Measurement of Molecular Diffusion Based onOptoelectrofluidic Fluorescence Microscopy

Hyundoo Hwang and Je-Kyun Park*

Department of Bio and Brain Engineering, College of Life Science and Bioengineering, KAIST, 335 Gwanhangno,Yuseong-gu, Daejeon 305-701, Republic of Korea

This technical note reports a method for measuring thediffusion coefficient of molecules based on an optoelec-trofluidic platform. Optoelectrofluidic fluorescence mi-croscopy, which is constructed with an optoelectrofluidicdevice and a conventional fluorescence microscope, is auseful tool for controlling and detecting local molecularconcentration in a fluid with a single light source. Whenwe project a light for fluorescence excitation and applyan ac signal of a few hundred Hertz frequency around 100Hz to the optoelectrofluidic device, a sudden decay ofmolecular concentration occurs within the illuminatedarea due to several mechanisms, including opticallyinduced ac electroosmosis, electrostatic interaction forcesamong the polarized molecules, and interactions amongthe molecules and between the molecules and the electricdouble layer. After the applied voltage was turned off, thedispersed molecules diffuse into the molecular depletionarea and the fluorescence signal is recovered. On thebasis of these phenomena, we successfully measured thediffusion coefficient of various dextran molecules. Astatistical analysis to determine the significance of ourexperimental values compared to the previously reportedvalues measured using fluorescence recovery after pho-tobleaching technology was also performed. This newtechnique demonstrates the first analytical measurementof diffusion based on the optoelectrofluidic platform andcan be a useful tool for measuring the mobility of mol-ecules in a simple and easy way.

Diffusion, which is the random motion of molecules that arisesfrom thermal energy transferred by molecular collisions, plays akey role in the transport of molecules in biological systems. Oneof the most widely used methods to measure the moleculardiffusion is fluorescence recovery after photobleaching (FRAP).1

In this technique, the recovery of fluorescence is monitored toestimate the diffusion coefficient of the molecules after bleachingof fluorophore-labeled molecules with a high-intensity laser beam.FRAP is a simple and powerful technology applicable for both invivo and in vitro and has been extensively investigated fromexperimental and theoretical points of view during several

decades.2-4 However, it always requires expensive and compli-cated microscope equipped with a high-intensity laser source forphotobleaching of fluorophores. In addition, high-speed imageacquisition technique should be accompanied for accurate mea-surements of fast diffusing molecules.

The microfluidic methods based on a capillary electrophoresischip without photobleaching have also been reported.5,6 In thosemethods, the fluorescence peak variance of migrated moleculeswas measured after their longitudinal diffusion for a certain timein an electric field. However, some significant problems such asadsorption of molecules onto the channel wall, Joule heating, andelectrodispersion were frequently contributed. In addition, a highvoltage source, miscellaneous fluidic components, and complicatedoptical components are always required. Here we suggest a newmethod based on optoelectrofluidics to easily measure themolecular diffusion in solution using a conventional fluorescencemicroscope without photobleaching, high power sources, andcomplicated components.

Optoelectrofluidics, which is also called optically inducedelectrokinetics, is based on the electrokinetic motion of particlesor fluid under an electric field induced by light. With the use ofoptically induced electrokinetic mechanisms, an image-basedmanipulation of several biological materials, including blood cells,7

oocytes,8 swimming bacteria,9 as well as separation10 and as-sembly11 of colloidal particles, has been demonstrated. Recently,dynamic control of local chemical concentration in a molecularsolution has been demonstrated by several frequency-dependentoptoelectrofluidic phenomena such as optically induced ac elec-troosmosis (ACEO), dielectrophoresis (DEP), and electrostaticinteraction forces.12 However, the optoelectrofluidic platforms havebeen applied only to manipulate various objects. Any analytical

* To whom correspondence should be addressed. E-mail: jekyun@kaist.ac.kr.Phone: +82-42-350-4315. Fax: +82-42-350-4310.

(1) Axelrod, D.; Koppel, D. E.; Schlessinger, J.; Elson, E.; Webb, W. W. Biophys.J. 1976, 16, 1055–1069.

(2) Gribbon, P.; Hardingham, T. E. Biophys. J. 1998, 75, 1032–1039.(3) Braga, J.; Desterro, J. M. P.; Carmo-Fonseca, M. Mol. Biol. Cell 2004, 15,

4749–4760.(4) Schnell, E. A.; Eikenes, L.; Tufto, I.; Erickson, A.; Juthajan, A.; Lindgren,

M.; Davies, C. d. L. J. Biomed. Opt. 2008, 13, 064037.(5) Yao, Y. J.; Li, S. F. Y. J. Chromatogr. Sci. 1994, 32, 117–120.(6) Culbertson, C. T.; Jacobson, S. C.; Ramsey, J. M. Talanta 2002, 56, 365–

373.(7) Hwang, H.; Choi, Y.-J.; Choi, W.; Kim, S.-H.; Jang, J.; Park, J.-K. Electro-

phoresis 2008, 29, 1203–1212.(8) Hwang, H.; Lee, D.-H.; Choi, W.; Park, J.-K. Biomicrofluidics 2009, 3,

014103.(9) Choi, W.; Nam, S.-W.; Hwang, H.; Park, S.; Park, J.-K. Appl. Phys. Lett. 2008,

93, 143901.(10) Hwang, H.; Park, J.-K. Lab Chip 2009, 9, 199–206.(11) Hwang, H.; Park, Y.-H.; Park, J.-K. Langmuir 2009, 25, 6010–6014.(12) Hwang, H.; Park, J.-K. Anal. Chem. 2009, 81, 5865–5870.

Anal. Chem. 2009, 81, 9163–9167

10.1021/ac9021709 CCC: $40.75 2009 American Chemical Society 9163Analytical Chemistry, Vol. 81, No. 21, November 1, 2009Published on Web 10/12/2009

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applications in biological and chemical sciences have never beendemonstrated on the basis of the optoelectrofluidic platform.

In this technical note, we demonstrate a new method tomeasure molecular diffusion using an optoelectrofluidic platformintegrated with a conventional fluorescence microscope, calledoptoelectrofluidic fluorescence microscopy (OFM). With the useof our system, diffusion coefficients of various dextran moleculeshave been determined. The t test was also performed fordetermining the significance of our experimental values incomparison with the previously reported values measured usingFRAP technology.

EXPERIMENTAL SECTIONFor the measurement of the molecular diffusion coefficient,

fluorescein isothiocyanate (FITC)-labeled dextran molecules ofsize 10, 40, and 500 kDa (Sigma-Aldrich, Milwaukee, WI) werepurchased. These molecules were diluted with deionized waterinto a concentration of 100 µM.

To fabricate a conventional optoelectrofluidic device, a 50 nm-thick heavily doped hydrogenated amorphous silicon (a-Si:H), an1 µm-thick intrinsic a-Si:H, and a 20 nm-thick silicon nitride weredeposited sequentially on a glass substrate coated with indiumtin oxide (ITO) (Samsung-Corning Precision Glass, Korea) bythe plasma enhanced chemical vapor deposition (PECVD) method.A 500 nL sample droplet was sandwiched between the bareITO-glass substrate and the a-Si:H-deposited substrate with aregular gap height of 30 µm, and a wrapping wire was connectedfor applying voltage. The detailed fabrication processes of thedevice are explained in the previous study.7

The optoelectrofluidic device containing a sample solution wasput on the stage of a conventional fluorescence microscope(BA400T; Martin Microscope Company, SC). A fluorescenceexcitation light was projected onto the optoelectrofluidic devicethrough an iris diaphragm for controlling the diameter of the lightpattern. At the same time, an ac voltage of 10 Vpp at 100 Hzfrequency was applied across the sample solution. The fluo-rescence signal from the sample solution was detected by acharge-coupled device (CCD) camera (DS-U2; Nikon Instru-ments Inc., NY) and analyzed with a conventional imageanalysis program (NIS-Elements; Nikon Instruments Inc.).

Calculation of the mathematical model and fitting of experi-mental results to the theoretical curve based on the model wereperformed using Matlab 7.0 (The MathWorks Inc., MA) andOrigin 7.0 (OriginLab Corp., MA). The statistical analysis suchas two-sample t tests was performed and all the curves wereplotted using Origin 7.0. The t tests were performed using thesignificance criterion of p e 0.05.

RESULTS AND DISCUSSIONA schematic diagram of the OFM system is shown in Figure

1. When a light for the fluorescence excitation was projected ontothe photoconductive surface of the optoelectrofluidic device, theelectric current resistance of the partially illuminated area wassignificantly decreased. As a result, a nonuniform electric field,which induces electrokinetic motions of the fluid and electrostaticinteractions among the molecules, was formed in the molecularsample solution. At the same time, we could detect the fluores-cence signal from the molecules, which allows us to determinethe amount of fluorophore-labeled molecules.12

With application of an ac voltage, the ACEO flow, which isconverged into the illuminated area with a slip velocity (vslip)defined as

⟨vslip⟩ )λDRe[σqEt*]

2η(1)

where λD is the Debye length, η is the fluid viscosity, and σq isthe charges contained in the electric double layer, whichoccurred due to the optically induced tangential electric field,Et.10,11 In addition, several mechanisms, including DEP andelectrostatic interactions between the polarized molecules, couldalso be involved in the molecular behaviors from which the localmolecular concentration is resulted. Consequently, a rapid andsignificant change of molecular concentration in the illuminatedarea could be observed as reported in the previous study.12

When an ac voltage of 10 Vpp at 100 Hz frequency was appliedto the optoelectrofluidic device, the molecules in the illuminatedarea were suddenly dispersed and disappeared from the area,resulting in a sudden decay of fluorescence signal as shownin parts A and B of Figure 2. The decay rate of the fluorescencesignal was increased and saturated as the applied voltage increasedto 10 Vpp without generation of gas bubbles by the electrolysisof the media. The 100 Hz frequency was an optimal conditionat which the fluorescence decay effectively occurred and theeffect of the electrophoretic motion of the charged moleculescould be negligible. The time for application of the voltage wasalso adjusted within 3 s, since it increased the size of themolecular depletion area (MDA). In addition, if the chemicalconcentration of the molecular solution was too high, we couldnot clearly observe the optoelectrofluidic molecular depletion.It might be due to a relatively high concentration of moleculesmoving along the ACEO flows within the MDA and strongelectrostatic forces among the polarized molecules over theACEO flows by small intermolecular distances.

The fluorescence intensity profile, after turning off the appliedvoltage and opening the iris diaphragm, was measured as shownin Figure 2C. Although the origin for this decrement of molecularconcentration at the low-frequency range was still not completelydetermined, in the opinion of many researchers, it might be due

Figure 1. Schematics of optoelectrofluidic fluorescence microscopyfor measurement of molecular diffusion based on the optoelectrofluidicmolecular depletion.

9164 Analytical Chemistry, Vol. 81, No. 21, November 1, 2009

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to the combination of optically induced ACEO, electrostatic inter-molecular forces, and interactions between the molecules and theelectric double layer.12-14 In the case of the optically inducedACEO and the electrostatic interactions among the polarizedmolecules, they concentrate the molecules into the illuminatedarea in the frequency range from about 1 kHz to about 100 kHz.12

In the low-frequency range around 100 Hz, however, an acelectroosmotic flow based on a nonzero lateral component ofelectric field within the electric double layer becomes significant15

and the molecular polarization properties might be changed,14

resulting in some different aspects such as molecular dispersionthat can be shown. In addition, the frequency-dependent formationof the electric double layer can also be involved in the suddendispersion of molecules in the low-frequency ac electric field.13

Further experimental and theoretical investigations should befollowed for understanding this phenomenon more completely.Nevertheless, the obvious fact is that the photobleaching of

fluorophores has never been observed in our experimentalconditions. When we projected a light with and without a voltageof high-frequency above 1 kHz for a long time, about 1 h, therewas not much change of the fluorescence signal in both cases.

After turning off the applied voltage, we could determine thatthe molecules, which dispersed out from the illuminated area,diffused into the empty space again, recovering the fluorescenceintensity of the area (Figure 3). The recovery rate was inverselyproportional to the molecular weight of FITC-dextran. In general,the diffusion coefficient of molecules decreased as the molecularweight increased. That is, the molecular recovery into theilluminated area due to the diffusion transport was faster as thediffusion coefficient of molecules increases. Therefore, we canestimate the molecular diffusion coefficient based on the measure-ment of fluorescence recovery after optoelectrofluidic moleculardepletion.

The MDA, which is a molecule-less space formed by theoptoelectrofluidic molecular depletion, could be simply modeledas a cylinder of radius R, which is the same as the radius ofprojected light fixed by an iris diaphragm. At the initial state(t ) 0), when the time the voltage turned off, the concentrationwithin and outside the illuminated area was assumed to be uniformat C0 and C1, respectively. The partial differential equation forthe molecular diffusion is

∂C*∂t*

) 1r*

∂

∂r*(r*∂C*∂r* ) (2)

where C* ) (Ci s C0)/(C1 s C0), r* ) r/R, and t* ) tD/R2 arethe dimensionless form of the molecular concentration, theradial coordinate, and the time, respectively. Here D is thediffusion coefficient of molecules. The boundary conditionsare ∂C*/∂r* ) 0 at r* ) 0 and C* ) 1 at r* ) 1 for all t. Thesolution of eq 2 is

C* ) 1 - 2 ∑n)1

∞ J0(Rnr*)RnJ1(Rn)

exp(-Rn2t*) (3)

where Jn(x) is the Bessel function of the first kind of order n,and J0(Rn) ) 0. The temporal and spatial change of thefluorescence intensity profile, which means the molecularconcentration, within the MDA could be calculated based oneq 3 as shown in Figure 4A. In this calculation, the diffusioncoefficient of the target molecules and the light radius wereassumed to be D ) 46.1 × 10-8 cm2/s, which is our experimentalvalue for 40 kDa FITC-dextran, and R ) 55 µm, which is ourexperimental condition, respectively.

(13) Wong, P. K.; Chen, C.-Y.; Wang, T.-H.; Ho, C.-M. Anal. Chem. 2004, 76,6908–6914.

(14) Du, J.-R.; Juang, Y.-J.; Wu, J.-T.; Wei, H.-H. Biomicrofluidics 2008, 2, 044103.(15) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Langmuir 2006, 22, 9846–9852.

Figure 2. (A) Microscopic pictures and (B) fluorescence intensitybefore and after applying a voltage of 10 Vpp at 100 Hz for 40 kDaFITC-dextran in solution. (C) Fluorescence intensity profile on the linea-b in panel A. The molecules in the illuminated area were rapidlydispersed out and depleted by optoelectrofluidics.

Figure 3. Microscopic pictures showing the recovery of 40 kDa FITC-dextran molecules by diffusion as soon as the voltage turned off.

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In this study, we experimentally measured the temporal changeof normalized fluorescence intensity at the center of MDA andcompared with the mathematical model to estimate the diffusioncoefficient of molecules. The temporal change of C* at the centerof MDA could be described by eq 3 with r* ) 0 condition asshown in Figure 4B. As our estimation, the molecular recoveryrate was proportional to the diffusion coefficient of molecules. Herethe initial profile of the fluorescence intensity in the real experi-ment was not completely the same as that in the mathematicalmodel (see Figure 2C). Therefore, a calibration process to adjustthe initial condition of C* within the illuminated area wasperformed before fitting the experimental results with the curvesin Figure 4B.

According to the theoretical model, the precision of measure-ment would become worse in this experimental condition, where

the radius of MDA was fixed as 55 µm as the diffusion coefficientof the target molecules becomes larger than about 100 × 10-8

cm2/s. However, the operation range can be tuned by adjustingthe dimension of the illuminated area or the time for voltageapplication, which affects the size of MDA. As the radius ofMDA, R, increases, the rate for the temporal change of C*would be slower as shown in Figure 4C. We determined thesephenomena through experiments with various conditions.

On the basis of this approach, the diffusion coefficient ofdifferent-sized molecules could be measured by analyzing thechange of fluorescence signal by diffusion transport. We measuredthe temporal change of C* using 10, 40, and 500 kDa FITC-dextransolution and fitted with the theoretical model. The measureddiffusion coefficients of 10, 40, and 500 kDa FITC-dextran were125.1 ± 7.1, 46.1 ± 2.9, and 22.5 ± 1.7 × 10-8 cm2/s, respectively.Figure 5A shows the measured values from an experiment foreach FITC-dextran, which is well matched with the curves fromthe theoretical model. In addition, we also determined the effectof R, which is the radius of MDA, as shown in Figure 5B. As theradius of MDA increased, the rate for fluorescence recovery atthe center of the area decreased. The measured diffusion coef-ficient was still well matched with the theoretical model. There-fore, we could obtain more precise values in the case of high-mobility molecules by increasing the size of MDA to increase themeasurement resolution.

Table 1 shows our experimental diffusion coefficients com-pared to the literature and theoretical values. The diffusioncoefficients reported in previous literature were measured basedon FRAP techniques. The measured values showed good agree-

Figure 4. (A) Calculated molecular concentration profile within themolecular depletion area (MDA) as soon as the voltage turned off.D ) 46.1 × 10-8 cm2/s and R ) 55 µm. Temporal change of calculatedmolecular concentration (C*) at the center of MDA (r* ) 0) according to(B) the diffusion coefficient of molecules when R ) 55 µm and (C) theradius of the light pattern when D ) 46.1 × 10-8 cm2/s.

Figure 5. Temporal change of the normalized concentration of FITC-dextran in solution against the (A) molecular weight and (B) radiusof the molecular depletion area (MDA). The fitting curves based onthe theoretical model were also plotted.

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ment with the previously reported values. According to a signifi-cance test, the p values of 10, 40, and 500 kDa FITC-dextran were0.38, 0.81, and 0.97, respectively. Since all the probabilities weremuch greater than 0.05, our method for the measurement of themolecular diffusion coefficient based on the OFM allows us tomeasure the mobility of molecules in solution, significant to theresults in previous literature measured by FRAP techniques.

The theoretical diffusion coefficient against the molecularweight could be estimated based on the Stokes-Einstein equation,

D ) kT6πηRh

(4)

where Rh, k, and T are the hydrodynamic radius, the Boltzmannconstant, and the absolute temperature, respectively. Here thehydrodynamic radii of 10, 40, 500 kDa FITC-dextran were about2.3, 4.6, and 16 nm, respectively.16-18 According to the experi-mental results, the experimental values for 10, 40, and 500 kDa

FITC-dextran molecules were larger than the theoretical values.This might be due to the hydrodynamic radii used for calculatingthe theoretical diffusion coefficient, which have various values aswell as do not completely reflect the real values.

CONCLUSIONSIn this technical note, we applied an optoelectrofluidic platform

called OFM to measure the molecular diffusion coefficient. Wecould successfully measure the diffusion coefficient of FITC-dextran molecules in solution based on the fluorescence recoveryafter the optoelectrofluidic local molecular depletion. We con-structed a simple mathematical model to explain the temporalchange of molecular distribution and exploited it to estimate thediffusion coefficient. The diffusion coefficient of 10, 40, and 500kDa FITC-dextran measured using the OFM were 125.1 ± 7.1,46.1 ± 2.9, and 22.5 ± 1.7 × 10-8 cm2/s, respectively. Theseexperimental values were significant to the previously reportedvalues measured by FRAP techniques and the theoretical valuescalculated from the Stokes-Einstein equation. This is the firstdemonstration of diffusion measurement based on optoelec-trofluidics, which has been applied for a practical applicationin analytical science. This new method will provide a simpleand easy way to determine the molecular mobility in solutionbased on optoelectrofluidics.

ACKNOWLEDGMENTSupport for this work from the Nano/Bio Science and Tech-

nology Program (Grant 2008-00771) and the National ResearchLaboratory (NRL) Program (Grant R0A-2008-000-20109-0) fundedby the Korean government (MEST) is gratefully acknowledged.The authors also thank the Chung Moon Soul Center forBioInformation and BioElectronics at KAIST and the TFT-LCDResearch Center at Kyung Hee University, Korea.

Received for review June 20, 2009. Accepted September30, 2009.

AC9021709

(16) Lang, I.; Scholz, M.; Peters, R. J. Cell Biol. 1986, 102, 1183–1190.(17) Armstrong, J. K.; Wenby, R. B.; Meiselman, H. J.; Fisher, T. C. Biophys. J.

2004, 87, 4259–4270.(18) Sandoval, C. M.; Salzameda, B.; Reys, K.; Williams, T.; Hohman, V. S.;

Plesniak, L. A. FEBS Lett. 2007, 581, 5464–5468.(19) Tanford, C. Physical Chemistry of Macromolecules; Wiley: New York, 1961.

Table 1. Diffusion Coefficients for Different-SizedFITC-Dextran Molecules in Solutiona

molecularweight (kDa)

Dexp(× 10-8 cm2/s)

Dlit(× 10-8 cm2/s)

Dtheo(× 10-8 cm2/s)

10 125.1 ± 7.1 75.7 ± 2516 93.113319

40 46.1 ± 2.9 51.5 ± 2.33 44.845.0 ± 1.64

46.3 ± 4.616

500 22.5 ± 1.7 22.02 13.523.2 ± 1.13

22.4 ± 2.64

a Experimental data are compared to literature and theoreticalvalues.

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