Sandwich complex assays were performed with biotin-coated particles as the analyte, which mimic a biological target. The concentration of biotin-coated particles was measured by observing the rate of rotation of the (solid phase sphere)–(biotin-coated particle)–(superparamagnetic label bead) sandwich complex. The 6.7 μm solid phase sphere has a surface area of 141 μm2
. Given that a 40 nm biotin-coated particle would occupy an area of 1.26 × 10−3
, one 6.7 μm sphere could bind up to 105
biotin-coated particles. The superparamagnetic label beads have a diameter of 1 μm, and occupy an area of 0.866 μm2
, which, given the limits of the packing efficiency of spheres, suggest that 145 superparamagnetic label beads can bind to that surface. This configuration would be expected to produce a sensor with approximately 2 orders of magnitude of dynamic range, as indicated by Eqs. (7)
, assuming that the magnetic moments of the beads are additive. The position at which the beads bind to the sphere should mostly affect the rotation at low numbers of binding beads. A variation in the binding location of a few beads could affect the rotational speed, which would result from differences in location-dependent torque and drag. However, as the number of beads on the sphere increases, this effect will have a smaller contribution. A full theoretical investigation into the specifics of this effect warrants further study, potentially using Hydro++ [41
], but is beyond the scope of this manuscript. Furthermore, the 6.7 μm “mother” sphere is more than 300 times bigger than a 1 μm label bead, thus the binding of a single bead to the sphere should not significantly alter the sphere’s center of rotation or shape factor. 1 μm beads were selected as labels for these experiments, so that they could still be individually distinguished by using light microscopy.
Scanning electron micrographs of the sandwich complexes are shown in . The three complexes shown were from samples with total biotin-coated particle concentrations of 2.88 × 107, 2.88 × 106, and 2.88 × 105 particles/μL. shows a reasonably dense coverage of the sphere by the superparamagnetic label beads, while shows fewer beads, and shows only two beads. This trend confirms that a greater number of superparamagnetic label beads are present with increasing amounts of biotin-coated particle.
Fig. 3 Scanning electron micrographs of sandwich complexes incubated with three different concentrations of biotin-coated particles, (a) 2.88 × 107, (b) 2.88 × 106, and (c) 2.88 × 105 μL−1. The 1 μm superparamagnetic (more ...)
The frame-by-frame analysis of sandwich complexes, from four 15 s videos recorded at 20 frames per second, is shown in . These four videos are included online as Supplementary Videos S1–S4
. The angle of the sandwich complex in each frame is calculated against the first frame in the video, which is defined as the zero angle. One complete rotation is 360°. The sandwich complexes occasionally were out of focus, which caused the tracker to mistrack the complexes for those frames. These outlying points were removed from , based on calculating the jackknife residuals for each point and discarding outliers, whose residuals exceeded the Bonferroni criteria [42
]. The four videos represent sandwich complexes with rotational frequencies of 133, 231, 303, and 396 mHz. The traces demonstrate the stability and consistency of the rotation of a sandwich complex during a 15 s observational period. Ten frames from each of the four videos, 0.5 s apart, are shown in . These images show the sandwich complexes rotating clockwise.
Fig. 4 Examination of the behavior of individual sandwich complexes. (a) Frame-by-frame analysis of four different rotating sandwich complexes. The angle at each time point represents the number of degrees through which the complex has rotated since t0 (360° (more ...)
The stability of the rotational frequency of sandwich complexes was also measured. Sandwich complexes were observed for 60 min, with 15 s videos of the rotating complex captured every 5 min. Eight sandwich complexes were observed in total; four adhered to the coverslip before the end of the 60 min, and were excluded from the analysis. The use of PBS-TB decreased nonspecific adherence to the coverslips, but did not completely prevent it. The average (±SD) rotational frequencies of the four complexes determined from the videos over the observational period are: 124.1 ± 6.2, 203.3 ± 5.1, 302.1 ± 4.2, and 410.8 ± 6.3 mHz. The rotational frequencies of the four sandwich complexes are shown in , and demonstrate that the rotational frequency of a rotating complex is stable over at least 60 min.
The behavior of individual sandwich complexes was found to determine the relationship between the rotational frequency and the number of attached superparamagnetic label beads. The number of superparamagnetic label beads attached to the complex was determined by visual inspection. The rotating magnetic field was then turned on, and the rotational frequency of each complex was measured. These results are shown in . (During observations, it was difficult to distinguish individual beads when more than 40 were on a solid phase sphere, so complexes with more than 40 attached beads were excluded from this analysis.) It should also be noted that a complex will rotate with as little as two attached superparamagnetic label beads, which suggests that the theoretical lower detection limit of the system could be on the order of a few analyte molecules bound to the surface, for this solid phase sphere and magnetic label bead combination.
Having established the stability of the rotation of a sandwich complex, and the relationship between rotational frequency and the number of attached superparamagnetic label beads, label-acquired magnetorotation (LAM) was then shown to be capable of measuring the concentration of biotin-coated particles in solution. Sandwich complexes with a range of biotin-coated particle concentrations were prepared as described in the experimental section, transferred into a coverslip fluidic cell, and placed in a rotating magnetic field. Eight sandwich complexes from each concentration of biotin-coated particles were chosen at random and 15 s videos of each sandwich complex were recorded. Complexes that adhered to the surface of the coverslip were not considered for analysis (the number of attached magnetic labels did not appear to be a factor in determining sandwich complex–surface adhesion). The results are shown in . The rotational frequency of the sandwich complex increases with increasing biotin-coated particle concentration over the range 1.62 × 105–9.70 × 106 biotin-coated particles/μL, and then plateaus at higher concentrations. This plateau is likely due to the saturation of the sphere by superparamagnetic beads labels. The lowest detected concentration of biotin-coated particles was 2.88 × 105 particles/μL. No formation of sandwich complexes, or rotation of the 6.7 μm spheres, was observed in control samples with no biotin-coated particles.
These results demonstrate that label-acquired magnetorotation can be used to detect the presence of biological targets. One of the challenges facing this system is the significant size distribution of beads and spheres, which accounts for the wide distributions and large standard deviations in our data ( and ). When comparing one sandwich complex to another, the uniformity of the solid phase is important. The 6.7 μm solid phase spheres had a coefficient of variability in the diameter of 5.8% as determined by fluorescent activated cell sorting [43
]. Since the rotational frequency of the sphere depends on volume, this results in up to a 17.4% variability in rotational frequency. Additionally, the superparamagnetic label beads, composed of magnetic nanoparticles embedded in a 1 μm non-magnetic bead, exhibit significant bead-to-bead variability in magnetic content. Similarly, 2.8 μm superparamagnetic beads from the same manufacturer have been reported to have a variability in magnetic responsiveness (a combination of bead magnetic moment and shape factor) on the order of 30% [44
], and observations in our laboratory suggest a similar variability for the 1 μm beads (data not shown). These high variabilities could be reflected by the data presented in . Despite the variabilities, averaging through multiple samples allows for validation of this new method.
The potential sensitivity of this method was indicated by the rotation of a sandwich complex which was observed after the attachment of just two superparamagnetic label beads. The system described here presents a number of potential advantages for diagnostic applications, and we are exploring a number of avenues that could turn this new method into a clinically useful technology. We envision that label-acquired asynchronous magnetic bead rotation will be used in future diagnostic devices. Such a system could be applied to detect a wide range of biological targets, including proteins, viruses, bacteria, and cancer cells, or any other target associateable with an affinity molecule. Currently, work is underway on label-acquired magnetorotation for the detection of antigens with antibodies, using a photodiode and a laser for monitoring rotation [15
]. Additionally, work is underway to transfer this system onto a microfluidic chip.