optical spectroscopy in studies of antibody-hapten interactions · 2020-04-16 · optical...

METHODS 20, 341–361 (2000)

d

Optical Spectroscopy in Studiesof Antibody–Hapten Interactions

Sergey Y. Tetin*,1 and Theodore L. Hazlett†

*Abbott Diagnostics Division, Abbott Laboratories, Abbott Park, Illinois 60064; and

oi:10.1006/meth.1999.0927, available online at http://www.idealibrary.com on

†Laboratory for Fluorescence Dynamics, Department of Physics, Universityof Illinois at Urbana-Champaign, Urbana, Illinois 61801

This article describes the use of optical spectroscopy in study-ing antibody–hapten interactions and in determining the equilib-rium binding constants. Along with equilibrium binding data, spec-troscopic tools often deliver structural information on binding-induced conformational changes of antibodies (or haptens).Structural implications of results from example antibody–haptensystems are included. Fluorescence spectroscopy has been par-ticularly useful in the area of ligand binding, and thus steady-statefluorescence quenching and fluorescence polarization are theprimary techniques under discussion. A brief description of fluo-rescence correlation spectroscopy is also provided. Absorptiontechniques, including circular dichroism, are mentioned to alesser extent. A basic description of the mathematical modelsinvolved in the analysis of binding equilibria is provided along withreferences to more complete works. Simulated and experimentaldata are used to illustrate the various experimental protocols andthe appropriate analytical methods. Typical sources of errors andexperimental precautions are indicated throughout the generaldiscussion. © 2000 Academic Press

The ability of the immune system to recognize andeliminate foreign material has been under intense in-vestigation for decades. The early research aims of thisfield focused on the capacity of the immune system torecognize a surprisingly wide variety of antigens andsubsequently construct specific antigen-directed anti-bodies. Biomolecular recognition, of course, is not thesole property of the immune system but is found invirtually every cellular process. As cellular functionsevolved, the cell required an increasingly complex

1 To whom correspondence should be addressed at D-4H4, AP-20,
Abbott Laboratories, 100 Abbott Park Road, Abbott Park, IL 60064-6016. Fax: (847) 938-2510. E-mail: [email protected].
1046-2023/00 $35.00Copyright © 2000 by Academic PressAll rights of reproduction in any form reserved.

mechanism for recognition. In the immune system, thisgeneral cellular feature was directed toward the sepa-ration of self from nonself agents and the elimination ofnonself material.

Clearly, understanding functional interactionsamong proteins, carbohydrates, lipids, DNA, RNA,substrates, and cofactors is a vital and critical researchendeavor in biology and biochemistry. The key processfor most protein functions is the specific recognition ofan appropriate ligand (substrate, allosteric regulator,transported metabolite, hapten, drug, or other mole-cules) or another protein (other subunits in multisub-unit proteins, receptor, the next protein in cascademechanisms, forensic protein). These processes resultin biological specificity. The strength of the interactionof reacting molecules is characterized by an equilib-rium binding constant expressing biological affinity.

The ability of the immune system to form antibodiesagainst foreign antigens makes antibodies extremelyuseful tools in biochemistry. Detection of known anti-gens, such as viral antigens, bacterial antigens, anddrug presence, is commonly used in biomedical practiceby means of the immunoassays. Additionally, antibod-ies can serve as model systems for probing the detailsof well-defined ligand–protein or protein–protein asso-ciations.

Antibodies and receptor proteins of the immune sys-tem demonstrate the range of typical biologically rele-vant specificities and affinities. The structure–functionrelationships in several antibody–antigen systemshave been intensively studied for the past three de-cades (recently reviewed (1)). Several antibody–haptencomplexes have been crystallized, and their three-dimensional structures can be found in the Protein
Structure Data Bank. It is generally accepted that theantibody binding site accommodates a single hapten
341

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342 TETIN AND HAZLETT

molecule and that the binding sites in immunoglobu-lins do not interact in binding of haptens in solution.This understanding allows us to restrict the discussionhere to the simple binding model (identical, noninter-acting binding sites). However, the researcher shouldnot overlook other binding mechanisms. It is possiblethat two or more hapten molecules can be simulta-neously accommodated at the antibody binding site orfor the hapten molecule to bind to the antibody outsidethe typical binding site in a nonspecific manner. Fur-thermore, occasional speculation on interactions be-tween binding sites of the same antibody after haptenassociation is often discussed, despite the absence ofexperimental support. Generally speaking, properlydetermining stoichiometry, carefully performing ex-perimental work, and minimizing data transformationduring analysis will provide the bases for application ofan appropriate binding model.

We will use the term ligand here for organic mole-cules (molecular mass 100–1000 Da) that are signifi-cantly smaller than antibody molecules (150,000 Da forIgG). The ligand usually is unable to induce an im-mune response alone but may act as an immunogenicepitope when attached to a macromolecular carrier.Subsequently, the ligand will be recognized by inducedantibodies and will act as an antigenic determinant (orantigenic epitope). The immunology literature identi-fies such ligands as haptens (2). Ligand is a morecommon term in protein studies, but it also has beenused often in immunochemistry. Therefore, in our fur-ther discussions, we use ligand and hapten as equiva-lent terms.

The overall aim of this article is to introduce the readerto the use of optical spectroscopy in the study ofantibody–ligand interactions and in the determination ofthe equilibrium binding constant. Various methodologiesin fluorescence spectroscopy have been particularly use-ful in the area of ligand binding and are the primarytechniques under discussion. Absorption techniques, in-cluding circular dichroism, are mentioned but to a lesserextent. Because the experimental design goes hand-in-hand with a firm basic understanding of the processesinvolved, a section is devoted to the general equilibriummodel and its mathematical description. We hope thefollowing discussions, although focused on simple single-site binding, will be of use to students and researchers inthe field. If the reader desires more elaborate and com-plete work on ligand binding, the literature contains avariety of excellent work (3–10).

THEORETICAL CONSIDERATIONS

Ligand Binding
A simple binding equilibrium between protein [P]
and ligand [L] is described by the reaction

@LP# º @L# 1 @P#, [1]

here the dynamic equilibrium between the protein–igand complex [LP] and the free species is related. Thequilibrium constants, the dissociation constant K d,

and the association constant K a, for this equilibriumare described by the relationship

Kd 51Ka

5@L#@P#

@LP#. [2]

For the simple equilibrium described in Eq. [2], thedissociation constant will have units of concentrationand the association constant will be in reciprocal con-centration units. For this reason, it is often more nat-ural to think in terms of dissociation constants, which,in these cases, also define the concentration at which50% ligand is bound.

The equilibrium constants are directly related to thebinding free energy, DG, the enthalpy, DH, and theentropy, DS, by the equation

DG 5 2RT ln~Ka! 5 DH 2 TDS, [3]

where R is the gas constant and T is the temperature.The enthalpic and entropic contributions to the bindingfree energy can be evaluated by measuring DG as afunction of temperature, which has a predominant ef-fect on the TDS term. The hydrophobic and electro-static contributions to the binding reaction tend tofavor entropic effects and can be explored by followingthe DG as a function of the solution ionic strength. Thepresence of electrolytes should weaken, via chargescreening, electrostatic forces and help in estimatingthe contributions of salt bridges to the binding ener-gies. Piecing together the forces involved in the bindingreaction can help to define the responsible contacts, butthis is not always the experimental aim. A great deal ofresearch is directed solely toward the detection of li-gand binding and the subsequent characterization ofthe dissociation constant. Rapid drug screening in thepharmaceutical industry is a good example of the de-tection of binding between potential drugs and targetmolecules being a primary research focus. In eithercase, determination of the equilibrium constant is oftena critical first step.

Equilibrium BindingExperiments designed to measure the binding be-

tween ligand and protein must have an observableparameter that is proportional to the fraction of bind-ing sites filled, F b. In our simple case above, with one
binding site per protein (Eq. [1]), F b will range from 0to 1 and will be defined as

wma

343OPTICAL SPECTROSCOPY AND ANTIBODY–HAPTEN INTERACTIONS

Fb 5@LP#

@P# 1 @LP#5

@LP#

@Pt#, [4]

where [Pt] is the total protein concentration. As men-tioned in the introduction, antibody binding sites areequivalent and noninteracting, qualities that permitus to treat each site as a distinct element. Equation [4]can be modified to accommodate IgG antibody andhapten binding by substituting the free protein concen-tration, [P], with the concentration of available sites,[S], and substituting [LS] for [LP] as the ligand–sitecomplex:

Fb 5@LS#

@S# 1 @LS#5

@LS#

@St#. [5]

Our experimental goal here is to accurately deter-mine the K d of a particular ligand and IgG pair. Thefraction of sites bound, F b, and the total solution con-centrations of sites, [St], and ligand, [Lt], will be knownquantities. The relationship between the fraction ofbound complex with S t, L t, and K d can be derived fromEqs. [2] and [5] and is given by

Fb 5

Kd 1 St 1 Lt 2 ~K d2 1 2KdSt 1 2KdLt

1 S t2 2 2StLt 1 L t

2! 1/2

2St. [6]

In conjunction with Eq. [9] (below), Eq. [6] can be usedto fit experimental data and resolve K d by successiveapproximations (11).

The classic description of the ligand binding problemis Adair’s equation (12), given below for n binding sites,

v 5¥ i51

n i~) i51n K i!@L# i

1 1 ¥ i51n ~) i51

n K i!@L# i , [7]

here v is the binding in moles of ligand bound perole of protein, L is the concentration of free ligand,

nd K i are the Adair constants, which is related, butnot identical, to the individual site dissociation con-stants. The Adair constants are also termed the mac-roscopic equilibrium constants and represent the affin-ity of a ligand for the nth binding site in a sequence ofbindings. These constants are not identical to the equi-librium constants for the individual sites, the micro-scopic equilibrium constants, because of statistical ef-fects (see (13) and references within for a more detaileddiscussion of micro- and macroequilibrium constants).In our discussions, we are interested in the microequi-librium constants that measure the affinity of the in-dividual sites and relate to the free energy of binding
(Eq. [3]). Obviously, for single-site proteins the macro-and microequilibrium constants are identical. In the
case of distinguishable noninteracting sites, the micro-equilibrium constants are measured directly, and Eq.[7] can be simplified (14) to

v 5 Oi

s i@L#

Kdi 1 @L#, [8]

where i is the number of site populations, K di is thecommon dissociation constant (the microequilibriumconstant) for the ith population, and s i is the number ofsites within the ith population. By introduction of theF b term and adaption for IgG, which contains twoequal affinity sites (i 5 1 and s i 5 2), Eq. [8] reduces to

Fb 5v2 5

@L#

Kd 1 @L#. [9]

Equation [9] can also be derived from Eqs. [2] and [5]and is the standard equation used to fit antibody bind-ing data. Binding curves for IgG–hapten pairs havingdissociation constants of 0.1, 1, and 10 nM are simu-lated in Fig. 1. In the traditional ligand binding exper-iment, the number of binding sites (or protein concen-tration) is kept constant while the concentration ofligand is progressively increased. The fraction of boundsites, F b, should be plotted as a function of free ligandconcentration. A logarithmic scale is recommended forthe abscissa to accommodate the wide range of ligandconcentrations required to span the complete bindingprofile. The data are then fit to Eq. [9] through the useof a regression procedure, such as the commonly ap-plied least-squares procedures or maximum likelihoodmethod (7), from which the K d is determined.

FIG. 1. Equilibrium binding curves for site–ligand dissociationconstants of 0.1 nM (dotted line), 1.0 nM (solid line), and 10 nM
(dashed line). Inset: Plot contains the identical curves plotted on areduced linear scale.

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The total ligand concentration is used routinely asan estimate of the free ligand concentration and is usedin the binding analyses. This assumption is acceptableas long as the concentration of bound ligand remainssmall relative to the total ligand. If, however, the frac-tion of ligand bound is significant, then one must find amanner to determine the amount of free ligandpresent. In experiments in which the fraction bound isdetermined directly, one can immediately and simplycalculate the free ligand concentration by L 5 L t2 (F b

3 S t). In cases where F b cannot be directly calculated,one can use the aforementioned stepwise procedureentailing the calculation of an apparent K d, using Eq.[9] with the total ligand concentration, from which anestimation of the apparent free ligand concentration ismade through application of Eq. [6], again to be appliedin calculating a new apparent K d. Several iterationsbetween Eqs. [9] and [6] should lead to accurate valuesfor K d and the free ligand concentrations. When theprecision of the data is poor or the fraction of ligandbound is large, this iterative procedure will not prop-erly converge. There are many more robust proceduresgiven in the literature (7, 9, 15, 16), but for a simplebinding problem the iterative method can suffice. As ageneral rule, if the ratio of sites to K d is below 0.1, thenthe total ligand should be a close approximation of thefree ligand concentration.

The effect of using total ligand for free ligand underinappropriate conditions is illustrated in Fig. 2, wherethe curves represent increasing ligand/K d ratios. As aconsequence of the increasing ligand/K d ratio, the ap-parent K d, often taken as the 50% bound point, shifts tohigher values as the stoichiometric limit is approached.

FIG. 2. The effect of stoichiometric binding conditions on the bind-ng isotherm. Curves are plotted as the fraction sites bound versushe total ligand concentration. The solid line (A) is the expectedurve, under conditions where [Ligand]total ' [Ligand]free, for a disso-iation constant of 1 nM. The dashed lines illustrate the resulting
urves when the concentration of sites is increased to 1 (B), 5 (C), and5 (D) times the K d.
A prudent investigator will verify the validity of abinding profile experimentally by repeating the titra-tion at a lower concentration of binding sites. Thedetermined K d should remain unchanged.

It is often preferable to fit raw data directly ratherthan to convert data to estimates of F b. If the observ-able parameter is linearly related to the fractionbound, then Eq. [9] can be applied but it must bemultiplied by a scaling factor (m), to match the param-eter’s range, and a constant (c) must be added to ac-count for the observed parameter having a nonzerovalue for the unbound state:

Fb 5m@L#

Kd 1 @L#1 c. [10]

The scaling factor and constant are usually fit as freeparameters in the data analysis. Examples of bindingexperiments are given later in this article, along withdiscussion on the appropriate calculations for F b.

The binding experiments described so far have fol-lowed protocols that hold the concentration of sitesconstant while the ligand concentration has been var-ied. One may also carry out the opposite, but equiva-lent, experiment in which the ligand is held constantand the site’s concentration is changed. The bindingplots from the two experiments should follow Eq. [9]and be essentially identical, as long as there is a singledissociation constant. In monoclonal IgG preparationsit is reasonable to assume a single K d. Polyclonal IgG,on the other hand, contains a population of IgG specieswith a distribution of binding constants and is thusmore complicated. The shapes of the resulting bindingprofiles will depend on the number of dissociation con-stants present, the range of dissociation constants, andthe experimental protocol used. For the condition whenthe concentration of sites, representing a number of K d

values, is held constant, the presence of additionaldissociation constants increases the span of the bind-ing profile. When there is a mixture of two antibodieswith a 100-fold difference in K d values, one can easilysee the impact of each equilibrium constant on thecomplete binding profile (Fig. 3A). In contrast, on thebinding plot for an experiment in which the ligand isheld constant and the IgG mixture is added, one ob-serves a binding curve possessing a normal profile thatcan be well fitted to a single K d. In the extreme casepresented in Fig. 3B, the fraction of bound ligand isalmost exclusively due to ligand association with thehigh-affinity site. The shift in the K d is a result of thefact that 50% of the added antibody, the weak bindingportion, participates little in the actual binding butcontinues to add to the total antibody concentration. In
situations in which the affinities are closer, the tightaffinity site remains the primary ligand binding site,

a

A

cco(at


and identifying the presence of multiple K d values isexceedingly difficult using this protocol.

Equilibrium DilutionA second, less common, experimental procedure for

measuring a binding profile is to prepare an equimolarsolution of ligand and binding sites at saturating con-centrations and proceed to dilute the mixture (8). Asthe concentration of ligand and protein fall, the proteinand ligand will dissociate. Given the definition of K d

and that the concentrations of the ligand and bindingsites are equal, the K d becomes

Kd 5@S# 2

@LS#, [11]

nd the relationship between the total sites, F b, and K d

is

Fb 5Kd 1 8St 2 ~K d

2 1 16StKd!1/2

8St. [12]

sample binding plot is given in Fig. 4, where F b isplotted as a function of the sum of the concentrations of

FIG. 3. Simulated binding curves for a two-component mixtureontaining 0.5 mol fraction for each of two IgG species having disso-iation constants for ligand of 1 and 100 nM. (A) Binding plot wasbtained by titrating ligand into a dilute solution of the IgG mixture.B) Plot obtained when a dilute solution of ligand is held constant
nd the IgG mixture is added. The dotted lines in both (A) and (B) arehe expected binding plots for the single IgG species.
ligand and sites which places the 0.5 fraction bound atthe K d.

The curves in Fig. 4 look similar to the standardbinding curves in Fig. 1 and are plotted in a mannersimilar to the standard plots with the dissociation con-stants at 0.5F b. The dissociation constants are thesame in both Figs. 1 and 4, but one should note that thespan of the dilution binding curve (0.1F b to 0.9F b) is2.86 log units and not 1.90 log units as in the standardbinding profile.

Stoichiometric BindingIn experiments designed to determine an equilibrium

constant, stoichiometric binding conditions are to beavoided, but in experiments designed to determine thenumber of sites per protein, stoichiometric conditions arerequired. An illustration of how the number of ligandbinding sites per protein is determined is given in Fig. 5.In this example, the ligand is held constant, at concen-trations well above the suspected dissociation constant,and protein is used as the titrant. The fraction of ligandbound is then plotted as a function of the moles of proteinadded per mole of ligand. Two dashed lines are drawnfrom the plot: (i) the stoichiometry line that is extrapo-lated from low protein additions where the change in Fb

is linear with addition of binding sites, and (ii) the satu-ration line drawn at high protein concentrations whenmost ligand is bound and further addition of protein haslittle effect on Fb. The intersection of these two lines,indicated by the dotted drop line, should mark the num-ber of moles of ligand bound per mole of protein, thebinding stoichiometry. It should be noted in Fig. 5 thatthe saturation line is not at 1.0, as it should be. With

FIG. 4. Characterization of dilution dissociation curves for anequimolar mix of ligand and sites. The fraction of sites bound isplotted as a function of the sum of the ligand and site concentrations.Curves for dissociation constants of 0.1 and 10 nM are shown. A line
is indicated for the 0.5 fraction dissociated point, and a drop line ateach intersection point is drawn.


experimental data, it is often not possible to accuratelycalculate the fraction bound nor to reach complete satu-ration. These effects result in the saturation line beingdrawn below its true position.

The number of binding sites per IgG molecule is knownand renders the stoichiometric binding experiment some-what superfluous. However, if one already has knowledgeof the stoichiometry, the same stoichiometric conditionscan serve as an assay for the concentration of IgG in agiven solution. The experimental protocol is identical tothe example above, but the abscissa would read theamount of sample added per mole of ligand. The inter-section point would then report the amount of samplecontaining the same moles of sites as moles of ligand inour solution from which the solution concentration of IgGwould be simply determined.

In the above examples the ligand concentration waskept well above the dissociation constant. If the ligandconcentration is too low, then at low protein concentra-tions there will not be complete binding and the stoi-chiometry line will have a reduced slope. The intersec-tion of the lines, in this case, will overestimate thenumber of sites per protein molecule (Fig. 6). Repeat-ing stoichiometry experiments at higher ligand concen-trations should lead to identical estimates, if ligandconcentrations are appropriate, and is a valuable checkon the experimental results.

Error in Kd DeterminationsThe precision and accuracy of a ligand binding ex-

periment are always research concerns. The accurate

FIG. 5. A simulated stoichiometric binding plot for an IgG–haptenbinding with a K d of 1 nM. The hapten concentration was keptconstant at 10 nM and the IgG concentration was varied. Dashedlines are drawn from slopes at the low and high protein concentra-tions. A reduced scale for the [IgG]/[Ligand] is used to emphasize theintersection point of the two lines and the estimation of the sites perIgG, 2. Ideally, the saturation line should be horizontal at F 5 1.0.
b
Here, to reflect many real experiments, saturation is not completelyreached (0.97), and the resulting line is below the ideal position.

identification of error sources within an experimentalprotocol is an invaluable process that can help guidethe researcher in the experimental design and in theeventual interpretation of the results. Unfortunately,the type and the extent of these errors are intimatelytied to the experimental protocol, making the discus-sion of error technique-dependent. We can, however,identify some limits for certain errors common to li-gand binding experiments.

Errors can be split into two types: systematic andrandom. Random error can be understood through sta-tistics, such as the standard deviation of a mean value,and generally influences the precision of the resolvedparameters. In contrast, systematic error biases re-sults and leads to errors in accuracy. Systematic errorsare particularly sinister because they appear as trendsand can mimic “reasonable” results. Let us first exam-ine a few points about random error elements in bind-ing studies.

Random error. How does an error in the determi-nation of the fraction bound, F b, translate into an errorin the dissociation constant? The relationship given inEq. [9] can be used to calculate the propagation of errorfrom F b to the dissociation constant K d. If we assumethat the error in the determined ligand concentrationis insignificant, then using basic error propagationrules for equations of a single variable (17), the generalrelationship between the error in F b and error in K d

FIG. 6. Simulated curves demonstrating the influence of equilib-rium conditions on an IgG stoichiometric binding experiment. Li-gand was held constant and antibody was added to given an F b rangefrom 0.03 to 0.97. Data are plotted as F b versus [IgG]/[Ligand]. Thedissociation constant was 1 nM. Curves are drawn, left to right, fordecreasing ligand concentrations of 10, 5, and 1 nM. Dashed lines aredrawn for the saturating line and the stoichiometric line determinedfrom the first and last two points, respectively. The intersection ofthe two lines is used to calculate the number of binding sites per
protein from the abscissa. Inset: Plot of the stoichiometry deter-mined as a function of the K d ligand.

w

Ta

l

v

ttd

FK


will be

dKd 5 U dKd

d~Fb!U d~Fb!, [13]

here dK d and d(F b) are the standard deviations inthe dissociation constant and fraction bound, respec-tively, and dK d/d(F b) is the derivative of K d with re-spect to F b. The derivative is easily solved from Eq. [9]and the specific error relationship of interest is shownin the equation (drawn in Fig. 7)

dKd 5 U2XF b

2 U d~Fb!. [14]

he same relationship was derived by quadratic sum inn earlier work of Weber (18).Graphed in Fig. 7A, Eq. [14] identifies two points about

igand binding data: the precision in our estimates of Kd

is not constant across Fb, and the highest precision is heldin the region around Fb 5 0.5. The error in the estimatedKd increases from four times the error in Fb, at the min-imum, to approximately six times at the 0.2Fb and 0.8Fb

points. Though these estimates are for calculations witha single data point, one can use this information to assesshow a particular error in data translates into precision inKd. It is interesting to note that random error in Fb willlead to systematic error in Kd (Fig. 7B). This is due to thefact that binding curves are not symmetric, and an errorin Fb will tend to push the apparent (fit) Kd to higheralues (20).

FIG. 7. (A) The error in K as a function of error in F . (B) The sys
d b
b. Data sets (n 5 5000) were simulated with a Gaussian error introduced/true K d was plotted as a function of the introduced error. A more ri

In addition to understanding the single point errorpropagation, the number of collected data points is acritical factor in determining precision of a resolved dis-sociation constant. One can correctly intuit that the errorin Kd can be reduced if more data are collected. Howshould one decide the number of data points necessary toachieve satisfactory results? In reality there is no singlebest number of points; the error in Kd decreases as morepoints are collected, so the number of points will dependon the required confidence for Kd. Information theoryindicates that the maximum information occurs whenpoints are spaced by 2d across Fb, where d is the standarddeviation in the calculation of Fb (18). However, informa-tion content is more a measure of the resolvability in thedata for model-dependent variables than an error in thedetermined parameters. From basic principles of erroranalysis we know that the statistical error in the deter-mined binding constant is reduced by the square root ofthe number of points collected. This tenet can be easilydemonstrated through simulating a large number of li-gand binding data sets, adding a random Gaussian errorto Fb, and then calculating the standard deviation of theresolved dissociation constants. Figure 8 shows the sim-ulation results as a function of the number of data pointscollected per data set, spanning from 0.2 to 0.8 in Fb, fora binding interaction with a Kd of 1 nM and an error in Fb

of 60.02. As one might expect, the more data points (p)per data set, the lower the standard deviation of Kd andhe better the certainty. If we eliminate the error reduc-ion due to the number of data points by multiplying theKd by p1/2 (Fig. 8), then the intrinsic error in the mea-

surement, as given by Eq. [14], should remain. We canestimate our expected error in Kd in the simulated data

atic deviation in K (apparent K /true K ) as a function of error in
tem d d d
d into F b. The sets for each error were then fit and the mean resolvedgorous simulation can be found in the literature (20).

F

T


from Fig. 7A at approximately 5 times the error in Fb.Our predicted standard deviation in Kd would then be 5 30.02 nM, or 0.1 nM. Indeed, our limit shown in Fig. 8turns out to be 0.107 nM, very close to the predictedvalue. The small increase in certainty early in the plot isexplained by the fact that finite numbers of data pointsdo not properly sample the errors across the chosen re-gion of Fb.

Systematic error. The source of error in ligandbinding experiments is not restricted to random error.In any measurement there is always a contribution tothe uncertainty, error that cannot be described by sta-tistics. Systematic error is related more to the accuracyof the measurements and less to the precision of themeasurements. The source of systematic error is highlydependent on the protocols used in preparing samples,the bias of the instruments, and the subsequent ma-nipulations of the raw data to deliver the estimate ofthe fraction bound. The potential sources for system-atic error vary greatly. In practice, the rule for dealingwith systematic error is a pragmatic one: identify theerror source and reduce its influence on the accuracy ofthe final result.

One obvious example of systematic error is in theaccuracy of the measuring instruments used in pre-paring the samples. When aliquots of hapten arebeing added to an IgG solution, the consistent addi-tion of too much or too little ligand will clearly shiftthe binding profile to the left or right. No amount ofsampling can correct for this error. A less obvious,sample-dependent error is introduced by the pres-ence of hapten in the preparation of IgG antibodies.Hapten-specific IgG antibodies are often purified by

FIG. 8. The standard deviation in K d is reported as a function ofnumber of data points ( p) per experimental set, spaced evenly from

b 5 0.20 to F b 5 0.8 (solid line). For each set, 2000 experimentswere simulated with a Gaussian error (60.02) introduced into F b.

he standard deviations for the resolved K d values were calculatedand plotted. The curve of K 3 p 1/ 2 versus p is given (dashed line) to
d
illustrate the inherent error of a given data span without the signal-to-noise reduction due to the measurement of multiple points.

means of affinity chromatography, where the haptenis linked to a solid support and used to bind and elutethe sought IgG. Unfortunately, elution of the anti-bodies from the support often requires harsh condi-tions, which can detach hapten and contaminate theIgG preparation. In a standard binding experiment,where ligand is progressively added to a solutioncontaining a fixed IgG concentration, there will be anerror in the concentration of ligand present as dic-tated by the amount of contaminating ligand. Thiserror will affect the determination of the bindingconstant. If, on the other hand, IgG is titrated into aconstant ligand concentration, the effects on the re-sulting binding plot are more subtle. As the IgGconcentrations are increased, the concentration offree ligand will be progressively underestimated andthe binding profile will be distorted.

Other Graphical AnalysesIn addition to directly fitting data to Eq. [10], several

linear transforms of this equation are commonly usedto evaluate binding data. The two most commonly usedtransforms are the double-reciprocal plot and the Scat-chard plot (4). These transforms are

Double-reciprocal plot:

1Fb

5Kd

nL 11n [15]

Scatchard plot:

Fb

L 5nKd

2Fb

Kd, [16]

where L is the free ligand concentration, n is the num-ber of sites (again we are using the concentration ofsites rather than protein and thus n 5 1), K d is thedissociation constant, and F b is the fraction of sitesbound. The purpose of these transformations is to lin-earize binding data and simplify the extraction of thebinding parameters. In Fig. 9, data on the associationof anti-theophylline IgG with fluorescein-labeled the-ophylline are shown. In this example, fluorescein-labeled theophylline (19) is held constant and the anti-theophylline IgG is added. The fraction bound is thendetermined and the data are plotted in standard form(A), in double-reciprocal form (B), and in Scatchardform (C). Analyses of the dissociation constant, K d, andthe stoichiometry, n, are given in each of the figures.To illustrate the potential for errors in using theselinear transformations, we chose to plot data in Fig. 9that have a sensible amount of error and that cover a
broad range of the binding profile. In some cases, re-searchers will eliminate what they consider statisti-

ets

r


cally meaningless points and the accuracy of their re-sults may be improved, but the subjective eliminationof points has obvious dangers. In the data presentedabove, the low F b points contain most of the apparentrror and might be removed. The accuracy of the fits tohe adjusted data set is improved, but the analysis stillhows significant error in the resolved K d and n. Elim-

ination of data points has the unfortunate function ofalso eliminating information. If one must use the linearequations, then the data should be weighted to correctfor the errors induced through transformation (20).

The use of the linear transformations is not recom-mended. Today, with easy access to computers and theavailability of many curve-fitting software applications,there is no need to linearize Eq. [9]. It is important tokeep in mind that transformed data contain no new in-formation; stoichiometries and binding constants can beresolved through fitting with Eq. [8], [9], or [10].

EXPERIMENTAL METHODS

Absorption SpectroscopyAbsorption spectroscopy can provide important in-

formation about the type and character of interactions

FIG. 9. Theophylline and anti-theophylline IgG binding data graphEq. [15], and (C) Scatchard plot fitted to Eq. [16]. The data set wasequations. The actual stoichiometry, n, is 1 and the dissociation con
transformed equations, the estimates of K d were particularly inaccuratemains poor. Proper weighting, of course, can compensate for the data
between a ligand and the corresponding antibody bind-ing site. Absorption spectra of a hapten and/or anti-body often demonstrate pronounced changes on bind-ing. For example, anti-fluorescein antibodies may shiftthe absorption maximum of fluorescein as much as 35nm to longer wavelengths in the antibody–hapten com-plexes. Such shifts reflect changes in the fluoresceinenvironment and its interactions with contact residuesin the antibody binding site (21, 22). For several anti-body systems, such as anti-opiate monoclonal antibod-ies (mAbs) (23) and anti-guanidinium sweetener mAbs(24), the appearance of a charge transfer band at 350nm is characteristic of the bound antibody. With ab-sorption data it is often possible to pinpoint a specificamino acid side chain in the antibody binding sitedirectly involved in the hapten interaction (25).

Unfortunately, application of absorption spectros-copy to the evaluation of antibody–hapten equilibriumbinding constants is limited. This restriction comesfrom the relatively low sensitivity of the method. Evenwith the best quality instruments, it is an experimen-tal challenge to record a spectrum with peak absor-bance below 0.01 OD unit with adequate precision.Usually, molar extinction coefficients for small haptensare in the range of 103 M21 cm21. For some highly

s (A) raw data fitted to Eq. [10], (B) double-reciprocal plot fitted withsen to exaggerate the defects in fitting with the linear transformednt should be 2 nM. The fit to Eq. [10] (A) is the superior fit. For the

ed achosta

e. If the low F b points are eliminated, the accuracy is improved buttransforms in (A) and (B) and deliver accurate K d estimates.

o


aromatic haptens such as fluorescein and rhodaminederivatives, it can range as high as 1.1 3 105 M21 cm21

(26). However, even the highest possible extinction co-efficients combined with the most sensitive instrumen-tation do not allow dilution of such haptens to concen-trations below 0.1 mM. Given these restrictions, theperational range for K d determination by methods of

absorption spectroscopy has a limit of 1027 M. In prac-tice, such sensitivity can be achieved only for antibody–hapten systems with strong absorption of the hapten atvisible wavelength regions and well-separated spectraof the free and bound forms. An example is illustratedin Fig. 10, where hydroxyphenylfluoron, a fluoresceinderivative, is titrated with an anti-fluorescein anti-body.

When absorption spectra of the bound and free hap-ten overlap, antibody binding experiments becomemore difficult. Certain modifications can enhance thesensitivity of absorption techniques and help to over-come the aforementioned restrictions. Application ofdifferential spectroscopy to the situation with overlap-ping spectra may provide marginal improvement inresolution for conducting binding experiments. In-creasing the optical path lengths to 10 cm or to evenlonger capillary cuvettes can increase the sensitivity ofabsorption methods by an order of magnitude or so. Ona practical note, careful correction for light scattering(27) is mandatory for all absorption measurements.Such correction may eliminate long-wavelength shoul-ders in absorption spectra that could be misinterpretedas indications of the binding-induced charge transfereffect. Programs using multiwavelength spectroscopicdata analysis and a global fit approach can also be veryhelpful in processing binding data and eliminatingspectral artifacts (SPECFIT, Spectrum Software Asso-ciates, Chapel Hill, NC; SpectraBind (28)).

FIG. 10. Binding of 6-hydroxy-9-phenylfluoron (HPF) with mAb 9tometer (Varian Optical Spectroscopy Instruments, Mulgrave, VictoM. All spectra were individually corrected for light scattering. Absor
were fitted with Eq. [10]. An identical binding constant was also obtaiPurified IgG 9-40 was kindly provided by Dr. James N. Herron (Univer
Circular Dichroism

Circular dichroism (CD) is a spectroscopic techniquebased on the difference in absorption of left and rightcircularly polarized light. Therefore, in binding exper-iments CD possesses all of the advantages and limita-tions of absorption spectroscopy. CD can provide im-portant structural information, but like otherabsorption techniques it has relatively low sensitivity.As a rule, hapten binding does not affect antibodysecondary structure, and CD spectra of antibodies inthe far-UV region (170–240 nm), where the peptidebond is the dominating chromophore, do not showchanges on binding. It is possible to expect the appear-ance of new CD bands in the area of hapten absorptionand in the near-UV region, 250 to 320 nm, whereprotein absorption is caused by tryptophan, tyrosine,and phenylalanine side chains. These residues arefound in close proximity to the hapten in the majorityof antibodies. CD bands that appear on binding to thehapten are known as induced, or extrinsic, CD effects.

A strong extrinsic CD signal (Fig. 11) in the region of400–600 nm is observed for several anti-fluoresceinantibodies (29, 30). Fluorescein is not an optically ac-tive compound, but it demonstrates induced opticalactivity when bound to the antibody binding site. Thistype of induced CD spectrum has the same shape asthe absorption band of coupled chromophores and, ac-cording to Strickland (31), such spectra may arise fromnongenerative exciton coupling. The intensity of anextrinsic CD band is proportional to the product of thedipole strengths of coupled electronic transitions. Thehighest amplitude of the induced CD signal can beobtained when two aromatic rings are parallel, but thevectors of coupling transitions are displaced by a 45°angle (32). The distance for such interactions is as-

. Absorption spectra (A) were recorded on a Cary 4 Bio spectropho-Australia) in a 1-cm cuvette. Concentration of HPF was 1.4 3 1026

on at 525 nm was used to calculate fraction hapten bound. Data (B)

-40ria,pti

ned from multiwavelength data analysis using SPECFIT software.sity of Utah).

sp


sumed to be in the range of 10 Å or less (31). Theappearance of CD bands in the near-UV region for theligand-complexed mAb also indicates a specific geomet-ric arrangement of the hapten and the binding sitearomatic residues. Calculation of the CD differencespectra (bound minus free) of stoichiometrically boundantibody–ligand complexes allows visualization of thenet spectral changes. In our study of antibodies thatbind trisubstituted guanidinium sweetener (33), wesuggested that the p-cyanophenyl moiety of the ligandacts as a molecular pointer in the CD spectra andidentifies contact aromatic residues L:96W or L:96Y inthe antibody binding pocket (Fig. 12).

Extrinsic CD bands are inherent only for anantibody–hapten complex. Such spectral data could bea perfect monitor of binding for the evaluation of bind-ing constants. However, as we already mentioned, CDhas restricted sensitivity. Its application depends onthe antibody–hapten system, and, in general, themethod can be recommended for determination of dis-sociation constants that are no lower than 1027 M.

Fluorescence SpectroscopyFluorescence spectroscopy has proven to be a power-

ful tool in the study of molecular interactions and mac-romolecular dynamics. Fluorescence of a fluorophorecan be influenced by many environmental factors suchas viscosity, solvent polarity, temperature, localquenching groups, and local pH. In ligand bindingstudies, the nature of the changes in the signal is oftenless important than the correlation of the changes withthe binding events. However, understanding the originof these fluorescence changes can provide us with valu-able information on the binding mechanisms and helpto clarify the ligand-associated structural perturba-tions of the antibody, or biomolecule, binding site.

The primary advantages offered by fluorescencespectroscopy to ligand binding studies are its high sen-

FIG. 11. Extrinsic CD effect (A) induced by mAb 4-4-20. Fluorescei
ites) concentrations of IgG. For comparison, absorption spectra (B) ofermission from Biochemistry, 1992, 31, pp. 12029–12034. Copyright 1
sitivity and the fact that samples can be examined inphysiological buffers at equilibrium. Two fluorescenceapproaches that have been particularly useful inantibody–hapten binding studies are fluorescencequenching and fluorescence polarization. Below, wediscuss the application of these techniques to specificantibody–ligand systems. We have also included ashort discussion on the use of fluorescence correlationspectroscopy (FCS), which in the past few years hasseen renewed interest.

Fluorescence Quenching

Interaction of an antibody with the hapten maychange the intensity of the antibody’s intrinsic fluores-cence. Conversely, binding to the antibody may changethe fluorescence intensity of a fluorescent hapten orhapten with an incorporated fluorophore. Thus, bind-ing assays for antibody–hapten systems have beenbased on either hapten quenching or antibody quench-ing phenomena.

Fluorescence quenching (Q) is calculated by the for-mula

Q~%! 5 S1 2Isample

I freeD 3 100, [17]

where I free and I sample are fluorescence intensities of thecomponent (antibody or hapten) before mixing and thesample with both components present, respectively.Some fluorophores show an increase in fluorescencewhen bound at the antibody binding site. A sign changein Eq. [17] will adapt it for fluorescence enhancement.Under the assumption that the observed change influorescent intensity is proportional to the fraction ofbound component, Eq. [10] can be used to fit the data.The scaling factor m in Eq. [10] will be equal to the

3 mM) is stoichiometrically bound by equimolar (in terms of binding
n (1 the free (1) and bound (2) hapten are also shown. Reprinted with992 American Chemical Society.

sieoocpiflIprttdmi

dr(wcE

a(Ns

7

tMbtcFtetf1S


quenching (or enhancement) value at saturation (Qmax)and the constant factor c should to be close to zero.

As a rule, the observed change in fluorescence inten-ity of antibody–hapten complexes is accompanied byncrease in fluorescence polarization. We discuss thisffect in the next section. Here, it is important to rec-gnize that the emission monochromator in the flu-rometer has a wavelength-dependent, nonlinear effi-iency for transmitting vertically and horizontallyolarized light. Consequently, increased sample polar-zation on hapten binding will unevenly weight theuorescence intensity measured in a binding titration.n the simple binding model discussed here, such ex-erimental error will affect the slope of the linear cor-elation between the fluorescence change and the frac-ion of the bound component. Setting the polarizers tohe appropriate “magic angle” conditions (see Appen-ix) corrects for this polarization effect. Another way toonitor changes in fluorescence intensity in the bind-

ng experiment is to calculate the G-factor-correctedtotal intensity value (see section on polarization and

FIG. 12. Difference spectra (ligand complexed minus uncomplexed)nd near-UV CD spectra of Fab fragments (solid lines) and IgGdashed lines) from mAb: NC6.8 (spectra 1, 2); NC10.8 (3, 4);C10.14 (5, 6). Antibodies NC 6.8, NC10.8, and NC10.14 bind the

weetener ligand N-(p-cyanophenyl)-N9-(diphenylmethyl)guanidineacetic acid with dissociation constants of 5.3 3 1028, 5 3 1029, and.3 3 1028 M, respectively. Antibody binding site concentrations

were maintained in the range of 5–10 3 1026 M and the concentra-ion of the ligand in the range of 1–2 3 1025 M in all experiments.ore than 99% of the binding sites were occupied (stoichiometrically

ound) under these experimental conditions (see Eq. [6]). Becausehe free ligand does not possess any intrinsic optical activity, allhanges in CD spectra on binding were induced by formation of theab–ligand complex. Expression of these CD spectral results inerms of the concentration of the bound Fab (which is essentiallyqual to the total Fab concentration in our experiments) allowed uso compare CD spectra of uncomplexed and ligand-complexed Fabragments. Reprinted with permission from Biochemistry, December

Rp

996, 35, pp. 12029–12034. Copyright 1996 American Chemicalociety.

the Appendix) obtained from single wavelength polar-ization measurements.

A binding-induced spectral shift and a shape changein the fluorescence spectrum are more severe problemsin data analysis. Often these distortions are minimalbut, if present, can destroy the linear relationship be-tween the observed fluorescence intensity and the frac-tion of bound component. To reduce this problem, it ispossible to collect the fluorescence through an opticalfilter, rather than through a monochromator, and someasure the complete emission of both free and boundspecies. One may also scan the emission spectra undermagic angle conditions and use the integrated emissionas the total fluorescence intensity. In a more compli-cated situation, when the excitation spectrum is alsoaffected, the data should be processed with programsdesigned for spectroscopic data and a global fittingapproach used to properly extract the binding param-eters (SPECFIT, Spectrum Software Associates; Spec-traBind (28)).

Tryptophan is the primary intrinsic fluorophore inproteins and is often useful in binding studies. Trypto-phan emission is highly sensitive to the microenviron-ment, which makes it an ideal intrinsic probe for mon-itoring changes in the local protein structure. The onlyother significant protein fluorophore is tyrosine, occa-sionally used for binding studies but generally lesssuitable for fluorescence measurements because of itslow extinction coefficient, poor quantum yield, and low

FIG. 13. Binding plots of oligodeoxythymidines and IgG 04-01.Quenching of protein fluorescence is shown as a function of freeoligonucleotide concentration. Total concentrations of antigen bind-ing sites (ABS) for d(pT)3-59-OH, d(pT)3-59-phosphate, d(pT)6, and

(pT)8 were 5.3 3 1027, 5.7 3 1027, 3.9 3 1027, and 2.9 3 1027 M,espectively. Emission spectra were obtained using an ISS Greg PCISS, Champaign, IL) photon-counting spectrofluorometer equippedith prism polarizers. Emission spectra of protein intrinsic fluores-

ence were taken in region of 315–460 nm on excitation at 295 nm.xcitation and emission bandpasses were 8 and 16 nm, respectively.
eprinted with permission from Biochemistry, December 1993, 32,p. 9011–9017. Copyright 1993 American Chemical Society.

hfaTmwh4

ssi

ATtwrto

oiqs

lrctflettttccwsqtd

rttdf

cL

1p9


sensitivity to environmental factors. Early applicationof tryptophan and tyrosine fluorescence in biochemicalstudies can be attributed to Weber (34, 35), whoseresearch promoted the use of intrinsic fluorophores inprotein biophysics (see recent review by Callis (36)).

Location of tryptophan residues in or near a proteinbinding site creates conditions causing ligand-inducedchanges in intrinsic protein fluorescence. Aromaticamino acid residues are preferentially located on theintervariable domain surfaces of antibodies, includingthe area of the antigen binding site (1). In antibodiesdirected against planar haptens, such as fluoresceinand trisubstituted sweetener ligands, tryptophan andtyrosine residues build up the actual “walls” of thebinding pocket (22, 37, 38). In these antibodies, inter-action of the hapten with the binding site substantiallychanges tryptophan fluorescence. This effect can beused to determine the extent of free and bound haptenand thus the stoichiometry of binding and the equilib-rium binding constant.

Velick et al. (39) were the first to report the use ofapten-dependent quenching of antibody fluorescenceor determination of the binding constant of rabbitnti-DNP antibodies toward 2,4-dinitrophenyl (DNP).heir work led to the discovery of the important im-unological phenomenon “affinity maturation” (40),hich was explained later by antigen-driven somaticypermutations in variable regions of antibodies (41,2).We applied a similar experimental approach to the

tudy of autoantibody BV 04-01, which binds single-tranded (ss) DNA (11), and to the work with antibod-es against trisubstituted sweetener ligands (43).

FIG. 14. Binding plots of different oligohomonucleotides and IgG04-01. Quenching of protein fluorescence is shown as a function offree oligonucleotide concentration. Total concentrations of antigenbinding sites (ABS) for d(pT)6, d(pG)6, d(pA)6, and d(pC)6 were 3.9 3027, 4.3 3 1027, 5.6 3 1027, and 4.9 3 1027 M, respectively. Re-
rinted with permission from Biochemistry, December 1993, 32, pp.011–9017. Copyright 1993 American Chemical Society.
dapted from the former study, Figs. 13 and 14 andable 1 illustrate binding of various unlabeled syn-hetic oligohomonucleotides by mAb BV 04-01. Dataere obtained from measurements of tryptophan fluo-

escence of the antibody on titration with oligonucleo-ides, and the best-fit curves were drawn as the resultf fitting with the simple binding model (Eq. [10]).As shown in Fig. 14 reliable binding data can be

btained when only a fraction of the fluorescences quenched. For example, hexadeoxyguanidylateuenched only 23% of antibody fluorescence at theaturation point.Antibody BV 04-01 binds trideoxythymidylates with

ow affinity; therefore, a high ligand concentration isequired to approach the saturation level. At theseoncentrations trideoxythymidylates begin to absorbhe excitation light, resulting in an apparent loss ofuorescence, unconnected to binding. Such a phenom-non, known as the inner filter effect, can be minimizedhrough the use of short path-length cells, or data needo be mathematically corrected (see Appendix). Never-heless, it was technically difficult to reach a satura-ion limit with trideoxythymidylates, and therefore, weould not be confident of the quenching value for theompletely bound antibody. To overcome this problem,e fitted the data through an iterative procedure de-

cribed earlier. From the analysis, the saturationuenching value, the free ligand concentrations alonghe titration curve, and the dissociation constant wereetermined.Additionally, we were able to refine the binding pa-

ameters of mAb BV 04-01 and different oligonucleo-ides (see Table 1). We confirmed a previous report thathe hexamer is the minimum length oligodeoxythymi-ylate required for effective binding (44). We alsoound that BV 04-01 binds hexadeoxyguanidylate

TABLE 1

Quenching of Intrinsic Protein Fluorescence and Disso-iation Constants of BV 0401 and Oligodeoxynucleotideigandsa

Antibody andligand Qmax (%) K d (mM)

DG (kcal/mol)(association)

IgG 0401dT3-59-OH 56.9 6 3.7 44.2 6 7.6 25.8 6 0.1dT3-59-phosphate 43.8 6 1.0 1.25 6 0.13 27.9 6 0.1dT6-59-OH 36.7 6 0.2 0.13 6 0.02 29.3 6 0.1dT8-59-OH 39.2 6 1.4 0.13 6 0.02 29.3 6 0.1dG6-59-OH 22.7 6 2.2 0.71 6 0.31 28.2 6 0.3dA6-59-OH — .100 —dC6-59-OH — .100 —

SCA 0401/212dT6-59-OH 76.3 6 6.5 3.21 6 0.89 27.4 6 0.2dT8-59-OH 70.9 6 1.9 1.60 6 0.17 27.8 6 0.1

a Reprinted with permission from Biochemistry, December 1993,32, pp. 9011–9017. Copyright 1993 American Chemical Society.

ori

ttrafe


[(dG)6] with an affinity comparable to that of oligode-oxythymidylates, a result not observed in binding ex-periments using radioimmunoassays. Comparison ofthe binding information with the three-dimensionalstructure of BV 04-01 (45) and the results from site-directed mutagenesis studies (46) allowed us to refinethe structure–function relationships between mAb BV04-01 and its ligands. In fact, the quenching data con-firmed the critical role of the antibody heavy-chainTrp-100a residue in interactions with oligonucleotides.Differences in fluorescence quenching value at satura-tion (Qmax in Table 1) indicated distinct arrangementsf the various oligonucleotides with contact amino acidesidues and demonstrated conformational adaptabil-ty of BV 04-01 binding site and ssDNA.

In the hapten-induced fluorescence quenching of an-ibodies against trisubstituted sweetener, we were ableo determine dissociation constants in the nanomolarange, significantly lower than those in the above ex-mples (43). Figure 15A shows typical quenching ef-ects of mAb NC10.14 on interaction with the sweet-ner N-(p-cyanophenyl)-N9-(diphenylmethyl)guanidine

acetic acid. The corresponding binding plot for thissystem is given in Fig. 15B.

The sensitivity of an experimental determination ofa binding constant based on quenching of intrinsicantibody fluorescence depends on the number of tryp-tophan residues in or near the antibody binding siteand the extent of their quenching on ligand binding.Because of an abundance of tryptophan residues inantibody variable domains, this approach can workreasonably well for various antibody systems. Usually,ligand-induced tryptophan quenching is substantiallygreater in binding-site-containing fragments (e.g., Fabor Fv). In these proteins, the contribution of nonbind-ing site tryptophan fluorescence is reduced to give a

FIG. 15. (A) Intrinsic fluorescence of mAb 10.14 in free form (soli(diphenylmethyl)guanidine acetic acid. Excitation was at 295 nm anligand were 0.23 and 16 mM, respectively. Spectra were obtainedpolarizers set to the “magic angle.” (B) Titration of mAb 10.14 with
Excitation was at 295 nm, emission was collected at 340 nm, and bandpa1995, 39, 395–406. Copyright 1995 John Wiley & Sons, Inc.
greater fraction of the quenched signal (see single-chain antibody SCA 04-01/212 in Table 1) and an im-proved signal-to-background difference. Combinedwith an optimized experimental setup (for example,replacement of the emission monochromator with anappropriate bandpass filter will increase instrumentthroughput), utilization of such fragments may permitdetermination of subnanomolar dissociation constants.

In addition to binding parameters, structural infor-mation can be obtained through an understanding ofthe mechanism of a ligand-induced quenching effect.DNP-induced quenching of tryptophan fluorescence inanti-DNP antibodies revealed the presence of trypto-phan residues at the antibody binding site and hasbeen explained by the energy transfer between excitedtryptophan(s) and DNP ligand (39). For anti-DNA an-tibodies and antibodies to trisubstituted sweetener li-gands, conditions for resonance energy transfer do notexist. Quenching in this case could occur by directinteraction of the tryptophan residue(s) with the ligandor, indirectly, on ligand-induced conformational adap-tation of the binding site by pulling tryptophans closerto local quenching groups. Intradomain disulfide bondsare likely groups because they are the strongest intrin-sic quenchers of protein fluorescence (47). Other eventslike hydrogen bonding, excited-state proton, or electrontransfer between tryptophans and the hapten or be-tween tryptophans and other amino acid residues inthe protein interior could also account for the observedquenching effects (48–50). Analysis of additional fluo-rescence data, e.g., comparison of emission and excita-tion spectra of free and hapten-bound antibody, mayhelp to define the specific changes in tryptophan envi-ronment induced by hapten. Thorough analysis of theinterrelations between the fluorescence data and theantibody’s three-dimensional structure helps to pin-

ne) and saturated (dashed line) with ligand N-(p-cyanophenyl)-N9-and paths were set to 1 nm. The concentrations of the IgG and theing an SLM 8100 photon-counting spectrofluorometer with prizmligand. The concentration of the antibody binding sites was 16 nM.

d lid bus

the
sses were set to 8 nm. Reprinted with permission from Biopolymers,


point the tryptophan residue(s) responsible for the ob-served spectral changes and suggests the conforma-tional shifts that could effect such a change.

Additional information can be also obtained fromfluorescence lifetime measurements. In fluorescencequenching studies, intensity changes reflect both dy-namic and static mechanisms of quenching, which inturn identify specific characteristics of the hapten–antibody complex. These two mechanisms can be dis-tinguished through a comparison of steady-state andfluorescence lifetime experiments. Whereas steady-state intensity quenching reflects both mechanisms,changes in fluorescence lifetime exclusively delineate adynamic, diffusion-based quenching (see review by Eft-ink (51)). In the anti-ssDNA antibody BV-0401 system,the difference in fluorescence quenching efficienciesobserved in fluorescence lifetime and steady-state mea-surements revealed that static quenching was the pri-mary quenching component. Applying this informationto the reported three-dimensional structure of mAb BV04-01 (45), we were able to conclude that the interca-lation of the ligand’s thymine base between Tyr-32Land Trp-100aH planar rings may result in the forma-tion of a dark complex and account for this staticquenching component.

Quenching of fluorescent haptens is also used exten-sively in antibody binding studies. As a rule, fluores-cent haptens developed for antibody structure–

FIG. 16. Determination of the dissociation constant of anti-fluorescein mAb 4-4-20 and fluorescein (Molecular Probes, Inc., Eu-gene, OR) by measuring the hapten quenching. Concentration offluorescein was 1.1 3 10210 M. The experiment was conducted in 0.1M phosphate buffer, pH 8.0. The quenching values were calculatedfrom the total intensity data obtained in the single point polarizationmeasurements on an SLM 8100 photon-counting spectrofluorometer.Excitation was at 470 nm with band path set to 4 nm. Emission lightwas collected through a 530-nm (25-nm bandwidth) optical filter(Schott Glass Technologies Inc., Duryea, PA). IgG 4-4-20 was puri-fied on a protein A–Sepharose column (Pharmacia Biotech Inc., Pis-
cataway, NJ). The hybridoma cell line 4-4-20 was kindly provided byDr. D. M. Kranz (University of Illinois at Urbana-Champaign).
function studies or immunoassays are designed toexhibit high extinction coefficients and high quantumefficiencies. For this reason, they are extremely brightand can be used for the determination of the bindingconstants in the picomolar range. To exemplify appli-cation of fluorescent haptens in affinity measurements,we include experiments with two different antibodysystems. The first example is the extensively studiedanti-fluorescein mAb 4-4-20 (22, 37, 52). As shown inFig. 16 this antibody quenches 96% of fluorescein flu-orescence. In the second example shown in Fig. 17, theoriginal hapten, digoxin, is labeled with fluorescein asa fluorescent reporter group (19). Binding of this con-jugate by the anti-digoxin antibody involves interac-tions between the binding site and the fluorescein moi-ety and results in 53% fluorescence quenching. Bothantibodies bind haptens with subnanomolar dissocia-tion constants. The same considerations that we havemade in studies using antibody fluorescence can beapplied to experiments with fluorescent haptens. Inaddition to an understanding of the quenching mech-anisms, studies with modified ligands contain impor-tant structural information. Fluorescence quenchingdata combined with measured binding constants mayprovide a researcher with complete characterization ofthe binding pair.

Fluorescence PolarizationFluorescence polarization is sensitive to changes in

fluorophore rotational motions and hence useful inmonitoring antibody–hapten association. Binding of asmall hapten to a relatively large antibody decreases

FIG. 17. Titration of the fluorescein-labeled digoxin (19) with anti-digoxin rabbit antibody. Concentration of the hapten was 8.1 3 10211

M. The experimental conditions and instrument setup were identicalto those given in the legend to Fig. 16. Antibody was purified from
hyperimmune rabbit serum on a protein A–Sepharose column (Phar-macia Biotech Inc., Piscataway, NJ).

w

w


the rotational diffusion of the hapten molecule, therebyincreasing the measured polarization of its fluores-cence. Reciprocally, bound hapten may affect local mo-tions of protein chromophores and change the polariza-tion of intrinsic antibody fluorescence. The firstsituation is far more common than the latter and willbe the focus of this section. Nevertheless, the followingconsiderations are also appropriate for the situationwhen a hapten-induced increase in the polarization ofantibody intrinsic fluorescence is used to monitor bind-ing.

Haptens labeled with fluorescent reporter groups areused extensively in various areas of immunology, es-pecially in antibody structure–function studies and im-munoassays. Often, the binding of such ligands doesnot affect the emission intensity, and an increase influorescence polarization may be the only detectablespectroscopic feature available for monitoring binding.

In 1952 Gregorio Weber published general principlesfor application of the fluorescence polarization ap-proach to studying macromolecules (53a,b). On thebasis of the Perrin equation for fluorescence depolar-ization of a spherical particle (54), Weber formulatedthe addition law, which relates polarization of a mix-ture of fluorophores to the individual componentspresent in solution,

S 1P#

213D

21

5 Oi

f i

~1/P i 2 1/3!, [18]

here P# is the polarization of the mixture, P i is thepolarization of each fluorophore, and f i are the frac-tional fluorescence intensities of fluorophores. In thesetwo papers, Weber also described the experimentaldetermination of polarization of macromolecules in so-lution and introduced labeling of proteins by conjuga-tion with fluorescent dyes. This work opened a success-ful era for implementation of fluorescence polarizationin biochemistry.

Later, the same addition law was expressed in termsof anisotropy (55),

r 5 Oi

f iri, [19]

here r is the anisotropy of the mixture, r i is theanisotropy of the ith fluorophore, and f i are the frac-tional fluorescence intensities (their sum is equal to 1).Definitions of the terms polarization and anisotropycan be found in the Appendix. These similar conceptsare interconvertible, and both terms are popular in theliterature. At present, many researchers prefer to ex-press binding data in terms of anisotropy because of its
simplicity in mathematical manipulations (for a gen-eral review see Lakowicz (56)).
Anisotropy (r) at any point in the titration is the sumof the products between the individual anisotropies ofthe free (r free) and the bound (r bound) species and theirrespective fractional intensities ( f free and f bound; notethat f free 1 f bound 5 1) as given by

r 5 f freer free 1 fboundrbound. [20]

If fluorescence intensity of the hapten is not changedon binding to the antibody, the respective fractionalcontributions of the free and bound hapten will beequivalent to their fractional concentrations. Conse-quently, to calculate the molar fraction of the boundhapten from anisotropy measurements, Eq. [20] can berearranged to solve for F bound (F b):

Fb 5r 2 r free

rbound 2 r free. [21]

Figure 18 presents such an example. Fluorescein-labeled digitoxin was titrated with the anti-digitoxinantibody and binding data were fitted with Eq. [10].

If antibody binding affects hapten fluorescence, frac-tional intensities of the free and bound hapten willshow unequal weighting and will no longer be equiva-lent to the respective molar fractions. Equation [21]must then be modified by including a factor, q, toadjust for this weighting,

Fb 5r 2 r free

~rbound 2 r!*q 1 r 2 r free, [22]

FIG. 18. Determination of the dissociation constant of anti-digitoxin rabbit antibody and digitoxin by anisotropy measurements.The concentration of the fluorescein-labeled digitoxin ligand was0.22 nM. The experimental conditions and instrument setup wereidentical to those given in the legend to Fig. 16. Antibody was
purified from hyperimmune rabbit serum on a protein A–Sepharosecolumn (Pharmacia Biotech Inc., Piscataway, NJ).


where q is the ratio of fluorescence intensities of thebound and free hapten measured under the same ex-perimental conditions. Because free and bound haptenpossess different fluorescence intensities, anisotropydata cannot be directly fitted with Eq. [10]. It is nec-essary to first calculate the fraction of the bound ligandwith Eq. [22] and then use Eq. [9] for fitting. Other-wise, it is possible to combine Eq. [22] with Eq. [9] to fitthe anisotropy data directly.

The importance of the above correction is illustratedin Figs. 19 and 20, which show the binding plots ob-tained by anisotropy measurements in the earlier pre-sented fluorescence quenching experiments (Figs. 17and 16) with anti-digoxin and anti-fluorescein antibod-ies. Anti-digoxin antibody moderately (56%) quenchesthe hapten fluorescence, whereas anti-fluorescein mAb4-4-20 quenches fluorescein hapten up to 96%. In themoderate example, anti-digoxin antibody, correctionfor quenching changes the determined K d more than2-fold. With anti-fluorescein antibody, similar correc-tion results in a 13-fold difference. Notably, the mostsubstantial correction occurs in the upper part of thebinding curve, at high antibody concentrations, whenthe fraction of the bound hapten approaches satura-tion.

As mentioned at the beginning of this section, fluo-rescence polarization (or anisotropy) depends on therotational diffusion of a fluorophore and is thus sensi-tive to the dynamics of macromolecules. The steady-state fluorescence anisotropy discussed here gives aweighted average of the rotational modes in the systemstudied. The more sophisticated measurement of time-resolved anisotropy can extract the individual rota-tional rates present in antibody–hapten complex. Be-

FIG. 19. Determination of the dissociation constant of anti-digoxinrabbit antibody and fluorescein-labeled digoxin by anisotropy mea-surements. Anisotropy data were obtained in the same experimentshown in Fig. 17, where the fluorescence quenching at saturation
was 56%. The solid line represents the data properly corrected for thequenching of the ligand fluorescence.
cause this technique is less likely to be used forevaluating binding constants, we will just note thattime-resolved anisotropy measurements provide infor-mation about local motion of the bound hapten andrigidity of the antibody binding site. It is also possibleto determine rotational rates of protein subunits anddomains in such experiments. In fact, independentmovements of the Fab fragments in the IgG molecule,the segmental flexibility of antibody in solution, werediscovered by means of fluorescence polarization (57,58).

Fluorescence Correlation SpectroscopyFluorescence correlation spectroscopy (FCS) is an-

other method for studying dynamic processes of fluo-rescent molecules in solution. The method was intro-duced by Magde et al. more than 20 years ago (59–61),but had limited application in biological studies be-cause of technical difficulties. Recent progress in thetheory and practice of single molecule detection hasrevived the technique and made FCS equipment reli-able. Rigler, Eigen, and co-workers (62–64) developedbiological applications of FCS and commercially avail-able instrumentation (Carl Zeiss Jena GmbH, Jena,Germany; EVOTECH BioSystems GmbH, Hamburg,Germany).

Basically, FCS measures fluorescence fluctuations ina small open volume of a solution, where fluorophore-containing molecules freely diffuse in and out. To reg-ister such fluctuations in solution with nanomolar con-centrations of fluorescent molecules, the observationvolume must be on the order of one femtoliter (10215 L).Small observational volumes can be achieved usingadvanced confocal microscopes (64–67) or, alterna-tively, with two-photon excitation method (68). Spikes

FIG. 20. Determination of the dissociation constant of mAb 4-4-20and fluorescein hapten by anisotropy measurements. Anisotropydata were obtained in the same experiment presented in Fig. 16.
Solid line shows the corrected results. This antibody quenches 96% ofthe hapten fluorescence.


of intensity over background, originating from singlemolecules, can be analyzed with the autocorrelationfunction. This number fluctuation analysis was origi-nally introduced many years ago for measuring diffu-sion coefficients of colloidal particles in a fixed volume(68–70). The autocorrelation analysis gives informa-tion on both the rate at which particles diffuse in andout of the observation (or excitation in two-photonFCS) volume and the number of particles in this vol-ume. The ability to measure the diffusion time, andtherefore the translational diffusion coefficient, makesFCS perfectly appropriate for studying protein–ligandassociation. For antibodies and haptens, the equilib-rium binding constants can be evaluated from diffusionparameters obtained in solution at equilibrium. To testthe FCS technique, we studied the binding of severalfluorescein-labeled haptens (theophylline, digoxin,digitoxin) with corresponding antibodies (71, 72). Theexperiments were carry out with the ConfoCor (CarlZeiss Jena GmbH) instrument, which is based on aconfocal fluorescence microscope, and a small air-cooled argon-ion laser (488-nm line) used for excita-tion. The intensity autocorrelation data were analyzedfor multiple diffusional components with ACCESS soft-ware (EVOTECH BioSystems GmbH; Carl Zeiss JenaGmbH). Fractions of the free and bound hapten weredetermined for each point of the binding titration, andthe dissociation constant was calculated. Comparisonof the binding constants obtained in FCS experimentswith those from the fluorescence polarization methodshowed excellent agreement. For example, the samesamples of the titration of fluorescein-labeled digitoxinwith anti-digitoxin antibody (Fig. 18) were examinedby FCS. The FCS experiments gave a dissociation con-stant of 1.1 nM.

There are other approaches to evaluating FCS data.Palmer and Thompson (73) have used high-order fluc-tuation moments, and Gratton and co-workers (74)have developed the method of photon counting histo-gram (PCH). PCH was used to evaluate the bindingconstant of anti-digoxin antibody (75). The dissociationconstant of 0.25 nM obtained by PCH analysis was in agood agreement with the result from fluorescence po-larization experiment.

A new means for expanding the capabilities of FCSin studying macromolecular association and ligandbinding is dual-color fluorescence cross-correlationspectroscopy, recently introduced by Rigler and co-workers (76) and Eigen and co-workers (77, 78). In thistechnique, two molecular species (i.e., protein and li-gand) are labeled with different fluorescent dyes, andonly the complex will produce the detected cross-correlated signal. Such an approach minimizes back-
ground interference and allows the detection of lowconcentrations of associated molecules. As a result, the
cross-correlation approach improves the sensitivity ofFCS by orders of magnitude.

With continued progress, FCS has a strong potentialto become the method of choice in the determination ofantibody–antigen binding affinities.

SUMMARY

We have attempted in this article to describe a vari-ety of UV–VIS absorption and fluorescence techniquesthat can be used to study antibody–hapten associa-tions. Clearly, these techniques are not limited to an-tibodies and can be used for other systems as well. Ingeneral, standard absorption methods, including circu-lar dichroism, are not inherently sensitive enough foraccurate determination of high-affinity binding con-stants. For systems with dissociation constants below1026 M, these methods are not suitable. Nevertheless,absorption techniques can be used in stoichiometryexperiments in which antibody and hapten concentra-tions must be high. In contrast to absorption, fluores-cence is an inherently sensitive methodology and hasbeen a common choice for the determination of tightantibody–hapten binding constants. Among the vari-ous fluorescence protocols, techniques based on fluores-cence intensity and fluorescence polarization measure-ments are the most common in ligand binding studies.In the future, we will likely be seeing more bindingstudies involving fluorescence correlation spectros-copy, considering the present interest in this tech-nique.

APPENDIX

There are numerous sources of information on fluo-rescence spectroscopy containing detailed descriptionsof the basic principles of fluorescence spectroscopy, ex-perimental techniques, and equipment (for a generaland broad discussion see Lakowicz (56)). Here, we pro-vide the reader with definitions of terms we have usedin the general text.

Polarization and anisotropy measurements. It isimportant to define our frame of reference in discuss-ing polarization. By common agreement, the plane ofthe laboratory (or tabletop) is defined as the horizontalplane, and the vector normal to this plane is the ver-tical axis. When a standard sample polarization is be-ing taken, the excitation light is polarized along thevertical axis. The emission is collected, as is routine influorescence spectroscopy, at right angles to the exci-
tation path. The vertically and horizontally polarizedemission intensities are measured separately and the

i

lcsv

m


polarization (P) and anisotropy (r) are calculated us-ng the equations

P 5Iv 2 Ih

Iv 1 Ih[23]

and

r 5Iv 2 Ih

Iv 1 2Ih, [24]

where I v is the emission intensity polarized along thevertical axis and Ih is the component of the emittedight polarized along the horizontal axis. It is alsoommon in the literature to find two other subscriptets: \ (parallel to the excitation light), or 0°, for theertical axis and ' (perpendicular to the excitation

light), or 90°, indicating the horizontal axis. Becausethe excitation light is generally set to vertical, thisdesignation is often not indicated. However, one maysee double symbols used to identify the polarization ofthe excitation and emission paths distinctly. Equations[23] and [24] can be rewritten as

P 5Ivv 2 Ivh

Ivv 1 Ivh[25]

and

r 5Ivv 2 Ivh

Ivv 1 2 3 Ivh, [26]

where the subscript symbols, from left to right, desig-nate the excitation and emission paths, respectively.As a rule, optical parts of fluorometers possess unequaltransmission (monochromators, lenses, filters) or vary-ing sensitivities (photodetector) for vertically or hori-zontally polarized light. Corrections for such instru-mental artifacts are made through the use of acorrection factor known as the G factor. The G factor is

easured according to the equation

G 5Ihh

Ihv, [27]

with the excitation polarizer set at the horizontal po-sition, a condition under which the horizontally andvertically polarized emission intensities should beequal.

Equation [26] must be modified to accommodate theG factor and gives

r 5Ivv 2 G 3 Ivh

Ivv 1 2G 3 Ivh. [28]

Most commercially available instruments have an op-tion for correcting the single-point polarization mea-surements with the G factor, and it is very importantto perform such corrections carefully.

Polarization artifacts in emission measurements.When a ligand binding experiment is performed bycollecting fluorescence intensity, the polarizationthroughout the titration is assumed to be constant. If,on the other hand, the polarization of the emissionchanges with binding, then a correction must be madeto the emission intensities, or spectra, that are col-lected. Because of the instrument polarization bias,polarization changes in the sample will lead to errone-ous intensities, which will be weighted by the polariza-tion, as well as by the fraction bound.

In a standard fluorometer, the sample emission ismeasured at right angles to the excitation path, asmentioned above. It can be easily shown that in thisgeometry, and with the excitation light polarized ver-tically, the total emission intensity is proportional toI total 5 I vv 1 2I vh (56, 79). Emission corrections can bemade by independently collecting the intensity compo-nents (or spectra) and calculating the corrected totalintensity. A simpler and more routine approach is toset the fluorometer polarizers to the magic angle con-ditions with the excitation polarizer set to 0° (vertical)and the emission polarizer set to 54.7° (56). This con-dition will essentially provide a twofold increase in I'

over I i to yield corrected I total at any wavelength. Analternative experimental setup for magic angle condi-tions entails setting the excitation polarizer to 35°while monitoring the emission without a polarizer. Thelatter setup is recommended when sample emissionintensities are weak and the instrument sensitivityneeds to be maximized.

Inner filter effect. The inner filter effect is the re-duction of the fluorescence of a given sample due to theabsorption of the excitation light and the absorption ofthe light emitted by the sample itself. To minimize thisartifact, the total sample absorption (antibody andhapten) should be kept low, less than 0.05 OD at theexcitation and emission wavelengths. If the sampleabsorption at either wavelength becomes large, thenone can use short-path-length cuvettes to reduce theabsorption or attempt to correct the fluorescence inten-sity by using the formula (56)

Icorr > Iem antilogSODex 1 ODem

2 D . [29]

Equation [29] is approximate only. For precise correc-tions it is essential to obtain a calibration plot (fluores-

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1

1

1

1

1

2

2

2

2

2

2

2

2

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3

33

3

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333

3

3

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4

4

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4

44

4

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cence intensity at emission wavelength vs optical den-sity at excitation wavelength) for a given fluorometerbecause the collection optics also play a role in theimpact of the inner filter effect.

ACKNOWLEDGMENTS

We thank Enrico Gratton (University of Illinois, Urbana) for help-ful discussions, William Mantulin (University of Illinois, Urbana)and David Jameson (University of Hawaii, Honolulu) for advice onmanuscript preparation, Edmund Matayoshi (Abbott Labs) for com-ments on FCS, and Philip Carrigan (Abbott Labs) for critical readingof the manuscript. S.Y.T. expresses special thanks to Darlene Cotterand Jose Pagan (Abbott Labs) for their interest and support. T.L.H.is supported by the National Institutes of Health (RR03155).

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