Subscriber access provided by READING UNIV
Article
Cellphone-Enabled Microwell-based Microbead Aggregation Assay for Portable Biomarker Detection Weiwei Cui, Meihang He, Luye Mu, Zuzeng Lin, Yanyan Wang, Wei Pang, Mark A. Reed, and Xuexin Duan ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.7b00866 • Publication Date (Web): 19 Jan 2018 Downloaded from http://pubs.acs.org on January 20, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
ACS Sensors is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 10 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
ACS Sensors
Cellphone-Enabled Microwell-based Microbead Aggregation Assay for Portable Biomarker Detection Weiwei Cui a,b)#, Meihang He a)#, Luye Mu b), Zuzeng Lin a), Yanyan Wang a), Wei Pang a), Mark Reed b), Xuexin Duan a)* a)
State Key Laboratory of Precision Measuring Technology & Instruments, College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China. b) Department of Electrical Engineering and Yale University, New Haven, Connecticut 06520, United States
KEYWORDS: microbead aggregation, microfluidics, cellphone-enabled detection, PSA detection, two-step reaction, POC. ABSTRACT: Quantitative biomarker detection methods featured with rapidity, high accuracy, and label-free are demonstrated for the development of point-of-care (POC) technologies or "beside" diagnostics. Microbead aggregation via protein-specific linkage provides an effective approach for selective capture of biomarkers from the samples, and can directly readout the presence and amount of the targets. However, sensors or microfluidic analyzers that can accurately quantify the microbead aggregation are scared. In this work, we demonstrate a microwell-based microbeads analyzing system, by which online manipulations of microbeads including trapping, arraying, and rotations can be realized, providing a series of microfluidic approaches to layout the aggregated microbeads for further convenient characterizations. Prostate specific antigen is detected using the proposed system, demonstrating the limit of detection as low as 0.125 ng/mL (3.67 pM). A two-step reaction kinetics model is proposed for the first time to explain the dynamic process of microbeads aggregation. The developed microbeads aggregation analysis system has the advantages of label-free detection, high throughput, and low cost, showing great potential for portable biomarker detection.
Since biomarkers are objectively measured and evaluated as indicators of normal biological processes, pathogenesis, or a pharmacological response to therapeutic intervention 1-3, accurate detection and quantification of biomarkers in a convenient way is a central goal of modern biotechnology. For clinical applications, sandwich immunoassays are the most widely applied assay formats for target biomarker detections. Generally, these methods require some type of labeling (enzymatic, or fluorescent, etc.) for selective and sensitive report of target analytes4-7. Specialized instruments (e.g. plate reader) and numerous washing steps are required as well. Recently, advances in quantitative biomarker detection methods featured with rapidity, high accuracy, portability, and label-free readout have enabled the concept of point-of-care (POC) technologies or “bedside” diagnostics8-13. Among them, affinity biosensors such as impedance spectroscopy14-17, potentiometric sensor18-21, surface-enhanced Raman scattering technologies22, 23 and gravimetric sensor24-27 have been developed to directly recognize and quantify the target biomarkers by immobilizing specific acceptors on the transducers, which do not require any type of labeling. Another promising label-free detection method is based on bio-functionalized micro/nanoparticles, which have been demonstrated and widely applied as molecule probes or carriers for direct capture of target protein or DNA from complex samples13, 28-30. Colorimetric method or particle size analyzer has been applied for
biomarker detection through analyzing the aggregation status of these particles31-34. Aggregations of nanoparticles are induced by the specific protein interactions (e.g. antibody-antigen) between the receptor immobilized on the particle surface and the target analyte in solution. Generally, more and larger aggregated clusters will be generated with higher biomarker concentrations. However, the accurate relationship between nanoparticle aggregations and the biomarker concentration has not been thoroughly understood because of the lack of compatible methods or tools to precisely quantify the aggregation status, including information regarding the number of the nanoparticles within each cluster. In addition to nanoparticles, aggregation of antibody functionalized microbeads for antigen detection has been recently demonstrated using an impedance sensor to count the number of the aggregated clusters35,36. Though impedance sensors can directly readout the number of clusters, it suffers problems such as easy congestion, low throughput, and limited resolution for different sized beads. Besides, the developed impedance analyzing system requires dedicated fluid delivery setup and expensive data acquisition system for fast and low noise electrical signal processing which hindered the development of such systems into portable assays. Microfluidic analyzers with the capability of processing the samples in a high throughput and well-controllable manner are attractive for microbeads characterizations. Especially, arraying microbeads
1
ACS Paragon Plus Environment
ACS Sensors 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
into a small space contributes to more efficient observation and characterization of their aggregations. In this work, a cellphone enabled microwell-based POC system is developed for biomarker detections by analyzing the aggregation status of the biomarker functionalized microbeads. The microfluidic chip is made of polydimethylsiloxane (PDMS) patterned using a re-usable silicon mold, with micro-sized features defined by standard optical lithography. Using the developed system, we demonstrated the successful detection of prostate specific antigen (PSA), a critical biomarker in early stage detection of prostate cancer using anti-PSA functionalized polystyrene (PS) beads. The system provides a dedicated tool for microbead trapping and arraying via fluidic approaches. Aggregation status, defined as the percentage of microbeads dimers, was acquired by a cellphone enabled portable imaging system. The limit of detection (LOD) of this system is demonstrated to be as low as 3.67 pM, which is beyond the requirement of clinical PSA detections. Based on the experimental results, the kinetics of microbeads aggregation is carefully studied, and a two-step reaction model is proposed to explain the aggregation process. These results demonstrate that this platform provides a
Page 2 of 10
simple, label-free, low-cost, and point-of-care system for biomarker detections.
EXPERIMENTAL SECTION Materials. Carboxyl-terminated PS beads (108/mL) with diameter of 5 μm were purchased from Sigma; Polyclonal PSA (prostate specific antigen) and anti-PSA (1 mg/mL) were purchased from Sigma-Aldrich (USA). Poly-L-lysine grafted with oligo ethylene glycol (PLL-OEG, MW = 15 kDa-30 kDa) is synthesized in our lab according to procedures described in previous publications37, 38. HEPES (N-2-hydroxyethylpiperazineN-ethane-sulphonicacid, 10 mM, pH=7) containing 0.2% v/v Tween (Sigma) as the surfactant was used as the solvent. Full serum (F2442, MFCD00132239) was purchased from Sigma. The portable microscope was purchased from Shenying Optics (SAGA002, Suzhou, China), and the cellphone can be any commercial cellphone with a camera of 12 Megapixels (more details about the cellphone enabled portable microscope system are presented in the Supporting Information, Figure. S1).
Figure 1. (a) Diagram of the microbeads aggregation process: mixing PSA into anti-PSA modified polystyrene microbeads suspension forms bead aggregations induced by the antibody-antigen interactions; and (b) image of the arrayed microbeads within microwells. (c) Statistics of the aggregated microbeads acquired by processing the photos. The scale bar in (b) is 40 μm.
Surface modifications of PS microbeads. Anti-PSA with a concentration of 8 µg/mL was applied to modify PS beads using EDC/NHS (N-(3-dimethylaminopropyl)-N’-ethylcarbodiimide hydrochloride and N-hydroxysuccinimide) activation approach39. Microbeads were washed twice with HEPES buffer (10 mM, pH=7.4), and then activated by EDC (N-3-dimethylanimopropyl-N-ethylcarbodimide) and sulfo-NHS (N-hydroxysulfosuccinimide) at a typical concentration of 2 mg/mL (EDC) and 0.5 mg/mL (NHS) in a shaker (800 rpm) at room temperature. After activation for 30 min, the microbeads were separated by centrifugation and washed twice again with HEPES. Antibodies (anti-PSA, 8 µg/mL) diluted in HEPES were then quickly added to the activated particles. After incubation at
room temperature for 40 min, the supernatant was removed after centrifugation. Ethanolamine aqueous solutions (20 mM, pH=7.4) were then added and reacted with microbeads for another 40 min to deactivate the unbound carboxyl groups on the surface, followed by twice washing with HEPES buffer. Finally, the antibody conjugated microbeads were resuspended in HEPES and stored at 4 oC. Chip design and fabrication. The MicroWell-based Microfluidic Chip (MW-MFC) consists of a micro-chamber for fluid delivery and microwell arrays on the bottom, both of which are made of PDMS. The microchamber is designed to be 30 mm in length, 5 mm in width, and 20 μm in height supported by a 4×25 pillars array to prevent channel collapse. Two input channels
ACS Paragon Plus Environment
Page 3 of 10 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
ACS Sensors
and one exit channel are connected with to the chamber, and the width of each is 600 μm. Microwell on the bottom of the chamber are 10 μm in depth and 20 μm in diameter. Silicon mold was fabricated by reactive ion etch process, and a releasing agent perfluorodecyltriethoxysilane (PFDTS) was vacuum deposited overnight and then cured in 85 oC for 30 min. Two-part Sylgard 184 was mixed with a mass ratio of 10:1 and then degassed for 30 min. The mixture was poured over the silicon mold and cured at 85 oC for 90 min, after which the cured PDMS was carefully peeled off and holes were punched to serve as the inlet and outlet ports. Each PDMS chip was cleaned with ethanol and deionized water (1:1) solution and gently dried with nitrogen, followed by treatment with O2 plasma cleaner under 120 W for 30 s. The PDMS was aligned and irreversibly bound together after 30 minutes curing under 85 oC. The inner surface of PDMS chip was incubated with the PLL-OEG solution (100 mM, dissolved in HEPES buffer, pH=7.4) for 30 min to achieve a hydrophilic coating. Principles of microbeads manipulations and quantifications. The sensing mechanism of our system is based on the counting of the number of the aggregated beads. Anti-PSA modified PS beads are mixed with different concentrations of PSA samples. After incubation at room temperature, the PS beads will aggregate together through the specific interactions between PSA and anti-PSA. In principle, when the number of the beads are designed to be in excess of the target biomarkers, dimers (two PS beads linked together as figure 1a shows) are the most likely aggregation status in the final product. 35, 36 The reacted microbeads were then processed by the microwell analyzing system to obtain the percentage of the dimers. Figure 1b presents the arrayed microbeads within the MW-MFC, which is imaged with a cellphone equipped with a portable optical microscope. The acquired images were processed with a home developed MATLAB program and the percentage of the dimer, i.e. aggregation ratio was calculated (as figure 1c shows) to represent the aggregation status by eq 1 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐷𝑖𝑚𝑒𝑟𝑠 𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 = × 100% 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐴𝑟𝑟𝑎𝑦𝑒𝑑 𝑀𝑖𝑐𝑟𝑜𝑏𝑒𝑎𝑑𝑠
(1) As figure 2c shows, the microbeads suspended within the MWMFC would be dragged by the fluidic drag force 40 𝐹𝑑 = 𝐾𝜇(𝑉 − 𝑉𝑃 )𝑅2 (𝛾/𝜈)1/2 (2) Wherein, K=81.2, R is the radius of the microbead, 𝜈 is the kinematic viscosity and 𝛾 is the fluidic shear rate induced by velocity gradient near the microbead. V and Vp represent the flow velocity and the microbead moving velocity respectively. When the flow rate is very low (below the flow rate Q1 labeled in figure 2c, which represents the case of a balance between gravity and drag force inside the microwell), most of the microbeads were deposited onto the substrate by gravity, G. While, the microbeads can be lifted from the substrate and the microwells when the flow rate is increased to be higher than Q2 (corresponding to the flow rate that induces a lift force equaling to the gravity). By tuning the flow rate (between Q1 and Q2), the micro-vortices induced by the microwells41-43 would contribute to trapping microbeads into the microwells. Finally, HEPES buffer was injected into the chip with a flow rate of 400 nL/min (referring to Q2), which is high enough to generate a shift force to release the microbeads outside the microwells and wash them away from the chamber, while the trapped beads inside the
microwells are well protected from lifting out. When increasing the flow rate up to 500 nL/min (higher than Q2), the trapped microbeads will also be released by the lift force induced by the flow rotation44, following the eq 3 𝐹𝐿 = 𝜋𝑅3 𝜌𝑓 𝜔(𝑉 − 𝑉𝑝 ) (3) Here, 𝜔 is the rotation angular velocity of microbeads. Image acquisition and microbeads detection. PSA of different concentration were respectively mixed with anti-PSA modified PS beads suspension in a 500 μL centrifugal tube, and then incubated for 30 min at room temperature. The final concentration of microbeads in the incubated mixture is 2×106 /mL. After incubation, the suspension was diluted four times with HEPES buffer. Typically, 20 µL aggregated microbeads suspension was introduced into the MW-MFC. By controlling the fluidic flow as outlined above, the suspended microbeads are well trapped and arrayed for imaging analysis. The manipulations of microbeads trapping and arraying requires 10 min, and the picture acquisition of the arrayed microbeads in the ROI takes 5 min. For all the experiments, a total population of approximately 3000 microbeads was trapped and arrayed corresponding to trap ratio of 3%. Typically, 70 images were taken to include enough number of beads. To effectively acquire the beads aggregation information from these images, a MATLAB image-processing program is developed to directly count the number of the dimers. Microbeads with diameter of 5 μm can be easily identified with Hough-transform algorithm. Furthermore, a cellphone APP has been developed, enabling the whole assay job, including the image capture, analysis and data processing all operated within a single cellphone (the source code of the APP can be downloaded at the GitHub page https://github.com/linzuzeng/Microsphere/releases, and detailed information can be referred to the Supporting Information, Figure S2-S4).
RESULTS Chip fabrication and system design. Figure 2a-b show the schematic of the MW-MFC and the fabrication process. The chamber is designed as 20 μm in height supported by micropillars. Two connecting channels are respectively used to introduce microbeads suspensions and HEPES buffer via syringe pumps. The depth of the microwell is set as 10 μm for high efficiency trapping of 5 μm microbeads in combination with the microchamber. Hydrophilic modification of the inner surface of the chip is required to reduce the nonspecific adsorption of suspended microbeads. This is achieved through coating the chips with PLL-OEG37, 38. Figure 2c presents the principles of the microbeads trap and release with MW-MFC, which forms the basis of microbeads arraying. Since the size of the particle and microwell is rather large, a cellphone camera assisted with a standard portable microscope is used to acquire the images of the arrayed microbeads by direct attached the camera to the objective lens of the microscope (figure 2d). Figure 2e presents a comparison of the MW-MFC images obtained by a professional microscope (the upper) and the cellphone (the below). The aggregation status of the micorbeads can be easily identified from the both images, proving the capability of the developed portable system for image-based microbeads analysis. It is noted that we used a portable microscope to demonstrate the portability of the system. It is also possible to use other commercial available cellphones attachment to achieve even better portability. 45, 46
ACS Paragon Plus Environment
ACS Sensors 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 4 of 10
Figure 2. (a) Schematic and (b) fabrication process of the MicroWell-based Microfluidic Chip; (c) principles of the microbeads trap and release, wherein the dotted arrow presents the integration force on the microbead; (d) set up of the cellphone-enabled image acquiring system; (e) comparison of the images taken by a professional microscope (upper) and by the cellphone (bottom). The labeled rectangle in (b) represents the region of interest (ROI) which is located at the center of the chip. Images of the particles were taken within the ROI to avoid the errors induced by the higher trapping efficiency near the entrance, side wall, and exit of the chip.
The arrayed microbeads within the MW-MFC are presented in figure 2e. Generally, there are four cases of the trapped microbeads within one microwell as shown in figure 3a: (1) no microbeads; (2) single; (3) dimer; (4) two separated microbeads. There exists one case that two microbeads may physically sink together into one microwell and contact each other without the real linkage through the antigens which would form a false dimer and hinder the detection accuracy. To solve this issue, rotation or swing of the trapped microbeads is introduced by changing the flow rate which could stretch the physically linked beads within the microwells. The advantage of using fluidic method is not only due to the capability to move microbeads into and out of the microwells by tuning the flow rate in real time, but the fluidic manipulation helps to reduce the false dimers. As Figure 3b shows, the trapped microbeads rotate or swing under the flow forces. The rotating motions of the microbead will divide the false dimers into two single beads as Figure 3c shows. In addition, ratio of trapped microbeads within the MW-MFC, µ (defined as the ratio of number of trapped microbeads to the number of microwells) is an important factor. The probability (P) of trapped microbeads number (x) within one microwell obeys to the Poisson distribution47 expressed as eq 4 𝑃(𝑋 = 𝑥) =
𝜇𝑥 𝑥!
𝑒 −𝜇 (4)
When 𝜇 = 0.03, the probability of false dimer in a single well is 0.044%. To reduce the false aggregated microbeads, the value of 𝜇 is kept below 0.03 in the experiments.
Figure 3. (a): four cases of the trapped microbeads within one microwell; (b) local rotation of the microbeads; and (c): the principle of rotation to identify the false dimer and the imaging algorithm to distinguish and count the single bead and dimers arrayed within the MW-MFC system. The diameter of the microwells in the (a)-(c) are all 20 μm.
ACS Paragon Plus Environment
Page 5 of 10 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
ACS Sensors
PSA detection. Figure 4a presents the size distribution of the applied microbeads with average diameter of 5.1 μm. The commercial counter instrument (Beckman Coulter Multisizer 3, USA) calculates the equivalent diameter of the counted particle by assuming it with spherical shape by fitting the electrical signal. To test the variation of the dimer number, PSA with concentration of 12.5 ng/mL, 0.125 ng/mL, and control group solution were respectively introduced into the anti-PSA modified microbeads suspensions, and incubated for 30 min. Figure 4b shows the microbeads size distribution changes because of the microbeads aggregation. It is easy to count the bead number, but the size is difficult to precisely distinguish between
aggregations and single beads via the diameter distribution curve. This is due to low-efficient of microbead aggregations via protein specific interactions. Moreover, the equivalent size of a dimer is comparable with single ones. Considering the wide distribution range of the single bead size shown in Figure 4a, the diameter distribution changes will be difficult to evaluate. Besides, the instrument is expensive and sample-consumed. While, the developed MW-MFC system can directly recognize the single and aggregated beads via microfluidic chip-assisted image methods, enabling an accurate description of the microbeads size distribution.
Figure 4. (a) Microbeads size distribution, and (b) microbeads aggregations measured by a commercial counter. Experimental results of PSA detection using MW-MFC: (c) negative corrective relationship between dimer percentage and PSA concentration from 3.67 pM to 7.35 nM, meanwhile the concerned concentration in diagnostic application is in the range from 30 pM to 300 pM; (d) response curve of PSA detection using microbeads aggregation method.
To demonstrate the capability of using microbeads aggregation for protein detections, PSA of different concentration (250, 125, 12.5, 1.25, 0.125 ng/mL, corresponding to 7.35 nM, 3.67 nM, 0.367 nM, 0.0367 nM, and 3.67 pM) were respectively detected using the developed system. Figure 4c presents the experimental results of PSA detection, showing a negative correlation between dimer percentage and PSA concentrations. The decrease of dimer percentage with increased biomarker concentration can be explained by the fact that the high concentrations of PSA will block the anti-PSA sites on the PS beads, thus preventing particle aggregations. Another evidence is that the
dimer percentage even dropped to a value close to the negative control for the highest concentration used in the experiment. It means that high concentrations of protein would block the particle aggregation process and increases the ratio of individual microbeads. As lower PSA concentration leads to more aggregations in figure 4c, it is possible to reduce the LOD of PSA detection. To further study the LOD of this method, PSA with concentration of 367 fM and 36.7 fM were respectively tested following the same process. The results are plotted in figure 4d, which shows a non-monotonous response curve of the relationship between dimer percentage and PSA concentration. The
ACS Paragon Plus Environment
ACS Sensors 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
result indicates that the microbeads aggregation system can achieve a rather low LOD. In practical applications, the clinical concerned concentration of PSA is about 10 ng/mL (corresponding to 0.3 nM)48, 49, which is shown as the shaded range in figure 4c. For real diagnosis applications, the target sample and a diluted solution of the target sample can both be measured, and the difference of aggregation ratio between the two experimental groups can be used to determine the relevant concentration region of the response curve. In order to test the practicality of this method for clinical applications, experiments in serum has also been performed to detect PSA with concentrations of 0, 2, 5, 25, and 100 ng/mL (corresponding to 0, 0.0588 nM, 0.147 nM, 0.735 nM, and 2.94 nM). The experiments were conducted following the detection procedure as buffer samples. For each case, PSA serum solution was added into and uniformly mixed with the anti-PSA functionalized microbeads suspension. Figure 5 presents the results of the serum test, which reveals a relationship consistent with that in buffer solution as shown in figure 4. The microbeads aggregation due to the beads interactions and non-specific serum protein adsorption is calculated to be 4.41%, which is a little higher than that in buffer solutions. The linear relationship between dimer percentage and PSA concentration demonstrates the great potential of the microbeads aggregation strategy for biomarker quantifications in clinical diagnostics.
Page 6 of 10
𝐾𝑜𝑛 𝐴1 + 𝑅 ⇌ (𝐴1 𝑅) (5) 𝐾𝑜𝑓𝑓 Wherein, A1 and R are molecule capture sites and target biomarker respectively. In the process I, anti-PSA on the microbeads surface works as the capture molecule (A1) to interact with PSA (R) in the bulk solution. Kon and Koff are the association and dissociation rate of PSA and anti-PSA interaction, and they define the equilibrium dissociation constant (KD). 𝐾𝐷 =
𝐾𝑜𝑛 𝐾𝑜𝑓𝑓
=
𝑁𝑠 𝑟 𝐷
(6)
Wherein, NS is the minimum number of molecules to be captured for detection, D is the diffusion coefficient of the molecules, and r is the radius of micro/nanoscale matters. For a simplified discussion, the molecule and microbeads are all considered as spheres in the following analysis. The number of captured PSA (N) by anti-PSA modified microbeads50,51 can be calculated with eq 7 𝑑𝑁 𝑑𝑡
= 𝐾𝑜𝑛 𝜌0 (𝑁0 − 𝑁) − 𝐾𝑜𝑓𝑓 𝑁 (7)
Wherein, N0 is the real density of the receptor molecules (antiPSA on the microbead surface), and ρ0 is the bulk concentration of analyte molecule (PSA). The diffusion of analyte molecules obeys the following eq 8 𝑁
𝑑𝜌 𝑑𝑡
= 𝐷𝛻 2 𝜌 (8)
As figure 6b shows, PSA captured on a microbead can react with residual anti-PSAs immobilized on an adjacent microbead to generate a dimer (process II). For microbeads aggregation, the interaction of PSA coated microbeads (A1R) and anti-PSA modified microbeads (A1) can be expressed as eq 9 𝐾𝑜𝑛 ′ (𝐴1 𝑅) + 𝐴1 ⇌ (𝐴1 2 𝑅) (9) 𝐾𝑜𝑓𝑓 ′
Figure 5. Experimental results of PSA serum detections. PSA serum with concentrations in the region that is relevant in the clinical diagnostics are detected, showing a negative corrective relationship.
Wherein, A1R is the PSA coated microbeads formed in the process I, and A12R is the aggregated microbeads formed in the process II. (A1R) and (A12R) represent the number of anti-PSA modified microbeads and PSA coated microbeads, respectively. The aggregation ratio (β) of the microbeads in the above process can be described with Heidelberger–Kendall (H–K) model52.
DISCUSSION
𝛽 = 5.2𝑏ℎ ∙ 4𝑆ℎ ∙ (𝐴1 𝑅)(𝐴1 )𝑓 3/2 (10)
To understand the special behaviors of the formation of the dimers, the contact probability and the aggregation kinetics of the microbeads were further studied. For microbeads, aggregation is less efficient compared with nanoparticles because of their different diffusion rate and size. As Brownian diffusion number of micro/nanoparticles scales with 1/R2, the diffusion of microbeads is much slower compared with nanoparticles 44, which prevents the aggregations of the microbeads. As figure 6a shows, PSA in the solution is primarily binding with anti-PSA and adsorbed onto the surface of the microbeads at the original period50 (this reaction step is named as process I) which follows eq 5
where bh is the steric hindrance coefficient for available binding sites on one PS bead bound to another bead (0
