Determination of protein-ligand affinity constants from direct migration time in capillary electrophoresis

Mikael Nilsson1

Valerie Harang2, 4

Maria Bergström1

Sten Ohlson1

Roland Isaksson1

Gunnar Johansson3

1Department of Chemistryand Biomedical Sciences,University of Kalmar,Kalmar, Sweden

2Division of AnalyticalPharmaceutical Chemistry,Biomedical Centre,University of Uppsala,Uppsala, Sweden

3Department of Biochemistry,Biomedical Centre,University of Uppsala,Uppsala, Sweden

4Product Analysis,Pharmaceutical and AnalyticalR&D, AstraZeneca,Södertälje, Sweden

Determination of protein-ligand affinity constantsfrom direct migration time in capillaryelectrophoresis

A simple method to calculate dissociation constants for protein-ligand interactionsby partial-filling capillary electrophoresis is demonstrated. The method uses rawmigration time data for the ligand and needs only additional information about capil-lary inner radius and the absolute amount of protein loaded. A theoretical study sup-ported by experimental data also demonstrates that the retention of analyte in affinitycapillary electrophoresis (ACE) using the partial-filling technique depends linearly onthe absolute amount of selector added but is independent of both selector zonelength and selector mobility. Factors such as field strength and electroosmotic floware also cancelled out if they are kept constant. The theory is confirmed and the use-fulness of the method is demonstrated by enantioseparations using a-acid glyco-protein (AGP) and cellulase (Cel 7A) as chiral selectors.

Keywords: a1-Acid glycoprotein / Capillary electrophoresis / Cellobiohydrolase / Dissociationconstant / Enantiomer / Migration time / Partial filling DOI 10.1002/elps.200405918

1 Introduction

1.1 General aspects

Methods based on capillary electrophoresis (CE) and/oraffinity capillary electrophoresis (ACE) are rapidly increas-ing in importance for the study of the interplay betweenbiomolecules exemplified, for instance, by enantiomerseparations using proteins as selectors. It is relativelyeasy to establish experimental conditions that mimic the“natural milieu” of the proteins. The protein binding ofdrugs is normally enantiospecific and proteins, includingenzymes, are thus useful as selectors for determination ofthe enantiomeric purity of drugs. Differences in affinityresult in different electrophoretic migration times of theenantiomers. CE techniques also allow determination ofaffinity constants.

During the last decade numerous reports includingreviews have appeared [1–15]. In most cases [12–15] thecapillary is completely filled with the selector. If a proteinserves as selector, a high background UV absorbance is

obtained, resulting in a lower detection sensitivity. Theproteins will also cause severe problems in CE-MS proce-dures. To prevent the detection disturbance, the partial-filling technique was introduced [16, 17]. Here, the selec-tor (protein) plug is first applied in a volume insufficient toreach the detector in the capillary, followed by the analytesample. If the pH of the background electrolyte (BGE) isproperly chosen, it is possible to prevent the selector fromreaching the detection window. The (enantio)separation isachieved during the passage of the analyte through theselector plug.

When the partial-filling technique is used in CE and CE-MS, there has been a focus on optimizing the plug lengthto achieve efficient separations of enantiomers [18–24].Compared to the effective capillary length, the pluglengths used in these studies have been rather short.This approach, wherein the plug length is adjusted to ob-tain an efficient separation, is practical due to the fact thatthe same selector (protein) stock solution can be used fora number of solutes. By adjusting the plug length it is pos-sible to achieve an efficient separation of any particularsolute. However, one major drawback of this method isthat there might be, for practical reasons, a significantvariation in the amount of protein injected, especiallywhen short plugs are used. It is also possible that a coun-termigrating selector at high concentration will transport asmaller or larger fraction of an analyte backwards out ofthe capillary, leading to integration errors. A recent study

Correspondence: Dr. Gunnar Johansson, Department of Bio-chemistry, Biomedical Centre, University of Uppsala, P.O. Box576, SE-751 23 Uppsala, SwedenE-mail: [email protected]: 1 46-18-552139

Abbreviations: ACE, affinity capillary electrophoresis; AGP,a1-acid glycoprotein; Cel 7A, cellulase

Electrophoresis 2004, 25, 1829–1836 1829

2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CE

and

CE

C

1830 M. Nilsson et al. Electrophoresis 2004, 25, 1829–1836

showed that the total amount of the selector rather thanthe plug length affected the chiral separation [25]. Thesepreliminary findings suggested that the plug length shouldbe kept as long as possible to minimize the relative varia-tion in the amount of protein injected and also to minimizethe internal variations in field strength [26].

So far, only a few reports on determination of affinity con-stants using the partial-filling technique are available [27–30]. The main reasons for this weak interest (so far) mightbe technical shortcomings of the instrument, difficulties inthe preparation or availability of suitable capillaries, andcomplicated data treatment. A further development ofthe partial-filling technique, a multiple-step ligand injec-tion technique, was recently reported [31]. In an ongoingpharmacological study at our laboratories we need a sim-ple and a not too protein-consuming method for quantifi-cation of the drug-protein binding. Attempts to adapt anearlier published method from another journal were, how-ever, unsuccessful. A careful evaluation of the algorithmrevealed some assumptions that we could not agreeupon and forced us to develop another algorithm. Themain purpose of this work is to demonstrate a robustand simple method based directly on retention times fordetermination of affinity constants, including enantio-selectivities based on partial-filling technique.

1.2 Theoretical

When interactions are studied by free electrophoresis, thewell-known relation

meff ¼ mf þðmc � mfÞS½ �

S½ � þ Kd(1)

is usually employed. The effective mobility meff of the ana-lyte depends on the free analyte mobility, mf, the selector-analyte complex mobility mc, and the free selector con-centration [S] according to a normal saturation function.[S] is here assumed to be in great excess and thus notinfluenced by the analyte interaction. Kd is the dissocia-tion constant for the selector-analyte binding equilibrium.In a CE partial-filling approach, however, this can not bedirectly applied since the average mobility calculated fromtotal migration time does not represent the meff above [26].

Now, one can recall that the difference in migration timecaused by the selector occurs only during the passage ofthe selector zone (Fig. 1). Let us first consider a stationary(nonionic) selector, which has negligible influence on con-ductivity and viscosity, resulting in uniform field strengthin the capillary and a stationary selector region. Whenthe capillary is filled to a length lp with a selector solutiongiving the analyte an effective mobility mp and a velocity vp

in that section, while the mobility in the remaining length lf,i.e., the mobility of free analyte, is mf and the correspond-

Figure 1. Definitions of the selector and analyte zonesused in the derivation of the equations.

ing velocity is vf , it is obvious that the migration time tp inthe selector section (lp ) and the migration time tf in theremaining part lf add up to the total migration time tend:

tp þ tf ¼ tend (2a)

lp þ lf ¼ ltotal (2b)

Using the relation

tp ¼ lpvp

¼ lpE mp

(3)

where E is electrical field strength,

and define

X0 ¼ lplpþ lf

and 1 � X0 ¼ lflpþ lf

(4a, b)

Combination of Eqs. (4a) and (1) results, using the relation

t0 ¼ ltotal

E � mf

in the following expression

Dt ¼ tend � t0¼X0 � ltotal

E1

mf þðmc� mfÞS½ �

S½ � þ Kd

� 1mf

0BBB@

1CCCA (5)


Electrophoresis 2004, 25, 1829–1836 Determination of protein-ligand affinity constants 1831

For a more extended approach we have to take intoaccount the case illustrated in Fig. 1 for a charged selec-tor, where the selector zone itself is migrating towards theanalyte sample, which, in turn, influences the time periodduring which the analyte and selector interact [18]. Forsimplicity, we still assume that the conductivity and thusthe field strength is kept uniform in the capillary. It is alsoassumed that a very short sample zone is applied andthat the selector zone starts directly at the applicationend of the capillary and ends originally at a position x0.

Obviously, at any certain time the position xs of the sam-ple zone migrating in the selector region is given as:

xs ¼ E � mp � t (6)

In parallel, the position xp of the further edge of the selec-tor region, the plug, varies with time as

xp ¼ x0 þE � msel � t (7)

The time when xs = xp, i.e., when the sample zone hastraversed the plug, is thus found from

E � ðmp � mselÞ � t ¼ x0 (8)

where msel is the mobility of the selector.

Defining x0 ¼ X0 � ltotal

xs ¼X0 � ltotal �mp

ðmp � mselÞ¼

X0 � ltotal ��mf þðmc � mfÞ�

S½ �S½ � þ Kd

��mf þðmc � mfÞ �

S½ �S½ � þ Kd

� msel

� (9)

if we study the binding of small ligands to proteins, usingthe protein as selector, it is reasonable to assume that

mc � mselj j55mf

allowing us to replace msel with mc to give

xs ¼ X0 � ltotal

�S½ �Kd

� mc

mf � mcþ mf

mf � mc

�(10)

Looking back at the simple case with an uncharged selec-tor in Eq. (5) and inserting xs as defined in Eq. (10)

Dt ¼ X0 � ltotal

E

�S½ �Kd

� mc

mf � mcþ mf

mf � mc

��

� 1

mf þðmc � mfÞ �S½ �

S½ � þ Kd

� 1mf

0BB@

1CCA (11)

which rearranges to

Dt ¼ X0 � ltotal

ES½ �

�mf � mc

ðmf � mcÞ � Kd � mf

�¼ X0 � ltotal

E � Kd � mfS½ � (12)

If we have a constant molar amount n of selector in thecapillary, i.e., [S] = m/X0

where m ¼ np � r2 � ltotal

(13)

(n is the total molar amount of selector and r is the innerradius of the capillary) we arrive at this final expression forthe retention Dt which is independent of both selectormobility and selector distribution within the capillary:

Dt ¼ m � ltotal

E � Kd � mf¼ n

p � r2 �E � Kd � mf(14)

In the partial-filling mode, the Dt defined for the end of thecapillary is directly applicable to on-capillary detection ifall selector is placed before the detector position:Dt ¼ tend � t0 ¼ tdet � t0;det

where tdet and t0,det represent the time needed for the ana-lyte to reach the detector in the presence and absence ofselector, respectively.

Looking at realistic experimental data using on-capillarydetection, we know that

mf ¼ldet

E � t0;det

Converting Eq. (14) for on-capillary detection the retentionwill be defined as

Dt ¼ tdet � t0;det ¼n � t0;det

p � r2 �Kd � ldet(15)

which, after rearrangement, allows calculation of the dis-sociation constant for the interaction directly from migra-tion time data without the need to introduce mobilityvalues

Kd ¼ n � t0;det

p � r2 �Dt � ldet(16a)

It is often convenient to measure Dt for a series of selectorloads n and determine Kd from a plot of Dt against n usingthe differentiated variant of Eq. (16a):

1Kd

¼ p � r2 � ldet

t0;det� dDt

dn(16b)

2 Materials and methods

2.1 Chemicals

a1-Acid glycoprotein (AGP) was purchased from Sigma(St. Louis, MO, USA). Cellulase Cel 7A was preparedfrom Trichoderma T. reesei culture filtrate according to apreviously published method [32].

Bis-Tris, Bis-Tris-HCl, (S)+-chlorpheniramine, rac-chlor-pheniramine, mesityloxide, (S)-and (R)-propranolol, rac-pro-pranolol, N,N,N’,N’-tetramethylethylenediamine (TEMED),



and g-methacryloxypropyltrimethoxysilane were purchas-ed from Sigma. rac-Mepivacaine was obtained from Astra-Zeneca (Södertälje, Sweden). The water used was of Milli-pore quality. All other chemicals were of analytical grade.The structures of the analytes are found in Fig. 2.

Figure 2. Structures of the chiral analytes: 1, propranolol;2, chlorpheniramine; 3, mepivacaine.

2.2 Apparatus

All CE experiments with AGP were performed in quadru-plicate on a Beckman 5510 CE system from BeckmanInstruments (Palo Alto, CA, USA) equipped with a linearpolyacrylamide-coated capillary (47 cm total length,40 cm effective length, 50 mm ID). Electropherogramswere monitored at 204 nm for chlorpheniramine andmepivacaine and at 223 nm for propranolol. BeckmanP/ACE station Version 1.0 was used for system control,data collection, and data analysis. The capillary tempera-ture was set at 257C and all separations were performedat 20 kV. Analytes were injected hydrodynamically.Experiments with cellulase (Cel 7A) were performed on aHewlett Packard 3DCapillary Electrophoresis system (Agi-lent Technologies, Waldbronn, Germany) using ChemSta-tion Version A.06.01 for system control, data collection,and data analysis. Separation was performed in polyvinylalcohol (PVA)-coated capillaries from Agilent Technolo-gies of 33 cm (effective length 24.5 cm) and 50 mm ID.UV detection was carried out at 210 nm. The sample solu-tions and BGEs were hydrodynamically injected at theanode at a pressure of 34.5 mbar (instrumental setting).A constant temperature of 257C was used. All runs weremade in triplicate and the mean value of each responsewas calculated.

2.3 Capillary coating and experimental design

2.3.1 AGP

A new fused-silica capillary was coated essentiallyaccording to Hjertén [33]. The selector was dissolved inthe BGE, whereas the analytes were dissolved in Milli-pore-filtered water to a concentration of 100 mM. Chlor-pheniramine and mepivacaine were analyzed as race-mates, whereas propranolol analyses were performedwith pure enantiomers (Fig. 2). The BGE was prepared bymixing 50 mM Bis-Tris buffer (pH 6.6), with KCl, giving anionic strength of 0.05 M. Prior to analysis, the running elec-

trolytes were degassed and filtered through 0.45 mm sy-ringe filters. Before and between the analyses, the capil-lary was rinsed in the high-pressure mode at the instru-mental setting of 20 psi for 5 min with the BGE containing0.05% Tween 20, followed by a 5 min rinse with BGE. Boththe selector and the analytes were injected hydrodynami-cally in the low-pressure mode at 0.5 psi. The injection timefor the analytes was 5 s, whereas the selector injectiontime varied between 60 and 360 s, depending on the lengthof the separation zone. In these cases, the selector con-centration was 3.7 mg/mL for chlorpheniramine/mepiva-caine and 5.50 mg/mL for propranolol. When applying dif-ferent selector concentrations, the plug length was 180 sfor chlorpheniramine and mepivacaine at concentrationsof 2.0, 4.0, and 6.0 mg/mL. In order to verify the migrationorder for chlorpheniramine, the analytes were spiked.None of the pure enantiomers of mepivacaine were com-mercially available and therefore the migration order couldnot be established.

2.3.2 Cel 7A

The BGE (0.02 M ammonium acetate) was prepared bydiluting an appropriate mass of acetic acid in approxi-mately 80 mL of water. The pH of the solutions wasadjusted to 5.0 using 1.00 M or 0.10 M ammonium hydrox-ide and then made up to 100 mL with water. All solutionswere filtered through a Gelman GHP Bulk Acrodisk 13 sy-ringe filter 0.45 mm (Ann Arbor, MI, USA). Solutions of Cel7A were prepared by diluting a 1.54 mM stock solution ofthe protein with filtered BGE to concentrations rangingfrom 15 to 219 mM. An analyte stock solution containing150 mM of rac-propranolol was prepared in water. Thesample (15 mM rac-propranolol) was prepared by dilutingthe sample stock solution with water and BGE. The bufferconcentration in the sample was always ten times lowerthan that of the BGE. New capillaries were flushed withwater for 10 min, 0.01 M H3PO4 for 20 min, and water for5 min. The capillaries were preconditioned before eachinjection with water for 3 min, 0.01 M H3PO4 for 5 min,water for 3 min, and BGE for 5 min. The applied voltagewas set at 15 kV. When Cel 7A was used [16], a proteinplug was first injected, then the analyte sample and finallya short plug of BGE to prevent diffusion back to theanode. To achieve constant plug lengths, the applicationtime (the time for a solution to reach the detection win-dow) was determined by applying a pressure of 34.5mbar to a vial containing 15 mM rac-propranolol in theBGE. The time required to obtain a response from thedetector was measured. The pressure was then appliedto a vial containing only BGE and the time for the UV ab-sorbance to drop to zero was measured. This procedurewas repeated twice and an average application time



could then be calculated. Eight different enantiosepara-tion experiments were performed with rac-propranolol.For each solution of Cel 7A used, the plug length wasadjusted so that a constant amount of selector wasinjected (volume6concentration = constant). Injectionsof rac-propranolol without selector were also performed.In each experiment the sample was injected for 5 s fol-lowed by the BGE for 2 s.

2.3.3 Calculations

Dissociation constants were calculated according to Eqs.(16a) and (16b). The apparent selectivity of the enantio-mer separation was calculated as

a� ¼ tlast

tfirst(17)

where tlast and tfirst represent the recorded migration timesfor the last and first migrating enantiomer, respectively.

The intrinsic selectivity may be calculated from

ai ¼ KdðRÞKdðSÞ

(18)

3 Results and discussion

The first conclusion drawn from the theoretical treatmentand supported by our experiments is that the retention ofthe analyte(s) depends only on the absolute amount ofselector employed and is not influenced by the volume/length of the selector zone. Furthermore, the mobility ofthe selector does not influence the final result. The finalalgorithm allows determination of Kd from simple migra-tion time data, requiring only supplementary informationabout selector load, start-detector distance, and capillaryinner radius. The Kd measurement can be performed evenif the capillary has an electroosmotic flow, provided itremains constant, since the algorithm is based on the dif-ference in directly observed migration time and does notrequire knowledge of the “true” mobilities.

The experimental results are shown in Table 1 andFigs. 3–6. In the AGP concentration series at constantplug length AGP was injected in the low-pressure modeuntil the protein reached the detector, allowing us toemploy the maximum possible length of the plug in orderto minimize the relative variations. For concentrations of2.0, 4.0, and 6.0 mg/mL AGP the application times were12.7 min. This consistency in time confirms that the differ-ences in viscosity due to the different protein concentra-tions were negligible, as further confirmed by the linearityof the slopes in Figs. 4 and 5. The electropherogramsobtained for chloropheniramine are shown in Fig. 3.

Table 1. Migration times, mobilities, and efficiencies forR- and S-propranolol. Resolution and apparentselectivity for experiments with constantamounts of selector but with different pluglengths (% of the effective capillary length)

Protein plugconsisting of

%Conc.

Mig.time R(min)

Mig.time S(min)

D Mig.time(min)

a*

No selector (0%) 4.34 4.34

6.5% 219 mM Cel 7A 1424 4.63 5.48 0.85 1.1813% 109.5 mM Cel 7A 1424 4.58 5.35 0.76 1.1726% 54.8 mM Cel 7A 1425 4.65 5.48 0.82 1.1850% 28.4 mM Cel 7A 1420 4.63 5.25 0.62 1.1463% 22.5 mM Cel 7A 1418 4.54 5.22 0.69 1.1575% 19.0 mM Cel 7A 1425 4.51 5.22 0.71 1.1685% 16.8 mM Cel 7A 1428 4.49 5.22 0.73 1.1695% 15.0 mM Cel 7A 1425 4.45 5.13 0.69 1.16

RSD % for experimentswith Cel 7A

1.6 2.4 10.2 1.2

The results shown in Figs. 4–6 using AGP as selectorwith different enantiomeric analytes confirm that theretention is governed by the absolute amount of selec-tor. Kd values differed very little, probably only withinexperimental error limits, whether the amount was var-ied by changes in concentration or by changes in selec-tor zone length. To ensure that the EOF did not affectthe study, the determinations were performed in fourseries, each series containing one measurement ateach concentration or plug length. This proceduremakes it possible to determine Kd even if EOF graduallyincreases during the analyses. However, the method isnot valid if EOF varies randomly between the experi-ments.

The data in Table 1a and Fig. 7 show that the separationof rac-propranolol using constant amounts of Cel 7A asselector is virtually independent of the dilution of theselector in the capillary even under real conditions, andnot only in the ideal mathematical study, meaning thatthe assumption introduced in Eq. (10) is acceptablefrom a practical point of view. The slight variations ob-served are probably due to system effects emanatingfrom small differences in conductivity [26]. Such fieldstrength effects are predicted to be less pronouncedwhen the selector is distributed at low concentration ina large volume. We find an apparent intrinsic selectivityof 7 at the most diluted selector application, in accor-dance with results obtained by chromatography in thepresence of a competing ligand [34].



Figure 3. Electropherograms of racemic chlorpheniramine with different selector concentrations.(A) 0 mg/mL; (B) 2.0 mg/mL; (C) 4.0 mg/mL; (D) 6.0 mg/mL. (R)-Enantiomer is first eluting.

4 Concluding remarks

The experimental data confirm the theoretical conclusionthat the retention is determined by the absolute amount ofselector in the system. As a consequence of this finding,it is often advantageous to employ a long plug with a lowconcentration of selector. Here, smaller relative errors inthe amount of selector added will result in a better repro-ducibility between experiments, and a long selector zoneof moderate concentration will result in adequate analyteretention without transient backwards migration with pos-

sible loss of analyte. Furthermore, disturbances due toconductivity differences between the background electro-lyte and the selector plug will be reduced [26]. The selectorsolubilitywill also be a smaller problem. Compared to othermethods for determination of binding constants such asHummel and Dreyer or vacancy peak, where analyte peaksare quantified, the method described only demands priorknowledge of the absolute selector load, effective capillarylength and the capillary inner radius. The only experimentaldata needed are directly recorded migration times. Somecare is needed to minimize variations in conductivity.



Figure 4. Determination of the dissociation constant forchlorpheniramine-AGP interaction where (a) the pluglength is varied for a constant selector concentration togive different selector loads; (b) the selector concentra-tion is varied at a constant plug length for the same pur-pose. The apparent dissociation constant Kd* was calcu-lated according to Eq. (16b).

Figure 5. Determination of the dissociation constant formepivacaine-AGP interaction where (a) the plug length isvaried for a constant selector concentration to give differ-ent selector loads; (b) the selector concentration is variedat a constant plug length for the same purpose. Theapparent dissociation constant Kd* was calculatedaccording to Eq. (16b).

Figure 6. Determination of the dissociation constant forpropranolol-AGP interaction where the plug length is var-ied for a constant selector concentration. The apparentdissociation constant Kd* was calculated according toEq. (16b).

Figure 7. Comparison of the enantioseparation of 15 mM

rac-propranolol using different plug lengths but with aconstant amount of Cel 7A (BGE, 0.02 M ammonium ace-tate, pH 5.0; 257C, 15 kV). (A) 85% of effective capillarylength with 16.8 mM Cel 7A; (B) 50% of effective capillarylength with 28.4 mM Cel 7A; (C): 13% of effective capillarylength with 109.5 mM Cel 7A.

We would like to thank Mr. Marcus Tysk for skilful experi-mental assistance, Jing Zhang and Anu Nutt for preparingthe Cel 7A protein. Linguistic revision was kindly per-formed by Dr. David Eaker. This project was financiallysupported by Faculty of Natural Sciences, University ofKalmar.

Received January 21, 2004



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Determination of protein-ligand affinity constants from direct migration time in capillary electrophoresis