MicroﬂuidicsBasedDNAHybridization: …repository.ias.ac.in/101239/1/196-571-1-PB.pdf · 2016. 11. 25. · appear to be 150 times faster over a distance of 500 µm5,6. Even though

Department ofMechanical Engineering,Indian Institute ofTechnology,Kharagpur 721302, [email protected]

Electrophoresis: Electrophoresisis the movement of anelectrically charged substanceunder the influence of anelectric field. In practice,electrophoresis offers with acommon method ofseparating large molecules(such as DNA fragments orproteins) from a mixture ofsimilar molecules. An electriccurrent is passed through amedium containing themixture, and each kind ofmolecule travels through themedium at a different rate,depending on its electricalcharge and size. Separation isbased on these differences.Agarose and acrylamide gelsare the media commonlyused for electrophoresis ofproteins and nucleic acids.

Gel Electrophoresis: GelElectrophoresis is a techniquein which components of amixture are separated fromone another on the basis ofdifferences in charge andattraction to a gel phase. Gelelectrophoresis is commonlyused to separate DNAfragments based on size,yielding a unique“fingerprint”. Gelelectrophoresis uses positiveand negative charges toseparate charged particles.Electricity travels through abuffer solution in theelectrophoresis chamber. Thebuffer allows the electriccurrent to flow from thecathode (negative electrode)to the anode (positiveelectrode). DNA is negativelycharged; therefore it travelstoward the positive electrode.

REVIEWS

MicrofluidicsBasedDNAHybridization:MathematicalModeling issuesandFutureChallenges

Suman Chakraborty

Abstract | In this paper, various mathematical modeling strategies associated with the analysis

of the kinetics and the transport processes pertinent to microfluidics-based DNA hybridization

methodologies are critically reviewed. In particular, the coupling of specific/non-specific

hybridization kinetics with the fluid flow, heat transfer and mass transfer equations is described

in detail. Methodologies for obtaining faster DNA hybridization rates are also discussed and the

corresponding mathematical modeling issues are identified to define the scope of ongoing and

future research endeavours.

1. Introduction1.1. The concept of DNA chipsA remarkable advancement in the technologyof the micro Total Analysis Systems (µ-TAS)over the past few years has made it possible toorganize and combine the processes of samplehandling, analysis and detection in stand-aloneintegrated microfluidic platforms. This allowsrapid biochemical analyses to be carried out overlength scales that are several orders of magnitudesbelow the conventional practice. Overall, bio-microfluidics has provided great promises inimproving the sensitivity, specificity and theprocessing time required for a sample analysis,which are the key requirements for advancedbiomedical applications. In order to appreciatethe significance of bio-microfluidics in advancedbiomedical and biotechnological applications, itneeds to be appreciated first that different methods,in principle, can be employed to detect eventualabnormalities or illnesses in patients. For viralinfections or blood-related pathologies, for example,immunoassays can be performed to determine thenature of organisms that are responsible to disturbthe inherent immunological defensive systems in

the living beings. One way of performing this isto use homogeneous systems in which the sampleand detection molecules are both in a liquid system.Another way is to employ a heterogeneous system, inwhich one type of molecules involved is bound to thesolid substrate. The DNA or the Deoxyribonucleicacid happens to play a critical role towards achievingthis goal, in many of the related applications. Assuch, DNA is found within the nucleus of eachcell. DNA carries the genetic information thatencodes proteins and enables cell to reproduce andperform their functions. Structurally, the DNAis a linear polymer made up of repeating sub-units (monomers) known as nucleotides that arecovalently bonded together. The sequence of thesenucleotides forms the hereditary information. Eachmonomer consists of a phosphate group that isresponsible for the negative charge on the DNA,a de-oxyribose sugar and a nitrogen containingbase. The backbone of a single stranded DNAmolecule contains a series of alternating sugarand phosphate groups, with one base attachedto each sugar molecule. The double-helical DNAstrands essentially contain linked nucleotides withone of the four bases adenine (A), thymine (T),

Journal of the Indian Institute of Science VOL 87:1 Jan–Mar 2007 journal.library.iisc.ernet.in 95

Gene expressionanalysis: Gene expressionanalysis deals with thedetermination of the activityof the genes in a cell/tissue oran organism. Currently, this ismainly achieved through thedetermination of the mRNAquantity of specific genes,and also by the quantificationof proteins.

DNA hybridization: DNAhybridization refers to the useof a segment of DNA, calleda DNA probe, to identify itscomplementary DNA; used todetect specific genes.

REVIEW Suman Chakraborty

guanine (G) and cytosine (C). One oxygen atomis missing in the sugar content of the nucleotide—thus the prefix “deoxy”. In the sequence of theirnucleotides, and thus their bases, both strands arecomplementary to each other—in each case anA is opposed by a T and a G by a C; this basepairing holds it together. For genetic ailments, DNAanalysis can be performed to know whether a patientpossesses a mutation in a specific gene1–3. One ofthe methods to analyze this condition is to performa gel-phase electrophoretic separation of fragmentsformed from the DNA under question. Differencesin fragment lengths from the patient’s DNA and ahealthy reference indicate the possibilities of certaingenetic ailments. Another method for accomplishingthis purpose is to introduce many different knownsingle stranded (ss) DNA sequences bound togetherwith particles or gels in a reactive microsystem. TheDNA sample under investigation can be ‘hybridized’with these different sequences. By identifying thespecific DNA sequence with which this samplereacts (note that there is only one complementarysequence with which such selective reaction becomespossible), one can determine the DNA sequence ofthe unknown sample. It has been well appreciatedthat this kind of hybridization of the DNAs to theircomplementary sequences plays a major role inreplication, transcription and translation, wherespecific recognition of nucleic acid sequences bytheir complementary strands is essential for thepropagation of information content. In practice,microchip based nucleic acid arrays presentlypermit the rapid analysis of genetic information byhybridization. The DNA chips have gained wideusage in bio-analytical chemistry, with applicationsin important areas such as gene identification,genetic expression analysis, DNA sequencing andclinical diagnostics.

1.2. Fundamental principles of DNAhybridization

As mentioned earlier, a general principle ofoperation of the heterogeneous DNA assays isto probe molecules that are bound to the solidsubstrates in order to detect the target molecules ina given sample. When a liquid sample is brought intocontact with the substrate-bound probe molecules,the target molecules migrate towards the substratesby diffusion and react with the probe molecules. Amajority of DNA microarray technologies are basedon such passive nucleic acid hybridization, i.e., thebinding event depends upon diffusion of target DNAmolecules to the probe DNAs. Unfortunately, passiveDNA hybridization approach may take several hours.This is because of the fact that the target DNAs,with a typical diffusion coefficient of the order

of 10−11 m2/s (for oligonucleotides that are 18base pairs in length, for example), only reach thecapture probes via Brownian (random) motionin order to hybridize4. Because of this diffusion-dependence, large amounts of target DNA and longhybridization times are often required to achievedetectable hybridization signals and repeatableresults. As a consequence, many researchers haveexplored alternative methods to make the DNAsensing faster and more sensitive in solutions withlow concentrations of target DNAs. One of theearlier alternative methods was to utilize electricfields to accelerate the rate of interaction betweenthe probe and target DNA molecules, because theDNA strand has multiple negatively charged groups.In diffusion-based transport of DNA, the time (τ) ittakes a DNA molecule to travel over a distance x isgiven as5

τ=x2

2D(1)

where D is the diffusion coefficient. In the case ofelectrophoresis, the time it takes to move a moleculein the electric field over a distance x, given by5

τ=x

µepE(2)

where µep is the electrophoretic mobility andE is the electric field strength. Using typicalvalues for D (9.943×10−11m2/s) and µep (15,000µm2/V-s), and under an applied electric field of0.004 V/µm, the electrophoretic transport mayappear to be 150 times faster over a distance of500 µm5,6. Even though fast DNA transport isdistinctly advantageous in many respects, onecritical disadvantage is that the sample solutioncontaining the target DNA must be desalted beforehybridization in order to establish an appropriateelectric field. This is because the electric field depthexists only in close proximity to the electrodes ina solution with high salt-concentration. A highconcentration of the ions nullifies the electricfield in the area away from the electrodes andreduces the effective electrophoretic mobility ofthe DNA molecules. Therefore, to facilitate therapid movement of DNA by an electric field, a lowconductive buffer solution needs to be used. Incontrast, in molecular biology, to achieve efficienthybridization, one always prefers to work with highconductivity solutions. Therefore, it is desirableto devise a DNA hybridization protocol that candeal with a wide range of buffer conductivities, andyet achieve an optimal performance. Microfluidics-based DNA hybridization holds the key towardsachieving this goal in the lab-on-a-chip basedmicrodevices of immense technological relevance.

96 Journal of the Indian Institute of Science VOL 87:1 Jan–Mar 2007 journal.library.iisc.ernet.in

Electric double layer: When asolid is in contact with anelectrolyte, the chemical stateof the surface is generallyaltered, either by ionizationof covalently bound surfacegroups or by ion adsorption.As a result, the surfaceinherits a charge whilecounterions are released intothe liquid. For example,common glass, SiOH, in thepresence of H2O, ionizes toproduce charged surfacegroups SiO− and release of aproton. At equilibrium, abalance between electrostaticinteractions and thermalagitation generates a chargedensity profile. The liquid iselectrically neutral, but for acharged layer adjacent to theboundary, which bears acharge locally equal inamplitude and opposite insign to the bound charge onthe surface. This chargedlayer is commonly known asthe electric double layer(EDL).

Electroosmosis/Electroosmoticflow: Electroosmosis refers tothe motion of an ionizedliquid relative to a stationarycharged surface by anapplied electric field. Insimple terms, electroosmoticflow originates from themotion of ions in a solventenvironment through verynarrow channels, where anelectric potential gradientcauses the ion migration.

Microfluidics based DNA Hybridization REVIEW

1.3. DNA hybridization through microfluidicsTo overcome the diffusion-controlled limitsassociated with passive DNA hybridizationtechniques, microfluidics-based DNA hybridizationstrategies have been proposed and implementedby a number of researchers in the recent past7–10.There are several advantages associated with suchmicrofluidic DNA arrays: these enable detectionat the lowest possible DNA concentrations, allowfor shorter times to achieve this detection becauseof enhanced mass transport, offer the ability tomonitor several samples in parallel by using amultichannel approach, reduce the potential forcontamination by relying on an enclosed apparatus,and hold the overall promise for integration ofseveral functions in a single apparatus.

Various flow-actuation methodologies havebeen proposed by the researchers for achievingtransport of the sample through the ‘active’DNA hybridization chips. One of the commonmethods, known as electro-osmotic (EO)pumping11–16, essentially relies on the mechanismof electroosmosis, which refers to the liquid flowby an applied electric field over charged liquid–solid interfaces. Fundamentally, electroosmosis canoccur due to the formation of an electrical doublelayer (EDL) at the charged surfaces. Immobilizedsurface charges can develop on a solid substrate(such as the walls of a microchannel) that is incontact with an electrolyte, as a consequence ofcomplex electro-chemical reactions. The layer ofions adsorbed and immobilized on the chargedsurface is called the Stern layer. Due to electrostaticand entropic interactions, the presence of suchsurface charges results in a re-distribution of nearbycounter-ions and co-ions in the liquid phase. Thisleads to the formation of an EDL, so that the localcharge density close to the interface is non-zero.In the diffuse layer of the EDL, the counter-ionspredominate over the co-ions, so as to neutralizethe net surface charge. This diffuse part of theEDL spans over a distance away from the liquid-solid interface. The characteristic order of thediffuse part of the EDL is commonly known as theDebye length. If a potential is applied along themicrochannel axis, the diffuse EDL tends to movedue to electrostatic interactions. Because of thecohesive nature of the hydrogen bonding of the polarsolvent molecules, the entire buffer is effectivelypulled along the microchannel axis, resulting in anelectroosmotic flow (EOF). Such electroosmoticpumping systems work without any movablemechanical parts, and thus increase the long-termstability and reduce the difficulty of production.Furthermore, electroosmosis allows pumping ofliquids over a wide range of conductivity, which iscritical for most biochemical applications.

From the implementation point of view, theintegration of micro or nano scale electrodes influidic devices is a relatively simple procedurewith the advancement of MEMS-based fabricationtechnologies. Consequently, electrokinetic forcesappear to be ideal for manipulating DNA moleculesand performing fluidic operations in the pertinentbiochemical systems. However, it also needs tobe recognized in this context that DNA has arelatively high negative electrophoretic mobility, onaccount of a large number of negative charges onthe molecule. Therefore, electroosmotic pumpingof DNA requires a buffer with a large electro-osmotic mobility so that the electroosmotic forcescan overcome the negative electrophoretic mobilityof the DNA molecules. Unfortunately, buffers usedin DNA hybridization often contain salts in highconcentrations, which reduce the electroosmoticeffects to a considerable extent. In that perspective,pumping using mechanical pressure17 might possesssome advantages over the electroosmotic approachin the sense that the former is insensitive tothe variations in pH, macromolecular chargesand the salt concentration. However, becauseof the huge pumping power requirements,considerable sample dispersion (associated with theparabolic-shaped characteristic velocity profiles)and the lack of precise control associated withpressure-driven microflows, mechanical pumpingalone could not emerge as one of the mostpreferred alternatives for driving fluid flow throughmicro-scale conduits for DNA hybridizationapplications. Furthermore, because of the highback-pressures generated due to the considerableflow resistances associated with mechanically-pumped microchannel flows involving largepressure gradients, leakage prevention might itselfpose a challenging operational problem, if the unitis not properly sealed. As a compromise, researchershave recently proposed18 the employment ofcombined electroosmotic and pressure-driventransport mechanisms, for driving DNA samplesthrough microfluidics-based hybridization chips.

In order to impose stringent controls overthe hybridization performance of these kinds ofDNA-microassays without going for too manyexpensive and tedious in-situ experimental trials,the researchers have well recognized the needsfor comprehensive mathematical modeling anddetailed simulation studies on microfluidics-basedDNA transport. This helps to obtain the optimalsystem parameters with the most favourablehybridization characteristics within the constraintsof the chosen configuration. A major emphasisof the present review article, is to outline andreview the various features of mathematical



modeling of DNA hybridization in the presenceof combined pressure-driven and electroosmotictransport mechanisms. First, a detailed reviewof the various kinetics-based models of DNAhybridization will be presented. Subsequently, thecoupling of the kinetics-model with the fluid flow,heat transfer and the species transport in thebulk phase are described. Some of the key resultsobtained by employing these considerations arehighlighted. Finally, some more recently introducedmethodologies of DNA hybridization and thepertinent issues of mathematical modeling arediscussed.

2. DNA hybridization reaction kinetics2.1. Basic reaction kineticsIn order to appreciate the intricacies associatedwith biochemical reactions in DNA hybridizationmicroassays, it may be instructive to revisit certainbasic definitions associated with the chemicalkinetics of reactive systems. These basic conceptsare briefly elucidated below19.(i) Rate of reaction: For a chemical reactionof the form A + nB → mC + D, the rateof reaction is defined as r = rD(=

d[D]dt ) =

1m rC (= 1

md[C]

dt ) = rA(= −dA]

dt ) =1n rB(= −

1n

d[B]

dt ),where the expressions in the square parenthesesrepresent the concentrations of the pertinent speciesin the reactive system. As such, r is a functionof the concentration of individual species, i.e.,r = r([A],[B],[C],[D]). For most substances, thisrelationship is of empirical in nature and needsto fitted experimentally. The most common formof this functional relationship is r = k[A]a [B]b,where k, a, and b are time-independent coefficients.The parameter k is called the ‘rate constant’, whichshould not be confused with the thermodynamicdefinition of ‘equilibrium constant’ of a specifiedreaction.(ii) Order of reaction: If the rate of reaction isdescribed by the above mentioned functional form,the order of reaction is defined as: o = a+b. It isimportant to note here that the unit of k dependson the order of the reaction. For example, for azero-order reaction k is expressed in the units ofmol/m3/s; for a first order reaction k is expressedin the units of 1/s and for a second order reactionk is expressed in the units of m3/mol/s. Therate constant is usually taken to vary with theactivation energy (Ea) and temperature (T) by theArrhenius law, as k = k0expEa/RT . From molecularinterpretations, the rate constant is the rate ofsuccessful collisions between the reacting molecules,the activation energy represents the minimumkinetic energy of the reactant molecules in order to

form the products and k0 corresponds to the rate atwhich these collisions occur.(iii) Adsorption and the Langmuir model: In case ofadsorption of molecules on a solid functionalizedsurface, there are basically three components inthe reaction. There is a free substrate in the bufferfluid (often called as the target or analyte), with aconcentration of [S]. Second, there is a surfaceconcentration of the ligands or capturing sitesimmobilized on a functionalized surface, with aconcentration of [0]0. Finally, there is a surfaceconcentration of the adsorbed targets (productsof the reaction), with a concentration of [0]. Theunits of [0] and [0]0 are in mol/m2, whereas [S]is expressed in the units of mol/m3. In case ofadsorption, the definition of the reaction rates aresomewhat modified from the usual rate constantdefinitions mentioned above, primarily because ofthe fact that the immobilization of the substrate Snot only depends on the volume concentrationat the wall, but also depends on the availablesites for adsorption. Accordingly, one can write

−d[S]dt = ka

([0]0 − [0]

)[S]w and −

d[0]dt = kd [0],

where ka and kd are the adsorption and dissociationrates, respectively. The concentration of 0 isincreased by the former and is decreased by the later,and the net rate of change is given by their balance,i.e.,

d[0]

dt= ka

([0]0 − [0]

)[S]w − kd [0] (3)

Equation (3) can be integrated to obtain

[0]

[0]0=

ka [S]w

ka [S]w + kd

[1−exp

(−

(ka [S]w + kd

)t)]

(4)Eq. (4) represents an exponential growth of [0] withtime, till a saturation (asymptotic) value is reached

( [0]a[0]0

=ka[S]w

ka[S]w+kdat t = ta, say). After this occurs,

the remaining targets or analytes may be suddenlywashed out. In that case, desorbtion becomes thedriving mechanism. With the asymptotic conditionas an initial condition for the desorbption reaction,the kinetics of desorbtion is now governed by

−d[0]

dt = kd [0], leading to the following timevariation of surface concentration:

[0]

[0]a= 1− kd (t − ta) (5)

2.2. Kinetics of DNA hybridizationSince the molecular diffusivity of DNA fragments istypically one to three orders of magnitude smallerthan the typical liquid phase diffusivity of smallmolecules (∼ 10−9m2/s), the accumulation of DNAon the target spots by surface diffusion mechanisms



is rather slow. Interestingly, despite such slow overallreaction rates, the basic reaction step leading toDNA hybridization takes place much faster20. In thefirst phase, the probe DNA strand diffuses towardsthe target strand. During the subsequent collision, aso-called nucleation site is formed, involving theformation of the first short stretch of base pairing,concerning at least 3 contiguous bases. In thesubsequent phase, a stable base pair may be formedduring a rapid ‘zippering’ reaction. Otherwise, inthe case of a mismatch, the nucleation site looses itsstability, and the probe strand detaches and preparesfor another attempt, either with the same, or witha different target strand. With the basic bindingstep occurring very rapidly, the overall slownessof the hybridization may be attributed to the largenumber of successive attempts necessary before asuccessful collision and/or to the limited rate ofsupply of the unbound probe DNA strands. Tillnow, it is still not very clear which one of these twopotential bottlenecks forms the actual rate-limitingstep for the over-all hybridization process. As such,controversies still exist on the existence of a singledominant mechanism dictating the entire DNAhybridization steps. Some researchers claim thatthe process is fully reaction-rate limited21,22, whilesome others claim it to be diffusion-controlled23,24.One group of researchers24,25 prefer to model theDNA hybridization process as a homogeneousreaction in which the target and probe strands areboth suspended homogeneously in a liquid phaseenvironment, so that one can describe the rate ofreaction as

dH/dt = k[P −DN A][T −DN A] (6)

where P and T refer to the probe and targetDNA molecules and k is the reaction rateconstant. However, other studies23,26 have clearlydemonstrated that the heterogeneous conditionson a biochip cannot be adequately described bymeans of a single kinetic constant, k. These studieshave revealed that the kinetic constant has a strongtime-dependence, which may be expressed in thefollowing form:

k = k′t−p (7)

where p is a time-dependent coefficient. Forintermediate times, the value of p has been proposedas 1/2.23,26

The controversial aspects in the description ofDNA hybridization rates may perhaps be attributedto the existence of widely differing time scales anddisparate experimental conditions being employedto establish the theory. Intuitively, it can be expected

that on the short time scale, the binding responsemay be dominated by the slow binding probability.On the other hand, in the long time range, the slowdiffusive DNA supply may become the rate limitingstep. One of the most fundamental models of thebinding kinetics on DNA biochips was presentedby Chen et al.21. However, their model dealt witha steady-state supply of DNA probes on the targetspot surface20, and hence, could not capture thetime-dependent effects attributed to the very slowdiffusion rates of the DNA molecules. Pappaert etal.27 attempted to overcome these limitations, byintroducing a time-dependent diffusion transportmodel. To verify their model, they also conductedan extensive random walk simulation study. Todetermine the number of collisions per unit of timewith the target spot, they adapted the classical workof Collins and Kimball28 on the modeling of thekinetics of colloidal agglomeration processes. Theircalculation was essentially based on the numberof collisions with a surface per time and per unitsurface area (N), for a collection of moleculespresent at a concentration C, given as29

N = AuC (8)

where u is the product of the mean molecularjumping frequency (υ) and the mean molecularfree path (l), and A is a dimensionless geometricconstant. For the case of a pure 1-D collisionprocess, this value can easily be shown to be givenby A = 1/2. The number of successful collisions, n,can accordingly be obtained as

nχ= 1/2.uCχ (9)

where χ is the binding probability. Further, forthe satisfaction of the conservation of mass atthe reactive boundaries, one must have, at thoselocations

n = kC (10)

where k is given by

k = 1/2.υlχ (11)

For the case of 1-D diffusion, these parameterslead to the description of a molecular diffusioncoefficient, by invoking the theory of Brownianmotion, as30:

Dmol = υl2/2 (12)

Thus, from eqs (11) and (12), one may express k as

k = Dmolχ/l (13)



Figure 1: A schematic diagram depicting the dual mechanism of DNAhybridization

Considering the Langevin model of Brownianmotion30, it may also be possible to express kdirectly as a function of the basic physico-chemicalmolecular parameters. For a particle of radius ofgyration R and mass m, subjected to a randomlyvarying external force (Brownian force) and afriction force, the mean persistence length can bedescribed as

l =

√kBTm

3πµR(14)

where µ is the viscosity of the surrounding fluid, Tis the absolute temperature and kB is the Boltzmannconstant. Similarly, the mean collision frequency isgiven as

ν=3πµR

m(15)

Inserting eqs (14) and (15) in eq. (22), an expressionfor the binding rate constant k can be obtainedas a function of the basic molecular parameterssuch as the molecular mass, radius of gyration, etc.This analysis may also be extended to 3-Ddiffusionsystems, by replacing the factor of 2 in eq. (12) bya factor of 620 and the factor 1/2 in eq. (11) by afactor 1/429, so that one may write

k = 3Dmolχ/2l (16)

Despite being fundamentally based, a majorshortcoming of the above description lies in thefact that it does not specifically relate the reactionkinetics with the detailed mechanisms of DNAhybridization. It can be noted in this context thatDNA hybridization essentially occurs by means oftwo basic mechanisms (see fig. 1 for a schematicrepresentation), namely, (a) a direct (specific)hybridization from the bulk phase to the surface-bound probes, and (b) an indirect (non-specific)hybridization in which the target is initially non-specifically adsorbed on the surface and then diffusesalong the surface before reaching an available targetprobe molecule31. Researchers have been successfulin demonstrating how the above reduction ofdimensionality (RD) might enhance the overallDNA capture rate. In general, when a partner in abiomolecular reaction is immobilized on a surface,the rate of capture would depend on events inthe bulk (3-D) as well as on the surface (2-D),and on the relative ratio of solute diffusion tothe intrinsic reaction rate. However, hybridizationthat occurs in the interphase between a solid andsolution is anticipated to demonstrate kineticsthat are different from those observed in the bulksolution. It has been suggested in the literature21

that non-selective adsorption of single-strandedoligonucleotide, followed by surface diffusion (2-Ddiffusion coefficients) to immobilized probes canenhance hybridization rates in contrast to directhybridization in the solution. This suggestion isbased on a reduction of dimensionality of diffusionfrom a 3-D to a 2-D phenomenon. Exact theories inthis regard, however, are yet to be well established.Nevertheless, theoretical postulates have been putforward in the literature to describe the interactionsbetween the bulk and the surface phase kineticsmentioned as above. The reactions occurring at theprobe locations can be described by the followingrate equation31:

Ri = −

(∂c2,s

∂t+∂c2,ns

∂t

)(17)

where, c2,s and c2,ns are the surface-phaseconcentration of specifically and non-specificallyadsorbed target molecules, respectively, and 2a.Along the non-reacting surface, the above termreduces to a zero flux boundary condition, in effect.The terms involved in equation (17) can furtherbe expressed as a set of coupled two-dimensionalkinetic equations as31:

∂c2,s

∂t= [k1

3c3,m(c2,s,max − c2,s)− k−13 c2,s]

+ [k12c2,ns(c2,s,max − c2,s)− k−1

2 c2,s] (18)



Figure 2: (a): A schematic diagram depicting the problem domain (b): Aschematic diagram depicting the probe arrangements at channel walls

W

y

x

2a

(a)

(b)

and

∂c2,ns

∂t= [kac3,m(c2,ns,max − c2,ns)− kd c2,ns]

−[k12c2,ns(c2,s,max − c2,s)− k−1

2 c2,s] (19)

where, c2,s,max is the maximum concentrationof the hybridized targets (equivalent to the localconcentration of the surface bound probes availablefor hybridization), c2,ns,max is the maximumconcentration of the non-specifically adsorbedmolecules, c3,m is the bulk-phase concentrationof the targets in surface film, k1

3 is the kineticassociation constant for direct hybridization (fromsolution phase), k−1

3 is the kinetic dissociationconstant for direct hybridization (from solutionphase), k1

2 is the kinetic association constantfor indirect hybridization of the non-specificallyadsorbed targets (from surface phase), k−1

2 isthe kinetic dissociation constant for indirecthybridization of the non-specifically adsorbedtargets (from surface phase), ka is the kineticassociation constant for nonspecific adsorptionof the targets to the surface, and kd is the kineticdissociation constant for nonspecific adsorption ofthe targets to the surface. Physically, equation (18)describes that the rate of change in surfaceconcentration of hybridized species is a combinationof the rate of change of targets getting hybridizeddirectly from the bulk phase and the rate oftargets getting hybridized after an initial non-specific adsorption. Equation (19) implies that

the rate of change in surface concentration ofnonspecifically adsorbed targets is increased bythe rate of adsorption from the bulk phase, but isdecreased by the rate at which the non-specificallyadsorbed targets become hybridized.

Determination of the kinetic constantsappearing in equations (18) and (19) needsmicroscopic and statistical theories of collisionto be essentially invoked. A physical basis ofthis lies in the fact that pure diffusion, with itsfractal-like path, necessarily leads to an infinitelyhigh collision rate for the situation representedhere, manifested by a non-zero average soluteconcentration immediately in contact with eachtarget. To account for finite reaction rates withnon-zero local concentration in a diffusion-based framework, one must assume that thereaction probability per collision is diminishinglysmall, which may be a major deviation from thereality. The other approach, as briefly describedearlier, recognizes that the molecules follow aBrownian motion path rather than a pure diffusion,which yields a finite number of collisions from afinite solute concentration near the target probe.In Brownian motion, molecular velocity has afinite persistence length, since the instantaneousmomentum of the molecule can be transferred to thesolvent only at a finite rate of solvent velocity. Hence,the Brownian motion persistence length plays acentral role in determining both reaction kineticrates and reduction of dimensionality enhancement.Following fundamental postulates of statisticalphysics29 and the work of Anlerod and Wang20, itcan be postulated that the reaction rate of directhybridization (R3) can be obtained as a productof bulk-phase flux of target molecules collidingwith the surface (F3), probability of collisionlocation being a probe site (Pp), probability thatthe probe is available for hybridization (Pa) andthe probability that the collision will result insuccessful hybridization (Pr ). All these effects canbe combined to obtain the following equation forrate of reaction31:

R3 = k13C3,m

(C2,ns,max −C2,s

)(20)

where k13 =

3D3NvπR2pχ3

2S3. In equation (20), Nv is the

Avogadro number, Rp is the radius of probe site,χ3 is probability that 3-D collision will result ina successful hybridization and S3 is frequency ofcollision in 3-D. A similar approach can be followedto determine the rate of reaction for non-specificallyadsorbed target, as:

R2 = k12C2,ns

(C2,s,max −C2,s

)(21)



where k12 =

8D2Nv Rpχ2

S2. In equation (21), D2, χ2and

and S2 are similar to D3, χ3and and S3, except forthe fact that the earlier group represents a 2-Dcollision behaviour.

Although equations (20) and (21) arefundamental in nature, the reaction probability,χn, is rather uncertain. Instead, a classical Wetmur-Davidson relationship32 may be used to estimatethe rate of hybridization for bulk-phase targets inthe surface film as:

k13 = 3.5×105 l0.5

N(22)

where N is complexity of the target sequence andl is the number of nucleotide units. In general,complexity of the sequence is taken as the totalnumber of non-repeating sequences in a DNAstrand. In absence of any steric interference, inwhich the bulk molecules are able to move freelywithin the surface film, the above is likely to be validin an approximate sense. In cases of more denseprobe spacings or a large quantity of nonspecificallyadsorbed targets, equation (22), however, is likely tooverestimate the pertinent kinetic constant.

With the above estimation of k13, k1

2can beobtained by dividing equations (20) and (21), andassuming that χ2 = χ3, S2 = S3, as

k12 = k1

3

(16

3π

)(D2

D3

)(1

Rp

)(23)

The reverse kinetic constant may be obtained byappealing to thermodynamic stability requirementsof the dissociation kinetics representing the solidphase hybridization reaction. Thermodynamicstability of the target probe complex is governed byGibbs free energy of binding as

k1

k−1= exp

(−1G

RT

)(24)

where 1G = 1H −T1S, 1H being the bindingenthalpy and 1S being the binding entropy. Forbulk-phase hybridization, a nearest-neighbourmodel33 can be used to calculate 1G for anycomplementary or single-base-pair mismatchedduplex. For heterogeneous hybridization, however,thermodynamic stability condition deviates fromthe above classical result, as the probe density isincreased. Consequently, the above approximationis somewhat accurate in the limit of low probedensity, with an underlying assumption that othersurface effects are not thermodynamically important.Although some other thermodynamic models havebeen proposed in this respect34, these are not

comprehensive in terms of a complete theoreticaldevelopment. Instead, one may alternatively utilizeequation (24), with the incorporation of Arrheniustype of formulation for k1 and k−1 as

k1 (T) = k10 exp

[−

Ea

R

(1

T−

1

T0

)](25a)

k−1 (T) = k−10 exp

[−

Ed

R

(1

T−

1

T0

)](25b)

where k10 and k−1

0 are values of k1 and k−1 at T0

(T0 is 25◦C below melting temperature of DNA).Further, using Ea −Ed = 1H , k−1 can be estimatedfrom the above, on estimation of either Ea or Ed

(both of which are case-specific in nature). Now,since

k−1= k−1

2 + k−13 (26)

separate equations are required to estimateindividual rate constants k−1

2 and k−13 . To achieve

this goal, one may assume that at steady state anindependent equilibrium exists between directlyhybridized probes and targets of bulk solution, aswell as between indirectly hybridized probes andnonspecifically adsorbed target molecules18. Withincorporation of these into equation (18), it follows:

[k13c3,m(c2,s,max − c2,s,eq)− k−1

3 c2,s,eq] = 0

(27)

[k12c2,ns(c2,s,max − c2,s,eq)− k−1

2 c2,s,eq] = 0

(28)

where the subscript ‘eq’ represents an equilibriumstate. Equations (26)–(28) can be simultaneouslysolved to yield k−1

2 , k−13 and C2s,eq, to be used for

the subsequent mathematical analysis.Regarding nonspecific adsorption kinetics, one

may note that

ka

kd=

C2,n,eq

C3,m,eq(C2,ns,max −C2,ns,eq

) (29)

The unknown terms appearing in right hand side ofequation (29), however, are yet to be theoreticallydetermined. Therefore, we use experimentaloutcomes of Chan et al.35,36 to estimate C2,ns,eq,C3,m,eq and kd for various types of glass substrates.The term C2,ns,max can be estimated by notingthat because of a prior presence of surface probes(captured by specific hybridization) on target area, afull monolayer of targets cannot be adsorbed there,


Joule heating: Joule heatingrefers to the increase intemperature of a conductoras a result of resistance to anelectrical current flowingthrough it. At an atomic level,Joule heating is the result ofmoving electrons collidingwith atoms in a conductor,where upon momentum istransferred to the atom,increasing its kinetic energy.


leading to an effective radius of adsorbed target, Rt .Accordingly,

C2,ns,max =1−πR2

pNv C2,s,max

NvπR2t

(30)

With the estimates mentioned as above, ka can beobtained from equation (29), leading to a completedetermination of kinetic constants appearing in thedescription of the rate of surface reaction, as givenby eq. (17).

3. Continuum conservation considerations3.1. Fundamental transport equationsDas et al.18 have recently extended the DNAhybridization model developed by Erickson etal.31 to include combined effects of electrokineticand pressure-driven transport. In their study, acomprehensive mathematical model was developed,quantifying the pertinent momentum, heat andspecies transfer rates. Influences of bulk and surfaceproperties on the velocity field were criticallyexamined, which in turn dictate the nature ofthermosolutal transport, and hence the DNAconcentration fields, in accordance with specificand non-specific hybridization mechanisms. Jouleheating37 and viscous dissipation effects werealso incorporated, which can cause a perceptibletemperature rise, and accordingly affect variousflow parameters as well as the rate constants for thehybridization.

The fundamental analysis executed by Das etal. (2006a)18 deals with the microfluidic transportthrough a parallel plate microchannel of height 2aand width w, with w � 2a (refer to fig. 2a). Lengthof the channel is taken to be L0. Two capturingDNA probes are assumed to be attached to thebottom wall, each spanning over a length of LP(refer to fig. 2b). A potential gradient is appliedalong the axis of the channel, which provides thenecessary driving force for electroosmotic flow.Under these conditions, an EDL forms near theliquid–wall interface. This EDL interacts with theexternally applied electrical field. For example,positively charged ions of EDL are attracted towardscathode and repelled by the anode, resulting in anet body force that tends to induce bulk motionof ionized fluid in the direction of electric field.When this voltage is applied to a buffer solutionwith a finite thermal conductivity, the resultingcurrent also induces an internal heat generation,often referred to as Joule heating. The thermal andfluid flow field, thus established within the channel,is responsible for the macromolecular transport,which is to be understood thoroughly to get acomplete picture of the hybridization model. Formathematical modeling of the problem mentionedas above, following major assumptions are made18:

(i) The temperature, velocity and concentrationfields are unsteady and two-dimensional.

(ii) The effect of pH change on the ensuingchemical reactions due to hydrogen andhydroxyl ions is neglected.

(iii) The effect of charges carried by the DNAspecies on the electric field is neglected.

(iv) The effect of permeation layer on the DNAtransport and accumulation and electric fielddistribution is neglected.

The governing transport equations, under thesecircumstances, can be described as follows:

Continuity Equation:

∂ρ

∂t+∇ .(ρEV) = 0 (31)

X-momentum equation:

∂

∂t(ρu)+∇ .(ρEVu) = −

∂p

∂x+∇ .(µ∇u)+bx

(32)

where bx is the body force term per unit volumein x-direction , given as: bx = −ρe

∂φ∂x , where ρe is

the net electric charge density and φ is the potentialdistribution due to an externally imposed electricfield.

Y-momentum equation:

∂

∂t(ρv)+∇ .(ρ EV v) = −

∂p

∂y+∇ .(µ∇v)+by

(33)where by is the body force term per unit volume

in y-direction , given as: by = −ρe∂φ∂y . In both

equations (32) and (33), the dynamic viscosity,µ, is a function of temperature, given as

µ= 2.761×10−6 exp

(1713

T

)(34)

where T is in K and µ is in Pa.s. It can be notedhere that the distribution of φ needs to be solvedfrom the Laplace equation, as a consequence of anexternally imposed electrical potential gradient. Thecorresponding governing differential equation is asfollows:

∇ . (σ∇φ) = 0 (35)

where σ is the electrical conductivity of thesolution. Further, distribution of the net electriccharge density, ρe, appearing in the momentum


Poisson-Boltzmannequation: ThePoisson-Boltzmann equationis a mathematicalcombination of the Poissonequation for the electrostaticpotential variation and theBoltzmann distribution ofionic charges.


conservation equations, is to be ascertained bysolving the Poisson–Boltzmann equation for surfacepotential distribution as:

∇ .(ε∇ψ) = −ρe

ε0(36)

where ψ denotes the electric double layer (EDL)potential, ε0 is the permittivity of free space, and εis the dielectric constant of the electrolyte which is afunction of temperature, given as

ε= 305.7exp

(−

T

219

)(37)

where T is in Kelvin. In equation (36), ρe isdescribed as:

ρe = −2n0ezsinh

(ezψ

kBT

)(38)

where, n0 is the ion density (in molar units), eis the electronic charge, z is the valence, kB isthe Boltzmann constant, and T is the absolutetemperature. To depict the relationship between thenet electric charge density and Debye length, onemay express n0 as a function of the Debye length, l,as

n0 =εkBT

8πe2z2l2(39)

Energy conservation equation:

∂

∂t(ρCP T)+∇ .(ρCP EV T) = ∇ .(k∇T)+ϕ+ q

(40)where k is the thermal conductivity of the electrolytesolution, which is a function of temperature, givenas

k = 0.6+2.5×10−5T (41)

where T is in K and k is in W/m2.K. Inequation (40), ϕ is the heat generation due toviscous dissipation, given as

ϕ= 2µ

[(∂u

∂x

)2

+

(∂v

∂y

)2]

+µ

(∂u

∂y+∂v

∂x

)2

(42)Further, q is the heat generation due to Joule heating,which, according to Ohm’s law, can be given as

q =I2

σ(43)

It can be noted here that the electrical currentdensity includes two parts, one is due to the applied

electric field imposed on the conducting solution(σEE), and the other is due to the net charge densitymoving with the fluid flow (ρe EV ). Therefore, theelectrical current density, I can expressed as

EI = ρe EV +σEE (44)

Using equations (43) and (44), one can obtain theheat generation due to Joule heating as:

q =

(ρe EV +σEE

).(ρe EV +σEE

)σ

(45)

Species conservation equation:

∂(ρci)

∂t+∇ .

(ρ EV ci

)= ∇ . (ρDn∇ci)

+µosziF∇ . (ρci∇φ)+ρRi (46)

where, ci is the concentration of the ith species inthe solution, µos is the electro-osmotic mobility ofthe concerned species, zi is the valence of the ith

species, F is Faraday’s constant. In equation (46),Dn is a generalized diffusion coefficient, which is theliquid phase diffusion coefficient (D3) in the bulkfluid and surface phase diffusion coefficient (D2) atthe nonspecific adsorption sites. The term Ri is ageneration/source term, as described by eq. (17) andas adjusted in terms of its units by dividing eq. (17)with the height of the boundary control volume.

The governing conservation equationsdeveloped here lead to a well-posed system ofpartial differential equations, on specification ofthe appropriate boundary conditions. It can benoted here that boundary conditions correspondingto DNA hybridization are already incorporatedthrough specification of the source term Ri

(equation (17)) for control volumes adjacent to thechannel–fluid interface, and need not be duplicatedin prescription of boundary conditions. Otherpertinent boundary conditions are summarized inTable 118.

3.2. Simplified analytical considerationsIt is important to note here that the numericalcomputations necessary to simulate the detailedtransport/hybridization model described above maybe somewhat involved in nature, primarily becauseof the strongly interconnected and complicatedfeatures of mass, momentum and species transportcharacterizing the entire sequence of events. Undercertain restricted conditions, however, approximateanalytical solutions can also be obtained, depictingthe interactions between an imposed electroosmoticflow-field and the transient DNA hybridization



Table 1: Table of boundary conditions

Boundary conditionsGoverning Equation Inlet (x = 0) Outlet (x = L0) Bottom wall (y = 0) Top wall (y = 2H)

Laplace eq. (eq. 35) φ= φ0 φ= 0∂φ

∂y= 0

∂φ

∂y= 0

Poisson-Boltzmannequation (eq. 36)

ψ= 0∂ψ

∂x= 0 ψ= ζ (zeta potential) ψ= ζ (zeta potential)

Continuity andMomentum conservation(eq. 31–33)

u = uin or∂p

∂x= K0(K0 is a

constant) v = 0

∂u

∂x= 0 v = 0

u = 0

v = 0

u = 0

v = 0

Energy conservation (eq.40)

T = T∞

∂T

∂x= 0 T = Tw T = Tw

Species conservationequation (eq. 46)

ci = c∞

∂ci

∂x= 0

∂ci

∂y= 0

∂ci

∂y= 0

occurring in a microchannel. Such models can turnout to be of immense scientific appeal, in terms ofhaving a quantitative capability of directly capturingthe influences of various consequential parameters(such as fluid flow) on DNA hybridization rates,through development of close-formed expressions,without demanding more involved numericalsimulations, in many cases. Keeping this in view,Das et al.38 have recently obtained closed-formexpressions depicting the role of flow field onDNA hybridization rates. For analytical treatment,they assumed the fluid to be of constant physicalproperties, and flow field to be fully developed.Furthermore, a linear bulk concentration gradient( ∂C∂x = M, say) was assumed to be imposed along

the microchannel axis (height of the microchannelbeing taken as H). The concentration boundaryconditions adopted in their study were as follows:

Initial Condition: C(0,y) = 0 for 0 ≤ y ≤ H

(47)

Boundary conditions:∂C(t ,H)

∂y= 0 for t > 0

(47a)

D∂C(t ,0)

∂y= −

∂CH

∂tfor t > 0

(47b)

where CH is the instantaneous surface phaseconcentration of the hybridized targets and D isthe diffusion coefficient of single stranded DNAmolecule. The relationship between CH and theconcentration in the bulk was given as

∂CH

∂t= ka(CH ,max −CH )Cf ilm − kd CH (48)

where ka is the kinetic association constant forhybridization of the target with complementaryprobes and kd is the kinetic dissociation constantfor hybridization. In equation (48), Cf ilm refersto the solution phase concentration of the DNAat the surface film, and CH ,max is the maximumconcentration possible for the hybridized targets(which is equal to the initial concentration of thepatterned probes on microchannel surface). The firstterm in R.H.S. of equation (48) represents secondorder kinetics of DNA hybridization, consideringthat the rate of hybridization depends on theconcentration of the target oligonucleotides closeto channel surface as well as the concentrationof hitherto non-hybridized free probe molecules.In contrast, the kinetics of dissociation of theprobe-target pair complex depends only on theconcentration of hybridized species, and fairlyfollows first order reaction kinetics (secondterm in R.H.S. of equation (48)). The analyticalsolution for the DNA concentration distribution, asobtained from the above mentioned study, can besummarized as follows (for details of the derivation,see Das et al.38):

C(y,t)=

∞∑n=1

αn(t)cos( nπy

H

)−

Ee−Ft

2HD(2Hy−y2)

(49)

In equation (49), αn(t) is given as:

αn(t) = −2EH

D(nπ)2e−M1 t

−2

He−M1 t

[I1L′2 + I2M ′

2

−I3N ′2 − I4P′

2 + I ′1L′

3 + I ′2M ′

3 − I ′3N ′

3 − I ′4P′

3] (50)

Various parameters appearing in equations (49),(49a) are described in Appendix A.



Figure 3: Variation of concentration of hybridized targets with time, atprobe location 1, for all cases. The pressure gradients taken for thecomputations are as follows: displaystyle ∂p

∂x= −105 Pa/m (favourable) and

∂p

∂x= 105 Pa/m (adverse).

0.1

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

00 10 20 30 40 50

C/C

in

time (s)

Pure electroosmotic flowMixed flow with adversepressure gradientMixed flow with favourablepressure gradient

3.3. Numerical simulation predictionsIn order to obtain significant insights regardingtemporal variations of DNA concentration(hybridized targets, c2,s) at the probes as a functionof prevailing flow conditions, one may refer tofig. 318. These simulations were carried out byemploying the physical parameters and problemdata enlisted in Table 2. Fig. 3, in essence, showsan initial slow rate of increment of c2,s, followedby a comparatively higher hybridization rate thateventually approaches towards a saturation statewith respect to time. It is observed that during initialtransients, the concentrations of hybridized targets,for each of the cases investigated, remain somewhatclose to each other. However at later instants oftime, as the system approaches towards a meta-stable state, concentration values correspondingto different situations investigated in the above-mentioned study start differing widely from eachother. For a pure electroosmotic flow, the steadyvalue of c2,s is found to be somewhat less than thatcorresponding to a mixed flow occurring under afavourable pressure gradient, but turns out to besignificantly greater than that observed for a mixedflow occurring under an adverse pressure gradient.This variation can be explained by arguing that forpure electroosmotic flows, the bulk concentration,and hence the film concentration (c3,m), is lessas compared to that established in presence of

a favourable pressure gradient, but more thanthat established in presence of an adverse pressuregradient. This, in turn, ensures the correspondingvariations in c2,s values, in an analogous fashion.It has also been earlier demonstrated that the rateof the hybridization reaction can be significantlyincreased due to a non-specific adsorption ofthe single stranded DNA on the surface, and asubsequent 2-D diffusion towards surface-boundcomplementary probe molecules, as compared tothe sole effect of 3-D hybridization from the bulk20.Hence, the initial slowness of hybridization can beexplained considering the ‘lag time’ between non-specific adsorption and consequent hybridization tothe probe, mediated by two-dimensional diffusion.During this time, three-dimensional hybridizationreaction dominates. However, once the lag phaseis over, the rate of hybridization reaction increasesat a faster pace, due to a coupled effect of thetwo types of mechanisms, and saturation reaction-kinetics are eventually achieved when all the singlestranded probe molecules become hybridized withtarget complementary oligonucleotides. Regardingthe specific impact of pressure gradients on DNAhybridization, it is revealed that steeper temporalgradients in concentration can be achieved withfavourable pressure gradients, especially duringearly stages of hybridization. On the other hand,imposition of an adverse pressure gradient of similarmagnitudes may not be consequential enough toretard the hybridization rates drastically. This maybe attributed to the fact that although such adversepressure gradient decelerates the flow locally, it alsoensures that the target DNAs have a greater exposuretime with the complementary capture probes, withan enhanced probability of hybridization. For theadverse pressure gradients reported in the above-mentioned study18, these two counteracting effectsalmost nullify each other, leading to relativelyinsignificant impacts on the resultant hybridizationbehaviour, especially during the early transients.

Typical cross sectional temperature distributions,as obtained from the above-mentioned study,are depicted in fig. 4(a). It is observed that thecurves corresponding to adverse and favourablepressure gradients almost merge with each other.This suggests that the effect of pressure gradients(within the range of values adopted in theirstudy) is relatively insignificant in determiningthe thermal field within the microchannel. Thiscan be justified by noting that the temperaturerise in the channel can be primarily attributedto Joule heating, which is solely dependent onthe applied potential gradients and the electricalconductivity of the medium. An order of magnitudeanalysis, assessing the relative contributions of


Onsager reciprocityrelationship: The Onsagerreciprocal relations expressthe equality of certainrelations between flows andforces in thermodynamicsystems out of equilibrium,but where a notion of localequilibrium exists. Forexample, it is observed thattemperature differences in asystem lead to heat flowsfrom the hotter to the colderparts of the system. Similarly,pressure differences will leadto fluid flow fromhigh-pressure to low-pressureregions. It was observedexperimentally that whenboth pressure andtemperature vary, pressuredifferences can cause heatflow and temperaturedifferences can cause matterflow. Even more surprisingly,the heat flow per unit ofpressure difference and thedensity (matter) flow per unitof temperature difference areequal. This was shown to benecessary by Lars Onsagerusing statistical mechanics.Similar “reciprocal” relationsoccur between different pairsof forces and flows in avariety of physical systems.


Table 2: Table of physical properties and problem data

Parameter Value

L0 8.5×10−3 mLF 5.0×10−3 mLP 1.7×10−4 mLD 1.7×10−3 m2H 50 µmσ 10−3 S/mε0 8.854×10−12 C/Vmn0 1 mol/m3

e 1.6×10−19 Cφ0 150 Vuinit ial 2.0 m/sξ −50 mVTw 300 KT∞ 300 Kρ 998 kg/m3

kB 1.38×10−23 J/Kµos 4×10−8 m2/Vsz 20cin 1.0×10−6 Mc3,m 1.9×10−7 Mc2,s,max 2.0×10−7 mol/m2

c2,ns,max 1.98×10−7 mol/m2

k13 1×106(1/Ms)

k−13 0.49(1/s)

k12 1×106m/Ms

k−12 0.51(1/s)

ka 9×103(1/Ms)kd 0.3(1/s)D3 1.3×10−10 m2/sD2 5.0×10−13 m2/s

the terms (σEE) and (ρe EV ) in the expression forthe net current (see Eq. 44), aptly justifies this

proposition (Noting that∣∣∣ EEσ

ρe EV

∣∣∣∼ O(105)). Another

important observation is that over typically shortdurations of time (O(s)), the temperature riseowing to Joule heating effects is virtually negligible.However, for larger time durations (fig 4b), thetemperature rise becomes much more consequential,and is likely to result in significant changes inDNA transport characteristics. This interesting issuemay be more critically analyzed by referring tothe energy equation (Eq. 40), in which one maycompare the order of magnitude of the advection

and the source terms, to obtain 1T ∼σE2

x tρCp

, where

1T is a characteristic temperature rise. This showsthat the rise in temperature scales linearly with theoperational time, all other parameters remainingunaltered. Moreover, the same scales with the squareof the electric field, corresponding to a specificbuffer solution and a given temporal instant. Hence,even slight increments in the electric field strengthcan result in significant rises in sample temperature.For transport and hybridization of macromoleculessuch as DNA, this rise of temperature may be of

immense consequence, primarily attributable to aphenomenon called ‘melting’ or ‘denaturation’ ofDNA, which is characterized by separation of thetwo DNA strands from an existing hybridized state.This splitting occurs at the melting temperature,Tm, defined as the temperature at which 50% ofthe oligonucleotides and their perfect complementsare in duplex. In order to avoid problems likeinappropriate duplex formation, primer mismatchetc., the hybridization is typically carried out5◦–10◦C below Tm. Hence it is important thatthe temperature rise due to Joule heating duringhybridization is not more than around 5◦C.Corresponding to typical physical parametersemployed in the study of Das et al.18, the order ofthe imposed electric field needed to be constrainedwithin 105V/m, so as to ensure that the temperaturerise is restricted within 5◦C, thereby avoidingdenaturation or melting of DNA samples. Moreover,during experimentation, it is also important to carryout the hybridization at a reasonably rapid rate, soas to ensure that the hybridized targets are saturatedwithout incurring any further denaturation due tooverheating.

4. Recent advancements and futuredirections

4.1. DNA hybridization by employing transverseelectric fields in conjunction with surfacepatterning

Extending the fundamental theoreticalunderstandings, researchers are in a continuousendevor to obtain faster rates of DNA hybridizationthrough the employment of a combination of several‘augmenting’ mechanisms in integrated microfluidicplatforms. Some of the recent findings on reactivesystems with electrokinetic transport have revealedcertain interesting propositions in this regard, whichcan be potentially exploited to obtain enhancedrates of DNA hybridization. For example, Das andChakraborty39, in a recent study, have theoreticallyestablished a novel proposition that the rate ofmacromolecular adsorption can be augmentedwith application of transverse electric fields acrosspatterned walls of a microfluidic channel. In theirstudy, first, an approximate fully developed velocityprofile was derived, which was subsequently utilizedto solve the species conservation equation pertainingto a combined advection-diffusion transport.Closed-form solutions for the concentration fieldwere subsequently obtained, in consistency with thetypical second order kinetics of macromolecularadsorption. The above-mentioned theoreticalanalysis has revealed that the favourable effect oftransverse electric fields can be best exploited when



Figure 4: (a): Temperature profiles within the channel, at location ofprobe 1 (curves corresponding to both adverse and favourable pressuregradients almost merge) (b) Temperature profiles within the channel, atlarge time instants at location of probe 1 (curves corresponding to bothadverse and favourable pressure gradients almost merge)

0

312

310

308

306

304

302

3000.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y/2H

Tem

pera

ture

(K

)

t=2000sect=1000sec

300.25

300.2

300.15

300.1

300.05

3000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y/2H

Tem

pera

ture

t=25sect=20sect=15sect=10sect=5sec

(a)

(b)

they are employed in conjunction with patternedmicrochannel surfaces. This is because of the factthat a transverse electric field, when applied acrossthe walls of a microchannel with periodic surfacepatterns, may result in an additional pressuregradient in the axial direction40, by followingOnsager reciprocity relations. This effect hasbeen subsequently utilized by us to study theenhancement in the surface adsorption of biologicalmacromolecules39, with a combination of transverseelectric fields and surface patterning effects. It wastheoretically demonstrated that with an externallyapplied favourable pressure gradient of the order of105 Pa/m, along with an axial electric field of theorder of 10000 V/m and a transverse electric fieldof the order of 1000 V/m, a DNA hybridizationtime of as low as 30 s could be achieved with a

pattern angle of 45◦. However, comprehensiveexperiments need to be conducted to demonstratethe practical consequences of this theoreticalproposition. Following major conclusions could bedrawn from the above-mentioned study:

(i) Benefits of transverse electric fields cannot beeffectively realized if the channel surfaces arenot patterned, which is primarily attributableto the excess equivalent pressure gradient thatcannot be exploited without surface patterning.

(ii) For moderate values of axial potentialgradient, increase in orders of magnitude oftransverse potential gradients can augmentthe rate of macromolecular adsorptionsignificantly. However, a large value of theaxial potential gradient may virtually suppressany contributions from an enhanced transverseelectric field, and can dictate the adsorptionrate by itself alone. Nevertheless, such extremesituations might be rather undesirable, becauseof adverse effects of Joule heating andsubsequent macromolecular degradation onaccount of high electrical field strength. Hence,in place of a strong axial electric field, acombination of moderate values of axial andtransverse electric fields can turn out to abetter proposition for the practical purposeof enhancement of macromolecular transportand adsorption rates.

(iii) The beneficial effects of transverse electricfields in terms of augmenting the rate ofmacromolecular adsorption can be bestexploited for pattern angles in the tuneof 45◦. While acute angles turn out to beadvantageous in this respect, in general, obtuseangles effectively slow down the rate ofmacromolecular transport by inducing anequivalent ‘adverse’ pressure gradient thatretards the rate of macromolecular transport.

(iv) In practice, a judicious combination oftransverse electric fields and surface patterningeffects can be employed, to augment the rate ofmacromolecular adsorption, without incurringany adverse implications of Joule heating andconsequent macromolecular degradation onaccount of axial electric fields of too high astrength.

4.2. DNA hybridization by rapid micromixingHeule and Manz41 explored the prospects ofperforming DNA hybridization assays in asequential scheme, containing a split channelsystem for fast micromixing and a subsequentmeandering channel to observe the evolution ofthe mixture by optical means. The problems of



limited mixing in the laminar flow regime wereovercome by reducing the average diffusion distanceto a few micrometers only. DNA oligomers (20-mers) of different sequences were injected on thechip for mixing. Two modes of operation wereinvestigated. First, the samples were injected into themicromixing device at a high flow rate of 40 µl/min.The flow rate through the micromixing unit wasreduced, when the sample was passed through thesame, to allow for the measurement of fluorescencelevels at various steady-state reaction times in therange of 2–15 s. In a buffer containing 0.2 M NaCl,2 basepair mismatches could routinely be detectedby employing this method within 5–20 s. Singlebase-pair mismatches were successfully identifiedwith low salt concentrations. In the second mode,the flow was completely stopped and the evolutionof the total fluorescence signal influenced by thehybridization of oligomers and photobleaching wasobserved. While certain technological difficulties(such as the periphery providing a steady streamof samples) still need to be addressed to ensure asuccessful operation of such hybridization assaysin practice, this method holds the potential ofproviding for a very flexible and versatile platformfor genomic analysis. A rigorous theoretical analysis,therefore, needs to be directed to substantiate thisviewpoint.

4.3. DNA hybridization by CMOS biochipsBarbaro et al.42 have recently developed low-cost,portable and fully integrated solid-state biosensorsfor the label-free detection of DNA hybridization.This new device was realized in a standardComplementary Metal Oxide Semiconductor(CMOS) process. The detection mechanism wasbased on the field-effect of the intrinsic negativeelectric charge of DNA molecules, which modulatesthe threshold voltage of a floating-gate MOStransistor. A fluid cell was developed for deliveringthe DNA samples on the active surface of the chip.Successful measurements on first prototype of thechip, hosting 16 individually addressable sensors,were also presented as a proof of this concept.Detailed mathematical analysis need to be carriedout to optimize the performance of these kinds ofCMOS-based DNA chips, based on the underlyingtransport processes, many of which are non-triviallyinterlinked.

4.4. Microwave-accelerated fast DNAhybridization

Aslan et al.43 designed a fast and sensitive DNAhybridization assay platform, based on microwave-accelerated metal-enhanced fluorescence (MAMEF).

In their experiments, thiolated oligonucleotideanchors were immobilized onto silver nanoparticleson a glass substrate. The hybridization of thecomplementary fluorescein-labeled DNA targetwith the surface-bound oligonucleotides could becompleted within 20 s, on heating with low-powermicrowaves. In these studies, a significantly reducednon-specific adsorption rate was noted when usingmicrowave heating near to silvered structures, ascompared to room temperature incubation. Thesefindings suggest that MAMEF could be a usefulalternative for designing DNA hybridization assayswith improved sensitivity and rapidity. Theoreticalmodeling efforts need to be directed to establishthis proposition from a rigorous mathematicalperspective, so as to impose more stringent controlson this suggested methodology.

4.5. DNA hybridization on a CDThe recent advent of CD-based microfluidics (lab-on-a-CD concept) has opened up the possibilitiesof implanting complicated bio-microfluidicarrangements in CD-based platforms44,45. Besidesbeing advantageous because of their versatilityin handling a wide variety of sample types, theability to gate the flow of liquids (non-mechanicalvalving), simple rotational motor requirements,economised fabrication methods, and large range offlow rates attainable, the possibility of performingsimultaneous and identical fluidic operations makesthe CD an attractive platform for multiple parallelassays. The CD platform (including the designedcircuitry embedded within the same), coupledwith automated liquid reagent loading systems,is ideal for a future commercial introduction ofmore compact and inexpensive lab-on-a-chip basedbio-microfluidic systems.

The technology developed by the optical discindustry can conveniently be utilized to imagethe CD at the micron resolution, and possibleextensions to DVD will allow submicron-scaleresolution, leading to the integration of fluidicsand informatics on the same disc. Moreover, thematerials of the CDs are conducive for elegantmicrofabrication and are also extremely bio-compatible in terms of handling the DNA molecules.In a study undertaken by Jia et al.46, an automatedflow-through DNA hybridization and detectionmethod was implemented and experimentallyvalidated on a CD-based fluidic platform. Amultilevel process utilizing SU-8 lithography wasdeveloped to obtain the fluidic structures withsufficient reagent storage volume and the desiredflowrate. Thiolated-ssDNAmonolayers on gold spotswere used as capturing probes and biotinylated



complementary DNA was used as the target probe.Hybridization was detected for DNA samples ofdifferent concentrations down to 100 pM. Thetheoretical analysis presented in this regard, however,was not detailed enough to involve the solutionof the kinetically-coupled transport equations.Further, from a practical viewpoint, it could alsobe recognized that with the aid of centrifugalforces alone, the CD-based DNA hybridizationarrangements, even under the most favourableconditions, could result in hybridization times ofonly of the order of few minutes. This is primarilybecause of the fact that the centrifugal force, being avolumetric (body) force, does not scale as favourablyas the surface forces over the micro-domain.However, with the additional flow-augmentingfeatures (such as, the application of transverse andaxial electric fields, surface patterning effects), anintegrated and portable CD-based biomicrofluidicplatform can indeed be conceptualized, with anideal combination of fast DNA hybridization andinexpensive device fabrication. Detailed theoreticalanalyses in this regard, indeed, fall in the scope offuture research in this area.

4.6. Some more fundamental considerationsIn the mathematical models outlined so far, theconformational aspects of the DNA molecules havenot been explicitly considered, for describing thetransport and hybridization processes within themicrofluidic conduits. Fundamentally, these issuescan be of significant consequence for deriving moreaccurate DNA transport models, in the contextof hybridization reactions. Although the DNAmolecules resemble coils in a non-flowing state,these DNA molecules stretch and orient in thesame direction in a flowing state47. According totheoretical studies of coil–stretch transition48, theextent of stretching and shrinking of polymer chainsdepends on the microchannel size, the polymerchain length, the flow speed, and the viscosity,density, and temperature of the solution. In fact,the DNA molecules change their conformationdepending on the flow rates. At lower flow rates,the DNA molecules move while expanding andcontracting, analogous to inchworms. On theother hand, at higher flow rates (>5 µl/min), theDNA molecules stretch and undulate, as if theyare swimming in a fluid-current. Moreover, theDNA strands became shorter in highly viscousenvironments and tend to become longer in highertemperature conditions, analogous to the coil–stretch transition48 behaviour of polymer molecules.The consequences of these mechanisms, in thecontext of DNA hybridization, may be far from

being trivial. In fact, it has been experimentallyrevealed that DNA stretching in microfluidicsengenders efficient hybridization of long-strandDNAs47. In a non-extensional flow, the short DNAprobes might not be able to interact with theircapturing counterparts, since these DNA moleculesform entangled coiled structures. In contrast,in extensional flows through microchannels, thehybridization is likely to occur more efficientlybecause of the promoted stretching. Control ofthe extent of this DNA stretch may be achievedby adjusting the solution chemistry and the flowconditions. Molecular dynamics and/or coupledcontinuum/molecular simulations may need tobe executed to quantitatively substantiate thisviewpoint. Not only that, detailed thermodynamicstudies also need to be executed to establish accuratetheoretical description of the variations in the freeenergy of the DNA molecules, while undergoingvarious bio-chemical reactions in the process oftheir hybridization. Carlon and Heim49, in a recentstudy, have recently presented a thermodynamicanalysis of RNA/DNA hybridization in high-densityoligonucleotide microarrays. This kind of analysis,however, needs to be theoretically extended inthe future to improve the parametrization ofthe pertinent experimental data and enhance thestability of the fitting parameters for predicting thehybridization free energies of a wide variety of DNAsamples.

4.7. Summary and OutlookPressure-driven transport has conventionally beenthe most popular method to achieve microfluidics-based DNA hybridization. However, pressure-driventransport of biological molecules in microchannelsis associated with several shortcomings, such as theloss of injected samples due to significant dispersioneffects, the necessity of a substantial pumpingpower, and the inability to generate complex flowpatterns. As an alternative, the electrokinetic flowactuating mechanisms have subsequently beenproposed. The advantages with such systems arethe ‘pumpless’ operation modes, minimized sampledispersion and an excellent integrability with bio-chip components. Researchers have demonstratedthat such mechanisms can be employed to enhancethe rate of accumulation of DNA molecules overthe electrodes (saturation is achieved in as low as2 minutes), by exploiting an interesting interplay ofthe dual mechanisms of 3-D and 2-D hybridizationkinetics and the applied electric fields. Extendingthis concept, it has been theoretically establishedthat a judicious combination of axial electric fieldsand favourable pressure gradients can, in principle,



reduce the hybridization time to as low as 1 minute.However, in the process, the researchers could alsorealize that one can only employ limited strengthsof the axial electric fields in practice, so as to avoidthe adverse consequences of the Joule heating effectsassociated with the conductive transport of ioniccharges in a fluidic medium. In fact, in order toavoid denaturation/melting of hybridized DNAsamples, one can only employ an axial electric fieldthat does not permit any rise of temperature beyondapproximately 5◦C.

Researchers have also independently attemptedto employ transverse electric fields instead ofthe axial ones, for favorably exploiting theelectrophoretic migration of the charged DNAmolecules towards the capturing probes. As ongoingand future endeavors, the researchers might seek ajudicious combination of the axial and the transverseelectric fields, so as to exploit a favorable couplingof the effects of the convective DNA transportand the electrophoretic DNA accumulation. Inparticular, one may be interested to obtain theoptimal combinations of the axial and the transverseelectric fields that can give the fastest possible DNAhybridization out of the chosen configuration,without violating the Joule heating constraints.Theoretical research has shown that with sucharrangements, one could possibly reduce the DNAhybridization time from minutes to seconds. Thereare several other microfluidic issues that also need tobe addressed to exploit the possibilities of achievingmuch faster DNA hybridization rates. These includethe variations in flow rate, channel height, inletbuffer composition, DNA concentration, surfacepatterning effects in conjunction with transverseelectric fields, centrifugal effects etc. Typical flowrates that are currently being employed for DNAhybridization through pressure-driven flows arein the tunes if 10 µL/min17,50. On the other hand,recent theoretical investigations18 have revealedthat the plug-like velocity profiles associated withthe electroosmotic transport might require a flowrate as small as 0.10 µL/min, to achieve identicalhybridization rates.

With a combination of various hybridization-augmenting mechanisms, one could, in principle,achieve the same task of DNA hybridization withthe nominal flow rates lowered even further. It isimportant to recognize in this context that this kindof lowering of the desired flow rates is also associatedwith the requirement of lower sample volumes, fora given sensitivity of the diagnostic device. Not onlythat, it has been comprehensively revealed that for alow concentration of target DNA samples, lowervolumetric flow rates favor the DNA hybridization

efficiency17,50. Thus, flow rate control appears tobe an essential aspect of designing faster DNAhybridization microarrays. Selection of an optimumchannel height is also critical in ensuring the bestpossible rate of DNA hybridization. This is becauseof the fact that over different length scales, disparatephysical features might play the governing role incontrolling the transport and the hybridizationmechanisms. For example, when the channel heightis of the order of 10–100 µm, decreasing the channelheight significantly enhances the DNA hybridization.However, research investigations have revealed thatbelow a threshold channel height (typically, of theorder of 1 µm), the electric double layer formed atthe channel walls can significantly protrude intobulk, thereby causing a significant dispersion in theelectroosmotic flow profile. As a result, the transportand hybridization mechanisms could be significantlyhindered. It has also been well-demonstrated in theliterature that increases in the bulk concentrationmay lead to higher concentrations of the target DNAmolecules close to the capturing probes, therebyaugmenting the rate of DNA hybridization17,50.51,for example, used a bulk concentration of 0.4 µM,so as to achieve DNA hybridization rates of theorder of a few minutes.

While it is well understood that a moreconcentrated DNA solution is expected to havefaster hybridization characteristics, an indefiniteincrease in the bulk concentration of the targetDNA molecules is also not advisable. This is becauseof the fact that beyond a critical concentrationlimit (depending on the channel dimensions andflow characteristics), the rheological behaviour ofthe microflow might get significantly altered, withstrongly-hindered solutal transport characteristics.Moreover, in a recent theoretical investigation52, ithas been demonstrated that a non-uniform wall zetapotential, created by employing localized transverseelectric fields, can augment DNA hybridizationrates, with an optimal concentration of the inletbuffer. A characteristic hybridization time ofaround 45 seconds could be estimated from thetheoretical analysis, for a buffer pH of 4. Since thebuffer composition essentially dictates the effectivemacromolecular charge53, its diffusion coefficient54,and its electrophoretic mobility, an optimal choiceof the inlet buffer composition may result in themost favourable hybridization characteristics; allother conditions remaining unaltered. However,insufficient quantitative information is availablein the reported literature to conclusively establishthis proposition.

Preliminary theoretical analysis has also revealedthat the favourable effect of transverse electric fields



can be best exploited when they are employed inconjunction with patterned microchannel surfaces.This is because of the fact that a transverseelectric field, when applied across the walls of amicrochannel with periodic surface patterns, mayresult in an additional pressure gradient in the axialdirection, by following Onsager reciprocity relations.This effect has been utilized by researchers39 tostudy the enhancement in the surface adsorptionof biological macromolecules, with a combinationof transverse electric fields and surface patterningeffects. It has been theoretically demonstrated inthe above work that with an externally appliedfavourable pressure gradient of the order of 105

Pa/m, along with an axial electric field of theorder of 10000 V/m and a transverse electric fieldof the order of 1000 V/m, a DNA hybridizationtime of as low as 30s could be achieved witha pattern angle of 45◦. However, more detailedstudies need to be conducted to demonstratethe practical consequences of this theoreticalproposition. Additionally, one may utilize thecentrifugal forces involved in the rotation of CDsin the transport and subsequent hybridization ofDNA molecules in microfluidic channels46, so as toexploit the pertinent techno-commercial advantagesmentioned as earlier.

One may attempt to utilize optimalcombinations of various actuating mechanismsand the critical system parameters to achievea faster yet inexpensive methodology of DNAhybridization than the state-of-the-art affairs, andpractically implement the same through the designand fabrication of novel bio-microfluidic devices.To achieve this purpose, one needs to investigatea wide variety of parameters and configurations, soas to come up with a practically-implementable andrelatively inexpensive optimal methodology for fastDNA hybridization. Fundamental studies on themathematical description of the underlying fluiddynamic and bio-chemical transport mechanisms,indeed, are likely to play vital roles towards achievingthis goal, without attempting for too many ‘hit-and-miss’ type of expensive experimental trials. Moreextensive and detailed simulation studies, therefore,need to be executed to map the variations in themicrofluidic system parameters/configurations withthe DNA hybridization rates, for a wide range ofpractical conditions in order to come up with themost optimal solution.

AcknowledgementsThe author gratefully acknowledges the financial support provided by the NSF,

USA, for the Project titled “IRES: U.S.-India Fast DNA Hybridization in MicrofluidicPlatforms”, the financial support provided by the DST, Govt. of India for the projecttitled “Experimental and Theoretical Studies on DNA Hybridization in Microchannelswith Electrokinetically driven Flow”, and the financial grants provided by the Indo-USScience and Technology Forum for the Project titled ‘Indo-US Center on FuturisticManufacturing’, for doing this work. The author is also grateful to the principalforeign collaborator of his research group, Prof. M. J. Madou (University of California,Irvine), for his valuable comments and active support. Finally, the author alsoacknowledges the contributions of his two doctoral students, Siddhartha Das andTamal Das, for their valuable work related to microfluidics based DNA hybridization.

Appendix A: Description of parametersappearing in equations (49), (49a)

I1 =H

nπ[sin(

nπ

2)]

I2 =H

nπ[

H

2sin(

nπ

2)−

H

nπ]

I3 =H3

nπsin(

nπ

2)[

1

4−

2

(nπ)2]

I4 =H

nπ{1+ ( H

nπl)2}

[e−

H2l sin(

nπ

2)+

H

nπl]

I ′

1 = −H

nπsin(

nπ

2)

I ′

2 =H2

nπ[

cos(nπ)

nπ−

1

2sin(

nπ

2)]

I ′

3 = −H3

4nπsin(

nπ

2)+

2H3

(nπ)2cos(nπ)+2(

H

nπ)3 sin(

nπ

2)

I ′

4 =H

nπ{1+ ( H

nπl)2}

[H

nπle

H

l cos(nπ)− eH2l sin(

nπ

2)]

L′

2 =MuHS

M1

[eM1 t−1]+

E

H(M1 −F)[e(M1 −F)t

−1]

M ′

2 =EF

D(M1 −F)[e(M1 −F)t

−1]−MuHS

M1le

−H2l [eM1 t

−1]

N ′

2 =EF

2HD(M1 −F)[e(M1 −F)t

−1]

P′

2 =M

M1 uHS

[eM1 t−1]

L′

3 =

MuHS −H

le

−H

l MuHS

M1

[eM1 t−1]+

E

H(M1 −F)[e(M1 −F)t

−1]

M ′

3 =EF

D(M1 −F)[e(M1 −F)t

−1]+MuHS

M1le

−H2l [eM1 t

−1]

N ′

3 =EF

2HD(M1 −F)[e(M1 −F)t

−1]

P′

3 =M

M1 uHS

[eM1 t−1]

with M1 = ( nπH

)2 .

Received 28 November 2006; revised 25 January 2007.

References1. Schena M., Shalon D., Davis R.W., Brown, P.O., Quantitative

monitoring of gene expression patterns with a complementaryDNA microarray, Science 270, 467–470 (1995)

2. Brown P., Botstein D., Exploring the new world of the genomewith DNA microarrays. Nature Genetics 21(1 Suppl), 33–37(1999)

3. Bier F.F., Kleinjung F., Scheller F.W., Real time measurementof nucleic acid hybridization using evanescent wave sensors—steps towards the genosensor. Sensors and Actuators B 38,78–82 (1997)

4. Nkodo A.E., Garnier J.M., Tinland B., Ren H., Desruisseaux C.,McCormick L.C., Drouin G., Slater G.W., Diffusion coefficientof DNA molecules during free solution electrophoresis,Electrophoresis 22, 2424–2432 (2001)

5. Kassegne S. K., Resse H., Hodko D.,Yang J. M., Sarkar K.,Smolko D., Swanson P., Raymond D. E., Heller M. J., MadouM. J., Numerical modeling of transport and accumulation ofDNA on electronically active biochips, Sensors and ActuatorsB 94, 81–98 (2003)

6. Heller M.J., Forster A.H., Tu E., Active microelectronic chipdevices which utilize controlled electrophoretic fields formultiplex DNA hybridization and other genomic applications,Electrophoresis 21, 157–164 (2000)

7. Fan Z.H., Mangru S., Granzow R., Heaney P., Ho W., DongQ., Kumar R., Dynamic DNA hybridization on a chip usingparamagnetic beads, Anal. Chem. 71, 4851–4859 (1999)



8. Benoit V., Steel A., Torres M., Lu Y.Y., Yang H.J., Cooper J.,Evaluation of three-dimensional microchannel glass biochipsfor multiplexed nucleic acid fluorescence hybridization assays,Anal. Chem. 73, 2412–2420 (2001)

9. Adey N.B., Lei M., Howard M.T., Jenson J.D., Mayo D.A., ButelD.L., Coffin S.C., Moyer T.C., Hancock A.M., EisenhofferG.T., Dalley B.K., Mcneely M.R., Gains in sensitivity witha device that mixes microarray hybridization solution in a25-mu m-thick chamber, Anal. Chem. 74, 6413–6417 (2002)

10. Wang Y., Vaidya B., Farquar H.D., Stryjewski W., HammerR.P., Mccarley R.L., Soper S.A., Microarrays assembled inmicrofluidic chips fabricated from poly(methyl methacrylate)for the detection of low-abundant DNA mutations, Anal.Chem. 75, 1130–1140 (2003)

11. Woolley T., Hadley D., Landre P., deMello A.J., Mathies R.A.,Northrup M.A, Functional integration of PCR amplificationand capillary electrophoresis in a microfabricated DNAanalysis device, Anal. Chem. 68 (1996) 4081–4086.

12. Waters C., Jacobson S.C., Kroutchinina N., Khandurina J.,Foote R.S., Ramsey J.M., Microchip device for cell lysis,multiplex PCR amplification, and electrophoretic sizing, Anal.Chem. 70, 158–162 (1998).

13. Hadd A.G., Raymound D.E., Halliwell J.W., Jacobson S.C.,Ramsey J.M., Microchip device for performing enzyme assays,Anal. Chem. 69, 3407–3412 (1997)

14. Chiem N., Harrison D.J., Microchip-based capillaryelectrophoresis for immunoassays: analysis of monoclonalantibodies and theophylline, Anal. Chem. 69, 373–378 (1997).

15. SalimiMoosavi H., Tang T., Harrison D.J., Electroosmoticpumping of organic solvents and reagents in microfabricatedreactor chips, J. Am. Chem. Soc. 119, 8716–8717 (1997)

16. Das S., Chakraborty S., Analytical Solutions for velocity,temperature and concentration distribution in electroosmoticmicrochannel flows of a non-Newtonianbio-fluid, AnalyticaChimica Acta 559, 15–24 (2006a)

17. Kim J. H-S., Marafie A., Jia X-Y, Zoval J. V., Madou M.J., Characterization of DNA hybridization kinetics in amicrofluidic flow channel, Sensors and Actuators B 113,281–289 (2006a)

18. Das S., Das T., Chakraborty S., Modeling of coupledmomentum, heat and solute Transport during DNAhybridization in a microchannel in presence of electro-osmotic effects and axial pressure gradients, Microfluidics andNanofluidics 2, 37–49 (2006a)

19. Berthier J., Silberzan P., Microfluidics for Biotechnology,Artech House, Boston, USA (2005)

20. Axelrod D., Wang M. D., Reduction-of-dimensionality kineticsat reaction-limited cell surface receptors, Biophys J 66, 588–600(1994)

21. Chan V., Graves D. J., McKenzie S. E., The biophysics ofDNA hybridization with immobilized oligonucleotide probes,Biophys J 69, 2243-2255 (1995)

22. Jensen K.K., Orum H., Nielsen P.E., Norden B., Kinetics forhybridization of peptide nucleic acids (PNA) with DNA andRNA studied with the BIAcore technique, Biochemistry 36,5072–5077 (1997)

23. Vontel S., Ramakrishnan A., Sadana A., An evaluation ofhybridization kinetics in biosensors using a single-fractalanalysis. Biotechnology and Applied Biochemistry 31, 161–170(2000)

24. Christensen U., Jacobsen N., Rajwanshi V. K., Wengel J.,Koch T., Stopped-Aow kinetics of locked nucleic acid (LNA)-oligonucleotide duplex formation: studies of LNA-DNA andDNA-DNA interactions, Biochemical Journal 354, 481–484(2001)

25. Stillman B.A., Tonkinson J.L, Expression microarrayhybridization kinetics depend on length of the immobilizedDNA but are independent of immobilization substrate.Analytical Biochemistry 295, 149–157 (2001)

26. Sadana A., Vo-Dinh T., Single- and dual-fractal analysis

of hybridization binding kinetics: Biosensor applications,Biotechnology Progress 14, 782–790 (1998)

27. Pappaert K., Van Hummelen P., Vanderhoeven J., BaronG.V., Desmet G., Diffusion–reaction modelling of DNAhybridization kinetics on biochips, Chemical EngineeringScience 58, 4921–4930 (2003)

28. Collins F.C., Kimball, G. E., Diffusion-controlled reactionrates. Journal of Colloid Science 4, 425–437 (1949)

29. Reif F., Fundamentals of Statistical and Thermal Physics.McGraw–Hill, New York (1984)

30. Berry R.S., Rice S.A., Ross J., Physical Chemistry. New York:Wiley (1980)

31. Erickson D., Li D., Krull U. J., Dynamic Modeling ofDNA Hybridization Kinetics for Spatially Resolved Biochips,Analytical Biochemistry 317, 186-200 (2003)

32. Wetmur J. G., Davidson N., Kinetics of renaturation of DNA, JMol Biol 31, 349–370 (1968)

33. SantaLucia J. Jr., Allawi H. T., Seneviratne P. A., Improvednearest-neighbor parameters for predicting dna duplexstability, Biochemistry 35, 3555–3562 (1996)

34. Vainrub A., Pettitt B. M., Thermodynamics of association tomolecule immobilized in an electric double layer, Chem PhysLett 323,160–166 (2000)

35. Chan V., Graves D., Fortina P., McKenzie S. E., Adsorptionand surface diffusion of DNA oligonucleotides at liquid/solidinterfaces, Langmuir 13, 320–329 (1997)

36. Chan V., McKenzie S. E., Surrey S., Fortina P., Graves D. J,Effect of hydrophobicity and electrostatics on adsorptionand surface diffusion of DNA oligonucleotides at liquid/solidinterfaces, J Colloid Int. Sci. 203,197–207(1998)

37. Chakraborty, S., Analytical Solutions of Nusselt numberfor Thermally Fully Developed Flow in Microtubes undera combined action of Electroosmotic forces and imposedPressure Gradients, International Journal of Heat and MassTransfer. 49, 810–813 (2006)

38. Das S., Das T., Chakraborty S., Analytical solutions for rate ofDNA hybridization in a microchannel in presence of pressure-driven and electroosmotic flows, Sensors and Actuators B 114,957–963 (2006b)

39. Das S., Chakraborty S., Augmentation of macromolecularadsorption rates through transverse electric fields generatedacross patterned walls of a microfluidic channel, Journal ofApplied Physics 100, 014098 (2006b)

40. Ajdari, A., Transverse electrokinetic and microfluidic effectsin micropatterned channels: Lubrication analysis for slabgeometries, Phys. Rev. E 65, 016301 (2001)

41. Heule M., Manz A., Sequential DNA hybridisation assays byfast micromixing, Lab Chip 4, 506–511 (2004)

42. Barbaro M., Bonfiglio A., Raffo L., Alessandrini A., Facci P.,Bar’ak I., Fully electronic DNA hybridization detection by astandard CMOS biochip, Sensors and Actuators B 118, 41–46(2006)

43. Aslan K., Malyn S. N., Geddes C. D., Fast and sensitiveDNA hybridization assays using microwave-accelerated metal-enhanced fluorescence, Biochemical and Biophysical ResearchCommunications 348, 612–617 (2006)

44. Zoval J.V., Madou M.J., Centrifuge-based fluidic platforms,Proc. IEEE 92, 140–153 (2004)

45. Madou M., Zoval J., Jia G., Kido H., Kim J., Kim N., Lab on aCD, Annual Review of Biomedical Engineering 8, 601–628(2006)

46. Jia G., Ma K-S, Kim J., Zoval J. V., Peytavi R., Bergeron M. G.,Madou M. J., Dynamic automated DNA hybridization on aCD (compact disc) fluidic platform, Sensors and Actuators B114, 173–181 (2006)

47. Yamashita K., Yamaguchi Y., Miyazaki M., Nakamura H.,Shimizu H., Maeda H., Direct observation of long-strandDNA conformational changing in microchannel flow andmicrofluidic hybridization assay, Analytical Biochemistry 332,274–279 (2004)



48. DeGennes P.G., Coil–stretch transition of dilute flexiblepolymers under ultra-high velocity gradients, J. Chem. Phys.12, 5030–5042 (1974)

49. Carlon E., Heim T., Thermodynamics of RNA/DNAhybridization in high-density oligonucleotide microarrays,Physica A 362, 433–449 (2006)

50. Kim D., Tamiya E., Kwon Y., Development of a novel DNAdetection system for real-time detection of DNA hybridization,Current Applied Physics 6, 669–674 (2006b)

51. Okahata Y., Kawase M., Niikura K., Ohtake F., FurusawaH., Ebara Y., Kinetic measurements of DNA hybridizationon an oligonucleotide-immobilized 27-mhz quartz crystalmicrobalance, Anal Chem. 70, 1288–1296 (1998)

52. Das S., Chakraborty S., Manuscript Under Consideration(2006c)

53. Carre A., Lacarriere V., Birch W., Molecular interactionsbetween DNA and an aminated glass substrate , J. Colloid Int.Sci. 260, 49–55 (2003)

54. Chen Z., Chauhan A., DNA separation by EFFF in amicrochannel , J. Colloid Int. Sci. 285, 834–844 (2005)

Suman Chakraborty (age 32 years) iscurrently an Assistant Professor at the IndianInstitute of Technology (IIT), Kharagpur,India. He obtained his Ph.D from theIndian Institute of Science (IISc), Bangalorein the year 2002. His current areas ofresearch include Transport phenomena inphase change processes, Computational fluid

dynamics, and Microfluidics/ microscale transport processes. Heis the recipient of INSA medal for Young Scientist, INAE YoungEngineering Award, Alexander von-Humboldt Fellowship, bestInternational CFD Thesis Award and he is a chosen member ofthe Indo-Japan and Indo-US teams of his area of expertise. Atpresent, he is an author of 74 International Journal papers and theprincipal investigator of 5 sponsored (R&D/Consultancy) Projects.


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MicroﬂuidicsBasedDNAHybridization: …repository.ias.ac.in/101239/1/196-571-1-PB.pdf · 2016. 11. 25. · appear to be 150 times faster over a distance of 500 µm5,6. Even though