Concurrent quantification of multiple nanoparticle bound states

Abstract

Purpose: The binding of nanoparticles to in vivo targets impacts their use for medical imaging, therapy, and the study of diseases and disease biomarkers. Though an array of techniques can detect binding in vitro, the search for a robust in vivo method continues. The spectral response of magnetic nanoparticles can be influenced by a variety of changes in their physical environment including viscosity and binding. Here, the authors show that nanoparticles in these different environmental states produce spectral responses, which are sufficiently unique to allow for simultaneous quantification of the proportion of nanoparticles within each state.

Methods: The authors measured the response to restricted Brownian motion using an array of magnetic nanoparticle designs. With a chosen optimal particle type, the authors prepared particle samples in three distinct environmental states. Various combinations of particles within these three states were measured concurrently and the authors attempted to solve for the quantity of particles within each physical state.

Results: The authors found the spectral response of the nanoparticles to be sufficiently unique to allow for accurate quantification of up to three bound states with errors on the order of 1.5%. Furthermore, the authors discuss numerous paths for translating these measurements to in vivo applications.

Conclusions: Multiple nanoparticle environmental states can be concurrently quantified using the spectral response of the particles. Such an ability, if translated to the in vivo realm, could provide valuable information about the fate of nanoparticles in vivo or improve the efficacy of nanoparticle based treatments.

INTRODUCTION

The functionalization of magnetic nanoparticles has important implications in determining both their circulation time in vivo and their biodistribution.¹ An ability to target the particles to a specific disease or tissue is critical in maximizing their delivery and subsequent diagnostic and therapeutic function. Much effort has focused on tumor targeting of nanoparticles, but the enhanced permeability and retention (EPR) effect complicates efforts to determine the mechanism of accumulation. The EPR effect can produce an increase in nanoparticle concentration within a tumor that might mask any increase due to binding of targeted particles.^{2, 3, 4} When molecular binding does occur, internalization is more probable, which can, in turn, increase therapeutic efficacy.⁵ While there are many methods to assess this binding ex vivo or in vitro, most are limited in their ability to perform at depth in vivo.⁶

Even if molecular binding does occur, the unbound pool can complicate efforts to quantify the bound fraction. Tumor receptors can rapidly saturate in the presence of their ligand, which hinders the ability to detect binding.² High affinity targets can also affect the distribution of the nanoparticles within a tumor. They often bind immediately around the tumor vasculature and do not penetrate into the tumor.⁷ Lower affinity agents might penetrate throughout the tumor more effectively but do not bind as much as would be desired. Some studies have shown uptake of targeted and nontargeted nanoparticles achieve comparable concentrations but different localizations.⁵ An imaging modality capable of separating the influences of increased accumulation and increased binding within a region of interest would be invaluable to the efforts of detecting, understanding, and treating disease.

Magnetic spectroscopy of nanoparticle Brownian motion (MSB) is a method of measuring characteristics of nanoparticles that affect their Brownian motion.⁸ The harmonic spectrum of a particle’s magnetization can be influenced by a number of physical parameters including temperature,⁹ viscosity,¹⁰ and binding.¹¹ The magnetic harmonics measured in MSB are also used in magnetic particle imaging (MPI), which images the concentration of magnetic nanoparticles with high speed, resolution, and sensitivity.¹² Continued development of the modality has produced in vivo murine images,¹³ demonstrating that the magnetic harmonics can be measured in vivo at biologically tolerable concentrations.

In the previous work, the unique spectral signature of different nanoparticle designs has allowed for multiple particle types to be quantified simultaneously.¹⁴ With proper nanoparticle selection, a single nanoparticle design should also generate unique spectral signatures when exposed to different physical environments. Indeed, we show experimentally that the spectral responses produced by magnetic nanoparticles in different physical environments are sufficiently unique to allow for concurrent quantification of the proportion of nanoparticles within each environmental state. We concurrently quantify up to three environmental states using an in vitro spectrometer and discuss how these methods could be translated to the in vivo realm.

METHODS AND THEORY

Experimental setup

These experiments were performed with a custom built magnetic spectrometer. The data acquisition sequence and subsequent data processing were performed in MATLAB. A Stanford Research Systems SR830 lock-in amplifier (Sunnyvale, CA) generated the sinusoidal drive signal. This signal was amplified by a PL236 audio amplifier (QSC Audio Products, Costa Mesa, CA) and delivered to a 2500-turn solenoid coil in series with a capacitor. To achieve resonance at a different frequency, this capacitor was changed. The magnetic field produced by the drive coil was measured with a F.W. Bell 5180 gaussmeter at the measurement region of the receive coil. Additionally, the voltage induced in a small coil positioned at the base of the drive coil was recorded every time a sample was measured. This coil was calibrated to report the field at the measurement region of the receive coil in units of mT∕μ₀ RMS. Within the excitation coil was a 500-turn pickup coil placed concentrically. A sample to be measured was then placed within the 12 mm bore of the pickup coil. A balancing coil was placed in the drive coil away from the nanoparticle sample so it measured signal only from the applied field. The pickup coil and the balancing coil were placed in series so that the current induced in the balancing coil by the drive field canceled the current induced in the pickup coil by the drive field, leaving only the signal from the nanoparticles. The pickup coil signal was then returned to the lock-in for measurement of the magnetization harmonics. The magnitude and phase of the third and fifth harmonics were recorded using the phase of the drive field as the reference.

Magnetization theory

The magnetization of nanoparticles is subject to both static and dynamic effects. An equilibrium between magnetic energy, which acts to align the particles, and thermal energy, seeking to randomize the particles’ orientation, determines the static magnetization of the nanoparticles. At low frequencies where the nanoparticle magnetization, M, is at equilibrium, it is described by the Langevin function,

$$\frac{M}{M_S}=L\left(\epsilon \right)=\text{coth}\epsilon -\frac{1}{\epsilon },$$ (1)

where M_S is the saturation magnetization and ε=μHμ₀∕k_BT, where μ is the magnetic moment of the particle, H is the applied field, μ₀ is the permeability of the free space, k_B is the Boltzmann’s constant, and T is the absolute temperature. As the applied field, H, increases in frequency, a relaxation time, τ, governs a particle’s ability to follow changes in the applied field via two distinct relaxation mechanisms, Brownian and Néel, which act in parallel. The physical environment of the particles will influence the Brownian relaxation time, which impacts the dynamic magnetization. In Brownian relaxation, the physical rotation of the particles’ hydrodynamic volume, V_H, is governed by a time constant

$${\tau }_{\mathbf{B}}=\frac{3\eta V_H}{k_{B}T},$$ (2)

where η is the dynamic viscosity.¹⁵ The second relaxation method, Néel, allows for internal reorientation of a particle’s magnetic moment according to

$${\tau }_N={\tau }_0\text{\hspace{0.17em}exp}\left(\frac{K{V}_M}{k_{B}T}\right),$$ (3)

where τ₀ is 10⁻⁹ s, K is the anisotropy energy density, and V_M is the magnetic core volume.¹⁵

RESULTS

Nanoparticle selection

The physical environment of the nanoparticles, along with the frequency and amplitude of the applied magnetic field, will uniquely impact the static and dynamic magnetization of the particles. In the frequency domain, this response can be analyzed using the amplitude and phase of the magnetization harmonics.^{9, 10} As the proportion of nanoparticles that undergo Brownian relaxation increases, the influence of the physical environment on the magnetization also increases. We demonstrate this experimentally in Fig. 1 using three distinct particle types. Equal quantities of each particle type were dissolved in both water and high concentration gelatin solution. The high viscosity of the solidified gelatin is known to suppress Brownian relaxation. The first column set in Fig. 1 displays the results for the commercial MRI contrast agent Feridex I.V.^™. The Feridex particles, which have a broad magnetic core size distribution with a mean <10 nm,¹⁸ lost only 10.4% of their third harmonic amplitude, suggesting a ready ability to undergo Néel relaxation, which would be expected with such a small iron-oxide core size. For maghemite particles, the transition from Néel to Brownian relaxation is expected to occur in the vicinity of a 25 nm magnetic core diameter.¹⁵ We repeated this experiment with Ocean Nanotech particles SHA-25 and SHP-40, which have a tight core size distribution centered at 25 and 40 nm, respectively. When solidified in gel, the SHA-25 particles lost 43.7% of their third harmonic amplitude, while the SHP-40 lost over 99%. This suggests an increasing dependence of these two particle types on external Brownian rotation of the magnetic core and coating. The results for the Feridex and Ocean Nanotech SHP-40 particles raise contrast-to-noise concerns for their use in detecting multiple bound states. The Feridex particles have little signal contrast between bound and unbound states, while the low harmonic amplitude of the bound 40 nm particles could lead to noise issues. In an effort to quantify multiple bound states, we have selected 30 nm particles, which represent a balance between contrast and noise.

Figure 1.

Impact of gelatin containment on different nanoparticle types measured at 320 Hz and 23 mT∕μ₀.

Quantification of multiple environmental states

In Fig. 1, we demonstrated the impact of gelatin containment on the amplitude of a single harmonic. A change in the physical environment of a nanoparticle, which undergoes Brownian relaxation, will also influence the phase of the third harmonic and the amplitude and phase of higher order harmonics. Such an influence is shown in Fig. 2 using nanoparticles dispersed in three different environments. Magnetite nanoparticles with 30 nm core diameter and a Streptavidin coating (SHS-30) were purchased from Ocean NanoTech (Springdale, AR). Particle samples in three different physical environments were prepared in 1.5 mm capillary tubes with each tube containing 5 μg of iron. The samples were positioned identically within each tube with a sample height of approximately 7 mm. The first environment consisted of the nanoparticles diluted in water, which has a viscosity of approximately 1 cP at room temperature. A second environment was prepared by diluting the particles in a 2 cP glycerol and water solution proportioned according to the formulas of Cheng.¹⁶ This viscosity simulates conditions that might be experienced in a cellular vacuole.¹⁷ For a third environment, we nonspecifically bound the particles to 2 μm polystyrene beads (Polysciences 19814-15). Binding was confirmed by centrifugal pelleting of the polystyrene beads, which left a clear supernatant with minimal harmonic response. A control was prepared by coating the beads with bovine serum-albumin before adding the nanoparticles. The control’s pellet had minimal harmonic content, while the supernatant had a strong response.

Figure 2.

Third (solid lines) and fifth (dashed lines) harmonic responses of SHS-30 nanoparticles in three different environments. These 30 nm core diameter particles were excited at 290 Hz and 11.1 mT∕μ₀. Each sample contained 15 μg of Fe.

By increasing the viscosity of the solution or binding to a larger nonmagnetic bead, the amplitude of the harmonics, the ratio of the fifth to third harmonic amplitudes, and the phase angles of the harmonics are all impacted (see Fig. 2). The unique spectral response of each of these environmental states should allow for concurrent quantification of the number of particles within each state. This quantification can be improved through the use of multiple excitation parameters if the responses are independent. As shown in Table 1, particles in these different environmental states respond uniquely to a change in the field strength. Similar results can be observed for changes in the excitation frequency.

Table 1.

Change in the spectral response of SHS-30 nanoparticles with an increase in the field strength from 11.1 to 16.6 mT∕μ₀. Results are the percent or degree change from the response at 290 Hz and 11.1 mT∕μ₀.

	|3rd| (%)	|5th| (%)	Angle 3rd (deg)	Angle 5th (deg)
Water—1cP	50.33	73.75	1.67	2.08
Glycerol∕water—2cP	69.14	85.54	1.69	0.83
Bead bound	133.80	220.27	4.63	−8.18

To demonstrate concurrent quantification, we started with the simplest case consisting of only two bound states: Unbound nanoparticles in water and nanoparticles bound to 2 μm beads in water. For an excitation of 290 Hz and 11 mT∕μ₀, these two physical environments produce nearly orthogonal harmonic responses (see Fig. 2). The spectral responses for each physical state normalized for mass of iron served as our response matrix. Though care was taken to ensure that the sample tubes for a given physical state had uniform spectral responses, some errors in sample volume and placement within the tube were present. To minimize these sources of error, an average response for the particular tubes to be used with each combination was used in the response matrix. We placed various combinations of these two samples’ tubes in our spectrometer and measured the complex third and fifth harmonics at 290 Hz and 11 mT∕μ₀. Using a linear least-squares, we solved for the concentration of particles in each bound state (see Fig. 3). For the 36 different combinations measured, the average error in our solution was 0.55% and the maximum single error was 1.59%. With each measurement, we attempted to keep tube placement within the receive coil consistent to limit errors caused by some inhomogeneity in the spatial sensitivity of the coil.

Figure 3.

Concurrent quantification of SHS-30 nanoparticles in two distinct environmental states. The asterisks indicate our linear least-squares solutions and the grid intersections indicate the actual concentrations. The average error was 0.55%.

We extended the technique to three environmental states by simulating environmental conditions the particles might experience during cellular uptake: Extracellular fluid, cell surface bound, and cellular vacuoles. These three environments were simulated by nanoparticles in water, nanoparticles bound to 2 μm beads, and nanoparticles in a 2 cP glycerol water solution, respectively.¹⁷ Measurements were acquired at 290 Hz and at two field strengths, 11.1 and 16.6 mT∕μ₀. The results, as shown in Table 2, had a maximum single error of 3.71% and a mean error of 1.47%.

Table 2.

Concurrent quantification of SHS-30 nanoparticles in different combinations (solved∕actual μg) of three distinct environmental conditions measured at 290 Hz and 11.1 and 16.6 mT∕μ₀.

	Bound state combinations
	A	B	C	D	E	F
Water	25.187∕25	20.055∕20	20.057∕20	15.527∕15	14.690∕15	10.126∕10
Beads	0.000∕0	4.978∕5	9.955∕10	19.258∕20	15.218∕15	9.980∕10
Glycerol∕water	0.000∕0	0.000∕0	5.066∕5	10.274∕10	15.434∕15	15.102∕15

DISCUSSION

A clear source of error in performing this technique in complicated in vivo conditions would be the finite number of physical environments represented in the response matrix. The extent of this error would depend on the knowledge of the biological environment and processes being monitored. Here, we used three pure states of viscosity or binding, but in vivo numerous degrees of binding, viscosity, particle aggregation, or combinations of these might be expected. The use of an array of different excitation frequencies and amplitudes would allow for the inclusion of a greater number of bound states but the complicating factors are clear. A more controlled environment for this technique may be in vitro diagnostic applications. Magnetic nanoparticles are central to numerous diagnostic techniques for detecting specific analytes.¹⁹ Critical to most of these is the specific binding of the particles to an analyte of choice. The ability to quantify bound particles in the presence of unbound particles could remove the need for the additional washing steps often needed to remove unbound particles. The use of several different nanoparticle designs could allow for multiplex detection without the need for washing or spatial resolution.

Though our results were acquired using an in vitro spectrometer, there are several potential paths for performing these measurements at depth. Magnetic particle imaging is capable of rapidly measuring the harmonic response of nanoparticles in vivo and the potential exists for eventually incorporating detection of multiple bound states. This ability would make MPI a valuable tool in the continued study of the biological response to nanoparticles and allow for separation of the influences of increased accumulation and increased binding. An ability to quantify the proportion of particles within a particular physical state could also benefit magnetic nanoparticle based treatments, such as magnetic fluid hyperthermia. Dennis et al.²⁰ showed an increased efficacy of hyperthermia after aggregation of the particles within cells. If this technique could remotely monitor this aggregation, then the time point at which the hyperthermia magnetic field is applied could be optimized. One could also monitor a single region of interest using DC gradients as demonstrated with the first generation MPI system.¹² Tasci et al.²¹ used a similar localization technique to limit the region of heating with magnetic fluid hyperthermia. The use of static fields would introduce even harmonics, which might improve the ability to separate the spectral signature of different bound states.

CONCLUSION

The binding of magnetic nanoparticles to their in vivo targets plays a critical role in their effectiveness for molecular imaging or therapy. We have shown that particles’ magnetization spectra in different physical environments are sufficiently unique to allow for simultaneous quantification of the proportion of particles in each state. In vitro we have quantified up to three physical states with errors of only 1.5%. This technique should be capable of overcoming the depth limitations, which complicate the translation of other in vitro techniques to the in vivo realm.