Magnetic nanowires for quantitative detection of biopolymers

Progress in molecular biology, nanomedicine, and medical therapeutics has urged Nanobiotechnology to prioritize the invention of ultrasensitive and rapid multiplexed detection techniques.¹ For example, rare cancer sites need to be detected early for the best diagnosis, staging, and prognosis of cancers. Practically, a change in the number of cancer cells reflects the chemotherapeutic sensitivity and growth activity of a tumor.² This causes a volatile concentration of the cancer cells leading to the failure of the medical treatments because the dosage of the medicine is restricted to a narrow therapeutic window in order to be effective while avoiding side-effects. In this context, new biolabels, such as quantum dots conjugated with magnetic nanoparticles, were proposed.³ Regardless of the requirement of expensive equipment for the optical techniques, their success drastically relies on the specificity of the employed biolabels to assure no spectral overlap between absorption/emission spectra and the biolabels emission spectra while achieving maximum signal-to-noise ratios.^4,5

Here, magnetic nanowires (MNWs) are proposed with great potential in transforming the current state of the art for enrichment and multiplexing techniques using a single source (an external magnetic field) with minimal biological side effects. The special cylindrical geometry of MNWs gives rise to a well-defined shape anisotropy that makes them suitable for many biological applications, such as magnetic resonance imaging (MRI) contrast, magnetic enrichment, and nanowarming.⁶ An external field can be remotely used to physically excite MNWs, which makes them suitable for cell tracking, separation, and manipulation,^7,8 drug delivery and activation,⁹ magnetic hyperthermia,¹⁰ and tissue engineering using magneto-elastic ferrogels.¹¹ Furthermore, the MNWs have shown a high internalization by cells in comparison to other magnetic nanoparticles, such as iron oxide nanoparticles, improving the enrichment and multiplexing yield.^12,13

Two fundamental problems are holding MNWs back from successes comparable to optical particles. First, magnetic characterization techniques are technically inefficient because they are slow. Second, the magnetic signatures of magnetic particles can overlap, which prevents their use as multiplexed biolabels. To overcome these substantial obstacles, we proposed the projection method that highly accelerates the detection of MNWs.¹⁴ The projection method directly measures and decouples the reversible switching field (RSF) and irreversible switching field (ISF) distributions of the MNWs by scanning a narrow area next to the upper branch of the hysteresis loop. The RSF distributions not only includes the reversible response of the MNWs but also the paramagnetic and diamagnetic responses of the surrounding materials (e.g. biopolymer). The ISF distribution, on the other hand, is a function of both coercivity and interaction fields, which are generated only by the MNWs, and they are a function of the MNWs diameter, inter-pore distances, and composition.

In our previous studies,^14,15 we showed that ISF distributions have two main advantages for demultiplexing of the MNWs embedded in biological tissues. First, it can be readily calculated from the projection method that is significantly faster than the FORC method, in both measurement and data analysis aspects. Second, since the ISF distributions carry information regarding both coercivity and interaction fields, the ISF distributions of unknown combinations can be demultiplexed even though they have overlapping coercivity or interaction field distributions. However, since the projection method measures the ISF distributions but not coercivity and interaction distributions directly, we found it beneficial to calculate these distributions from the projection method results and to elucidate the correlation between these distributions and the ISF distributions. We also compare the coercivity and interaction distributions achieved from the projection method and the FORC method to further analyze the reliability of the projection method for quantitative demultiplexing.

Three different types of MNWs were synthesized inside the porous polycarbonate using the well-established electrodeposition technique.^4,5,15 We chose polycarbonate in this study because polycarbonate is a biopolymer and has been widely used in bone/organ repairing, drug delivery, and tissue regenerative engineering.¹⁶ We managed to tailor the magnetic signatures (coercivity, interaction, and ISF distributions) of the MNWs using their compositions. To do so, we use similar polycarbonate temples (having the same pore diameters, ∼30nm, and the average inter-wire distance, ∼420nm) while electrodepositing different magnetic components including nickel (Ni), cobalt (Co), and iron-cobalt (FeCo). In this way, the coercivity, interaction field, and ISF distributions are only a function of the magnetic properties of the component, such as crystal anisotropy and saturation magnetization.

We employed standard procedures of the FORC method and projection method, as explained to calculate the coercivity and interaction field distributions of each type of MNWs.¹⁴ According to our previous works,^4,14 the projection method protocol is exactly similar to the FORC method except it measures only a few data points (5 points) at the beginning of each reversal curve instead of fully measuring each reversal curve. The projection method was also conducted on several combinations of the MNWs with at least two different types. Since the MNWs in each array does not cross-talk with the MNWs in the other array, the ISF distributions of the combinations are expected to be a linear summation of the ISF distributions of the individual MNWs arrays in the combination.⁴ Therefore, for quantitative analysis, the measured signatures for the combinations were compared with the corresponding calibration curves, which were defined as a linear superposition of the weighted corresponding signatures. For example, for the combination of Ni and Co arrays, the calibration curve was

where, α_i are volume percentages for the present MNWs in a combination that are being calculated by minimizing the root mean square (rms) between the calibration curve and the experimental data measured on the combination. Note, the ratio of the α_i gives the volume ratio of MNWs types in the combination.

The irreversible switching field (ISF) distribution can be fully demonstrated using the coercivity and interaction field distributions. Here, we used the data analysis of the projection method to determine the coercivity (H_c), its standard deviation (σ_c), and the maximum interaction field (H_u^max), shown in Figure 1. Due to the symmetry of MNWs arrays, the H_u distribution can be indexed using an average value of zero (where equal numbers of MNWs are up and down) and its maximum and minimum values that are equal. Assuming the MNWs as single domain Stone-Wohlfarth particles, the H_c is a function of the crystal anisotropy and shape anisotropy. Since Co has a large crystal anisotropy coefficient, the Co MNWs have larger H_c compared to Ni and FeCo MNWs. The Ni and FeCo MNWs have fairly similar H_c that indicates the shape anisotropy is the dominant term in their H_c.

In addition to the crystal anisotropy and shape anisotropy, the σ_c is also a function of the templates pores sizes. Regardless of the MNWs type, all arrays have a σ_c that is within 11%-14% of the corresponding H_c. Since all templates were prepared through the same method, the ratio of the σ_c to H_c indicates all samples had fairly similar pore sizes. Note the spatial distribution of the pores (how close or far they are from each other) only impacts the H_u interaction. Theoretically, the H_u^max among bistable MNWs can be approximated by¹⁷ 

where, D and L are the average diameter and length of the MNWs, respectively, M_s is the saturation magnetization, and x is the inter-pores distance. It is hard to expect a trend in the H_u^max values because the inter-pore distances are random. Generally speaking, since the MNWs were electrodeposited in the similar templates with the same lengths, we would expect the FeCo and Co MNWs arrays to have larger H_u^max compared with Ni MNWs arrays because they have a larger M_s compared with Ni MNWs arrays, see Figure 1c.

The projection method results were used to plot the H_c and H_u distributions, and they are compared with the first-order reversal curve (FORC) method in Figures 2 and 3. A very good agreement was observed between the H_c distributions measured from both methods. Both methods calculate the H_u distributions to be fairly similar but they do not match perfectly. The differences come from the differences in the projection method and the FORC method data analyses and processing. According to Eq. (2), the H_u is independent of the applied field direction, it is only a function of the MNWs dimensions and inter-pore distance. Therefore, it is expected that H_u distributions are symmetric with the same maximum and minimum values but different signs. The projection method determines the H_u^max and uses the symmetric conditions of the H_u distributions (the average H_u is zero and H_u^max is considered 3 times of the H_u standard deviation to include over 99% of data) to demonstrate the H_u distribution. On the other hand, the FORC method calculates the H_u distribution by taking two derivatives of the FORCs followed by taking an integral over the H_c-axis. Previously, it was shown this data processing can cause significant alteration of the H_u interaction as the results of noise amplification during the derivatives and noise accumulation during the integral that make the H_u interaction asymmetric.^18–21 

For quantitative demultiplexing, the calibration curve was constructed using Eq. (1) and the corresponding ISF distributions. Then the calibration curve is compared with the measured data from the corresponding combination to find the volume ratios (α) while minimizing the root mean square (rms) errors. Figure 4 shows the ISF distributions of the MNWs and their combinations. The ISF distributions can be characterized by the location of their peak and their distribution width. The location of the ISF peak is the H_c of the MNWs, and its width is related to the σ_c and the H_u effects on the MNWs switching field. For example, since the Co MNWs have larger H_u and σ_c (∼0.12 * 2100 = 252 Oe), its ISF distribution is wider comparing to others, see Figure 4. Therefore, changing the MNWs compositions is sufficient to tune the H_c, σ_c, and H_u to generate diverse ISF distributions for quantitative demultiplexing.

Table I shows the results for the quantitative demultiplexing of the prepared MNWs arrays. The error is defined as the difference between the known volume ratio and the fitting results. As can be preserved from Figure 4, the calibration curves (cal. curve) match the experimental data (exp. data) very well leading to a maximum error of 9%, see Table I. These results indicate that the ISF distribution, which is rapidly measured using the projection method, is a strong probe for quantitative demultiplexing of the magnetically enriched biopolymers.

In this paper, different magnetic nanowires (MNWs) were investigated as biolabels for the quantitative demultiplexing of biopolymers. The magnetic properties of the MNWs were tailored using the composition and were characterized using the projection method and first-order reversal curve (FORC). A good agreement between the measured magnetic properties was found indicating the reliability of these methods for demultiplexing. Since the projection method characterizes the magnetic properties, by measuring the irreversible switching field (ISF) distributions, of the MNWs in much less time than the FORC method, we used the projection method for quantitative demultiplexing. It was observed that the ISF distribution is able to quantify the MNWs embedded in biopolymers with the maximum quantitative error of 9%. This low quantification error of the projection method, along with its rapid measurement protocol, smooths the path for MNWs to further advance the state of the art of the biolabels in nanomedicine and molecular biology.

This work is primarily supported by the National Science Foundation (NSF) under grant number CMMI-1762884. Part of this work was performed at the Institute for Rock Magnetism (IRM) at the University of Minnesota. The IRM is a U.S. National Multi-user Facility supported through the Instrumentation and Facilities program of the National Science Foundation, Earth Sciences Division (NSF/EAR 1642268), and by funding from the University of Minnesota. Portions of this work were conducted in the Minnesota Nano Center, which is supported by the National Science Foundation through the National Nano Coordinated Infrastructure Network (NNCI) under Award Number ECCS-2025124. Parts of this work were also carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program.

The data that support the findings of this study are available from the corresponding author upon reasonable request.