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Journal of Biotechnology 139 (2009) 179–185

Contents lists available at ScienceDirect

Journal of Biotechnology

journa l homepage: www.e lsev ier .com/ locate / jb io tec

ass transfer effects on DNA hybridization in a flow-through microarray

aniel Mocanu ∗, Aleksey Kolesnychenko, Sonja Aarts, Amanda Troost-Dejong,nke Pierik, Erik Vossenaar, Henk Stapert

hilips Research, High Tech Campus, 5656 AE Eindhoven, The Netherlands

r t i c l e i n f o

rticle history:eceived 19 January 2008

a b s t r a c t

The goal of this study is to assess the influence of mass transfer phenomena on DNA hybridization kineticsin a flow-through, porous microarray for fast molecular testing. We present a scaled mathematical model

eceived in revised form 24 August 2008ccepted 2 October 2008

eywords:NA hybridizationlow-through microarray

of coupled convection, diffusion and reaction in porous media, which was used to simulate hybridizationkinetics and to analyze the influence of convective transport on the reaction rate. In addition to computersimulations, we also present experimental data of hybridization collected on our microarray system fordifferent flow rates. The results reported in this paper provide for a better understanding of the interactionbetween reaction and mass transfer processes during flow-through hybridization and suggest criteria forsystem design and optimization.

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orous membraneathematical modeling

. Introduction

The technological development of DNA microarrays holds greatromise in many important areas such as gene sequencing, drugiscovery and clinical diagnostic (Schulze and Downward, 2001;eller, 2002). These bio-analytical devices exploit one fundamentalroperty of DNA: under appropriate conditions, two single-tranded nucleic acid molecules with matching base sequencesombine readily and form a hybridized, double-stranded moleculeccording to the Watson-Crick pairing rule. A microarray hybridiza-ion assay involves using known nucleic acid probes to identifyelated DNA molecules (the targets) in complex mixtures of nucleiccid molecules. The target analyte is typically labeled with fluores-ent tags and allowed to come into contact with the oligonucleotiderobes immobilized on a flat, impenetrable substrate in an orderedattern of microscopic spots.

In passive assays, the overall hybridization rate is stronglyimited by the slow diffusion of DNA, leading to long chemical equi-ibration times (Gadgil et al., 2004; Kim et al., 2006). Microfluidic,ow-over hybridization systems have been shown to increase theeaction rate. However, they suffer from the formation of a diffu-ion boundary layer above the flat reactive surface, which limits

heir performance (Kim et al., 2006). To circumvent this limita-ion, we have recently developed a flow-through microarray whichses a porous nylon membrane as the substrate for DNA hybridiza-ion. Due to the small pore size (0.5 �m in diameter) the diffusion

∗ Corresponding author.E-mail address: moccad@yahoo.com (D. Mocanu).

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168-1656/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.jbiotec.2008.10.001

© 2008 Elsevier B.V. All rights reserved.

f targets to probes is very fast. In addition, this porous mediumffers an increased surface area available for probe immobilizations compared to flat substrates for the same spot diameter. To ournowledge, there have been only a few reports on the developmentf porous, flow-through microarrays. Benoit et al. (2001) reportedhe development of a flow-through biochip for multiplexed, fluo-escence hybridization assays. This microarray uses a 500 �m-thickorous glass substrate with a channel diameter of 10 �m andporosity of 55%. Spots of ∼260 �m diameter are produced by

ispensing 50 nL of solution onto the substrate. Hybridization ischieved by circulating a 50 �L sample through the chip at a con-tant flow rate of 500 �L/min. Another flow-through microarrayas proposed by Wu et al. (2004). Their design is based on aorous aluminum-oxide substrate with a much smaller microchan-el diameter (0.2 �m). The oligonucleotide probes are printed usingon-contact ink-jet technology and are covalently linked to the poreurface. A 20-�L sample solution is pumped back and forth by airressure (100 mbar) through the porous medium during incuba-ion.

Flow-through microarrays are complex systems, in whichhe interaction between convection, diffusion and reaction playsn important role in their overall performance. Since fast andobust assays are desirable, especially for molecular diagnostics,good understanding of the physicochemical phenomena duringybridization is required. The focus of this study is to analyze

he mass transfer effects on DNA hybridization in porous sub-trates using both experimental and computer modeling methods.athematical modeling has been previously used to character-

ze biochemical assays in both passive (Chan et al., 1995; Livshitsnd Mirzabekov, 1996; Erickson et al., 2003; Pappaert et al., 2003;

1 iotechnology 139 (2009) 179–185

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adgil et al., 2004; Pappaert and Gert, 2006) and pressure-drivenystems (Myszka et al., 1998; Edwards, 1999; Lee et al., 2006). Incomprehensive theoretical study, Gervais and Jensen (2006) pre-

ented a systematic analysis of different regimes of diffusion, flownd reaction relevant to biochemical assays performed in microflu-dic devices. Lenigk et al. (2002) used a numerical model to simulateransport and reaction in a novel microfluidic DNA hybridizationevice and to assess the influence of different chemical and physicalarameters on the hybridization rate.

In this paper we present a simple yet efficient mathematicalodel of coupled convection, diffusion and reaction in porousedia. The scaling of the model equations reveals a set of

imensionless parameters that capture the system behavior instraightforward way. The numerical and experimental results

eported in this study provide for a better understanding of thenterplay between reaction and mass transfer processes duringow-through hybridization and suggest criteria for system designnd optimization.

. Microarray system and hybridization experiments

The nylon membranes used for hybridization are 6 mm in diam-ter, 200 �m thick, with an average pore diameter of 0.45 �m andporosity of 57% (Nytran SPC, Schleicher & Schuell BioScience).

he probes are inkjet printed onto the membrane in an array ofpots having ∼200 �m in diameter. The printed volume for eachpot is 1 nL. Probe binding to the pore surface is achieved byxposing the membrane to 254 nm UV light, with a total dose of00 mJ/cm2 (Saiki et al., 1989). Two oligonucleotide probes weresed in this study (P1 and P2, Table 1), each of them bearing a6 thymine spacer on their 5′ end. To prevent background sig-al, the membranes are treated for 1 h at 50 ◦C with a blockinguffer containing 5x SSC, 0.1%SDS and 100 �g/ml herring spermNA. During this step, the excess of printed material that has notound to the membrane surface is washed away. After a short rins-

ng step, the membranes are dried in an oven for 30 min at 40 ◦Cnd finally transferred to the flow cell. Hybridization experimentsre performed at 50 ◦C in singleplex format with Cy5-tagged shortargets complementary to P1 (antisense) and with PCR products466 nucleotides in length) complementary to P2. The hybridizationolution contains 5x SSC, 0.1%SDS and 100 �g/ml herring spermNA. The sample is circulated through the membrane in cycles, oneycle consisting of pumping the solution up and down between twoow chambers separated by the porous membrane, allowing foreal time hybridization kinetics measurements without washing.

schematic of the flow cell is shown in Fig. 1. When the sampleolution is in the lower chamber, the membrane is automaticallymaged from the top with a CCD camera and the fluorescent signals quantified and stored for further processing. Parameters such aspplied pressure P and cycle time Tc are programmed by the usert the beginning of the experiments.

. Computational modeling

.1. Physical model

The theoretical formalism used in this study is based on a con-inuum approach, in which the phenomena associated with DNAybridization in the porous membrane are described at a larger

able 1robe sequences.

1: 5′-T16-GCTACTCACACCGGCATTCTCACT-3′

2: 5′-T16-TGTGTTTTTGATAAACAGTCGCTT-3′

wvaaorti

ig. 1. Schematic of the flow cell: (1) upper flow chamber, (2) lower flow chamber,nd (3) nylon membrane.

cale than the pore size by employing volume-averaged physico-hemical quantities (Bear, 1972; Nicholson, 2001; Whitaker, 1998).

The hybridization reaction at the pore surface is described as aecond-order, reversible process. Effects such as electrostatic repul-ion between the probe layer and the target DNA (Halperin etl., 2004; Vainrub and Pettitt, 2002) or steric hindrance are notccounted for.

Finally, the model assumes continuous, unidirectional flow ofhe sample solution through the porous membrane and uses a one-imensional approximation of a single capture probe spot.

.2. Mathematical model

Let V be a representative elementary volume (REV) of membranehich containes many pores but is small enough that it has localeaning with respect to physicochemical variables, and V0 be the

olume of voids within the REV. If ct is the concentration of targetNA in the pore volume, than the volume average of ct over V isefined as

= 1V

∫V0

ct dV (1)

nd the volume average of c over V0 is

0 = 1V0

∫V0

ct dV (2)

uch that c = �c0, where � = V0/V is the porosity of the mem-rane. It can be shown that the reactive flow of DNA targetshrough the porous membrane is described by the followingonvection–diffusion–reaction equation (Aharonov et al., 1997;icholson, 2001):

∂c0(x, t)∂t

= �Dmol∂2c0(x, t)

∂x2− �u

∂c0(x, t)∂x

− S∂h(x, t)

∂t(3)

here Dmol is the molecular diffusion coefficient of DNA, u is theolume-averaged pore fluid velocity, S is the specific surface areavailable for reaction (defined as the ratio between the pore surfacerea and the volume of the membrane) and h is the concentrationf the hybridized duplex (the reaction product). The last term in theight hand side of Eq. (3) reflects the consumption and generation of

he target DNA molecules during the hybridization reaction, whichs described by the following rate equation:

∂h(x, t)∂t

= konc0(x, t)[Cp − h(x, t)] − koff h(x, t) (4)

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D. Mocanu et al. / Journal of B

In Eq. (4), Cp is the initial concentration of immobilized cap-ure probes, kon and koff are the association and dissociation rateonstants, respectively. Eqs. (3) and (4) are supplemented with theollowing boundary conditions:

0(0, t) = C0 (5)

∂c0(x, t)∂x

∣∣∣∣x=L

= 0 (6)

nd initial conditions

0(x, t = 0) = C0 (7)

(x, t = 0) = 0 (8)

Here, L is the depth of the spot and C0 is the concentration of thenalyte molecules above the spot. In real experiments, the reportedeasured hybridization signal is spot-averaged and therefore in

ur numerical experiments we monitor hybridization kinetics byntroducing the average bound DNA concentration along the spotepth

av = 1L

∫ L

0

h dx (9)

In the case of efficient transport (well-mixed system), theybridization process is reaction-limited, Eq. (4) decouples fromq. (3) and has the following closed form solution:

rl = konC0CP

konC0 + koff(1 − e−(konC0+koff )t) (10)

.3. Nondimensional model equations

After the introduction of the following dimensionless variables:

= c0

C0, X = x

L, � = t

u

L, H = h

Cp

Eqs. (3) and (4) reduce to the following dimensionless forms:

∂C

∂�= 1

Pe

∂2C

∂X2− ∂C

∂X− 1

�A

∂H

∂�(11)

∂H

∂�= Da A[C(1 − H) − KDH] (12)

ubject to non-dimensional boundary conditions

= 1, X = 0 (13)

∂C

∂X= 0, X = 1 (14)

nd non-dimensional initial conditions

(0) = 1 (15)

(0) = 0 (16)

The spot-averaged concentration of the hybridized duplex at theuid–solid interface takes the dimensionless form

av =∫ 1

0

H dX (17)

nd the reaction-limited solution becomes

rl = 1(1 − e−DaA(KD+1)�) (18)

1 + KD

Four controlling dimensionless parameters result from theon-dimensionalization process: Pe, Da, A and KD. The Pecletumber, Pe = Lu/Dmol, is the ratio between the characteristic dif-

usion time and the convection time. Typically, flow-through and

tbteo

nology 139 (2009) 179–185 181

icrofluidics-based assays are characterized by high Peclet num-ers (Pe � 1), such that the convective transport dominates overiffusion. The second dimensionless parameter is the Damkohlerumber, Da = SkonCpL/u, which measures the amount of reactionhat occurs in the time it takes the fluid to travel a characteristicength L. When Da > 1 hybridization is convection-limited, whereas

hen Da < 1 hybridization becomes reaction-limited. A = C0/(SCp)s the surface adsorption capacity relative to the bulk and it is anndicator of the saturation time scale (a small A indicates a longaturation time). And finally KD = koff/(konC0) is the dimensionlessquilibrium dissociation constant and it is a measure of the equi-ibrium efficiency of the hybridization reaction.

.4. Numerical solution method

The system of differential Eqs. (11) and (12) subject to the bound-ry and initial conditions (13)–(16) was solved numerically withhe finite element method using Comsol Multiphysics softwareComsol Inc., Burlington, MA). The one-dimensional computa-ional domain was discretized in 352 quadratic Lagrange elements,eading to 1410 degrees of freedom. We used an implicit time dis-retization scheme with variable time steps. The resulting systemf nonlinear algebraic equations was solved using the Newton itera-ion in combination with a direct solver, as implemented by Comsol.

.5. Parameter values

The interstitial surface area of the porous membranep = 1.5 × 10−2 m2 was determined with the Brunauer–Emmett–eller (BET) method using the Gemini 2380 analyzer (Micromerit-cs, GA, USA). Based on this measurement we calculated thepecific surface area (defined as the total pore surface area pernit bulk volume of the membrane) to be S = 3 × 106 m−1. Theepth of the probe spot L ∼= 50 �m was estimated using confocalicroscopy measurements. Assuming a cylindrical shape of the

pot and uniform probe distribution, it results that the probeurface concentration corresponding to 200 �M printed probeoncentration is Cp = 2 × 10−8 mol/m2. Association and dissocia-ion constants of the hybridization reaction with antisense targetso probe P1 were obtained in a separate kinetic study and areon = 200 m3/mol s and koff = 3 × 10−4 s−1 (Mocanu et al., 2008). Theverage velocity was estimated by dividing the flow rate to theross-sectional area of the membrane. Typical mean pore velocitiesesulted from the flow rates used in our experiments range from.1 mm/s to 1.5 mm/s. The diffusion coefficient for single-strandedNA is approximately Dmol = 10−11 m2/s (Liu and Giddings, 1993;appaert et al., 2005). It follows that for 10 nM (10−5 mol/m3)arget concentration, 200 �M printed probe concentration and a

ean pore fluid velocity u = 1 mm/s the dimensionless parametersre: Da = 0.3, A = 1.6 × 10−4, KD = 0.15 and Pe = 5000.

. Results

.1. Modeling

A qualitative understanding of the transport and reaction pro-esses may be obtained by analyzing the separate influence ofhe dimensionless parameters in Eqs. (11) and (12). The effect ofransport on the hybridization rate is captured by the Damkohlerumber, which compares the time scales for an analyte molecule

o either react at the pore surface or exit the reactive regiony convection. When efficient transport is achieved, hybridiza-ion is reaction-limited and a constant concentration profile isxpected along the spot depth. In this regime, the time coursef the hybridized duplex concentration is described by Eq. (10).

182 D. Mocanu et al. / Journal of Biotechnology 139 (2009) 179–185

Fig. 2. Influence of the Damkohler number on the hybridization rate: (a) hybridiza-tion kinetics for Da = 0.2, 1 and 5. Comparison with the reaction-limited solutionnormalized to the initial probe concentration, Cp . The dimensional time t is usedida

TtttiDcaanbihedDkrtaisrbDs

FmA

a7 × 10 mm/s, almost four orders of magnitudes smaller than thefluid velocity which is 0.1 mm/s in this computer simulation. In thebeginning, hybridization takes place mostly at the entrance, totallydepleting the solution. When these surfaces saturate, more targetsare available for reaction at sites further down the pores. Thus, the

nstead of �. (b) hybridized duplex and target concentration profiles along the spotepth at t = 8 min for Da = 1. Direction of flow is from left to right. Other parametersre: A = 1.6 × 10−4 and KD = 0.15.

he reaction-limited solution hrl normalized to the initial concen-ration of capture probes Cp was used for comparison purposeso assess the influence of the Damkohler number. Fig. 2a showshe averaged hybridized duplex concentration resulted from solv-ng the convection–diffusion–reaction system (Eqs. (11)–(16)) foramkohler numbers Da = 0.2, 1 and 5. These Damkohler numbersorrespond to the following pore velocities: u = 3 mm/s, 0.6 mm/snd 0.12 mm/s respectively. The Peclet number was changedccordingly: Pe = 15,000, 3000 and 600. The other dimensionlessumbers were kept constant at A = 1.6 × 10−4 and KD = 0.15. It cane observed that for small Damkohler numbers (Da ≤ 1) the kinet-

cs is very close to the reaction-limited solution, indicating thatybridization is not affected by the convective transport. How-ver, as the Damkohler number increases, the hybridization curveeviates more and more from the reaction-limited regime. Fora > 1, the reaction becomes limited by convection, resulting in slowinetics and long chemical equilibration time. In contrast with theeaction-limited regime, the target and hybridized duplex concen-rations exhibit decaying profiles, with high concentration valuest the inlet and low at the outlet (shown in Fig. 2b for Da = 1). Thisndicates that hybridization takes place at different rates across thepot, leading to slower overall kinetics (Hav) as compared to the

eaction-limited regime. A further increase in the Damkohler num-er results in the development of a concentration wave of boundNA, which travels along the direction of flow at a velocity much

maller than the fluid velocity. Fig. 3 shows the propagation of

Fthi

ig. 3. Hybridized DNA concentration profiles along the spot depth for equidistantoments in time between t = 0 and 65 min in the convection-limited regime (Da = 10,= 8 × 10−5, KD = 0.15, Pe = 600). The direction of flow is from left to right.

H wave from left to right for Da = 10. The wavefront velocity is−6

ig. 4. Influence of dimensionless numbers A and KD on the hybridization reac-ion: (a) hybridization kinetics for A = 0.01, 0.005, 0.001 (Da = 0.1, KD = 0.2) and (b)ybridization kinetics for KD = 1, 0.1, 0.01 (Da = 0.1, A = 0.001). The hybridization kinet-

cs is plotted as a function of the dimensional time.

iotechnology 139 (2009) 179–185 183

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D. Mocanu et al. / Journal of B

harp wavefront delineates reactive surfaces that approach satura-ion levels from those where hybridization just begins.

The next dimensionless number, the surface adsorption capac-ty, A = C0/(SCp), expresses the need for targets from the bulk. A small

number indicates a high surface adsorption capacity and longerquilibration time (Fig. 4a for Da = 0.1 and KD = 0.2). The equilib-ium value of Hav in Fig. 3a is given by 1/(1 + KD), consistent withq. (18). The interpretation of the dissociation equilibrium con-tant, KD = koff/(konC0), is straightforward: high KD results in lowerybridization efficiencies due to either a small concentration ofarget DNA, C0, small association constant or high dissociation con-tant (Fig. 4b).

.2. Microarray experiments

.2.1. Influence of flow rate on hybridization kineticsTo investigate the effect of fluid velocity on the reaction kinetics

e performed experiments at different flow rates. Fig. 5a dis-lays the kinetic curves during hybridization with 1 nM perfectatch targets (antisense) to probe P1 at 200 �L/min, 800 �L/min

nd 1600 �L/min flow rates. The probe surface concentrations C = 10−8 mol/m2 (100 �M printed probe concentration). The

p

orresponding pore velocities u were estimated to approxi-ately 0.1 mm/s, 0.7 mm/s and 1.5 mm/s, respectively. The signal

ncrease per time unit is almost the same for 200 �L/min and00 �L/min, but significantly slower as compared to the flow

ig. 5. Experimental data points obtained during hybridization at different flowates: (a) experiments performed with 1 nM antisense targets complementary to1 at flow rates 200 �L/min, 800 �L/min and 1600 �L/min, (b) experiments per-ormed with 20 nM PCR product complementary to P2 at flow rates 1.5 mL/min,mL/min and 4 mL/min. For clarity the fitting curves with Eq. (10) through the datare displayed. The fluorescence intensity is reported in arbitrary units.

ocaahfl

4

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Ft2ti

Fig. 6. Applied pressure vs. cycle time characteristic curve.

ate of 1600 �L/min. The Damkohler numbers associated withhese experiments are Da ∼= 3, 0.4 and 0.2, respectively. A sec-nd set of experiments was performed with 20 nM PCR productomplementary to P2 at flow rates 1500 �L/min, 3000 �L/minnd 4000 �L/min. Fig. 5b shows that increasing the flow ratebove 1500 �L/min does not lead to a significant change in theybridization rate, suggesting a reaction-limited regime at theseow parameters.

.2.2. Influence of cycle time on hybridization kineticsOne important parameter that affects the overall hybridization

ate in our microarray setup is the cycle time Tc. This is defined ashe time necessary for the fluid to transverse the Nytran SPC mem-rane from the lower to the upper flow chamber and back, plushe time required to image the membrane, which is approximatelys. The cycle time dependence on the applied pressure was deter-ined experimentally and it is shown in Fig. 6. For example, it takes

pproximately 12 s for 20 �L of fluid to move from one chamber to

he other at 200 mbar applied pressure. Overestimating Tc may slowown the hybridization rate significantly by not supplying enoughresh analyte molecules to the reaction sites. This is shown in Fig. 7,hich displays the fluorescence signal during two hybridization

ig. 7. Hybridization signal during experiments performed with two different cycleimes: (�) optimal, Tc = 30 s, and (©) overestimated, Tc = 60 s. Applied pressure is00 mbar, printed capture probe concentration is 50 �M and the target concen-ration is 20 nM of PCR product complementary to the probe P1. The fluorescencentensity is reported in arbitrary units.

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xperiments performed at 200 mbar applied pressure and cycleimes Tc = 30 s (optimal value) and Tc = 60 s (overestimated value).he reaction kinetics is slower in the second case (Tc = 60 s) because,ccording to Fig. 6, the fluid flows through the membrane only for4 s, the rest of the time being stationary in the flow chambers.

. Discussion

The development of optimized flow-through microarraysequires a fundamental understanding of the physicochemical pro-esses associated with DNA hybridization. In this study we focusedarticularly on the analysis of transport effects on the reactionate. Our results show that the optimization of flow-through assaysequires a careful choice of physical and chemical parameters suchs: flow rate, cycle time, probe concentration and geometrical fea-ures of the membrane. In general, the overall hybridization rates affected by three physicochemical phenomena which take placen different time scales: the reaction time tr = (SKonCp)−1, the con-ection time tc = L/u and the diffusion time td = R2

0/Dmol (R0 is theore radius). For the reaction-limited regime to occur both theiffusion time and the convection time must be smaller than theeaction time. The diffusion time characteristic to porous substratess typically the smallest between the three due to the very smallore radius. For example, in our experimental set-up the nylonembrane has a pore radius of R0 = 0.25 �m, which causes theolecular diffusion time to be as small as 6 ms. This is significantly

horter than the estimated reaction time tr = 80 ms and the convec-ion time tc = 50 ms (td < tc < tr). These values were calculated usingp = 2 × 10−8 mol/m2 (∼200 �M printed probe concentration) and= 1 mm/s. The fast radial transport by diffusion from the bulk to

he pore surface is one of the main advantages of using porousedia for hybridization as compared to flat surfaces characteristic

o microfluidics DNA arrays. The microchannels in these systemsave typical heights of ≥10 �m resulting in long diffusion times

d ≥ 10 s. In this situation, the analyte molecules exit the microchan-el without having the time to reach the reactive surface, leadingo the formation of a depletion zone above the capture probe spotsalso called mass transfer boundary layer or diffusion boundaryayer) (Gervais and Jensen, 2006). This effect was clearly demon-trated by (Kim et al., 2006) in a polydimethylsiloxane microfluidicystem, which was used to assess the influence of channel heightnd flow rate on the hybridization kinetics. Their experimental datahowed that increasing the flow rate from 1 �L/min to 10 �L/minesults in a decrease in the hybridization signal at the end of thexperiment. A similar behavior was observed when the channeleight was increased from 8 �m to 50 �m. The reduction in sig-al was explained by either the increase in the convective flux asompared to the diffusion flux in the flow rate experiments or byhe increase in the total diffusion distance in the case of the vari-ble channel height experiments. Since the porous substrate used inur DNA microarray has very narrow pores, the radial diffusionalransport takes place on a very short time scale and should notffect the reaction speed. Nonetheless, hybridization may be lim-ted by the convective transport in cases where the surface probeensity is very high and the fluid velocity is too small. The competi-ion between reaction and convection is expressed qualitatively byhe Damkohler number, which compares the reaction and the con-ection time scales Da = tc/tr = SkonCpL/u. The computer simulationshowed that for Da < 1 (tc < tr) hybridization is reaction-limited,hile for Da > 1 (tc > tr) the convective transport limits the reac-

ion rate by inefficiently supplying fresh analytes to the reactionites. The convection-limited regime is best illustrated in Fig. 3,hich shows the formation of a concentration wavefront which lags

ehind the fluid flow. In this situation, the surface saturates grad-ally, starting from the inlet, and the overall hybridization rate Hav

N

P

nology 139 (2009) 179–185

s significantly decreased (Fig. 2a, Da = 5). For a given substrate androbe molecule, the Da number increases either with the increase

n capture probe surface concentration Cp or with the decrease inore fluid velocity u. Thus, although a high number of probes isesired to enhance the assay sensitivity, a balance must be achievedetween Cp and u in order to keep the Damkohler number close to. The experiments performed at different flow rates also displayedsignificant decrease in the hybridization rate for 200 �L/min as

ompared to 800 �L/min, suggesting a convection-limited regimes discussed above. The influence of flow rate on hybridization waslso investigated by (Wu et al., 2004). They showed a decreasen the hybridization rate when the flow rate was decreased from00 �L/min (5 cycles/min) to 80 �L/min (2 cycles/min) to 6 �L/min0.3 cycles/min). Our experiments performed with PCR analyte

olecules indicate that hybridization is already in the reaction-imited regime for 1500 �L/min and above, since no significantifference in the kinetic fluorescence signals were observed at theseow rates. Finally, we showed that a proper choice of the appliedressure must be correlated with an optimal cycle time in order topeed up the hybridization process.

cknowledgments

Daniel Mocanu acknowledges the financial support offered byhe European Commission under a Marie Curie Transfer of Knowl-dge fellowship (contract MTKD-CT-2004-014460).

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