sensors Article

Rapid ELISA Using a Film-Stack Reaction Field with Micropillar Arrays Yuma Suzuki 1 , Kazuhiro Morioka 2 , Soichiro Ohata 1 , Tetsuhide Shimizu 1 Hizuru Nakajima 3 , Katsumi Uchiyama 3 and Ming Yang 1, * 1

2 3

*

,

Graduate School of System Design, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan; [email protected] (Y.S.); [email protected] (S.O.); [email protected] (T.S.) Department of Biomedical Analysis, School of Pharmacy, Tokyo University of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan; [email protected] Graduate School of Urban Environmental Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan; [email protected] (H.N.); [email protected] (K.U.) Correspondence: [email protected]; Tel.: +81-42-585-8440

Received: 20 May 2017; Accepted: 9 July 2017; Published: 11 July 2017

Abstract: A film-stack reaction field with a micropillar array using a motor stirrer was developed for the high sensitivity and rapid enzyme-linked immunosorbent assay (ELISA) reaction. The effects of the incubation time of a protein (30 s, 5 min, and 10 min) on the fluorescence intensity in ELISAs were investigated using a reaction field with different micropillar array dimensions (5-µm, 10-µm and 50-µm gaps between the micropillars). The difference in fluorescence intensity between the well with the reaction field of 50-µm gap for the incubation time of 30 s and the well without the reaction field with for incubation time of 10 min was 6%. The trend of the fluorescence intensity in the gap between the micro pillars in the film-stack reaction field was different between the short incubation time and the long incubation time. The theoretical analysis of the physical parameters related with the biomolecule transport indicated that the reaction efficiency defined in this study was the dominant factor determining the fluorescence intensity for the short incubation time, whereas the volumetric rate of the circulating flow through the space between films and the specific surface area were the dominant factors for the long incubation time. Keywords: ELISA; microbioanalysis device; theoretical equation

film-stack reaction field;

circulating flow;

1. Introduction Immunoassays, such as enzyme-linked immunosorbent assay (ELISA), are the gold-standard methods for the detection of biomolecules such as proteins and DNA fragments in immunological reactions with applications in numerous disciplines, including the diagnosis of infectious diseases [1–3]. ELISAs are usually performed in 96-well microtiter plates, which provide advantages such as high specificity, sensitivity, and the ability to carry out multiple assays in a parallel manner [1–3]. However, it takes a long time to complete the assays due to the large diffusion distance of the target biomolecules, the need for large volumes of reagents, and the lack of portability [4–6]. Currently, microbioanalysis devices (MBDs), such as micro-total analysis systems and lab-on-a-chip, are being developed to achieve the rapid detection of biomolecules thanks to the development of suitable microfabrication techniques [7–10]. Miniaturizing the biomolecule- incubation region in MBDs, called the reaction field, results in a short diffusion distance of biomolecules and a high specific surface area, which is the ratio of surface area to volume. Many researchers have developed microstructured reaction fields in MBDs to increase the surface area of a reaction field for Sensors 2017, 17, 1608; doi:10.3390/s17071608

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high detection sensitivity and to limit the diffusion distance of biomolecules for a rapid reaction [11–13]. On the other hand, the amount of biomolecules adsorbed on the surface of a reaction field is reduced due to the low sample volume used in MBDs, resulting in low detection sensitivity [14,15]. Moreover, ELISAs are also performed by reaction fields such as microchannels in two-dimensional microfluidics chips [5,6]. However, the surface area of the reaction field is small and the increase of the surface area is limited by adding microstructures such as microbeads [12] and nanomaterials with high aspect ratio [13] to a reaction field. Hence, the two-dimensional reaction field is not enough to achieve high detection sensitivity with a rapid reaction and both a higher volumetric flow rate and a higher specific surface area with a small diffusion distance are necessary for the simultaneous pursuit of high detection sensitivity and rapid reaction in MBDs. Our research group has developed a film-stack reaction field with a micropillar array for an ELISA device using 96-well microtiter plates. This reaction field is composed of several films stacked three-dimensionally in the reaction field and a magnetic sheet at the bottom of the reaction field. The surface area contributing to a reaction is increased by the stacked films, resulting in high detection sensitivity. Furthermore, there is an array of micropillars on the films, which additionally increases the surface area and limits the diffusion distance of biomolecules, contributing to high detection sensitivity and a rapid reaction. In the ELISA procedure, this reaction field in a well is rotated by a magnetic stirrer, which induces a circulating flow around the film-stack reaction field and through the inertial space between films in an ELISA procedure. Many biomolecules are rapidly transported to the reaction-field surface by the circulating flow. Moreover, a high volumetric flow rate through the inertial space in this reaction field can be effectively provided by the circulating flow with the limited solution volume. Therefore, the reaction time can be expected to be much reduced in addition to achieving higher detection sensitivity in ELISAs using this reaction field compared with the reaction field in the two-dimensional microchip. Additionally, the solution volume used in immunoassays is reduced by a few percent compared to that in traditional ELISA in general microfluidic devices such as microchannels for immunoassays [4–6]. However, the dead solution volume increases because of continuous solution supply to the microchannel for high detection sensitivity. On the other hand, ELISAs with film-stack reaction fields can achieve volumes less than half that used in traditional ELISAs and the dead solution volume decreases because of the circulating flow with the limited solution volume in wells. Therefore, the film-stack reaction fields can be expected to reduce more total solutions volume used in immunoassays compared with microfluidics devices including microchannels. Singh et al. [16] investigated the efficiency of this reaction field in ELISAs and demonstrated the increase of the detection sensitivity using the film-stack reaction field. Furthermore, our previous study [17] showed the effect of the structural dimensions of a micropillar array in the film-stack reaction field on the fluorescence intensity of ELISAs by fluid-flow and particle-trajectory analyses by performing a computational simulation in addition to IgA ELISA tests for the optimized design of the film-stack reaction field. According to the computational simulation analysis in this previous study, the factors determining the fluorescence intensity in terms of the transport of biomolecules in the film-stack reaction field were identified, such as the surface area, the structural dimensions, the flow velocity, and the supplied number and diffusion distance of the biomolecules to the inertial space in the film-stack reaction field. However, the effect of the film-stack reaction field on the shorter incubation time for the rapid diagnosis was not investigated. The dependence of the incubation time on the fluorescence intensity of ELISAs might be related to the volumetric rate of the circulating flow in a well with the rotation of the reaction field. Additionally, the computational simulation analysis was not enough to quantitatively evaluate these dominant factors although this analysis presented these factors. Hence, their evaluation is necessary for the optimization of a film-stack reaction field and an ELISA procedure for the reduction of the incubation time. Nevertheless, the rotation of film-stack reaction fields by a magnetic stirrer is not stabilized because of the imbalance between the magnetic force, the gravity force of a film-stack reaction field, and the buoyancy force acting to the reaction field in a well. Furthermore, the rotation time of the

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procedure. Therefore, correct rotation control reaction field is required forthe thecorrect quantitative reaction field has notthe been strictly controlled in of thethe ELISA procedure. Therefore, rotation evaluation of the time dependence and the effect of the circulating flow. control of the reaction field is required for the quantitative evaluation of the time dependence and the In of this a film-stack effect thestudy, circulating flow. reaction field using a motor stirrer was developed to stabilize the rotation and for the easy control of the speedstirrer and time of reaction. Furthermore, the In this study, a film-stack reaction fieldrotation using a motor was developed to stabilize the rotation dependence of the incubation time on the fluorescence intensity in the ELISA was investigated using and for the easy control of the rotation speed and time of reaction. Furthermore, the dependence of this and time the on film-stack reaction intensity field with micropillar of different dimensions. the stirrer incubation the fluorescence in the ELISA wasarrays investigated using this stirrer and Moreover, this study performed the theoretical modeling and analysis of the physical parameters the film-stack reaction field with micropillar arrays of different dimensions. Moreover, this study related with the transport of biomolecules, such as the specific surface area, the diffusion time and performed the theoretical modeling and analysis of the physical parameters related with the transport distance, and the volumetric flow rate, in wells without and with film-stack reaction fields based on of biomolecules, such as the specific surface area, the diffusion time and distance, and the volumetric the computational analysis in our previous study [17] in light of the results of the ELISA tests for the flow rate, in wells without and with film-stack reaction fields based on the computational analysis in optimization the reaction-field and the ELISA procedure with high sensitivity a rapid our previousofstudy [17] in light ofdesign the results of the ELISA tests for the optimization of theand reaction-field reaction. design and the ELISA procedure with high sensitivity and a rapid reaction. 2. 2. Materials and Methods Materials and Methods 2.1. Fabrication Film-Stack Reaction Field with a Micro-PillarsArray Array 2.1. Fabrication of of thethe Film-Stack Reaction Field with a Micro-Pillars Figure11 shows images thethe film-stack reaction field. field. Film-stack reactionreaction fields were fabricated Figure imagesofof film-stack reaction Film-stack fields were by a nanoimprint process and a punch-press process for the molding micropillars arrayed on fabricated by a nanoimprint process and a punch-press process for the of molding of micropillars base films, andfilms, the shaping stacking base films, respectively, in accordance with our previous arrayed on base and theand shaping andofstacking of base films, respectively, in accordance with studies [16,17]. A polyethylene terephthalateterephthalate (PET) sheet and acrylic resin used for the base film our previous studies [16,17]. A polyethylene (PET) sheet andwere acrylic resin were used respectively. Micropillar arraysMicropillar on PET films wereon fabricated using a nanoimprint forand themicropillars, base film and micropillars, respectively. arrays PET films were fabricated technique. Five films with a micropillar arraya were automatically punched and stacked by a and press using a nanoimprint technique. Five films with micropillar array were automatically punched machine. punched films Five were punched fixed by two metal pins. Moreover, magnetic sheet, which was stacked by Five a press machine. films were fixed by twoa metal pins. Moreover, a punchedsheet, in a cross shape, fixed atin thea bottom of the film-stack field. The diameter magnetic which waswas punched cross shape, was fixedreaction at the bottom of outside the film-stack and central-hole of the punched film are 5.0 and 2.0of mm, reaction field. The diameter outside diameter and central-hole diameter therespectively. punched filmMicropillar are 5.0 andarrays 2.0 withrespectively. different dimensions were prepared design dimensions a highly effective Table 1a gives the mm, Micropillar arrays with to different were reaction preparedfield. to design highly effective reaction field. Table gives the array. structural dimensions of the micropillar array. Figure 2 structural dimensions of the 1micropillar Figure 2 shows scanning electron microscopy (SEM) shows scanning electronarrays microscopy (SEM) images of micropillar arrays of different dimensions. images of micropillar of different dimensions.

Figure the film-stack film-stackreaction reactionfield. field. Top-view image. (b) Side-view The Figure1.1.Images Images of of the (a)(a) Top-view image. (b) Side-view image.image. The number number of stacked film in a film-stack reaction field is five. Two metal pins fix five films and of stacked film in a film-stack reaction field is five. Two metal pins fix five films and magnetic sheet. magnetic sheet. The outside diameter and central-hole theare punched are 5.0 and 2.0 The outside diameter and central-hole diameter of thediameter punched of film 5.0 and film 2.0 mm, respectively. mm, respectively. Table 1. Structural dimensions of the micropillar arrays. Table 1. Structural dimensions of the micropillar arrays. (a) (a) (b) (b) (c) (c)

Diameter[µm] [µm] Height Height [µm]Gap [µm] Gap [µm] Diameter [µm] 50 5 50 10 10 5 50 10 50 10 10 10 50 50 50 10 10 50

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Figure Figure2.2.SEM SEMimages imagesofofthe themicropillar micropillararrays arrayson onthe thebase basefilm. film.The Thediameter diameterand andheight heightofof the the Figure 2. SEM images of the micropillar arrays on the base film. The diameter and height of the Figure 2. SEM images of the micropillar arrays on the base film. The diameter and height of the micromicromicro-pillars pillarsfor forall alldimensions dimensionsare are50 50and and10 10µm, µm,respectively. respectively.The Thepillar pillargaps gapsare are(a) (a)5,5,(b) (b)10, 10,and and micropillars for all dimensions are 50 and 10 µm, respectively. The pillar gaps are (a) 5, (b) 10, and pillars for (c) (c)50 50µm. µm.all dimensions are 50 and 10 µm, respectively. The pillar gaps are (a) 5, (b) 10, and (c) 50 µm. (c) 50 µm.

2.2. Experiment 2.2.Experiment ExperimentSetup Setup 2.2. Experiment Setup Figure experimental ELISA procedure. Figure33presents presentsaaschematic schematicimage imageofofthe theexperimental experimentalsetup setupfor forthe theELISA ELISAprocedure. procedure.This This Figure 3 presents a schematic image ofplate, the experimental setup for the ELISA procedure. This setup is composed of a 96-well microtiter film-stack reaction fields and a motor stirrer is composed of a 96-well microtiter plate, film-stack reaction fields and a motor stirrer as shown setup is composed of a 96-well microtiter plate, film-stack reaction fields and a motor stirrer as as setup isincomposed of astirrer 96-well microtiter plate, film-stack reaction and fields and aeasy motor stirrer as shown Figure 4.4.This was totostabilize the for control of in Figure This stirrer developed to stabilize the rotation and for the easy control the rotation shown in4. Figure Thiswas stirrer wasdeveloped developed stabilize therotation rotation and forthe the easyof control ofthe the shown inspeed Figure 4. This stirrer was developed to stabilize the rotation and for the easy control ofand the rotation time ititcan rotate sixteen fields parallel speed andspeed timeand of reaction. Furthermore, it can rotate sixteen reaction fields in parallel perform rotation and timeof ofreaction. reaction.Furthermore, Furthermore, can rotate sixteenreaction reaction fieldsin inand parallel and rotation speed and time of reaction. Furthermore, it can rotate sixteen reaction fields in parallel and perform multiple ELISAs for various biomolecules. In the ELISA procedure, film-stack reaction multiple forELISAs variousfor biomolecules. In the ELISAInprocedure, reaction fields reaction are put perform ELISAs multiple various biomolecules. the ELISAfilm-stack procedure, film-stack perform multiple ELISAs forofvarious biomolecules. In the ELISA procedure, film-stack reaction fields the bottom rotated part in stirrer this isisset aa on theare bottom of in the motor stirrer andmotor this stirrer isand set onstirrer a microtiter plate fields areput puton onthe therotated bottompart ofthe the rotated part inthe the motor stirrer andup this stirrer setup upon onto fields are put ontothe bottom of the rotated part in the motor stirrer and this stirrer is set up on a microtiter plate reaction place reaction fields in wells. microtiter plate toplace place reactionfields fieldsin inwells. wells. microtiter plate to place reaction fields in wells.

Motor Motorstirrer stirrer Motor stirrer

96-well 96-wellmicrotiter microtiterplate plate 96-well microtiter plate

Time Time&&Rotation Rotationspeed speed Time &controller Rotation speed controller controller Motor Motorstirrer stirrer Motor stirrer

Biomolecules Biomolecules Biomolecules

Film-stack Film-stackreaction reactionfield fieldwith withmicro-pillars micro-pillarsarray array Film-stack reaction field with micro-pillars array

Schematic image the Figure Figure3.3.Schematic Schematicimage imageofofthe theexperimental experimentalsetup setupfor forthe theELISA ELISAprocedure. procedure. Figure 3. Schematic image of the experimental setup for the ELISA procedure.

Figure Images ofofthe the developed motor stirrer. Whole image. view ofofrotated the Figure4.4.Images Imagesof the developed motor stirrer. (a) Whole image. (b)Bottom Bottom view therotated rotated developed motor stirrer. (a)(a) Whole image. (b) (b) Bottom view of the part Figure 4. Images of the developed motor stirrer. film-stack (a) Whole reaction image. (b) Bottom view of the rotated part ininmotor the stirrer. In the procedure, fields are on the ofof in the stirrer. In the procedure, film-stack reaction fields are put on of the part themotor motor stirrer. InELISA theELISA ELISA procedure, film-stack reaction fields areput putthe onbottom thebottom bottom partrotated in the motor stirrer. In thestirrer ELISAand procedure, film-stack reaction fields are put on plate the bottom of the part in the motor this stirrer is set up on a 96-well microtiter to place rotated part in the motor stirrer and this stirrer is set up on a 96-well microtiter plate to place reaction the rotated part in the motor stirrer and this stirrer is set up on a 96-well microtiter plate to place the rotated part in the motor stirrer and this stirrer is set up on a 96-well microtiter plate to place reaction fields in fields wells. reaction fieldsininwells. wells. reaction fields in wells.

2.3. 2.3.IgA IgAELISA ELISA 2.3. IgA ELISA 2.3. IgA ELISA IgA ELISA was carried with or film-stack reaction IgAELISA ELISAwas was carried out using using wellsor with or without without film-stack reaction fields with with IgA carried outout using wellswells with without film-stack reaction fields withfields micropillar IgA ELISA was carried out dimensions using wellsatwith ortemperature. without film-stack reaction fields iswith micropillar arrays having different room The procedure followed micropillar arrays having different dimensions at room temperature. The procedure followed is the arrays having different dimensions at room temperature. The procedure followed is the samethe as micropillar arrays in having differentstudy dimensions atthe room temperature. The procedure followed is the same as described our previous [17]. For incubation of human IgA (Bethyl Laboratories, same as described in our previous study the incubation of human IgA (Bethyl Laboratories, described in our previous study [17]. For[17]. theFor incubation of human IgA (Bethyl Laboratories, Inc., sameMontgomery, as described in our previous study [17].of For the and incubation of human IgA (Bethyl Laboratories, Inc., TX, wells the fields, 100 of Inc., Montgomery, TX,USA) USA) onthe thesurfaces surfaces wells thefilm-stack film-stack reaction fields, 100 µL of1% 1% Montgomery, TX, USA) on theon surfaces of wellsof and the and film-stack reactionreaction fields, 100 µL of 1%µL purified Inc., Montgomery, TX, USA) on the surfaces of wells and the film-stack reaction fields, 100 µLtoofeach 1% purified human IgA diluted in 0.1 mol/L carbonate buffer solution (CBS, pH = 9.5) was added purified human IgA diluted in 0.1 mol/L carbonate buffer solution (CBS, pH = 9.5) was added to each human IgA diluted in 0.1 mol/L carbonate buffer solution (CBS, pH = 9.5) was added to each well. purified human IgA diluted in 0.1 mol/L carbonate buffer solution (CBS, pH = 9.5)rotated was addedatomotor each well. well.In Inthe thewells wellswith withthe thefilm-stack film-stackreaction reactionfields, fields,these thesereaction reactionfields fieldswere were rotatedby by a motor well. In the wells with the film-stack reaction fields, these reaction fields were rotated by a motor

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In the wells with the film-stack reaction fields, these reaction fields were rotated by a motor stirrer for 1 min and left for 59 min. The well without the reaction field was left for 1 h. After the incubation, the human IgA solution was removed from each well and each well was washed with 300 µL of Tris-buffered saline (TBS, pH = 8.0) containing 0.05% Tween-20 (TBS-T). Then, blocking was performed using 200 µL of TBS containing bovine serum albumin (EMD Millipore Corp., Billerica, MA, USA, TBS-BSA) for 30 min. In the case of the wells with the film-stack reaction fields, these reaction fields were rotated by a motor stirrer for 1 min and left for 29 min. After the blocking, the TBS-BSA solution was removed from each well and each well was washed with 300 µL of TBS-T. Furthermore, for the incubation of horseradish peroxidase conjugated goat human IgA antibody (HRP-IgA, Bethyl Laboratories, Inc., Montgomery, TX, USA) in each well, 100 µL of 0.01% HRP-IgA diluted in TBS-BSA was added to each well. This step was performed with three incubation times of 30 s, 5 min, and 10 min to evaluate the effect of HRP-IgA incubation in each well. The reaction fields were continuously rotated during HRP-IgA incubation. After the incubation, the HRP-IgA solution was removed from each well and each well was washed with 300 µL of TBS-T. Finally, 100 µL of 1% Amplex® Red (Thermo Fisher Scientific Inc., Waltham, MA, USA) solution diluted in 50 mmol/L phosphate-buffered saline (PBS, pH = 7.4) and hydrogen peroxide solution was added to each well. Then, the plates were developed in a dark place for 15 min, while the reaction fields were continuously rotated. After Amplex® Red stop reagent (Thermo Fisher Scientific Inc., Waltham, MA, USA) was added to each well, 80 µL of the reaction solution was moved to another well in order to align the height of the solution level in all wells. The fluorescence intensity in each well was measured using a plate reader (SpectraFluor, TECAN, Männedorf, Switzerland). The rotating speed of the film-stack reaction field in each step was 1000 rpm, which is the maximum speed for the motor stirrer, which generates a sufficient circulating flow in a well. 2.4. Theoretical Modeling of Physical Parameters Related with Biomolecule Transport 2.4.1. Geometric Model of Well and Space between Films To verify the effect of the film-stack reaction field with a micropillar array on the fluorescence intensity in terms of physical phenomena, a theoretical analysis of the physical parameters related with biomolecule transport was performed. This analysis is based on the computational simulation of its transport in a film-stack reaction field as shown in our previous study [17]. Figure 5a,b shows the two-dimensional geometry models of the wells with and without the film-stack reaction field including the biomolecule transport in the theoretical analysis, respectively. The initial position of a biomolecule was assumed to be the well center. This biomolecule was assumed to move to the side wall of the well in a horizontal direction. In the well with the film-stack reaction field, the biomolecule was assumed to be transported through the space between films. Like in our previous study, the space between films was assumed to be composed of multiple microchannels with a micropillar array, as shown in Figure 5c. The number of microchannels per space between films Nc is given by: Nc =

πdhole , gp + dp

(1)

where dhole is the central-hole diameter of a film, gp is the gap between micropillars, and dp is the pillar diameter. Furthermore, this channel was approximately modeled as a circular tube with a certain hydrodynamic diameter to simplify the theoretical analysis. The hydrodynamic diameter dhydro is expressed in terms of the dimensions of the micropillars as: dhydro =

2g p h p , gp + hp

(2)

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where, hp is the height of a micropillar. The initial position of a biomolecule was assumed to be the center of the circular-tube inlet. This biomolecule was assumed to move through the space between Sensors 2017, 17, 1608 6 of 14 the films. (a) Well without film-stack reaction field

(b) Well with film-stack reaction field

Biomolecule

(c) Space between films in film-stack reaction field Micro channel with micro-pillars array

Assumption Circular tube with hydrodynamic diameter Inlet

Outlet

Figure5.5.Geometric Geometric models of well the well (a) and with(b)and (b) without the film-stack reaction field Figure models of the (a) with without the film-stack reaction field including including the transport of one biomolecule. (c) Conceptual model of the fluid flow and biomolecule the transport of one biomolecule. (c) Conceptual model of the fluid flow and biomolecule transport transport the space between films. , dare film, the andwell dhole diameter, are the well the outside through thethrough space between films. dwell , dfilm , anddwell dhole the diameter, outside diameter of a diameter of central-hole a film, and the central-hole diameter of a film, respectively. p and dp are the between film, and the diameter of a film, respectively. gp and dp are the ggap between the gap micropillars is the hydrodynamic diameter of a the the micropillars and the pillar diameter, dhydro diameter and pillar diameter, respectively. dhydro is respectively. the hydrodynamic of a circular tube. circular tube.

2.4.2. Physical Parameters in Theoretical Analysis for the Well without the Film-Stack Reaction Field 2.4.2. Physical Parameters in Theoretical Analysis for the Well without the Film-Stack Reaction Field The specific surface area of the well without the reaction field, SSw , is given by: The specific surface area of the well without the reaction field, SSw, is given by: Sw SSw = . (3) = (3) VL . In of of a well, and VL VisL the solution volume which is 100 µL for Inthis thisequation, equation,SwSwisisthe thesurface surfacearea area a well, and is the solution volume which is 100 µL the procedure. Biomolecules in the without a film-stack reaction fieldfield are transported by for ELISA the ELISA procedure. Biomolecules in well the well without a film-stack reaction are transported diffusion. The biomolecule arrival time at the at side wall of wall the well, tw , well, is expressed by the diffusion by diffusion. The biomolecule arrival time the side of the tw, is expressed by the time in Fick’s as: diffusion timelaw in Fick’s law as: d 2 tw = well , (4) 16D (4) = b , 16 where Db is the diffusion coefficient of a biomolecule given by Db = k B T/6πµrb (kB Boltzmann ⁄6in a well, (kB Boltzmann theatmosphere diffusion coefficient of a µbiomolecule by solution = where DbTisthe constant; temperature; viscosity ofgiven the buffer rb is the constant; T radius). the atmosphere temperature; µ viscosity of the buffer solution in a well, rb is the biomolecule biomolecule radius).

2.4.3. Physical Parameters in Theoretical Analysis for the Well with the Film-Stack Reaction Field The specific surface area of the well with the reaction field, SSf, is given by:

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2.4.3. Physical Parameters in Theoretical Analysis for the Well with the Film-Stack Reaction Field The specific surface area of the well with the reaction field, SSf , is given by: SS f =

Sw + n f S f . VL

(5)

In this equation, Sf is the surface area of a film and nf is the number of films per film-stack reaction field, which is five in the fabricated reaction field. Biomolecules in the well with a film-stack reaction field are transported by the convection flow generated by the rotation of the reaction field in addition to their diffusion. During the rotation of a film-stack reaction field in the well, the buffer solution flows through the space between the films in a laminar flow according to the analysis result of a computational simulation in our previous study [17]. Therefore, biomolecules can be assumed to be adsorbed on the film wall in the space between the films owing to their diffusion. The biomolecule-arrived time at the film wall in the space between films by its diffusion corresponds to the diffusion time of a biomolecule in the model of a circular tube with the hydrodynamic diameter tf,d as shown in Figure 5c, which is given by: dhydro 2 t f ,d = . (6) 16Db Furthermore, the transit time of the biomolecules transport by the convection flow though the space between the films is provided by: tf,f =

d f ilm − dhole . 2v f

(7)

In this equation, vf is the average velocity of the convection flow in the circular tube with the hydrodynamic diameter. To investigate the dominant factor in the biomolecule transport in the circular tube such as the convection flow or its diffusion, Peclet number, Pe, which is the non-dimensional number in fluid mechanics expressing the ration of the diffusion time to the convection-flow time, was calculated as: t f ,d v f dhydro 2  . Pe = = (8) tf,f 8D d −d b

f ilm

hole

In the case of the convection flow for the biomolecule transport through the space between the films, this transport was evaluated on the basis of the volumetric flow rate in this space. To calculate the volumetric flow rate in the space between the films, the volumetric flow rate in the circular tube was calculated as: 1 Qc = v f Ac = πv f dhydro 2 , (9) 4 where Ac is the diameter of the circular tube. Therefore, the volumetric flow rate in the space between the films was calculated by multiplying the volumetric flow rate in the circular tube and the number of micro channels per space between the films as:  2 v f dhole πdhydro
Q f = Nc Qc = . 2 gp + dp

(10)

Moreover, the volume of the buffer solution transiting through all the spaces between the films during the proteins incubation with the reaction-field rotation, VT , is calculated as:   VT = Q f ti n f − 1 .

(11)

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In this equation, ti is the protein incubation time. As another factor related to the fluorescence intensity in addition to the volumetric flow rate, the reaction efficiency of the film-stack reaction field was evaluated in this study. The reaction efficiency in this study corresponds to the probability of biomolecule adsorption on the wall in the space between the films with the circulating flow during the rotation of the reaction field. Here, to define this reaction efficiency, the simple model shown in Sensors 2017, 17,assumed. 1608 of 14 Figure 6 was This model shows the biomolecule trajectory during its transport from the8inlet to the outlet of a circular tube with a hydrodynamic diameter as shown in Figure 5. The diffusion The diffusion distance of in a biomolecule in thedirection perpendicular the tube axis during its distance of a biomolecule the perpendicular to the direction tube axis to during its transport by the transport by the convection flow from the inlet to the outlet of the tube, x D , is expressed by Fick’s convection flow from the inlet to the outlet of the tube, xD , is expressed by Fick’s law: law: v   u u 2Db d f ilm − dhole q t 2 − x D = = 4D4b t f , f ,== .. (12) v f

Inlet

Outlet Biomolecule Center line

Figure 6. 6. Model the biomolecule biomolecule trajectory trajectory in a circular circular tube tube with with aa hydrodynamic hydrodynamic diameter diameter as as Figure Model of of the in a shown in Figure 5. x D is the diffusion distance of a biomolecule during its transport by the convection shown in Figure 5. xD is the diffusion distance of a biomolecule during its transport by the convection flow from from the the inlet inlet to to the the outlet outlet of of the the tube. tube. flow

Using Equation (12), the reaction efficiency in this model was defined as the ratio of the Using Equation (12), the reaction efficiency in this model was defined as the ratio of the diffusion diffusion distance to half of the hydrodynamic diameter, which is the probability of the adsorption distance to half of the hydrodynamic diameter, which is the probability of the adsorption of the of the biomolecule on the tube wall during its transport by the convection flow from the inlet to the biomolecule on the tube wall during its transport by the convection flow from the inlet to the outlet of outlet of the tube. Therefore, the reaction efficiency, ER, is given by: the tube. Therefore, the reaction efficiency, ER , is given by: − 2 2v 2   u (13) = = u 2Db d f ilm − dhole . 2x D 2 t ER = = . (13) dhydro dhydro vf Moreover, the volumetric flow rate contributing to the reaction or the adsorption of the biomolecules in the the wells with the film-stack reaction field defined by multiplying the volumetric Moreover, volumetric flow rate contributing toisthe reaction or the adsorption of the flow rate in Equation (8) and the reaction efficiency in Equation (13) as: biomolecules in the wells with the film-stack reaction field is defined by multiplying the volumetric flow rate in Equation (8) and the reaction efficiency in Equation (13) as: = 2 − . (14) , = + r 2   π dhole dhydro − dhole . The viscosity indicated (14) R = f ,E = Q f Efor f Db d f ilm Table 2 shows the Q conditions the calculation of2v physical parameters. gp + dp in Table 2 is the water viscosity since the viscosity of the buffer solution was assumed to be similar to Table viscosity 2 shows the conditions for the calculation physical parameters. viscosity indicated the water according to our previous studyof[17]. Furthermore, the The average velocity of the in Table 2 isflow the water viscosity since thediameter viscositywith of thea buffer solution was assumed to calculated be similar convection for each hydrodynamic rotation speed of 1000 rpm was to viscosity according to our previous in study Furthermore, bythe thewater analysis of the computational simulation our [17]. previous study. the average velocity of the convection flow for each hydrodynamic diameter with a rotation speed of 1000 rpm was calculated by Table 2. Conditions for thesimulation calculationin of our physical parameters the analysis of the computational previous study.in the theoretical analysis. Characteristic parameters for physical parameters

Values

Gap between micro pillars gp (µm) Pillar diameter dp (µm) Pillar height hp (µm) Well diameter dwell (mm) Outside diameter of a film dfilm (µm) Central-hole diameter of a film dhole (µm) Surface area of a well Sw (mm2)

5, 10, 50 50 10 7 5 2 93

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Table 2. Conditions for the calculation of physical parameters in the theoretical analysis. Characteristic Parameters for Physical Parameters

Values

Gap between micro pillars gp (µm) Pillar diameter dp (µm) Pillar height hp (µm) Well diameter dwell (mm) Outside diameter of a film dfilm (µm) Central-hole diameter of a film dhole (µm) Surface area of a well Sw (mm2 )

5, 10, 50 50 10 7 5 2 93 4.18 (5-µm gap), 4.00 (10-µm gap), 5.08 (50-µm gap) 5 100 6.5 0.001 293.15 1.74 (5-µm gap), 1.01 (10-µm gap), 0.35 (50-µm gap) 30, 300, 600

Surface area of a film Sf (mm2 ) Number of films per film-stack reaction field nf Solution volume used in ELISA procedure VL (µL) Biomolecule radius rb (nm) Viscosity of buffer solution µ (Pa) Atmosphere temperature T (K) Average velocity of the convection flow in a circular tube with the rotation speed of 1000 rpm vf (m/s) Protein incubation time (s)

3. Results 3.1. Fluorescence Intensity in IgA ELISA Figure 7 shows the fluorescence intensities of IgA ELISA in relation to HRP-IgA incubation time for wells without and with the film-stack reactions with the micropillar arrays having different dimensions. For each incubation time, the fluorescent intensities in the wells with the film-stack reaction fields were higher than those in the wells without the reaction fields. The average intensities in the wells with the reaction fields for the incubation times of 30 s, 5 min, and 10 min were 2.0-fold, 1.6-fold, and 1.4-fold higher than those in the wells without the reaction fields, respectively. Thus, the film-stack reaction field with a motor stirrer was most effective with the short incubation time. Table 3 shows comparisons of the specific surface areas obtained using Equations (3) and (5), and the diffusion times obtained using Equations (4) and (6) between the wells without and with the reaction field. The specific surface area of the well with the reaction field was 3.1-fold higher than that of the well without it. The diffusion time of the well with the reaction field was five orders of magnitude less than that of the well without it. Furthermore, the difference in fluorescent intensities between the well with the reaction field of 50-µm gap for the incubation time of 30 s and the well without the reaction field for the incubation time of 10 min was 6%. Hence, these results indicated that the use of the film-stack reaction field with a motor stirrer can reduced the incubation time in ELISAs by 95% compared with the traditional ELISA using only 96-well microtiter plates. Figure 8 presents the transitions of the fluorescence intensity in the wells with the micropillar arrays having different dimensions in relation in relation to HRP-IgA incubation time. For the long incubation time, the fluorescence intensity in the 10-µm gap was the highest and that in the 50-µm gap was the lowest among all the gaps. For the short incubation time, however, the fluorescence intensity in the 50-µm gap was the highest and that in the 10-µm gap was the lowest among all the gaps. Hence, the trend of the fluorescence intensity in the gap of the micropillar arrays in the film-stack reaction field was different for the long incubation time and the short incubation time. Furthermore, the fluorescence intensity in the 50-µm gap was highest and its gradient was smallest among all the gaps in the short incubation time. This means that the film-stack reaction with the 50-µm gap was closest to the optimum solution of the reaction-field design for rapid diagnosis with high detection

Table 3 shows comparisons of the specific surface areas obtained using Equations (3) and (5), and the diffusion times obtained using Equations (4) and (6) between the wells without and with the reaction field. The specific surface area of the well with the reaction field was 3.1-fold higher than that of the well without it. The diffusion time of the well with the reaction field was five orders of magnitude less than that of the well without it. Furthermore, the difference in fluorescent intensities between Sensors 2017, 17, 1608 10 of 15 the well with the reaction field of 50-µm gap for the incubation time of 30 s and the well without the reaction field for the incubation time of 10 min was 6%. Hence, these results indicated that the use of the film-stack reaction with a motorthis stirrer cana reduced theanalysis incubation in ELISAstransport by 95% sensitivity among all thefield gaps. To discuss result, theoretical of thetime biomolecule compared withflow the in traditional ELISA using 96-well microtiter with the fluid a well was carried out,only as described in the nextplates. section.

Fluorescence intensity [a. u.]

20000

30 s

5 min

10 min

16000 12000 8000 4000 0

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Well without filmstack reaction field

5-μm gap

10-μm gap

50-μm gap

10 of 14

Fluorescence intensity [a. u.]

incubation time, the fluorescence intensity in thein 10-µm gap the highest andtime thatfor in wells the 50-µm Figure Fluorescence intensities of relation to HRP-IgA incubation Figure 7. 7. Fluorescence intensities of IgA IgA ELISA ELISA in relation to was HRP-IgA incubation time for wells and with the film-stack reactions with the micro-pillars array having different dimensions. gap without was the lowest among all the gaps. For the short incubation time, however, the fluorescence without and with the film-stack reactions with the micro-pillars array having different dimensions. The The number of experiments is three. arein the maximum and minimum intensities. intensity in the 50-µm gap was the highest andbars that the 10-µm was the lowest among all the trial trial number of experiments is three. ErrorError bars are the maximum andgap minimum intensities. gaps. Hence, the trend of the fluorescence intensity in the gap of the micropillar arrays in the Table 3. areas and times. film-stack reaction field was different forsurface the long incubation time and the short incubation time. Table 3. Specific Specific surface areas and diffusion diffusion times. Furthermore, the fluorescence intensity in the 50-µm gapField was highest and gradient was smallest Well without a Reaction Average of its Reaction Fields Well without a Reaction Fieldthat the Average of Reaction Fields among all the gaps in area the short time. This means film-stack reaction with the Specific surface (m−1) incubation 930 2871 5 − 1 50-µm gap was closest to the optimum solution of the reaction-field design for rapid diagnosis with Diffusion time 3.71 930 × 10 1.07 2871 Specific surface area (m (s)) 5 Diffusion time (s) among all the gaps. 1.07 analysis of the 3.71To × 10 high detection sensitivity discuss this result, a theoretical biomolecule with the fluid flow influorescence a well was carried out,inasthe described in the section. Figure 8 transport presents the transitions of the intensity wells with thenext micropillar arrays having different dimensions in relation in relation to HRP-IgA incubation time. For the long 20000

16000

12000

5-μm gap 10-μm gap 50-μm gap

8000 0

200 400 Incubation time [s]

600

Figure8.8.Transitions Transitionsof ofthe thefluorescence fluorescenceintensity intensityin inthe thewell wellwith withthe thefilm-stack film-stackreaction reactionfields fieldswith with Figure the micro-pillars array having different dimensions in relation in relation to HRP-IgA incubation the micro-pillars array having different dimensions in relation in relation to HRP-IgA incubation time. All All fluorescence fluorescence intensities intensities are are the the same same with with Figure Figure 7.7. Error Error bars bars are are the the maximum maximum and and time. minimum intensities. minimum intensities.

3.2. Theoretical Analysis of Physical Paramters Related with Biomolecule Transport For all dimensions of the micropillar arrays, Peclet numbers calculated using Equation (6) were more than 100, which indicated that the convection flow was the dominant factor in the case of the ELISA procedure using the film-stack reaction field with the rotation speed of 1000 rpm. Figure 9 shows the volumetric flow rate through a space between films calculated using Equation (10). The

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3.2. Theoretical Analysis of Physical Paramters Related with Biomolecule Transport For all dimensions of the micropillar arrays, Peclet numbers calculated using Equation (6) were more than 100, which indicated that the convection flow was the dominant factor in the case of the ELISA procedure using the film-stack reaction field with the rotation speed of 1000 rpm. Figure 9 shows the volumetric flow rate through a space between films calculated using Equation (10). The trend of the volumetric flow rate in the gap between micropillars was similar to that of the fluorescence intensity for the long incubation time, as shown in Figure 8. Moreover, the specific surface area of the reaction field with the 50-µm gap was lowest among all the gaps, as shown in Table 4. Therefore, the high volumetric flow rate and high specific surface area contributed to the high fluorescence intensity for the long incubation time. Table 4. Specific surface areas calculated using Equation (5). Structural Dimension of a Micropillar Array

Specific Surface Area SSf (m−1 )

5-µm gap 10-µm gap 50-µm gap

3010 2930 2674

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Volumetric flow rate through a space between films [10-5 m3/s]

1.8

1.2

0.6

0 5-μm gap

10-μm gap

50-μm gap

Figure 9. Volumetric flow rate through a space between films calculated using Equation Equation (10). (10).

To verify verify the the trend trend of of the the fluorescence fluorescence intensity intensity for for the the short short incubation To incubation time time shown shown in in Figure Figure 8, 8, the volume of the buffer solution transiting through all the spaces between the films in the short the volume of the buffer solution transiting through all the spaces between the films in the short incubation time time was was firstly firstly calculated calculated by by Equation Equation (11). the case case of of using using the the reaction reaction incubation (11). The The volume volume in in the field with the 50-µm gap for the incubation time of 30 s was the minimum and 1.1 L, which is more field with the 50-µm gap for the incubation time of 30 s was the minimum and 1.1 L, which is more than than ten-thousand-fold the buffer solution volume of 100 µL used in the ELISA procedure. This ten-thousand-fold the buffer solution volume of 100 µL used in the ELISA procedure. This indicated indicated that the circulating sufficient circulating flow foradsorption proteins adsorption was generated by thespeed rotation that the sufficient flow for proteins was generated by the rotation of speed of 1000 rpm for the short incubation time. Figures 10a,b present the reaction efficiencies of the 1000 rpm for the short incubation time. Figure 10a,b presents the reaction efficiencies of the film-stack film-stack reaction with the arrays micropillar arrays having differentobtained dimensions obtained using reaction fields with fields the micropillar having different dimensions using Equation (13) Equation (13) and flow the volumetric flow to rate toadsorption the reaction or biomolecules the adsorption of the and the volumetric rate contributing thecontributing reaction or the of the obtained biomolecules obtained using Equation (14), respectively. All the reaction efficiencies, however, were using Equation (14), respectively. All the reaction efficiencies, however, were approximately 0.1 and the approximately 0.1 and the trend of the volumetric flow rate contributing to the reaction in the gap trend of the volumetric flow rate contributing to the reaction in the gap between films was unchanged between films was unchanged from that of the flow rate shown in Figure 9 by the reaction efficiency. from that of the flow rate shown in Figure 9 by the reaction efficiency. This might be due to the This might be due to the difference between the theoretical model in Figure 6 and the actual situation difference between the theoretical model in Figure 6 and the actual situation of the biomolecule of the biomolecule adsorption on the wall in the space between the films. In the next section, this adsorption on the wall in the space between the films. In the next section, this difference is discussed difference is discussed and the reaction efficiency given by Equation (13) is modified. and the reaction efficiency given by Equation (13) is modified. (a)

(b) 0.1 0.08 0.06 0.04

4

lumetric flow rate buting to the reaction [10-7 m3/s]

tion efficiency [a. u.]

0.12

3

2

biomolecules obtained using Equation (14), respectively. All the reaction efficiencies, however, were approximately 0.1 and the trend of the volumetric flow rate contributing to the reaction in the gap between films was unchanged from that of the flow rate shown in Figure 9 by the reaction efficiency. This might be due to the difference between the theoretical model in Figure 6 and the actual situation of the biomolecule adsorption on the wall in the space between the films. In the next section, this Sensors 2017, 17, 1608 12 of 15 difference is discussed and the reaction efficiency given by Equation (13) is modified. (a)

(b) 4

Volumetric flow rate contributing to the reaction [10-7 m3/s]

Reaction efficiency [a. u.]

0.12 0.1 0.08 0.06 0.04 0.02 0

3

2

1

0 5-μm gap

10-μm gap

50-μm gap

5-μm gap

10-μm gap

50-μm gap

Figure 10. thethe film-stack reaction field calculated using Equation (13).(13). (b) 10. (a) (a)Reaction Reactionefficiency efficiencyofof film-stack reaction field calculated using Equation Volumetric flow rate contributing to to thethe reaction (b) Volumetric flow rate contributing reactionororadsorption adsorptionofofthe thebiomolecules biomoleculesin inthe the wells wells with with the film-stack reaction field calculated using Equation (14).

4. 4. Discussion Discussion Although Although the the characteristic characteristic length length of of the the reaction reaction efficiency efficiency given given by by Equation Equation (13) (13) is is the the hydrodynamic the biomolecules, in in fact, preferentially adsorb on hydrodynamic diameter diameterin inthe themodel modelofofFigure Figure6,6, the biomolecules, fact, preferentially adsorb the wall closest to the biomolecules’ position. Figure 11 shows a schematic image of the situation on the wall closest to the biomolecules’ position. Figure 11 shows a schematic image of the situation indicating which exists in in thethe space between the the films of the indicating the thebiomolecule biomoleculeadsorption adsorptionon onthe thewall, wall, which exists space between films of film-stack reaction field. While the biomolecules preferentially adsorb on the micropillar walls in the the film-stack reaction field. While the biomolecules preferentially adsorb on the micropillar walls in the 2017, case 17, of 1608 5-µm gap, the biomolecules preferentially adsorb on the back and top sides of the Sensors 12 film of 14 in the case of 50-µm gap. Hence, the reaction efficiency might need to be altered to the ratio of the case of 5-µm gap, the biomolecules preferentially adsorb on the back and top sides of the film in the diffusion distance to half of the minimum length in the structural dimensions of a micropillar array. casemodified of 50-µm reaction gap. Hence, the reaction The efficiency, E’R , isefficiency given by: might need to be altered to the ratio of the diffusion distance to half of the minimum length in the structural dimensions of a micropillar array. The v   u by: ( modified reaction efficiency, E’R, is given u 2Db d f ilm − dhole gp , gp < hp 2 2x t D 0 = , Lmin = . (15) ER= Lmin2 Lmin2 vf − h p ,, g p > ℎh p 2 (15) = , = . ′ = ℎ , ℎ In this equation, Lmin is the minimum length in the structural dimensions of a micropillar array. thisgap equation, Lmin is the minimum length in theheight, structural micropillar WhenInthe between films is shorter than the pillar Lmindimensions , is equal to of thea gap, while Larray. min is Whento the between shorter thethan pillar Lmin, is Moreover, equal to the while Lmin is equal thegap pillar heightfilms whenisthe gap isthan longer theheight, pillar height. thegap, volumetric flow equal to the pillartoheight when obtained the gap is longer than the Moreover, rate contributing the reaction from Equation (15),pillar Q’f,E ,height. is expressed as: the volumetric flow rate contributing to the reaction obtained from Equation (15), Q’f,E, is expressed as:  2   dhole πdhydro r 0
2v Q0 f ,E′ = Q E = D d − d .. (16) R f f b f ilm hole = ′ = − 2 , Lmin g p ++d p

Figure 11. 11. Schematic Schematic image image of of the the situation situation indicating indicating that that the the biomolecule biomolecule adsorption adsorption on on the the wall wall in in Figure the space between films of the film-stack reaction field. (a) 5-µm gap. (b) 10-µm gap. (c) 50-µm gap. the space between films of the film-stack reaction field. (a) 5-µm gap. (b) 10-µm gap. (c) 50-µm gap.

Figures 12a,b shows the reaction efficiency obtained using Equation (15) and the volumetric flow rate obtained using Equation (16), respectively. In Figure 12a, the trend of the reaction efficiency in the gap between the films was in agreement with that of the fluorescence intensity in the case of the short incubation time. On the other hand, all the volumetric flow rates shown in Figure 12b were comparable. Furthermore, the volume of the transited buffer solution which

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Figure 12a,b shows the reaction efficiency obtained using Equation (15) and the volumetric flow rate obtained using Equation (16), respectively. In Figure 12a, the trend of the reaction efficiency in the gap between the films was in agreement with that of the fluorescence intensity in the case of the short incubation time. On the other hand, all the volumetric flow rates shown in Figure 12b were comparable. Furthermore, the volume of the transited buffer solution which contributes to the reaction was calculated by assigning Q’f,E to the volumetric flow rate in Equation (11). The volumes of all the gaps between films in the case of the short incubation time were more than 40 mL, which is 400-fold higher than the buffer solution volume used in the ELISA procedure. Hence, the small diffusion distance and the low velocity with a sufficient circulating flow through the spaces between the films provided the high fluorescence intensity for the short incubation time in the ELISA procedure. Therefore, these results indicated that the reaction efficiency defined in this study was the dominant factor determining the fluorescence intensity for the short incubation time, whereas the volumetric flow rate and the specific surface area were the dominant factors for the long incubation time. Furthermore, the smaller diffusion distance provided by the structural dimension of a micropillar array and the lower rotation speed with the sufficient circulating flow through the spaces between the films can induce the higher fluorescence intensity for the shorter incubation time in addition to the higher specific surface area, which is achieved by increasing the number of films in the film-stack reaction field. Moreover, the equations proposed in this study can be used to quantitatively evaluate the function of the film-stack reaction field and are expected to be powerful tools for optimizing the design of the film-stack reaction Sensors 2017, 17, 1608 13 of 14 field and the ELISA procedure to achieve high detection sensitivity and a rapid reaction.

(a)

(b) 4 Volumetric flow rate contributing to the reaction [10-7 m3/s]

Reaction efficiency [a. u.]

0.16

0.12

0.08

0.04

0

3

2

1

0 5-μm gap

10-μm gap

50-μm gap

5-μm gap

10-μm gap

50-μm gap

Figure calculated Figure 12. 12. (a) (a) Reaction Reaction efficiency efficiency calculated calculated using using Equation Equation (15). (15). (b) (b) Volumetric Volumetric flow flow rate rate calculated using Equation (16).

5. Conclusions Conclusions A film-stack reaction field with a micropillar array using a motor stirrer was developed and IgA ELISA tests using this device were demonstrated. The The effects effects of the incubation time of HRP-IgA on the fluorescence fluorescenceintensity intensity in ELISA investigated using film-stack reaction with in ELISA were were investigated using film-stack reaction fields withfields micropillar micropillar arraysdimensions. of differentThe dimensions. The average fluorescence intensity of all wells with arrays of different average fluorescence intensity of all wells with film-stack reaction film-stack fields was higherwithout than that wells without reaction the fields. In particular, fields was reaction higher than that of wells theof reaction fields. Inthe particular, average intensity the for average intensity for the reaction fieldtime withof the timehigher of 30 sthan was that 2.0-fold higher than that the reaction field with the incubation 30incubation s was 2.0-fold of wells without the of wells without the reaction the fields. Furthermore, the difference inbetween fluorescent the reaction fields. Furthermore, difference in fluorescent intensity the intensity well withbetween the reaction well the reaction of incubation the 50-µm gap timewithout of 30 s and well without field with of the 50-µm gapfield in the timeinofthe 30incubation s and the well the the reaction field in the reaction field in of the10incubation time of 10the min was 6%. time Thus,inthe incubation time inreduced ELISA can be incubation time min was 6%. Thus, incubation ELISA can be greatly by the greatly reduced by the reaction field with a motor stirrer. On the other hand, the trend of the reaction field with a motor stirrer. On the other hand, the trend of the fluorescence intensity in the gap fluorescence intensity of thereaction micro-pillars array in the film-stack reaction field time was of the micro-pillars arrayininthe the gap film-stack field was different between the short incubation different between the short incubation time and the long incubation time.transport The theoretical of and the long incubation time. The theoretical analysis of the biomolecules with theanalysis fluid flow the biomolecules transport with the fluid flow indicated that the reaction efficiency defined in this indicated that the reaction efficiency defined in this study was the dominant factor determining the study was the dominant factor determining the fluorescence intensity for the short incubation time while the specific surface area was the dominant factor for the long incubation time. Furthermore, the smaller diffusion distance provided by the structural dimension of a micropillar array and the lower rotation speed with the sufficient circulating flow through the spaces between the films can induce the higher fluorescence intensity for the shorter incubation time in addition to the higher

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fluorescence intensity for the short incubation time while the specific surface area was the dominant factor for the long incubation time. Furthermore, the smaller diffusion distance provided by the structural dimension of a micropillar array and the lower rotation speed with the sufficient circulating flow through the spaces between the films can induce the higher fluorescence intensity for the shorter incubation time in addition to the higher specific surface area, which is achieved by increasing the number of films in the film-stack reaction field. Moreover, the models and equations proposed in this study can be used to quantitatively evaluate the function of the film-stack reaction field and are expected to be powerful tools for optimizing the design of the film-stack reaction field and the ELISA procedure to achieve high detection sensitivity and a rapid reaction. The effectivity of the film-stack reaction field for immunoassays can be additionally presented to investigate solution volumes used in immunoassays, detection sensitivity, reproducibility, and applications on other immunoassays for biomolecules. Acknowledgments: This work was supported by the Tokyo Metropolitan Government High Technology Research Fund. Author Contributions: Y.S. and S.O. conceived, designed and performed the experiments; Y.S. performed the theoretical modeling and analyses; K.M. assisted the experiments; Y.S. wrote the paper; T.S., H.N., K.U. and M.Y. provided guidance and comments. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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Fatoyinbo, H.O.; Labeed, F.H. Microfluidics in Detection Science; Royal Society of Chemistry: London, UK, 2014. Jomeh, S.; Hoorfar, M. Numerical modeling of mass transport in microfluidic biomolecule-capturing devices equipped with reactive surfaces. Chem. Eng. J. 2010, 165, 668–677. [CrossRef] Singh, H.; Morita, T.; Suzuki, Y.; Shimojima, M.; Van, A.L.; Sugamata, M.; Yang, M. High sensitivity, high surface area Enzyme-linked Immunosorbent Assay (ELISA). Biomed. Mater. Eng. 2015, 26, 115–127. [CrossRef] [PubMed] Suzuki, Y.; Morioka, K.; Shimizu, T.; Nakajima, H.; Uchiyama, K.; Yang, M. Influence of structural dimensions of micro-pillar array in reaction field on sensitivity of Enzyme-linked Immunosorbent Assay (ELISA). Biotechnol. Biotechnol. Equip. 2017. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).