when the concentration of AFP increases. The change of effective relaxation time and saturation magnetization shows a behavior of logistic function, which provides a foundation for assaying an unknown amount of biomolecules. Thus, we demonstrate sensitive platforms for detecting AFP by characterizing [subscript]τeff[/subscript] . The detection platform is robust and easy to use and shows promise for further use in assaying a broad number of biomarkers.

Shu-Hsien Liao 1 and Jean-Hong Chen 2 and Yu-Kai Su 1 and Kuen-Lin Chen 3 and Herng-Er Horng 1 and Hong-Chang Yang 4

Academic Editor:Yali Cui

1, Institute of Electro-Optical Science and Technology, National Taiwan Normal University, Taipei 116, Taiwan
2, Department of Materials Engineering, Kun Shan University, Tainan 710, Taiwan
3, Department of Physics, National Chung Hsing University, Taichung 402, Taiwan
4, Department of Electro-Optical Engineering, Kun Shan University, Tainan 710, Taiwan

Received 12 September 2014; Accepted 9 February 2015; 28 May 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Assaying biomarkers based on electrical [1], optical [2, 3], and magnetic technologies [4, 5], and so forth, has been reported, in which, immuomagnetic assays based on magnetic detection using biofunctionalized magnetic nanoparticles (BMNs) have received considerable attention. Magnetic detection has a negligible magnetic background, and thus high detection sensitivity and specificity can be achieved. Magnetic detection can be done through the measurements of magnetic relaxation [6, 7], magnetic remanence [8], immunomagnetic alternating current (ac) susceptibility reduction [9], saturated magnetization [10], spin-spin relaxation [11], and so forth. Detection sensors include SQUIDs [12], magnetoresistive sensors [13], Hall sensors [14], and on-chip magnetic resonance sensors [15]. Many of these techniques, however, have a time- consuming stage of sample preparation. On the contrary, detecting biomarkers using the immunomagnetic reduction (IMR) assay [9], which detects the change of the amplitude at the mixed-frequency. The method shows high sensitivity and specificity. Additionally, sample preparation is simple and easy to operate. Some studies involving this approach include the detecting of cytokines [16] and alpha-fetoprotein (AFP) for human expressing tumors in clinical research [17].

In contrast to direct detection of magnetic susceptibility reduction at the mixed-frequency, we have recently developed a new magnetic sensing platform, single-frequency ac susceptometer for biodetection [18]. The ac susceptometer detects the phase lag of the magnetization, [figure omitted; refer to PDF] , of BMNs with respect to the applied field, [figure omitted; refer to PDF] , as the detection mechanism. During the association of BMNs with biomarkers the magnetic clusters are conjugated, which changes the phase lag and in turn changes the time-dependent relaxation rate. In this work, the detection platform was used to assay the biomolecule abundance of alpha-fetoprotein (AFP) by measuring the time-dependent effective relaxation time and saturation magnetization of reagents conjugating with the AFP. Reagents consisted of antiAFP coated onto the Fe₃ O₄ magnetic oxides and labeled as Fe₃ O₄ -antiAFP. AFP can be used as a biomarker to detect liver tumors. A level above 500 ng/mL of AFP in adults can be indicative of hepatocellular carcinoma, germ cell tumors, and metastatic cancers of the liver. Biomarkers of AFP are first characterized by measuring the phase lag [figure omitted; refer to PDF] , which is between the applied magnetic field [figure omitted; refer to PDF] and magnetization [figure omitted; refer to PDF] . Then the dynamic effective relaxation time [figure omitted; refer to PDF] was estimated through the following formula: [figure omitted; refer to PDF] , where [figure omitted; refer to PDF] is the exciting angular frequency. It was found that the change of effective relaxation time, [figure omitted; refer to PDF] , increases when the AFP completed the association with Fe₃ O₄ -antiAFP. Additionally, the saturation magnetization increases as the concentration of AFP increases. We attribute this to the presence of magnetic clusters during the conjugation. A detection sensitivity better than 100 ng/mL of AFP is demonstrated. The detection platform is robust and easy to use, showing promise for further use in a broad number of biomedical applications, such as viruses, proteins, and tumor markers.

The reagent for assaying AFP consists of magnetic nanoparticles (MF-DEX-0060, MagQu, New Taipei, Taiwan) functionalized with antibodies (ab40942; Abcam, Cambridge, MA), against AFP (EA502-Q1053; EastCoast Bio, North Berwick, ME). These magnetic nanoparticles are dispersed in phosphoryl buffer solution with pH = 7.4. Measured with a vibration sample magnetometer, the concentration of magnetic reagents containing Fe₃ O₄ -antiAFP was 0.3 emu/g which corresponds to a concentration of 1.2 mg-Fe/mL.

2. Experiments

2.1. Biodetection System

Figure 1 shows the unique design of the sensitive ac magnetic susceptometer. The sensing coils consist of an input coil, pick-up coil, and compensation coil. The input coil, pick-up coil, and compensation coil are, respectively, 4800 turns (4.9 Ω), 1260 turns (1.2 Ω), and 2 turns of wound copper coils. The pick-up coil consisted of two coils wound in opposite directions. The excitation frequency was 9 kHz. The signal from the function generator is first attenuated with a variable resistor (~1 MΩ). A compensation coil was applied to improve the balance of the detection coil. A balance of 30 parts per trillion (ppt) is achieved in such a sensing unit. Due to the nonlinear magnetic characteristics of magnetic nanoparticles, when the excitation frequency [figure omitted; refer to PDF] is applied to the input coil, an excited signal with [figure omitted; refer to PDF] components will be generated in the pick-up coil. In the present study, the dynamic [figure omitted; refer to PDF] and amplitude, [figure omitted; refer to PDF] , of the fundamental component, [figure omitted; refer to PDF] , are detected through lock-in detection.

Figure 1: The detection scheme of an ac magnetic susceptometer with a lock-in detection technique.

[figure omitted; refer to PDF]

2.2. Detection Mechanism

Due to the molecular interaction, BMNs are associated with biomarkers and the magnetic clusters are conjugated. The magnetization from magnetic clusters will affect the physical properties of the BMNs during the association of BMNs with the biomarkers, for instance, the dynamic phase lag [figure omitted; refer to PDF] of [figure omitted; refer to PDF] with respect to [figure omitted; refer to PDF] in ac susceptibility and the saturation magnetization, [figure omitted; refer to PDF] , and so forth. By characterizing the dynamic [figure omitted; refer to PDF] or [figure omitted; refer to PDF] , we can therefore determine the unknown amount of biomarkers.

We consider the ac magnetic susceptibility of BMNs, [figure omitted; refer to PDF] , in an applied ac magnetic field. [figure omitted; refer to PDF] is a function of [figure omitted; refer to PDF] and exciting angular frequency [figure omitted; refer to PDF] . The [figure omitted; refer to PDF] can be expressed as follows [19]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the component of [figure omitted; refer to PDF] at [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] . [figure omitted; refer to PDF] is the phase lag of the time-varying magnetization [figure omitted; refer to PDF] with respect to the applied ac magnetic field [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] is the effective relaxation rate. Using (1) and (2), we obtained [figure omitted; refer to PDF] with [figure omitted; refer to PDF] . The [figure omitted; refer to PDF] of BMNs can be written as [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the effective relaxation rate due to Brownian relaxation and [figure omitted; refer to PDF] is the effective relaxation rate due to Brownian relaxation due to Neel relaxation. We note that [figure omitted; refer to PDF] characterizes the ability to retain the magnetization after the applied dc field is removed and it reflects the influences of clustered magnetic nanoparticles on Brownian and Neel relaxation.

Since [figure omitted; refer to PDF] is related to the effective relaxation time, [figure omitted; refer to PDF] , by the relation [figure omitted; refer to PDF] , where [figure omitted; refer to PDF] is the excitation frequency, we can understand the dynamic characteristics of [figure omitted; refer to PDF] by measuring the time-dependency of [figure omitted; refer to PDF] with a lock-in amplifier. Furthermore, the formation of the magnetic clusters during conjugation affects the relaxation and therefore changes the [figure omitted; refer to PDF] . To quantitatively describe this assay we define [figure omitted; refer to PDF] , where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . We will analyze [figure omitted; refer to PDF] to determine amount of biomarkers.

2.3. Reagents

The reagent for assaying AFP consists of magnetic nanoparticles (MF-DEX-0060, MagQu, New Taipei, Taiwan) functionalized with antibodies (ab40942; Abcam, Cambridge, MA) against AFP (EA502-Q1053; EastCoast Bio, North Berwick, ME). These magnetic nanoparticles are dispersed in phosphoryl buffer solution (PBS). The BMNs for assaying AFP are Fe₃ O₄ -antiAFP dispersed in phosphate buffered saline solution with a pH value of 7.4. The magnetic core is Fe₃ O₄ , which is coated with dextran. Cartoons of the AFP, Fe₃ O₄ -antiAFP, and conjugated magnetic clusters of Fe₃ O₄ -antiAFP-AFP are represented in Figure 2(a) while the SEM picture of the reagent Fe₃ O₄ -antiAFP is shown in Figure 2(b). The size of the Fe₃ O₄ -antiAFP is ~37 nm, which is close to the average hydrodynamic diameter of ~45 nm detected with the dynamic light scattering. To achieve the association between AFP and Fe₃ O₄ -antiAFP, we used the saturated magnetization of a 0.3 emu/g magnetic reagent. To assay AFP, 60 μ L magnetic reagents consisting of Fe₃ O₄ -antiAFP are mixed with 60-μ L AFP of different concentrations, varied from 10 ng/mL to 10000 ng/mL.

Figure 2: A cartoon drawing of AFP, Fe₃ O₄ -antiAFP, and magnetic clusters of Fe₃ O₄ -antiAFP-AFP.

(a) [figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF]

3. Results and Discussion

3.1. Time Dependence of Phase Lag [figure omitted; refer to PDF]

Figure 3 shows the time dependence of [figure omitted; refer to PDF] after mixing the reagents with AFP at 300 K. It was found that [figure omitted; refer to PDF] is independent of time before the reagent is mixed with the to-be-detected AFP. After mixing the reagent with AFP, the [figure omitted; refer to PDF] increases monotonically and reaches saturated behavior when the association is completed. The [figure omitted; refer to PDF] degrees was observed at [figure omitted; refer to PDF] and [figure omitted; refer to PDF] increases monotonically to 1.3 degrees at [figure omitted; refer to PDF] s when we assay 1000 ng/mL of AFP, and a change of the phase lag [figure omitted; refer to PDF] degrees was detected. The [figure omitted; refer to PDF] degrees at [figure omitted; refer to PDF] and [figure omitted; refer to PDF] increases to 1.05 degrees at [figure omitted; refer to PDF] s when we assay 100 ng/mL of AFP, and a change of the phase lag [figure omitted; refer to PDF] degrees was observed.

Figure 3: Time-dependent [figure omitted; refer to PDF] for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.

[figure omitted; refer to PDF]

Figure 4 shows [figure omitted; refer to PDF] as a function of AFP concentration in a semilog plot, where [figure omitted; refer to PDF] . The [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] ) degrees when the concentration of AFP is 10000 ng/mL. The [figure omitted; refer to PDF] decreases systematically when the concentration of AFP decreases and [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] ) degrees when the concentration of AFP = 100 ng/mL. If we further decrease the concentration of AFP to 10 ng/mL, the [figure omitted; refer to PDF] is saturated to = 0.37. The lowest detection limit is about 100 ng/mL of AFP in this work. The detection sensitivity can further be improved if we further reduce the noises of the detection system or if SQUID sensors are used [20].

Figure 4: [figure omitted; refer to PDF] as a function of the AFP concentration in a semilog plot.

[figure omitted; refer to PDF]

3.2. Dynamic Effective Relaxation Time [figure omitted; refer to PDF]

Figure 5 shows the time dependence of [figure omitted; refer to PDF] after mixing the reagents with AFP at 300 K. For instance, after mixing the reagent with 5000 ng/mL AFP, [figure omitted; refer to PDF] increases from [figure omitted; refer to PDF] μ s at [figure omitted; refer to PDF] to [figure omitted; refer to PDF] μ s at [figure omitted; refer to PDF] s. When assaying 1000 ng/mL AFP, we found that [figure omitted; refer to PDF] μ s and [figure omitted; refer to PDF] μ s at [figure omitted; refer to PDF] s. When assaying 100 ng/mL AFP, we found that [figure omitted; refer to PDF] μ s at [figure omitted; refer to PDF] and [figure omitted; refer to PDF] μ s at [figure omitted; refer to PDF] s. It takes ~1.0 hour to complete the association between 1000 ng/mL AFP and the reagent. However, the association time is reduced to 0.5 hours when we assay 100 ng/mL AFP. Consequently, there is a systematic decrease in assaying time when the AFP concentration is reduced. The [figure omitted; refer to PDF] μ s when the concentration of AFP is 10000 ng/mL and [figure omitted; refer to PDF] μ s when the AFP concentration decreases to 100 ng/mL. If we further reduce the AFP concentration to 10 ng/mL, then [figure omitted; refer to PDF] remains as 0.08 μ s. This is the system noise which limits the detection sensitivity. When AFP is conjugated with the reagents which consisted of Fe₃ O₄ -antiAFP, AFP and Fe₃ O₄ -antiAFP will form magnetic clusters. There is an increase in [figure omitted; refer to PDF] during the association because of the formation of magnetic clusters, which depresses the Brownian relaxation and therefore increases [figure omitted; refer to PDF] .

Figure 5: Time-dependent [figure omitted; refer to PDF] for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.

[figure omitted; refer to PDF]

Molecule-assisted nanoparticle clustering effect in immunomagnetic reduction assay was reported [21]. In that study, the clustering association was manipulated by controlling the concentrations of BMNs in the reagent. It was found that particle clustering is enhanced by an increase in the concentration of BMNs. As the reagents conjugate with biomarkers, magnetic clusters are formed, which depress the Brownian motion. In this work, we show the phase lag of [figure omitted; refer to PDF] with respect to [figure omitted; refer to PDF] , which was characterized to estimate the time-dependency of [figure omitted; refer to PDF] through the following relation: [figure omitted; refer to PDF] .

A detection scheme for real-time Brownian relaxation of magnetic nanoparticles was also investigated by using a mixed frequency method [22], in which a low frequency of [figure omitted; refer to PDF] Hz with a large amplitude and a higher frequency of 20 kHz with a lower amplitude were applied. Instead of detecting the change of amplitudes, the phase delays of the mixed-frequency signals are investigated during the binding process between proteins on BMNs' surface and their respective antibodies. In the present work, instead of using two excitation frequencies, only one exciting frequency was applied with a compensation current to the sensing coil to achieve a high balance. Additionally, the real-time [figure omitted; refer to PDF] is measured to characterize real-time [figure omitted; refer to PDF] . By analyzing the changes of real-time [figure omitted; refer to PDF] , a detection sensitivity of human AFP better than 100 ng/mL is demonstrated.

3.3. Universal Logistic Function in [figure omitted; refer to PDF]

Figure 6 shows the normalized effective relaxation time reduction [figure omitted; refer to PDF] as a function of AFP concentration in a semilog plot at 300 K, where [figure omitted; refer to PDF] μ s is the effective relaxation time at [figure omitted; refer to PDF] . The [figure omitted; refer to PDF] for assaying 10000 ng/mL of AFP, and then the [figure omitted; refer to PDF] decreases to 0.61 when we assay 1000 ng/mL of AFP and the [figure omitted; refer to PDF] is further saturated to 0.35 when we assay 10 ng/mL.

Figure 6: [figure omitted; refer to PDF] as a function of the AFP concentration in a semilog plot. The solid line is the fitting curve to (4).

[figure omitted; refer to PDF]

The [figure omitted; refer to PDF] as a function of AFP concentration will follow a universal characteristic logistic function as follows [16]: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the effective relaxation time at [figure omitted; refer to PDF] . [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] are dimensionless parameters. [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are in units of ng/mL. The solid line is the fitting curve with parameters [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] ng/mL, and [figure omitted; refer to PDF] . Due to the presence of noises, the [figure omitted; refer to PDF] signal shows a nonzero value of [figure omitted; refer to PDF] . This universal logistic function provides a basis for estimating the unknown amount of biomolecules [16]. Versatile categories of bioentities, for example, proteins, viruses, small-molecule chemicals, and cytokines, despite being different from each other, have all shown to behave similarly, resulting in a general logistic function for all biotargets. The present concentration-dependent [figure omitted; refer to PDF] also shows this behavior of logistic function, which provides a foundation for assaying an unknown amount of biomolecules. The detection threshold of the detected signal is defined as that higher than the noise level of the detected signal at low concentrations. In this work, the lowest noise level of [figure omitted; refer to PDF] is about 0.35. Therefore, the detection threshold of AFP concentration can be determined via (4), which results in 55 ng/mL.

Figure 7(a) shows the magnetization as a function of the applied magnetic field for different concentrations of AFP when the association of Fe₃ O₄ -antiAFP with AFP is complete. The magnetization was measured with a vibrating sample magnetometer. The concentrations of AFP varied from 10 ng/mL to 10000 ng/mL. It was found that the [figure omitted; refer to PDF] increases when the concentration of AFP increases. The increased [figure omitted; refer to PDF] is due to the fact that more magnetic clusters of Fe₃ O₄ -antiAFP-AFP are formed during the association. The [figure omitted; refer to PDF] is 0.32 emu/g when the concentration of AFP is 10000 ng/mL and [figure omitted; refer to PDF] decreases to 0.06 emu/g when the concentration is 10 ng/mL, where [figure omitted; refer to PDF] is the change [figure omitted; refer to PDF] at [figure omitted; refer to PDF] T in the reagent with and without AFP. The [figure omitted; refer to PDF] as a function of AFP concentration is shown in Figure 7(b). As the concentration of AFP decreases, less magnetic clusters are formed. Therefore the [figure omitted; refer to PDF] decreases monotonically when the concentration of AFP decreases. The [figure omitted; refer to PDF] reaches a saturated behavior when the concentration of AFP is 10 ng/mL. Hence, a detection sensitivity of 10 ng/mL of AFP by measuring the variation of saturated magnetization is demonstrated.

Figure 7: (a) Magnetization as a function of applied magnetic field for different concentrations of AFP when the association of Fe₃ O₄ -antiAFP with AFP is complete and (b) [figure omitted; refer to PDF] as a function of AFP concentration.

(a) [figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF]

The [figure omitted; refer to PDF] data are fitted to the universal logistic function: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the saturated magnetization of Fe₃ O₄ -antiAFP. The fitting parameters [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are in units of emu/g, while [figure omitted; refer to PDF] is in units of ng/mL, and [figure omitted; refer to PDF] is dimensionless. The solid curve is the fitted line with parameters [figure omitted; refer to PDF] emu/g, [figure omitted; refer to PDF] emu/g, [figure omitted; refer to PDF] ng/mL, and [figure omitted; refer to PDF] . This solid curve provides a foundation for assaying unknown amounts of AFP.

The molecule-assisted nanoparticle clustering effect was reported in immunomagnetic reduction assay [21]. In that study, magnetic particle clustering was manipulated by controlling the concentrations of antibody-functionalized magnetic nanoparticles in the reagent. The results show that particle clustering is enhanced by an increase in the concentration of the to-be-detected biotargets. In the present study, we found that [figure omitted; refer to PDF] increases when the concentration of AFP increases. This is due to the fact that more magnetic clusters are associated in the reagent, and therefore the [figure omitted; refer to PDF] increases when the concentration of AFP increases.

Figure 8 shows the representative time-dependent amplitude, [figure omitted; refer to PDF] , for assaying 10000 ng/mL AFP (Figure 8(a)) and 50 ng/mL AFP (Figure 8(b)). For assaying 10000 ng/mL AFP, [figure omitted; refer to PDF] μ V at [figure omitted; refer to PDF] and decreases to 12.06 μ V at [figure omitted; refer to PDF] s. Therefore, we obtain [figure omitted; refer to PDF] for assaying 10000 ng/mL AFP. For assaying 100 ng/mL AFP, [figure omitted; refer to PDF] μ V at [figure omitted; refer to PDF] and decreases to 12.22 μ V at [figure omitted; refer to PDF] s. Therefore, [figure omitted; refer to PDF] for assaying 100 ng/mL AFP. It was observed that the amplitude reduction decreases when the concentration of AFP decreases. The amplitude of (1) is [figure omitted; refer to PDF] . Therefore an increase in [figure omitted; refer to PDF] during the association will cause a reduction in [figure omitted; refer to PDF] . We have shown that the magnetic clustering effect is enhanced by increasing the concentration of the AFP. Furthermore, the amplitude reduction shows characteristics similar to that observed in a mixed-frequency IMR [21].

Figure 8: Representative time-dependent ac susceptibility for assaying (a) 10000 ng/mL AFP and (b) 50 ng/mL AFP.

(a) [figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF]

A method of wash-free IMR assay using mixed excitation frequencies was previously proposed [9]. In such detection, the sensing coils consist of two excitation coils and one pick-up coil. Two excitation currents at frequencies [figure omitted; refer to PDF] and [figure omitted; refer to PDF] were applied to the excitation coils. The reduction of [figure omitted; refer to PDF] for the BMNs conjugated with the target biomarkers is analyzed at a target frequency of [figure omitted; refer to PDF] to qualitatively determine the amount of biomarkers, where [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are the excitation frequencies of the input coils. This mixed-frequency ac susceptibility reduction has been successfully used to assay AFP [17], which shows a high sensitivity and specificity. In the present work a detection threshold better than 100 ng/mL is demonstrated by characterizing the change in the effective relaxation time. The present biosystem has been applied to detect the C-reactive protein via the characterization of [figure omitted; refer to PDF] [18]. In practice, the reference criteria of the AFP serum level for the diagnosis of hepatocellular carcinoma (HCC) are above 20 ng/mL. To achieve a higher detection sensitivity, we can couple the sensing coil to high- [figure omitted; refer to PDF] SQUID via a flux transformer [20].

4. Conclusion

In this work, we report a platform for assaying biomarkers of AFP by using reagents that consisted of Fe₃ O₄ -antiAFP and a highly sensitive ac susceptometer. By monitoring [figure omitted; refer to PDF] , we found that the effective relaxation time increases monotonically and becomes saturated when the association between AFP and Fe₃ O₄ -antiAFP is complete. Additionally, the change of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] increases when the concentration of AFP increases after the association. This is due to the fact that more and larger magnetic clusters consisting of Fe₃ O₄ -antiAFP-AFP are formed during the association. The concentration-dependent [figure omitted; refer to PDF] and [figure omitted; refer to PDF] show a universal behavior of the logistic function, which provides a foundation for estimating an unknown amount of biomolecules. The detection platforms are robust and easy to use and show promise for further use in biomedical applications.

Acknowledgments

This work is supported under Grants nos. NSC101-2120-M-168-001, NSC99-2112-M-168-001-MY3, NSC102-2112-M-003-017, NSC101-2112-M-003-009, NSC102-2923-M003-001, NSC102-2622-M002-001-CC2, NSC102-2112-M-003-008-MY2, and NSC 100-2112-M-003-011-MY2 and the Ministry of Health and Welfare under Grants nos. DOH102-TD-PB-111-TM007 and DOH102-TD-N-111-002.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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