Magnetic Clustering Effect during the Association of Biofunctionalized Magnetic Nanoparticles with Biomarkers

Abstract

We report herein an investigation into dynamic magnetic clustering that occurs during immunoassays as biofunctionalized magnetic nanoparticles (BMNs) become associated with biotargets. We measure the dynamic effective relaxation time τ _eff(t) and use scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to investigate the C-reactive protein (CRP) as it associates with the BMN Fe₃O₄-antiCRP to form the magnetic cluster Fe₃O₄-antiCRP-CRP. The results indicate that τ _eff(t) increases with increasing association time. In addition, the ration Δτ _eff/τ ₀ as a function of CRP concentration follows a characteristic logistic function, which provides a basis for estimating the quantity of biomolecules with a detection sensitivity close to 0.1 ppm. After the association, SEM and TEM images show that CRP and Fe₃O₄-antiCRP conjugate to form Fe₃O₄-antiCRP-CRP clusters hundreds of nanometers in size. The SEM and TEM images provide direct evidence of the formation of magnetic clustering.

Introduction

Magnetic detection using biofunctionalized magnetic nanoparticles (BMNs) has recently received considerable attention [1]. In general, biological samples have negligible magnetic backgrounds, therefore a high detection sensitivity and specificity is possible with magnetic detection. Magnetic detection for assaying biomolecules can be done by measuring the magnetic relaxation [2,3], magnetic remanence [4], immunomagnetic reduction (IMR) [5], saturated magnetization [6], reduction in spin-spin relaxation time [7], etc. In immunomagnetic assays, the relaxation in the presence of magnetic clustering during association plays an important role in the detection of biomolecules [1–3,5,7]. Because relaxation mechanism dominates the magnetic variance of sample, it is also the key point of sensitivity limit of the immunomagnetic assay. However, the effects of dynamic magnetic clustering on the characteristics of relaxation are seldom studied. A previous report [8] discusses the molecule-assisted nanoparticle clustering effect in immunomagnetic reduction (IMR) assay. In that study, clustering effects were manipulated by controlling the concentrations of anti-body-functionalized magnetic nanoparticles in the reagent. Mixed-frequency IMR was used to study the clustering effect, and the experimental results show that particle clustering is enhanced by increasing the concentration of BMNs. In addition, this report claims that the effects of magnetic clustering dominate the increased rate of the IMR signal in mixed-frequency ac susceptibility. It clearly showed that the variance of ac susceptibility due to magnetic clustering effect is a promising method for biomolecule detection. Another report [9] shows real-time Brownian relaxation of BMNs by using a mixed frequency method. Due to clustering effects, the phase delay θ(t) between magnetization M(t) and applied field H(t) was varied during association. The dynamic behavior of the phase delay angle was studied for assay biomolecules. However, there are few reports on the direct observation of magnetic clustering. Liao et al. [10] reported the time-dependent phase lag of BMNs conjugated with biotargets, as studied with ac magnetic susceptometry for liquid phase immunoassays. Because of the clustering effect, Brownian relaxation of BMNs is suppressed, which in turn enhances the effective relaxation time. By monitoring the dynamic phase lag, a sensitive platform for assaying human C-reactive protein (CRP) was demonstrated. The research goal of the present work is to study the effects of magnetic clustering on the dynamic effective relaxation time τ _eff(t) and provide evidence of magnetic clustering by imaging with scanning electron microscopy (SEM) and transmission electron microscopy (TEM).

In the present work, we report how dynamic magnetic clustering affects τ _eff(t) by measuring the time-dependent phase lag θ(t) between the applied field H(t) and magnetization M(t) and by imaging with SEM and TEM. The measured phase lag θ is used to estimate τ _eff by using the relation tanθ(t) = ωτ _eff(t), where θ(t) is the time-dependent phase lag of M(t) with respect to H(t), and ω is the angular frequency of the excitation. The BMNs used in this study were anti-goat C-reactive protein coated onto dextran-coated magnetic nanoparticles (Fe₃O₄-antiCRP), and the biotargets were human C-reactive protein (CRP). The results show that τ _eff for the reagents increases as association evolves, which we attribute to suppressed Brownian motion due to the presence of magnetic clusters during the association of CRP with Fe₃O₄-antiCRP. We also find that the ratio Δτ _eff/τ ₀, as a function of CRP concentration follows a universal characteristic logistic function, where Δτ _eff = [τ _eff (t = 0) − τ _eff (t = ∞)]. Finally, direct evidence of magnetic clustering is provided by SEM and TEM images, which show that the average particle size is about 67.5 ± 11.5 nm for Fe₃O₄-antiCRP, whereas the conjugated clusters of Fe₃O₄-antiCRP-CRP are about 250 nm in size.

Materials and Methods

Materials

The magnetic reagents used in this study were composed of biocompatible magnetic Fe₃O₄ nanoparticles with dextran shell (MagQu Co, Ltd). To synthesize BMNs, polyclonal goat anti-CRP (Sigma-Aldrich, St Louis, MO, USA) was covalently bound to the dextran shell of Fe₃O₄ via −CH = N− [11, 12]. BMN, which consisted of Fe₃O₄-antiCRP, was then dispersed in phosphate buffered saline (PBS) solution with a pH of 7.4. In this study, the mean hydrodynamic diameter of Fe₃O₄ nanoparticle was 45.8 nm with a standard deviation of ±15.0 nm, as determined by dynamic light scattering (Nanotrac-150, Microtrac). Fig 1a shows the magnetization data of the BMN reagent, which was measured by vibrating sample magnetometer (Model 4500, EG&G), and the saturated magnetization was about 0.29 emu/g.

Fig 1. Detection scheme for homemade ac magnetic susceptometer for measuring dynamic τ _eff(t).

Magnetic ac susceptibility measurement

Fig 1b shows the design of the highly balanced homemade ac magnetic susceptometer used to study the time-dependent phase lag angle θ(t). A detailed description of the measurement technique for characterizing θ(t) is given in Ref. [10], so we only briefly describe the method here. The sensing unit of the ac susceptometer consists of an input coil, a first-order gradient pick-up coil, and a compensation coil. The first-order gradient pick-up coil is composed of two identical coils wound in opposite directions. The compensation coil is used to precisely balance the sensing unit in the ac susceptometer. Therefore, their phase difference can be adjusted to optimize the balance of the sensing unit. The balance of the sensing coil is defined as the output signal of the two coils of the pick-up coil divided by the output signal from one of the two coils under the excitation of the input coil. This sensing unit achieves a balance of 30 parts per trillion (ppt). The signal from the pick-up coil and the reference frequency component from the function generator were input to a lock-in amplifier, and the time-dependent τ _eff(t) was estimated by using tanθ(t) = ωτ _eff(t).

SEM and TEM images

The morphologies of Fe₃O₄, Fe₃O₄-antiCRP nanoparticles, and CRP conjugated Fe₃O₄-antiCRP were investigated with field-emission scanning electron microscope (FESEM) (Hitachi S-4700), and field emission gun transmission electron microscope (FEI-TEM) (Philips Tecnai F20 G2). Before taking the electron microscopy, the nanoparticles and magnetic clusters were dispersed in a super-diluted solvent (1:50) and then drying the magnetic samples under vacuum at room temperature for 48 hours.

Results and Discussion

By means of the surface modification for specific biotargets, BMN is a good reagent for the immunomagnetic assay. By means of antigen-antibody interaction, BMNs will be gathered to form bigger clusters when the BMN reagent is mixed with antigen. Therefore, the magnetic characteristics of BMN reagent are going to change, and the variation of magnetic characteristics could be used to identify the quantity of antigen. An illustration depicting the human CRP, Fe₃O₄-antiCRP, and magnetic clusters consisting of Fe₃O₄-antiCRP-CRP is shown in Fig 2. In this work, we used magnetic ac susceptibility measurement to investigate the clustering effect of antiCRP coated BMNs interacting with CRP antigen. To study the phase lag dynamics θ(t), 60 μl of Fe₃O₄-antiCRP reagent of which saturated magnetization is 0.29 emu/g was mixed with 40 μl of CRP with concentrations varying from 0.1 to 10 ppm (1 ppm = 1 μg/mL). θ(t) is also related to τ _eff(t) by tanθ(t) = ωτ _eff(t), where f = ω/(2π) = 9 kHz is the excitation frequency used in the experiment. The presence of dynamic magnetic clustering during the association affects θ(t), which in turn modifies τ _eff(t). We investigated the dynamics of θ(t) and τ _eff(t) via lock-in detection, as shown in Fig 1b. The results show that τ _eff increases and saturates when association is complete. Furthermore, the ratio Δτ _eff/τ ₀ as a function of CRP concentration provides a basis for estimating the quantity of biomolecules. Finally, we directly observed the formation of magnetic clusters by SEM and TEM images.

Fig 2. Illustration depicting conjugation of human CRP and Fe₃O₄-antiCRP to form Fe₃O₄-antiCRP-CRP cluster.

Fig 3a shows the time-dependent τ _eff(t) after mixing the reagent (0.29 emu/g) of Fe₃O₄-antiCRP with 5 ppm CRP at 300 K. The results show that τ _eff increases from τ _eff = 0.62 μs at t = 0 to τ _eff = 0.83 μs at t = 4800 s. Fig 3b shows τ _eff as a function of time after mixing Fe₃O₄-antiCRP with 0.1 ppm CRP at 300 K. The results show that τ _eff increases from 0.62 μs at t = 0 to τ _eff = 0.72 μs at t = 1800 s. The increase of τ _eff is attributed to the formation of magnetic clusters during the association, which depresses the Brownian relaxation. Completing the association of 5 ppm CRP with the reagents takes 1.5 hours. The association time decreases to 0.5 hours to assay 0.1 ppm CRP. Consequently, a shorter association time results from reducing the CRP concentration. Thus, characterizing the dynamics of τ _eff is done with a detection sensitivity of 0.1 ppm.

Fig 3. Time-dependent τ _eff(t) for assaying (a) 5.0 ppm and (b) 0.1 ppm of human CRP.

Upon conjugating Fe₃O₄-antiCRP and CRP antigen, τ _eff(t) becomes larger and gradually approaches equilibrium.

The mechanism behind the dynamics of τ _eff for BMNs during association can be understood as follows: Consider the ac magnetic susceptibility of BMNs, χ(ω), in an applied ac magnetic field. χ _ac(ω,t) is a function of τ _eff and has angular frequency ω. The magnetic susceptibility χ _ac(ω,t) can be expressed as [13,14]

$${\chi }_{\text{ac}}(\omega ,t)=\chi \prime +i\chi \prime \prime$$ (1)

$$={\chi }_0{\left\{{\left[\frac{1}{1+{(\omega {\tau }_{\text{eff}})}^2}\right]}^2+{\left[\frac{(\omega {\tau }_{\text{eff}})}{1+{(\omega {\tau }_{\text{eff}})}^2}\right]}^2\right\}}^{1/2}{\text{e}}^{-i\theta (t)},$$ (2)

where χ ₀ is the component of χ _ac at ω = 0, i = (−1)^1/2, χ' = χ ₀{1/[1+(ωτ _eff)²]}, χ'' = χ ₀{(ωτ _eff)/[1+(ωτ _eff)²]}, and θ is the phase lag. χ''(t)/χ'(t) = tanθ, so Eqs 1 and 2 lead to tanθ = ωτ _eff. For BMNs, τ _eff can be written as

$$1/{\tau }_{\text{eff}}={\displaystyle {\sum }_{\text{i}}1/{\tau }_{\text{i,B}}+}{\displaystyle {\sum }_{\text{i}}1/{\tau }_{\text{i,N}}=1/{\tau }_{\text{B}}+1/{\tau }_{\text{N}}},$$ (3)

where Σ_i indicates summation over all BMN sizes, 1/τ _i,B is the relaxation rate due to the Brownian motion of nanoparticle i, and 1/τ _i,N is the relaxation rate due to the Néel relaxation of nanoparticle i. Using tanθ(t) = ωτ _eff(t), the dynamics of τ _eff can be understood by monitoring the time evolution of θ. As Fe₃O₄-antiCRP conjugates with CRP, magnetic clusters form, which depresses the Brownian motion and in turn increases τ _eff.

Fig 4 shows the ratio Δτ _eff/τ ₀ as a function of CRP concentration at 300 K, expressed on a semilog plot, where Δτ _eff = [τ _eff (t = 0) − τ _eff (t = 6000 s)] when the association of CRP with Fe₃O₄-antiCRP is complete. The effective relaxation time τ ₀ = 0.62 μs at t = 0 is derived from tanθ = ωτ _eff. When the concentration of CRP is 20 ppm, Δτ _eff = 0.26 μs (Δτ _eff/τ ₀ = 41.9%) and, when the CRP concentration decreases to 0.1 ppm, Δτ _eff saturates at 0.11 μs (Δτ _eff/τ ₀ = 17.7%). If we further reduce the CRP concentration to 0.01 ppm, Δτ _eff remains at ~0.11 μs, which is close to the experimental noise. Thus, for the present system, the lowest concentration for which detection is possible is 0.1 ppm.

Fig 4. Δτ _eff/ τ ₀ as a function of CRP concentration in semilog plot at 300 K.

τ ₀ is the effective relaxation time at t = 0. Δτ _eff is the effective relaxation time between the beginning and the end of the reaction, and is defined as Δτ _eff = [τ _eff (t = 0) − τ _eff (t = 6000 s)].

The ratio Δτ _eff/τ ₀ as a function of CRP concentration follows a characteristic logistic function [15] given by

$$\Delta {\tau }_{\text{eff}}/{\tau }_{\text{0}}=\frac{A-B}{1+{\left(\frac{{\varphi }_{\text{CRP}}}{{\varphi }_0}\right)}^{\beta }}+B$$ (4)

where A and B are dimensionless parameters, and ϕ _CRP and ϕ ₀ are in the units of ppm (or μg/mL). The solid line in Fig 4 shows a fit with parameters A = 17.3, B = 41.0, β = 3.79, and ϕ ₀ = 3.60 ppm. Because of environmental and system noise, Δτ _eff/τ ₀ is nonzero at ϕ _CRP = 0. In practical applications, this universal logistic function provides a basis for estimating the quantity of biomolecules [16].

From Eq 2 we obtain the magnitude of the ac susceptibility, χ _amp, which is given by

$${\chi }_{\text{amp}}(t)=\frac{{\chi }_0}{{[1+{(\omega {\tau }_{\text{eff}}(t))}^2]}^{1/2}}.$$ (5)

Based on Eq 5 we see that an increase in τ _eff induces a reduction of χ _amp after association. Additionally, assaying a higher concentration of CRP leads to a larger reduction in Δχ, which is observed in experiments. Fig 5 shows the time-dependent amplitude of the ac susceptibility for assaying 10 and 1.0 ppm CRP. The susceptibility χ(t) decreases from 2.83 μV at t = 0 to 2.70 μV at t = 6000 s when assaying 10 ppm CRP, and from 2.87 μV at t = 0 to 2.84 μV at t = 6000 s when assaying 1 ppm CRP. The percent reduction Δχ/χ ₀ × 100% = 4.6% when assaying 10 ppm CRP, and Δχ/χ ₀ was reduced to 0.8% when assaying 1.0 ppm CRP.

Fig 5. Representative amplitude of ac susceptibility as a function of time when assaying (a) 10 ppm CRP and (b) 1.0 ppm CRP.

The increase in τ _eff induces a reduction of χ _amp during particle association.

Although the measurement of ac susceptibility provides evidence for magnetic clustering from the conjugation of CRP and Fe₃O₄-antiCRP, the aggregation is not directly observed. Fig 6 is the picture of the solutions of Fe₃O₄ nanoparticles, Fe₃O₄-antiCRP, and CRP conjugated Fe₃O₄-antiCRP after 1.5 hours mixture. It clearly shows that there are not any observable aggregations and precipitations in these solutions even though CRP had conjugated with Fe₃O₄-antiCRP for 1.5 hours. Therefore, we used the SEM and TEM to investigate the effect of clustering. The inhomogeneity of BMNs usually leads to large variations in results. Thus, to enhance the stability and reproducibility of assaying biomarkers, highly homogeneous Fe₃O₄ is necessary for the Fe₃O₄-antiCRP preparation. We used SEM to check the homogeneity of the Fe₃O₄ use for BMN synthesis. Fig 7a shows a typical SEM image of Fe₃O₄, and Fig 7b shows a magnified SEM image of Fe₃O₄, with the particle size indicated. The diameters of the Fe₃O₄ are almost all the same, which indicates that the Fe₃O₄ used in the BMN synthesis is highly homogeneous. The particle size of Fe₃O₄ was measured to be ~ 48.4 ± 9.9 nm on average, which is very close to the result obtained with dynamic light scattering.

Fig 6. The picture of the solutions of Fe₃O₄ nanoparticles, Fe₃O₄-antiCRP, and CRP conjugated Fe₃O₄-antiCRP after 1.5 hours mixture.

(a) Fe₃O₄ 60μl + PBS 40μl, (b) Fe₃O₄-antiCRP 60μl + PBS 40μl, and (c) Fe₃O₄-antiCRP 60μl + 10 ppm CRP antigen 40μl after 1.5 hours.

Fig 7. SEM images of (a) Fe₃O₄ applied to BMN synthesis. (b) Magnified SEM picture of Fe₃O₄ with the particle size indicated.

The average size of Fe₃O₄ particles is ~ 48.4 ± 9.9 nm.

Fig 8a shows a TEM image of the reagent composed of Fe₃O₄-antiCRP. The average particle size varies from (60 ± 5.0) to (70 ± 5.0) nm with an average size of ~ 67.5 ± 11.5 nm. The core of Fe₃O₄ and the outer shell of the coated antiCRP are apparent. Moreover, Fig 8b shows a TEM image of CRP. The average particle size of CRP is 10 ± 0.5 nm which is consistent with the data reported in Ref. [17]. TEM shows that CRP conjugates with Fe₃O₄-antiCRP upon adding CRP to the reagent of Fe₃O₄-antiCRP. Fig 8c shows a TEM image of the magnetic cluster of Fe₃O₄-antiCRP-CRP at t = 1 h after mixing CRP with Fe₃O₄-antiCRP. In addition to the unconjugated CRPs, the conjugated Fe₃O₄-antiCRP-CRP single particles and the Fe₃O₄-antiCRP-CRP cluster are also apparent. These results show clearly that CRP adheres to the surface of Fe₃O₄-antiCRP via antigen-antibody interactions [18] and aggregates Fe₃O₄-antiCRP together to form bigger clusters. The size of magnetic clusters of Fe₃O₄-antiCRP-CRP varies from ~ 80 to 250 nm at t = 1 h and increases with association time. Thus, the effect of magnetic clustering is directly revealed by SEM and TEM.

Fig 8. TEM images of (a) Fe₃O₄-antiCRP nanoparticles and (b) CRP antigens. (c) TEM image of conjugated Fe₃O₄-antiCRP-CRP particles and cluster after association time of 1 h.

A method to conduct a wash-free magnetically labeled immunoassay using mixed excitation frequencies was previously proposed [4]. As a detection method, two excitation currents at frequencies of f ₁ and f ₂ were applied to the excitation coils. The reduction of χ _ac for BMNs conjugated with biotargets was analyzed at the target frequency f ₁+2f ₂ to qualitatively determine the amount of biotarget, where f ₁ and f ₂ are the excitation frequencies of the input coils. The IMR assay in the frequency domain was used to assay CRP [19,20]. Real-time Brownian relaxation of BMNs was also investigated by using a mixed frequency method, and the phase delay between M(t) and H(t) was investigated to detect biomolecules [9]. In the present work, the phase delay of M with respect to H and the reduction of χ _amp was investigated to assay CRP by using single frequency ac susceptometry. The results indicate that τ _eff increases with association time. We attribute this result to the suppression of Brownian motion, which is due to the magnetic clustering during association. Additionally, the ratio Δτ _eff/τ ₀ follows a logistic function, which provides a basis for estimating the quantity of biomolecules. Furthermore, the effect of magnetic clustering is directly revealed via SEM and TEM.

CRP levels in blood are key indicators of infectious disease, noninfectious disease, and acute tissue. The normal concentration in healthy human serum is usually less than 10 μg/mL, which slightly increases with age. Higher levels are found in late-pregnancy women and in people with mild inflammation or viral infection (10–40 μg/mL), in people with active inflammation or bacterial infection (40–200 μg/mL), and in people with severe bacterial infections or burns (>200 μg/mL) [21]. By using BMNs and the technique of mixed-frequency ac susceptmetry, quantitative immunoassays for CRP were demonstrated in clinical diagnoses [22]. In the present work, we investigate the dynamics of τ _eff and use SEM and TEM to show magnetic clustering. By using θ(t) and τ _eff(t), this method provides a detection sensitivity of 0.1 ppm.

Conclusions

We investigate the dynamics of τ _eff(t) during association of Fe₃O₄-antiCRP with CRP. The results show that τ _eff increases and saturates when association is complete. In addition, the ratio Δτ _eff/τ ₀ as a function of CRP concentration follows a characteristic logistic function, which provides a basis for estimating the quantity of biomolecules and a detection sensitivity of 0.1 ppm is demonstrated. Finally, SEM and TEM images directly revealed the formation of magnetic clusters. This magnetic detection platform is promising for future use in assaying a broad number of biomarkers, such as viruses, proteins, tumors, etc.

Data Availability

All relevant data are within the paper.

Funding Statement

This work was supported by Ministry of Science and Technology of Taiwan under grants: MOST103-2112-M-005-005-MY3, NSC101-2120-M-168-001 and NSC99-2112-M-168-001-MY3. http://www.most.gov.tw/. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.