# Effects of Salt Concentration on a Magnetic Nanoparticle-Based Aggregation Assay with a Tunable Dynamic Range

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}exhibited optimal cell targeting. This topic is expanded upon in Alkilany et al., 2019 review [29] of the relationship between a NP’s (including MNPs, AuNPs, and quantum dots) ligand density and its cellular uptake. The relationship between MNP ligand density and protein sensing dynamics, transduced via MPS, were reported by Wu et al., 2021. They functionalized MNPs with polyclonal antibodies (pAbs), to lend the MNPs and affinity for SARs-CoV-2 spike or nucleocapsid proteins and monitored odd harmonic amplitudes of magnetization as the pAb-MNPs were exposed to varying concentrations of their target [30]. MNPs were functionalized with 1, 2, 3, or 4 pAbs per MNP. For pAb-MNPs targeting spike protein, a pAb:MNP ratio of 3:1 yielded a linear ${A}_{3}$ response from 0 to 12.5 nM spike protein. Additionally, for pAb-MNPs targeting nucleocapsid protein, a pAb:MNP ratio of 4:1 yielded a linear ${A}_{3}$ response from 3.13 to 400 nM nucleocapsid protein. pAb-MNPs with 1:1, 2:1, or 3:1 pAb:MNP ratios did not yield linear ${A}_{3}$ responses with respect to target concentration, regardless of target protein (splike or nucleocapsid). Our work differs from that of Wu et al., 2021 in that we are studying changes in biotin-MNP biosensor response characteristics (the dynamic range, slope and $\Delta {\varphi}_{3}$), via investigating changes in biotin-MNP ${\varphi}_{3}$ as a function of target concentration, instead of odd harmonic amplitudes. Given previous work investigating NP dynamic range tunability with ligand density, we expect an increase in biotin-MNP sensitivity with decreasing biotin density.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Physical Characterization of SHA 25 MNPs

#### 2.3. Biotinylation of SHA 25 MNPs

#### 2.4. Physical Characterization of Biotin-MNPs

#### 2.5. Magnetic Particle Spectroscopy Measurements

#### 2.6. xDLVO Interparticle Energies

^{+}, 142.00 mM Cl

^{−}, 4.45 mM K

^{+}, and 7.30 ${\mathrm{HPO}}_{4}^{-2}$, and 4.60 mM H

_{2}${\mathrm{PO}}_{4}^{-1}$. We assumed electrolyte concentration decreased linearly with decreasing PBS strength. Therefore, we assumed 0.50x PBS had 50% less electrolytes than 1.00x PBS, for example. However, we handled the EDL energy calculation for DI differently to agree with reported values of the Bjerrum length ${\lambda}_{B}$ in pH 7 DI at room temperature. ${\lambda}_{B}$ is the interparticle distance at which the EDL energy is comparable in magnitude to the thermal energy of the system [33]. ${\lambda}_{B}$ in pH 7 DI water at room temperature is 1 $\mu $m, which corresponded to a Debye length ($\frac{1}{\kappa}$) of 4.10 $\mu $m for our biotin-MNPs in DI. van der Waals and dipolar energies remain constant with respect to electrolyte concentration. The van der Waals energy between 2 NPs was calculated as [31]

## 3. Results

#### 3.1. Physical Characterization of SHA 25 MNPs

#### 3.2. Effects of Biotin Density on Streptavidin Induced Biotin-MNP Aggregation

#### 3.3. Effects of Salt Concentration on Biotin-MNP Zeta Potential and ${D}_{Hyd}$

#### 3.4. Effects of Salt Concentration on Streptavidin Induced Biotin-MNP Aggregation

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rauwerdink, A.M.; Weaver, J.B. Measurement of molecular binding using the Brownian motion of magnetic nanoparticle probes. Appl. Phys. Lett.
**2010**, 96, 033702. [Google Scholar] [CrossRef] - Zhang, X.; Reeves, D.B.; Perreard, I.M.; Kett, W.C.; Griswold, K.E.; Gimi, B.; Weaver, J.B. Molecular sensing with magnetic nanoparticles using magnetic spectroscopy of nanoparticle Brownian motion. Biosens. Bioelectron.
**2013**, 50, 441–446. [Google Scholar] [CrossRef] [PubMed] - Jyoti, D.; Gordon-Wylie, S.W.; Reeves, D.B.; Paulsen, K.D.; Weaver, J.B. Distinguishing nanoparticle aggregation from viscosity changes in MPS/MSB detection of biomarkers. Sensors
**2022**, 22, 6690. [Google Scholar] [CrossRef] - Jans, H.; Liu, X.; Austin, L.; Maes, G.; Huo, Q. Dynamic light scattering as a powerful tool for gold nanoparticle bioconjugation and biomolecular binding studies. Anal. Chem.
**2009**, 81, 9425–9432. [Google Scholar] [CrossRef] - Dobrovolskaia, M.A.; Patri, A.K.; Zheng, J.; Clogston, J.D.; Ayub, N.; Aggarwal, P.; Neun, B.W.; Hall, J.B.; McNeil, S.E. Interaction of colloidal gold nanoparticles with human blood: Effects on particle size and analysis of plasma protein binding profiles. Nanomed. Nanotechnol. Biol. Med.
**2009**, 5, 106–117. [Google Scholar] [CrossRef] - Perez, J.M.; Simeone, F.J.; Saeki, Y.; Josephson, L.; Weissleder, R. Viral-induced self-assembly of magnetic nanoparticles allows the detection of viral particles in biological media. J. Am. Chem. Soc.
**2003**, 125, 10192–10193. [Google Scholar] [CrossRef] - Reeves, D.B.; Weaver, J.B. Approaches for modeling magnetic nanoparticle dynamics. Crit. Rev. Biomed. Eng.
**2014**, 42, 85–93. [Google Scholar] [CrossRef] - Eberbeck, D.; Wiekhorst, F.; Steinhoff, U.; Trahms, L. Aggregation behaviour of magnetic nanoparticle suspensions investigated by magnetorelaxometry. J. Phys. Condens. Matter
**2006**, 18, S2829. [Google Scholar] [CrossRef] - Yari, P.; Rezaei, B.; Dey, C.; Chugh, V.K.; Veerla, N.V.R.K.; Wang, J.P.; Wu, K. Magnetic particle spectroscopy for point-of-care: A review on recent advances. Sensors
**2023**, 23, 4411. [Google Scholar] [CrossRef] - Zhong, J.; Rosch, E.L.; Viereck, T.; Schilling, M.; Ludwig, F. Toward rapid and sensitive detection of SARS-CoV-2 with functionalized magnetic nanoparticles. ACS Sens.
**2021**, 6, 976–984. [Google Scholar] [CrossRef] - Wu, K.; Liu, J.; Saha, R.; Su, D.; Krishna, V.D.; Cheeran, M.C.J.; Wang, J.P. Magnetic particle spectroscopy for detection of influenza A virus subtype H1N1. ACS Appl. Mater. Interfaces
**2020**, 12, 13686–13697. [Google Scholar] [CrossRef] [PubMed] - Safavi-Sohi, R.; Maghari, S.; Raoufi, M.; Jalali, S.A.; Hajipour, M.J.; Ghassempour, A.; Mahmoudi, M. Bypassing protein corona issue on active targeting: Zwitterionic coatings dictate specific interactions of targeting moieties and cell receptors. ACS Appl. Mater. Interfaces
**2016**, 8, 22808–22818. [Google Scholar] [CrossRef] [PubMed] - Mirshafiee, V.; Kim, R.; Park, S.; Mahmoudi, M.; Kraft, M.L. Impact of protein pre-coating on the protein corona composition and nanoparticle cellular uptake. Biomaterials
**2016**, 75, 295–304. [Google Scholar] [CrossRef] - Nikam, D.S.; Jadhav, S.V.; Khot, V.M.; Ningthoujam, R.; Hong, C.K.; Mali, S.S.; Pawar, S. Colloidal stability of polyethylene glycol functionalized Co
_{0.5}Zn_{0.5}Fe_{2}O_{4}nanoparticles: Effect of pH, sample and salt concentration for hyperthermia application. RSC Adv.**2014**, 4, 12662–12671. [Google Scholar] [CrossRef] - Ficko, B.W.; NDong, C.; Giacometti, P.; Griswold, K.E.; Diamond, S.G. A feasibility study of nonlinear spectroscopic measurement of magnetic nanoparticles targeted to cancer cells. IEEE Trans. Biomed. Eng.
**2016**, 64, 972–979. [Google Scholar] [CrossRef] - Elrefai, A.L.; Yoshida, T.; Enpuku, K. Viscosity dependent amplitude and phase of harmonic signals of magnetic nanoparticles. J. Magn. Magn. Mater.
**2020**, 507, 166809. [Google Scholar] [CrossRef] - Du, Z.; Sun, Y.; Wang, D.; Higashi, O.; Bai, S.; Noguchi, Y.; Enpuku, K.; Yoshida, T. Amplitude and phase of higher harmonic of magnetic nanoparticles’ magnetization under low frequency magnetic field. J. Magn. Magn. Mater.
**2020**, 508, 166886. [Google Scholar] [CrossRef] - Remmo, A.; Löwa, N.; Ludwig, A.; Wiekhorst, F. Magnetic particle spectroscopy for monitoring the cellular uptake of magnetic nanoparticles: Impact of the excitation field amplitude. Int. J. Magn. Part. Imaging Ijmpi.
**2023**, 9. [Google Scholar] [CrossRef] - Hotze, E.M.; Phenrat, T.; Lowry, G.V. Nanoparticle aggregation: Challenges to understanding transport and reactivity in the environment. J. Environ. Qual.
**2010**, 39, 1909–1924. [Google Scholar] [CrossRef] - Trefalt, G.; Borkovec, M. Overview of DLVO Theory; Laboratory of Colloid and Surface Chemistry, University of Geneva: Geneva, Switzerland, 2014; Volume 304. [Google Scholar]
- Yeap, S.P.; Lim, J.; Ooi, B.S.; Ahmad, A.L. Agglomeration, colloidal stability, and magnetic separation of magnetic nanoparticles: Collective influences on environmental engineering applications. J. Nanopart. Res.
**2017**, 19, 368. [Google Scholar] [CrossRef] - Zhang, J.X.; Hoshino, K. Molecular Sensors and Nanodevices: Principles, Designs and Applications in Biomedical Engineering; Academic Press: Cambridge, MA, USA, 2018. [Google Scholar]
- Takae, S.; Akiyama, Y.; Otsuka, H.; Nakamura, T.; Nagasaki, Y.; Kataoka, K. Ligand density effect on biorecognition by PEGylated gold nanoparticles: Regulated interaction of RCA120 lectin with lactose installed to the distal end of tethered PEG strands on gold surface. Biomacromolecules
**2005**, 6, 818–824. [Google Scholar] [CrossRef] [PubMed] - Chen, X.; Zu, Y.; Xie, H.; Kemas, A.M.; Gao, Z. Coordination of mercury (II) to gold nanoparticle associated nitrotriazole towards sensitive colorimetric detection of mercuric ion with a tunable dynamic range. Analyst
**2011**, 136, 1690–1696. [Google Scholar] [CrossRef] [PubMed] - Wei, B.; Zhang, J.; Ou, X.; Lou, X.; Xia, F.; Vallée-Bélisle, A. Engineering biosensors with dual programmable dynamic ranges. Anal. Chem.
**2018**, 90, 1506–1510. [Google Scholar] [CrossRef] - Shang, Z.; Deng, Z.; Yi, X.; Yang, M.; Nong, X.; Lin, M.; Xia, F. Construction and bioanalytical applications of poly-adenine-mediated gold nanoparticle-based spherical nucleic acids. Anal. Methods
**2023**, 15, 5564–5576. [Google Scholar] [CrossRef] - Li, C.M.; Zhen, S.J.; Wang, J.; Li, Y.F.; Huang, C.Z. A gold nanoparticles-based colorimetric assay for alkaline phosphatase detection with tunable dynamic range. Biosens. Bioelectron.
**2013**, 43, 366–371. [Google Scholar] [CrossRef] - Elias, D.R.; Poloukhtine, A.; Popik, V.; Tsourkas, A. Effect of ligand density, receptor density, and nanoparticle size on cell targeting. Nanomed. Nanotechnol. Biol. Med.
**2013**, 9, 194–201. [Google Scholar] [CrossRef] - Alkilany, A.M.; Zhu, L.; Weller, H.; Mews, A.; Parak, W.J.; Barz, M.; Feliu, N. Ligand density on nanoparticles: A parameter with critical impact on nanomedicine. Adv. Drug Deliv. Rev.
**2019**, 143, 22–36. [Google Scholar] [CrossRef] - Wu, K.; Chugh, V.K.; D. Krishna, V.; di Girolamo, A.; Wang, Y.A.; Saha, R.; Liang, S.; Cheeran, M.C.; Wang, J.P. One-step, wash-free, nanoparticle clustering-based magnetic particle spectroscopy bioassay method for detection of SARS-CoV-2 spike and nucleocapsid proteins in the liquid phase. ACS Appl. Mater. Interfaces
**2021**, 13, 44136–44146. [Google Scholar] [CrossRef] [PubMed] - Hong, Y.; Honda, R.J.; Myung, N.V.; Walker, S.L. Transport of iron-based nanoparticles: Role of magnetic properties. Environ. Sci. Technol.
**2009**, 43, 8834–8839. [Google Scholar] [CrossRef] - Givens, B.E.; Wilson, E.; Fiegel, J. The effect of salts in aqueous media on the formation of the BSA corona on SiO
_{2}nanoparticles. Colloids Surf. Biointerfaces**2019**, 179, 374–381. [Google Scholar] [CrossRef] - Phillips, R.; Kondev, J.; Theriot, J.; Garcia, H. Physical Biology of the Cell; Garland Science: New York, NY, USA, 2012. [Google Scholar]
- Faure, B.; Salazar-Alvarez, G.; Bergstrom, L. Hamaker constants of iron oxide nanoparticles. Langmuir
**2011**, 27, 8659–8664. [Google Scholar] [CrossRef] [PubMed] - Wu, K.; Liu, J.; Saha, R.; Peng, C.; Su, D.; Wang, Y.A.; Wang, J.P. Investigation of commercial iron oxide nanoparticles: Structural and magnetic property characterization. ACS Omega
**2021**, 6, 6274–6283. [Google Scholar] [CrossRef] [PubMed] - Lisjak, D.; Mertelj, A. Anisotropic magnetic nanoparticles: A review of their properties, syntheses and potential applications. Prog. Mater. Sci.
**2018**, 95, 286–328. [Google Scholar] [CrossRef] - Lim, J.; Yeap, S.P.; Che, H.X.; Low, S.C. Characterization of magnetic nanoparticle by dynamic light scattering. Nanoscale Res. Lett.
**2013**, 8, 381. [Google Scholar] [CrossRef] - Smith, A.M.; Johnston, K.A.; Crawford, S.E.; Marbella, L.E.; Millstone, J.E. Ligand density quantification on colloidal inorganic nanoparticles. Analyst
**2017**, 142, 11–29. [Google Scholar] [CrossRef] [PubMed] - Chen, H.; Paholak, H.; Ito, M.; Sansanaphongpricha, K.; Qian, W.; Che, Y.; Sun, D. ‘Living’PEGylation on gold nanoparticles to optimize cancer cell uptake by controlling targeting ligand and charge densities. Nanotechnology
**2013**, 24, 355101. [Google Scholar] [CrossRef] - Pamies, R.; Cifre, J.G.H.; Espín, V.F.; Collado-González, M.; Baños, F.G.D.; de la Torre, J.G. Aggregation behaviour of gold nanoparticles in saline aqueous media. J. Nanopart. Res.
**2014**, 16, 2376. [Google Scholar] [CrossRef] - Bhattacharjee, S. DLS and zeta potential–what they are and what they are not? J. Control Release
**2016**, 235, 337–351. [Google Scholar] [CrossRef] - Ha, J.M.; Katz, A.; Drapailo, A.B.; Kalchenko, V.I. Mercaptocalixarene-capped gold nanoparticles via postsynthetic modification and direct synthesis: Effect of calixarene cavity-metal interactions. J. Phys. Chem. C
**2009**, 113, 1137–1142. [Google Scholar] [CrossRef] - Wang, Y.; Zeiri, O.; Neyman, A.; Stellacci, F.; Weinstock, I.A. Nucleation and island growth of alkanethiolate ligand domains on gold nanoparticles. ACS Nano
**2012**, 6, 629–640. [Google Scholar] [CrossRef] - Zhang, X.; Fan, X.; Wang, Y.; Lei, F.; Li, L.; Liu, J.; Wu, P. Highly Stable Colorimetric Sensing by Assembly of Gold Nanoparticles with SYBR Green I: From charge screening to charge neutralization. Anal. Chem.
**2019**, 92, 1455–1462. [Google Scholar] [CrossRef] [PubMed] - Vikesland, P.J.; Rebodos, R.; Bottero, J.; Rose, J.; Masion, A. Aggregation and sedimentation of magnetite nanoparticle clusters. Environ. Sci. Nano
**2016**, 3, 567–577. [Google Scholar] [CrossRef] - Afrooz, A.N.; Khan, I.A.; Hussain, S.M.; Saleh, N.B. Mechanistic heteroaggregation of gold nanoparticles in a wide range of solution chemistry. Environ. Sci. Technol.
**2013**, 47, 1853–1860. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Focused ion beam scanning electron microscope (FIB-SEM) image of Ocean Nanotech’s SHA 25 MNPs. The SHA 25 MNPs had an average diameter of 23.35 ± 4.29 nm. (

**b**) Corresponding log-normal size distribution plot for the SHA 25 MNPs.

**Figure 2.**(

**a**) 10 and 90 biotin-MNP ${\varphi}_{3}$ as a function of streptavidin concentration (streptavidin-response curve) in 1.00x PBS. Where 90 biotin-MNP ${\varphi}_{3}$ in 0.00x PBS was regarded as zero. (

**b**) Zeta potential and (

**c**) ${D}_{Hyd}$ of 10 and 90 biotin-MNPs in 1.00x PBS. The streptavidin response curve shows that the assay’s sensitivity increases as biotin density decreases.

**Figure 3.**(

**a**) Zeta potential of 90 biotin-MNPs in 0.05x, 0.045x, 0.04x, 0.035x, 0.03x, 0.025x, 0.02x, 0.015x, 0.01x, 0.005, and 0.000x PBS solutions. (

**b**) Hydrodynamic diameter of 90 biotin-MNPs in 0.03x, 0.025x, 0.02x, 0.015x, 0.01x, 0.005, and 0.00x PBS solutions.

**Figure 4.**(

**a**) 90 biotin-MNP ${\varphi}_{3}$ as a function of streptavidin concentration (streptavidin-response curve) in 1.00x, 0.50x, and 0.03x PBS solutions. Where 90 biotin-MNP ${\varphi}_{3}$ in 0.00x PBS was regarded as zero. (

**b**) The linear region of each curve was fit with a linear regression, where there were no statistically significant variations amongst regression model slopes. (

**c**) Total interparticle energy profiles for 90 biotin-MNPs in 1.00x, 0.50x, and 0.03x PBS solutions, where the energy profiles are indistinguishable and overlay each other. These data show that 90 biotin-MNP sensitivity to streptavidin induced aggregation was constant for 0.03x, 0.50x, and 1.00x PBS solutions. Our experimental results were supported by xDLVO simulations demonstrating that the total interparticle energy profile corresponding to each PBS solution came from the same continuous distribution.

**Figure 5.**(

**a**) 90 biotin-MNP ${\varphi}_{3}$ as a function of streptavidin concentration (streptavidin-response curve) in 0.015x, 0.005x, and 0.00x PBS solutions. Where 90 biotin-MNP ${\varphi}_{3}$ in 0.00x PBS was regarded as zero. (

**b**) The linear region of each curve was fit with a regression, where the 0.00x PBS regression model slope had statistically significant variations from the regression model slopes corresponding to the 0.015x and 0.005x PBS solutions. (

**c**) Total interparticle energy profiles for 90 biotin-MNPs in 0.015x, 0.005x, and 0.00x PBS solutions, where the 0.00x PBS total interparticle energy profile had statistically significant variations from the energy profiles corresponding to the 0.015x and 0.005x PBS solutions. These data show that 90 biotin−MNP senstivity to streptavidin induced aggregation was significantly decreased in 0.00x PBS. Our experimental result was supported by xDLVO simulation demonstrating that the total interparticle energy profile corresponding to the 0.00x PBS was dominated by the attractive van der Waals force for separation distances between 0 and 22 nm, while interactions were dominated by the repulsive EDL force for separation distances between 23 and 50 nm. However, total interparticle energies corresponding to the 0.015x and 0.005x PBS solutions were dominated by the attractive van der Waals force for separation distances between 0 and 50 nm.

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**MDPI and ACS Style**

Moss, G.; Knopke, C.; Diamond, S.G.
Effects of Salt Concentration on a Magnetic Nanoparticle-Based Aggregation Assay with a Tunable Dynamic Range. *Sensors* **2024**, *24*, 6241.
https://doi.org/10.3390/s24196241

**AMA Style**

Moss G, Knopke C, Diamond SG.
Effects of Salt Concentration on a Magnetic Nanoparticle-Based Aggregation Assay with a Tunable Dynamic Range. *Sensors*. 2024; 24(19):6241.
https://doi.org/10.3390/s24196241

**Chicago/Turabian Style**

Moss, Gabrielle, Christian Knopke, and Solomon G. Diamond.
2024. "Effects of Salt Concentration on a Magnetic Nanoparticle-Based Aggregation Assay with a Tunable Dynamic Range" *Sensors* 24, no. 19: 6241.
https://doi.org/10.3390/s24196241