Zeptomole Detection Scheme Based on Levitation Coordinate

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Zeptomole Detection Scheme Based on Levitation Coordinate Measurements of a Single Microparticle in a Coupled Acoustic-Gravitational Field Akihisa Miayagawa, Makoto Harada, and Tetsuo Okada Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b04752 • Publication Date (Web): 12 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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Analytical Chemistry

Zeptomole Detection Scheme Based on Levitation Coordinate Measurements of a Single Microparticle in a Coupled Acoustic-Gravitational Field

Akihisa Miyagawa, Makoto Harada, and Tetsuo Okada* Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan

Phone and fax: +81-3-5734-2612 Email: [email protected]

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Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We present a novel analytical principle in which an analyte (according to its concentration) induces a change in the density of a microparticle, which is measured as a vertical coordinate in a coupled acoustic-gravitational (CAG) field. The density change is caused by the binding of gold nanoparticles (AuNPs) on a polystyrene (PS) microparticle through avidin-biotin association. The density of a 10-µm PS particle increases by 2 % when 500 100-nm AuNPs are bound to the PS. The CAG can detect this density change as a 5–10-µm shift of the levitation coordinate of the PS. This approach, which allows us to detect 700 AuNPs bound to a PS particle, is utilized to detect biotin in solution. Biotin is detectable at a picomolar level. The reaction kinetics plays a significant role in the entire process. The kinetic aspects are also quantitatively discussed based on the levitation behavior of the PS particles in the CAG field.


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Introduction The progress of analytical chemistry has allowed us to quantify trace amounts of analytes in a wide variety of samples and has opened new eras in a number of scientific disciplines, including environmental, life, medical, pharmaceutical, and forensic sciences.1-6 Modern commercial apparatus, such as inductively coupled plasma-mass spectrometry and liquid chromatography-mass spectrometry, is routinely used in the laboratories of these fields.7-10 These methods detect elements or molecules in biological and environmental samples at a trace level (e.g., nanomolar concentrations or lower).9-11 Electrophoresis after a polynuclease chain reaction is a powerful tool, not only in medical and life science but also in food and forensic research.12-13 Recent developments of microchip-based technologies allow us to manipulate a single biological cell and to analyze its contents.14-15 The spatiotemporal analysis of a cell is a current interest in related disciplines. Single cell analyses are now feasible for DNA, which facilitate an understanding of cell-to-cell variations.6 Thus, lowering the detection (or quantification) limit is a crucial challenge to achieve scientific progress and to facilitate innovation or breakthroughs. The entire analytical process should be carefully designed to establish robust trace quantification because current analytical instruments have intrinsic sensitivity and



selectivity limitations. Therefore, reproducible and/or selective enrichments of analytes are often required in practical analyses. Solid-phase extraction, for example, is an indispensable method to analyze environmental and bio-fluid samples.16-19 New methods and materials are also studied to enhance the efficiency and selectivity of pretreatment processes.17, 20-21 Developments in particle preparation technologies have significantly impacted the design of analytical systems. Nanoparticle aggregation induces physicochemical changes in their spectroscopic nature, which are detectable using dark-field microscopy, spectroscopy, or the naked eye.22-25 Surface-enhanced Raman scattering (SERS) is particularly attractive in nanoparticle-based measurements because of its high selectivity and applicability to various target compounds. Chan et al.26 reported highly sensitive SERS detection of prostate-specific antigen. In this scheme, the antigen was trapped by a capture antibody anchored on a glass substrate. The antigen then interacted with the Raman probe (4-chlorobenzenthiol) to form an immune complex, which was detected by area-scanning SERS. Surface-enhanced resonance Raman scattering detection of cancer cells was also reported using graphene-encoded Ag nanoshell particles.27 Particles are often involved in chemical amplification analyses for enhancing the


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sensitivity because the particles allow versatile schematic designs. Enzyme-linked immunosorbent assay (ELISA) is a widely employed bioassay in which an enzymatic reaction amplifies the formation of colored or fluorescent products and eventually provides a high sensitivity in the spectrometric detection of proteins.28 Use of nanoparticles in ELISA allows introduction of more enzymes to the system, providing a high sensitivity.29 Zhou et al.30 proposed a novel strategy for detecting DNA using liposomes containing quantum dots. The reporter DNA molecules bound to the liposomes formed hybrids with the capture DNA molecules anchored on magnetic microspheres, but only in the presence of target DNA molecules. After collecting the magnetic beads, the liposome disruption produced intense fluorescence from the released quantum dots. When particles are used for designing analytical schemes, they should be separated or trapped at an appropriate location for subsequent measurements. In the study by Zhou et al.,30 a magnetic field was utilized to trap and collect the magnetic beads. Other physical forces, such as electric, dielectric, and acoustic forces, have been used to separate and manipulate particles.31-38 The particle behavior in a physical field is determined by the physical properties of the particle, such as size, surface charge, magnetic susceptibility, and density. An appropriate field should be chosen so that the



particle nature of interest is well differentiated therein. In the manipulation and sorting of biological cells, the effectiveness of physical fields has been well demonstrated by their integrations on microchip devices.34-38 Because a microparticle (MP) generally has a very small volume, reactions on MPs can induce a substantial change in its physical and chemical properties. If we can capture these changes from the behavior of MPs in a physical field, trace analysis should be feasible. Additionally, information on the reaction dynamics and thermodynamics can be deduced from the particle behavior in a physical field. Suwa and Watarai studied the magnetophoresis of various particles39-41 and evaluated the interfacial adsorption of laurate complexes with dysprosium ions on fluorotoluene microdroplets from their magnetophoretic velocities.40 The surface complexation between laurate and the paramagnetic dysprosium ion largely modifies the magnetic property of the microdroplet and allows detection of the reaction that occurs on the droplet. We evaluated the kinetic process of ion-exchange reactions in a single ion-exchange resin bead with an acoustic-gravitational field.42-43 The ion intrusion into the resin bead changed its acoustic properties and eventually affected its behavior in the field. Only a few reports have successfully gained quantitative molecular information from particle behaviors in a physical field. Thus, the combination of particles and a


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physical field has a high potential in designing trace analytical methods. We studied a coupled acoustic-gravitational (CAG) field for particle separation.44-46 One of the key features of this field is that it resolves the density and compressibility of particles but does not recognize their sizes.47 Therefore, a reaction that affects the acoustic properties of an MP can be detected by the CAG field; we do not need to consider size changes during the reaction process. In the present work, changes in the density of an MP are induced by binding with gold nanoparticles (AuNPs) and detected in the CAG field. A novel principle is proposed for trace analyses.

Experimental Instruments Sinusoidal signals were generated with a function generator (model WF1946, NF Co.). The signals were amplified by a bipolar high-speed amplifier (model 4015, NF Co.) and drove a transducer (2 cm × 2 cm lead zirconate titanate, resonance frequency of 500 kHz, Fuji Ceramics). The particle behavior was observed using a charge-coupled device camera (model CS220, Olympus) and a zoom lens (maximum magnification of 24×). The levitation positions of the particle were determined using digital images. The



size of the pixels on the images was calibrated by vertically moving a z-stage on which the transducer was installed. A fused silica cell (30 mm in length, 8 mm in width, and 12.62 mm in height) with a rectangular through-channel (3.0 mm in width and 1.5 mm in height) was pasted on the transducer using nail enamel. The cell wall thickness (5.56 mm) and the channel height (1.50 mm) were adjusted so that resonance for the 500-kHz ultrasound occurred in silica glass and water. The node of the standing wave was formed at the half height of the water-filled channel. Because the resonance frequency depends on the instrumental setup and the experimental conditions, the frequency was optimized to ensure stable levitation of particles. The levitation behavior of a single MP was observed. Although the acoustic wave was vertically generated, the particles were subjected to horizontal and vertical acoustic forces.46 Several particles were introduced into the cell to determine the horizontal equilibrium position, at which all of the horizontal forces were balanced. This position was identified at the axial center of the cell. After the horizontal equilibrium position was determined, the particles were removed from the cell. A diluted particle suspension was then introduced into the cell so that a single particle was entrapped at the horizontal equilibrium position. The levitation behavior of the particle was then observed by


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changing the voltage supplied to the transducer. The levitation coordinate is defined as the average of the upper and lower edge position of a single particle. Preparation of AuNP-bound polystyrene particles Biotin-bonded AuNPs (B-AuNPs, 100 nm in diameter) were purchased from Cytodiagnostics (Burlington, Canada). Avidin-bonded polystyrene (PS) MPs (Av-PSs, 10 µm in diameter) were purchased from Micromod (Rostock, Germany). Phosphate buffered saline (PBS) and (+)-biotin were obtained from Wako Pure Chemical Industries (Osaka, Japan). Biotin-4-fluorecein was obtained from Sigma-Aldrich (St. Louis, USA). The size of the Av-PS was estimated to be 10.0 ± 0.1 µm using a microscope (Figure S1). The number of avidin molecules on the surface of a single PS particle ( navPS ) was 1.09 × 106, as determined by fluorometry using the reaction of Av-PSs with biotin-4-fluorescein. The concentration of the Av-PSs in a stock solution was determined by counting the number of the particles in 1 µL of the solution under a microscope. The concentration of B-AuNPs was 1.76 × 1011 mL-1 in an original stock solution using the spectrometric method developed by Fernig et al.48 Various amounts of B-AuNP were added to 20 µL of Av-PS aqueous suspensions (5.50 × 107 mL-1). The mixture was diluted to 1 mL with PBS and shaken for 4 h. The



avidin-biotin reaction produces strong binding between the B-AuNPs and the surface of the PS particles; the dissociation constant of avidin-biotin binding is approximately 10-15.49 This binding rarely dissociated, even when the sample was diluted to evaluate the levitation behavior. The number of B-AuNPs bound to each Av-PS was controlled by changing the number ratio of B-AuNPs to PS particles (rAuNP/PS) in a reaction solution.

Quantification of dissolved biotin Various amounts of biotin were added to 2-µL fractions of Av-PSs (5.50 × 107 mL-1). The mixtures were diluted to 1 mL with PBS and shaken for 4 h. Then, a 2.5 µL aliquot of B-AuNPs (rAuNP/PS = 4000) was added to the biotin-bound Av-PSs and shaken for 4 h. The levitation of this particle in the CAG field was studied using the procedure described above.

Results and Discussion Levitation of a single Av-PS in the CAG field and its density modification by B-AuNP binding The levitation coordinate of a particle, z, in a CAG field is represented by42, 46-47, 50


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z=

A=

 (ρ − ρ ′)gλ  λ sin −1   4π  AEac 2π 

(1)

5ρ ′ − 2 ρ γ ′ − 2ρ ′ + ρ γ

(2)

where λ is the ultrasound wavelength, Eac is the average ultrasound energy density, g is the gravitational acceleration, ρ and γ are the density and compressibility of the medium (in this case, water), respectively, and the asterisk represents the corresponding properties of the particle. Eq. (1) suggests that z is independent of the particle size but is a function of the properties of the particle, i.e., density and compressibility. Thus, we can resolve these properties of a particle according to the different levitation coordinates in the CAG field. Eq. (1) indicates that the levitation position of a particle in the CAG field is lowered (z becomes more negative) with an increase in its density. In this work, the density increase was induced by binding B-AuNPs to Av-PS, as schematically shown in Figure 1. In our preliminary work,50 the density of epoxide resin particles was modified by AuNP binding, and the levitation behavior of the resulting resin particles was studied in the CAG field. We measured the levitation coordinate of an aggregate of some tens of MPs. Experiments using the particle aggregate show some intrinsic disadvantages: the levitation coordinate of a particle aggregate cannot be precisely determined and the interparticle acoustic forces affect the particle levitation behavior, which cannot be 11 ACS Paragon Plus Environment


described by Eq. (1).51 These problems can be avoided by evaluating the behavior of a single particle. A single particle is trapped in the CAG field by introducing a dilute particle suspension in the cell. Figure S2 shows a change in the density of a 10-µm PS particle with the number of 100-nm AuNPs bound to it. The density linearly increases with increasing number of AuNPs bound to the PS particle. The binding of 1000 AuNPs, for example, induces nearly a 2% increase in the density of the PS particle. This increase in the density lowers the levitation position in the CAG field. Eq. (1) can be used to estimate the levitation coordinate change by this density increase, as shown in Figure S3. Although the compressibility change caused by AuNP-binding was considered in this calculation, its effect is so small that ∆z is not affected by the small compressibility change. Thus, the binding of 1000 100-nm AuNPs induces more than a 10-µm shift of the levitation coordinate of a PS particle. Figure 2 shows the calculated relationship between the radius of a PS particle and the density of the particle that binds 500 100-nm AuNPs. The AuNP binding induces a larger density increase for smaller PS particles, suggesting that using smaller particles allows a higher sensitivity because a larger levitation coordinate shift is expected from the binding of fewer AuNPs. However, commercially available monodispersed PS


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particles have size distributions of a few percent. Figure 2 suggests that the uncertainty in the density of AuNP-bound PSs caused by their size distribution is larger for smaller PS particles; i.e., from Figure 2, dρ/dr = 0.73 g cm-3 µm-1 and 0.04 g cm-3 µm-1 at r = 2.5 and 5 µm, respectively, where r is the particle radius. A size deviation of 1 %, for example, causes density deviations of 7.3 × 10-3 g cm-1 (0.4%) and 4 × 10-4 g cm-3 (0.034 %) for r = 2.5 and 5 µm, respectively, when 500 AuNPs are bound to a PS particle. On the other hand, the acoustic force is proportional to the volume of a particle. A relatively longer time is required before it moves to the equilibrium levitation position because a smaller force can be applied on a smaller particle. Thus, we used a 10-µm-diameter PS particle in this work. This particle rapidly responds to a change in the acoustic force, and its density uncertainty, which is based on the size distribution, is negligible. PS particles of different densities were prepared by treating Av-PSs with various numbers of B-AuNPs (rAuNP/PS = 800-4000). The equilibration of the interparticle reaction was assessed by measuring the levitation coordinate of the AuNP-bound PS (AuNP-PS) prepared by changing the reaction time. Figure 3 shows the effect of the reaction time on ∆z of AuNP-PS (rAuNP/PS = 4000); ∆z represents the difference in z between untreated Av-PS and AuNP-PS. ∆z becomes constant within 2-3 h of the start



of the reaction. Therefore, a constant reaction time (4 h) was used for all experiments. The Stokes-Einstein equation predicts that the diffusion coefficients of Av-PS and AuNPs are 5 × 10-14 m2 s-2 and 5 × 10-12 m2 s-2, respectively, which are much lower than the typical values for molecules (10-10 m2 s-2). Small diffusion coefficients suggest that the interparticle reaction takes a longer time for equilibration than molecular-based reactions. The red curve in Figure 3 predicts the kinetics between Av-PS and AuNPs by assuming a second-order reaction with reaction rate constants of k1 = 4.0 ×105 M-1 s-1 and k-1 = 1.0 ×10-4 s-1. The detailed derivation of the kinetic equations is given in the Supporting Information. The validity of these values is discussed later. Figure 4A compares photos of single AuNP-PSs (rAuNP/PS = 0, 2400, and 4000) that are levitated in the CAG field with a constant-strength acoustic force. A particle binding more AuNPs is levitated at lower positions; i.e., z becomes more negative with increasing rAuNP/PS. Figure 4B shows the dependence of z for single AuNP-PSs (rAuNP/PS = 0-4000) on the voltage supplied to the transducer (V); V2 is proportional to Eac. As the ultrasound radiation force decreases, z becomes negative. If the ultrasound radiation force becomes smaller than a threshold voltage, a particle is no longer levitated and settles to the bottom of the cell. As rAuNP/PS increases, the value of z at a given V decreases because of an increase in the density of the PS particle. The detection limit is


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700 AuNPs per PS. Thus, we can detect the formation of 700 avidin-biotin bonds on a single PS particle. Figure 5 shows the relationship between ∆z (z between untreated Av-PS and AuNP-PS; measured at V = 3.3 V) and rAuNP/PS. ∆z is proportional to rAuNP/PS when rAuNP/PS = 0–5000, but becomes nearly constant for further increases in rAuNP/PS, suggesting that the interparticle reaction no longer proceeds when rAuNP/PS exceeds 5000. For rAuNP/PS = 5000, the surface coverage of the PS particle is no more than 12.5% and space remains to accommodate AuNPs. Additionally, only 0.4% of the avidin molecules on the PS surface participate in biotin binding. If one AuNP (its largest cross section is 7.9 × 103 nm2) is bound to an avidin site, more than 108 avidin molecules that are anchored near the AuNP-bound avidin cannot participate in additional binding with B-AuNPs, as schematically illustrated in Figure S4. This explains the low reaction ratio of avidin molecules on the PS surface (0.4 %).

Quantification of dissolved biotin The present method is directly applicable to determine the inhibitors for the biotin-avidin reaction that mediates the binding between Av-PS and B-AuNPs. As the simplest case, the quantification of biotin in solution was examined. Biotin is an



important vitamin because it is involved in significant metabolic reactions and biochemical processes. Biotin deficiency causes biochemical disorders in animals, such as reduced carboxylase activity, inhibition of protein and RNA synthesis, and reduced antibody production.52 Thus, the sensitive and rapid determination of biotin has been studied because biotin significantly affects human health. Most of the developed methods rely on liquid chromatography53-56 or enzymatic reactions.57-59 The present approach provides a novel principle for biotin quantification. The principle for biotin quantification is schematically illustrated in Figure 6. The Av-PSs were first treated with a biotin solution. The binding sites on avidin molecules on the PSs are partly occupied by biotin molecules. Then, the biotin-bound Av-PSs reacted with B-AuNPs. Because a part of the binding-sites of avidin molecules on the MP have already been blocked by biotin molecules, the number of B-AuNPs, which can be bound on the Av-PSs, decrease as a function of the biotin concentration used for the first treatment of Av-PS. Figure 7 shows the relationship between ∆z and the number of biotin molecules used for treating an Av-PS (rB/PS). The biotin-treated Av-PS reacted with B-AuNPs (rAuNP/PS = 4000) for a reaction time (tPS-AuNP) of 2 or 4 h; the results obtained with varying times are compared. For small rB/PS, ∆z is constant, suggesting that biotin


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binding to the Av-PS does not interfere with the subsequent reaction with B-AuNPs. The inhibition of B-AuNP binding occurs when rB/PS increases to 1 × 106 for tPS-AuNP = 2 h and 2 × 106 for tPS-AuNP = 4 h, and B-AuNP binding is completely inhibited when rB/PS reaches 4.3 × 106 irrespective of tPS-AuNP. As noted above, navPS is 1.09 × 106. Because PS avidin is a tetrameric protein, n bind = 4nav = 4.36 × 106 on a single PS particle. The

value of rB/PS (4.3 × 106), at which the binding of B-AuNP on Av-PSs is completely inhibited, agrees with the total number of binding sites for avidin molecules in the system. The relationship between ∆z and rB/PS (Figure 7) is interpreted by considering the reaction kinetics. The curve in this figure represents the calculation for tPS-AuNP = 4 h using the reaction rate constants for binding between Av-PS and Au-NPs, i.e., k1 = 4.0 × 105 M-1 s-1 and k-1 = 1.0 × 10-4 s-1; these values are the same as those shown in Figure 4. We assume that the reaction between Av-PS and biotin proceeds to completion, as justified by the reaction rate analysis shown later. The experimental results can be explained by the reaction rate constants described above. Thus, the dependence of ∆z on rB/PS in Figure 7 is of kinetic origin rather than thermodynamic origin. Plots enlarged in the range of rB/PS = 1.5–4.0 × 106 are shown in the inset. We can see linear relationships between ∆z and rB/PS in this range for both tPS-AuNP = 2 and 4 h, suggesting that the



present principle can be utilized to quantify biotin. Also, this result indicates that we can adjust the linear range of the calibration graph by changing tPS-AuNP. When 3σ is taken as the detection limit, 4 × 106 biotin molecules can be detected per PS for tPS-AuNP = 4 h. The concentration-based detection limit under this condition is some tens of picomolar. The reaction between Av-PSs and biotin was performed in diluted solutions with a constant rB/PS = 4.3 × 106 to check the effect of the reaction kinetics between Av-PSs and biotin on the entire analytical procedure of biotin. After the treatment of Av-PSs with biotin in diluted solutions, the reaction mixtures were treated with B-AuNPs (rAuNP/PS = 4000); then, the levitation coordinate was measured. The results are summarized in Figure 8, which shows a relationship between ∆z and the biotin concentration (cB). The biotin binding to the Av-PS becomes incomplete with decreasing cB. The rate constants for the reaction between Av-PSs and biotin were estimated by curve-fitting, as shown in Figure 8; k1 = 2.0 × 108 M-1 s-1 and k-1 = 1.0 × 10-4 s-1. The association constant is thus calculated as K=k1/k-1 = 2. 0 × 1012 for the reaction between Av-PSs and biotin. These values indicate that the reaction between Av-PS and biotin is almost completed under the conditions shown in Figure 7. The association constant is three orders of magnitude smaller than the corresponding value between avidin and biotin in solution. This difference occurs because the avidin


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molecules are anchored on the PS molecule, which lowers the diffusion coefficient of avidin. In a diffusion-controlled reaction, the rate constant is proportional to the diffusion constants of the reactants. Because the size of an avidin molecule is four orders of magnitude smaller than that of a 10-µm PS particle, this difference in K is reasonable. Similarly, K is estimated as 4. 0 × 109 for the reaction between Av-PS and B-AuNP. This is also interpreted by the reduced diffusion of biotin by anchoring on 100-nm AuNPs.

Conclusion We presented an interparticle reaction that can change the density of a MP; the density shift of the MP can be precisely determined using the CAG field. Additionally, the reaction kinetics can be deduced from experimental data. With a single MP, we can detect zeptomole bonding and molecules by appropriately designing the reaction and detection systems. This approach is versatile, and various analytes can be determined by anchoring appropriate capture or host molecules on the particles. The present instrument allows us to detect the binding of several hundred 100-nm AuNPs using a 10-µm PS particle. One feasible way to enhance the detectability in the present approach is to use smaller MPs,



which induce a larger density shift when binding with the AuNPs. However, because the acoustic radiation force is a function of the volume of a particle, the force experienced by a particle becomes weaker as its size decreases. A higher ultrasound frequency can compensate this to some extent. Thus, smaller detection limits can be attained by further optimizing the entire system.

Supporting Information Size distribution of PS particles (Figure S1), relation between the density of a PS particle and the number of AuNPs bound to the PS (Figure S2), relation between the calculated levitation coordinate and the number of AuNPs bound to the PS (Figure S), schematic explanation of AuNP binding on the PS surface (Figure S4), and the derivation of kinetic equations.

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Figure captions Figure 1 Schematic representation of the reaction between Av-PS and B-AuNPs in the CAG field. The AuNP-bound PS has a higher density than bare PS; thus, the levitation coordinate (z) becomes negative.

Figure 2 Relationship between the radius of a PS particle (r) and the density (ρ) when 500 100-nm AuNPs are bound on the PS particle.

Figure 3 Reaction time dependence of the levitation coordinate shift (∆z) for an Av-PS particle when treated with B-AuNPs at rAuNP/PS = 4000. The red curve represents the results of curve-fitting with reaction rate constants k1 = 4.0 × 104 M-1s-1 and k-1 = 1.0 ×10-5 s-1.

Figure 4 (A) Images of a PS and AuNP-bound PS levitated in the CAG field. (B) Dependence of the levitation coordinate (z) on the voltage (V). Symbols (top to bottom): rAuNP/PS = 0, 800, 1600, 2400, 3200, and 4000.

Figure 5 Relationship between the number of AuNPs per PS (rAuNP/PS) and the levitation


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coordinate (∆z). Error bars represent the standard deviations based on five measurements for each point.

Figure 6 Schematic representation of the quantification of biotin.

Figure 7 Relationship between the levitation coordinate (∆z) and the number of biotin molecules per PS particle (rB/PS) for the reaction time for Av-PS/B-AuNP reaction (tPS-AuNP) = 2 h (red) and 4 h (black). Error bars represent the standard deviations based on five measurements. The black curve shows the result of curve-fitting for tPS-AuNP = 4 h with the same rate constants for the reaction between Av-PS and B-AuNPs as those indicated in Figure 4. The reaction between Av-PS and biotin was assumed to proceed to completion. The inset shows an enlargement of the main plot. Other conditions are given in the text.

Figure 8 Effect of the concentrations of Au-PS and biotin on the levitation coordinate (∆z) after the reaction with B-AuNPs. Error bars represent the standard deviations based on five measurements. rB/PS and rAuNP/PS were kept constant at 4.3 × 106 and 4000, respectively. The reaction rate constants for the Av-PS reaction with



biotin were assumed (green: k1 = 2.00 × 107 M-1 s-1 and k-1 = 1.00 × 10-4 s-1, blue: k1 = 4.00 × 105 M-1 s-1 and k-1 = 1.00 × 10-4 s-1, red: k1 = 2.00 × 108 M-1 s-1 and k-1 = 1.00 × 10-4 s-1.


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Fig. 1



2 1.8

ρ / g cm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.6 1.4 1.2 1

2

4

6

8

10

r / µm

Fig. 2


12

14

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70 60 50

∆z / µm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40 30 20 10 0

0

1

2

3

4

t/h

Fig. 3


5

6

7


A

B

Fig. 4


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Fig. 5



Fig. 6


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Fig. 7



80

60

∆z / µm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 37

40

20

0 0

100

200

300

400

CB / pM

Fig. 8


500

600

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TOC


Zeptomole Detection Scheme Based on Levitation Coordinate

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