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Progress in Nuclear Magnetic Resonance Spectroscopy 51 (2007) 219–242

NMR methods for the determination of protein–liganddissociation constants

Lee Fielding *

Organon BioSciences, Newhouse, Scotland ML1 5SH, United Kingdom

Received 27 February 2007Available online 24 April 2007

Keywords: NMR spectroscopy; Protein-ligand interactions; Binding affinity; Quantitative methods; Drug discovery

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

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1.1. Ligand–protein interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2201.2. NMR of dynamic equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2201.3. Accuracy and precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

2. Evolution of methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2233. Protein observed chemical shift titrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

3.1. 1D 1H NMR studies of hevein domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2253.2. 1D 1H NMR studies of kringle fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2253.3. Other examples of 1H detected measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2253.4. Heteronuclear HSQC detected titrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

4. Ligand observed methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
4.1. Ligand observed chemical shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2284.2. Ligand observed relaxation rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
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4.2.1. Ligand observed transverse relaxation rates 1/T2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2294.2.2. Ligand observed longitudinal relaxation rates (1/T1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

4.3. Ligand observed translational diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2304.4. Ligand observed magnetization transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

4.4.1. Saturation transfer difference NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2324.4.2. WaterLOGSY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2334.4.3. Comment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

4.5. Ligand observed binding to serum albumins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
5. Competition binding experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
5.1. Graphical data treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2355.2. Magnetization transfer for sub micromolar binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

6. 19F NMR studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.1. Fluorine labelled proteins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2376.2. Fluorine labelled ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2376.3. Fluorine observed competition binding experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
7. KD from ligand dissociation kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

ee front matter � 2007 Elsevier B.V. All rights reserved.

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mailto:[email protected]

220 L. Fielding / Progress in Nuclear Magnetic Resonance Spectroscopy 51 (2007) 219–242

8. Alternative measures of protein–ligand binding affinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
8.1. Affinity index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2388.2. Affinity ranking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2398.3. NMR as a functional biological screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9. Applications of CP-MAS NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23910. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

1. Introduction

1.1. Ligand–protein interactions

Molecular recognition lies at the heart of biological pro-cesses. At the molecular level the biological activity of drugscorresponds to the binding of small molecules to macromo-lecular receptors, usually proteins. This binding process isregarded as an equilibrium condition which results from abalance between association and dissociation events. Thequantitative foundations of pharmacology are mathematicalmodels that describe these processes [1], and accordingly,biological activity is expressed as the affinity of the partnersfor each other as a thermodynamic equilibrium quantity.Binding affinities are usually determined in a binding assay,but increasingly in recent years, a large variety of physico-chemical methods have been established for the quantitativedetermination of ligand–protein dissociation constants.

This article looks at cases where NMR spectroscopy hasbeen used to determine the equilibrium binding constantfor small molecule–biomolecule complexes, with a focuson ligand–protein work. There are many diverse strategiesfor making these measurements by NMR, so the main aimof the review is to discuss the available NMR experimentsand to illustrate, by means of examples the data analysismethods that are applied. The variety of approaches toanalysis of NMR data can obfuscate the underlying sim-plicity of the methods. It should be noted that identicalexperimental approaches and data analysis methods areused in other areas of chemistry, most notably in host–guest chemistry. And, since such studies have been of inter-est since the earliest days of NMR in chemistry, much ofwhat follows is not necessarily new.

An enormous amount has been published on NMR inves-tigations of protein–ligand interactions. As much again hasbeen published on NMR studies of more general intermolec-ular interactions involving species other than proteins.Much of this literature deals with qualitative structuralissues. Useful earlier protein–ligand reviews that did addressquantitative issues are the works of Dwek [2] and Gemmec-ker [3]. In order to have a clear focus and keep this review toa manageable size, the following discussion deals only withthe quantitative analysis of protein–ligand interactions.The discussion does not aim to completely cover everythingthat has been published on quantitative descriptions of pro-tein–ligand interactions, but it does aim to be wide rangingand it does comprehensively cover all possible approaches.

An earlier review [4] covered all of the early literaturepertaining to the determination of stability constants byNMR methods. This earlier report describes the graphicalmethods, which are now becoming only of historical inter-ests. Examples were drawn from the field of host–guestchemistry, but much is relevant to the study of the stabilityof protein–ligand complexes. The monograph by Connors isthe definitive work on binding constants [5]. A bindingmodel is a prerequisite to any kind of data analysis. Usuallya 1:1 complex is assumed and this is very often taken forgranted. The classical NMR approach to the determinationof stoichiometry is the method of continuous variations(Job’s method) [6], but this is rarely applied to protein com-plexes. In most reports the stoichiometry of the complex iseither well known from other studies, or it is safely assumed.

An advantage of using NMR to measure protein–ligandinteraction is that the NMR method extends the range ofmeasurable interactions into the mM range, a region notwell covered by traditional biochemical binding assays.

1.2. NMR of dynamic equilibrium states

A protein and a ligand in thermodynamic equilibrium ischaracterised by the dissociation constant KD, which forthe simplest case of a protein with a single binding site isdefined as

KD ¼ ½P�½L�=½PL�; ð1Þ

where [P], [L] and [PL] are the equilibrium concentrationsof protein, ligand and complexed state, respectively. [P]and [L] are also referred to as the free or non-bound states,e.g., ‘free ligand’, ‘non-bound protein’; and [PL] is vary-ingly referred to as ‘bound ligand’ or ‘saturated receptor’depending on the context of the experiment. KD has theunits of concentration. Therefore a value of KD in themM range implies an approximately 1:1000 ratio of freeto bound states in an equimolar mixture of P and L anda KD in the lM range implies an approximately1:10,00,000 ratio of these states, i.e., a much more stablecomplex with less of the ‘free’ species present.

In order to measure the dissociation constant of a pro-tein–ligand complex we have to measure the equilibriumconcentrations of free and bound species. Traditionally thisis done by equilibrium dialysis, but a great variety of otherexperimental approaches have been applied, includingNMR methods. To measure KD by means of NMR experi-ments implies quantitative analysis of solutions that are

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Fig. 1. Simulated speciation curves for protein (n) and for ligand (¤) for aseries of solutions with [P]0 = 0.1 mM, and [L]0 is incremented through0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5–10 mM. The assumed associationconstant for a single binding site is 2 mM. The solution composition ispresented as the ligand:protein ratio. Mole fraction bound represents theconcentration of species in the complexed state relative to the totalconcentration of that species, XP(bound) and XL(bound) in the text.

L. Fielding / Progress in Nuclear Magnetic Resonance Spectroscopy 51 (2007) 219–242 221

potentially lM in the observed nucleus. The object of theNMR observation might be the ligand, or the protein orboth. In practice just one species is chosen as the observa-tional target – the ligand or the protein and only very rarelyare both species viewed together. Hence, when viewing theligand, the NMR experiment has to be able to distinguishbetween the free non-bound ligand and the ligand in thebound state, so that [L] and [PL] can be quantified. Alterna-tively, when observing the protein, the experiment has to dis-tinguish between and quantify [P] and [PL]. Protein–ligandcomplexes are dynamic systems and therefore the rate atwhich the components of the protein–ligand complexexchange between free and bound forms is central to theNMR method.

For a system in slow exchange on the chemical shift timescale (in general terms this would be a protein–ligand systemwith high binding affinity and low dissociation constant,KD = lM or lower), resolved signals might be expected forthe free and bound states, and using the ligand observedexample, [L] and [PL] are in principle available by integra-tion of separate resolved signals. In practice this is extremelydifficult because of the difficulty of detecting lM signals inwhat is likely to be a complex and crowded spectrum.

For a system in fast exchange the observed NMRresponse of a ligand is the mole fraction weighted averageof the NMR parameters of the free and bound states

Mobs ¼ X LðfreeÞMLðfreeÞ þ X LðboundÞMLðboundÞ; ð2Þ

where Mobs is any NMR observable characteristic of theequilibrium system, XL(free) and XL(bound) are the mole frac-tions of free and bound ligand, and ML(free) and ML(bound)

are the NMR parameters of the ligand in its free and boundstates, respectively. Similarly for observation of the protein,

Mobs ¼ X PðfreeÞMPðfreeÞ þ X PðboundÞMPðboundÞ; ð3Þ

where XP and MP are now the mole fraction and the NMRcharacteristic of the non-bound protein and occupiedprotein. The mole fractions are defined as, XL(free) +XL(bound) = 1 and XP(free) + XP(bound) = 1.

Describing species distributions in terms of mole frac-tions is a very useful concept and ‘mole fraction bound’is a term that occurs frequently in accounts of bindinginteractions. It is generally used to describe the proportionof a species present in the bound state relative to the totalamount. Both the ligand and the protein speciation can bedescribed in this way. So, whereas the mole fraction ofbound protein, XP(bound) might range from 0 to approach-ing 1 over the course of a titration with a ligand, the molefraction of bound ligand XL(bound) might at the same timerange from near 1 to approaching 0. Although these termsnever reach their absolute limits (except for XP(bound) = 0 atthe start of a titration), in practice at experimental endpoints they approach them closely enough that settingX(bound) = 0 or 1 is a reasonable approximation. Thealmost complete approach of one of these parameters tothe end point conditions (0 or 1) under conditions of satu-

rated binding sites is what allows graphical solutions to thebinding equations.

Fig. 1 illustrates the formation of a 1:1 protein–ligandcomplex for a hypothetical low affinity system withKD = 2 mM. The protein and ligand concentrations arepresented as a ratio, as is commonly encountered. This isa typical example of NMR titration data. The XP(bound)

trace would result from observation of the protein NMRsignals, and the XL(bound) trace would result from observa-tion of the ligand. The figure shows that the protein speci-ation varies considerably over the course of the titration,and suggests that a spectroscopic detector that was sensi-tive to this speciation would be a good means to measureKD. The ligand speciation curve appears rather flat andunpromising as a measure of KD, but under appropriateconditions, ligand observations are just as effective.

The relationships between the relative responses ofXP(bound) and XL(bound) become clearer when the solutioncomposition is plotted on a log scale and this is shown inFig. 2A. Moreover, the dependence of this speciation onKD is highly informative and this is shown in Fig. 2B andC. It can be seen that as KD decreases (corresponding totighter binding) the protein and ligand speciation curvesbecome more like each other and more like standard doseresponse curves. XP(bound) always starts at zero and mayclosely approach the limit of 1 providing that KD is smallor that the titration reaches high enough ligand concentra-tions to saturate the binding site. The starting value ofXL(bound) is very dependent on the simulated conditionsand in most practical cases will not even come close tothe limit of 1. XL(bound) will be approximately zero forthe duration of most NMR experiments. The usefulnessof the mole fraction units is that this is what is measuredby the equilibrium state analytical probe (the NMR data).So, the process of measuring KD is one of transformingmole fraction to concentration units (molarity).

Eqs. (2) and (3) are general for all NMR experimentobservables. The NMR parameter may be the position of

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Fig. 2. Simulated speciation plots utilizing a logarithmic concentrationscale and showing the effects of varying KD. (a) The same data as forFig. 1, utilizing log [L]0/[P]0, KD = 2 mM. (b) and (c), Speciation plotssimulated for identical solution compositions with, (b) KD = 0.2 mM, and(c) KD = 0.02 mM.


a resonance expressed in ppm or Hz, a linewidth, or eitherof the relaxation rates 1/T1 or 1/T2, or any other feature ofthe system that reports on the dynamic averaging, e.g.,NMR measured translational diffusion coefficients. The sit-uation of fast exchange also corresponds to the conditionof the great majority of NMR based KD measurements,and so forms of Eqs. (2) and (3), written in terms of a spe-cific NMR parameter account for a large part of whatfollows.

For the single site protein (1:1 complex), the solutioncomposition is defined as:

½P�0 ¼ ½P� þ ½LP�; ð4Þ

and

½L�0 ¼ ½L� þ ½LP�; ð5Þ

where [L]0 and [P]0 are the total concentrations of proteinand ligand, respectively. These total concentrations are usu-ally known. They represent the composition of the solutionas constructed by the investigator. The key to the determi-nation of KD then, is to relate the known solution composi-tion [L]0 and [P]0 to the equilibrium concentrations of ligandand protein, [L] and [P], by means of the NMR observables.

Note though that the relationship between Mobs and KD

is non linear, and the parameter ML(bound) or MP(bound) isfrequently not observable, so that it cannot be directlydetermined. There are two ways forward. Traditionally,experiment protocols have been designed that linearizethe relationship between Mobs and KD. The data are thenanalysed graphically and Mbound and KD come from theslopes and intercepts. Alternatively (and more often), therelationship between Mobs and KD is solved computation-ally and data analysis consists of determining a computedbest fit binding curve to the experimental data [7–9]. Thisinvolves a two parameter fit to a binding curve. The bot-tom line is that it is not possible to measure KD from a sin-gle NMR data point and NMR protocols invariablyinvolve monitoring some NMR signal as a function ofvarying solution composition. It is useful to talk not aboutabsolute peak positions or linewidths, but the changes tothese parameters that occur during a titration. Hence:

Dobs ¼Mobs �M free; ð6Þ

is the change in the NMR parameter induced by the equi-librium condition relative to the free or non-bound state,e.g., the induced chemical shift of a protein proton causedby adding an interacting ligand, and:

Dmax ¼Mbound �M free; ð7Þ

is the limiting case of the above expression. Following theabove example, for a protein reporter proton this would bethe chemical shift difference between the bound and non-bound forms. These two general terms, Dobs – the observedeffect at any arbitrary equilibrium state, and Dmax – the lim-iting effect representing a fully bound state occur repeat-edly throughout the following text.

1.3. Accuracy and precision

The highest quality information on KD is in the curvedregions of graphs such as Fig. 1 and in the steepest gradientregion of Fig. 2. The regions of slowly changing mole frac-tion (near to 0 and 1) are regions where the analyticalresponse is insensitive to solution composition. Severaldetailed analyses of the errors associated with fitting spectro-scopic data to binding models have appeared [10–14]. Theissues of concern revolve around obtaining spectroscopictitration data that is actually responsive to the equilibriumstate and is not simply a response to binding; and how muchof a binding isotherm needs to be observed in order to sup-port the hypothesis of the binding model. The differencebetween observing an equilibrium state and observing abinding event is illustrated by many of the figures in the liter-


ature. Straight line regions of binding curves correspond toeither the progressive saturation of a species that is presentin sub stoichiometric amounts, or to a titration end pointwhere one species is fully saturated. Such regions containno information on KD. Information on the equilibrium con-dition is only present in the curved middle region of thegraph. The principal findings are as follows:

A ‘probability of binding’ (p) is defined as the ratio of con-centration of complex to the maximum possible concentra-tion of complex. This formulation recognises that themaximum possible concentration of complex is always theinitial concentration of the minor component (usually pro-tein). A ‘saturation fraction’ has also been defined as theratio between the actual complex concentration and the ini-tial concentration of the reagent, the chemical shift of whichis being measured. This term is less useful for describing pro-tein binding situations because it does not reflect the factthat, at the start of the binding curve the concentration ofcomplex is limited by the concentration of added ligand.

The minimum error in the measurement of KD occurs atp = 0.5, and the ‘best’ data are obtained from the range0.2 < p < 0.8. In other words, the most accurate valuesfor KD are obtained when the equilibrium concentrationof the complex is approximately the same as the free con-centration of the most dilute component.

The maximum information on the system comes fromstudying the widest possible range of p. At least 75% ofthe saturation curve is required in order to show correspon-dence between the equation of the model and the equationfitting the data (i.e., to verify that the binding model isbased on the correct stoichiometry). In other words anybinding data will be fit by any model over a suitably shortrange of p. If the experimental data are limited, higherorder complexes should be verified to be absent. Determi-nation of the stoichiometry of a complex requires measure-ments at p = 1 (i.e., at undetectable protein or ligandconcentrations). Since these conditions are the oppositeof those required for an accurate measure of KD, the twoexperiments should be separated.

The above comments cover the most important consider-ations regarding experimental procedures. Some further rec-ommendations for the optimization of experimentalconditions for the determination of Ka, written in the contextof host–guest chemistry, but appropriate to this discussionhave been discussed [4]. These mostly relate to the graphicalmethods. Wilcox has discussed these issues from the perspec-tive of a more up-to-date NMR curve fitting context [15].

This then is the reason that sensitivity considerationslimit the ability of NMR protocols to directly measureKD. Regardless of which NMR parameter is observed,the experiment must be sensitive to analyte concentrationsthat are approximately of the same magnitude as KD. Inother words, NMR techniques cannot directly measure avalue of KD smaller than the limit of detection of the exper-iment. Typically this is around 10–100 lM for routinecases. The limit may be overcome by using competitionexperiments, as described in Section 5.

2. Evolution of methods

Approaches to the study of protein–ligand interactions,and the measurement of binding affinities, have naturallybeen limited by whatever at the time was state-of-the-arttechnology.

The organization of this review broadly reflects the pro-gression of the implementation of methods. At the startthere was little choice. Only one or two methods were avail-able. In the 1970s, the only way that the stability constantof a protein–ligand complex could be measured by NMRwas by means of 1/T2 or 1/T1 relaxation rate observations.With the available 100 MHz spectrometers, there was littlehope of resolving any protein signal. So the earliest NMRmeasurements of protein–ligand stability constants werebased on relaxation rates of ligands in fast exchange withthe protein. Increases in spectrometer operating frequen-cies coupled with the availability of pure protein and moreimportantly, isotope enriched (15N and 13C) preparations,allowed direct protein observed titrations starting fromthe mid 1980s to the present. Now, twenty years later thereare many different tools available. Most recently, due to thedevelopment of a new range of ligand observed methodsbased on magnetization transfer effects, there has been areturn to ligand observed experimentation, with a lot ofinterest in saturation transfer difference NMR.

Methods to deconvolute the concentrations of free andbound species from exchange averaged NMR observationswill be presented in Section 3 and early in Section 4. Thisrepresents the bulk of the published literature. The meth-ods are conceptually easy to understand and easy to carryout. Magnetization transfer difference experiments, whicheffectively deconvolute the bound ligand fraction fromthe total ligand concentration within the exchange experi-ment, are the most up-to-date approaches and are consid-ered at the end of Section 4. Most of the material inSections 5 and 6 can then be viewed as special cases andas extensions of the general methods because no newNMR detection is introduced. Some new ideas that workbest with 19F NMR are introduced at the end of Section6. The review ends with a consideration of several otherdiverse approaches that do not fit comfortably in the dis-cussion so far.

NMR observations of protein–ligand systems are alwaysset up to observe either the protein or the ligand, neverboth together. So it is convenient to organize the followingdiscussion according to whether the protein or the ligand isthe observed NMR active species. One of the challenges inunderstanding the published literature in this area, is thatof understanding the various data treatments that havebeen applied. As discussed by Conners [5], there are threedifferent ways in which to linearize the hyperbolic bindingcurve. To add further confusion, sometimes the protein,sometimes the ligand is at fixed concentration. Sometimesneither component is held constant and the data analysisapplied may even be inappropriate. Add to this a fewunique and individual approaches to data analysis and this


leads to many representations of graphs that illustrate thederivation of KD from NMR titration data.

3. Protein observed chemical shift titrations

In this class of experiments, an NMR property of anucleus in the protein is the marker of the binding equilib-rium. Normally the response of this signal, perhaps thechemical shift or linewidth of a protein proton, would bemonitored as ligand was titrated into the solution. It isobvious that this method is only applicable to pure, solu-ble, modest molecular weight proteins and is subject toall of the constraints that go with protein structure investi-gations by NMR. Isotope labelling is helpful, but notessential. Titrating ligand into protein so that the ligandeventually finishes in excess, thus saturating the proteinbinding site is the only way to perform this study. Littleuseful information would come out of a protocol wherethe ligand concentration never exceeded that of the protein.Neither will much useful information come from a systemwhere the ligand concentration vastly exceeds the proteinconcentration unless the binding event is very weak (andthis case seems not to be interesting). Accordingly, theexperiments discussed in this section all follow protocolswhere the ligand:protein ratio is varied within a modestrange, 0.1–3 or 5. The linear graphical methods that occurwidely in host–guest chemistry (see Box 1), are seldom ifever applied to the study of protein–ligand interactions.

Box 1

There are three non-logarithmic linear solutionsto the NMR binding isotherm [5]. Written in termsof the NMR observables (for a titration of ligandinto protein, and where the protein is the focusof the NMR observation), they are

½L�0=Dobs ¼ ½L�0=Dmax þ K D=Dmax; ð8ÞDobs=½L�0 ¼ �Dobs=K D þ Dmax=K D; ð9Þ1=Dobs ¼ K D=Dmax½L�0 þ 1=Dmax: ð10Þ

The graphs of these solutions are often referredto by the names of early researchers, so that thegraph of Eq. (8) is a Scott plot, the graph of Eq. (9)is a Scatchard plot, and that of Eq. (10) is the Bene-si–Hildebrand plot. Connors terms them as a y-reciprocal plot, an x-reciprocal plot and a doublereciprocal plot, respectively, according to whetherthe dependent parameter (y the NMR observa-tion), the independent parameter (x the ligandconcentration), or both appear in reciprocal terms.This terminology has the advantage that it identi-fies the plot more precisely, and avoids the confu-sion caused by application of yet more names, asoccurs when parallel developments are made indifferent fields, but communication between

different specialists does not take place. Howeverthe aforementioned names have gained wide-spread acceptance.

In the y-reciprocal plot (Scott plot) the ligandconcentration is plotted linearly along theabscissa, thus retaining the scaling of the directbinding curve, but straightening the line. TheNMR description of the bound state is obtainedfrom the reciprocal of the slope of the curve. They intercept (crossing the ordinate at [L]0 = 0) givesKD/Dmax.

In the x-reciprocal plot (Scatchard plot) theratio of the NMR effect to ligand concentration isplotted against the size of the NMR effect. Theslope of the line is the negative reciprocal of KD

and the NMR property of the bound state isobtained from the intercept with the abscissa.This data analysis has two distinct advantagesover the others, KD is obtained from the slopeof the curve, independent of any extrapolations,and the graph is ‘closed’ so that extrapolationat each end leads to an intersection with an axis.

The double reciprocal plot (Benesi–Hildebrandplot) graphs the reciprocal of the NMR effect ver-sus the reciprocal of the ligand concentration.The slope gives KD/Dmax, and the intercept on they axis (1/[L]0 = 0), is the bound NMR parameter(1/Dmax). This data treatment has the advantagethat it does not mix the dependent variable withthe independent variable (Dobs remains distinctfrom [L]0).

Note that the protein concentration does notappear in any of these solutions. So there is noneed for [P]0 to be accurately measured. The onlyrequirement is that [L]0 > [P]0. All three data treat-ments are likely to be found in the literature, butwith the Scatchard and Benesi–Hildebrandnames occurring more frequently than Scott.The Scatchard plot is generally preferredbecause KD comes without extrapolation to apotentially remote axis intersection.

The examples that follow are all based on the 1:1 bind-ing model, and an assumption that the system is in fastexchange. The case of insufficiently rapid exchangebetween the two species being observed in the titration(protein and bound protein) has been examined by Sudme-ier et al. [16].

An advantage of protein observed NMR titrations, andsomething that sets this method apart from ligand observedNMR titrations, is that it is often possible to directly observethe fully bound state. That is, a protein spectrum may beobtained under conditions of a fully saturated binding site.When this is the case, Dmax (corresponding to dbound) canbe measured directly, and at the risk of introducing some


greater variance in the result, one unknown drops out of thebinding isotherm. Most workers prefer to treat dbound as anunknown and find the best fit of both parameters to a bindingcurve, but KD is occasionally reported derived from the(shorter) single parameter observation, see below.

3.1. 1D 1H NMR studies of hevein domains

The group of Jimenez-Barbero has made extensive use ofprotein observed chemical shift changes to quantify the bind-ing affinity of carbohydrates to hevein domains [17]. For themost part these studies exemplify the use of non-linear leastsquares fitting of the observed 1H chemical shifts versus [L]0binding curve to find values for KD and dbound.

Hevein is a small, cystein rich, single chain protein of 43amino acids. The signals from Gln20 NH and Hc in the1D 500 MHz 1H NMR spectrum can easily be followed dur-ing titrations with chitobiose and chitotriose [18], or a varietyof N-acetyl glucosamine containing oligosaccharides [19], inorder to determine the association constants of the carbohy-drate–protein complexes. In a typical experiment [P]0 wasaround 0.7–1 mM and [L]0 reached 15 or 30 mM at the endof the titration. The experiment protocol was designed sothat [P]0 remains constant as [L]0 varies. This simplifies thedata analysis. A further series of communications from thisgroup describe the thermodynamics of binding as deter-mined by variable temperature 1H NMR studies and isother-mal titration calorimetry [20–22]. The close agreementbetween the NMR derived values and the directly measureddata is a verification of the applicability of the equilibriumNMR method to systems with mM binding affinity.

3.2. 1D 1H NMR studies of kringle fragments

A sequence of papers from the group of Llinas exem-plify the 1D 1H NMR chemical shift titration methodand illustrate a special data analysis for the case whereDmax can be observed directly, thus in principle reducingthe dimensionality of the problem to one. But there wassome uncertainty in measuring the protein concentrationso [P]0 was treated as an unknown, thus increasing thedimensions of the problem back to two.

Human plasminogen is a single chain protein of 791amino acids. The molecule has a mosaic structure whichincludes five kringle modules, each containing between 78and 80 amino acids, and with a value of Mr of �9 kDa.The binding of small molecule ligands to several of thedomains was studied by following the 1H NMR (300 or500 MHz) chemical shifts of hydrogens on aromatic resi-dues such as His, Trp and Tyr during a titration of theligand up to ratios of around 15:1. The values of KD wereextracted from the data by either a graphical method [23–27], or by least squares fitting of the hyperbolic bindingcurve [28]. In their (unique) graphical method the fractionof ligand bound protein is obtained from the 1H NMR fre-quency of the reporter proton in free protein (dfree), the

fully saturated state (dbound), and at the equilibrium condi-tion (dobs) according to:

X PðboundÞ ¼ ½PL�=½P�0 ¼ ðdobs � dfreeÞ=ðdbound � dfreeÞ: ð11Þ

Assuming single site binding and fast exchange, it can beshown that:

1=X PðboundÞ ¼ 1þ KDf1=ð½L�0 � X PðboundÞ½P�0Þg: ð12Þ

Thus a plot of 1/XP(bound) versus ([L]0 – XP(bound)[P]0) is linearwith slope KD and intercept 1. Since [P]0 was not accuratelyknown, it was considered an adjustable parameter and wasfound by iteration to minimize the linear correlation coeffi-cient of the plot. This is not a conventional data treatmentand does not correspond with any of the treatments in Box1. The aromatic signals were selected for study because theycould often be detected as resolved signals in these modestmolecular weight proteins, and they were also sensitive tothe binding event. This later observation is indicative thatthese residues are in the vicinity of the ligand binding pocket.The 1H chemical shift changes induced by ligand binding aresmall. Typically, they are within the range 0.01–0.1 ppm andmostly only around 0.02–0.05 ppm. The values of KD werefound to be in the range 5 lM to 1 mM.

3.3. Other examples of 1H detected measurements

Trp–Trp (WW) domains are compact modules of 38–40amino acids, folded into a three stranded b sheet. They arefound in single or tandem repeats in over 25 unrelated cellsignalling proteins. The binding of two phosphothreoninepeptides to a synthetic construct of the N-terminal WWdomain of Pin 1 has been studied by 600 MHz 1H NMRtitrations [29]. Addition of increasing amounts of peptideligands caused chemical shift changes for several protonsin the WW domain. During the titration several proton res-onances broadened until they disappeared and then reap-peared at large excess of ligand, indicating slowexchange, with the difference in chemical shift betweenthe free and bound forms being of the same order of mag-nitude as the exchange rate. The Ser11 amide proton reso-nance which moved gradually and was more evidently infast exchange throughout the titration was chosen as anappropriate marker of the equilibrium conditions. Titra-tions with 1 mM protein, taken to [L]0/[P]0 ratios of 4.5and 11, established values of KD of 117 and 230 lM forthe peptides by fitting the data to the equation

Dobs¼ 0:5Dmaxf1þXþKD=½P�0�½ð1þXþKD=½P�0Þ2�4X�1=2g

ð13Þ

where X is the molar ratio of ligand to protein.During a study of bepridil binding to cardiac troponin C

it was noticed that addition of the drug caused well definedand specific changes of chemical shift and linewidth in the1H NMR spectrum (360 MHz) of the protein [30]. Thesechanges occur throughout the spectrum. The most evidentchanges occur in the aromatic region, in the region corre-


sponding to the terminal methyl groups of methionine res-idues, and in the aliphatic methyl region. The chemicalshifts of three of these peaks plotted against [L]0/[P]0 pro-duced smooth curves which reached limiting values nearthe 1:1 ratio. The binding affinity (20 lM) was then esti-mated by the abbreviated method using the directlyobserved saturated shift as a reference. The concentrationof bound protein can be calculated from the known totalprotein concentration using the relationship

Dobs ¼ ½PL�Dmax=½P�0; ð14Þ

and KD can be estimated from Eq. (15) which is based onthe assumption that the concentration of bound ligandequals that of bound protein,

KD ¼ ð½P�0 � ½PL�Þð½L�0 � ½PL�Þ=½PL�: ð15Þ

A study of the interaction of DMSO with the FKBP12 pro-tein is a good example of the utility of NMR to quantifyweak binding events [31]. Proteins commonly co-crystallizewith small molecules and solvents, and crystalline FKBP12was known to be associated with six molecules of DMSO.The NMR study was based on the specific perturbation ofa few 1H NMR chemical shifts of the protein (0.3 mM)during a titration with up to 1.5 M DMSO. The bindingisotherm (Fig. 3) clearly covers a large part of the boundmole fraction range (see Section 1.3), and is well fitted bythe 1:1 isotherm for KD = 275 mM, a very weak interac-tion. Using an existing 1H assignment and the known ter-tiary structure of the protein, it was possible to identifythe single binding site. Note that the plot in Fig. 3 is a clas-sic example of an NMR titration curve and is identical inform to that of Fig. 1. Dd is directly proportional toXP(bound) as [L]0 is proportional to [L]0/[P]0.

3.4. Heteronuclear HSQC detected titrations

In these experiments ligand binding is detected from per-turbations to the inverse detected 15N-1H HSQC spectra of

Fig. 3. Chemical shift changes (Dd) for one of the CcH3 resonances of Val-55 of FKB12 protein as a function of DMSO concentration (correspond-ing to [L]0). The curve represents the best fit solution of the quadraticequation that describes 1:1 complex formation. The curve corresponds toKD = 275 mM and Ddmax = 0.35 ppm [31]. Reproduced with permission.� 1999 Kluwer Academic Publishers.

the target protein. Dissociation constants are then obtainedby monitoring the chemical shift changes of the backboneamide as a function of ligand concentration. This methodhas been widely adopted. It is easy to implement, 15Nlabelled materials are often available, the enhanced disper-sion of 2D spectroscopy allows ready identification of suit-able reporter signals (often several of them) and the highsensitivity of gradient selected HSQC experiments allowrapid data acquisition. This last point is a critical issue. Itis not practical to follow a titration strategy if the NMRdetection experiment takes a long time.

A study of the binding of three potential ligand peptidesto the SH3 domain from the Src family tyrosine kinase Fynexemplifies the experiment. The uniformly 15N labelled pro-tein comprised 69 residues. The peptide ligands comprised14 residues. Multiple binding curves were determined bytitrating each peptide into separate samples of 15N SH3and acquiring 15N-1H HSQC spectra at as many as 14 differ-ent ligand:protein ratios from the range 1:10 to 4:1 [32].Chemical shift changes in both 1H and 15N dimensions werelogged and fitted by non-linear regression analysis to

Dobs¼Dmax

ðKDþ½L�0þ½P�0Þ�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðKDþ½L�0þ½P�0Þ

2�ð4½P�0½L�0Þq

2½P�0:

ð16Þ

The measured KD values are 3 mM, 50 and 300 lM.The group of Fesik in particular has pioneered the use of

protein observed 15N-1H HSQC as a tool for drug discov-ery (SAR by NMR [33]) and has used 15N-1H HSQC spec-troscopy for high throughput determination of values ofKD [34–37]. Data are fitted to a single site binding model,using a least squares fitting search to find the values ofKD and the chemical shift of the fully saturated proteinas described above. In this way the protein binding affini-ties of collections of several dozen ligands at a time canbe quantified. Observations of protein 15N-1H HSQC spec-tra in conjunction with ligand titrations is now an estab-lished favourite method for determining KD by NMR,but with variations on the data treatment [38,39].

Sometimes Dmax is assumed to be the Dobs at highest[L]0. Ligand induced chemical shift changes in the15N–1H HSQC spectrum of a recombinant two-domainfragment of barley lectin revealed well resolved, indepen-dent responses from the two domains, allowing the simul-taneous determination of the binding affinities of bothsites [40]. Assignment of the 500 MHz 15N–1H HSQC spec-trum gave dfree for each residue. Chemical shift changes ofseveral residues were then monitored during titration of theligand and dbound was taken from the observations at themaximum ligand concentration (Mr 9 kDa; [P]0 1 mM;[L]0–12 mM). This was justified because almost no changein chemical shifts was observed between the last and thepenultimate titration point, indicating a saturation of bind-ing sites. These limiting values were then used to translatethe chemical shift data at each titration point into the frac-tions of occupied protein binding sites (fB and fC) at each


ligand concentration. The concentration of free ligand inthe sample is given by

½L� ¼ ½L�0 � ½PLB� � ½PLC�; ð17Þ

and the concentration of protein that remains unbound ateach domain is

½PB� ¼ ½P�0 � ½PLB� and ½PD� ¼ ½P�0 � ½PLD�: ð18Þ

The equilibrium constant characterizing ligand binding toany one domain is then given by

fB ¼1

2

(� �f C � 1� ½L�0½P�0

� 1

KD½P�0

� �

�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�f C � 1� ½L�0½P�0

� 1

KD½P�0

� �2

� 4½L�0½P�0� �f C

� �s );ð19Þ

where �f C is the average of the individual values of fC foreach monitored residue at domain C.

A natural continuation from the 15N–1H HSQC proteindetection approach is to apply 13C-1H HSQC detection.Hajduk et al. have studied ligand binding to isotopically13C(methyl) labelled domain 3A of human serum albumin[41]. More than 1800 ligands were screened and bindingwas detected by acquiring 13C-1H HSQC spectra(500 MHz) on 50 lM protein solution in the presence andabsence of added compound. The compounds wereassigned a score based on the magnitude of the change inthe HSQC spectrum and the highest scoring compoundswere progressed to a more complete characterisation bymeans of additional ligand titrations. In this way 232ligands with binding affinities in the range 10 lM to2.0 mM were measured.

4. Ligand observed methods

The drive to make NMR into a tool for drug discoveryhas lead to a resurgence of interest in ligand detected inter-action studies [42–45]. There has been particular interest inthe transfer NOE experiment and many new ideas havebeen based on intermolecular magnetization transfer.Although primarily designed to detect ligand binding, theseexperiments can also provide information on KD.

In these experiments the observed species is the smallmolecule and it is almost always titrated into the proteinuntil present in a considerable excess concentration. It isconvenient to consider the experiments as being of twotypes. In one class, conventional NMR parameters suchas chemical shift, linewidths, relaxation rates which reporton the equilibrium condition of the solution are measured.These data are then processed in a similar fashion to thepreceding section after making appropriate adjustmentsto the data analysis to account for the switch of observedspecies. The other class of experiments are based on obser-vations of intermolecular transfer of magnetization, andthese have become very popular recently. A major advan-tage of monitoring the small molecule is that there is no

upper limit to the size of the protein that can be studied.There is also no need to isotopically enrich the protein.

Most of the ‘‘traditional’’ ligand observed NMR studieshave been analysed by linear methods. This is appropriatebecause the requirement to observe any high resolutionligand signal, that it must be in fast exchange with thebound form, and present in considerable excess to the pro-tein concentration, is the same as that required to apply lin-earized data analysis. Hence [L]0� [P]0, [L] = [L]0 and thelinearized form of the binding equation is completely justi-fied. The method that has been most widely used is thatbased on the relationship

½L�0 ¼ ½P�0Dmax=Dobs � KD; ð20Þ

and in this case, a plot of [L]0 versus 1/Dobs gives �KD asthe intercept on the [L]0 axis.

This is a y-reciprocal plot in Connors’ terms because thedependent variable is plotted on the reciprocal scale. Theseplots are most frequently presented with [L]0 on the ordi-nate (y axis) and 1/Dobs on the abscissa (x axis), which isunfortunate because this orientation obscures any relation-ship with other graphical methods. It would be preferable ifsuch graphs were rotated and inverted, so that [L]0 is plot-ted along the abscissa. An alternative form which is alsoencountered (usually in the 1/T1 studies) has the proteinconcentration factored into the y axis

½P�0=Dobs ¼ ð½L�0 þ KDÞ=Dmax: ð21Þ

For this solution a plot of [P]0/Dobs versus [L]0 gives �KD

when the line is extrapolated to the x axis crossing. Thisform is preferred because the graph is shown the rightway round and the slope gives directly, the bound NMRparameter. Whichever plot is chosen, and whichever axisis chosen to be plotted on the abscissa, all plots give�KD at the intersection with the [L]0 axis, independent of[P]0.

It is worth noting again that in order to apply this kindof data analysis one of the species present has to be main-tained at a constant concentration during the course of thetitration. Usually this is the species which is not observed inthe NMR spectrum (protein in this section), but this is notalways the case and there are examples of titrations of pro-tein into constant concentration solutions of ligand. In this‘inverse’ protocol, it is still a requirement that [L]0 at alltimes greatly exceeds [P]0. This requirement to control solu-tion compositions has some implications for the design ofthe experiment and may (due to solubility, stability andavailability) be difficult to achieve.

Two effects might interfere with this kind of study: fail-ure to meet the fast exchange condition, and non specificbinding. Feeney et al. have made a study of the effects ofintermediate exchange processes on NMR observed bind-ing curves [46]. For a nucleus on a ligand undergoing fastchemical exchange between two sites, the transverse relax-ation rate (and hence linewidth) is given by

Fig. 4. Ligand N-acetyl chemical shift data that were used to calculate KD

for interactions of sialyllactose isomers with haemagglutinins. Each plotshows the variation of ligand Dd with [L]0 at a constant [P]0. Data for fourdifferent systems are shown. Experiments in panels (a), (b) and (d) wererepeated at different protein concentrations, which is reflected in the factthat the second plots have different slopes [49]. Reproduced withpermission. � 1989 American Chemical Society.


1=T 2;obs ¼ X PL=T 2;bound þ X L=T 2;free þ X PLX 2LsB4p2Dd2;

ð22Þ

where sB is the lifetime of the bound state (equivalent to1/koff). The last term is the exchange contribution, whichreduces to zero in the case of very fast exchange. The com-mon assumption (implied throughout this review) is thatthe protein–ligand complex is in fast exchange on theNMR time scale, so that whatever NMR parameter is ob-served, it is proportional to the mole fraction weightedaverage of the bound and free states. For many such com-plexes the association rate constant will be diffusion lim-ited, with a value in the range 107–108 M�1 s�1. If theligand binds tightly (KD < 0.1 lM) the slow exchange con-dition usually applies and separate spectra are observed forthe free and bound ligand. For ligands with weaker affinity(KD > 1 mM) the fast exchange usually applies and thereare no problems. Feeney et al. point out that in order tofacilitate the analysis, there is often a general assumptionof fast exchange, without any check that this is in factthe case. Considerable errors (up to two orders of magni-tude) in KD can arise by indiscriminate assumption of thefast exchange condition.

In a situation where the ligand is present in considerableexcess over the receptor it is likely that after saturation ofthe specific binding site, the ligand will bind at non specificsites. Hence, when interpreting the spectra it should alwaysbe borne in mind that the spectra represent an averageacross all the states that the nuclei experience. It may notbe known a priori how many states there are, or what theirparameters may be. This is a common and recognisedproblem in studies of serum albumin (discussed in depthlater), and studies of whole biological entities, e.g., mem-brane bound receptors. The presence of additional bindingsites has to be acknowledged and built into the model, andthis makes the binding models increasing mathematicallycomplex. Klotz has provided a very useful account of thequantitative analysis of this kind of sequential binding [47].

4.1. Ligand observed chemical shifts

One of the early reported applications of this method isthe study by Perkins et al. of the binding of monosaccha-ride inhibitors to hen egg-white lysozyme [48]. They used270 MHz 1H NMR to observe the binding induced chemi-cal shift of the sugar signals. This paper has a useful fourpage appendix which derives formulae that are useful forthe analysis of the NMR data from ligand-macromoleculeequilibria, and gives formalisms for a ligand binding in sit-uations other than the simple two site model.

The binding of sialic acid derivatives to haemagglutininwas studied by following perturbations to the 500 MHz 1Hchemical shift of the sialic acid resonances in the presenceof protein [49]. The major perturbation observed was tothe chemical shift of the ligand N-acetyl methyl resonance,presumably due to the proximity of this methyl group tothe shielded region of an aromatic residue in the binding

site. Several similar ligands were studied at concentrationsaround 0.5–12 mM, and in the presence of typically 20–40 lM protein. The 1H chemical shift effects observed weretypically of the order of 0.02 ppm at the highest [P]0/[L]0ratios and values of KD in the range 2–10 mM were accu-rately measured for several dozen ligand–protein systems.Data were analysed by the above mentioned linearizationroutine. Under the conditions where the fraction of ligandbound to protein is small, KD is given by Eq. (20) and aplot of [L]0 versus 1/Dobs gives KD at the y intercept. Theresult is shown in Fig. 4.

The N-acetyl methyl group exhibits an upfield shift in allof the ligands that bind. The 1H NMR shift of the boundligand is available from the extrapolation of the graphshown and the upfield shift for this proton on all of theligands is around 2 ppm. This is consistent with a modelwhere the methyl protons sit directly over the six mem-bered ring of tryptophan 153.

A study of sialyloligosaccharides binding to wheat germagglutinin dimers used the constant [P]0 (0.1 mM), [L]0titration (0–15 mM) method again, but extended the dataanalysis to include consideration of the ligand linewidthsand also incorporated the Swift-Connick equations [50]as an additional means to estimate the NMR parameters(shift and linewidth) of the bound ligand [51].

The binding of L-tryptophan to the trp repressor pro-vides an example of a system where the ligand is not in fastexchange between the free and bound states. The trp

Fig. 5. (a) Generic data treatment for the graphical determination of KD

from ligand observed NMR data. KD is obtained from the verticalintercept. The fast exchange parameters Mobs can be Dm, Dd, 1/T2 or 1/T1.(b) Experimental data from the interaction of the antibiotic telithromycin(ligand) with bacterial ribosomes. The plots shows [P]0/Dobs versus [L]0 forfive different reporter protons of the telithromycin molecule [57]. Repro-duced with permission. � 2000 The Royal Society of Chemistry.


repressor binds two molecules of tryptophan in two inde-pendent sites with identical affinities. Since no cooperativ-ity is involved, the system was treated as a simple twosite exchange model. In variable temperature experimentsat different protein:ligand ratios the L-tryptophan protonswere observed to be in the slow exchange, intermediateexchange and fast exchange regimes. The low temperaturedata were used to find dfree and dbound for the H-4 proton ofL-tryptophan. Full line shape analysis of ligand resonancesyielded the dissociation and association rate constants, thebinding constant, and the thermodynamic parameters ofthe process [52].

4.2. Ligand observed relaxation rates

Because binding induced chemical shift changes are rel-atively small compared to the linewidth changes, mostligand observed NMR studies have focused on the relaxa-tion rate effects. A review of binding induced relaxationenhancements which includes an excellent discussion oftheir application to the measurement of equilibrium bind-ing constants is that by Ni [53].

4.2.1. Ligand observed transverse relaxation rates 1/T2

Fischer and Jardetzky performed the first quantitativeNMR estimation of a protein–ligand interaction with a60 MHz 1H NMR study of the interaction of penicillinbinding to serum albumin, KD = 10–20 mM [54]. Theseexperiments were performed with penicillin solutionsaround 10–500 mM and at a [L]0/[P]0 ratio of around200:1. At 60 MHz, there was no prospect of making anykind of useful observation of the protein. They estimatedthat the maximum likely effect on the ligand chemicalshift upon binding in the vicinity of the diamagneticregion of an unsaturated ring may be around 200 Hz(0.33 ppm). Since only about 1% of the ligand wasexpected to be bound, the observed change Ddmax for afast exchange system was predicted to be about 2 Hzand this would not be detectable. However the ligandlinewidths were extremely sensitive to the addition ofalbumin. This pioneering study demonstrated that thepenicillin–albumin system is indeed in fast exchange,and that both KD and 1/T2bound could readily be extractedfrom the titration data. The calculated relaxation rates (1/T2bound) for bound penicillin were found to be in therange 2000–7000 Hz. Shortly afterwards Gerig estimatedthe 1H linewidths of tryptophan bound to a-chymotrypsinat around 30–70 Hz, and put KD in the range 3–12 mMby observing the ligand line broadening during the courseof a titration [55].

An instructive example is the one by Miller et al. [56]which describes the binding of choline to the intact mem-brane bound acetylcholine receptor by measuring the line-width of the choline methyl 1H NMR (100 MHz) signalduring a titration of the ligand. An equilibrium dissocia-tion constant of 190 ± 65 lM was obtained from five datapoints (solutions were 5 lM in receptor and ranged from

0.23 to 1.1 mM in ligand). In another good example, thelow affinity interaction of antibiotics with bacterial ribo-somes were quantified by following ligand 1H transverserelaxation times, T2 measured by the Carr–Purcell–Mei-boom-Gill spin echo method [57]. Ligand concentrationswere around 0.5–3 mM, ribosomes around 0.2–0.8 lM,and KD values in the range 0.3–13 mM. The data analysisis illustrated in Fig. 5.

Further discussion of the graphical fitting of linewidthdata can be found in a report on the binding of sialyloligo-saccharides to wheat germ agglutin, itself a popular subjectof NMR protein–ligand studies [58]. The hits from anexploratory screening exercise to find new inhibitors ofhuman factor Xa were followed by construction of 1HNMR linewidth isotherms to establish quantitative bindingaffinities [59].

4.2.2. Ligand observed longitudinal relaxation rates (1/T1)

It has been shown that the selective 1H longitudinalrelaxation rate (1/T1(sel)) of the ligand is a more sensitiveindicator of binding than is the nonselective rate [60].

Studies of agonist binding to the acetylcholine receptorprovide straightforward and clear examples of the use ofT1 data to measure dissociation constants. The relaxationtimes were measured by the inversion recovery pulsesequence and the data were analysed by means of the y-reciprocal plot (Eq.(8)). In a ligand–receptor system wherethe ligand is present in large excess over the receptor bind-ing sites, the ligand relaxation rate is described by

1=T 1obs ¼ 1=T 1free þ fbound=ðT 1bound þ sboundÞ; ð23Þ


where fbound is the fraction bound ([PL]/[L]0) and sbound isthe lifetime of the bound state. The relationship betweentotal ligand concentration and T1 is then

½P�0T 1obs ¼ ð½L�0 þ KDÞðT 1bound þ sboundÞ; ð24Þ

and a plot of [P]0T1obs versus [L]0 gives a straight line withKD obtained from the intercept of the x axis. Thisapproach was used to study the binding of various agoniststo the intact acetylcholine receptor of Torpedo californica

Fig. 6, [61]. In an extension of this work, the binding ofa number of cholinergic agonists and antagonists to syn-thetic and recombinant peptides representative of subunitsof the receptor were studied [62]. In a typical experiment,the ligand was titrated into a 0.2–0.3 mM solution of pro-tein until ligand concentrations around 10 mM werereached. It is not clear that the protein concentration wasproperly held constant during this protocol.

The serum albumin system also provides several exam-ples of the use of ligand 1/T1 data to determine KD.Because of the large amount published on this protein dis-cussion of serum albumins is deferred until Section 4.5.

4.3. Ligand observed translational diffusion

NMR measurements of translational diffusion (D) bymeans of pulsed-field gradient (PFG) spectroscopy havereceived much attention since the mid 1990s. Essentiallythese experiments use spin echo pulse sequences with a z-axis magnetic field gradient applied during the first dephas-ing time, and again after the refocusing pulse. The effect ofthe first gradient is to spatially encode and the second gra-dient decodes the nuclear spins. Only spins that are still intheir original locations will contribute to the spin echo andso it is possible, by incrementing the gradient strength orduration, to measure molecular displacement or translationdiffusion coefficients. Many pulse programs have beendevised to optimize the performance and D can generally

Fig. 6. Plot of nicotine concentration versus [P]0 T1(sel) for multiplemeasurements on two different acetylcholine receptor preparations (circlesand squares). The pyridinyl H-4 proton of nicotine was used for therelaxation measurements. Similar results were obtained from the otheraromatic protons. The data show the typical scatter in the selective T1

measurements, and estimated error bars [61]. Reproduced with permis-sion. � 1988 Biophysical Society.

be measured in NMR experiment times that are somewhatlonger than to those required to measure relaxation rates.

The reason of course that the diffusion coefficient is use-ful is that D is closely related to size. A small molecule willdiffuse faster than a large molecule. So if the diffusion coef-ficient of a small molecule is measured in the presence of alarge molecule to which it binds, the observed diffusioncoefficient will be the weighted average of the coefficientsof the free and bound states. In the presence of a receptorprotein, the diffusion coefficient of the ligand will be lessthan that measured for the free ligand. The usual assump-tions of fast exchange apply, only this time the ligand needsto be in fast exchange on both the chemical shift time scaleand also the timescale of the diffusion measurement (usu-ally several hundred milliseconds). From the point of viewof data analysis, D is just another NMR parameter, like dor 1/T2 and (Eq. (2)) applies again. Hence,

Dobs ¼ X LðfreeÞDLðfreeÞ þ X LðboundÞDLðboundÞ: ð25Þ

Also, as in the earlier discussion, NMR diffusion studies ofprotein ligand interactions are just a special case of moregeneral intramolecular interaction studies, and again alarge amount of relevant information exists but withoutthe ‘protein–ligand’ label. Two authoritative reviews thatcover the specific protein–ligand area are those by Price[63] and Lucas and Larive [64].

Larive et al. have coined the term ‘diffusion dynamicrange’ to describe the ability of a PFG diffusion experimentto respond sensitively to the binding constant, and there-fore measure KD accurately [65]. In the context of thePFG experiment, KD is given by

KD ¼ ½P�0ðDbound � DobsÞ=ðDobs � DfreeÞþ ½L�0ðDobs � DboundÞ=ðDbound � DfreeÞ: ð26Þ

Fig. 7. Simulation of the diffusion dynamic range DD (DDfree�DDobs) as afunction of the ligand:protein ratio for various dissociation constants, (A)KD = 1000 lM, (B) KD = 100 lM, (C) KD = 10 lM, (D) KD = 1 lM and(E) KD = 0.001 lM. The simulation was performed for a fixed [P]0. Thediffusion coefficient of the ligand (DDfree) was set at 6.9 · 10�10 m2 s�1,and that of the protein (DDbound) at 0.76 · 10�10 m2 s�1 [64]. Reproducedwith permission. � 2004 Wiley Periodicals, Inc.


Fig. 7 was produced by calculating the values of DD for ahypothetical system with ligand:protein molar ratios rang-ing from 0.1 to 500 and for five different values of KD. Theuseful dynamic range is region 2 where Dobs depends onboth KD and the ligand:protein ratio. Region 1 corre-sponds to low ligand:protein ratios, Dobs–Dbound and DDconverges to the difference between Dfree and Dbound. Attoo high ligand:protein ratios (region 3), Dobs–Dfree andDD converges to zero.

Note that this graph is simply a special case of the dis-cussion of Section 1.3. It is axiomatic that an experimentaimed at measuring KD has to be sensitive to the bindingevent. The diffusion experiment is measuring a propertyof the ligand which changes as a function of the ratio ofthe free and bound forms.

A 162 MHz 31P NMR study of the binding of 2,3-biphos-phoglycerate to haemoglobin is the first documented appli-cation of the diffusion technique to a protein–ligandcomplex [66]. The diffusion coefficient of the ligand was mea-sured from a series of solutions that were around 3–5 mMhaemoglobin and ranging from 2 to 80 mM ligand over 10data points (see Fig. 8). The data analysis consisted of fittingDfree and KD to the titration curve, with Dbound set to thevalue of Dprotein that was measured in a separate experiment.The resulting values of KD for the binding of 2,3-biphospho-glycerate with carbonmonoxy-, oxy-, and deoxy- haemoglo-bin are, respectively, 1.98 ± 0.26 mM, 1.8 ± 0.5 mM and

Fig. 8. The diffusion coefficient of 2,3-biphosphoglycerate (DPG) incarbonmonoxyhaemoglobin solutions as a function of [DPG]. Each valueof D was derived from a PFGLED NMR experiment. The threeparameters that define the solid line are the diffusion coefficient of non-bound DPG (Dfree = 1.8 · 10�10 m2 s�1), the diffusion coefficient of thecarbonmonoxyhaemoglobin (Dbound = 0.1 · 10�10 m2 s�1), and the disso-ciation constant (KD = 1.98 mM) [66]. Reproduced with permission. �1994 Biophysical Society.

0.39 ± 0.26 mM. This plot shows how the observed diffusioncoefficient of the ligand is strongly attenuated by binding andis very sensitive to the ligand:protein ratio at low [L]0(<25 mM). At higher [L]0 most of the ligand is unbound,so the curve levels and approaches Dfree.

Lennon et al. [66] noted that this PFG 31P NMRmethod has an advantage over the more obvious 31P chem-ical shift perturbation method because several factors otherthan binding to haemoglobin influence the 31P chemicalshifts. The PFG NMR method is one of only a few tech-niques available in which these interactions can be studiedin intact erythrocytes. However the experiments do take along time. Each titration data point is the result of an incre-mented NMR experiment that especially at low ligand con-centrations required substantial signal averaging. The datashown in Fig. 8 are clearly in the correct part (region 2) ofLarive’s diffusion dynamic range graph. An earlier study ofthe same 2,3-biphosphoglycerate/haemoglobin system addsa novelty footnote to this discussion [67]. The 1990 studywas an equilibrium dialysis determination of KD and 13PNMR was used to determine the concentration of 2,3-diphosphoglycerate with the dialysis cell nestled inside a10 mm NMR tube.

Some 15N filtered diffusion experiments have been usedto study of the binding of a peptide to the Src homology3 domain of phox47 (60–70 amino acids). A binding iso-therm was constructed from the diffusion coefficients ofthe species in solutions that were 0.46 mM in protein andranging from 0.23 to 10.5 mM in ligand (ligand:proteinratios from 0.5:1 to 23:1) and Dobs varied over the fairlynarrow range 0.95 · 10�10 m2 s�1 to 1.55 · 10�10 m2 s�1.This was sufficient to measure KD at 21 ± 14 lM, compara-ble with a value of 29 ± 3 lM established by fluorescencespectrophotometry [68].

It is fair to ask ‘‘what is the advantage of diffusion basedestimates of KD over more classical relaxation rate experi-ments?’’ The preferred experiment will be the one that bestdiscriminates between the bound and non-bound forms ofthe ligand. For a small molecule binding to a large proteinin dilute non viscous solution D is likely to change byaround a factor of 10. This is a good ‘dynamic range’.The relaxation rate difference between bound and freestates will be much more variable, depending on whatnucleus is observed and what relaxation rate is measured,but will often be in the same range or greater. Probablyrelaxation rate experiments are more direct and faster.

One clear advantage of the diffusion coefficientapproach is the possibility of determining KD from singledata point experiments, thus eliminating the need forassembling a titration curve at different ligand concentra-tions. In contrast to most of the preceding experimentswhere the NMR parameter of the bound state (Dmax) can-not be directly observed, (the exception is that sometimesDmax is assumed to have been observed in some proteindetected studies), the two limiting diffusion parameters,that of the ligand (Dfree) and that of the protein–ligandcomplex (Dbound) can both be directly measured in separate


PFG experiments. The diffusion coefficient of the boundligand is simply that of the protein. In practise many work-ers continue to create binding isotherms from titration dataas discussed above, but the short cut route to single pointmeasurements is attractive for high throughput determina-tions and has been demonstrated as a viable means toquantitatively rank order screening hits from the SHAPESstrategy for drug discovery [69]. The cost of a faster exper-iment is some degradation in the precision of the method.Small errors in the measured diffusion coefficients arisingfrom any sources will result in large errors in KD. A simpleanalysis based on propagation of random errors found thatin the specific case of the SHAPES screen a 5% error inDobs translated to a 125% error for KD = 1 mM, a 57%error for KD = 100 lM, and a 127% error for KD = 10 lM[69]. This is yet another manifestation of the material dis-cussed in Section 1.3.

4.4. Ligand observed magnetization transfer

Two completely new NMR methods for measuring dis-sociation constants have been available since 1999-2000.Both techniques are based on observing the intensity ofmagnetization transferred to free ligand via the boundligand from the protein protons. This is accomplishedeither by direct selective excitation of the protein protons,or by relaying magnetization via the solvent and protein.

The responses of magnetization transfer experiments arenot classical NMR parameters like chemical shifts or relax-ation rates. They are exchange averaged parameters, buttheir magnitudes are not simply determined by the respec-tive populations and NMR parameters of free and boundstates, so Eq. (2) cannot be applied. The responses donot have absolute values, they are dimensionless and areaffected by a host of experiment parameters. These experi-ments are fundamentally different to those discussed in thepreceding sections because they report on the concentra-tion of bound ligand [LP].

The well known transfer NOE effect might be regardedas the forerunner to the following two methods. It is theapplication of the 2D NOE experiment to exchanging sys-tems. Typically a small molecule (ligand) is characterizedby a short correlation time and small positive NOE values.A large molecule (protein) is characterised by a long correla-tion time and large negative NOE values. So that for a pro-tein–ligand system where the ligand is present in excess[L]0 > [P]0 and is in fast chemical exchange, the large negativeNOE acquired by the ligand while it was at the binding siteoverwhelms the small positive NOE of the unbound ligand.The observed response will be dependent on the fraction ofbound ligand (amongst many other parameters) [70].

The potential of NOE experiments to be used quantita-tively in this fashion seems not to have been exploredexcept to note that the affinity of ligands can be rankordered from the NOE pumping response [71]. A funda-mental problem with using the transfer NOE response toquantify binding is that it changes sign between the bound

and free states. Hence there is a risk that part of the bind-ing curve will originate in a zero signal to noise region.

4.4.1. Saturation transfer difference NMR

The saturation transfer difference (STD) experiment wasdevised to screen compound collections for binding activityto proteins [72]. Saturation transfer refers to the mecha-nism whereby magnetization introduced into a large pro-tein molecule is able to very rapidly spread around all ofthe constituent spins, including any attached ligand, suchthat when the ligand leaves its binding site it carries withit information in the form of spin polarization from theprotein. Thus the bulk NMR response of the ligand is anaveraged response, composed of the sum of signals fromnon interacting ligands and previously bound ligands. Thissaturation process is very efficient, so the modulation of theligand signal induced by the protein is readily detected,even in the presence of a large excess of ligand. In orderto make the interaction apparent, the experiment is imple-mented as a difference experiment. Two 1D spectra areacquired– one with selective excitation of the proteinturned on, and one where the selective excitation is movedto an empty spectral region. The difference spectrum willshow a response only of ligands that were at some timeassociated with the protein. The sensitivity to discriminatebetween binders and non binders is excellent, and thisexperiment has been successfully used to identify ligandswith binding activity from multicomponent mixtures. TheSTD experiment has been authoritatively reviewed byMeyer and Peters [44]. A recent review by Krishnan con-tains a good discussion of the quantitative analysis [73].

How is the STD response related to KD? Because theSTD experiment is a difference experiment, the STD spec-trum contains only signals from the bound state of theligand. Hence the STD response reports on the concentra-tion of the protein–ligand complex. As with all of the pro-cedures so far, a titration with ligand is carried out to mapthe response as a function of [L]0. Some normalization ofthe STD signal intensity is then required. A relative STDeffect is defined by normalizing the STD signal to the inten-sity of the same peak in the off-resonance spectrum, andthen a correction for total ligand concentration is intro-duced to arrive at an ‘STD amplification factor’ ASTD. Aplot of the parameter ASTD versus [L]0 is a normal bindingisotherm and can be fitted to derive KD [74]. So, althoughthe observed STD NMR intensity is not a direct measure ofthe affinity of a particular ligand, KD can be obtained fromthe titration curve ASTD versus [L]0. The method is illus-trated by Fig. 9 which shows the binding of methyl b-D-galactoside to the 120 kDa lectin ricinus communis agglutinI (RCS120) [74].

Ligand binding to human integrin aIIbb3 incorporatedinto liposomes has also been studied in this way. This mem-brane bound fibrinogen receptor consists of two sub units125 and 108 kDa. The binding affinity of the peptide ligandcyclo(RGDfV) was estimated at 30–60 lM, from observa-tions of a solution that was 5 lM in protein and 29–

Fig. 9. (a) The normalised saturation transfer difference response of theH-4 signal of b-GalOMe as a function of [L]0/[P]0 during a titration of b-GalOMe into 40 lM RCA120 protein. (b) Display of the same data interms of the STD amplification factor. This second plot shows that eventhough the fraction of ligand which is saturated decreases at a higherligand concentrations, the absolute STD signal intensity increases in theform of a saturation curve. The STD amplification factor is obtained bymultiplying the fractional STD effect shown in (a) with the ligand excess[74]. Reproduced with permission. � 2001 American Chemical Society.


275 lM in the peptide, corresponding to ligand:proteinratios from 6:1 to 55:1 [75]. A more recent STD NMRstudy reports on the binding of a peptidomimetic ligandto human CD4 protein [76]. STD amplification factor titra-tion curves from several of the ligand protons were pre-sented. The STD derived KD (9 lM) compares favourablywith that derived from surface plasmon resonance (10 lM).

The STD method is greatly advantaged for ligand–pro-tein interaction studies because it is a method that is com-pletely unlimited by the size of the protein. It works betterfor larger proteins. Most of the published STD NMR stud-ies that have been published in the last five years are aimedprimarily at gaining structural information by epitopemapping. These reports have not usually addressed theissue of measuring dissociation constants, other than twostudies which rank-ordered the ligands according to their(unquantified) binding affinities [77,78].

Fig. 10. WaterLOGSY responses for the C2-H resonance of L-tryptophanas a function of ligand concentration during a titration into protein. Thecircles and triangles are the experimental intensities recorded in thepresence and absence of 10 lM HSA, respectively. The WaterLOGSYresponse without protein is linear with [L]0 and can be used to apply acorrection for effect of non bound ligand. The square points are theintensity difference graph and the line is the best fit calculated quadraticcurve. The signal intensity is on an arbitrary scale [79]. Reproduced withpermission. � 2001 Kluwer Academic Publishers.

4.4.2. WaterLOGSY

In the second magnetization transfer experiment, bulkwater magnetization is transferred to the ligand via theligand–protein complex. This is termed WaterLOGSY(Water-Ligand Observed by Gradient SpectroscopY).The experiment relies upon the water molecules presentat the protein–ligand interface and uses intermolecularNOE and chemical exchange with labile hydrogens totransfer magnetisation from bulk water to the protein.The acquired magnetization is in turn transferred to anybound ligand which, when appropriate dissociation ratesapply, can leave the binding site carrying with it magnetisa-tion which has the same sign as the starting magnetization

[79]. The result is that the resonances of non-binding com-pounds appear with opposite sign and tend to be weakerthan those of interacting ligands. In order to make quanti-tative estimates of KD, some normalisation of the Water-LOGSY signal intensity has to be made. This is necessarybecause the ligand acquires some magnetisation directlyfrom bulk solvent irrespective of what is happening at thebinding interface. The correction is made simply by per-forming the WaterLOGSY experiment again, this time onthe ligand solution without the protein present. The exper-iment is performed at several different ligand concentra-tions and the corrected response can be plotted against[L]0 to produce the normal binding isotherm. This is anal-ogous to the correction that has to be made to ASTD in theprevious experiment. The experiment is illustrated inFig. 10 with data from the tryptophan/human serum albu-min system. The circles are the uncorrected responses andthe triangles are the response of ligand without protein thatare used to apply the correction. The corrected responsehas the profile of a familiar binding curve.

4.4.3. Comment

The magnetization transfer experiments are best viewedas a measure of the bound ligand concentration, for a sit-uation where the proportionality constant between thespectroscopic response and [PL] is unknown. In this respectthe data are not different to, for instance, the chemical shifttitration where the limiting chemical shift is unknown. Sothere is no difficulty in producing binding curves such asFigs. 9 and 10 and fitting them to a parabolic curve. KD

arises from the curvature, thus acquiring the concentration

Table 1Dissociation constants (KD (mM)) and stoichiometries (n) obtained fromNMR studies of ligand binding to serum albumins

Protein Ligand NMRmethod

KD

(mM)n Reference

HSA TFBAa D 2.2 9 [81]BSA Phenylbutazone 1/T2 3 �100e [82]BSA Azathioprine 1/T2 3 �100e [83]HSA Ibuprofen D 17 ± 4b 50 [84]HSA Ibuprofen 1/T1 49 ± 15b 36 ± 8b [84]HSA Ibuprofen 1/T1 1.5 ± 0.2 22 ± 1c [85]HSA Ibuprofen 1/T1 2.0 ± 0.4 15 ± 2d [85]BSA Ibuprofen 1/T2 50–100 3–7 [86]HSA Ibuprofen 1/T1 1.4 ± 0.2 33 ± 2 [87]HSA Salicylate D 17 ± 8 35 [88]HSA Salicylate 1/T1 15 ± 2 32 [88]BSA Salicylate D 30 ± 4 33 ± 3 [89]BSA Salicylate Dd 1.2 ± 0.6 8 ± 3 [86]HSA Salicylate 1/T1 4.3 ± 0.5 35 ± 2 [87]

a 4-Trifluoromethylbenzoic acid.b Entry is the simple mean and standard deviation of the range of results

quoted in the original communication.c pH 6.8.d pH 8.0.e Assumed.


units of [L]0, and the proportionality constant is given bythe asymptote, but is a meaningless parameter.

Neither the direct STD experiment, nor the directWaterLOGSY responses appear to have been widely usedfor the determination of KD. The disadvantage of thesemethods appears to be the need to correct the responseof these experiments with a second reference experimentwhich doubles the length of what is already a lengthy pro-tocol. For a simple system consisting of only one proteinand one ligand, chemical shift or relaxation rate methodswill be faster and easier to implement. The STD andWaterLOGSY experiments would be expected to workand would have an advantage when directly quantifyingbinding in a mixture of tentative ligands. Both STD andWaterLOGSY have been used to monitor binding (quanti-tatively) in competition binding studies and these studiesare discussed in Section 6.

4.5. Ligand observed binding to serum albumins

Ligand detected studies of protein–ligand systems arevulnerable to interference from non-specific binding. Math-ematical models of multisite binding have been summa-rized by Klotz [47]. The simplest approach, and the onethat is widely used, is to assume that the protein has nequivalent and non-interacting binding sites,

Pþ nL ¡PLn

and therefore

KD ¼ ½P�½L�n=½PLn�: ð27Þ

In this model the parameter n works as a scaling on theNMR parameter of the bound state (Dmax). The boundpopulation of ligand given by

X LðboundÞ ¼ a� ða2 � bÞ1=2; ð28Þ

where

a ¼ ð½L�0 þ n½P�0 þ KDÞ=2½L�0; ð29Þ

and

b ¼ n½P�0=½L�0: ð30Þ

Eq. (28) can be inserted into Eq. (2) to calculate a bindingcurve to match experimental NMR data. The widespreaduse of this formula is undoubtedly due its simplicity ratherthan its validity. It is straightforward to introduce the newterm n into computer enabled data fitting routines.

Serum albumins are able to bind drugs specifically athigh affinity binding sites (KD = lM), and non-specificallyat several, possibly dozens, of low affinity sites (KD = mM)[80]. It commonly occurs that different studies of drug-serum albumin interactions report binding affinities thatdiffer by orders of magnitude because different protocolsexplore different parts of the specific–non-specific bindingcontinuum. Ligand observed NMR methods are carriedout at high ligand:protein ratios and so by definition areweighted to report on non-specific binding. The one (or a

few) molecules that bind specifically make no significantcontribution to the experimental observable which is dom-inated by the behaviour of non-specific binding interac-tions and free ligand.

The PFG diffusion method, relaxation rate methods andchemical shift perturbation methods have all been success-fully applied in several studies of non-specific binding toserum albumins. Table 1 summarises some of these studies.This table illustrates the wide range of ligand observedNMR parameters that can successfully be used as a handleon the dissociation constant. Also noteworthy are the highvalues of n showing that as well as being a promiscuousbinder of ligands, serum albumins are also polygamous.Also noteworthy are the wide range of reported values ofKD, indicating that either these data are not precise mea-sures, or that the system is itself is somewhat fuzzy. Bothexplanations are valid. The discussion in the later salcy-late/BSA report contains a more complete account ofnon-specific drug-albumin interactions and NMR studies[86].

It should be recognised that for systems with multiplebinding sites, and where the stoichiometry (n) is introducedas an additional parameter, the binding curve is now a fourparameter fit (Mfree, Mbound, KD and n) and a cosmeticallyappealing fit is guaranteed to be obtained for the limitednumber of data points that define the usual NMR experi-ment. Further, the four parameters are highly interdepen-dent and it may not be possible to obtain a uniquesolution. As always, a good fit of the calculated curve tothe experimental data is not a validation of the bindingmodel. A good fit of a four parameter curve to a handfulof data points should justly be viewed with somescepticism.

Fig. 11. 500 MHz 1H NMR linewidth data from the titration of a(2,6)-sialyllactose (L1) using Neu4Pp5Aca2Me (L2) as a reporter ligand toprobe the interaction with haemagglutinin. [L2]0 is fixed at 1.0 mM and[P]0 is fixed at 2 mg/ml. (a) The linewidths of two protons (N-acetyl methyland 2-O-methyl) on the reporter ligand (L2) as a function of [L1]0. (b) Theresponse of the N-acetyl methyl protons of the analyte ligand (L1) as afunction of [L1]0. In both cases KD is derived from the y- intercept [90].Reproduced with permission. � 1992 Academic Press, Inc.


5. Competition binding experiments

A general drawback of all ligand observed NMR meth-ods is their failure to work directly with high affinityligands. It is generally accepted that the lower limit ofapplicability of the NMR method is KD to 10–100 lM.Ligands with dissociation constants lower than this aretightly bound which means that there is little exchange withfree ligand during the time scale of the NMR experiment(typically a few hundred milliseconds) and therefore noinformation about the bound state is detectable. This limithas become smaller as the sensitivity of NMR hardwarehas increased. This difficulty can be overcome by exploitingthe well known phenomenon of competition binding. Thebinding experiment is performed in the presence of a sec-ond ligand which occupies the same binding site as the tar-get ligand. The competition process effectively modulatesthe NMR response of the observed ligand and scales itback into the region p = 0.2–0.8. No new NMR detectiontechniques are introduced in the following discussion.The experiments are based on exactly the same parameters(e.g., linewidths, relaxation rates, and NOE responses) thathave been previously described in Sections 3 and 4, exceptthat they are now applied to a three component system.The experiment protocols and the data analysis methodsare the points of interest.

A few of the competition methods have been purposedesigned to push the limits of NMR quantification tosub-micromolar levels. Other studies have arisen fromNMR screening methods to identify new ligands for phar-macologically interesting receptors and were driven by aneed to circumvent the false negative issue with high affin-ity ligands. Although designed primarily to detect and sig-nal the binding event, it turns out that these data can alsobe used, often quickly and with little extra effort, to quan-tify KD.

5.1. Graphical data treatment

A study of the binding of some sialic acid derivatives tohaemagglutinin in intact influenza virus is the first reportedapplication of quantitative NMR competition methods tothe study of protein–ligand interactions [90]. Althoughnowadays this method is not likely to be used, this commu-nication is instructive because it contains clear accounts ofthe data analysis. The linewidth of the N-acetyl or O-methyl 1H resonances of a reporter or reference ligand(L2) were followed during titration with sialic acid deriva-tives of interest (L1). Typically titrations were carried outat 1 mM in the reference ligand and the ligand of interestwas incremented up to 15 mM. As is usual in graphicalmethods the solution compositions were contrived to bringabout a reduction in the number of degrees of freedom ofthe system. In this case the titrations were performed atconstant reference ligand concentration [L2]0 and constantprotein concentration [P]0. Graphical data analyses werepresented for two possible cases depending on whether

L1 or L2 is the observed species. In the case where the con-centration of the measured ligand [L1]0 is varied while theNMR property of the reference ligand L2 is observed

½L1�0 ¼KDDmaxðL2Þ½P�0KDðL2ÞDobsðL2Þ

� KD 1þ ½L2�0KDðL2Þ

� �; ð31Þ

and a plot of [L1]0 versus 1/Dobs(L2) is a straight line with ay-intercept of –KD(1 + [L2]0/KD(L2). Thus, if KD(L2) hasbeen measured independently, KD can be determined fromthe chemical shift or (as in this case) from the linewidthbehaviour of species L2 as a function of [L1]0. This proto-col is useful for ligands whose resonances are difficult toanalyse due to overlap or poor signal-to-noise ratio. Theoutcome is illustrated in Fig. 11a from which KD =2.7 ± 0.2 mM.

The other scenario is where the NMR parameter of thetitrating ligand L1 is monitored as a function of varying[L1]0. In this case it can be shown that

½L1�0 ¼DmaxðL1Þ½P�0

DobsðL1Þ� KD 1þ ½L2�0

KDðL2Þ

� �; ð32Þ

and a plot of [L1]0 versus 1/Dobs(L1) is again a straight linewith a y-intercept of –KD(1 + [L2]0/KD(L2). This is illus-trated for the same ligand system in Fig. 11b, which leadsto KD = 1.8 ± 0.5 mM.

In these experiments the reporter ligand has a bindingaffinity which is not very different from those of the inter-esting ligands. It is an important study because it expands

Fig. 12. WaterLOGSY signal attenuation of the reference compound as afunction of the dissociation constant KI of the competitor. The simulationwas performed using Eq. (34) with a competitor concentration of 5 lM, areference (ligand of interest) concentration of 50 lM, and a proteinconcentration of 2 lM [91]. Reproduced with permission. � 2002 AmericanChemical Society.


the applicability of the NMR titration method to systemswhere tighter binding constants may be determined. Eqs.(31) and (32) are based on an assumption that the concen-tration of free ligand is approximately the same as [L]0, sothe dissociation constants that can be measured are limitedto the range �[P]0.

5.2. Magnetization transfer for sub micromolar binding

Some more recent developments to competition bindinghave successfully extended the range of NMR measurablevalues of KD to lM levels. The interest in this topic canbe traced back to a communication from Mayer and Meyer[74]. They observed that the STD response of a boundligand was reduced by the presence of a competitor ligand,and noted that it is possible to determine the KD value of aligand from the IC50 value of any competitor ligand whichhas a known dissociation constant, thus

KD ¼ ð½L1�0KIÞ=ðIC50ðL2Þ � KIÞ: ð33Þ

In the above equation, and in the remainder of this section,the symbol KI is used to indicate the dissociation constantof the competitor, reference or reporter ligand (L2) and KD

is used to indicate the dissociation constant of the ligand ofinterests (L1).

Dalvit [79,91] recognised that the waterLOGSYresponse (see Section 4.4.2) of a system comprising of areceptor and a specific, but medium affinity (mM) ligandcould be used as a screen to detect the presence of compet-ing higher affinity ligands. Remembering that the water-LOGSY response arises from bound ligand, any moleculethat competes with the bound ligand will result in adecrease in intensity of the waterLOGSY signal. Knowl-edge of the binding affinity of the reporter ligand, coupledwith some careful experiment design permits quantitativedetermination of the binding constant for the competitionligand. Setting up the experiment conditions (solution com-positions) so that waterLOGSY responses of investigativeligand (L1), reporter ligand (L2) and protein are comparedwith directly corresponding reporter ligand (L2) and pro-tein data simplifies the data analysis. The relationshipbetween attenuation of waterLOGSY response I(+)/I(�)

and the dissociation constants of the two ligands is givenby

I ðþÞI ð�Þ¼½P�0þ½L1�0þKD 1þ½L2�0

KI

� ��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½P�0þ½L1�0þKD 1þ½L2�0

KI

� �n o2

�4½P�0½L1�0

r

½P�0þ½L1�0þKD�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½P�0þ½L1�0þKD

� �2�4½P�0½L1�0q

ð34Þ

Fig. 12 is plotted directly from solutions of Eq. (34) to illus-trate the dependence of the response ratio I(+)/I(�) on [P]0,[L1]0, [L2]0, KD and KI, respectively [91]. This chart demon-strates that the ratio I(+)/I(�) is effectively modulated as afunction of the inhibitor binding affinity. The inhibitor dis-places the monitored ligand, thus reducing the water-LOGSY response. The chart shows that more effectiveinhibitors (KI approaches zero) displace more of the ob-

served ligand and the ratio I(+)/I(�) approaches zero. Thefour curves illustrate the dependence of the function onthe binding affinity of the reference molecule. Weaker affin-ity reporter ligands are more easily displaced. The effect ofhigher affinity reference molecules is to move the curves to-wards the left and top of the graph (mirroring the effect ofdecreasing KD).

The experiment has been validated with the model sys-tem serum albumin with 6-methyltryptophan as a referenceligand (KD = 37 lM) and diazepam as the high affinitycompetitor ligand. A single point experiment establisheda 65% reduction in the reporter ligand waterLOGSY signalwhen diazepam was added. This translated toKD = 2 ± 1 lM for the diazepam binding [91]. The samegroup have demonstrated that transverse relaxation andlongitudinal relaxation parameters of a reference ‘reporter’ligand are equally effective for quantifying high affinitybinding [92]. Further work on competition methods fromthis group are discussed in Section 6.3.

The HSA/tryptophan/diazepam system was also usedrecently to demonstrate that competition STD NMR canalso be put into a quantitative context [93]. The principlesand experiment protocols are almost identical to thatdescribed above, except that magnetization transfer isinduced by the STD pulse sequence instead of water-LOGSY. Again, binding of the high affinity ligand is sig-nalled by a decrease in the intensity of the reporter ligandSTD response, and the magnitude of this attenuation isused to deduce KI for the strong binder. The dissociationconstant of diazepam was estimated at 2.4 ± 0.5 lM fromthe observed fractional reduction of 0.41 in the 6-methyl-tryptophan STD signal. Fig. 13 is complementary toFig. 12. It shows the modulation of the STD response of

Fig. 13. STD signal reduction of the indicator as a function of thecompetitor concentration. The concentration of the STD indicator(KD = 10 lM) and the protein are 100 and 5 lM, respectively. Simulationswere performed according to Eq. (20) for five different dissociationconstants (KI) of the inhibitor (100, 10, 1, 0.1 and 0.01 lM). The STDsignal reduction is expressed as a fraction and is equal to the ratio of theSTD signal intensities in the presence and absence of the competitor. [P]0 isincluded in the simulation. The dashed lines represent simulations with [P]0omitted [93]. Reproduced with permission. � 2004 John Wiley & Sons, Ltd.


a reporter ligand as a function of the inhibitor concentra-tion for a range of values of KI. This chart shows thatthe fractional reduction of the STD signal of the reporteris most sensitive to the competitor concentration in therange 0.2–0.8 (this is yet another statement of the materialin Section 1.3). The chart suggests that there is no lowerlimit to the KI values that can be measured in this way.The KI of any higher affinity ligand can be accurately mea-sured by lowering the concentration of inhibitor until theSTD modulation is in the 0.2–0.8 range [93].

Another discussion of NMR detected competition bind-ing noted that KI was in principle available from knowl-edge of the KD of the reporter ligand but stopped shortof reporting quantitative figures [94].

6. 19F NMR studies

Introduction of a fluorine atom into either the protein orthe ligand opens the door to 19F NMR observation andthis has an enormous range of benefits. 19F has nearlythe same sensitivity as 1H. It is a spin 1/2 nucleus and itschemical shift range in proteins and small organics is usu-ally around 100 ppm. There is essentially no biologicalbackground of 19F signals, thus only the site of interest willappear in the experimental spectrum. These factors makethe 19F NMR spectrum easy to acquire and easy to analyse.Furthermore, 19F occurs frequently as a motif in man madedrugs (it is usually put in to improve adverse metabolicprofiles). Consequently there is a large body of literaturethat reports on the use of 19F NMR to study protein–ligand interactions [95,96].

From the perspective of quantifying the protein–ligandinteraction, nothing that follows is new to what has beenpresented in the preceding sections. The concern is still to

deconvolute the bound and free mole fractions of the spe-cies that is observed and the only change is that we are nowlooking at 19F as a reporter nucleus. This review could wellhave been written with the discussion of 19F experimentssprinkled around the text under the other appropriatesub headings. However there is a didactic advantage in pre-senting this material separately. At the risk of being repet-itive, the papers cited in the following discussion illustrateall of the experiment protocols and data analysis tech-niques again, but often with greater clarity.

6.1. Fluorine labelled proteins

A study of oligosaccharide binding to AcAMP2-likepeptides provides a recent example. A 30 amino acidresidue analogue corresponding to the hevein domain wassynthesised with Phe18 and Tyr20 changed to 4-fluorophe-nylalanine. The mM binding of chitotriose was evaluatedfrom 19F NMR titration data [97].

6.2. Fluorine labelled ligands

The binding of N-trifluoroacetyl-D-(and L-)p-fluorophe-nylalanine to a-chymotrypsin was quantitatively measuredfrom perturbations to the 19F chemical shifts of both fluo-rine nuclei upon interaction with the active site [98]. Thedownfield shifts of the bound ligand are attributed to inter-actions with His, Ser and Asp residues in the bindingpocket. The communication includes a full and cleardescription of a unique data analysis which is based onarithmetic iterations of the quadratic binding equation todetermine Dmax and KD. Although obsolete, the procedureis worth noting. Mathematical procedures to account fordimerization of the protein add interest to the data analy-sis. Data were collected under conditions of constant [P]0(1.9 mM) and varying [L]0 (from 0.5 to 20 mM); and forthe reverse case of constant [L]0 (1.5 mM) and varying[P]0 (0.05 to 1.9 mM). It was found that the L isomer bindsabout 10 times less strongly than the D isomer(KD = 0.32 mM at pH 6.0).

A consequence of the large chemical shift range of 19Fis that dynamic systems may often be in the intermediateor slow exchange regime when observed via 19F. In theslow exchange case the data treatment becomes trivial.Integration of the free and bound signals gives [L] and[LP] directly. Much of the 19F NMR protein–ligandinteraction literature reports on systems that are on thistime scale. A study of the binding of trifluoromethyl ana-logs of 6,7-dimethyl-8-ribityllumazine to lumazine apo-protein is such an example. The bound ligands giverise to additional broad signals several ppm downfieldof the free ligand signal, KD = 3–5 lM, analysed by Scat-chard plots [99]. This system is discussed further in Sec-tion 7.

19F spin–spin relaxation rates (1/T2) measured by theCPMG sequence have been successfully applied to measurethe low affinity binding of the volatile anaesthetic isoflu-


rane to BSA [100]. In this study, only one 19F signal wasobserved, but exchange is sufficiently slow that exchangebroadening had to be allowed for [54]. This was achievedby varying the interval between the 180� refocusing pulses.The data analysis then proceeded exactly as described pre-viously in Section 4.2. A plot of 1/T2(obs) versus [L]0 gives –KD at the x intercept, (1.4 mM).

6.3. Fluorine observed competition binding experiments

The large chemical shift anisotropy of 19F results in verybroad lines for bound fluorinated ligands and thereforevery large differences in line widths between the boundand free states. This makes fluorinated ligands particularlywell suited for competition binding experiments. The trans-verse relaxation rate 1/T2 of fluorine in a reference ligand isan ideal parameter to monitor as a function of test ligandconcentration. For instance, the low affinity ligand 2-hydroxy-3-fluorobenzoic acid has been used as a reporterligand for the Sudlow site 1 of human serum albumin. Dis-sociation constants for hundreds of compounds in therange from a few nM to high lM are claimed to have beenmeasured by this method [101].

Dalvit et al. have recently provided an in depth theoret-ical analysis of 19F NMR competition binding using weakaffinity reporter ligands. This includes several instructivesimulations showing the relationships between the equilib-rium parameters – fraction bound, fractional reductions inNMR responses etc., and the defining parameters of thesystem – KD, KI, [P]0, [L1]0, and [L2]0 [102].

7. KD from ligand dissociation kinetics

KD was defined earlier (Eq. (1)) in terms of the equilib-rium concentrations of bound and free species. An equiva-lent definition of KD is in terms of the equilibriumcondition established by the balance of the ligand associa-tion (kon) and dissociation (koff) rates

KD ¼ kon=koff : ð35ÞSo instead of quantifying the solution speciation, onemight aim instead at measuring these rates. In very generalterms the first order ligand dissociation rate (units M�1) isa reflection of the strength of the intermolecular complex,whereas the ligand association rate is a measure of howquickly the ligand can arrive at the protein. An assumptionis frequently made that the kon is diffusion limited and isthus independent of the system. A value of 1 · 109 M�1 s�1

is usually cited for kon. When this condition is satisfied koff

is a useful proxy for the dissociation constant. There aremany NMR protocols for measuring these rates [103].

Information on ligand exchange kinetics (koff and kon

rates and hence KD) can be derived from complete line shapeanalysis of individual NMR peaks. Jardetzky et al. havereported on a 1H NMR (500 MHz) study of the binding ofL-tryptophan to the trp repressor of Escherichia Coli [52].This study is interesting because it used a full line shape anal-

ysis of the ligand H-4 proton over a range of protein andligand concentration (mM) and over a temperature rangefrom 20 �C where the system is in slow exchange to 65 �Cwhen it is in fast exchange. This thorough analysis resultsin a full thermodynamic picture of complex formation inthe form of a KD versus 1/T Arrhenius plot.

The thermodynamic and kinetic parameters associatedwith the binding of N-acetylgalactosamine to Artocampus

integifolia agglutin were determined from the temperaturedependence of line broadening in the 19F and 13C NMRspectra of the ligand [104]. In this system chemical shiftchanges were not observed on binding. Campbell et al.reported a full line shape analysis of the 1D profiles of indi-vidual 15N–1H HSQC peaks at each point of a titration of a12-residue phosphopeptide into a solution of the SH2-Ndomain of the p85a subunit of PI 3 0-kinase [105]. This anal-ysis gave information about the kinetics of complex forma-tion in a system with KD in the nM range. A software toolis available to facilitate the analysis of line shapes fromtitration generated two-dimensional spectra [106].

Again, 19F NMR observations of fluorinated ligandsprovide some of the clearest examples of such studies. Allof the kinetic parameters, including kon and KD wereobtained from quantitative analysis of NOESY spectra ofthe lumazine protein/ligand system [107]. Peng hasdescribed in detail the use of cross-correlated 19F relaxationmeasurements for the study of ligand–receptor interactionsand show how these data provide estimates of KD [108].

8. Alternative measures of protein–ligand binding affinity

Although the dissociation constant KD is the preferredquantitative measure of stability for bimolecular complexes(because its meaning is clear), some other measures of affin-ity are also used. It may not always be possible to define thebinding interaction in terms of a simple 1:1 complex. Some-times an experiment observable is related to KD, but in anindeterminate way, so that the response can only be used asan indication of binding strength or as a ranking parame-ter, but not as an absolute measure.

8.1. Affinity index

Rossi et al. have advocated the ‘affinity index’ as a mea-sure of ligand macrocycle affinity [109]. Using the selectivespin–lattice relaxation rate R1 (1/T1(sel)) as the NMR obser-vable, it can be shown that

1

DR¼ 1

KD

þ ½L��

1

R1ðboundÞ½P�0; ð36Þ

and therefore a plot of D1/T1(sel) versus the protein concen-tration will be a straight line passing through the origin andwith a slope

½A�TL ¼KDR1ðboundÞ

1þ KD½L�

� �; ð37Þ

Fig. 14. IC50 of an experimental drug (known as H89) determined by 19FNMR detection of the CF3 labelled starting and enzymatically modifiedsubstrate. The test system comprised of a protein kinase and a 19F labelledsubstrate peptide. This plot shows the unphosphorylated peptide concen-tration, [pep], as a function of the inhibitor concentration [H89]. The best fitinhibition curve to the experimental data gives an IC50 of 0.72 ± 0.05 lM[114]. Reproduced with permission. � 2003 American Chemical Society.


which is defined as the ‘affinity index’. The dimensions of½A�TL are M�1 s�1 and the T and L superscripts and sub-scripts signify the temperature and ligand concentrationat which the measurement was made. The advantage of thisterm is that it provides a measure of ligand-macromoleculeglobal affinity which is independent of the number of bind-ing sites. A disadvantage of this parameter is its depen-dence on the ligand concentration. So, although it can bea useful way to rank order a series of ligands (or receptors)within a single study where [L]0 can be controlled, it isnot a very efficient way to communicate knowledge ofreceptor–ligand binding strength. The method has beenused to study the interaction of carbamazepine withalbumin [110], chloramphenicol and thiamphenicol withalbumin [111], and anandamide with multiple cannabinoidreceptors [112].

8.2. Affinity ranking

NMR is now commonly used in the pharmaceuticalindustry as a lead discovery tool in the drug discovery pro-cess. Relatively small compound collections are screenedfor receptor binding and the NMR response is used to sig-nal binding. The usual outcome from such an endeavour isa subset of ‘hits’ that have some affinity for the receptor. Itis highly desirable to rank order these hits, but there maynot be enough time or resource to apply the titration meth-ods. One crude but pragmatic way forward is to rank theligands according to the magnitude of the NMR measuredbinding response.

A search for ligands of human adipocyte fatty acid bind-ing protein (FABP4) is a recent example. A 1H 1D T1q

relaxation filter experiment was used to identify ligandsfrom a collection of 531 compound which was initiallyscreened as cocktails of 5–10 compounds. The ligands werethen classified as weak or strong binders according to theamplitude of the attenuation response in a second T1q

relaxation filter experiment applied with a shorter spin locktime [113].

8.3. NMR as a functional biological screen

The requirements of the pharmaceuticals industry toinvent more effective lead discovery programs has alsoled to the development of an NMR based functionalscreen. A functional screen is one where tentative newdrugs are tested against the fully functional target, e.g.,an enzyme that is actively turning over a substrate. Themethod, termed 3-FABS (three fluorine atoms for bio-chemical screening) by its inventors, uses NMR to analysethe progress of the enzyme reaction and is able to reportthe 50% mean inhibition concentration (IC50) of the activeligand [114,115]. It is interesting that neither the receptor(the enzyme), nor the screened ligand are observed in thisexperiment. The method requires the substrate of theenzyme to be labelled with 19F. NMR analysis of the reac-tion progress is then based on straightforward integration

of 1D 19F NMR data to quantify the amount of substrateand the product of the enzyme reaction. The compoundlibrary is added to 384 well plates containing the activeenzyme and substrate and the reaction is quenched at atime when some fraction of the substrate is expected tobe consumed. Automated processing of the 19F NMR spec-tra is able to quickly identify the active compounds. TheIC50 can be determined by collecting a full inhibition bind-ing curve (Fig. 14), or it can be estimated approximatelyfrom a single point measurement because the values forboth plateaus of Fig. 14 are known from references andblanks.

Cryogenically cooled probes permit the application ofthis kind of screening with femtomole levels of targetenzyme, a concentration similar to that required for tradi-tional high throughput screening methods [102].

9. Applications of CP-MAS NMR

No information about the equilibrium binding affinity isavailable from solid crystalline protein–ligand complexes.However the techniques of solid state NMR can be usefullyapplied to the hydrated gelatinous samples that are typicalof membrane bound protein preparations. Cross-polariza-tion magic angle spinning (CP-MAS) NMR goes someway to resolving the technical difficulties of studying verylarge proteins embedded in a lipid membrane. Add to thisthe simplification resulting from isotope labelled ligands,usually labelled at a single site with either 13C, 15N or19F, and direct observation of the dynamics of receptorbound ligands becomes possible. Unlike the high resolutionsolution phase techniques which sample an exchange aver-aged population, the CP-MAS experiment only sees theligand that is bound to the receptor. Thus the few reportsof quantitation of KD by these methods are a special caseof ligand observed experiments.

Fig. 16. Simulations of cross polarization intensity profiles for a ligandinteracting with a membrane protein, calculated for different values of thedissociation rate constant (koff) and the dissociation constant (KD). Thevirtual system was [L]0 = 6 mM, THC = 1.5 ms, T free

1qH ¼ 100 ms, andT bound

1qH ¼ 2 ms. The simulations represent [P]0 = 2.4 mM (dashed line),2.0 mM (solid line) and 1.6 mM (dotted line) [117]. Reproduced withpermission. � 2004 American Chemical Society.


CP-MAS works because it distinguishes bound fromnon-bound ligand. The 13C CP-MAS experiment generatessignals from 13C nuclei in rigid solids by transferring mag-netization from abundant 1H nuclei. The experiment firstexcites 1H magnetization and then transfers magnetizationfrom 1H to 13C during the contact time. The 1H-13C dipolecoupling is averaged to zero for rapidly reorienting smallmolecules, so the 13C magnetization in the non-boundligand remains at equilibrium (weak), and is essentiallynot detected. If at some point during the contact time(spin-lock field applied) the ligand binds to the protein, itwill build up 13C magnetization at a predictable rate andwill produce a signal during the detection period. Theresult is that the CP-MAS experiment can give a direct readout of [PL] unperturbed by [L]. Measuring [PL] is the keyto knowing KD.

A study of the weak affinity binding of galactose to thelactose transport protein LacS in native membranes is thefirst reported estimation of KD from CP-MAS data [116].Use of [1-13C]D-galactose allowed clear observation of thebound ligand against the background of natural abun-dance carbon. Cross polarization NMR had not beenthought to be amenable to quantitative interpretation sincethe response of the observed nucleus is dependent on multi-ple and difficult to quantify interactions with nearby spins.However, a selectively bound substrate should experience aconsistent environment throughout a titration, and theresponse can be analysed as a function of [L]0. This isshown in Fig. 15. The two data points at the highest [L]0were deemed to have been corrupted and were discardedfrom the Scatchard plot. Note that the normalization stepin this example assumes that saturation binding hasoccurred at 5 mM ligand (certainly not the case) and is adrastic simplification of the data analysis.

Fig. 15. Binding isotherm for [1-13C]-D-galactose to LacS membranes asdetermined from the intensity of the substrate signal in the CP MAS 13Cspectrum. The ratio of occupied binding sites was established bynormalizing the response to the maximum observed response (the responseat 5 mM ligand). The inset is a Scatchard plot of the first four data points[116]. Reproduced with permission. � 1999 American Chemical Society.

The rate at which 13C magnetization builds up in theligand is a balance between the positive addition of magne-tization through the dipolar coupling and loss throughrelaxation. These factors in turn depend on the bindingconstant and also the number of times that the ligandmight exchange on and off the protein during the contacttime. Hence the response is a function of both KD and koff.Simulated profiles of expected signal intensity are shown inFig. 16. The experiment has been demonstrated with stud-ies of the binding of methyl [1-13C]-b-D-glucuronide to theGusB membrane transport protein from Escherichia coli

[117], and as a 19F NMR version for the anti-psychoticdrug trifluoroperazine binding to membrane embeddedgastric H+/K+ ATPase [118]. Under optimum conditionsthe variable contact time CP-MAS experiment can be a sin-gle point experiment. It is able to establish KD from a singleprotein/ligand sample at just one protein:ligand ratio.

10. Conclusion

The use of NMR to determine quantitatively the associ-ation constants of protein–ligand complexes is firmly estab-lished. NMR might not always be the optimum means tomeasure KD for a system, but NMR specialists obviouslyenjoy pushing the boundaries and expanding the applica-bility of magnetic resonance methods and the result is thatthere are a lot of NMR experiments available for the task.The tried and tested titration methods of sections 3 and 4are used very widely.

The opportunity to observe cleanly the species of inter-est with high sensitivity and often with no additional chem-ical manipulation has resulted in the accumulation of hugeexperience with 19F NMR. Few would consider putting


fluorine into a ligand solely for the purpose of measuringKD perhaps, but for systems where fluorine is already pres-ent in the ligand, the 19F NMR experiments might be con-sidered as first choice methods for measuring KD.

The most recent developments with magnetizationtransfer experiments, competition binding and CP-MASapproaches, have resulted in novel, sensitive and specificNMR methods to measure KD that have moved far fromthe original linewidth and chemical shift perturbationapproaches. They illustrate the breadth of interest in thisscience and suggest that more interesting developments willcontinue to come. The most useful experiments will bethose that establish [PL] directly and expeditiously.

References

[1] D. Colquhoun, Trends Pharmacol. Sci. 27 (2006) 149.[2] R.A. Dwek, Nuclear Magnetic Resonance (NMR) in Biochemistry,

Clarendon Press, Oxford, 1973.[3] G. Gemmecker, in: U. Holzgrabe, I. Wawer, B. Diehl (Eds.), NMR

Spectroscopy in Drug Development and Analysis, Wiley-VCH,Weinheim, 1998, p. 135.

[4] L. Fielding, Tetrahedron 56 (2000) 6151.[5] K.A. Connors, Binding Constants, John Wiley & Sons, New York,

1987.[6] V.M.S. Gil, N.C. Oliveira, J. Chem. Ed. 67 (1990) 473.[7] R.S. Macomber, J. Chem. Ed. 69 (1992) 375.[8] R.E. Barrans, D.A. Dougherty, Supramol. Chem. 4 (1994) 121.[9] P. Gans, A. Sabatini, A. Vacca, Talanta 43 (1996) 1739.

[10] G. Weber, S.R. Anderson, Biochemistry 4 (1965) 1942.[11] W.B. Person, J. Am. Chem. Soc. 87 (1965) 167.[12] D.A. Deranleau, J. Am. Chem. Soc. 91 (1969) 4044.[13] D.A. Deranleau, J. Am. Chem. Soc. 91 (1969) 4050.[14] J. Granot, J. Magn. Reson. 55 (1983) 216.[15] C.S. Wilcox, in: H.-J. Schneider, H. Durr (Eds.), Frontiers in

Supramolecular Organic Chemistry and Photochemistry, VCH,Weinheim, 1991, p. 123.

[16] J.L. Sudmeier, J.L. Evelhoch, N.B.-H. Jonsson, J. Magn. Reson. 40(1980) 377.

[17] A. Poveda, J. Jimenez-Barbero, Chem. Soc. Rev. 27 (1998) 133.[18] J.L. Asensio, F.J. Canada, M. Bruix, A. Rodriguez-Romero, J.

Jimenez-Barbero, Eur. J. Biochem. 230 (1995) 621.[19] J.L. Asensio, F.J. Canada, M. Bruix, C. Gonzalez, N. Khiar, A.

Rodrıguez-Romero, J. Jimenez-Barbero, Glycobiology 8 (1998) 569.[20] J.F. Espinosa, J. L Asensio, J.L. Garcia, J. Laynez, M. Bruix, C.

Wright, H.-C. Siebert, H.-J. Gabius, F.J. Canada, J. Jimenez-Barbero, Eur. J. Biochem. 267 (2000) 3965.

[21] J.L. Asensio, H.-C. Siebert, C.-W. von der Lieth, J. Laynez, M.Bruix, U.M. Soedjanaamadja, J.J. Beintema, F.J. Canada, H.-J.Gabius, J. Jimenez-Barbero, Proteins 40 (2000) 218.

[22] N. Aboitiz, M. Vila-Perello, P. Groves, J.L. Asensio, D. Andreu,F.J. Canada, J. Jimenez-Barbero, Chem. Bio. Chem. 5 (2004) 1245.

[23] A. De Marco, S.M. Hochschwender, R.A. Laursen, M. Llinas, J.Biol. Chem. 257 (1982) 12716.

[24] A. De Marco, A.M. Petros, R.A. Laursen, M. Llinas, Eur. Biophys.J. 14 (1987) 359.

[25] A.M. Petros, V. Ramesh, M. Llinas, Biochemistry 28 (1989) 1368.[26] T. Thewes, K. Constantine, I.-J.L. Byeon, M. Llinas, J. Biol. Chem.

265 (1990) 3906.[27] I.-J.L. Byeon, R.F. Kelly, M.G. Mulkerrin, S.S.A. An, M. Llinas,

Biochemistry 34 (1995) 2739.[28] D.N. Marti, C.-K. Hu, S.S.A. An, P. von Haller, J. Schaller, M.

Llinas, Biochemistry 36 (1997) 11591.[29] R. Wintjens, J.-M. Wieruszeski, H. Drobecq, P. Rousselot-Pailley,

L. Buees, G. Lippens, I. Landrieu, J. Biol. Chem. 276 (2001) 25150.

[30] L.K. MacLachlan, D.G. Reid, R.C. Mitchell, C.J. Salter, S.J. Smith,J. Biol. Chem. 265 (1990) 9764.

[31] C. Dalvit, P. Floersheim, M. Zurini, A. Widmer, J. Biomol. NMR14 (1999) 23.

[32] C.J. Morton, D.J.R. Pugh, E.L.J. Brown, J.D. Kahmann, D.A.C.Renzoni, I.D. Campbell, Structure 4 (1996) 705.

[33] S.B. Shuker, P.J. Hajduk, R.P. Meadows, S.W. Fesik, Science 274(1996) 1531.

[34] P.J. Hajduk, G. Sheppard, D.G. Nettesheim, E.T. Olejniczak, S.B.Shuker, R.P. Meadows, D.H. Steinman, G.M. Carrera, P.A.Marcotte, J. Severin, K. Walter, H. Smith, E. Gubbins, R. Simmer,T.F. Holzman, D.W. Morgan, S.K. Davidsen, J.B. Summers, S.W.Fesik, J. Am. Chem. Soc. 119 (1997) 5818.

[35] P.J. Hajduk, M. Bures, J. Praestgaard, S.W. Fesik, J. Med. Chem. 43(2000) 3443.

[36] H. Mao, P.J. Hajduk, R. Craig, R. Bell, T. Borre, S.W. Fesik, J. Am.Chem. Soc. 123 (2001) 10429.

[37] A.M. Petros, J. Dinges, D.J. Augeri, S.A. Baumeister, D.A.Betebenner, M.G. Bures, S.W. Elmore, P.J. Hajduk, M.K. Joseph,S.K. Landis, D.G. Nettesheim, S.H. Rosenberg, W. Shen, S.Thomas, X. Wang, I. Zanze, H. Zhang, S.W. Fesik, J. Med. Chem.49 (2006) 656.

[38] H.-J. Boehm, M. Boehringer, D. Bur, H. Gmuender, W. Huber, W.Klaus, D. Kostrewa, H. Kuehne, T. Luebbers, N. Meunier-Keller,F. Mueller, J. Med. Chem. 43 (2000) 2664.

[39] L. Parsons, N. Bonander, E. Eisenstein, M. Gilson, V. Kairys, J.Orban, Biochemistry 42 (2003) 80.

[40] J.L. Weaver, J.H. Prestegard, Biochemistry 37 (1998) 116.[41] P.J. Hajduk, R. Mendoza, A.M. Petros, J.R. Huth, M. Bures, S.W.

Fesik, Y.C. Martin, J. Computer-Aided Mol. Design 17 (2003) 93.[42] B.J. Stockman, C. Dalvit, Prog. NMR Spectrosc. 41 (2002) 187.[43] E.R. Zartler, J. Yan, H. Mo, A.D. Kline, M.J. Shapiro, Curr. Topics

Med. Chem. 3 (2003) 25.[44] B. Meyer, T. Peters, Angew. Chem. Int. Ed. 42 (2003) 864.[45] J.W. Peng, J. Moore, N. Abdul-Manan, Prog. NMR Spectrosc. 44

(2004) 225.[46] J. Feeney, J.G. Batchelor, J.P. Albrand, G.C.K. Roberts, J. Magn.

Reson. 33 (1979) 519.[47] I.M. Klotz, Acc. Chem. Res. 7 (1974) 162.[48] S.J. Perkins, L.N. Johnson, D.C. Phillips, R.A. Dwek, Biochem. J.

193 (1981) 553.[49] N.K. Sauter, M.D. Bednarski, B.A. Wurzburg, J.E. Hanson, G.M.

Whitesides, J.J. Skehel, D.C. Wiley, Biochemistry 28 (1989) 8388.[50] T.J. Swift, R.E. Connick, J. Chem. Phys. 37 (1962) 307.[51] K.A. Kronis, J.P. Carver, Biochemistry 24 (1985) 826.[52] T.H. Schmitt, Z. Zheng, O. Jardetzky, Biochemistry 34 (1995) 13183.[53] F. Ni, Prog. NMR Spectrosc. 26 (1994) 517.[54] J.J. Fischer, O. Jardetzky, J. Am. Chem. Soc. 87 (1965) 3237.[55] J.T. Gerig, J. Am. Chem. Soc. 90 (1968) 2681.[56] J. Miller, V. Witzemann, U. Quast, M.A. Raftery, Proc. Natl. Acad.

Sci. USA 76 (1979) 3580.[57] L. Verdier, J. Gharbi-Benarous, G. Bertho, N. Evrard-Todeschi, P.

Mauvais, J.-P. Girault, J. Chem. Soc. Perkin Trans. 2 (2000) 2363.[58] K.A. Kronis, J.P. Carver, Biochemistry 21 (1982) 3050.[59] L. Fielding, D. Fletcher, S. Rutherford, J. Kaur, J. Mestres, Org.

Biomol. Chem. 1 (2003) 4235.[60] G. Valensin, T. Kushnir, G. Navon, J. Magn. Reson. 46 (1982) 23.[61] R.W. Behling, T. Yamane, G. Navon, M.J. Sammon, L.W. Jelinski,

Biophys. J. 53 (1988) 947.[62] Y. Fraenkel, G. Navon, A. Aronheim, J.M. Gershoni, Biochemistry

29 (1990) 2617.[63] W.S. Price, Aust. J. Chem. 56 (2003) 855.[64] L.H. Lucas, C.K. Larive, Concepts Magn. Reson. 20A (2004) 24.[65] T.S. Derrick, E.F. McCord, C.K. Larive, J. Magn. Reson. 155

(2002) 217.[66] A.J. Lennon, N.R. Scott, B.E. Chapman, P.W. Kuchel, Biophys. J.

67 (1994) 2096.[67] R.J. Labotka, C.M. Schwab, Anal. Biochem. 191 (1990) 376.


[68] M.L. Tillett, M.A. Horsfield, L.-Y. Lian, T.J. Norwood, J. Biomol.NMR 13 (1999) 223.

[69] J. Fejzo, C.A. Lepre, J.W. Peng, G.W. Bemis, M.A. Murcko, J.M.Moore, Chem. Biol. 6 (1999) 755.

[70] A.P. Campbell, B.D. Sykes, J. Magn. Reson. 93 (1991) 77.[71] A. Chen, M.J. Shapiro, J. Am. Chem. Soc. 122 (2000) 414.[72] M. Mayer, B. Meyer, Angew. Chem. Int. Ed. 38 (1999) 1784.[73] V.V. Krishnan, Curr. Anal. Chem. 1 (2005) 307.[74] M. Mayer, B. Meyer, J. Am. Chem. Soc. 123 (2001) 6108.[75] R. Meinecke, B. Meyer, J. Med. Chem. 44 (2001) 3059.[76] A.T. Neffe, M. Bilang, B. Meyer, Org. Biomol. Chem. 4 (2006) 3259.[77] A. Blume, A.J. Benie, F. Stolz, R.R. Schmidt, W. Reutter, S.

Hinderlich, T. Peters, J. Biol. Chem. 31 (2004) 55715.[78] A.J. Benie, A. Blume, R.R. Schmidt, W. Reutter, S. Hinderlich, T.

Peters, J. Biol. Chem. 31 (2004) 55722.[79] C. Dalvit, G. Fogliatto, A. Stewart, M. Veronesi, B. Stockman, J.

Biomol. NMR 21 (2001) 349.[80] T. Peters, All About Albumin: Biochemistry, Genetics and Medical

Applications, Academic Press, San Diego, 1996.[81] M. Liu, J.K. Nicholson, J.C. Lindon, Anal. Commun. 34 (1997) 225.[82] M. Tanaka, Y. Asahi, S. Masuda, T. Ota, Chem. Pharm. Bull. 37

(1989) 3177.[83] M. Tanaka, Y. Asahai, S. Masuda, T. Ota, Chem. Pharm. Bull. 39

(1991) 2771.[84] R.-S. Luo, M.-L. Liu, X.-A. Mao, Appl. Spectrosc. 53 (1999) 776.[85] C.-G. Li, M.-L. Liu, C.-H. Ye, Appl. Magn. Reson. 19 (2000) 179.[86] L. Fielding, S. Rutherford, D. Fletcher, Magn. Reson. Chem. 43

(2005) 463.[87] Y.F. Cui, G.Y. Bai, C.G. Li, C.H. Ye, M.L. Liu, J. Pharm. Biomed.

Anal. 34 (2004) 247.[88] R-S. Luo, M.-L. Liu, X.-A. Mao, Spectrochim. Acta A 55 (1999) 1897.[89] W.S. Price, F. Elwinger, C. Vigouroux, P. Stilbs, Magn. Reson.

Chem. 40 (2002) 391.[90] J.E. Hanson, N.K. Sauter, J.J. Skehel, D.C. Wiley, Virology 189

(1992) 525.[91] C. Dalvit, M. Fasolini, M. Flocco, S. Knapp, P. Pevarello, M.

Veronesi, J. Med. Chem. 45 (2002) 2610.[92] C. Dalvit, M. Flocco, S. Knapp, M. Mostardini, R. Perego, B.J.

Stockman, M. Veronesi, M. Varasi, J. Am. Chem. Soc. 124 (2002)7702.

[93] Y.-S. Wang, D. Liu, D.F. Wyss, Magn. Reson. Chem. 42 (2004) 485.[94] W. Jahnke, P. Floersheim, C. Ostermeier, X. Zhang, R. Hemmig, K.

Hurth, D.P. Uzunov, Angew. Chem. Int. Ed. 41 (2002) 3420.

[95] B.G. Jenkins, Life Sci. 48 (1991) 1227.[96] J.T. Gerig, Prog. NMR Spectrosc. 26 (1994) 293.[97] M.I. Chavez, C. Andreu, P. Vidal, N. Aboitiz, F. Freire, P. Groves,

J.L. Asensio, G. Asensio, M. Muraki, F.J. Canada, J. Jimenez-Barbero, Chem. Eur. J. 11 (2005) 7060.

[98] K.L. Gammon, S.H. Smallcombe, J.H. Richards, J. Am. Chem. Soc.94 (1972) 4573.

[99] J. Scheuring, J. Lee, M. Cushman, H. Patel, D.A. Patrick, A.Bacher, Biochemistry 33 (1994) 7634.

[100] B.W. Dubois, A.S. Evers, Biochemistry 31 (1992) 7069.[101] C. Dalvit, P.E. Fagerness, D.T.A. Hadden, R.W. Sarver, B.J.

Stockman, J. Am. Chem. Soc. 125 (2003) 7696.[102] C. Dalvit, N. Mongelli, G. Papeo, P. Giordano, M. Veronesi, D.

Moskau, R. Kummerle, J. Am. Chem. Soc. 127 (2005) 13380.[103] O. Monasterio, Methods 24 (2001) 97.[104] M.V. Krishna Sastry, M.J. Swamy, A. Surolia, J. Biol. Chem. 263

(1988) 14862.[105] M. Hensmann, G.W. Booker, G. Panayotou, J. Boyd, J. Linacre, M.

Waterfield, I.D. Campbell, Protein Sci. 3 (1994) 1020.[106] U.L. Gunther, B. Schaffhausen, J. Biomol. NMR 22 (2002) 201.[107] J. Scheuring, M. Fischer, M. Cushman, J. Lee, A. Bacher, H.

Oschkinat, Biochemistry 35 (1996) 9637.[108] J.W. Peng, J. Magn. Reson. 153 (2001) 32.[109] C. Rossi, A. Donati, C. Bonechi, G. Corbini, R. Rappuoli, E.

Dreassi, P. Corti, Chem. Phys. Lett. 264 (1997) 205.[110] C. Rossi, C. Bonechi, S. Martini, M. Ricci, G. Corbini, P. Corti, A.

Donati, Magn. Reson. Chem. 39 (2001) 457.[111] S. Martini, C. Bonechi, A. Magnani, N. Marchettini, P. Corti, G.

Corbini, C. Rossi, Magn. Reson. Chem. 41 (2003) 489.[112] C. Bonechi, S. Martini, V. Brizzi, P. Massarelli, G. Bruni, C. Rossi,

Eur. J. Med. Chem. 41 (2006) 1117.[113] M.J.P. van Dongen, J. Uppenberg, S. Svensson, T. Lundback, T.

Akerud, M. Wikstrom, J. Schultz, J. Am. Chem. Soc. 124 (2002)11874.

[114] C. Dalvit, E. Ardini, M. Flocco, G.P. Fogliatto, N. Mongelli, M.Veronesi, J. Am. Chem. Soc. 125 (2003) 14620.

[115] C. Dalvit, E. Ardini, G.P. Fogliatto, N. Mongelli, M. Veronesi,Drug Discov. Today 9 (2004) 595.

[116] P.J.R. Spooner, L.M. Veenhoff, A. Watts, B. Poolman, Biochemistry38 (1999) 9634.

[117] S.G. Patching, A.R. Brough, R.B. Herbert, J.A. Rajakarier, P.J.F.Henderson, D.A. Middleton, J. Am. Chem. Soc. 126 (2004) 3072.

[118] M.P. Boland, D.A. Middleton, Magn. Reson. Chem. 42 (2004) 204.

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