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

Authors: Shu-Hsien Liao; Jean-Hong Chen; Yu-Kai Su; Kuen-Lin Chen; Herng-Er Horng; Hong-Chang Yang
Journal: Journal of Nanomaterials
 (2015)

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## Abstract

An assay of biomarkers consisting  of alpha-fetoprotein (AFP) is reported. Real-time measurements of the effective relaxation timeτeff, 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, τeff, 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, Ms, 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 Ms 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 τeff. The detection platform is robust and easy to use and shows promise for further use in assaying a broad number of biomarkers.


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## Body

## 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, M(t), of BMNs with respect to the applied field, H(t), 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 Fe3O4 magnetic oxides and labeled as Fe3O4-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 θ(t), which is between the applied magnetic field H(t) and magnetization M(t). Then the dynamic effective relaxation time τeff was estimated through the following formula: tan⁡θ=ωτeff, where ω is the exciting angular frequency. It was found that the change of effective relaxation time, Δτeff, increases when the AFP completed the association with Fe3O4-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 Fe3O4-antiAFP was 0.3 emu/g which corresponds to a concentration of 1.2 mg-Fe/mL.


## 2. Experiments

### 2.1. Biodetection System

Figure1 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 f1(t) is applied to the input coil, an excited signal with nf1(t) components will be generated in the pick-up coil. In the present study, the dynamic θ(t) and amplitude, χamp, of the fundamental component, f1(t), are detected through lock-in detection.Figure 1
The detection scheme of an ac magnetic susceptometer with a lock-in detection technique.


### 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 lagθ(t) of M(t) with respect to H(t) in ac susceptibility and the saturation magnetization, Ms, and so forth. By characterizing the dynamic θ(t) or Ms, we can therefore determine the unknown amount of biomarkers.We consider the ac magnetic susceptibility of BMNs,χ(ω), in an applied ac magnetic field. χ(ω) is a function of τeff and exciting angular frequency ω. The χ(ω) can be expressed as follows [19]:(1)χac=χ′+iχ″(2)=χ011+ωτeff22+ωτeff1+ωτeff221/2e-iθ,where χ0 is the component of χac at ω=0, i=-11/2, χ′=χ0{1/[1+ωτeff2]}, χ″=χ0{(ωτeff)/[1+ωτeff2]}, and χ″/χ′=tan⁡θ. θ is the phase lag of the time-varying magnetization M with respect to the applied ac magnetic field H, and τeff is the effective relaxation rate. Using (1) and (2), we obtained tan⁡θ=ωτeff with χ″/χ′=tan⁡θ. The τeff of BMNs can be written as (3)1τeff=1τB,eff+1τN,eff,where 1/τB,eff is the effective relaxation rate due to Brownian relaxation and 1/τN,eff is the effective relaxation rate due to Brownian relaxation due to Néel relaxation. We note that τeff 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 Néel relaxation.Sinceθ is related to the effective relaxation time, τeff, by the relation tan⁡θ=ωτeff, where ω is the excitation frequency, we can understand the dynamic characteristics of τeff(t) by measuring the time-dependency of θ(t) with a lock-in amplifier. Furthermore, the formation of the magnetic clusters during conjugation affects the relaxation and therefore changes the τeff(t). To quantitatively describe this assay we define Δτeff/τ0=[τeff(t=0)-τeff(t=∞)]/τeff(t=0), where Δτeff=[τeff(t=0)-τeff(t=∞)] and τeff(t=0)=τ0. We will analyze Δτeff/τ0 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 Fe3O4-antiAFP dispersed in phosphate buffered saline solution with a pH value of 7.4. The magnetic core is Fe3O4, which is coated with dextran. Cartoons of the AFP, Fe3O4-antiAFP, and conjugated magnetic clusters of Fe3O4-antiAFP-AFP are represented in Figure 2(a) while the SEM picture of the reagent Fe3O4-antiAFP is shown in Figure 2(b). The size of the Fe3O4-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 Fe3O4-antiAFP, we used the saturated magnetization of a 0.3 emu/g magnetic reagent. To assay AFP, 60 μL magnetic reagents consisting of Fe3O4-antiAFP are mixed with 60-μL AFP of different concentrations, varied from 10 ng/mL to 10000 ng/mL.Figure 2
A cartoon drawing of AFP, Fe3O4-antiAFP, and magnetic clusters of Fe3O4-antiAFP-AFP.
(a)
(b)


## 2.1. Biodetection System

Figure1 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 f1(t) is applied to the input coil, an excited signal with nf1(t) components will be generated in the pick-up coil. In the present study, the dynamic θ(t) and amplitude, χamp, of the fundamental component, f1(t), are detected through lock-in detection.Figure 1
The detection scheme of an ac magnetic susceptometer with a lock-in detection technique.


## 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 lagθ(t) of M(t) with respect to H(t) in ac susceptibility and the saturation magnetization, Ms, and so forth. By characterizing the dynamic θ(t) or Ms, we can therefore determine the unknown amount of biomarkers.We consider the ac magnetic susceptibility of BMNs,χ(ω), in an applied ac magnetic field. χ(ω) is a function of τeff and exciting angular frequency ω. The χ(ω) can be expressed as follows [19]:(1)χac=χ′+iχ″(2)=χ011+ωτeff22+ωτeff1+ωτeff221/2e-iθ,where χ0 is the component of χac at ω=0, i=-11/2, χ′=χ0{1/[1+ωτeff2]}, χ″=χ0{(ωτeff)/[1+ωτeff2]}, and χ″/χ′=tan⁡θ. θ is the phase lag of the time-varying magnetization M with respect to the applied ac magnetic field H, and τeff is the effective relaxation rate. Using (1) and (2), we obtained tan⁡θ=ωτeff with χ″/χ′=tan⁡θ. The τeff of BMNs can be written as (3)1τeff=1τB,eff+1τN,eff,where 1/τB,eff is the effective relaxation rate due to Brownian relaxation and 1/τN,eff is the effective relaxation rate due to Brownian relaxation due to Néel relaxation. We note that τeff 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 Néel relaxation.Sinceθ is related to the effective relaxation time, τeff, by the relation tan⁡θ=ωτeff, where ω is the excitation frequency, we can understand the dynamic characteristics of τeff(t) by measuring the time-dependency of θ(t) with a lock-in amplifier. Furthermore, the formation of the magnetic clusters during conjugation affects the relaxation and therefore changes the τeff(t). To quantitatively describe this assay we define Δτeff/τ0=[τeff(t=0)-τeff(t=∞)]/τeff(t=0), where Δτeff=[τeff(t=0)-τeff(t=∞)] and τeff(t=0)=τ0. We will analyze Δτeff/τ0 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 Fe3O4-antiAFP dispersed in phosphate buffered saline solution with a pH value of 7.4. The magnetic core is Fe3O4, which is coated with dextran. Cartoons of the AFP, Fe3O4-antiAFP, and conjugated magnetic clusters of Fe3O4-antiAFP-AFP are represented in Figure 2(a) while the SEM picture of the reagent Fe3O4-antiAFP is shown in Figure 2(b). The size of the Fe3O4-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 Fe3O4-antiAFP, we used the saturated magnetization of a 0.3 emu/g magnetic reagent. To assay AFP, 60 μL magnetic reagents consisting of Fe3O4-antiAFP are mixed with 60-μL AFP of different concentrations, varied from 10 ng/mL to 10000 ng/mL.Figure 2
A cartoon drawing of AFP, Fe3O4-antiAFP, and magnetic clusters of Fe3O4-antiAFP-AFP.
(a)
(b)


## 3. Results and Discussion

### 3.1. Time Dependence of Phase Lagθ

Figure3 shows the time dependence of θ(t) after mixing the reagents with AFP at 300 K. It was found that θ(t) is independent of time before the reagent is mixed with the to-be-detected AFP. After mixing the reagent with AFP, the θ(t) increases monotonically and reaches saturated behavior when the association is completed. The θ(t=0)=0.8 degrees was observed at t=0 and θ(t=6000s) increases monotonically to 1.3 degrees at t=6000 s when we assay 1000 ng/mL of AFP, and a change of the phase lag Δθ=0.5 degrees was detected. The θ(t=0)=0.8 degrees at t=0 and θ(t=6000s) increases to 1.05 degrees at t=6000 s when we assay 100 ng/mL of AFP, and a change of the phase lag Δθ=0.25 degrees was observed.Figure 3
Time-dependentθ for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.Figure4 shows Δθ/θ0(t=0) as a function of AFP concentration in a semilog plot, where Δθ=θ(t=6000)-θ(t=0). The Δθ/θ0=1.76 (Δθ=1.44) degrees when the concentration of AFP is 10000 ng/mL. The Δθ decreases systematically when the concentration of AFP decreases and Δθ/θ0=0.32 (Δθ=0.26) degrees when the concentration of AFP = 100 ng/mL. If we further decrease the concentration of AFP to 10 ng/mL, the Δθ/θ 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
Δ
θ
/
θ
0 as a function of the AFP concentration in a semilog plot.


### 3.2. Dynamic Effective Relaxation Timeτeff

Figure5 shows the time dependence of τeff after mixing the reagents with AFP at 300 K. For instance, after mixing the reagent with 5000 ng/mL AFP, τeff increases from τeff=0.26 μs at t=0 to τeff=0.55 μs at t=6000 s. When assaying 1000 ng/mL AFP, we found that τeff=0.26 μs and τeff=0.38 μs at t=6000 s. When assaying 100 ng/mL AFP, we found that τeff=0.26 μs at t=0 and τeff=0.32 μs at t=6000 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 Δτeff=0.41 μs when the concentration of AFP is 10000 ng/mL and Δτeff=0.06 μs when the AFP concentration decreases to 100 ng/mL. If we further reduce the AFP concentration to 10 ng/mL, then Δτeff remains as 0.08 μs. This is the system noise which limits the detection sensitivity. When AFP is conjugated with the reagents which consisted of Fe3O4-antiAFP, AFP and Fe3O4-antiAFP will form magnetic clusters. There is an increase in τeff during the association because of the formation of magnetic clusters, which depresses the Brownian relaxation and therefore increases τeff.Figure 5
Time-dependentτeff for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.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 M with respect to H, which was characterized to estimate the time-dependency of τeff through the following relation: tan⁡θ=ωτeff.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 f2=10 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 θ is measured to characterize real-time τeff. By analyzing the changes of real-time τeff, a detection sensitivity of human AFP better than 100 ng/mL is demonstrated.


### 3.3. Universal Logistic Function inΔτeff/τ0

Figure6 shows the normalized effective relaxation time reduction Δτeff/τ0 as a function of AFP concentration in a semilog plot at 300 K, where τ0=0.26 μs is the effective relaxation time at t=0. The Δτeff/τ0=1.9 for assaying 10000 ng/mL of AFP, and then the Δτeff/τ0 decreases to 0.61 when we assay 1000 ng/mL of AFP and the Δτeff/τ0 is further saturated to 0.35 when we assay 10 ng/mL.Figure 6
Δ
τ
eff
/
τ
0 as a function of the AFP concentration in a semilog plot. The solid line is the fitting curve to (4).TheΔτeff/τ0 as a function of AFP concentration will follow a universal characteristic logistic function as follows [16]: (4)Δτeffτ0=a-b1+ΦAFP/Φ0β+b,where τ0 is the effective relaxation time at t=0. a, b, and γ are dimensionless parameters. ΦAFP and Φ0 are in units of ng/mL. The solid line is the fitting curve with parameters a=0.34, b=29.9, Φ0=224900 ng/mL, and β=0.961. Due to the presence of noises, the Δτeff/τ0 signal shows a nonzero value of ΦAFP=0. 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 Δτeff/τ0 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 Δτeff/τ0 is about 0.35. Therefore, the detection threshold of AFP concentration can be determined via (4), which results in 55 ng/mL.Figure7(a) shows the magnetization as a function of the applied magnetic field for different concentrations of AFP when the association of Fe3O4-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 Ms increases when the concentration of AFP increases. The increased Ms is due to the fact that more magnetic clusters of Fe3O4-antiAFP-AFP are formed during the association. The ΔMs is 0.32 emu/g when the concentration of AFP is 10000 ng/mL and ΔMs decreases to 0.06 emu/g when the concentration is 10 ng/mL, where ΔMs is the change Ms at H=1 T in the reagent with and without AFP. The ΔMs,AFP/Ms,0 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 ΔMs decreases monotonically when the concentration of AFP decreases. The ΔMs 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 Fe3O4-antiAFP with AFP is complete and (b) ΔMs as a function of AFP concentration.
(a)
(b)TheΔMs,AFP/Ms,0 data are fitted to the universal logistic function:(5)ΔMs,AFPMs,0=A-B1+ΦAFP/Φ0β+B,where Ms,0 is the saturated magnetization of Fe3O4-antiAFP. The fitting parameters A and B are in units of emu/g, while Φ0 is in units of ng/mL, and β is dimensionless. The solid curve is the fitted line with parameters A=0.62 emu/g, B=4.3 emu/g, Φ0=5430 ng/mL, and β=0.88. 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 Ms 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 Ms increases when the concentration of AFP increases.Figure8 shows the representative time-dependent amplitude, χamp, for assaying 10000 ng/mL AFP (Figure 8(a)) and 50 ng/mL AFP (Figure 8(b)). For assaying 10000 ng/mL AFP, χamp=13.4 μV at t=0 and decreases to 12.06 μV at t=6000 s. Therefore, we obtain Δχamp/χamp(t=0)=10% for assaying 10000 ng/mL AFP. For assaying 100 ng/mL AFP, χamp=12.33 μV at t=0 and decreases to 12.22 μV at t=6000 s. Therefore, Δχamp/χamp(t=0)=0.9% 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 χamp=χ01/1+ωτeff22+ωτeff/1+ωτeff221/2=χ0{1/1+ωτeff21/2}. Therefore an increase in τeff during the association will cause a reduction in χamp. 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)
(b)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 f1(t) and f2(t) were applied to the excitation coils. The reduction of χac for the BMNs conjugated with the target biomarkers is analyzed at a target frequency of f1(t)+2f2(t) to qualitatively determine the amount of biomarkers, where f1(t) and f2(t) 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 Δθeff/θ0 [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-Tc SQUID via a flux transformer [20].


## 3.1. Time Dependence of Phase Lagθ

Figure3 shows the time dependence of θ(t) after mixing the reagents with AFP at 300 K. It was found that θ(t) is independent of time before the reagent is mixed with the to-be-detected AFP. After mixing the reagent with AFP, the θ(t) increases monotonically and reaches saturated behavior when the association is completed. The θ(t=0)=0.8 degrees was observed at t=0 and θ(t=6000s) increases monotonically to 1.3 degrees at t=6000 s when we assay 1000 ng/mL of AFP, and a change of the phase lag Δθ=0.5 degrees was detected. The θ(t=0)=0.8 degrees at t=0 and θ(t=6000s) increases to 1.05 degrees at t=6000 s when we assay 100 ng/mL of AFP, and a change of the phase lag Δθ=0.25 degrees was observed.Figure 3
Time-dependentθ for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.Figure4 shows Δθ/θ0(t=0) as a function of AFP concentration in a semilog plot, where Δθ=θ(t=6000)-θ(t=0). The Δθ/θ0=1.76 (Δθ=1.44) degrees when the concentration of AFP is 10000 ng/mL. The Δθ decreases systematically when the concentration of AFP decreases and Δθ/θ0=0.32 (Δθ=0.26) degrees when the concentration of AFP = 100 ng/mL. If we further decrease the concentration of AFP to 10 ng/mL, the Δθ/θ 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
Δ
θ
/
θ
0 as a function of the AFP concentration in a semilog plot.


## 3.2. Dynamic Effective Relaxation Timeτeff

Figure5 shows the time dependence of τeff after mixing the reagents with AFP at 300 K. For instance, after mixing the reagent with 5000 ng/mL AFP, τeff increases from τeff=0.26 μs at t=0 to τeff=0.55 μs at t=6000 s. When assaying 1000 ng/mL AFP, we found that τeff=0.26 μs and τeff=0.38 μs at t=6000 s. When assaying 100 ng/mL AFP, we found that τeff=0.26 μs at t=0 and τeff=0.32 μs at t=6000 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 Δτeff=0.41 μs when the concentration of AFP is 10000 ng/mL and Δτeff=0.06 μs when the AFP concentration decreases to 100 ng/mL. If we further reduce the AFP concentration to 10 ng/mL, then Δτeff remains as 0.08 μs. This is the system noise which limits the detection sensitivity. When AFP is conjugated with the reagents which consisted of Fe3O4-antiAFP, AFP and Fe3O4-antiAFP will form magnetic clusters. There is an increase in τeff during the association because of the formation of magnetic clusters, which depresses the Brownian relaxation and therefore increases τeff.Figure 5
Time-dependentτeff for assaying 10000 ng/mL, 5000 ng/mL, 1000 ng/mL, and 100 ng/mL of AFP.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 M with respect to H, which was characterized to estimate the time-dependency of τeff through the following relation: tan⁡θ=ωτeff.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 f2=10 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 θ is measured to characterize real-time τeff. By analyzing the changes of real-time τeff, a detection sensitivity of human AFP better than 100 ng/mL is demonstrated.


## 3.3. Universal Logistic Function inΔτeff/τ0

Figure6 shows the normalized effective relaxation time reduction Δτeff/τ0 as a function of AFP concentration in a semilog plot at 300 K, where τ0=0.26 μs is the effective relaxation time at t=0. The Δτeff/τ0=1.9 for assaying 10000 ng/mL of AFP, and then the Δτeff/τ0 decreases to 0.61 when we assay 1000 ng/mL of AFP and the Δτeff/τ0 is further saturated to 0.35 when we assay 10 ng/mL.Figure 6
Δ
τ
eff
/
τ
0 as a function of the AFP concentration in a semilog plot. The solid line is the fitting curve to (4).TheΔτeff/τ0 as a function of AFP concentration will follow a universal characteristic logistic function as follows [16]: (4)Δτeffτ0=a-b1+ΦAFP/Φ0β+b,where τ0 is the effective relaxation time at t=0. a, b, and γ are dimensionless parameters. ΦAFP and Φ0 are in units of ng/mL. The solid line is the fitting curve with parameters a=0.34, b=29.9, Φ0=224900 ng/mL, and β=0.961. Due to the presence of noises, the Δτeff/τ0 signal shows a nonzero value of ΦAFP=0. 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 Δτeff/τ0 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 Δτeff/τ0 is about 0.35. Therefore, the detection threshold of AFP concentration can be determined via (4), which results in 55 ng/mL.Figure7(a) shows the magnetization as a function of the applied magnetic field for different concentrations of AFP when the association of Fe3O4-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 Ms increases when the concentration of AFP increases. The increased Ms is due to the fact that more magnetic clusters of Fe3O4-antiAFP-AFP are formed during the association. The ΔMs is 0.32 emu/g when the concentration of AFP is 10000 ng/mL and ΔMs decreases to 0.06 emu/g when the concentration is 10 ng/mL, where ΔMs is the change Ms at H=1 T in the reagent with and without AFP. The ΔMs,AFP/Ms,0 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 ΔMs decreases monotonically when the concentration of AFP decreases. The ΔMs 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 Fe3O4-antiAFP with AFP is complete and (b) ΔMs as a function of AFP concentration.
(a)
(b)TheΔMs,AFP/Ms,0 data are fitted to the universal logistic function:(5)ΔMs,AFPMs,0=A-B1+ΦAFP/Φ0β+B,where Ms,0 is the saturated magnetization of Fe3O4-antiAFP. The fitting parameters A and B are in units of emu/g, while Φ0 is in units of ng/mL, and β is dimensionless. The solid curve is the fitted line with parameters A=0.62 emu/g, B=4.3 emu/g, Φ0=5430 ng/mL, and β=0.88. 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 Ms 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 Ms increases when the concentration of AFP increases.Figure8 shows the representative time-dependent amplitude, χamp, for assaying 10000 ng/mL AFP (Figure 8(a)) and 50 ng/mL AFP (Figure 8(b)). For assaying 10000 ng/mL AFP, χamp=13.4 μV at t=0 and decreases to 12.06 μV at t=6000 s. Therefore, we obtain Δχamp/χamp(t=0)=10% for assaying 10000 ng/mL AFP. For assaying 100 ng/mL AFP, χamp=12.33 μV at t=0 and decreases to 12.22 μV at t=6000 s. Therefore, Δχamp/χamp(t=0)=0.9% 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 χamp=χ01/1+ωτeff22+ωτeff/1+ωτeff221/2=χ0{1/1+ωτeff21/2}. Therefore an increase in τeff during the association will cause a reduction in χamp. 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)
(b)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 f1(t) and f2(t) were applied to the excitation coils. The reduction of χac for the BMNs conjugated with the target biomarkers is analyzed at a target frequency of f1(t)+2f2(t) to qualitatively determine the amount of biomarkers, where f1(t) and f2(t) 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 Δθeff/θ0 [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-Tc 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 Fe3O4-antiAFP and a highly sensitive ac susceptometer. By monitoring θ, we found that the effective relaxation time increases monotonically and becomes saturated when the association between AFP and Fe3O4-antiAFP is complete. Additionally, the change of τeff and Ms increases when the concentration of AFP increases after the association. This is due to the fact that more and larger magnetic clusters consisting of Fe3O4-antiAFP-AFP are formed during the association. The concentration-dependent Δτeff/τ0 and ΔMs,AFP/Ms,0 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.



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*Source: 497296-2015-05-28.xml*