Journal of the Korean Physical Society, Vol. 59, No. 4, October 2011, pp. 2847∼2854

Single Molecule Tracking of a Semiflexible Polyelectrolyte Chain in SolventUnder Uniform Electroosmotic Flows

Sunghun Choung and Myung-Suk Chun∗

Complex Fluids Laboratory, National Agenda Research Division,Korea Institute of Science and Technology (KIST), Seoul 136-791, Korea

Chongyoup Kim

Department of Chemical and Biological Engineering, Korea University, Seoul 136-713, Korea

(Received 13 June 2011, in final form 16 August 2011)

Direct single molecule tracking of a polyelectrolyte chain by using fluorescence microscopy hasallowed both the assumptions and the predictions of relevant theories to be tested. The center-of-mass displacement is determined as a function of the time that elapses between images, where theradius of gyration can be estimated from a first moment of the image distribution. The translationalself-diffusion for the molecule is an ensemble property of the mean square displacement (MSD) withlag time in each trajectory. Experimentally viable two-dimensional imaging of semiflexible poly-electrolyte was performed on a fluorescein-labeled xanthan chain in electroosmosis-driven uniformflow fields. The radius of gyration was almost constant under variations of the electroosmotic flowvelocity determined by an externally applied electric field. We try to develop a correction of theMSD in flow field, taking into account the velocity fluctuations. Its advantage allows acquiringthe linear fit for the MSD vs lag time, for a good estimate of the translational diffusion. Increas-ing behavior of the diffusion with increasing fluid velocity ensures a quadratic equation fit, whichshould connect with the convective effect. Our results exhibit a screening effect such that strongscreening caused by a high ionic concentration leads to higher diffusion due to the compact chainconformation. Considering the uniform flow serves as a basis for understanding the behavior ofindividual polyelectrolyte chains under controlled fluidic flow in confined spaces.

PACS numbers: 87.15.Vv, 83.50.Ha, 82.35.Rs, 87.15.HeKeywords: Single molecule tracking, Polyelectrolyte, Chain conformation, Translational diffusion, Uniformflow, RheologyDOI: 10.3938/jkps.59.2847

I. INTRODUCTION

For many decades, polymer dynamics was experimen-tally studied by using indirect methods such as bulk rhe-ology, light scattering, and birefringence. Single moleculetracking, developed within the last 20 years, uses fluo-rescence microscopy, which permits a passive visualiza-tion of the position, conformation, and motion of sin-gle molecules. Investigation of single molecule propertiesand dynamics provides not only the average values of ob-servables for ensembles of molecules but also reveals thecharacteristics of individual molecules with precision atthe submicron level [1–3]. In particular, the conforma-tional dynamics of a single molecule in confined spaces ofmicro/nanofluidic channels has attracted increasing at-tention because it is important in many biophysical ap-

∗E-mail: mschun@kist.re.kr; Tel: 82-2-958-5363; Fax: 82-2-958-5205

plications, for instance, DNA separation, gene delivery,and gene mapping by using lab-on-chips [4–6]. Theseapplications require controlled manipulations subject tostretching, condensing, moving, and packing of individ-ual molecules.

A polyelectrolyte, a kind of complex fluid, representsan interesting and broad class of soft matter that shouldbe considered as an additional complication arising fromthe Debye screening of the long-range electrostatic inter-action by ions [7]. These characteristics prevent directapplication of many reliable theories developed for neu-tral polymers, although polyelectrolytes have stimulatedinterest from a fundamental, as well as from a technologi-cal, point of view due to their fascinating conformationalchanges even in an aqueous medium that is a poor sol-vent for most synthetic polymers. It is usually necessaryto consider more system-specific aspects represented bythe surface charge, relaxation, and the condensation ofcounterions and salt ions. A precise understanding ofcharged soft matter has received great attention in life

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science and molecular biology because polyelectrolytesinclude many proteins and other biopolymers, such asDNA, polysaccharides, and microtubules [8].

Properties of a semiflexible or wormlike polyelectrolytechain in solvent have been investigated by employing ei-ther computations or experiments. The model polyelec-trolytes in the previous studies were almost always con-fined to a DNA molecule with a contour length of aboveseveral micrometers. Mesoscale simulations were per-formed by using the Brownian dynamics (BD) methodwith a hydrodynamic interaction (HI), where the sol-vent was treated as a continuum, while the molecule wasusually represented by a coarse-grained model, such asa bead-spring chain [9]. Many studies have contributedto an understanding of how a single polyelectrolyte chainbehaves when exists in either unbounded bulk [10] or con-fined spaces [11–14]. As a study of the submicron sizedpolyelectrolyte chain, which had not been attempted tillthen, Jeon and Chun [15] developed coarse-grained mod-els of polysaccharide xanthan in bulk solution as well asunder confinement, taking into account both HIs andelectrostatic interactions between pairs of beads. Subse-quently, Chun et al. [16] explored experimental verifica-tions on changes in the conformation and translationaldiffusion, by comparing the results obtained by BD sim-ulations and single molecule tracking. It revealed thattheir BD simulations successfully represented the prop-erties of a single xanthan chain, discussing in-depth theexperimental restrictions.

Note that, despite the many practical applicationshave yielded, a complete theoretical explanation under-lying polymer physics and micro-rheology has not beendeveloped. Thus, a final goal of the present study is toprovide a connection between the microscopic and themacroscopic properties of a single polyelectrolyte chain.We examine the conformation and translational diffusionof a single xanthan chain under an external flow field,which can serve as an extended experimental work forfurther understanding the behavior of submicron sizedsemiflexible or wormlike polyelectrolyte chains in solvent.In view of the initial stage, we consider here the uniformflow driven by an electric field, so-called the electroos-motic flow (EOF).

II. SINGLE MOLECULE TRACKING

1. Epi-fluorescence Microscopy

Recently, observations at the level of individual atomsand molecules have become possible with microscopy andspectroscopy. Imaging of a single fluorescence moleculehas been achieved to find non-uniform molecule distribu-tion and hidden mechanism from the averaging process.The direct observation of molecular motion by using epi-fluorescence microscopy has some essential advantages inaccessing single molecule trajectories, which cannot be

Fig. 1. (Color online) Schematic of inverted epi-fluorescence microscopy utilized in single molecule imagingof xanthan.

realized in conventional methods [16]. Single moleculeimaging has some challenges. First, optical imaging sys-tems have an inherent limitation on their spatial resolu-tion due to the diffraction of light. The resolution R ofan optical microscope is defined as the shortest distancebetween two points on a specimen that can still be dis-tinguished by the observer or camera system as separateentities. Shorter wavelengths λ and higher numericalaperture (NA) number yields higher resolution, becauseR = λ/NA. Second, real-time imaging of fast changeablephenomena is difficult to detect due to the limitation onthe temporal resolution. The speed at which one com-plete image is acquired determines the temporal resolu-tion of camera, combining with readout speed and thetime of signal integration.

In this study, fluorescein-labeled xanthan moleculesin a microfluidic channel were monitored using an in-verted epi-fluorescence microscope (Nikon, Eclipse Ti-E,Japan) with a 100× [NA of 1.3, resolution of 0.2 µm,focal depth of 0.41 µm, working distance of 200 µm]oil immersed objective, as depicted in Fig. 1. Withthe excitation filter, only 450 ∼ 500 nm wavelengthsfrom the mercury laser can pass through the fluorophore.The emitted light, wavelength of 520 nm or above, canpass through both the dichroic mirror and the emissionfilters. Images were taken by a digital 12-bit charge-

Single Molecule Tracking of a Semiflexible Polyelectrolyte Chain · · · – Sunghun Choung et al. -2849-

coupled device (CCD) camera (Nikon, Digital Sight DS-Qi1, monochrome cooled, Japan). The exposure timeof the CCD camera was set in the range of 4 – 20 ms,recording 1280 × 1024 (for 1 × 1 binning) and 640 ×480 (for 2 × 2 binning) pixels. Under 100× magnifi-cations, images were recorded at 10 frames per second(fps), in which each image pixel corresponds to 91 nm.The use of 40× magnification was able to improve theframe rate up to 32 fps, but the resolution of the imagepixel was reduced (i.e., 450 nm). The data acquisitionwas performed using the NIS-Elements software.

2. Uniform Flow Driven by an Electric Field:EOF

Due to the fixed surface charge at the solid interface,an oppositely charged region of counterions develops inthe liquid to maintain the electroneutrality of the solid-liquid interface. This screening region is called an electricdouble layer (EDL), which is divided into two parts: aninner layer (namely, the Stern layer) and an outer diffu-sive layer. The EDL thickness increases with decreasingelectrolyte concentration. As the surface is negativelycharged, the viscous interaction between net excess ofpositive ions in the EDL and the liquid causes flow to-ward the cathode along the channel. The liquid velocityis zero at the wall and increases to a maximum value withthe EOF velocity at some distance from the wall, afterwhich it remains constant as a plug type. When theEDL thickness decreases, the flow rate dependence onthe zeta potential becomes more linear. In the thin EDLlimit, one obtains a straight line in accordance with theHelmholtz-Smoluchowski (H-S) equation for the EOF ve-locity inside a channel of arbitrary shape [17]:

VEOF = −εζEx

η. (1)

Here, Ex is the applied electric field (voltage per unitlength) in the x direction, η the viscosity of fluid, ζ thezeta potential, and the dielectric constant ε (= ε0εr) isdefined as dielectric constant at vacuum ε0 and relativepermittivity εr.

In order to have xanthan molecule be injected into andmoved with uniform flow fields in the microchannel, weused a high-voltage power supply (HVS448, LabSmith,CA) capable of providing from 0 to 3 kV. Channel reser-voirs were connected to the electrodes as Ag wire. Toprovide the microchannel, a microfluidic chip was fabri-cated by O2 plasma bonding with a 1-mm thick PDMS(polydimethylsiloxane) replica and 100-µm thick slideglass (Marienfeld, Germany). Chip fabrication proce-dures were general and similar to those in the literature.The straight channel had dimension of 3-cm long, 250-µm wide, and 50-µm deep so that the channel volume of0.375 µl was large enough not to be disturbed by temper-

ature rise during the course of each experiment, whichspanned less than 30 sec.

3. Model Polyelectrolyte Xanthan

Xanthan, a polyelectrolyte, is an extracellular polysac-charide produced by bacterium. Its primary structureconsists of a main chain with charged trisaccharidesidechains on every second residue and the side chain.Its secondary structure is known to undergo an order→ disorder (i.e., helix → coil) transition, depending onconditions of temperature and salinity. Native xanthanis generally believed to be in a double strand [18,19]. Forlow ionic strength at room temperature (RT, i.e., 25 ◦C),the extension of xanthan and the corresponding increasein the solution viscosity are likely to involve a transitionof the secondary structure from a double strand to a dis-ordered form with lower strandedness. This denaturedxanthan can undergo a transition from the double to thesingle helical state when sufficient salt is present. Xan-than can also be ordered if it is gradually cooled afterheating.

The powdered xanthan was purchased from SigmaChemical Co. (St. Louis, MO). Following the proceduredescribed in detail in a previous study, native xanthanwas tagged by attaching 5-amino fluorescein to the car-boxyl groups of the side chain, which was first outlined byHolzwarth [20]. After purifications, fluorescein-labeledxanthan was stored in a refrigerator before being usedwith a sufficiently dilute concentration in the range from0.1 to 1 ppm. The degree of fluorescein labeling wasfound to be 0.5 ∼ 1.0 wt%, as determined by UV-Visibleabsorption spectrophotometry (S-3100, Scinco, Seoul).When the polyelectrolytes are dissociated in aqueous so-lutions, the chain is extended or coiled due to the elec-trostatic repulsion between monomers. Adding the saltresults in the polyelectrolyte chain being screened by op-positely charged salt ions.

The shear viscosity was measured at different xan-than concentrations ranging from 50 to 1000 ppm at 0.1-mM NaCl using a rheometer (AR2000ex with bob andcup fixtures, TA Instrument, DE). Figure 2 shows thetypical non-Newtonian character of the pseudoplasticity.Here, shear thinning behaviors over a wider shear rateare known to be described by the Carreau A constitutivemodel [21,22]:

η(γ) =η0[

1 + (λT γ)2](1−n)/2

, (2)

where η0 is the zero-shear-rate viscosity, γ the shear rate,λT the empirical time constant, and n is the power-lawexponent. It possesses two asymptotes: the xanthan so-lution shows a constant viscosity of η0 (Newtonian re-gion) as γ → 0; on the other hand, the viscosity decreaseslinearly in a log-log plot (shear thinning region) as γ →

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Fig. 2. Viscosity as a function of shear rate and xanthanconcentration at RT, where dotted curves indicate fitting re-sults.

∞. From the best fit of each data for different xanthanconcentrations C up to 1000 ppm, the parameters in Eq.(2), η0, λT , and n can be empirically expressed as a func-tion of C in percent by weight:

η0 = −1.67× 10−2 +(1.65× 10−2

)exp(25.37C), (3)

λT = 4.01× 10−1 + 10.88C +(2.21× 102

)C2, (4)

n = 9.28× 10−1 − 1.29C4.83×10−1. (5)

III. RESULTS

1. Correct Analysis of Image Tracking

Various distinction of the real image of fluorescein-labeled xanthan (Fig. 3(a)) can be analyzed using theimage processing algorithm based on Crocker and Grier’sInteractive Data Language (IDL) code (RSI, Boulder,CO) [23]. At first, each pixel intensity of the real imagewas obtained (Fig. 3(b)) by suitable IDL-based software(MatLab Particle Tracking Code provided by D. Blairand E. Dufresne). Pixel images were spatially filtered.Then, white noises could be minimized, and unneces-sary blobs could be removed in the image (Figs. 3(c)and 3(d)). The next step should be to identify the blobslocating all peaks that are above a given threshold valueand can estimate the brightest feature. According tothe post-processor developed in our laboratory, the to-tal intensity, the center-of-mass, and the radius of gyra-tion were finally computed. Note that determining theboundary of the pixel intensity of images was guaranteedby accomplishing the same procedure with latex spheresof 1-µm in diameter.

Fig. 3. (Color online) (a) Fluorescence image of nativexanthan at 10−4 mM KCl solution, (b) pixel intensity of thefluorescence image, (c) pixel intensity after subtracting thenoise, and (d) its 3D plots.

The zeroth moment accounts for the total intensityI(t) of a single molecule, which can be calculated fromthe intensity distribution function I(r,t) of a pixel witha set of coordinates r [24,25]:

I(t) =∫

I(r, t)dr ∼=∑p,q

Ipq(t). (6)

We assumed that the fluorescent label was uniformly dis-tributed within a molecule and that the camera gain wasa linear function of the fluorescent signal with an inten-sity Ipq for the pixel {p,q}. The first moment of theintensity distribution denotes the position of the center-of-mass:

RCM(t) =1

I(t)

∫rI(r, t)dr ∼=

1I(t)

∑p,q

Ipq(t)rpq(t). (7)

The second moment determines the radius of gyrationtensor [26]:

Gij(t) =1

I(t)

∫(ri−RCM,i)(rj−RCM,j)I(r, t)dr. (8)

Single Molecule Tracking of a Semiflexible Polyelectrolyte Chain · · · – Sunghun Choung et al. -2851-

Fig. 4. (a) Time evolution of the total intensity of xanthanmolecules under an electric field of 100 V/cm in 10−4 mM KClsolution, (b) probability distribution of the radius of gyrationfor one subset with an average RG of 386 nm, and (c) dis-tribution of the displacement length for one subset with anaverage value of 2 µm.

For x and y directions, Eq. (8) is expressed as

Gxy(t) ∼=1

I(t)

∑{[rpq,x(t)−RCM,x(t)]

× [rpq,y(t)−RCM,y(t)] Ipq(t)} . (9)

Then, note that the common radius of gyration can beobtained as R2

G(t) = trace(Gij). The RG of a trajectorydescribes the amount of space that the molecule exploresduring its movement.

As the instantaneous evolution of each moment,Fig. 4(a) shows that the zeroth moment giving I(t) ofa single xanthan molecule appears to be almost con-stant over time with small fluctuations. Once photo-bleaching begins, the intensity of fluorescence emissionmay decay over the observation time. As displayed inFigs. 4(b) and 4(c), both the radius of gyration and thedisplacement length follow Gaussian distributions. Inthis, the displacement direction in each step is a randomprocess exhibiting Brownian motion. Figure 5 showsan illustrative example for trajectories of the center-of-mass in streamwise (x) and transverse (y) directions un-der electroosmosis-driven uniform flows. We recognizethat y-displacements are really small compared to x-displacements and that most of the displacements haveapproximately the same length.

For an in-depth interpretation, the molecular trajec-tories in the x and y directions were plotted as a func-tion of time, as shown in Fig. 6(a). The linear increasein the x directional displacement over time indicates awell-defined average EOF velocity. A net velocity is ob-served in the y direction. The x and the y components

Fig. 5. Center-of-mass trajectories for different EOF ve-locities in 10−4 mM KCl. Filled circles and triangles indicatethe start and the stop positions, respectively.

Fig. 6. (Color online) (a) Xanthan molecular trajectoriesalong the streamwise (x) and the transverse (y) directionsas a function of time, and (b) x and y components of theinstantaneous molecular velocity in time.

of the instantaneous molecular velocity are provided inFig. 6(b) as a function of time. The y-directional dis-placements are independent of the applied EOF velocityand reflect thermal Brownian diffusion alone.

A diffusive motion of the Brownian particle isparametrized by its translational self-diffusion coefficientthrough the Einstein-Smoluchowsky relation within theframework of Kirkwood theory in Cartesian coordinates[26]:

DT,β = limδt→∞

12δt

⟨[RCM,β(t)−RCM,β(t− δt)]2

⟩for β = x, y, z. (10)

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Fig. 7. (a) MSDs of the center-of-mass vs lag time, and(b) the correct MSDs of the center-of-mass (x-component ofthe molecular velocity subtracted) vs lag time. Each curverepresents the average of 5 submovies, and the frame rate fordata is 32 frames/sec.

Here, δt is the lag time and the average < · · · > is themean square displacement (MSD) carried out over theentire trajectory. In order to better approach the ex-perimental situation, we adopt the 2-dimensional (2D)diffusion coefficient D2D

T = (∑

β=x,y DT,β)/2 with suffi-cient accuracy compared to the 3D one, as noted in theprevious study [27]. For the case of no-flow field, theself-diffusion of the xanthan chain is determined fromthe MSD with the δt in each trajectory:

D2DT = lim

δt→∞

⟨R2

CM (t)⟩

4δt, (11)

where the MSD is given as⟨R2

CM (t)⟩

=⟨[RCM,x(t)−RCM,x(t− δt)]2

+ [RCM,y(t)−RCM,y(t− δt)]2⟩. (12)

Binning the trajectory into several segments is needed;then, the RCM displacement for each individual moleculewithin each segment is calculated as a function of thetime elapsed between frames. In general, the MSD with-out an external field increases linearly with lag time, dueto the isotropic random walk of the chain. For somewhatdifferent chains of a stiff semiflexible filament, detailedresults for the kinetics and dynamic properties in 2D con-fined space were reported by using the transverse and thelongitudinal components of the MSD [28,29].

In the case of flow situations, the correct MSD shouldtake into account the velocity fluctuations (i.e., mean-velocity-shifted RCM ) in the time interval, expressed as⟨

R2CM (t)

⟩=

⟨[RCM,x(t)−RCM,x(t− δt)− Vmδt]2

+ [RCM,y(t)−RCM,y(t− δt)]2⟩. (13)

In Eq. (13), the average molecular velocity of the ensem-ble trajectory along the flow direction, Vm, is estimatedby averaging instantaneous center-of-mass velocities foreach electric field, as provided in Fig. 6(b). Here, theEOF does not affect the y directional displacement of amolecule [30]. Figure 7 shows that adopting the correctMSD changes the characteristic form of the plot betweenthe MSD and the lag time, providing a fairly linear fit.

Let us provide further considerations in no-flow case.The translational self-diffusion of xanthan can be eval-uated in the short-time Kirkwood value DT,short whenthe chain does not involve the HI in wide channels. Inthis case, a scaling prediction for the diffusivity is inagreement with the Zimm model. While the HI getsto be involved in actually confined channels, the self-diffusion coefficient shows an asymptotic long-time valueDT,long, as represented by Eq. (10). Then, the depen-dence of the diffusivity on the chain length agrees wellwith the scaling prediction of Rouse dynamics [31], sug-gesting that HIs are at least partially screened. Accord-ing to Fixman’s Green-Kubo formula, DT,long is lowerthan DT,short, however, it turns out that its difference ina single chain system is very small with a few percent.Details of the crossover between the short-time and thelong-time behaviors can be found in the literature [31].

2. Conformational Dynamics of a XanthanChain in Uniform Flows

We changed the magnitude of plug-type EOF velocity(VEOF ) by applying an external electric field Ex rang-ing from 0 to 200 V/cm. The screening effect repre-sented by the EDL thickness κ−1 was also consideredwith variations of the medium ionic strengths of xanthandispersion, which was adjusted by using the KCl elec-trolyte concentration at a fixed pH of 6.2. The changeover an experimental time course was quite small notto affect the medium ionic strength. The concentra-tion of a symmetric monovalent electrolyte (e.g., KCl)equals the medium ionic strength IS. From the electro-static principle with the Poisson-Boltzmann equation,the EDL thickness κ−1is given by [IS (M)]−1/2/3.278 atRT [16,17].

Figure 8 shows that the radius of gyration RG is al-most independent of variations in the linear EOF veloc-ity VEOF , but certainly depends on κ−1. Independenceof VEOF is attributed to the nature of its uniform flowfield, where the isotropic stretching plays a role due tothe nonexistence of the velocity gradient in transversedirection of the channel. We also plot as a functionof the Peclet number Pe = VEOF lP /D0 (i.e., ratio ofconvection to diffusion). Here, the persistence length ofthe xanthan chain, lP , which is a statistical concept onthe chain flexibility, increases with decreasing IS, andD0 (= kT/6πηa) is the Stokes-Einstein diffusion coeffi-cient of the coarse-graining modeled xanthan molecule.

Single Molecule Tracking of a Semiflexible Polyelectrolyte Chain · · · – Sunghun Choung et al. -2853-

Fig. 8. Variations in the radius of gyration of a singlexanthan with EOF velocity and Pe for different screeningeffects with IS = 1.0, 10−2, and 10−4 mM KCl. IS = 1.0,10−2, and 10−4 mM corresponds to κ−1= 9.7, 97, and 970nm and to lP = 160, 460, and 600 nm, respectively. Theerror bars represent standard deviations.

With the Boltzmann thermal energy kT and the hydro-dynamic radius of coarse-grained bead a taken as 5 nm,D0 corresponds to 4.91 × 10−11 m2/s [15]. The extendedRG with decreasing screening effect (i.e., decreasing ISor dimensionless inverse EDL thickness κlP ) is accompa-nied by an increase in chain stiffness, which can be foundin the further results of previous studies [15,16].

The in-plane diffusion coefficient was obtained fromthe initial slope of the correct MSD of the ensemble av-erage vs lag time using Eqs. (11) and (13), in which er-ror estimates were made using the bootstrap method forlots of subensembles of molecule paths. In Fig. 9, wesee the dependence of VEOF on the translational self-diffusion DT , ensuring quadratic equation fits. Increas-ing DT with increasing external flow field results fromthe convective effect on the xanthan chain. The self-diffusion increases with increasing screening effect (i.e.,increasing IS or κlP ) since the xanthan chain becomesmore compact, which is attributed to the decreased elec-trostatic repulsion by the high screening effect. Duringthe image analysis, we set up the desirable range of flu-orescence intensity and ignored xanthan molecules thatappeared too dim due to an escape from the focal plane,which conflicts with 2D translational diffusion. As a re-sult, the microscope allowed the motion of a xanthanchain in the focal plane of the channel to be observedin the x-y direction. The velocity profile also developsat the edge of the EDL, but we adjusted the focal plane

Fig. 9. Variations in the translational self-diffusion of asingle xanthan with EOF velocity and Pe for different screen-ing effects. κlP and error bars represent the same conditionsas those in Fig. 8.

toward the channel center by means of a precise z-axisfocus module.

IV. CONCLUSION

By using an inverted epi-fluorescence microscope,single molecule tracking of semiflexible polyelectrolytewas performed on fluorescein-labeled xanthan inelectroosmosis-driven uniform flow fields. Consideringthis flow attempts to understand the behavior of indi-vidual chains under controlled fluidic flows. We mea-sured the average behavior of ensemble trajectories andsubsequently ignored uncorrelated fluctuations in the dy-namics of single molecules, enabling a valid analysis ofthe properties in real time.

The radius of gyration was almost constant under vari-ations of EOF velocity determined by the H-S equationfor a given electric field. The self-diffusion coefficientwas evaluated from the variation in the MSD with thelag time for each Brownian trajectory, in which the ve-locity along the flow direction was estimated by aver-aging the instantaneous center-of-mass velocity for eachfield. The behavior of EOF velocity dependence on thetranslational self-diffusion ensures a quadratic equationfit, which should be related to the convective effect. Ourresults show clearly the screening effect caused by theEDL, where strong screening caused by high salt con-centration leads to higher diffusion. Experimental results

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on the conformation and the translational diffusion be-havior qualitatively agree with the previous simulations,although there was a spatial limitation due to incomplete2D image tracking.

ACKNOWLEDGMENTS

This work was supported by the Basic Research Fund(No. 20100021979) from the National Research Founda-tion of Korea.

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