Kinetic CE: Foundation for homogeneousElectrophoresis 2007, 28, 69–88 CE and CEC 71 neous kinetic...

Sergey N. Krylov

Department of Chemistry,York University,Toronto, Ontario, Canada

Received September 11, 2006Revised October 21, 2006Accepted October 21, 2006

Review

Kinetic CE: Foundation for homogeneouskinetic affinity methods

Kinetic capillary electrophoresis (KCE) is defined as capillary electrophoresis of spe-cies that interact during electrophoresis. KCE can serve as a conceptual platform fordevelopment of homogeneous kinetic affinity methods for affinity measurements(measurements of binding parameters and quantitative measurements) and affinitypurification (purification of known molecules and search of unknown molecules). Anumber of different KCE methods can be designed by varying initial and boundaryconditions – the way interacting species enter and exit the capillary. KCE methods willfind multiple practical applications in the designing of biomedical diagnostics and thedevelopment of drug candidates. Here, the concept of KCE, its up-to-date applica-tions, and future prospective are reviewed.

Keywords: Affinity measurements / Affinity purification / Kinetic CEDOI 10.1002/elps.200600577

1 Introduction

1.1 Affinity interactions

Affinity interaction is highly selective non-covalent binding ofmolecules at least one of which is a biopolymer. Affinityinteractionsplay a very important role in biology: they controlcell recognition, signal transduction, immune response,DNA replication, gene expression, etc. Affinity interactionsare also pivotal to a number of widely used technologiesincluding immunoassays, hybridization analyses, affinitypurification, sensors, fluorescent staining, selection of drugcandidates and affinity probes from combinatorial libraries,etc. In this review, two molecules capable of affinity interac-tions will be called a target (T) and a ligand (L). When diag-nostic or therapeutic applications are discussed, by default,

Twill be assigned to diagnostic and therapeutic targets andL will be assigned to their affinity partners (e.g., diagnosticprobesand affinity ligands). Affinity interactionof Land Twiththe formation of an affinity complex (L?Tor C) is described bythe following equation:

Lþ Tkon�!

koff

� L�T

or

Lþ Tkon�!

koff

� C (1)

where kon and koff are rate constants of complex formationand dissociation, respectively. In this review, L?T and Care used interchangeably to denote the complex; L?T isused to emphasize the non-covalent nature of the com-plex and C is used to simplify mathematical expressions.Complex stability is typically described in terms of theequilibrium dissociation constant, Kd = koff/kon (or in termsof the equilibrium binding constant, Kb = 1/Kd). Studies ofaffinity interactions or the use of affinity interactions forother purposes are performed with affinity methods.

1.2 Affinity methods

Affinity methods play an important role in biomolecularsciences. Their applications include affinity measure-ments (studies of biomolecular interactions and quantita-

Correspondence: Professor Sergey N. Krylov, Department of Chem-istry, York University, Toronto, Ontario, Canada M3J 1P3E-mail: [email protected]: 11-416-736-2100

Abbreviations: cNECEEM, continuous NECEEM; ECEEM, equilibri-um CE of equilibrium mixtures; KCE, kinetic CE; L, ligand; L?T or C,non-covalent ligand-target complex; NECEEM, non-equilibrium CEof equilibrium mixtures; ppKCE, plug-plug KCE; SELEX, systematicevolution of ligands by exponential enrichments; SPR, surface plas-mon resonance; SSB, ssDNA-binding protein; sSweepCE, shortSweepCE; sSweepCEEM, short SweepCE of equilibrium mixtures;SweepCE, sweeping CE; T, target

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© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com

70 S. N. Krylov Electrophoresis 2007, 28, 69–88

tive analyses of biomolecules) and affinity purification(purification of known molecules and search of unknownmolecules) [1–4]. The major industrial uses of affinitymethods are in biomedical diagnostics and drug devel-opment [5, 6].

Affinity methods can be classified in a number of ways.One of the classifications distinguishes separation-freeand separation-based affinity methods. Separation-freemethods are suitable only for affinity measurements,while separation-based methods can facilitate both affin-ity measurements and affinity purification. Here we onlyconsider separation-based affinity methods.

1.2.1 Heterogeneous vs. homogeneousmethods

In separation-based methods, L (or T) is physically sepa-rated from L?T. Separation-based methods can be furtherclassified as heterogeneous or homogeneous, dependingon how separation of L from L?T is achieved (Fig. 1). Inheterogeneous methods, L is separated from L?T on thesurface of a solid substrate, such as a filter, chromato-graphic support, or a sensor [7–9]. In homogeneousmethods, L is separated from L?T in solution based ondifferences in the mobility of L and L?T. A differential mo-bility in solution can be induced by centrifugal or electro-static forces [10–12]. Both heterogeneous and homoge-neous approaches have advantages and limitations. Thecommon drawback for all heterogeneous methods isnonspecific binding of L to the surface. Methods thatrequire immobilization of T (or L) on the surface are char-acterized by additional limitations. Depending on the typeof immobilized molecules, the immobilization procedure

Figure 1. Classification of separation-based affinitymethods.

can be challenging, expensive, and time consuming.Molecules immobilized on the surface often degraderapidly, thus decreasing the reliability of the method withincreasing the cost of analyses. In addition, immobiliza-tion can change the affinity of L to T, making the results ofmeasurements inaccurate [13]. Finally, due to the com-plexity of reactions on the surface, heterogeneous meth-ods are difficult to model in detail mathematically. Theadvantage of heterogeneous methods is the simplicity ofseparation; since T is fixed on the surface, separation of Lfrom L?T is trivial. Therefore, heterogeneous methods aregreat for routing affinity purification. The major limitationof homogeneous methods is the need for finding suitableconditions to separate L from L?T in solution. However, foraffinity measurements and advanced affinity purificationhomogeneous methods are preferable over hetero-geneous.

1.2.2 Kinetic vs. non-kinetic methods

Separation-based affinity methods can also be catego-rized as kinetic or non-kinetic (see Fig. 1). Kinetic meth-ods are those that do not assume equilibrium in reac-tion (1) and can, thus, be used for measuring kon and koff

and selection of binding ligands with pre-determined kon

and koff. In addition, kinetic methods can be used forquantitative affinity analyses of targets (measuring con-centrations of T) with “weak” affinity probes (high koff).Non-kinetic methods, in contrast, assume equilibriumand, thus, are not used for these tasks. It should beemphasized, that the assumption of equilibrium in non-kinetic methods is somewhat artificial and not theoreti-cally required. Furthermore, strictly speaking equilibriumcannot be maintained in separation-based affinity meth-ods as separation disturbs equilibrium. All non-kineticmethods can be potentially converted into kinetic meth-ods by modifying experimental settings and approachesto data analysis.

Among conventional separation-based affinity methodsonly surface plasmon resonance (SPR) could be char-acterized as a kinetic method [14]. It facilitates directmeasurements of Kd and koff values; the kon value can bethen calculated, kon = koff/Kd. SPR is currently the majorplatform for studying kinetics of non-covalent biomole-cular interactions [15, 16]. It can be potentially used forselection of binding ligands with pre-defined binding pa-rameters from combinatorial libraries. However, SPR is aheterogeneous method with all the limitations and draw-backs associated with heterogeneous methods in gen-eral. Our recent work has focused on the development ofkinetic capillary electrophoresis (KCE), which serves as aconceptual platform for the first generation of homoge-


Electrophoresis 2007, 28, 69–88 CE and CEC 71

neous kinetic separation-based affinity methods [17–40].This is the first comprehensive review of KCE, whichcovers the concept of KCE and its multiple fundamentalapplications.

2 The concept of KCE

2.1 Theoretical bases of KCE

CE is an instrumental platform of KCE. CE is a matureanalytical technique with tens of thousands of paperspublished and hundreds of patents issued over the lasttwo decades. CE can be advantageously interfaced withall types of quantitative detection: optical, electro-chemical, and mass spectrometric. The method can beperformed either in capillaries or in channels on micro-chips. Commercially available instrumentation supportsvirtually all developed modes and formats of CE. Practicalapplications of CE range from analysis of all classes ofmolecules to genome sequencing and analyses of singlecells. Despite such a great progress in CE in general, itscapabilities as a base of kinetic affinity methods had notbeen realized prior to our introducing KCE methods. Pre-KCE work on kinetic applications of CE to affinity interac-tions is virtually limited to a single study by Whitesidesand co-authors [41].

KCE is defined as CE separation of species, whichinteract during electrophoresis. It should be noted, that,strictly speaking, KCE is a non-equilibrium concept as itis impossible to maintain equilibrium during separation.KCE involves two major processes: affinity interaction ofL and T, described by Eq. (1), and separation of L, T,and C based on differences in their electrophoretic ve-locities, vL, vT, and vC. These two processes are de-scribed by the following general system of partial dif-ferential equations:

qLðt; xÞqt

þ uLqLðt; xÞ

qx¼ �konLðt; xÞTðt; xÞ þ koffCðt; xÞ

qTðt; xÞqt

þ uLqTðt; xÞ

qx¼ �konLðt; xÞTðt; xÞ þ koffCðt; xÞ (2)

qCðt; xÞqt

þ uLqCðt; xÞ

qx¼ �koffCðt; xÞ þ konLðt; xÞTðt; xÞ

where L, T, and C are concentrations of L, T, and C,respectively; t is the time passed since the beginning ofseparation; x is the distance from the injection end of thecapillary. System 2 describes the two basic processesthat are always present in KCE. Depending on the speciesstudied and the specific analytical setup, other pro-cesses, such as binding with complex stoichiometry, dif-fusion, adsorption to capillary walls, etc. can play signifi-cant roles in KCE. In such cases, mathematical terms,

describing additional processes, must be added to sys-tem 2. The solution of system 2 depends on the initial andboundary conditions: initial distribution of L, T, and Calong the capillary and the way L, T, and C are introducedinto the capillary and removed from the capillary duringseparation. This solution can be found non-numericallyfor specific sets of initial and boundary conditions andspecific assumptions [17, 18, 26]. For KCE to be a genericapproach, it is required that system 2 be solved for anyset of conditions; such solutions can be found onlynumerically.

2.2 Designing KCE methods by changing initialand boundary conditions

Every set of qualitatively unique initial and boundaryconditions for system 2 defines a unique KCE method.Table 1 compares seven previously published KCEmethods. Every method has a unique and descriptivename: non-equilibrium capillary electrophoresis of equi-librium mixtures (NECEEM) [17–32], sweeping capillaryelectrophoresis (SweepCE) [17, 33], continuousNECEEM (cNECEEM) [17], short SweepCE (sSweepCE)[17], plug-plug KCE (ppKCE) [17, 34], short SweepCE ofequilibrium mixtures (sSweepCEEM) [17], and equilibri-um capillary electrophoresis of equilibrium mixtures(ECEEM) [30, 35–38]. Dynamic kinetic capillary iso-electric focusing (DKCIEF), the most recent KCE meth-od, is not presented here, as it has not been publishedyet (Liu, Z., Drabovich, A.P., Krylov, S.N., Pawliszyn, J.,Anal. Chem. 2007, in press). The first column in thetable contains drawings, which schematically illustrateinitial and boundary conditions. The second and thirdcolumns show the mathematical representation of initialand boundary conditions, respectively. The last columncontains representative functions L(t), T(t), and C(t) for afixed x for each method. The notion of “equilibriummixture” refers to the mixture of L, T, and C at equilibri-um, typically prepared outside the capillary. However,the recent invention of a generic method for mixingsolutions inside the capillary, which is called transversediffusion of laminar flow profiles (TDLFP), allows con-trolled preparation of the equilibrium mixture inside thecapillary [39]. The concentrations of the three compo-nents, eT , eL and eC, in the equilibrium mixture are inter-connected through the equilibrium dissociation con-stant, Kd, as Kd = (eTeL/eC). As an example, we assumethan vT . vL. New KCE methods can be designed byarbitrarily selecting new qualitatively different sets ofinitial and boundary conditions.

In NECEEM, a short plug of the equilibrium mixture isinjected into the inlet of the capillary, which is pre-filledwith the run buffer. Separation is carried out with both inlet



Table 1. KCE methods



and outlet reservoirs containing the run buffer only. Ccontinuously dissociates during electrophoresis. Ifseparation is efficient, re-association of T and L can beneglected. The resulting concentration profiles (timedependencies of concentrations for a fixed x) containthree peaks of T, C, and L and two exponential “smears”of L and T, which occur from the dissociation of C.

In SweepCE, the capillary is filled with L, while the inletreservoir contains Tand the outlet reservoir contains a runbuffer. During electrophoresis, T continuously movesthrough L, causing continuous binding of T to L. Althoughbinding is a prevalent process in SweepCE, dissociationof C can also contribute to the resulting concentrationprofiles, which contain a single peak of C and plateaus ofTand L.

In cNECEEM, the inlet reservoir is filled with the equilibri-um mixture, while the capillary and the outlet reservoircontain the run buffer. During electrophoresis, C is sepa-rated from T, which moves faster, and from L, whichmoves slower. As a result, C continuously dissociatesinside the capillary. Although dissociation is a prevalentprocess in cNECEEM, re-association can also contributeto the resulting concentration profiles, which are repre-sented by smooth functions of T(t), L(t), and C(t) with nopronounced peaks.

In sSweepCE, a short plug of T is injected into the cap-illary pre-filled with L. Both inlet and outlet reservoirscontain the run buffer. T moves through L during elec-trophoresis causing both association of T and L and dis-sociation of resulting C to occur. The concentration pro-files of T and C are peak-like, while that of L is a smoothfunction.

In ppKCE, the plugs of L and T are injected into the capil-lary pre-filled with the run buffer. The inlet and outletreservoirs contain the run buffer as well. During electro-phoresis, T moves through L, causing the formation of C.When the zone of T passes L, C starts to dissociate.ppKCE can be considered as a functional hybrid ofNECEEM and sSweepCE. The resulting concentrationprofiles resemble those of NECEEM with a smaller peakof C and “smears” of Tand L.

In sSweepCEEM, a short plug of T is injected into thecapillary pre-filled with the equilibrium mixture. Both inletand outlet reservoirs contain the run buffer. During elec-trophoresis, an intricate interplay of dissociation of C andassociation of T and L occur resulting in sophisticatedconcentration profiles containing peaks and plateaus.

In ECEEM, a short plug of the equilibrium mixture isinjected into the inlet of the capillary, which is pre-filledwith solution of T at the same concentration as that in

the equilibrium mixture. Separation is carried out withboth inlet and outlet reservoirs containing the same so-lution of T.

2.3 KCE mathematics

2.3.1 General solution: numerical approach

In general, the numerical simulation of electrophoresis ischallenging. The difficulties are associated with theincompatibility of a single “space” grid with different ve-locities of separated species, whose electrophoreticpeaks may have sharp fronts. All conventional methods ofelectrophoretic simulations rely on using a single grid forx, x = n Dx, where Dx is the length of the x increment and nis an integer representing the point number in calcula-tions. The grid is usually associated with the velocity, v, ofone of the separated species: x = Dx 1 vDt, where Dt isthe time increment. As a result, the species, whichmigrate with velocities different from v, are simulated “outof the grid”. This leads to rounding errors that are severelyaggravated by sharp fronts of electrophoretic peaks [42,43]. This problem was addressed by developing a multi-grid algorithm for solving system 2 with an individual Dxfor every one of the three components [17]:

DxL = vLDtDxT = vTDt (3)DxC = vCDt

The multi-grid algorithm can be used to write a computerprogram, which calculates L(t,x), T(t,x), and C(t,x). Thesedependencies can, in turn, be used to build simulatedelectropherograms, which can be compared with experi-mental ones. The multi-grid approach provides a newpowerful tool for modeling chromatographic and electro-phoretic data. It tolerates sharp fronts of peaks typical forchromatograms and electropherograms and increasesthe speed of calculations.

2.3.2 Simple mathematics: non-numericalapproaches

Numerical calculations represent the most generalapproach to solving differential equations in KCE, but theyrequire a great deal of expertise in computational meth-ods. Such expertise is not common among analyticalscientists. To make KCE methods accessible to a widescientific community, it is important to augment KCEmethods with simple mathematical approaches for pro-cessing the experimental data. It should be understoodthat a simplified solution of a system of differential equa-



tions is only possible under certain simplifying assump-tions about the interaction of L and T. The simplification ofdata processing, therefore, is achieved by sacrificing thegenerality of the approach and the accuracy of calcula-tions.

3 Applications of KCE

3.1 Measuring binding parameters

3.1.1 Multi-method KCE toolbox

Although individual KCE methods with numerical model-ing can be used for measuring binding parameters, thereis always an uncertainty in the accuracy of binding pa-rameters found from a single method – the more param-eters are fitted, the higher the uncertainty. The alternativeto a single KCE method is a multi-method KCE toolbox[17]. The multi-method KCE toolbox constitutes a pow-erful approach not only to measuring binding parametersbut also to testing hypotheses about the mechanisms ofbiomolecular interactions. Figure 2 summarizes the gen-eral approach to the development and analytical utiliza-tion of the multi-method KCE toolbox. Conceptually,experimental electropherograms are obtained by multi-ple KCE methods first. A hypothetical model of interac-tions between L and T is suggested, and the system ofdifferential equations (system 2) is built to describe thehypothesis. The experimental KCE electropherogramsare fitted with simulated electropherograms simulta-neously to obtain the best fits with one of the criteriaused for non-linear regression analysis, for example,minimum chi-square. If the quality of fitting is not satis-factory, a new hypothesis is suggested for the interactionand the procedure is repeated until a satisfying hypoth-

esis is found. The best fits for the accepted hypothesislead to the determination of stoichiometric and kineticparameters of the interaction.

The proof of principle for a multi-method KCE toolboxwas performed with six KCE methods and a well-studiedexperimental system: interaction between ssDNA-bind-ing (SSB) protein and ssDNA [17–24, 27, 33, 34, 44, 45].First, a hypothesis was tested that SSB protein and DNAinteraction is described by Eq. (1). The best fit of sixexperimental KCE electropherograms for this hypothesiswas obtained but the deviations between experimentaland simulated electropherograms were unacceptablyhigh for three of six KCE methods (Fig. 3A), thus sug-gesting that hypothesis 1 was not valid. Second, anotherhypothesis, which was based on existing empirical dataabout the interaction of SSB protein and ssDNA, wastested. Two types of interactions have been previouslyhypothesized for SSB protein and ssDNA: high-affinityspecific binding and low-affinity nonspecific binding [44,45]. Non-specific binding was hypothesized to occur dueto electrostatic attraction between SSB protein and DNA,which does not necessarily involve the DNA-binding siteof SSB protein. To account for the two types of binding,reaction 1 was modified to include two types of com-plexes and two sets of rate constants. The system of dif-ferential equations for the formation of two types of com-plex was built and the experimental KCE electro-pherograms were then fitted with simulated ones for thenew model. The best fit was found to be in satisfactoryquantitative agreement with the experimental data(Fig. 3B), which allowed the acceptance of the new modeland rate constants obtained from the non-linear regres-sion analysis for the best fit. The multi-method KCE tool-box facilitated, for the first time, the determination ofkinetic parameters of specific and nonspecific protein-DNA interactions.

Figure 2. Flow chart depictingthe general approach to thedevelopment and utilization of amulti-method KCE toolbox.First, a system of differentialequations is written to describethe mass transfer processes,which are governed by inter-

molecular interactions and electrophoresis. Second, qualitatively independent sets of initial and boundary condition aredefined to define several KCE methods. Third, KCE experiments are performed with initial and boundary conditionschosen. Fourth, simulated electropherograms are built through numerical modeling. Finally, non-linear regression is used tofind kinetic and thermodynamic parameters at which simulated electropherograms fit experimental data the best.



Figure 3. Application of the six-method KCE toolbox to testing hypotheses about the nature of interaction between fluor-escently labeled ssDNA and SSB protein and finding rate constants of interactions. Black traces show experimental elec-tropherograms for six KCE methods. Blue traces show simulated electropherograms corresponding to the best fitting usingthe minimum chi-square criterion. Experimental electropherograms are identical in both panels; simulated electro-pherograms differ in (a) and (b). (a) Simulated electropherograms for the unsatisfactory model, which assumes one type ofinteraction only; ovals indicate areas of fitting with unacceptably large deviations between experimental and simulatedelectropherograms. (b) Simulated electropherograms for the satisfying model, which assumes two types of interactions,specific and nonspecific.

The multi-method KCE toolbox requires simultaneouslyfitting experimental electrophoretic data for multiple KCEmethods. This is currently performed with a custom-designed computer program. To become accessible tothe majority of CE-practicing laboratories, the multi-method KCE toolbox has to be augmented with a com-mercial user-friendly computer program. Such a program

can be potentially integrated into software packages ofcommercial CE instruments. We created a DLL library thatallows numerical modeling of KCE using unitless vari-ables and any initial and boundary conditions. Differentinterfaces can be used to work with the library; we areusing Excel Spreadsheet.



3.1.2 KCE methods with simple mathematics

3.1.2.1 NECEEM

In NECEEM, an equilibrium mixture of L, T, and L?T is pre-pared first. Second, a short plug of the equilibrium mixtureis injected by pressure into the capillary, which is free of L, T,and L?T. Third, a high voltage is applied to separate L, T, andL?T under these non-equilibrium conditions. As an exam-ple, it is assumed that the velocity of L is greater than that ofT; the velocity of L?T is typically intermediate. As soon asthe zones of L, T, and L?Tare separated, L?T is no longer atequilibrium with L andT; it continuouslydissociates with theunimolecular rate constant koff. The extent of re-associationof L and T decreases with increasing efficiency of theirelectrophoretic separation. While equilibrium fractions of L,T, and L?T migrate as short bands, L and T, which are pro-duced from the dissociation of L?T, have exponential con-centration profiles. Figure 4 depicts a schematic NECEEMelectropherogram in which all peak-dispersion effects areneglected so that the peaks have ideal rectangular shapes.If re-association of L and T is negligible, system 1 can beeasily solved to give algebraic equations for concentrationdependencies of L, T, and L?Ton the migration time to thedetector [22]. Further, algebraic equations can be obtainedfor finding koff and Kd or the concentration of T (see below)using only shapes and areas and migration times of peaksin a NECEEM electropherogram. In addition, ligands withpre-defined binding parameters can be selected fromcomplex mixtures (e.g., combinatorial libraries) if fractionsare collected in specific time windows of a NECEEM elec-tropherogram (see below).

A single NECEEM electropherogram contains data suffi-cient for finding Kd and koff. NECEEM starts with theequilibrium mixture and, therefore, has a memory of the

Figure 4. Schematic NECEEM or ppKCE electro-pherogram with experimental parameters used for quan-titative measurements: A1 is the peak area of L that eitherwas free in the equilibrium mixture (for NECEEM) or didnot form the complex during the mixing of zones of L andT (for ppKCE), A2 is the peak area of intact L?Tat the timeof its passing the detector, A3 is the peak area of L dis-sociated from L?T during the separation, tL, tL?T, and tT aremigration times from the capillary inlet to the detector ofL, L?T, and T, respectively.

equilibrium, which is necessary for finding Kd. The L?Tcomplex dissociates during NECEEM and the kinetics ofcomplex dissociation is recorded in the smears, allowingfor the calculation of koff. The areas of peaks and smearsin a NECEEM electropherogram are proportional to theamounts of corresponding species. A single NECEEMelectropherogram can be used to find four measurableparameters required for the determination of Kd and koff

(Fig. 4; color-enhanced figures are available in the Sup-porting Information). A1 is the area of the peak corre-sponding to L, which was free in the equilibrium mixture.A2 is the area of the peak corresponding to L?T, which wasstill intact at the time of passing the detector. A3 is thearea of the exponential smear left by L dissociated fromL?T during the separation. Finally, tL?T is the migration timeof the complex. The values of Kd and koff can be calcu-lated using the following algebraic equations or their var-iations [18–32]:

Kd ¼½T�0ð1þ A1=ðA2 þ A3ÞÞ � ½L�0

1þ ðA2 þ A3Þ=A1(4)

and

koff ¼ lnA2 þ A3

A2

� �

=tL�T (5)

Here, [T]0 and [L]0 are total concentrations of Tand L in theequilibrium mixture. Advantageously, areas and migrationtime associated with a single species only (L in thisexample) are required. This simplifies the use of fluores-cence detection since finding a strategy for labeling asingle species is relatively easy. A major step in themethod development for NECEEM involves finding con-ditions for good-quality separation of L from L?T.

If fluorescence detection is used, the potential change ofthe quantum yield of fluorescence upon complex forma-tion should be taken into consideration. Relative quantumyields of fluorescence can be measured in NECEEM in asimple procedure and included in Eqs. (4) and (5) to cor-rect for its change through dividing the areas by the rela-tive quantum yield [19]. When on-column detection isused, the areas must be divided by the migration times ofcorresponding species. These rules originate from thebasic CE principles and are common for all KCE methods.

Figure 5a depicts an experimental NECEEM electro-pherogram for the interaction between fluorescentlylabeled ssDNA and SSB protein. While defining the areas,it is important to accurately define the boundary betweenthe areas. The boundary between A1 and A3 can be foundby comparing the peaks of free L in the presence andabsence of T. Our study shows that the uncertainty indefining the boundaries between the areas leads toexperimental errors in the range of 10%, which is anacceptable level of experimental errors for most applica-



Figure 5. Example of NECEEM (a) and ppKCE (b) elec-tropherograms for the interaction between fluorescentlylabeled ssDNA and SSB protein. Compare them with theschematic electropherogram in Fig. 4.

tions. Alternatively, mathematical modeling of a NECEEMelectropherogram can be used to find both Kd and koff

from the non-linear regression analysis without the needto define the areas. We typically use the area method, as itis simple, fast, and acceptably accurate. For the samereasons, the area method is also more appealing for otherresearchers [46].

NECEEM-based determination of Kd and koff is fast,accurate, and has a wide and adjustable dynamic range.The upper limit of Kd values depends on the highest con-centration of T available and can be as high as millimolar.This allows for the measurement of Kd values for very lowaffinities (high Kd values), e.g., bulk affinities of naïvecombinatorial libraries [25, 30–32, 35]. The lower limit ofKd depends on the concentration limit of detection. Forfluorescence detection, it can be as low as picomolar. Thedynamic range of koff values is defined by the migrationtime of the complex, which can be easily regulated by thelength of the capillary, electric field, or electroosmotic ve-locity. The practically proven dynamic range of koff spansfrom 1024 to 1 s21 [18, 19, 46].

Although only one electropherogram is required for find-ing both Kd and koff, the concentration of T (if L is used as adetectable species) should be within an order of magni-tude from the Kd value. Titration of T with tenfold incre-

ments in concentration is recommended as the fastestway of finding suitable T. Furthermore, conducting severalexperiments may be required to find the experimentaldeviation of the Kd value.

The equilibrium is typically established in the incubationbuffer, while dissociation occurs in the electrophoresis runbuffer. The values of Kd and koff are, thus, measured for theincubation buffer and run buffer, respectively. If the incu-bation buffer and the electrophoresis run buffer are iden-tical, then Kd and koff are determined under the sameconditions and kon can be calculated as kon = koff/Kd. It istypically possible to match the incubation and run buffers.An example of when such matching is difficult is when T isthe protein requiring the use of a high salt concentration.CE cannot tolerate high salt concentrations in the runbuffer due to the high Joule heating, which can deterio-rate the quality of separation.

So far, NECEEM was used to measure binding parame-ters for the interaction of DNA with a number of proteins(SSB protein [17–24, 27, 33, 34], MutS protein [36], tauprotein [26], designed photo-controlled GCN4-bZIP pro-tein [28], and AID protein [29]), and protein-peptide inter-action [46].

3.1.2.2 ppKCE

In ppKCE, short plugs of L and T are injected into thecapillary sequentially; the component with a lower mobil-ity is injected first [17]. When the voltage is applied, thefaster moving component passes through the slowermoving component resulting in complex formation.Eventually, the electrophoretic zones of L and Tare sepa-rated and the complex starts dissociating. The resultingelectropherogram is qualitatively similar to that ofNECEEM: it has peaks of L, T, and L?T and “smears” of Land T dissociated from L?T (see Fig. 4). However, sinceppKCE does not start with the equilibrium mixture of Land T, the resulting electropherogram does not have a“memory” of Kd but rather has a memory of kon and koff.Both kon and koff can, thus, be calculated from a ppKCEelectropherogram using areas of peaks and smears andmigration times of peaks. A simple mathematicalapproach has been recently developed for processing theppKCE data [34]. The approach is based on three simpli-fying assumptions for reaction 1. First, it is assumed thatthe stoichiometry of interaction between L and T is 1:1; forhigher-order stoichiometries, numerical modeling of thedata has to be used. Second, it is assumed that only theforward reaction occurs when the zone of T movesthrough that of L. Finally, there is an assumption that onlythe reverse process in reaction 1 occurs after the zones ofL and Tare separated.



Figure 4 shows a schematic ppKCE electropherogramwith all measurable parameters required for koff and kon

calculation. The complex dissociation processes areidentical in NECEEM and ppKCE; therefore, approachesdeveloped for the calculation of koff in NECEEM are ap-plicable to ppKCE as well [18, 19, 22]. For example, koff

can be calculated using Eq. (5), which employs only theareas and migration times. The value of kon can be foundfrom the following equation:

kon = el(1/tT 2 1/tL)/([L]lL) (6)

where l is the length of the capillary from the inlet to thedetector; lL is the length of the plug of L; tL and tT aremigration times to the detector of L and T, respectively;[L] is the concentration of L in the solution it is injectedfrom; e is a parameter which is found from the followingequation:

A1/(A1 1 A3 1 A2) == 1/e6ln{(exp(e) 2 1)exp(2e6([T]lT/([L]lL))) 1 1} (7)

where [T] is the concentration of T in solution it is injectedfrom; lT is the length of the plug of T; A1 is the peak area ofL that did not form the complex during the mixing of zonesof L and T, A2 is the peak area of intact L?Tat the time of itspassing the detector, and A3 is the peak area of L dis-sociated from L?T during the separation. The easiest wayto solve Eq. (6) for e is through a numerical calculationwith one of the commercially available solvers, for exam-ple a Microsoft Excel solver. The Excel spreadsheet forsolving Eq. (6) can be downloaded from the Internet(www.chem.yorku.ca/profs/krylov).

The ppKCE method was used to calculate kon and koff forthe interaction between SSB protein and fluorescentlylabeled ssDNA [34]. Figure 5b show an example of anexperimental ppKCE electropherogram. To find themigration time of SSB protein, tT, a separate CE experi-

ment with SSB protein only and UV detection was con-ducted (not shown). The values of kon and koff obtainedwith ppKCE were in good agreement with those obtainedwith other methods.

In ppKCE with fluorescence detection, very low con-centrations of reacting components can be used, allow-ing for reliable measurement of kon values as high as thediffusion controlled ones (,109 M21s21). The mixing of thereacting components in KCE methods proceeds in apseudo-continuous mode, thus excluding “dead” time,inevitable in stopped-flow methods.

3.1.2.3 SweepCE

The concept of SweepCE is based on the sweeping of aslowly migrating component (e.g., L) by a fast-migratingcomponent (e.g., T) during electrophoresis. The capillaryis pre-filled with a solution of L and electrophoresis is thencarried out from a solution of T in a continuous mode.Because the electrophoretic mobility of T is greater thanthat of L, T continuously mixes with L and forms the L?Tcomplex (C is used instead of L?T in the mathematicalequations). The complex migrates with a velocity higherthan that of L and causes sweeping of L. The value of kon

for complex formation can be determined from the timeprofile of concentration of one of the interacting species(e.g., L). This can be done with a simple mathematicalmodel of the sweeping process obtained under theassumption that the dissociation process is slow enoughto be neglected with respect to the process of complexformation. Under this assumption, the general solution forsystem 2 can be obtained analytically [33]. The resultingexpression for concentrations of L, T, and C as functionsof the migration time (t) and the distance from the capil-lary inlet (x) are shown in Eq. (8).

Lðt; xÞ ¼ L0

exp konL0x � vLtvT � vL

� �

yðx � vLtÞ

exp �konT0x � vTtvT � vL

� �

� 1�

yð�x þ vTtÞ þ�


� ��

� 1�

yðx � vLtÞ þ 1

Tðt; xÞ ¼ T0

exp konT0x � vTtvT � vL

� �

yðx � vTtÞ

exp �konT0x � vTtvT � vL

� �

� 1�

yð�x þ vTtÞ þ�


� ��

� 1�

yðx � vLtÞ þ 1

Cðt; xÞ ¼ kon

Z

t

0

Lðt � t; x � tvcÞTðt � t; x � tvcÞdt (8)



Here, T0 and L0 are the concentrations of T and L,respectively, before the start of the sweeping process; y isthe parameter which equals 0 if x , 0 and equals 1 if x� 0.The three expressions can be used to build simulatedelectropherograms. All parameters in the three expres-sions, except for kon, are either defined (y), or controlled(T0, L0), or can be found in independent CE experiments(vT, vL, and vC). Therefore, fitting experimental electro-pherograms with the simulated ones requires the optimi-zation of a single parameter, kon, only. Standard proce-dures for non-linear regression of experimental data canbe used for fast and accurate determination of kon.

This SweepCE approach was used to find kon for theinteraction of fluorescently labeled ssDNA with SSB pro-tein [33]. SweepCE electropherograms for three differentconcentrations of DNA are presented in Fig. 6 (bluelines). Simulated SweepCE electropherograms, whichprovide the best fitting of experimental data, are shownin the figure by red lines. The kon value obtained fromSweepCE analyses was in satisfactory agreement withkon indirectly determined as kon = koff/Kd using koff and Kd

obtained by NECEEM under conditions identical to theexperimental conditions of the SweepCE. It is remark-able that a simple model of SweepCE can provide verygood quantitative description of experimental electro-pherograms. The simple mathematical model ofSweepCE works if complex dissociation during the timeof SweepCE separation is negligible. With the shortestseparation times in CE being in the order of a few sec-onds, the simple model can be used for finding kon ofcomplexes, whose koff values are as high as 0.1 s21. Forgreater koff, the system of partial differential equationsshould include the rate of complex dissociation andshould be solved numerically.

Similar to ppKCE, if fluorescence detection is used inSweepCE, very low concentrations of reacting compo-nents can be used, which facilitates reliable measurementof kon values as high as the diffusion controlled ones(,109 M21s21). The mixing of the reacting components inSweepCE proceeds in a continuous mode, thus com-pletely excluding “dead” time, inevitable for all stopped-flow methods.

3.2 Temperature-controlled KCE

KCE with a well-controlled temperature inside the capil-lary can be used to study thermochemistry and measureDH and DS of affinity interactions. One of the problemsalong this way is the temperature control itself. CE is aheat-generating technique. The ability to control the tem-perature inside the capillary depends on the quality of

Figure 6. Example of fitting experimental SweepCEelectropherograms with simulated SweepCE electro-pherograms. Experimental SweepCE electropherogramswere obtained for the interaction between SSB proteinand fluorescently labeled ssDNA at three different con-centrations (increasing from a to c). Simulated SweepCEelectropherograms were obtained by non-linear regres-sion of the experimental data using the least squaremethod. The quality of fitting is good for all three electro-pherograms. As the three simulations were done with thesame kon value this value can be considered as correct.

heat exchange between the media inside the capillaryand the environment outside the capillary. The best qual-ity heat exchange is achieved through washing the capil-lary with a liquid heat exchanger. This approach has beenrealized in commercially available CE instruments.Depending on the amount of heat generated, heatexchange can be more or less efficient and the tempera-ture inside the capillary can differ from that of the heat



exchanger to a certain degree. This emphasizes the needfor measuring the temperature inside the capillary. Typi-cally, spectroscopic methods are used to measure thetemperature inside the capillary. They rely on the de-pendence of spectroscopic properties of molecularprobes (such as fluorophores) on temperature. Althougheasy to use, spectroscopic methods have two major lim-itations. First, they measure temperature at the detectionpoint only. In most of instruments, the thermostabilizationof the capillary at the detection point is either less efficientthan in the rest of the capillary or absent, making spec-troscopic measurements inaccurate. Another limitation ofspectroscopic methods is that a calibration curve needsto be built with the same instrument, which is to be cali-brated; on the other hand the calibration curve can bebuilt only with a trusted instrument. This contradiction isreminiscent of the “hen and egg” problem; to calibrate anon-trusted instrument we have to assume that it istrusted. The two limitations make spectroscopic methodsof temperature determination unreliable.

3.2.1 KCE-based measurements of temperatureinside the capillary

KCE offers a viable alternative to spectroscopic methodsfor measuring temperature inside the capillary – it isbased on the dependence of one of the binding parame-ters, kon, koff, or Kd, on temperature. First, a calibration

curve of “binding parameter versus temperature” is builtfor an affinity pair of choice, which can be, for exampleSSB protein and ssDNA, described above. Advanta-geously, the calibration curve does not need to be builtwith the CE instrument in question; it can be built withanother (trusted) CE instrument or with another kind oftechnique, for example SPR. Then, the same binding pa-rameter is measured in a CE instrument in question andthe calibration curve is used to find the temperature. Inaddition to solving the “hen and egg” problem, thisapproach also measures an effective temperature in thetotal volume of the capillary, which is a more relevantvalue than the one measured in the detection point.

The use of KCE for measuring temperature inside thecapillary has been experimentally demonstrated bymeasuring koff as a function of temperature for the inter-action between SSB protein and fluorescently labeledssDNA [23]. The calibration curve was built with a Beck-man MDQ CE instrument, which uses a liquid heatexchanger (Fig. 7). The calibration curve was then used tomeasure the temperature inside the capillary in a custom-built instrument with the capillary exposed to the ambientatmosphere at 207C. It was found that the temperatureinside the capillary was 357C. As affinity interactions arevery sensitive to temperature, assuming that the capillarytemperature is equal to the ambient temperature couldpotentially lead to dramatic misinterpretations of experi-mental results.

Figure 7. KCE-based determination of temperature inside the capillary. (a) Temperature dependence of NECEEM elec-tropherograms for the interaction between SSB protein and fluorescently labeled ssDNA. The data in (a) are used to find koff

values for different temperatures and build a calibration curve “koff vs. T” shown in (b).



3.2.2 Thermochemistry of interaction betweenTaq DNA polymerase and its DNA aptamer

Temperature-controlled NECEEM was used fordetailed study of the thermochemistry of interactionbetween Taq DNA polymerase and its DNA aptamers.Taq DNA polymerase is widely used in PCR. An apta-mer for the enzyme was previously selected for hot-start PCR. It binds the enzyme and inhibits it at lowtemperature, thus preventing the amplification of non-specific DNA hybrids. It dissociates from the enzyme,however, at higher temperatures, making the enzymefunctional. Figure 8 shows temperature dependenciesof three binding parameters, kon, koff, and Kd, and Van’tHoff plots for the calculation of DH and DS [24]. Thevalue of Kd does not change until the temperaturereaches 367C; Kd grows rapidly with the temperatureincreasing above 367C. Thus, the equilibrium stabilityof the complex decreases as temperature growsabove 367C. The decrease of stability can be due totwo reasons: the decreased rate of complex formation,kon, and the increased rate of complex dissociation,koff. In this case, kon changes more dramatically thankoff, indicating that the equilibrium stability decreasesdue to the decreased rate of complex formation. Mostlikely, the secondary structure of the aptamer starts“melting” at 367C and loses its binding function. Onthe other hand, if the aptamer is bound to the protein,the protein stabilizes its structure and the temperatureincrease does not lead to a significant increase in therate of complex dissociation. Thus, the knowledge oftemperature dependencies of kon and koff, which canbe obtained with KCE methods, helps us to under-stand mechanisms of temperature dependencies ofcomplex stability.

3.3 Quantitative affinity analysis of theconcentration of T

3.3.1 Concept of affinity measurements of con-centrations

An unknown concentration of an undetectable target canbe measured through its affinity reaction with a detect-able ligand; the ligand in such an analysis is used as anaffinity probe. Classical immunoassay and hybridizationanalysis are examples of such affinity measurements,with antibodies and hybridization probes as ligands [47,48]. Typically, the kinetic and equilibrium binding param-eters of interaction between L and T are unknown;instead, a calibration curve is built for the dependence ofa signal (fluorescence, absorbance, radioactivity, etc.)from the detection of L on the concentration of T. Clas-sical affinity methods, thus, have a general dis-advantage: a new calibration curve has to be built forevery new concentration of L.

KCE methods provide a calibration-free alternative toclassical affinity analysis. The general theory of suchmeasurements has not been developed yet, but theirfeasibility becomes clear when we notice that con-centrations of T and L in the starting solution (or in theequilibrium mixture) are parameters in equations (see, forexample, Eqs. 4, 6–8) used for the determination ofbinding parameters, kon, koff, and Kd. When determiningthe binding parameters, we assume that the concen-trations of L and T are known. This problem can bereversed – if the binding parameters are known, theunknown concentration of T can be found. The problemcan be considerably simplified if the concentration of theaffinity probe L is also known, which is typically easy tomeasure. KCE methods with a developed apparatus for

Figure 8. KCE-based study ofthermochemistry of interactionbetween Taq DNA polymeraseand its DNA aptamer. (a) Tem-perature dependencies of kon,koff, and Kd. The data suggestthat the decrease of affinity(increase of Kd) at temperatureabove 367C is mainly due to lessefficient binding (decreasing kon)rather than more efficient dis-sociation (increasing koff).(b) Van’t Hoff plot obtained fromdata in (a) and used for thedetermination of DS and DH forthis interaction.



simple mathematics are immediately applicable to cali-bration-free affinity measurements of the unknown con-centration of T.

This review describes affinity measurements of con-centrations by two methods only: NECEEM andSweepCE. It is important to emphasize that every KCEmethod can be used for quantitative measurements ofconcentrations if the kinetic nature of the method isappreciated and the experimental results are analyzedaccordingly. Comparative analysis of different KCEmethods would considerably enrich our understanding ofKCE capabilities in this important application. An effort isnow needed in developing the general theory of KCE-based affinity analyses of concentrations.

3.3.2 NECEEM

NECEEM appears to be the simplest KCE method for af-finity-based measurements of the concentration of T. Ifthe Kd value is known, the unknown concentration of Tcan be found from an algebraic equation obtained byrearranging Eq. (4):

½T�0 ¼ KdA2 þ A3

A1þ ½L�0

11þ A1=ðA2 þ A3Þ

(9)

Advantageously, NECEEM does not require a typicalcalibration procedure; the Kd value serves as a “calibra-tion” parameter. This equation includes the concentrationof L and requires no re-calibration if the concentration of Lchanges, which is often required to change the dynamicrange of the method. Furthermore, the method can beused even if the L?T complex completely dissociates dur-ing separation (Fig. 9). In this case, A2 < 0 and Eq. (4)reduces to [20]:

½T�0 ¼ KdA3

A1þ ½L�0

11þ A1=A3

(10)

Due to this feature, ligands with high koff values can still beused for quantitative affinity analyses by NECEEM. Thisalso makes the method applicable to systems in whichL?T migrates so slowly, that L?T dissociates to an unde-tectable level by the time it reaches the detector (seeFig. 9).

When the koff value is much lower than the reciprocalmigration time of L?T, no detectable dissociation of L?Toccurs and only the peaks of L and L?T are observed (nosmears are detected). An example of this is a NECEEM-based hybridization analysis, in which DNA or RNA ofinterest is detected with a fluorescently labeled DNAhybridization probe (Fig. 10) [21, 38]. In this case, the dis-sociation constant can be as low as 10230–10240 M and

Figure 9. Example of NECEEM-based measurement of Tusing L as an affinity probe (T is thrombin and L is itsaptamer). Under the experimental conditions used Tmigrates slower than L and no peak of L?T is detected asmost of L?T dissociates before it reaches the detector andcannot be detected (A2 = 0).

Figure 10. Example of NECEEM-based measurement ofT using L as an affinity probe for the DNA hybridizationreaction: T is DNA and L is a fluorescently labeled DNAprobe. Dissociation of the DNA hybrid is very slow so thatit is not detectable (A3 = 0).

koff is negligibly small. Thus, both Kd and A3 can beassumed to equal zero, and Eq. (4) can be reduced to astoichiometry-controlled one:

½T�0 ¼ ½L�0A2

A1 þ A2(11)

NECEEM-based quantitative affinity and hybridizationanalyses are simple, fast, and accurate. The limit ofdetection is defined by the sensitivity of the detectionsystem used. For best systems utilizing laser-inducedfluorescence detection, the mass limit of detection can beas low as one thousand molecules, while the concentra-tion limit of detection can reach picomoles per liter.



Another advantage of the NECEEM-based affinity andhybridization analyses is that they do not require calibra-tion. If the Kd value is in the range of the measured targetconcentration, knowledge of Kd is required as Eq. (4) or (5)is used. If Kd is much less than the measured target con-centration, no calibration and no knowledge of Kd arerequired [38].

DNA aptamers as affinity probes considerably enrich thecapabilities of KCE in analyses of a variety of targets.Aptamers have a number of advantages over antibodies.First, DNA aptamers are highly negatively charged and,thus, they do not adhere to the bare silica of uncoatedcapillaries. Second, aptamers are relatively small mole-cules; this simplifies the separation of free DNA (L) fromthe DNA-target complex (L?T). Third, aptamers can bechemically synthesized; moreover, this synthesis is nowcommercially available at a very low cost. Fourth, apta-mers can be easily end-labeled with fluorophores withoutaffecting the aptamer-target interaction, which facilitatestheir fluorescence detection. If constant regions (used forPCR amplification) are not truncated, quantitative PCRcan be used to quantitatively detect aptamers, thus,improving the limit of detection to as few as a hundredmolecules [49]. Advantageously, aptamers can beselected using KCE methods (see below).

3.4 Kinetic selection of ligands

3.4.1 Concept of smart ligands

Selection of target-binding ligands from combinatoriallibraries (and other complex mixtures) is one of the main-stream approaches in identifying leads for drugs and af-finity probes. Typically, affinity chromatography or filtra-tion is used for the partitioning of binders from non-bin-ders [4, 50]. Affinity chromatography suffers from arelatively high background level; the background isdefined as the relative amount of non-binders collected inthe absence of the target. Moreover, conventional parti-tioning methods can hardly be used for selection of“smart” ligands, i.e., ligands with pre-defined values ofkon, koff, and Kd. Smart ligands will be required for thedevelopment of drugs with pre-defined pharmacokineticsand for designing detection schemes with controlled andwide dynamic ranges. Therapeutic agents, which act overdifferent periods of time, are one of the possible applica-tions of such smart ligands. Ligands with fast kon and fastkoff could be used as pharmaceutical agents for acutedisorders, while ligands with slow kon and slow koff arepreferable for treating chronic diseases. An accuratequantitation of a target in the range of concentrationsfrom 1 pM to 1 mM requires a panel of affinity probes witha similar (9 orders of magnitude) range of affinities (Kd).

Diverse analytical and biomedical applications may alsorequire ligands with different rate constants of complexdissociation (koff). Initially, the idea of exploiting a set ofligands with different affinities for the same target (protein)was raised in proteomic research and the development ofprotein microarrays [51]. As concentrations of proteins inreal samples vary significantly, affinity probes need to bemodified so that lower-affinity ligands are used for highlyexpressed proteins and higher affinity ligands are used forproteins with low expression levels. Antibodies proved tobe an unreliable ligand in such detection schemes asthere are no simple ways of modifying the affinity of anti-bodies. The inability to develop panels of smart anti-bodies emphasizes the need to look at other types ofligands, preferably those that can be chemically synthe-sized. DNA aptamers are examples of such ligands withmultiple advantages over antibodies (see above). Most ofwork on selecting smart ligands focused so far on theselection of smart aptamers [25, 30, 35].

3.4.2 Selection of smart ligands by NECEEM

Smart ligands are selected from highly diverse combina-torial libraries; it is assumed that ligands with desirablebinding parameters are present in the library. First, it isnecessary to find a CE run buffer that separates T fromthe combinatorial library but does not separate the com-ponents of the library. In other words, the library has tomigrate as a single electrophoretic zone in such a buffer.The diversity of the chemical structures of species withinthe library typically makes the peak of the library relativelywide. The goal is to find separation conditions underwhich the peak of T is very well separated from the widepeak of the library. T is then mixed with the combinatoriallibrary of L and incubated to obtain the equilibrium mix-ture. A plug of the equilibrium mixture is injected into thecapillary and high voltage is applied to separate free Lfrom the L?T complexes. To ensure a reasonable amountof the collected ligands, the diameter of the capillary istypically chosen to be greater than that in kinetic meas-urements and quantitative affinity analyses. Finally, frac-tions are collected in different time windows within therange between peaks of L and L?T. The closer the timewindow is to the peak of L, the more weak ligands (withhigh koff) there are in the fraction. The closer the collectionwindow is to the peak of L?T, the more strong aptamers(with low koff) there are in the fraction. Figure 11 schemati-cally illustrates the selection of smart ligands with pre-defined koff by NECEEM. The selection of smart ligandsrequires multiple rounds of selection for tuning the range ofparameters approximately within the following inequality:

1tL�T

tT � tL�TtL � t1

> koff >1

tL�T

tL � tL�TtL � t2

(12)



Figure 11. Schematic representation of selection ofsmart ligands with pre-defined koff by NECEEM. Theschematic NECEEM electropherogram is identical toelectropherograms on Fig. 4; see legend to Fig. 4 fordetails. The width and position of the ligand-collectionwindow define the range of koff values of ligands in thecollected fraction.

Strictly speaking, if the library contained an infinite num-ber of ligands with a continuum of koff values and if aninfinite number of selection rounds were performed,ligands would be selected with a narrowing range of koff

around the following value:

k1off ¼tL � tL�T

tL�Tðt2 � t1Þln

tL � t1

tL � t2

� �

(13)

In contrast to a schematic electropherogram depicted inFig. 11, real NECEEM electropherograms contain non-rectangular peaks with more or less significant frontingand tailing. As a result, the background of the selectionprocedure is a strong function of the position of the frac-tion collection window. Figure 12 illustrates this state-ment; it contains a modeled NECEEM electropherogramwith gaussian peaks of the library and L?T [25]. For thewider fraction collection window, non-binders from the

Figure 12. Schematic representation of the influence ofthe fraction-collection window on the background of theligand-selection procedure in NECEEM. The shape of thepeaks in this simulated NECEEM electropherogram isgaussian. The background corresponds to free L that“leaks” into the fraction-collection window even with-out T.

library “leak” into the window and result in a backgroundof 1023. A small shift of the right boundary of the fractioncollection window to the left decreases the backgroundby two orders of magnitude, while the efficiency of thecollection of binders decreases only slightly (from 0.7 to0.6).

The principle of NECEEM-based selection of smartligands was proved with the selecting of smart DNAaptamers [30]. Aptamers are DNA or RNA oligonucleo-tides, which can strongly bind targets with high selectivity.They have the potential to replace antibodies in all theiranalytical and therapeutic applications. Aptamers areselected from libraries of random DNA (RNA) sequencesin multiple rounds of alternating partitioning and PCRamplification. Typically, more than ten rounds are requiredfor aptamer selection. It was recently demonstrated thatNECEEM can facilitate selection of aptamers (non-smart)in a single round of selection [25].

Smart aptamers with pre-defined ranges of koff valueswere selected for MutS protein as a target. Fractions werecollected in two rounds of selection within two ligand-collection windows (Fig. 13). Every round of selection

Figure 13. NECEEM-based selection of two pools ofsmart aptamers with different and pre-determined koff

values. The upper panel shows two fraction-collectionregion with respect to the peak of the DNA library with thecorresponding theoretical koff values. The two lowerpanes show NECEEM-based binding analyses of en-riched pools of aptamers collected within the two regionsalong with the bulk koff values.



consisted of NECEEM separation, fraction collection,PCR amplification, separation of strands, and measuringthe bulk affinity of the enriched library with NECEEM. Inregion I, the theoretically predicted range of koff was0–1.061023 s21, and in region II it was 1.761023–2.561023 s21. After two rounds of selection in regions Iand II, the pools of DNA had the experimental bulk koff

values of 0.461023 and 1.761023 s21, respectively.Thus, the theoretical consideration was proven experi-mentally.

3.4.3 Selection of smart ligands by ECEEM

While NECEEM can be used to select smart ligands withpre-defined koff values, ECEEM facilitates selection ofsmart ligands with pre-defined Kd values [35]. Con-ceptually, the capillary is filled with a solution of the targetand a plug of the equilibrium mixture of the target and thelibrary is injected into the capillary. The high voltage isapplied and the target-ligand complexes migrate underthe conditions of quasi-equilibrium, meaning that ligandsspend some time within the complex and some time asfree molecules. If it is assumed that koff and kon are highenough to maintain the quasi-equilibrium between com-plexes and free molecules, the effective migration time tof the ligand will depend on Kd and the concentration offree target [T]free in the following way:

1t¼ 1

tL

Kd

½T�free þ Kdþ 1

tL�T

½T�free

½T�free þ Kd(14)

The effective migration time of the ligand can change be-tween tL?T and tL depending on Kd and [T]free. [T]free isassumed to be equal to the overall concentration of thetarget [T] because of the constant supply of the targetfrom the run buffer. As a result, the interaction of thelibrary with a constant flow of the target distributes ligandmolecules along the capillary according to their Kd values:

KdðtÞ ¼ ½T�tL

tL�T

t � tL�TtL � t

(15)

Ideally, ligands with the same Kd values should migrate asa single peak with a small width (Fig. 14). Thus, Eq. (2)allows one to calculate a theoretical range of Kd values ina fraction collected between times t1 and t2:

½T� tL

tL�T

t2 � tL�TtL � t1

> Kd > ½T�tL

tL�T

t1 � tL�TtL � t1

(16)

Experimentally, peak broadening and nonspecific inter-actions with other components in the system may intro-duce a bias of unbound ligands into the collected fraction.That is why the selection procedure may require a fewrounds of selection to approach the theoretically pre-dicted Kd values. However, well-optimized CE separation

Figure 14. Concept of selection of smart ligands withpre-defined Kd by ECEEM. The maximum fraction-col-lection window spans from the migration time tL?T ofcomplexes with Kd ? 0 to the migration time tL of the freelibrary. Ligands collected in the time window t1–t2 in aniterative fashion will have Kd values defined by the equa-tion in the figure.

conditions, such as the choice of the running buffer andcapillary coatings, will ensure the minimal effect of diffu-sion and nonspecific interactions upon the predicted dis-tribution of species along the capillary during the run.

The unique feature of ECEEM for the selection of ligandsarises from its simple mathematical description. Therange of the affinity distribution along the capillary isdetermined by [T], tL?T, and tL. By changing these param-eters, it is theoretically possible to select from the combi-natorial libraries ligands with affinities ranging from pico-molar to millimolar values of Kd, which covers nine ordersof magnitude. It should be noted that the simple mathe-matical description only works under the assumption ofquasi-equilibrium: the re-equilibration time in reaction 1should be much shorter than the characteristic time ofelectrophoretic separation.

The experimental evaluation of ECEEM was done forselection of DNA aptamers for MutS protein [35]. Frac-tions were collected within three ligand-collection win-dows (Fig. 15) in three rounds of selection. Each roundconsisted of ECEEM separation, fraction collection, PCRamplification, separation of strands, and measuring thebulk affinity of the enriched library with NECEEM. After thelast round of selection, the three pools of aptamers werecloned into bacteria. Selected bacterial clones werescreened for the aptamer insert into the plasmids, andindividual aptamers were obtained. As the next step, Kd

and koff values of individual sequences were measuredwith NECEEM. Figure 16 shows NECEEM electro-pherograms and binding parameters for six aptamers:three with similar Kd values and varying koff and three withsimilar koff values and varying Kd. Changing Kd affectedthe ratios between free DNA and the complex (Figs. 16a–c), while changing koff influenced the ratio between theintact and dissociated complex (Figs. 16d–f).



Figure 15. Affinity convergence to the theoretically pre-dicted (red line) in three rounds of ECEEM-based selec-tion of aptamers (black). Fractions were collected in threeligand-collection windows (blue). Round refers to oneround of SELEX that involves one step of partitioning andone step of PCR amplification.

KCE-based methods of aptamer selection are character-ized by exceptionally high efficiency of partitioning ofaptamers from non-aptamers. For the overall aptamer-selection procedure to be efficient, the high efficiency ofnew partitioning methods has to be matched by high effi-ciency of PCR. PCR amplification of random DNA librar-ies used in aptamer selection has been recently studied indetail [40]. With CE as an analytical tool, fundamental dif-ferences between PCR amplification of homogeneousDNA templates and that of large libraries of random DNAsequences were found. Product formation for a homoge-neous DNA template proceeds until primers are exhaus-ted. With a random DNA library as a template, productaccumulation stops when PCR primers are still in excessof the products. The products then rapidly convert to by-products and virtually disappear after only five additionalcycles of PCR. The yield of the products decreases withthe increasing length of DNA molecules in the library. Itwas also proven that the initial number of DNA moleculesin PCR mixture has no effect on the by-products forma-tion. The increase of the Taq DNA polymerase con-centration in the PCR mixture selectively increases the

Figure 16. NECEEM electro-pherograms illustrating bindingof six different aptamers toMutS protein. (a–c) Aptamerswith similar koff values, but vary-ing Kd values. (d–f) Aptamerswith similar Kd values, but differ-ent koff values.



yield of PCR products. These findings suggest thatstandard procedures of PCR amplification of homogene-ous DNA samples cannot be transferred to PCR amplifi-cation of random DNA libraries; to ensure highly efficientselection, PCR has to be optimized for the amplification ofrandom DNA libraries.

3.4.4 Prospective of KCE methods in selectionof smart ligands

Selection of smart ligands by KCE methods can be con-sidered to still be in its infancy – only NECEEM andECEEM have been evaluated and only in application toselection of DNA aptamers. Due to the importance of oli-gonucleotide aptamers, the work on the selection ofaptamers will certainly continue and other KCE methodwill be adopted for this application. A Non-SELEX (SELEXstands for systematic evolution of ligands by exponentialenrichment) process was recently invented for the selec-tion of aptamers [31, 32]. In contrast to SELEX, Non-SELEX does not involve intermediate steps of amplifica-tion of aptamers (typically by PCR) between the rounds ofpartitioning of aptamers from non-aptamers. Non-SELEXis faster than SELEX but the number of steps in Non-SELEX is currently limited to three or four due to a partialsampling of collected aptamers. Due to this restriction,Non-SELEX has limited capabilities with respect toselection of smart aptamers as the latter may requiremore than three or four partitioning steps to tune thebinding parameters to narrow ranges. Future efforts willaim at overcoming this limitation of Non-SELEX to make itfully applicable to selection of smart aptamers.

If Non-SELEX proves to be able to select smart DNAaptamers, the technology will be eventually adopted tothe selection of smart ligands from non-DNA libraries. Thechallenges lie in the ability to (i) separate a library from thetarget without separating the components of the librarybetween themselves, and (ii) arrange for sensitive detec-tion when fluorescence detection cannot be used (it isimpossible to fluorescently label small molecules withoutaffecting their binding ability to the target). NECEEM andECEEM can be immediately applied to the selection ofligands from libraries of small molecules tagged with DNA(DNA sequence barcodes the structure of the small mol-ecule is attached to) [52, 53]. The electrophoretic proper-ties of such libraries are defined largely by the DNA tagrather than the small molecule; thus, they are similar tothose of pure DNA libraries. KCE methods promise agreat potential in the development of smart drug candi-dates and smart affinity ligands of different natures.

4 Conclusions

KCE establishes a new paradigm: “Separation methodscan be used as comprehensive kinetic tools”. Most pre-vious attempts to use chromatography and electropho-resis for studying biomolecular interactions were restrict-ed to assuming equilibrium between interacting mole-cules [11, 12]. Such an assumption dramatically limitsapplications for measuring equilibrium constants only.Furthermore, this assumption is theoretically wrong sinceseparation disturbs equilibrium. KCE is based on theparadigm that kinetics must be appreciated whenseparation methods are used for studies of biomolecularinteractions. As demonstrated with KCE, appreciation ofkinetics significantly enriches the analytical capabilities ofthe methods.

Future KCE work will focus on: (i) detailed study ofrecently introduced KCE methods, (ii) development ofnew KCE methods, (iii) development of KCE tools forstudying binding stoichiometry, (iv) development of sim-ple mathematics for KCE methods, (v) application of KCEmethods to new target-ligand systems, and (vi) applica-tion of KCE methods to the development of drugs andaffinity probes. An important step will be the extension ofKCE methods to other ways of detection, in particular, toMS. The challenge here is the limit of detection of MS,which is still several orders of magnitude below than thatof fluorescence detection. An important task will bedesigning a system of descriptive names for KCE meth-ods. A joint work of teams, which use electrophoresis foraffinity studies, will be needed. Clarity of the nomen-clature is required for KCE methods to become attractiveto a wide community of molecular scientists.

Methods of KCE use a single instrumental platform and asingle conceptual platform for solving multiple tasks ofaffinity methods. Due to their comprehensive analyticalcapabilities, KCE methods have the potential to becomea workhorse in many areas of affinity measurements andaffinity purification. This makes KCE methods highlyattractive for the pharmaceutical industry as a novelapproach to selection and characterization of drug can-didates and affinity probes.

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