126 Reprinted from.Iourrral of Medicinal Chemistry, 1993,36.Copynght O 1993 by the Aierican Chemical Society and reprinted by perrnission of the copyright owner.

Use of Affinity Capillary Electrophoresis To Determine Kinetic and EquilibriumConstants for Binding of Arylsulfonamides to Bovine Carbonic Anhydraser

Luig Z. Avila, Yen-Ho Chu, Erich C. Blossey,z and George M. Whit€sides'

Department of Chemistry, Haruord Uniuersity, 12 Otford Street, Cambridge, Massachtsetts 021fi

Receiued August 24, 1992

Affinity capillary electrophoresis (ACE) provides a new approach to studying protein-ligandinteractions. The basis for ACE is the change in the electrophoretic mobility of the protein whenit forms a complex with its ligand. This binding interaction can be quantified directly for chargedligands or indirectly for neutral ligands in competition with a previously characterized chargedligand. Determination of kinetic and equilibrium constants using ACE relies only on the changesin the migration time and shape (but not the area) of the peak due to protein. Simulation of theprotein mobility under conditions of ACE suggests that the experimentally obtained electro-pherogrnmscanbeexplainedintermsof fewvariables: onand off ntes(andthus,bindingconstant),concentration of the ligand(s), and relative mobilities of the protein and its complex(es).

IntroductionAffinif capillary electrophoresis (ACE)s-s can be used

to determine the binding constants, Kb, and lrineticconstants, froo and lo6, for the interaction of proteins withligands. ACE is athactive becaue the procedures are rapidand only small quantities of protein and ligands arerequired. The potential of ACE to provide simultaneousevduation of binding and kinetic constants of enz5me-inhibitor interactions is especidly appeding when takenin the contert of methodologies for generating andscree.ing drug candidat€s. The effectiveness of a moleculeaB an enzyme inhififpl, and thus possibly as a drug, maydepend not only on how tightly the inhibitor is bound bythe enz5rme but also on the rate of association of the enz5meand the inhibitor and the rate of dissociation of theenzlmrinhibitor compler.o

Here we describe several useful protocols for theseandyses using as a model system carbonic anhydrase (CA,EC 4.2.1.1) as enzlme and arylsulfonamides as inhibitors.In principle thege procedures ca! be used for analysis ofbinding in other systems of protein and ligands, providedthat protein adsorption on the surface of the capillary isnot significant and that a charged ligand is available orcan be slmthesized.

There are two tlpes of procedures. Determination ofthermodyanmic binding constants involving measuringshenges in mobility of the protein as a function of theconcentration of a ligand (or ligands) in the electrophoresisbuffer. We describe two variations in the procedure forstudying protein-ligand interactions: in one, the proteininteracts with a single charged ligand; in the second case,tbe protein interacts with a mixture of, two ligands, onecharged and one electricallyneutral. The firstprocedureyields the binding constant of the charged ligand directly.The second allows the measurement of the bindingconstant of the neutral ligand, relative to the charged one,and thus provides a protocol for measuring bindingconstsnts of uncharged ligands. Both of these tlpes ofprocedrrre involve only measurements of the positions ofpeaks (that is, migration times t-). The intensity and theshape of the peak are not required.

This paper also describes a procedure for analyzing thedisplacement and shape of the protein peak, using a simplecomputer-based simulation, to obtain information con-cerning the lrinetics of the interaction between the protein

and the ligand(s). In this procedure, matching of erper-imental and calculated peak shapes is an integral part ofthe procedure.

Complex Formation and Electrophoretic Mobility.The com-on basis of each procedure is the arralysis of thechanges in the electrophoretic mobility of a protein onconplexation with a ligand (L) present in the electro-phoresis buffer (Figure 1). The electrophoretic nobilityp (cmz V-l s-1) of a protein induced by a voltage gradientalong the capillary is related to the net charge of the proteinand to the inverse of its mass (eq 1). A nr:mber of

G(=LC.')M m M + m

NctChargc Z x.z 7s.z

l r - Z I M B - * z t m f r - ( Z x , z ) l ( M + m f f

functional forms have been empiricdly determined toapprorimate these relationships:? one is p - zl(mzts!.Knowledge of the exact form is not necessary for ACE, solongas itdoes not change as a function of ligand orproteinconcentration. When a protein forms a complex with acharged ligand of relatively small mass, the change in theelectrophoretic mobility of the protein-ligand complexresulting from the change in charge is large, while thecontribution to the change in electrophoretic nobility dueto the change in mass is negligible (eq 1). The protein-ligand compler nay then have a measurable difference inelectrophoretic mobility relative to the free protein.sScatchard analysis of the change in the electrophoreticmobility of the protein as a function of the concentrationof the ligand in the electrophoresis buffer allows thedetermination of the binding constant (Kd for theinteraction.3

Interaction of a protein and a ligand that induces achange in the migration time of the protein may alsobroaden the peak due to the protein in the region ofconcentrations coresponding to migration times inter-mediate between that of free protein and that of itssaturated compler with ligand (Figure 1). This broade'ingis most pronounced if the dissociation time (1/&"m) is ofthe same magnitude as the migration time of the protein.

1993 American Chemical Society0022-2623/93/1836-0126$04.00/0 @

Af firtty Copillary Electrophoresis Jourrul of Medicitul ChemistrT, 1993, Vol. 36, No' I 127

consisting of the same glycine'Tris buffer and known

concentrationg of the charged ligand l. The idtisl

erposure of the enzJrme to the ligand(e) occured on

introduction of the cA into the preequilibratcd capillary.

In the case of the competition erperiment to deternine

the binding constant of a neutral ligand relative to the

charged liiand l, the electrophoresis buffer contained

known concentrations of the two ligands. The elec'tropherogrnme obtained using different concentrations of

iigand(s) in the electrophoresis buffer were analfzed for

.f,"og"t in the migration tine t- of CA as a function of

the liland concenlration(s). Scatchard analygis dlowed

the measurement of the binding constant for the inter-

action of the ligand with CA. The nigration tines aDd

peak widths of the neutral (MO) and protein markerg

IHHU, G6PDH, STI) were essentially invariant in each

set of erperiments. The some series of electropherogramswere analped by comparing with electropherogramsgenerated by simulation using dilferentvalues for hoo and

&or ss input Parnmeters.t" tUit study, we slmthesized a low molecular weight

arylsulfonamide ligand I designed to bear a charge of -3

at the pH of the electrophoresis buffer (Scheme I). Th.

three key elements in the structure of the charged liganq

1 are: "

iuffoo"-ide group, the moiety that ia recognized

by CA; a tail group compoeed of three carborylate groups

constructed on a tris(hydrorlmethyl)avninometbane core

which glvee ligand I a net charge of -3 at pH 8.3; and an

adipate sp"."t at-. The three sections of the charged

Ug;d *.tt conveniently assembled using anide bond-

forming reactions (Scheme I).Scatchard Analysis of CA Interacting with e

Charged Ligand (L*). Figure 2a presents an erpanded

set of erperimental electropherogrsms showing the clange

in the nigration time and peak shspe of the CA peak with

increasing concentration of charged ligand ! in the

electrophoresis buffer. The basis for using stachard

anatysis to determine the binding constsDt t$l of

chargedligand 1to CAfrom thie setof electropherogramsis gummarized in eqs 2-5. The assumptionsls associated

Ifi = [CA'L+]/[CA][L+] (2t

6Af.,ll*l = Afm,t1,rl - Atm,[L.]-o (3)

81= dAt-,&.t/dAt.-r,

= [CA.L+]/(ICA] + [CA'LI]) (4)

R, = frtl,+l/(t + rftl,+l) (5)

n/tL*t=I(-GRr (6)

with the use of eq2-5 for anallzing the interaction of cA

with ligand I include the following: (a) the interastion

between the ligand and the cA molecule ie monovdent,(b) the n'hount of CA is much lower than the total g'nount

of ligand available for binding, and (c) that equilibriumie aihieved during the electrophoretic run. An added

assurnption, unique to ACE, is thst the interaction of the

ligand and the CA with the capillary wall doee not

.igoin.-tly alter the binding interaction of the CA with

tne Ugand. This assumption ie not that the CA does not

associate with tbe capillary wall, only that the ertent of

any association is the-game with CA and with CA'L+, &d

t r l p M

r00

6.2

0

r",'tec) 24

Figure l. Electrophoresia of a mirture of carbonic anhydrase(Oi mesityl oridelUO), soybean t4pain inhibitor (STI), andgfuioee-eibosphat€ dehydrogenase (C'6PDH) in buffer corsist'in' of gl'cfue (1-92 mM), Tlis (25 mM), and variow concentrationsof"figaii l. The variations in abeolute migration timee t' of thenoninteracing markerg ar e 12Vo . The total length of the capillarywas ?0 cm (45 cm from injection to detection).

Analysis of this broadening makee it possible to estimate

vdues for hos and hoo in certain cases.

We choge CA from bovine erythrocytes as the protein

for this study for several reasons. The cA doee not adsorb

to the wall of the capillary under our experimental

conditions.s The protein ie com-ercially available and

inerpensive. The mechanigm of its action is well-char-

actciized.e The reaction it catalfzes-the hydration of

carbon dioxide-is medicindly important.e The specificinhibition of CA in the eye has been erploited in the

development of new antiglaucoma agents.lf The single-

crystat X-ray structure of the carbonic anhydrase has been

carried ouL at 2.GA resolution.u A broad range of

arylsulfonomides inhibit the enzyme.e The binding of

arylsulfonomides to the active site of the enzyme is well-

understood'e'l2 16t active gite is a cavity, approrirnately

1b A deep and 15 A wide. The dissociation constants of

complexes of arylsulfona-ides and CA range from 10{ to

10€ M.eWe3,13 and othersl4-u have demonstrated changes in

mobility of receptors on binding of ligand under conditions

of CE. -

Binding interactions between vancomycin and

peptides,ls'rs 5";**n ewzyme and cofactors,s and between

i""tiot and sugarsla have been quantified using CE'

Qhnnges in electrophoretic nobilities of two cdciun

binding proteins, parvalbunin and calmodrrlin' upon

bindid calciqm present in the electrophoresisbuffer have

been demonstrat€dlG and subeequently quantifred.s Bind-

ing of ethidium bromide, a positively chargedintercalating

agent, to DNA restriction fragments in a polyacrylnrnids

g-t-rtued electrophoresis capillary result€d in an increase

L migration time.l? Affinity methods have aleo been

develJped using tube and slab gel electrophoreeis'6'l8

Resultg and Diecuesion

Capillary Electrophoresis of CA. The sample CA

was dissolved in electrophoresis buffer (pH 8.3) consisting

of glycine (192 mM) and Tris (25 mM). This CA sample

.olotioo also contained mesityl oxide (Mo) as neutral

marker (to meaeure the rate of electroosmotic flow in the

capillary) and atleast one of the following as noninteractingpt-ot"io -arkers: horse heart myoglobin (HH-M), glucose-

&phosphat€ dehydrogensse (C,6PDH) from Leuconostoc

,*rrnirroides, and soybean trypsin inhibitor (STI)' The

capillary was equilibratcd with electrophoresie buffer

128 Journal of Medicinal Chemistry, IggJ, Vol. 86, No. I

Scheme It'*o*Q.-*r,

t'*olQ.,.x

K; = tCA.L"l/tCAlll,.l

B, = 6Lt^,rLJ/6AtE,-sr

= [cA.Lo]/(tCAI + [CA.L"I + [CA.L+I)

n, = (Kil[L,]/(r + tKptl,j + trfltl,*ll

R/IL"I = tr<$l - rrq-lnr

(7)

o

1. DUF, TEA

2. NaOH

3. HCI

o

l. 7, Dcc, HoBt, EtoAc, Acetone

2. NaOH

3. Hct {o*s-.r.cooMexrtt-C9A,.As^coot e

-o-.r^.-S ., cooMe

7

One way of estimating the binding constant (Kil of aneutral ligand Lo is to allow it to compete with a chargedligand L+ of known binding constantKf. Figrue Sashowg3 s9t of electropherogrn"'s for cA in an electrophoresisluffe-r containing a fixed concentration (b0 pM) of ligand!_anf increasing concentration (f100 pM) of tigana e.The binding constant for the electrically neutral ligand 2can then be determined by Scatchard analysis teqJZ-fO)following a procedure analogous to that used ior the

Auila et al.

(8)

(e)

(10)

1

that this association is independent of the concentrationof L+ in the buffer.

Here 6Af6,11a1 is the change in the migration time dueto the presence of the ligand in the electrophoresis buffermand Adt.".", is the value of DAt. at saturating concen-trations of charged ligand L+. The ratio,l?l alsogives theaveraged fraction of the cA sit€s occupied'by the ligand.F4 6 grves a convenient linearized foim appropriaL fo,scatchard analysis. For the set of data ptesented in Figure2a, the binding constant ̂ ffi obtained using eq 6 was l.bx 108 M-1 (r > 0.98). The dissociation constant Kd+ =(l/-IG),which is the concentration of the charged ligandI that causes the migration tine of CA to change bfnAfthe marimum attainable change (dAt--"r), was found tohzrM '

Scatchard Analysig of Competitive Binding ofElectrically Neutral (L") and Charged Ligands iL+)to CA. Direct analysis of the interaction of CA withelectrically neutral, low molecular weight ligands (L) usingAcP is notpossible because the electrophoretic -obiliti.iof CA and CA.fu compler are relatively similar. Theneutral ligand Lo does not introduce a change in chargeof tbe protein-ligand compler, and complei formationresults in an undetectable increase in the mass. Thtrs, theanalysis outlined in the preceding section is not directlyapplicable.

N; = rq rr + rfitl*t) (11)

charged ligand alone. In this case the change in themrgration time (6AtJ is measured relative to the migrationof cA in the presence of the electrophoresis buffe-r of aninitial' fired concentration of the charged ligand I alone.

Affnity C apillory Electrophore sis Journol of Medicirwl Chemistry, 1993, VoI. 36, No. I 129

LO

15nr/ nl

: - - . 1 .0(l0t I'fr)

05

0

----e- F.xpcriocotd (r)* Simuletcd (c)

0.2 0.4 . 0.6&

l r l F M

I I I F M

0 Compartments t(Xr0

15&/t21

tros n'rl l'o05

-* ErDcdncDtrl-# Sirirutrtcd

Rf

?N10050EL26.23.11 .60.0

N1005025t26.23.11.60.0

2345

so2NH2

,.9'R2

R3

H

H

23

n - 6ar, -{ l2l FM

- '$fu zsA l 0- n - s sJ^------/ )nt-- i

\ . - 0

Figure 2. The migration tine of CA changes with increasingconcentration of charged tigand I in the electrophoresis_ buffer.The nonmobile peak fu dusto horse heart myoglobin.- Stacked

electropherogrnms a wele obtained experimentally (tQA19 = l0pM; 19:2 mM glycinr25 mM Tris buffer, pH 8.3) nnd H weregenerated ly iimutation. Simulation parnmeters: (b) rto6 = 1'g

i-t; hoo = l.b x lgs M-l .-t. (c) Aor = 0.1 s-r; por = 1.5 x 10 M-1

s-ti td) hon = 0.01 e-ri froo = 1.5 x 163 M-1 s-1. In the simulation,the concintration in each compartment was adjusted every l0

me and the contents of the compartments for the mobile complexwas transfened every 100 ms. The granh is a Scatchard plot of

the experimental data a and simulation data c using eq 6'

R1 R2

H H

H CHg

4 C l C l C l

5 H N o z H

Eq 8 is analogous to eq 4 and eq 10 to eq 6. The termf<i it the apparent binding constant of the neutralsuifonamide in the presence of the charged ligand. Eq 11gives the relationship between the apparent (KB') andactual (Iq) binding constsnts for the neutral ligand whereIf, *d [L+l are the binding constant and fixed concen-tritionof the charged ligand inthe electrophoresis buffer,respectively. For the data presented in Figure 3a, theappatent binding constant I4' of the neutral ligand 2 inthe presence of the charged ligand I using eq 10 was 1.3x 105 M-1 (r > 0.99). The actual binding constant K; =

1.1 x lff M-l was obtained using eq 11 and the values 1.5

l 2 l F M1003025

0 Comprrtncnts tfln0

Figure 3. The migration time of CA changes with-rncreasingconcentration of neutral ligand 2 in the presence of 50 pM of

charged ligand 1 in the electrophoresis buffer. The nonmobilepeak is duC to horse heart myoglobin. Stacked electrop_hgroglalngawere obtained experimentally ([CA]" = 10 pM; 192 mM glycine-

25 mM Tris buffei, pH 8.3) and b were generated by simulationusing the parameters,to6 = 0.1s-r and koo = 1.1 X 1S M-1s-lforthe neutral ligand. CA.L" is not mobile within the referencefro-e. The remainderof the simulation paraneterswere similsrto Figure 2c. The graph is a Scatchard plot of the data uging eq10.

d

A---------------- t

CoDpafiDcnts

0 CompofiDcnts {Xn

n b/ \ _LL

L_

l05I0

Table I. Binding Constants of Ligands 2-6 to Bovine CA-BObtained by ACE

IigandACE'

(ls M-r)literatureb(1s M-t)

literature'(lff M-r)

1 .1r.94.57.0

0.72.06.8

16

0.30.7

2.6o The concentration of the charged ligand I was 50 pM. b Literature

values are for bovine CA-B measured at 25 oC in 0.1 M Tris'HClbuffer (pH ?.2) and are taken from ref 23. ' Literatue values are forhunan CA-C -e""ured at 25 oC in 0.02 M phoephate buffer (pH 6'5)and are taken from ref 24.

x 105 M-l and b0 pM for If, and [L*], respectively. TableI shows the binding constants fq of a number of neutralsulfonamides to bovine cA obtained using this competitionprocdure. For comparison, Table I also shows the bindingaffiniff of the snme set of ligands reported for bovine2land humirn CA.n

Simulation of CA Interacting with a ChargedLigand (L+). Figure 2a shows thatthe migration time ofthe CA changes with the concentration of L+. The peakfor CA also broadens in the region of intermediatemigration time. This tlpe of broade''i'g has been observedpreviously in nany forms of chromatography,s and reflectgequilibration between species with different migrationtimes (in this instance, free protein and protein-ligand

Jourrul of Medicirul Chemistry, Iggg, Vol. 86, No.

ffi---

rnjrto" caPittarY

o.lr,o,.

Auila et al.

formation of the CA-ligand compler (eq 12) was approx_imated using first-order kineticrs by asEuming a deadvstate concentration for the ligand (L+) equal to its initialconcentration in the electrophoresis buffer. Eqe tB and14 update the concenhation in each compartment to reflectthe new concentrations of CA and Ci.L* after a timeintervd of At using the value obtained fron eq fi.

A[CA]r,at = ,to6[CA.L*l,,rAt - &oo[CA].,t[L*]At (L2,1

lCAJ,,r*o, = [cA],,t + AlCAJ,,at

[CA.L*Jr,t+At = [CA.L+J.,I - A[CA]r,o,

The content of the.rth_ compartment for CA.L+ complerwas periodically shifted to the (r + 1)th compartmentevery time intprval (100 ms) equivalent to the time requiredby the CA.L* complex to travel the width of the cbm_partment of the reference frnme under the conditions ofelectrophoresis.s This trn''slation step stimulated thefact that the cA.L* was mobile within th; reference frn-e;the free cA remnined immobile in the reference frame bydefinition.

The simulation was terminated when the total time forthe simulation equaled the experimentally determinedmigration time (t-) for the CA in the electroploresis bufferwithout ligand. The contents of each pair of comparfuents(CA and CA.L+) were sunmed andthrn ptotted ver.,u'distance from the origin of the moving refeience frame toprovide the distribution of the cA af direrent poeitionsof the reference frame. This distribution pt*iara

"'snapshot" appro-imation of the experimenial electro-pherogran. IVe assumed that the erlerimental electro-pherogrn- was a real-time record of ihe uv absorbancedue to the protein as the hSpothetical reference franemoved past the detector.

we caried out a number of simulations to approrirnate'ire erperimental electroplerograms (Figure i"l UV *i"gdifferent combin-alions of &oo and hon foi eq 12. figrrres2H are three of -th9 simulation-generat€d electropherogr"ms. The search for the correct combination of &* and&on to use in the simulation was rimited to combinationethat gave a binding constant equal to the binding constantobtained experimentally. scatchard analysis oi tle .i--ulation-generated electropherograrn. (Figure 2c) using eq6 gave a ̂ S of 1.5 x 1S M-l (r > 0.9g1.n

An important finding from the simulation was that onlyone set of the simulation-generated electropherogranslFigure_ 2c) appro*irnated the peak widths oi th. Jrp"r-lT9"g electropherogram (Figure 2a). The values of hoff(0.1s-1) and,too (l.E x ltrM-r s{) usedtogenerate Fig,rr;2c fall within the_range of values of ,to6 IO.OS-O.S s-t) and&oo (104-106 M-l s{) reported for a number of aryl-sulfon"mides.22bp4 The increase in the peak width didnot result from the ertra time the cA spent in thecapillary.31 I" f1.!'the cA peak sharpens at saturatingconcentrations of the charged ligand despite having longermigratiou tine.

Simulation of CA Interacting with One Chatged(L*) and One Neutral (Lo) Liginds. The nodel weused can be readilyertended tosimulate the nigration ofcA in the capillary while interacting simultanrJ*tv *itltwo -gr mo-re ligands. For the case of cA interactini witntwo ligands: L+ (charged ligand) and Lo (neutral liiand),a third linear array of compartmente was added L tu.

ffJ

(J

ff

O

U

(14)nJ

(.)(J

fl-J

U

O

1 2 3 4 5Compartments

to-eM

| 2 3 4 5Compartments

t 2 3 4 5Compartments

(13)

Figure 4. The eimulation continuously adjusts the contents ofeach compartment of the reference frarne "r

tl. fiame travetsthrguSh t\" opt{"ty. For eimplicity, the propagation of thegnte.nts- of a single compartment is ihown.- rl.-.t"psed time(ms) in the series of frames are (a) 0, (b) 100, (c) 800,

"ia ial aoo.

compler) occurring with rates comparable to the timerequired for the electrophoresis erperinent. To extracttheeerate congtants forthe peatwiatus, we simulated thebehavior of cA under conditions of the AcE erperiment.

The modelF?E we 'sed to analpe the ni$ation of CAin an electrophoresis buffer .oot"ioiog tigaia ass'm"a areferenc'e frane that traveled along tle Lpiuary at thevelocity of the free CA (Figure al. ne origin of thereferencr frame was designated as the position oftigrationof cA without bound ligand in the electrophoresisf,uffer.The terminus of the refercnce frnt," *'' r.i * the positionof the rDarimrrnn displacement.D This latt€r condition issatisfied at saturating concentrations of the ligand in theelectrophoresis lurft,t. Thus, the cA-ligand cimplexwasmobile within this reference frane, anditg velocitywithinthe frane was determined from the diffetrorJ in themigration tines of cA with no ligand in the electrophoresisbuffer and with sat'rating concentration of the ligand.

The reference frane was subdivided into two lineararrays of conpartments: one array represented thecompartments for the free cA and the other for the cA.L+compler. The unbound cAwas introduced in a Gauesiandiehibution into the compartments regerved for free cAcentered on the origrn of the reference frane. The widthof the Gauseian distribution was adjusted to match thepeakwidth of cAinthe electropherogmm obtained in the3beence^qf ligand in the buffei. As in the actual erper-iment, cA was introduced in the compartments as freecAand did notinteractwith the ligand.-tltn ri.ul"tioowas initiated.

The main element of the simulation was a continuousiteration cycle that consist€d of two steps: an equilibrationstep and a translatlon s!ep. Figure 4 glows the early stepsof the simulation for the propagation of the conients aplug of cA initially occupyingi single compartm""i. tu.equilibration etep involved periodic adjushent (At = 1-10ms)30 of the concentrations of the free and compleredprot€in8 in ev_ery setof paired compartnents (eqs iZ_t+1.The term A[CA]',{ io

"q 12 represents the oet cna"ge io

concentration of cA in xth paired compartments ovei thetime interval At. To simplify the simulation, the rate of

t0-e Mro'eM

Af finity C opillary Electro phore sis

reference frame to contain the CA'L complex. Thisvariation agsund that the interconversion between CA'L*and CA.L. had to proceed through free CA (eq 15).

__

Joumal of Medicinal Chernistry, 1gg3, Vol. 36,No' I 131 \

protein) can be achieved by increasing the residence time

of tne protein in the capillary to allow for equilibration totake place. This will also require adjusting the amountof protein so that it is lower than the amount of ligand

available for binding.le Qualitative screening of strong

binding ligands can be undertaken using shorter run times;

the erpected electropherogra-s will resemble Figure 2d.For weak protein-ligand interactions, high backgroundabsorbance and changes in buffer properties due to theIigand should be anticipated at the high concentration ofliiand required to influence tbe mobility of the protein.s

Erperimental Section

Apparatue. The ISCO 3140 capillary electrophoresis appa't"t* ilSCO, [nc., Lincoln, NE) was used in this studywith theanode on the injection side and the cathode on the detectionside. The capillary tubing (Pollmicro Technologies, In9., Phoe'nix, AZ) was of uncoated fused silica with an internal dinrneterof50 pm and a total length of 100 cm (75 cm from the injectionside to the detector) unless stated otherwise. The elution wa8monitored on-column at 200''m. The tcmperature of the columnwas naintained at 30 + 1 oC. The electropherogtan raw datawere collected using ICE software (ISCO, Inc-, Lincoln, NE) andlater erported as ASCII files for proceesingad analyais ugingKaleidagraph (Spergy Software, Rcading' PA).

simulation. The sinulation programs were written in pascer-

The reference frnrne was constructed by dividing the fr"-e intotwo arrays of compartments parallel to the direction of travel.The widih of the compartments corregponds to the distance thatthe protein-ligand compler would have traveled in the referenceframe using elperimentally determined velocities for the freeand the complered CA. The concentration in each pahedcompartment was iteratively adjust€d every 1-10 ms using eqsL2-I4. The concentration of the ligand was altsuned constsntand equal to the concentration in the electrophoresis buffer. Theconcentration of the complexed CA in the rth compartmentwastransferred to the (r + l)th compartment every 100 me. Thesimulation generatcd data were also anallzed and plottcd usingKaleidagraph.

C hemicals. Bovine carbonic anhydrase B (EC 4.2. 1. 1 ), glucoee6-phosphate dehydrogena* (Leuconostoc mesenteroides, ECf.i.f.agl and soybean trypsin inhibitor were purchased fromSigma. Horse heart myoglobin was purchased from U.S' Biochemical corp. stock solutions (1 nglml/) of bovinc carbonicanhydrase, horse heart myoglobin, glucooe-&phosphate dehy-drogenase, and soybean trypsin inhibitor were each preparqd bydissotving the lyophilized proteins in glycine (f92 vnM) and Ttie(25 mM) Uufer. Benzenesulfonamide, 4-toluenesulfonamide, and4-nitrobenzenesulfonamide were purchased from Aldrich. 2,4,5-trichlorobenzenesulfono-ide was prepared from 2,4,Strichlo-robenzenesulfonyl chloride (TCl-America) a4d recrystallizedftom95% ethanol, mP 187-189 oC.36

Procedures. Eight nanoliters of a ssmple solution containing0.3 mglmT. of CA and 0.3 mg/mT' of each of the nonintetactingprotein markers and mesityl oride (neutral marker) in 192 mM

ilycinr2S mM Tris buffer (pH 8.3) was introduced into the."pitt"ty by vacuum injection. The electrophoresis was carriedout using an electrophoresis buffer (pH 8.3) consisting of 192mM glycine, 25 mM Tris, and appropriate concentrationg (0-200pMl of arylsulfonamide tigand(s). The electrophoresiswas carriedout under constant voltage of 30 kV generating a cunent ofapprorimately 10 rrA.-

Pteparation of 6. To a solution of &(aminomethyl)ben'rerresulfonanide hydrochloride (10.0 g, 45 mmol) and trieth'ylnmine (9.0 g, 89 -mol) in dimethylformanide (150 mL) at 0iC *as added methyl adipoyl chloride (8.0 g, 45 -mol). Themixture was stirred at 0 oc for t h and then at room tenperaturefor 6 h. The solution was filtered and concentrated in vactro.Flash chromatography on silica gel (chloroform-methanol, 9:1)afforded the methyl est€r of 6 as a eolid (14.0 g, g5%r. Theproduct was recrystallized from a mirture of chloroform andmethanolto yield planar crystals: mpL24-L25 oC;t11NMR (400MHz, DMS0-d6) O e.43 (t, J =5.9 Hz, 1 H, N.ED' 7.77 (d'J = 8.3Hz,2 H, aryl H), ?.41 (d, J = 8.3 Hz,2 H, aryl H), 7.33 (s,2 H,

cA.L+ ff.o fi ca.l" (15)

Thus, the equilibration step of the simulation was ex-panded to compute the emounts of CA'L+ and CA'L.alternately using eqs 12-14. The translation step shiftedonlythe contents of the compartments for CA'L* becausethe CA.L+ complex was mobile within the reference frame@u * pcA.L*) and the free CA and the CA'L. complexwere immobile (pcl - trcA.d. The rest of the simulationwas basically the sane.

Figure 3b shows the electropherograms predicted bythe model for the migration of CA in an electrophoresisbuffer containing 50 pM of charged ligand 1 and increasingnmountg of neutral ligand 2. The binding constantsI( *d Ki *td as input parameters in the simulationwere 1.5 t lff M-l and 1.1. x lff M-1, respectively.Scatchard analysis of the simulation-generated electro-pherograms (Figue 3b) using eq 10 did not return theorigind value of the binding constant used in the simu-lation but instead gave a vdue of 1.3 x 1ff M-l (r > 0.99);this value was equal to the apparent Ki' measurederperimentally (Figure 3a). The original value of thebinding constant (Iq) used in the simulation was ob-tained using eq 11.

Conclusion

ACE is a useful method to study protein-ligand inter-actions. The attractive features of ACE include its abilityto provide assessment of protein-ligand interactions uslngvery snall nmounts of samples and ligands in relativelyshort time. ACE relies only on the migration time andshape of the peak and not on its area. The concentrationof the protein in the gnmpl€ does not appear in theequations used for Scatchard analysis (eqs 6 and 10). Theprotein need not be pure; simultaneous determination ofindividud binding constants using s snmpl€ of a mixtureof isozlmes or different proteins is possible.s [n this study,ACE dlowed gimultaneous measrrrement of the bindingconetsnt of 1 to CA, through changes in migration timeand of the off rate for the binding interaction from thepeak width.33

A najor consideration in using ACE is6qinn f,[etendency of proteins to adsorb on the wall of uncoatedcapillaries; this tendency becomes more pronounced whenthe pH of the electrophoresis buffer is close to or lowerthan the pf of the protein. A number of approaches areavailable to control this int€raction between protein andcapillary wall including the use of additives to the bufferand chemical modification of the silanol groups of thecapillary wall.s ACE requires that at least one of theligands should have a sufficient charge to cause a mea-surable change in the migration time of the protein-ligandcompler.

The simulation suggests that the electropherogra-sreeulting from protein-ligand interaction can be explainedin terms of relatively few variables: on and o// rates (andthus, binding congtant), concentration of the ligand(s),and the relative mobilitiee of the protein and the protein-Itgand compler(es).4 The gimulation also suggests thatquantitative determination of high binding conetants(aseociated with slow dissociation of the ligand from the

132 Journal of Medicinal Chemistry, IggS, VoL J6, No. I

SO2NIlt, 4.32 (d,J = 5.9 Hz, 2H, ATCHIN), B.Sg (s, B H, OCHa),2.32 (t, J = 6.9 fu,2 H, CHzCIIzCOzCHg), 2.L7 (t,J = G.9Hz,2H, CH2CH2CONH), 1.53 (m, 4H,CHzCHd; r3C NMR (100.6MHz, DMSO-dd 6 L73.4,172.2,143.9, 142.6, L27.5,125.g, 51.3,41.7,35.0,33.1, 24.8,24.1; HRMS (FAB) mleB29.LLS1 (tr,t + H)*:calcd for CrrlIzrNzOs,S 329.11?1.

To a solution of sodiun hydroride (0.1 N, 200 mL) was addedthe nethyl est€r of 6 (4.0 g, 12.2 mmol). The solution was stirreda! room temperature for z h and then acidifi ed with concentratedHC-l to pH - 3. The resulting precipitate 6 was filtered, washedwith acidic water, and air-dried. This solid was recrystallizedfrom acidic water to yield white needles (B.b g, gT%)i mp r2L-L22 oC; tH NMR (400 MHz, DMSO-d6) 6 8.42 (t, J

'= 5.ti Hz, I

l{r_NH), 7-76 (d, J = 8.9 Hz,2 H, aryl H), ?.40 (d, J = g.g Hz,2 I!, arfl H), 7.3t (s, 2 H, SOzNIld,4.Bt (d, J ='5.9 Hz,2 H,fuCIlzN), 2.22 (t, J = 7.0 Hz, 2H, CHzCHzCOzH), 2.L6 (t, J =7.011z,,2 H, CH2CIi2CONH), 1.52 (m, 4H,eHzCliil;rsC NMR(100.6 MHz, DMSO-dd 6 L74.4, t72.t,143.9, L42.5,127.+, L25.7,4L7,35.0,33.4,24.8,2a.2; HRMS (FAB) mle\L5.t00b (M + Hy+'calcd for CrgHrgNzOoS 915.1015.

Preperation of rrimethyl Eeter of l. To an ethyl acetatcsolution (10 nL) of the Boc-protected tris(trimethyli est€r Zs?(1.0g, 1.5 mmol) was added trifluoroacetic acid (0.6 mi, ?.S mmol).The solution was sti*ed at room temperature for 2 h. Thereaction mixture was diluted with ethyl acetate, washed with20% aqueous sodium bicarbonate, water, and saturajsd godirrmchloride, respectively. The organic rayer was dried using an-hydrous magnesium gulfate and concentrated in vacuo. Theproduct, isolatedas thefree aynine (0.S2g,61% ), wasuseddirectly!o1^the next coupling reaction. To a solutioo of amio e Z (0.52 i,0.93 mmol) in ethyl acetate (20 mL) and 6 (0.2g 9,0.92 mmel;in acetone (lb mL) at0 oC was added dicyclohexyl-carbodiimide(0.2L -g, 1.01 mmol) and l-hydroxybenzotriazoll tO.ta g, 0.g2mmol). Aftcr mixing, the reaction was allowed to warm to roomtemperature and stirred for 24 h. The solution was filtered andconcentrated in vacuo. Flash chromatography on silica gel(chloroform-methanol,20:1) afforded the dejirea product as ayellgw oil !0rT0 s,89%): rH NMR (400 MHz, DMSO_d6) d 8.g8(t, J = 5.9 Hz, 1 H_, NID, ?.?G (d, J = 8.8 lfz,zH,aryl H), Z.AO!{,_J = 8.3 Hz,2 H, aryl H),7.92 (s, 2 H, SOzNIIzi, Z.Oe (., f U,NIf), 4.31 (d,./ = b-.8 H2, 2H, AreHzN), 3.69 (s, 9 H, (COTCI/dJ;3.54 (s,6 H, C(CIl2O)g), 8.44 (t,J = 5.5H2,6 H, (OCH;CH;;i;3,3! (s, 6 H, SCII2CO2CHJJ, 2.60 (t, J = Z.Z lli, e g,(OCH2CH2CHaS)d, 2.13 (t, J = 6.9 Hz,2 H, CfIrCl:g)NH);2.07 (t,./ = 6.9 Hz, 2 H, CII2C(:O)NH), f.iZ'(m, S ft,(O_CH2CI/2CHzS)d. L.47 (m, 4 H, CHzcHzCHzC(-O)Nir1; ro5NMR ( 100.6 MHz, DMSO-d6) 6 LT z.g, LT 2:L, ti o.z, 14b.8, L42.s,\?7,a,125.6,69.0, 6g.0, 59.6, 52.0, 49.6,41.6, 35.6, 35.2, gZ.6,Zg.a,25.L,24.9; HRMS (FAB) mle 878.2679 (nA * Na)+, calcd forCssHszNsorsSrNa 87 8.2G7 2.

Preparation of Ligand l. To a methanol solution (b mT.; ogthe himethyl ester of I (0.b g, 0.6 mmol) was added l N sodiumhydroride (5 -L, 5 mmol). The reaction was carried out at roomtemperature and monitored by TLC (chloroform-methanol =9:1, v/v). The hydrolysis of the triester was completed afber oneday. Dowex 50W-X8 (H+ form, 2fS0 mesh) ,"r^io r* adaea tothe solution that its pH was 3.b. The solution was stirred atroorn temperature for 2 h, and acidity of the solution waslonitorgd 11sing pH indicator strips. The desired product I9b!"i"9d following filtration and concentration in vacuo wasP_9F4 * "

yellow oil (free acid form; 0.4 g, 84%): rH NMR (400MHz,_DMSO-dr) a 8.88 (t, J = b.9 Hz, t Ii, NID;?.?6 (J,J = A.g\?,?\, aryl H), 7.!0-ld-_,! = 8.3 Hz, z H, arytit), z.iz'(.,2H,SOzN/Id,7.06 (s, l_H, NIf),4.91 (d, J = 5.9 ilz,2H, ArCI/rN);3_._5_a_!t, 6 H, C(CII2O)r), 3.41 (t, J = 6.L Hz,6 H, tOCfr-_C_Hr9IrS)s), 3.21 (s, 6 H, (SCllrg6rH)d, 2.00 (t, J = 7.2H2,6lll IOCH2CHzCHzS)s) , 2.14 (t, J = 7 .t Hz',Z H,CfrCt:O)NH),2.07 (t, J = 7.t Hz, 2 H, CII2C(:OiNHj, t.73'(m,'6 H;l9CtlrCHrCHzS)s),_ 1.48 (m, 4 H, CH zCHzCHrCt:OlNif l ; "il!y! ( 100.6 MHz, DMSO-dd 6 L7 2.4,- r7 2.2, ti t.t, 143.9, itz.s,\27 :5, !?! 3 169. 1, 6g_.0, 59.6, 4 1. 7, 35.7, 35.2, 93.2, 2g.7, 2g.6, 25.L.,2a.9; HRMS (FABI mle 886.2192 (M'+ Na)+,'calcd forCszHsr NgO rsSrNa 836.2202.

Auih et al.

Acknowledgment. We thank Hans A. Biebuyck forhelpful discussions and comments about the work. EcBthanks NSF for partial support under a NSF-ROAfellowship.

Supplenentary Material Availeble: Codes (pescru,) forthe simulation of one enz]mmne ligand and one enzlme-twoligands interactions are available (z pages). ordering infornationis given on any current masthead page.

References(1) This reeearchs'as supported by the National IDstitutes of Health(Grant GM30367), the Nationd Science f,ou"aiiioo-iCi"nt CHE-

91-22331 to GMW) lnd the M.I.T. Biotechnolggy n"o".irg_^. Pnqo""rgs Ce3t4-r. (Cooperativ-e Agreement Cnn:5gborll.(2) On leave from Roqns Coilege, Winier p"r[, Fi rggi-riilz.(3) C_hu,_Y-H; Avila, L.-2.; BieEuycb H. e.; WhiGiao, C. fA. Ur"

of Affrnity capillary Electr_optoreeis To Measr'e Binding bonetants. .. 9f Lleands-to Prot€ins. J. Med. Chem.lgg2, 15, nl,-E

-nn.

(4) Reviews of capillary electrophoreeis of pro6in;: -k-rU,

W. C.;llg1nic,_C. A. Capillary pleclorholare. eit. Ciin. iggz, 64',389R-402R. Maz.z.eo, J. R.; Iftul, I. S. Coated Capiiiarieg andAdditives for the Separation of.proteins Uid"iiUr"y Zoo"E- ]qggphq"sis and Capillary Isoelectric F**i"g.

-B{"filirrrioi;*

1991, I0,63&-645-.- Novotny, M.V.; Cobb, K. I.; Liu, J. i?cLntAdvances in capillary Tectrophg,resis of prot€irE, Feitides, aoaAmino Acids. Electrophores,s lgg0, II,7g*7ii.'

- -r---r

(5) Reviews of affinity.electrophoresis (AE): Taleo, K. AtridtyllectroRhoresis. In Adu ances in Erectrophorisis;Ch;6;.h a,Pq1rg, M. J., Radola, B. J,,.P{g.;_BCX pu'blieher: N.", Vo*, fOAZiVoL l^pp Zn-27-9.^Lee, M. K.; Lander,_A O,,A""tplrli-nif-itvand structural sele_ctivity in the'Bindini oi-Froteins toGlycosamino_glycn _n!: Development of a seneitiie aectoploreticA_pproach. hoc. Natl. Acad. Sci. U.S.A.l99l, g8, %6VZZZZ.-S$mura, I!, Progress_in Af- finop_hgrqis. J. Cn i,rrtobii66o, .lro,25L-270. Horejsi,_V-; Ticha,- M. eualitstive and Qnantit"tir"$nRlications of Affinity ElectrophoreeiE fot tre stuav-orpiotein-!,_igand Interactions: A Rcview.- J.Chronutojr. i9#, gi-6,&afl.H_orejsi,V._Affi nity_Elggtrgeho-resis.Uetnias"piy:,it.tdU,tU,?7-??L. Horejsi, V. AffinityElectrophoreeir* ernt. n;iii. ig8f ,112, l-9.

(6) white' E._J.;_Philipns, D._e. Transcriptional Analyei' of MultisiteDrug-DNA Dissociation Kinetics: pit"v"a t"r-i"ati"" oTr*-friptrgl_Lv 4$:o-y9ln D. Biochemistry rgtt, n,glii+:flZ.PaFn, W. D. M.; Rang, H. p. A Kinetic Appr-oach to th" M;;b""i".

__. 9f D^g Action. Adi. Drug. ges. 1966,'.i, S?_90.-(7) A number of functional forms have been suggestpd to describe therelationship between electrophoretic nobiliiy *a tne-clr,.g" a"amgl? of the protein-entity Compton, g. .I.;b'Grady, E. A: R"l;of Charge^Suppression and Ioniistreneth in f,reu

.6"e niect"o-phoresis of Proteins. Arwl. Chem. l9gl, 63, 25 g7 _2ffi2. Compton,

B. J..Electrophoretic Mobility Modelirig dr piot"i" i" rr* zo""capillary _Elect_rophoresis and its Apf,licati*-t" lroro"roo.rl*i$vlnclohgerogeleity_AnalysU.',t.Ciri,,*ii.igdi,ssg,357-366. Rickard,-E. C.; Strohl, U. M.; Nielsen, n Cldoo"LtioogtElectrophoreticlvlobilities Fro! capiuaty E drt ophoioi" withPhysicochenical _p_ropertiee of protcine a"JF"p'tiao. er.r.Biochem. tggt, tgz,7gz-zol. Grosen4., p.b; ii"iU-,r-, .r. C.;I,gq"t, H. H. A Semiempirical Modet fbr tJ'plectropioreticl4effiliJiesof Peptides in Flee-solution Capillary ptect oJUor"sir.Ana l. B i o c he rz. I gE9, I 7 g,-Z8-gg. Deyl, Z. ;'Rohtil"k, V.; ;id"-, M.separation of c_o-llag_ens bv capillary'n""ttoploil.i.' ilcn o-nuttogr. 1989, 480, gZl-BZg.

(8) Alternativ-ely, a measurable difference in the elechophoreticpobility of the compler may also be achie'ed by ca,eing;t-;*r*in f[g mara of the compler without proportio-natety cianging themagnitude of its charge, i.e. by usiirg ligande of fith nii;uhrwerghts.

(9) Eeviewsl Qotre, F.; Groe, G.; Storey, B.T. Carbonic Anhydrose:From Bioche mistlt, and G e ne t ici io phy siitoii- ii-' i{in;"at\e(iginerV_CH Publsbers: New yor!, -t99r. "boagro", 3. J.;Tashign,R. E.; Gros, G.; Carter, N. D. ?he CirUodi-iiii:i*"r,p3ltyl.gylbsiotogy ,d Motecutar Genettcs; iienirn ii.i"i N"*York, 1991.

(10) B_aldwin,_.1. J.;_Pon!i".9{9., g. S.; Anderson, p. S.; Christy, ilf. E.;Murcko, M. A.; Rgnd3ll, W. 9.i9"!t*r-,H.; Susrd M. F;6;;osrr,{.. P.; Gautheron, P; Grovs.f .; Mqugua, p.; Viff i, iia-i; ivt.fri".r,P. M.;.-Navia, Iq. 4. Thienothiopyra":Z-rufoianiitoi- iorefTopically Active carbonic Anhydrasitntribitom ior the Treat-*tof Glaucona. J. Med. Chem.lgtg, J2, 251f251g.( I 1 ) Eriksson, A. !.;,Jone.s, T. A. ; I,iljas, A. R€fiDA S-tru;trut s sf flr,-apcarbonic Anhydrase II at 2.0A riesolution. protaru, st *it-. i"*t.and Genet. lgtt, 4, 274-282.

(f2) Erikssog, 4.E.; Kyle-ten, p. I[; Jones, T. A.; Liljas, A.Crrntal-l.og.rap.hic studies_of Inhibitgr Binding'sit€8 ii tti-1"-br"[ro"i"fghydrge Il A Pentacoordinated Biiding ortue scN ron to tle? cat High pH. proreirc: Struct. Funit. and Giii.-tgils, n,283-293.

Af finity C apillary Ele ctr ophoresis

(13) Chu, Y.-H.; Whitesideg,-G. M. Af-frnity CgPillry Electrop,horesis'--' c."'sinuitaneorulv

-M"""*. Binding constants _o^f M_ultiple

i.ptid;t Vaocooivcin. !: 9!e.^cnei- 1992, 57,35?4-3525'G4) il;;e;,b; ttg".l.;-S*ttki, f.; Su?Y\i'S'; {ake$' D'.Determi-'- '

*ti- ittii. Ai.&ialion Constant of Monovalent Model Protein-

G;fit"t;.tion nv Cgplttarv Tnne Electrophoresis' J' Chro'motogr. Lggz, 597, 377 -382. -

tr1'C'frlnli, l-.' i; C.-iUeri, P-;. Dhan*, o'; qodd"!' D''{ Studv' --' Jr-ti" Eiirai"g' or Vancom-ycin ^to Dipeptides uslng- c^a^4riuqryEil;;tff;ii. ,t. Cnem. Soc- Chem' Commun' 1992, 804-806'

OSI Xaiiwaii-fi.; -Hit-q,

-H'; Oono., K' Binding Shift Assav of'--' pfi"lbu-io,' C"noa'"n"'and Carbonic Anhydrase by. High-i"tf;;;.1' Capillarv Electrophoresis' J' Biochem' Biophvs'Methods lg9l, 22, 263-26E.

(lD -G;;;;,

.q,.;t;t., N. Ca-pillarv^$l Affinilv E-lectrophoresis of'-'

DNC Fragrnints. Annt. Chem. 1991, 63, 2038-2042'tfgl Chu,y.-fi.; Whiteeides, G' M' Unpublished results'iisi H"iiiri, v.'so-r Theoretical Atpg_"ts of Af- finity-Ele-ctrophoresis.'- '

i. Ciro^otogr.7979,I78,l-L3.-Horejsi, V'; TttF'M' Theory of|fi,oit' bteitropUoreais.. E-vduation of the Effects of Proteiniia"fti"'h"*v, li-oUitir.a LigaD! Fetfrogeneity and. Microdis-l;ih;iil;,i Detcrmination 6f Effective Concentration of Im-.oUUir.a Ligand. J- Chromatogr' 1981, 216,-4342' . -

(20) F;;eG; tor"tt "

.ff""t" of the cf,anges in the buffer viscosity and'--' ai"f".fuc constant on the electrophoretic mobility-of CA, At-,u.*1is the conect€d migration time ior the_protein of i.te1".1 ,aO,relative to a refere-nce protein (horse heart myoglobin in thiserarnple).

tZU fne difiirence in the linflin_g-constants are within the limits due---' ;;H;-X"-ott*, {- C, 4 l'e-tbod.for-Slu$vmg the Kinetics oftne nUibiUon oi["tUo*. e*ydrase by Sulphonamides. Binchim.Biophys. Acto 1966, 118,405.-412'

(22) F;;'di6",r".ioo of inhibition of carbonic anhydl_ase ftom.different'--' ;;.o W tuffo"t-idee see: (a) Maren, T' H'i Sa1rv{' G' TheA;;tyA Su[onamides and Anions Against the Carbo_nic An-t-jt"",! oia"i-"r", nuqt and Bacteria (b) Maren, T. H. DirectMeasurements-of

,t,he Rate Const,nts of Suuonamides With

d"rUo"i..q*w dra*. Mot. Pharmocol. 1992, 4J 11F426. (c) King,R. W.;--n*g.& A. s. v. {!e_tic Aspects of structure-Activitytirf"til,*. fheBinding of Sulphonamidee by Carbonic Anhydrase.hoc. R. Soc. London, B 1976, 193,107-125'

(23) b;;tii, A.; Ragus€o, C, Ca4Pqgna, F; Langridge, R; and Klein T'E. Inhibition of carbonic Anhydrase by substttuted 5^enzene-;.ip""r-id*.,1 neinveetigation byQSAn and Molecular GraphicsAnalysis. Quant. Struct.-Act. Relat' 1989, 8, 1-10'

(24) Tatff, F. iV.; King, R. W.; Burgen, A' S' V' Kinetics of Compler'--' foi-"iion B6tn'ee"n Hunan Cirbonic Anhydrase and AromaticSulfonamidee - Biochemistry 1970, 9, 2638-1264.5.'

(25) Miu;;t i. cn:o*otography: _concepts and contrasrs; wiley:,-' ilewiork, 16'6&.n! fs-'ss. Brainthwailer A.! Sm--ith, F' J'Chromatograii;r'Uitno*; Chapman and Hall: New YorL 1985;oo 1 1-23.

-Ciiai"gt, .l . C. n Cnr 6mat o graphy ; Heftmann' E" Ed' ;

Vlo N*tt-d Re-inhold: New York, 19?5; pp ry.-41'(26) F;;;;ht€d ri-ul8tioo of time dependent distribution of solutes'--'

a*i"g atu.tofienl of a chromatogrlphit 1* see: ,Stevens' F' J'A"Gir ;i Fioteln-p rotein Interictidn bv .Silytltion oJ Small-zone si"e-nrch:sion chromatogaphy. stoclastic Formulation off i""ti. n"trg-ontriUutioos to dbsarved HigLPerf- ormgge- LiOuidChromatographyElutionCharacteristics.-Blophy-s.J.19t9'55'iiSS. St"i""i, ir. j. Analysis of Protein-Protein Interaction bySi-.tt ti r" ;f Smnll-Zone-SizeErclusion Cbr-on'atogrphv' Ag-pu*ti"" to Antibody-Antigen Association. Biochemistry 19t6,25,981-993.

tZZl F&ie[tBa nodels for the tranepo:t behavior of protcin interacting,- ' '

",ith;;b:it. Uiands on sizeerclugion HPLC see: Endo' S; Hava'shi'

H.;-W;6 A] Afirnitv Chromatographv Without rJ"mobilized

Lii-a"; A New Method for Studying Macromolecular Interactions

Journal of Medicinal Chemistry, 1993, Vol' 36, No' I 133

Using High'Performance I,iqui{-9hronatogaphy' Anai' I Yh"^'IgezT nZ,312-379. Endo, S; Wada, A. Theoretical and Erperi-il;t t Siudies on Zone-Interference Chromatogr"p UV^* a Nesffila for Determining Macromolecular Kinetic Congtents.Biophys. Chem.lg&|, 18, 291-301' ...

(2S) F;i;;ore rigorous -oa"t for capillary zone electrophoreeis of'-' ilyt* ihat h-aveinvariantproperties d'ring-the chroma$qrphict"";;; O"*, n. V.; Guiociron-, G' A' High Resolution Modeling;f

-Cbi1rry i",'." il"*rophoresis and Ieotachophoreeie. Anal.

Chem. 1991, 63, 1063-1072.(29) ihe el..troptto't"tic mobility gf the. .cgnpl^el was -estimated bv'--'

"-rti"pof"ti"g tU" electrophoietic mobility of CA at [L] - - 'sin8

a cuwe-fitting Progrnrn'(80) Time inc.ements, "At, io the simulation were choeen eo that the'- -'

*o""rrtration i" ""V

compartment doee not change bV.Pore thnn

iOZ i* "q"itibration ste-p (eq 12); a sigtrificantly.emallvalue for

ai i"q"it"i "

.o*id"t"ble anount of computcr ̂ ti-er Pl a highvalue-for At caused negative concentrations for cA in eome

comPartments.taU Sfigftaeviation (<|Vo )of the value of the binding :"","$tt :!$hd'- -'

;t"S;;nard anatysis of the siPulation-generated. electropheroelo-s from the vatue of the binding constant used in the simulation;;b.;;J;hen data .epre"eoiiog low concentrations of ligandioTn" J".ttophoresis buffer (compared to the initid concentrationof the enzyme) were included in the regteasion endysie' This

deviation was more pronounced at lowei concentratione of theIieand. closer eramination of the simulation indicated that thig

"itlf".t ** aue to some amount of the total simulation time being

used achie"ing.qoitiuriu- conditions- we also observe thie trend

;il1-.;trUy, ih"t i", data obtained athigher concentrations of

Iig;nd gave better fits on Scatchard qPd.y"it'^., . ,- , ,.(32) We haie determined the rate of broadening of,the pea'k (oz) as a

function of tine aJrd have concluded that the broadentng due to

It " "aaitio"al

24 s of migration time should be negligible (<0.1 % )'($t Frevious determinations relied on fluorescence meaEurenents or

titration of Products.(A4) S;;;;sl approaches h've been reportcd to ryduge nrgteinrdsorption'- -'

i; ;tlld; elecirophoresis: T-owns, J' K'; Regprer' T' E'. Polv';;hr6;ili".-gooi"a Phases in the Separation o!-f1o^teins bvC"iiUarv nfectrophoresis .- J. Qhrgnltto-gr' 1990, 5Iq' 6ts78' Bruin'C..1. lt.; Huisd;, R.; Kraak, J' C'; Fop-pe' H' Perfo:mance ofC*thtdr;te-Modifrei F'sed-silica Capillaries for the Se-parationof-p-tot6i". by Zone Electrophoreeis. J. Chromotogr. 19t3,4{10'339-349.Towns,J.K.;Regnier,F.E.CapillaryElectrophoreticS"p*"ii"* ;ifit"i* iJsini N_onionic Surfactant Coatings. Anal-

bir*.1991, ff;ilie-flszl llf'iqqss, J' R; Krull'.I' Siapillarvl.o"t""tri" rocusing of Proteins in uncoat€d Fused-silics capillarieeU.G Fofv.eric idditives. An'al' Chem' 1991, 63, 2852-2857'ilE; nA. U.; Jortenson, J--W' -Capillarv nUctr;gr.91eslE 9!Proteins in Buffers Containing High ConcentratioDs of Zwrtt€nonrcS"rt". "L Chroiiogr. 19t9, 4b0, aor-gro' Zhu, MiRodriguez' R;ft-""", p.; Weh, t. Capiliarv Electrophgle"-ry-of-ry^ote11n UnderAIk"["; Conditions- J.- Chromatogr' 1990, 516' 123-131'

tgsl Ttre nigration timee can be corrected usbg migration.indicca 8ee:'--' i;;-,"T.; Yeung, E. S. Facilitating.Data Ttansfer and lnproringFi.iai* i" C"piii"w Z"o" Electrophoresis With Mi'ation Indicee.eit. cnern tigt,6ii, 2gp12-2549. The effects of backgor.rnd noisecan be mininized.l3

(36) F;;, W. O- n"".Uons of Some Arene-gulf-onvl CUl"tlft J' Chem''- ' s;. rbso, eoel--s069- El-Hewehi, Z'; $unge, F' Sulfonic Acidblii*tiu6., Preparation and Applicability as MothproofingAgents. J. &:aht. Chem.1962' 297^-336'

(3D b;;; e. ; rraatnfi, .1. p. ; whit"tides, G' M' Molecular Self'Ageemblv'- ' ' iL;Giinvarogl" gond: A_ggregation of Five Molecules To Formn bisciet€ Sup.Lot"cular s-tru&ure. J. Am. chem. soc. 1992, inpress.