radioligand

UNIT 1.3Practical Aspects of Radioligand Binding

The technique of radioligand binding hasrevolutionized the ability to characterize bothreceptors and the ligands (substrates) that in-teract with them; in this context, the term “re-ceptor” is used to define any protein of biologi-cal interest that interacts with a ligand (or sub-strate) that can be radiolabeled. Radioligandbinding can be used to characterize receptorsin their natural environment (wild type) as wellas those transfected into cell lines. It can be usedto study receptor dynamics and localization, toidentify novel chemical structures that interactwith receptors, and to define ligand activity andselectivity. The technique thus serves as a valu-able adjunct to other pharmacological and mo-lecular biological approaches. This unit re-views the major approaches to developing abinding assay. A number of other excellentarticles dealing with the practical and theoreti-cal aspects of ligand binding assays are alsoavailable (Motulsky and Neubig, 1997; Lim-bird, 1996; Williams et al., 1995; Kenakin,1993; UNIT 1.1).

For many routine binding assays, essentiallyall that is required is a suitable radioligand anda crude homogenate of a tissue known to con-tain the receptor. The homogenate and the ra-dioligand are mixed, and at an appropriate time(empirically determined by trial and error) theunbound radioligand (L*, or free) is rapidlyseparated from the ligand bound to the receptor(L*R, or bound), usually by rapid filtration.Tissue sources in a radioligand binding assaycan include tissue slices (UNIT 8.1), subcellularfractions of a tissue, or intact cellular prepara-tions that include native, immortalized, ortransfected cells (UNIT 6.3).

Historically, the existence of receptors, orspecific ligand binding sites, was inferred frompharmacological data (UNIT 1.1). The biochemi-cal demonstration that these low-abundanceproteins actually existed required the inventionand development of radioligand binding as-says. Until the advent of molecular cloningtechniques (UNITS 6.1 & 6.3), relatively little wasknown about the molecular nature of receptors,except for what could be gleaned using radio-ligand binding. Binding assays have now be-come routine, and computer programs foranalysis of binding data are commonplace(Motulsky and Neubig, 1997).

In contrast to other biochemical assays, ra-dioligand binding assays can yield large

amounts of data in a very short time (on theorder of days) using minimal amounts of tissueand ligand. This advantage has led to the tech-nique of high-throughput screening, a majormilestone in the drug discovery process thatallows hundreds of thousands of compounds tobe evaluated for in vitro activity using a mi-crotiter plate format (Williams and Gordon,1996). Compounds can currently be runthrough a battery of more than 80 in vitroradioligand binding assays to assess their se-lectivity to a variety of receptors, enzymes, andsignal transduction targets. These data providea valuable starting point in assessing functionaland in vivo activity, and may provide informa-tion on potential side effect liabilities in a can-didate molecule.

Radioligand binding is also used in combi-nation with autoradiography (UNIT 8.1) to visu-alize receptors in situ: thin microtome-gener-ated sections of tissue are labeled and juxta-posed to X-ray film to produce photographicimages of receptor density. Ligands labeledwith short-lived isotopes (e.g., 11F, 13C, or 99Tc)can be used in vivo in both animals and humans,using positron emission tomography (PET) tovisualize ligand bound to receptor in livingtissue. This technique is used to measure recep-tor dynamics in various disease states, espe-cially in the central nervous system (CNS); toassess the access of drugs to tissues; and tomeasure receptor occupancy in real time, whichmay make it possible to titrate drug efficacy inthe clinical setting and avoid side effects.

The following series of criteria must be metin order to validate the binding assay (Cuatre-casas and Hollenberg, 1976).

1. Binding should be saturable, indicatinga finite number of receptor sites. However, insome instances, nonspecific binding can appearto be saturable (see Binding Specificity, discus-sion of nonspecific binding behavior).

2. The binding affinity, defined as the dis-sociation constant (Kd), should be consistentwith values determined for physiological re-ceptors (e.g., 100 pM to 10 nM).

3. Binding should be reversible, consistentwith a physiological mechanism for terminat-ing the effect of a ligand at the receptor.

4. The tissue and subcellular distribution ofthe specific binding should be consistent withwhat is known about the proposed physiologi-cal effects of the endogenous ligand, and with

Contributed by Michael McKinneyCurrent Protocols in Pharmacology (1998) 1.3.1-1.3.33Copyright © 1998 by John Wiley & Sons, Inc.

1.3.1

Receptor Binding

what is known about the localization of thereceptor.

5. The pharmacology of binding for bothagonists and antagonists should be consistentwith the pharmacology of the natural ligand infunctional and whole-animal test paradigms.By extrapolation, there should also be negativepharmacological data (e.g., ligands that areknown not to interact with the targeted receptorshould not affect radioligand binding).

6. A simultaneous correlation of bindingwith biological concentration-response curvesin identical tissue preparations should be gen-erated.

7. Activity in a binding assay should bepredictive of activity in a relevant animal modelof receptor function.

In general, items 1 through 5 are part of theprocess of characterizing a binding assay, whileitems 6 and 7 address additional properties ofcompounds examined in the assay.

Radioligand binding assays only measurethe affinity and density of a ligand binding site.The efficacy and the pharmacodynamic andpharmacokinetic properties of the ligand arenot measured, and must be assessed by func-tional and in vivo analysis of ligand properties.For G protein–coupled receptors, it is possibleto assess whether a ligand is an agonist or anantagonist (UNITS 1.1 & 1.2) by conducting a GTPshift experiment. This is not always a robustmeasure, and it is more useful to assess func-tional activity using a reporter system (UNIT 6.2)or an intact tissue system (see Chapter 4). Thetechniques of molecular cloning have provideda considerable amount of additional data incharacterizing receptor subtypes, their pharma-cological and molecular properties, and theiranatomical distribution (UNIT 6.1).

FUNDAMENTALS OFRADIOLIGAND BINDING ASSAYS

In its simplest form, the binding of a radi-oligand to a receptor is analogous to a bi-molecular reaction according to the Law ofMass Action. The radioligand (L*) combineswith the receptor (R) to form a complex (L*R).

The rate of the forward reaction (left to right)is determined by the concentrations of L* andR, and by the forward rate constant (k+1), asfollows.

The constant k+1 has units of (time−1 × con-centration−1). Generally, this reaction is revers-ible, with the L*R complex dissociating toreform L* and R. The rate of the reverse reac-tion is dependent on the amount of L*R and themagnitude of the reverse rate constant (k−1).The constant k−1 is expressed in units of time−1.

At equilibrium, the forward and reverse re-actions are equal in rate. Therefore, the amountsof L*, R, and L*R remain constant. Like abimolecular chemical reaction, the ratio of therate constants in a radioligand binding reactionis equal to the thermodynamic equilibriumbinding constant (Kd).

The Kd is expressed in molar units of concen-tration (e.g., nanomolar or picomolar). Thebinding affinity of a receptor for a ligand is amolecular consequence of its structure, and theKd is used to identify and classify receptorsbased on this affinity. Therefore, the determi-nation of Kd is a primary goal in developing abinding assay once the optimal conditions forspecific binding (see Binding Specificity) havebeen established.

In the assay, the species measured is thebound ligand (i.e., the L*R complex). The re-ceptor, which is embedded in the plasma mem-brane, is readily isolated from the aqueousreaction mixture by filtration. By quantifyingthe radioactivity trapped on the filter, theamount of radioligand bound to the tissue dur-ing the incubation is quantified. In equilibriumbinding assays, the unbound and bound ligandare separated from each other after the forwardand reverse binding reactions achieve equiva-lent velocities. In kinetic binding assays, thereaction is interrupted at various times duringthe formation or dissociation of the L*R com-plex. The Kd value can be determined witheither type of assay. If the binding is bimolecu-lar, the Kd will be similar using the two differentapproaches. The kinetic binding assay also al-

L R L R* *++

−

k

k

1

1

�

Equation 1.3.1

forward rate L R= × ×+k 1 [ *] [ ]

Equation 1.3.2

reverse rate L R= ×−k 1 [ * ]

Equation 1.3.3

Kk

kd

L R

L R= =

×−

+

1

1

[ *] [ ]

[ * ]

Equation 1.3.4

Current Protocols in Pharmacology

1.3.2

Practical Aspectsof Radioligand

Binding

lows for the determination of the associationand dissociation rate constants (k+1 and k−1,respectively).

In an equilibrium binding assay, the radio-ligand is incubated with a receptor source untilsufficient time has elapsed for the forward andreverse reactions to attain equal velocities be-fore separating free from bound ligand. With asaturation binding experiment, assays are per-formed using a series of radioligand concentra-tions, ranging up to a concentration at whichvirtually all of the receptors are occupied withligand. An example of this is shown in Figure1.3.1, where the binding of [3H]N-methylsco-polamine ([3H]NMS), a muscarinic cholinergicreceptor antagonist, to muscarinic receptors inN1E-115 mouse neuroblastoma cells is shown.The concentration of [3H]NMS is plotted on theabscissa, and the amount of radioligand boundto the filters at each concentration is plotted onthe ordinate. The figure shows total, specific,and nonspecific binding, where total binding isthe sum of specific and nonspecific binding (seeBinding Specificity).

While a certain amount of nonspecific bind-ing is always present, the more useful radioli-gands and assays display minimal nonspecificbinding (<20% of the total), enhancing theprecision of the assay by increasing the signal-to-noise ratio. Because there are a finite numberof physiologically relevant receptors in the tis-sue, specific binding becomes maximal (i.e.,approaches Bmax) as the concentration of radi-oligand increases (Fig. 1.3.1). However, non-specific binding is not saturated with radioli-gand and therefore continues to increase as afunction of radioligand.

The concentration of radioligand at whichthe amount of specific binding is one half theBmax approximates the equilibrium binding dis-sociation constant (Kd). However, obtaining theKd and Bmax from a plot such as that shown inFigure 1.3.1 is inappropriate because it is nec-essary to locate the top of the curve (Bmax)precisely. To use a graphical method, the dataare usually transformed to yield a straight line(see Graphical Methods). However, it is pref-erable to fit the specific binding data with a

nonspecific binding

specific binding

total binding

Bmax

0 0.5 1.0 1.50

5

10

15

20

25

30

Bou

nd [3

H]N

MS

(fm

ol/t

ube)

Free [3H]NMS (nM)

Figure 1.3.1 Saturation binding to muscarinic receptors on N1E-115 mouse neuroblastoma cells.Six concentrations of [3H]N-methylscopolamine ([3H]NMS), with or without 10 µM unlabeled NMS,were incubated with ∼300,000 intact cells/tube for 45 min at 15°C before rapid filtration wasperformed to separate bound from free. The total binding is the sum of the specific and nonspecificbinding. Nonspecific binding is defined as the amount of binding found in the tube containing boththe radioligand and unlabeled NMS.


1.3.3

Receptor Binding

mathematical model in a computer program todetermine these parameters (see Use of Com-puter Modeling Techniques).

The traditional graphical method is theScatchard (or Rosenthal) plot (Fig. 1.3.2).However, this plot of the concentration ofbound/free ligand (B/F) versus the concentra-tion of bound ligand (B) is invalid as both theordinate and abscissa contain a common termthat influences the slope of the plot indepen-dently of the data. For this reason, all bindingdata should routinely be evaluated using a non-linear regression analysis program (e.g.,GraphPad, LIGAND, or EBDA) that allows thecomputer to fit alternative models to the data.Refined analysis of a saturation isotherm re-veals whether the binding represents a simplebimolecular association or is more complex(e.g., if multiple subtypes of receptors havedifferent binding properties or if there is coop-erativity between receptors).

An alternative to the saturation experimentis the competition (or displacement) bindingassay, where increasing concentrations of un-labeled ligands ([D]) compete for the receptorwith a fixed concentration of radioligand. Thecompetition between the muscarinic receptorantagonist [3H]quinuclidinyl benzilate([3H]QNB) and the unlabeled agonist carba-mylcholine (carbachol) illustrates this point(Fig. 1.3.3). The displacement assay is moreeconomical than a saturation binding assay

because a single, low concentration of radioli-gand is used, conserving the expensive radio-labeled compound. When it is known that com-petition between the two ligands is for a singleclass of binding site (nominally, the Hill slope= 1; see Graphical Methods), the displacementcurve is analyzed by computer to obtain the IC50

(the concentration of unlabeled competitor nec-essary to displace 50% of the specifically boundradioligand), and this value is mathematicallycorrected using the Cheng-Prusoff equation(Cheng and Prusoff, 1973; see Graphical Meth-ods, discussion on semilogarithmic plots) toobtain the Ki, the equilibrium dissociation bind-ing constant for the unlabeled species.

Because the displacement of [3H]QNB bycarbachol in N1E-115 neuroblastoma cells oc-curs over a concentration range spanning sixorders of magnitude, it appears that the inter-action between R and L* is quite complex (Fig.1.3.3). The curve passing through the data isthe computer-assisted fit of a receptor model,which suggests that there are three separatebinding sites for this radioligand in these cells.

Kinetic radioligand binding assays are usedto determine the association and dissociationrate constants (k+1 and k−1, respectively). Toobtain the k+1 value, known amounts of theligand and receptor are incubated together andthe amount of binding is determined as a func-tion of time. To determine the k−1, the dissocia-tion of ligand from the receptor is monitored

B

B/F

Bmax

slope = –1

Kd

Figure 1.3.2 The Scatchard (Rosenthal) plot. The specific bound (B) is plotted on the x axis, andthe ratio of specific bound to free (B/F) is plotted on the y axis. The x intercept is the maximal amountof specific binding (Bmax). The slope of the plot is the negative of the inverse of the equilibriumbinding dissociation constant (Kd).


1.3.4


Binding

over time. For examples of kinetic experimentsand their analysis, see Determination of RateConstants. When the L*R binding reaction issimple bimolecular, the semilogarithmic plotsof transformed binding data are linear, and theslopes of such plots are used to determine thek+1 and k−1 values. When the ratio of the tworate constants, determined by kinetic experi-ments, is found to approximate a value of Kd

that has been determined independently in anequilibrium binding assay, there is evidencethat the ligand-receptor reaction is simple bi-molecular. In cases where the receptor-ligandreaction is more complex, it is necessary to usea computer with an appropriate model to deter-mine rate and equilibrium constants (see Useof Computer Modeling Techniques).

GUIDELINES FOR ESTABLISHINGA RADIOLIGAND BINDING ASSAY

Radioligand SelectionThe selection of the radioligand depends on

ligand stability, specific activity, and pharma-cological selectivity. It is always preferable,when possible, to use an antagonist radioligandthat is able to recognize and bind to the receptorregardless of whether the receptor is coupled tomembrane-associated signal transduction ele-

ments (e.g., G proteins) or is in a desensitizedstate. Antagonists bind to receptors with muchhigher affinity than do agonists. Additionally,agonists induce conformational changes in re-ceptor-effector complexes that can cause li-gand-receptor complexes to exist in multiplestates with different binding potencies. Anotheradvantage of antagonist radioligands is thatthey do not activate the receptor, which, in thecase of binding with metabolically active cells,could result in the desensitization of the site.Agonists tend to label only a portion of theactual receptor present. Almost all receptorsexist at concentrations of less than 10 pmol/mgprotein, and usually considerably less. Forthese reasons, most binding assays are designedfor labeled antagonists.

In many cases, the radioligand is commer-cially available from either NEN Life Sciencesor Amersham. For many receptors there areseveral radioligands that may be used. Theradioligand is usually labeled with tritium (3H),although 32P, 33P, or 35S can also be used (Fileret al., 1989). With peptides and proteins, tyro-sine residues can be labeled with 125I or 123I.The effect of incorporation of a radioactivemoiety must be evaluated to determine that thepharmacological properties of the ligand arenot significantly altered. This is a particular

0

10

20

30

40

50

60

–9 –8 –7 –6 –5 –4 –3 –2

log[carbachol] (M)

[3H

]QN

B b

ound

(fm

ol/m

illio

n ce

lls)

Figure 1.3.3 Competition between a radiolabeled antagonist and an unlabeled agonist for mus-carinic receptors on N1E-115 cells. [3H]Quinuclidinyl benzilate ([3H]QNB; 0.2 nM) was incubatedwith 200,000 intact cells/tube and various concentrations of carbachol for 75 min at 15°C, and thesuspensions were rapidly filtered to terminate the reactions. The level of nonspecific binding wasdetermined using 1 µM atropine.


1.3.5

Receptor Binding

concern with iodine radionuclides because oftheir size. The specific activity of the isotope,measured either in bequerels (Bq, where 1 Bq= 1 disintegration/sec) or in Curies/mmol(Ci/mmol, where 1 Ci = 3.7 × 1010 Bq), mustbe sufficiently high to allow detection of low-abundance binding sites. In general, com-pounds with a specific activity of <20 Ci/mmoldo not make good radioligands. Producing 14C-labeled ligands of sufficiently high specificactivity is expensive and difficult, so they arerarely used. After labeling, the radioligand mustbe purified. It is prudent to routinely verify thepurity of the starting material, whether it ispurchased or synthesized in the lab (Filer et al.,1989).

StabilityThe level of purity of the radioligand must

be assayed periodically. In some cases the ra-dioligand requires special storage procedures(e.g., the addition of antioxidants or proteaseinhibitors, in the case of a peptide radioligand)to slow or prevent its degradation. These pro-cedures are similar to those used to prevent thedegradation of receptors in the tissue prepara-tion (see Tissue Preparation, discussion on re-ceptor stability).

Affinity and pharmacological selectivityThe development of a binding assay and its

subsequent validation requires the demonstra-tion of high-affinity binding of the radioligandto the receptor. A high-affinity radioligand isdesirable because it allows separation of boundfrom free ligand by filtration. A high-affinityligand-receptor complex will not dissociatesignificantly during filtration. For further de-tails on the advantages of filtration over cen-trifugation as a separation method, see Separa-tion of the Receptor-Ligand Complex (L*R)from Unbound (Free) Ligand.

In selecting a radioligand, the primary con-sideration is its pharmacological selectivity forthe receptor of interest, e.g., whether the ligandbinds only to the targeted receptor. The majorityof commercially available ligands have suffi-cient selectivity (i.e., they are >100 times morespecific for their target receptor than for othersites). The receptor selectivity of the radioli-gand at the concentration(s) used must be takeninto consideration, since the specificity of acompound can vary with concentration. Athigher radioligand concentrations, interactionsmay occur with other, nontargeted receptors. Ifit is not possible to obtain a selective ligand, itmay be possible to block binding of the ligand

to nontargeted receptors with another unla-beled selective compound, thus reducing theinherent complexity of the data analysis.

Optically active radioligandsIf a ligand is racemic containing a chiral

center, use of the stereochemically active formof the radioligand is preferable. With few ex-ceptions, most receptors will differentiate be-tween the optical isomers of compounds. Thatis, the receptor will typically bind one of theisomers with higher affinity than the other.

Tissue Preparation

Tissue disruption and washingGenerally, the tissue must be disrupted to

increase access of the radioligand to the recep-tor population. A tissue homogenizer (e.g.,Polytron) or a sonicator is usually used to dis-rupt tissue for use in a binding assay. Typically,the tissue is kept cold or frozen until it isdisrupted in the ice-cold homogenizing vesseland buffer. Allowing the temperature to rise, orrunning the homogenizer/sonicator for toolong, can result in significant loss of receptorbinding from denaturation or from activationof proteolysis.

Tissue disruption is not necessary when per-forming in situ receptor autoradiography(where thin tissue sections, prepared using amicrotome, are used to retain anatomical rela-tionships), or when performing binding assaysusing intact cellular preparations (e.g., to ad-dress regulation of binding sites; UNIT 8.1). Be-cause of diffusion barriers, release of interme-diary agents, uptake of radioligand, and otherfactors, the relative affinity of compounds forbinding sites in intact cellular preparations maydiffer from those found using tissue homogen-ates, receptors removed from their membraneenvironment, or those transfected into novelcell systems (Kenakin, 1993).

Endogenous ligands for the targeted recep-tor can interfere with radioligand binding. Thisis prevented by using a series of washing stepsand incubations (with or without degradativeenzymes, depending on the ligand in question)to remove the endogenous ligand. Extensivewashing (repeated pelleting via centrifugationfollowed by resuspension in fresh buffer) isrequired to remove endogenous γ-amino-butyric acid (GABA). For monoamines, incu-bation at 37°C is required to allow endogenousenzymes to degrade the endogenous ligand(e.g., norepinephrine, dopamine). For adeno-sine receptors, incubation with the catabolic


1.3.6


Binding

enzyme adenosine deaminase (ADA) is re-quired to remove endogenous adenosine. Simi-larly, binding to G protein–coupled receptors(GPCRs) can be affected by GTP, which ispresent in relatively high concentrations in thecell. The nucleotide should be removed fromthe homogenate by washing to avoid modula-tion of the binding state of GPCRs.

Buffer selectionIn most cases, a homogenization/assay buff-

er is selected that yields the highest signal-to-noise ratio for specific and nonspecific binding.As a consequence, almost all binding assays areperformed under nonphysiological conditions,in a medium having an ionic strength or pHunlike anything that would exist in vivo. Whenit is preferable to measure binding under physi-ological conditions, a solution such as KrebsRinger or Hanks’ balanced salt solution(HBSS) may be used.

Some receptor-radioligand combinationsrequire special ions. For example, opioid recep-tor binding is modulated by sodium (UNIT 1.4),GABAA receptor binding is modulated by chlo-ride (UNIT 1.7), and the N-methyl-D-aspartate(NMDA) subtype of the glutamate receptor ismodulated by magnesium.

Receptor stabilityMany receptors are stable when frozen in

situ. Tissue blocks may be kept at −80°C or inliquid nitrogen for long periods of time(months) before use in a binding assay. Bindingbehavior may change as a consequence offreeze-thaw cycles or long-term storage (>3months), and the stability of binding must beevaluated as part of the characterization of thebinding assay. When tissues are homogenized,the receptors are relatively stable as long as theyremain in their membrane phospholipid envi-ronment. However, tissue homogenization canliberate high levels of proteases, sometimesrequiring the addition of protease inhibitors(e.g., phenylmethylsulfonyl fluoride, an inhibi-tor of trypsin-like proteases) or calcium-chelat-ing salts (e.g., EDTA or EGTA) to the buffersystem in order to preserve the receptor. Like-wise, peptide radioligands are susceptible todegradation by proteases in tissue homogen-ates. When adding protease inhibitors, it isimportant to ensure that the inhibitors do notthemselves interact with the ligand. Proteolysiscan also be reduced, but not eliminated, byconducting the assay at lower temperatures.However, reducing the temperature slows reac-tions; at low temperatures, several hours may

be required for the system to achieve equilib-rium.

The receptor or ligand may also be suscep-tible to destruction in an oxidative or reductiveenvironment. For example, it may be necessaryto retain the methionine residues in a reducedstate by including a sulfhydryl reagent, such as2-mercaptoethanol or dithiothreitol, in the buff-er. Catecholamine ligands are readily oxidizedby dissolved oxygen, requiring the addition ofascorbic acid or other antioxidants to enhancetheir stability.

Binding Assay Conditions

Protein (receptor) concentrationThe equations used to analyze binding data

are based on two assumptions: that the receptorconcentration is low and that the free radioli-gand concentration (F) at the end of the assayis essentially equivalent to the concentration ofligand present at the beginning of the assay. Ifthe receptor concentration is increased suchthat F changes significantly (by virtue of asignificant proportion of the ligand beingbound), the receptor binding site affinity willbe underestimated. As a general rule, the recep-tor concentration should be <10% of the radi-oligand Kd. For example, if the Kd for theradioligand is 1 nM, the assay volume is 1 ml,and the Bmax is 100 fmol/mg tissue, the tissueconcentration in the assay should not exceed 1mg/tube. If it is important to identify the “true”Kd (that determined at an infinitely low receptorconcentration), several saturation binding as-says should be performed over a range of tissueconcentrations (typically over the range of 100to 1000 mg tissue/tube). The apparent Kd de-termined at each tissue concentration is plottedversus the tissue concentration, and the resultsextrapolated to zero tissue.

Example 1: Calculation of the amount ofexpected binding in a radioligand bindingassay

The expected amount of ligand binding isdependent in part upon the receptor concentra-tion in the assay. The majority of receptors arepresent in tissues at a concentration of 10 to1500 fmol/mg protein. Radioligands are typi-cally labeled to a specific activity of 20 to 60Ci/mmol, although iodinated radioligands havea theoretical specific activity of 2200 Ci/mmol.

In this example, an assay is conducted todetect a receptor present at 500 fmol/mg pro-tein. For each assay, 0.1 mg protein is includedin a total assay volume of 1 ml. The specific


1.3.7

Receptor Binding

activity of the radioligand is 50 Ci/mmol, thescintillation counter efficiency is 50% (1 cpm/2dpm), and 2.2 × 1012 dpm correspond to 1 Ci.If one ligand molecule binds to each receptor,the amount of radioactivity associated with10−15 mole (1 fmol) of receptor molecules is:

If the binding sites are fully occupied with theradioligand, the amount of specific binding perassay tube is:

TemperatureMost receptor proteins, and many proteins

involved in signal transduction, are embeddedin a lipid bilayer. Conformational changes aredependent in part on the constitution of thelipids in the cell membrane, from both a bulkperspective and a microscopic level. Receptorconformation may also vary as a function of theintrinsic ligand efficacy. The binding of a ligandto a receptor involves the displacement of watermolecules from the binding site and the forma-tion of noncovalent bonds between the ligandand receptor. Receptor- and ligand-specific dif-ferences exist in the chemical nature of thesebonds and the amount of water displaced. Im-portantly, all these processes are affected bytemperature.

From a practical viewpoint, it is importantto control the incubation temperature to reducevariability in the assay. From a theoretical per-spective, the dependence of equilibrium bind-ing on temperature provides insight into the mo-lecular nature of ligand-receptor interactions.

Differences in the enthalpy or entropy ofbinding among receptors in different tissueshave been used to support the concept of dis-tinct opioid receptor subtypes (Wild et al.,1994). The thermodynamics of equilibriumbinding is also used to differentiate betweenmodes of ligand-receptor interaction. For ex-ample, the effect of temperature on β-adreno-

ceptor binding is more pronounced withagonists (for which binding is largely enthalpicin nature) than with antagonists (for whichbinding mainly involves a decrease in entropy;Weiland et al., 1979). Agonist binding to adeno-sine receptors is entropy-driven, which is inter-preted to result from removal of water from thebinding pocket (Borea et al., 1996). Agonistbinding to the GABAA receptor is also entropy-driven. In this case, conformational changes inthis multimeric ion channel receptor to producean active conformation have been used to ex-plain differences between agonists and antago-nists (Maksay, 1994). For muscarinic receptors,the hydrogen bonding potential of ligand resi-dues, rather than agonist efficacy, appears to bethe main determinant of binding thermodynam-ics (Waelbroeck et al., 1993).

Binding assays can be performed at a varietyof temperatures, depending on the require-ments of the experiment. Room temperature(25°C) is convenient, but temperature variationmust be controlled to obtain reproducible re-sults. Membranes undergo a transformationfrom a liquid crystalline phase to a liquid phasethat is determined in part by the content ofunsaturated fatty acids and in part by tempera-ture. Typically, the transition temperature is∼21° to 22°C. Although Arrhenius (or van’tHoff) plots for equilibrium receptor binding toadrenergic (Contreras et al., 1986) or mus-carinic (Waelbroeck et al., 1993) receptors donot display a pronounced inflection at this tem-perature, it is conceivable that some receptorprocesses are affected by the lipid phase of themembrane. Because variations in room tem-perature can occur over the time period of theassay, they can skew the results of a given assay,or produce artifactual variability among assaysperformed over a period of time. Thus, assaysperformed at room temperature should bemaintained in a thermostatically controlledwater bath or incubator to stabilize the tempera-ture.

In some instances, the assay is performed atphysiological temperature (37°C), so the re-sults may be compared more readily to in vivoligand-receptor behavior. In other cases, bind-ing assays may be performed well below roomtemperature (e.g., on ice) to prevent proteinconformational changes such as those associ-ated with receptor desensitization, or to slowthe action of proteases. In some instances, thechoice of assay temperature and duration maybe determined empirically to provide the bestsignal-to-noise ratio for the particular receptorand ligand combination.

50

1

2 2 10

1

1

10

1

255

12

12

Ci

mmol

dpm

Ci

mmol

fmol

cpm

dpmcpm / fmol

××

× ×

=

.

Equation 1.3.5

500

1

0 1 55

1

2750

fmol

mg protein

mg protein

tube

cpm

fmol

cpm / tube

× ×

=

.

Equation 1.3.6


1.3.8


Binding

Separation of the Receptor-LigandComplex (L*R) from Unbound (Free)Ligand

Since most of the radioligand remains un-bound at the end of a binding reaction, anefficient method for its removal, without theloss or dissociation of the receptor-ligand com-plex, is necessary to accurately quantify theamount of bound ligand. Separation is usuallyperformed at low temperatures in order to re-duce the ligand dissociation rate. Bennett andYamamura (1986) have characterized variousseparation methods by considering the typicalrange of dissociation rates for radioligands.

Removal of excess, unbound radioactivityby various washing procedures allows the de-termination of bound radioactivity directly byconventional spectrometry or by use of scintil-lation proximity assays (SPA, Amersham). Theradioactivity thus determined is considered thetotal binding. However, in a typical experiment,the radioligand is bound by, adsorbed onto, orsequestered into many sites or compartments(nonspecific binding), in addition to beingbound to the receptor target (specific binding).The chemical nature of the radioligand, themethod of tissue homogenization, and tissue-specific biochemical processes all influence thedegree of nonspecific radioligand binding.

FiltrationFiltration is the most efficient and conven-

ient method of separating free from boundradioligand, because it requires less handlingand manipulation of samples. For instance,using a microtiter-plate format, nearly 300separate reactions can be terminated andwashed in less than 5 min. To terminate thereaction and wash 180 tubes using high-speedcentrifugation can take more than 3 hr. Filtra-tion is also preferable to centrifugation becausethe nonspecific binding is usually lower, as aresult of the more thorough washing of thetissue homogenate.

After incubation of the ligand with the tissuepreparation, the contents of the assay tubes (ormicrotiter plates) are aspirated onto filterswhere the tissue particles and bound ligand aretrapped, while the unbound ligand passes intothe effluent. The filters are then washed repeat-edly with cold buffer using a commerciallyavailable manifold and house vacuum. Whileglass fiber filters can be used when assayingsolubilized receptors, microfiltration is alsopossible. Filtration can be used for radioligandswith Kd values in the range of 10 to 30 nM andbelow, since the L*R complex does not disso-

ciate significantly (<10%) during the 15 secrequired to rinse the filters four or five times.

CentrifugationWhen radioligand affinity approaches a Kd

of >100 nM, rapid centrifugation using eithera microcentrifuge or a full-sized centrifuge canprovide a reliable estimate of binding. How-ever, it is more difficult to extensively wash theL*R complex to reduce the amount of unboundligand, so that the level of nonspecific bindingis usually much higher than with filtration.Centrifugation binding experiments are typi-cally performed in 1.5-ml plastic microcentri-fuge tubes or 15-ml polypropylene tubes. L*Rcomplexes are then pelleted using either a re-frigerated high-speed microcentrifuge or a re-frigerated full-sized centrifuge.

In some instances, the homogenate is lay-ered on top of an oil phase and the experimentterminated by centrifuging the L*R complexthrough the oil; the unbound radioactivity re-mains in the aqueous phase above the oil. Mi-crocentrifugation can be completed with a 60-sec burst. With a full-sized centrifuge, 5- to10-min centrifugations are required to effec-tively pellet the L*R complex, and subsequentcareful washing of the pellet (using a syringeand ice-cold buffer) removes excess unboundradioactivity. When using a low-affinity radi-oligand, the choice between the two centrifu-gation methods is decided on the basis of theevaluation of ligand binding characteristics.The microcentrifuge oil method can often resultin radioligand dissociation as the L*R complexmoves through the oil.

Other methodsMore specialized separation methods in-

clude the use of column chromatography, se-lective adsorption with activated charcoal, se-lective precipitation with salts or an antibody,and dialysis. However, these methods are rarelyused today due to their inconvenience.

Binding Specificity

Minimizing nonspecific bindingIn a typical binding assay, the radioligand

will become bound or sequestered into nonre-ceptor sites. Some nonspecific binding sites arein the tissue preparation, others may be on thefilters or centrifuge tubes or pellets used toseparate bound from unbound radioactivity.For some ligands, nonspecific binding can bereduced by presoaking filters in 0.1% poly-ethyleneimine (PEI) at room temperature for

Current Protocols in Pharmacology Supplement 8

1.3.9

Receptor Binding

30 min. Also, certain ligands, especially pep-tides and proteins, adhere to assay tubes andsignificantly reduce the concentration of freeradioligand, resulting in erroneous data. Insome cases, it is possible to prevent this bypreabsorbing an excess of unlabeled ligand tothe tubes. The best radioligands yield nonspe-cific binding well below 10% of the total bind-ing when assayed at a radioligand concentra-tion equivalent to its Kd value. However, whenthe choice of radioligand is limited, it may benecessary to perform experiments with highlevels of nonspecific binding.

Nonspecific binding behavior andquantitation

In some instances, nonspecific binding mayappear to be saturable (e.g., when the concen-tration of unlabeled drug is low, or when thedrug interacts with a receptor that is not com-pletely blocked). However, nonspecific bind-ing sites are sometimes described as nonsatur-able in the range of ligand concentrations thatare used to specifically saturate the targetedreceptor (generally <100 nM). The amount ofnonspecific binding is then linearly related toligand concentration. That is, while specificbinding describes a hyperbola with an asymp-tote at the maximal equilibrium concentrationof receptor-ligand complex, nonspecific bind-ing appears as a straight line (Fig. 1.3.1).

Nonspecific binding must be quantitated atevery concentration of receptor and radioligandby including assay tubes that contain, in addi-tion to receptor and radioligand, a 100- to 1000-fold excess of an unlabeled ligand known tobind specifically to the targeted receptor. If theunlabeled ligand is present at a concentrationsufficient to occupy more than 99% of thereceptor, it will prevent the radioligand frombinding to the receptor. The remaining boundradioactivity that is measured represents thenonspecific binding. The nonspecific bindingat each radioligand concentration is subtractedfrom the total binding to obtain the specificbinding, which is defined as that ligand boundto the pharmacologically relevant receptor (Fig.1.3.1).

Ideally, the unlabeled ligand used to definenonspecific binding should be structurally dis-similar from the radioligand in order to avoid aphenomenon known as isotope dilution. Thisrefers to the situation where an excess of anunlabeled ligand identical in structure to theradioligand provides an apparent reduction intotal binding that in reality is only a reductionin specific activity of the radiolabeled species.

If assays are conducted without taking intoaccount nonspecific binding, erroneous datacan be generated. For many binding assays,specific binding is 70% to 95% of the totalbinding, providing a good signal-to-noise ratioand reproducibility for the assay. In developingnew radioligand binding assays where neitherthe radioligand nor the assay conditions areoptimal, specific binding may be 50% or less,making the assay less reproducible and precise.As the conditions for binding assays are devel-oped empirically and are usually nonphysio-logical, the process of developing an assay isiterative and dynamic (see Developing a NewBinding Assay).

When a radioligand is known to bind to morethan one receptor and only one of these recep-tors is targeted in the binding assay, it is some-times possible to use an unlabeled (“cold”)compound that is selective for the receptor ofinterest. When this unlabeled competitor is pre-sent at the proper concentration, it displaces thespecific binding to the receptor of interest, butnot the radioactivity bound either to the otherreceptors in the preparation or to nonreceptorsites. When measuring nonspecific binding itis advisable to use the lowest possible concen-tration of unlabeled ligand, because the dis-placement of radioligand from nonspecificsites or from nontargeted receptors can occurwith excessively high concentrations.

With saturation binding, the level of nonspe-cific binding can be assessed mathematicallyby fitting the data to a model containing termsfor both the receptor-dependent binding and thenonspecific binding. The disadvantage of thismethod is the difficulty in assessing whethernonspecific binding is linear, as it should be.

Allosterism, or cooperativity, adds anotherlayer of complexity to binding studies. Thisoccurs when the ligand binds to more than onesite on a receptor, or when receptors in closeassociation with one another are influenced bythe binding of a ligand to another receptor site.Data analysis of allosterism or cooperativity isdifferent from that which applies to simplecompetitive interactions. The effect of positiveand negative cooperativity (nH > 1 and nH < 1,respectively) on equilibrium binding is shownin Figure 1.3.4 (see Graphical Methods, discus-sion on Scatchard plots and Figure 1.3.8).

Receptors with even a minor difference incomposition, such as those which occur in spe-cies orthologs, may display marked differencesin binding behavior. A classical example of thisphenomenon is the case of the human 5-HT1Db

and the rat 5-HT1B serotonin receptors. These

Supplement 8 Current Protocols in Pharmacology

1.3.10


Binding

receptors are 93% identical in amino acid se-quence, but display different pharmacologicalprofiles. Site-directed mutagenesis of threon-ine-355 in the human sequence to the aspara-gine found at this location in the rat sequenceyields a mutant human receptor that has thesame pharmacological profile as the native ratreceptor (Metcalf et al., 1992). Studies withhuman and rat neurotensin receptors provideanother example of this phenomenon (Pang etal., 1996). A β-napthalene derivative of neuro-tensin (8-13) binds more avidly to the rat thanto the human ortholog. Computer modelingsuggested that the tyrosine in the human recep-tor sequence was responsible for the differencein binding. Site-directed mutagenesis estab-lished that the difference in binding potencywas actually due to a tyrosine at residue 339 inthe human receptor sequence. Thus, when thisresidue was mutated to the phenylalanine pre-sent in the rat sequence, the binding potency

converted to that displayed with the wild typerat receptor (Pang et al., 1996).

Because receptors are composed of L-aminoacids, they bind ligands in a stereoselectivemanner. If the ligand has a chiral center andexists in optical isoforms, the receptor mayrecognize the enantiomers or diastereomerswith differing energies of binding. A recentlydeveloped glycine antagonist for the metabo-tropic glutamate receptor has 16 optical forms,each with distinct binding properties (Pellic-ciari et al., 1996). However, stereoselectivity isnot an absolutely reliable criterion. For in-stance, the binding of the R- and S-enantiomersof the nicotinic analgesic epibatidine to theα4β2 form of the nicotinic cholinergic receptor,labeled by [3H]cytisine, does not exhibit stereo-selectivity (Sullivan et al., 1994).

In a time dependence study, the on- andoff-rates for a radioligand should be compatiblewith the known rate of action of the ligand in

0 1 4 52 3

1.0

0.8

0.6

0.4

0.2

0

Fra

ctio

n bo

und

[L]/Kd

nH = 0.5

nH = 1.0

nH = 1.5

Figure 1.3.4 Effects of allosterism or cooperativity on receptor binding. The x axis is the freeconcentration of the ligand, expressed in relationship to the Kd value. The y axis is the fractionalspecific binding to the receptor, where 1.0 is equivalent to full saturation of the binding sites (Bmax).The nH is the Hill coefficient, a number that can be used to express the degree of cooperativity inthe binding reaction. When |nH| > 1, the receptors interact with positive cooperativity; when |nH| < 1,the receptors interact with negative cooperativity.


1.3.11

Receptor Binding

functional assays. For an agonist ligand that hasbeen characterized extensively in classicaldose-response studies, this rate may be known.In this instance, the association rate constantfor binding should approximate the value ob-tained in the functional assay under similar con-ditions (e.g., buffer composition, temperature).

When agonists bind to metabolically activecells, the binding characteristics may be modu-lated in several ways. The ligand may be accu-mulated or metabolized by the cells, or maycause desensitization of the receptors. Theseprocesses alter the apparent pharmacologicalcharacteristics of the L*R interaction (Motul-sky et al., 1985).

Developing a New Binding AssayAs noted above, many of the characteristics

of a binding assay are highly empirical. Thus,the buffer used, the tissue preparation, the assaytemperature, and the duration of the reactionare all derived on a trial-and-error basis. Theinitial binding experiment described below isdesigned to test each of these variables.

When developing a new binding assay, theligand must be rigorously checked for purityand stability. It is often prudent to dilute thenew radioligand in alcohol and store aliquotsat −20°C to avoid excessive radiolysis (Filer etal., 1989). The initial binding experimentshould use a thoroughly washed tissue homo-genate known to contain the receptor target.The tissue may be preincubated alone or withappropriate enzymes or detergents to removeendogenous ligands. Tissue homogenates maybe made from fresh or previously frozen tissue.In some cases, use of frozen tissue can improvethe signal-to-noise ratio.

To test a variety of assay conditions, thehomogenate is resuspended in a series of dif-ferent buffers (e.g., 50 mM Tris⋅Cl, pH 6.0, 6.5,7.0, 7.5, and 8.0; HEPES buffer; Krebs Ringer,pH 7.4) and incubated with ligand for differentperiods of time (e.g., 10, 30, 45, 60, 90 and 120min) at a variety of controlled temperatures(e.g., 4°, 22°, and 37°C). Conditions for bothtotal and nonspecific binding should be deter-mined in triplicate, and the reaction should beterminated by filtration over PEI-soaked glassfiber filters. At this point, binding will havebeen assessed as a function of temperature, pH,incubation time, and the need for ions (as as-sessed by any improvement in binding in KrebsRinger). In the initial binding assay for thebenzodiazepine receptor, a physiological bufferwas used. It was subsequently shown that 50mM Tris⋅Cl, pH 7.5, yielded the same data,

thereby reducing the time and cost of bufferpreparation.

If the signal-to-noise ratio is poor (<40%),additional trials should be performed to deter-mine more optimal conditions. There are in-stances where a radioligand has identical phar-macology to its unlabeled species, but does nothave similar binding characteristics. Thus, forunknown reasons, the radioligand may not pro-vide any specific binding at a receptor for whichoptimal binding conditions have been estab-lished for the unlabeled ligand. If no specificradioligand binding is obtained, or if there isminimal overall binding, a centrifugation assayshould be attempted to check for low-affinitybinding to the receptor. This can be done usinga microcentrifuge and conducting the assay ina small aqueous volume on top of an oil layer.The incubation is then terminated by a rapid,cold centrifugation, which pellets the L*Rcomplex, leaving the unbound radioactivity inthe aqueous layer. The tip of the polypropylenemicrocentrifuge tube can then be cut with ablade and the protein in the tip solubilized inscintillation fluid containing a detergent. Analternative is to use a high-speed (e.g., 48,000× g) centrifuge, where pelleting of the L*Rcomplex requires a 10-min centrifugation andwashing is carefully performed using ice-coldbuffer and a syringe so as not to agitate the pelletand reduce specific binding. If no binding isobserved at this time, the purity, stability, andstructure of the radioligand should be assessed.

Whether the incubation is terminated byfiltration or centrifugation, some time shouldbe spent optimizing the specific binding, per-haps by screening other unlabeled ligands. TheKd and Bmax values for the new ligand shouldbe determined by both saturation and kineticanalysis (see Analysis of Binding Data) and thesubcellular and regional distribution of specificbinding correlated with the reported functionalpharmacology of the ligand. The pharmacologyof the radioligand should be determined usinga set of unlabeled ligands that are known tointeract with the target receptor. Ideally, someof these should exist as isomers to permit as-sessment of the stereospecificity of the binding.Finally, a series of ligands thought to be inactiveat the target receptor should be assessed at aconcentration up to 100 µM to provide addi-tional information regarding the pharmacologi-cal properties and substrate selectivity of thebinding site.

Radioligand binding assay development isan iterative process. This is exemplified by thedevelopment of 4-phosphonomethyl-2-piper-


1.3.12


Binding

idinecarboxylic acid (CGS19755), a specificligand for inhibiting the NMDA receptor (Mur-phy et al., 1987, 1988). In 1985, the only selec-tive ligands for the NMDA receptor were 2-amino-5-phosphonopentanoic acid (AP-5) and2-amino-7-phosphonoheptanoic acid (AP-7),both of which have receptor affinities in themicromolar range. A rigid analog of AP-7, 3-(2-carboxypiperazine-4-yl) propyl-1-phos-phonic acid (CPP), was found to be more potentand a high-speed centrifugation binding assayusing [3H]CPP was developed (Murphy et al.,1987). The assay was time-consuming and la-borious, but provided a Kd measurement forCPP of 201 nM. The availability of this assayresulted in the identification of the even higher-affinity ligand, CGS19755 (Kd = 9 nM; Murphy

et al., 1988), which reached Phase III clinicaltrials for the treatment of stroke. BecauseCGS19755 had a high affinity for the receptor,it was the first radioligand that could be used in ahigh-throughput filtration assay for this site.

ANALYSIS OF BINDING DATAThe mathematical models used for analyz-

ing binding data are based on considerations ofmolecular interactions in solution phase. Themodels do not take into consideration the factthat, in reality, the receptor is almost always ina lipid membrane phase. In practice, however,if the concentrations of the receptor and ligandare kept low, the solution phase equations aresufficiently accurate (Kenakin, 1993; UNIT 1.2).Of the various models proposed for receptors,

A B

C D

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

1.0

0.5

0

Fra

ctio

n bo

und

Fra

ctio

n bo

und

Saturation binding

1 2 3 4 5 –2 –1 0 1 2

21 3 4 5 –2 –1 0 21

[L]/Kd log([L]/Kd)

[D]/IC50 log([D]/IC50)

Competition binding

Figure 1.3.5 Appearance of binding data using different methods of plotting. Saturation binding(A and B) and competition binding data are shown (C and D). The lefthand panels (A and C) showspecific binding (expressed as fraction bound) plotted versus ligand concentration (expressed asa concentration ratio with respect to the Kd) on the x axis, on arithmetic plots (both axes plotuntransformed values). The righthand panels (B and D) are semilogarithmic plots, which showspecific binding plotted on the y axis (untransformed) versus the logarithm of the ligand concentra-tion.


1.3.13

Receptor Binding

the occupancy model is most often invokedwhen describing radioligand binding (Fig.1.3.5, panels A and C; UNIT 1.2).

Graphical Methods

Semilogarithmic plotsThe response of a tissue to a ligand, L (or

L*, if the ligand under discussion is radioac-tive), is usually displayed as a function of thelogarithm of the ligand concentration, [L]. Theshape of the resulting curve described over alarge range of drug concentrations is sigmoidal.The center of the curve, or the inflection point,is where 50% of the total response is observed.When the binding interaction is simple bi-molecular, the slope of the fractional bindingcurve at the region of inflection in a semiloga-rithmic plot (Fig. 1.3.5B,D) is 0.576, if theamount of ligand bound is low and the totalligand concentration can be considered equalto the free ligand concentration. The value of0.576 is derived as shown in Equations 1.3.7 to1.3.13.

The concentration of bound ligand, B, is asaturable function of the concentration of freeligand (F = [L]), the Kd, and the Bmax.

Substituting [L] = Kd (at the point of half-satu-ration) into Equation 1.3.7 and differentiatinggives

If the binding is expressed fractionally, thenBmax = 1. In a semilogarithmic plot as shown inFigure 1.3.5, the x axis is dependent on log[L],not on [L]. The slope of a semilogarithmic plotmust then be the derivative, dB/d(log[L]).Equations 1.3.9 through 1.3.11 provide an ex-pression for d(log[L]) in terms of d[L].

Substituting Equation 1.3.11 into Equation1.3.8 gives

Again, the substitution [L] = Kd (at half-satu-ration) can be made, giving the slope for thebinding curve at the inflection point.

This slope should not be confused with the Hillslope (see below), which is an exponent in anequation and which will have an absolute valueof 1.0 for all of the data in Figure 1.3.5.

The sigmoidal shape of the specific bindingcurve is a consequence of the transformationof the abscissa, because in a simple arithmeticplot the curve is hyperbolic with a maximumvalue that approaches a constant ordinatevalue (Fig. 1.3.5A,C). Theoretically, the li-gand concentration must be increased to in-finity to determine the ordinate value of theasymptotes of hyperbolic or sigmoidalcurves. The asymptote must be estimated byextrapolation. A more accurate way to establishthis value is with a Scatchard plot. However,the most accurate and most mathematicallyappropriate way of determining the parametersof saturation and competition curves is a directfit to the equilibrium binding equation by non-linear regression analysis on a computer (UNIT

1.2).In a competition between a radioligand and

an unlabeled ligand (D), the position of thebinding curve in a semilogarithmic plot is afunction not only of the affinity of the unlabeledligand, but also of the affinity and concentrationof the radioligand (Fig. 1.3.6; see Example 2,below). With a high-affinity (low Kd) radioli-gand, or at higher ligand concentrations, theIC50 for the unlabeled compound will be higherand the curve will be shifted rightward (as withcurves 2 and 3 in Fig. 1.3.6), suggesting a loweraffinity of the unlabeled ligand. In analyzingsuch competition curves, the Cheng-Prusoffcorrection (Cheng and Prusoff, 1973) is used

BB

K=

×+

[ ]

[ ]maxL

L d

Equation 1.3.7

dB

d

B

K[ ]max

L d

=4

Equation 1.3.8

ln[ ] . log[ ]L L= ×2 303

Equation 1.3.9

d d d(ln[ ]) [ ] / [ ] . (log[ ])L L L L= = ×2 303

Equation 1.3.10

d d[ ] [ ] . (log[ ])L L L= × ×2 303

Equation 1.3.11

dB

d K[ ] . (log[ ])L L d× ×=

2 303

1

4

Equation 1.3.12

dB

d

K

K(log[ ])

. ..

Ld

d

=×

= =2 303

4

2 303

40 576

Equation 1.3.13


1.3.14


Binding

to convert the IC50 to Ki, which is an absolutevalue. Thus,

where Ki and IC50 refer to the unlabeled ligand,[L] is the concentration of the radioligand usedin the assay, and Kd is the equilibrium bindingdissociation constant for the radioligand. Thefollowing postulates and assumptions shouldbe kept in mind when using this correction.

First, equilibrium is assumed, because equa-tions for steady state yield invalid data whenthe binding system is not at equilibrium (Ehlertet al., 1981). If the correct kinetic equations areused in such nonequilibrium situations, it ispossible to indirectly derive the correct bindingconstants for unlabeled compounds (Schreiberet al., 1985).

Second, the reaction is presumed to be sim-ple bimolecular. If the reaction is not and if theHill slope is significantly different from unity,the resulting value is not the Ki but the K50 (a

“pseudo-Ki”), a number with little meaning(i.e., it equates to Ki only under conditions ofcompetitive inhibition). Binding is not of asimple competitive nature when (1) the recep-tors bind ligand cooperatively, (2) the receptorsare desensitized or internalized during the as-say, or (3) the receptors exist in multiple inde-pendent forms with different binding affinitiesfor the ligands.

Because of the dependence on simple bi-molecular binding, the Cheng-Prusoff correc-tion is usually inappropriate for use when anantagonist is used to inhibit the response to anagonist in a functional assay (a “null” method).Because the Hill slopes for agonist dose-re-sponse curves in functional assays are fre-quently of nonunit value, simple bimolecularmodels cannot be used. It is thus inappropriateto use the Cheng-Prusoff correction to calculatethe Ki value for an antagonist in a functionalassay unless it can be shown that the Hill slopefor the agonist dose-response curve is unity(Lazareno and Birdsall, 1993).

Third, the concentration of receptors in thebinding assay must be much lower than the

KK

id

IC

L=

+50

1 [ ] /

Equation 1.3.14

curve 1 2 3

–7 –6 –5 –4 –3 –20

0.2

0.4

0.6

0.8

1.0

Fra

ctio

n bo

und

log[D] (M)

Figure 1.3.6 Effect of increasing the radioligand concentration in a competition binding assay. Thisis a semilogarithmic plot of specific binding (expressed on the y axis as fraction of maximal binding)in a hypothetical experiment. The drug D is an unlabeled competitor and the logarithm of itsconcentration is plotted on the x axis. Curves 1, 2, and 3 represent the appearance of the data whenprogressively larger concentrations of the radioligand are used. For further explanation, seeExample 2: The Cheng and Prusoff Correction.


1.3.15

Receptor Binding

binding constants for the ligands since higherreceptor concentrations require the use of amore complex correction to obtain the Ki value(Jacobs et al., 1975; Linden, 1982).

Example 2: The Cheng-Prusoff correctionIn Figure 1.3.6, bound ligand from an assay

experiment is shown as a function of log[D],where [D] is the concentration of a competingunlabeled ligand. The concentrations of radio-ligand ([L*]) for curves 1, 2, and 3 are 1 nM,10 nM, and 30 nM, respectively. Note that theabsolute levels of specifically bound radioli-gand are normalized to 100% for all threecurves. The equilibrium dissociation constantfor the radioligand (Kd) under these conditionsis 0.5 nM, and the shapes of the displacementcurves are consistent with a simple competitiveinteraction (Hill slope = 1). By computer analy-sis, the IC50 values for the unlabeled compoundwere found to be 3 µM, 21 µM, and 61 µM forcurves 1, 2, and 3, respectively. The followingcalculations demonstrate that the Ki for theunlabeled compound is 1 µM in all three ex-periments.

Curve 1Radioligand concentration = 1 nMRadioligand Kd = 0.5 nMCheng-Prusoff correction =

1 + (1 nM/0.5 nM) = 3Ki of the competitor = IC50/3 = 3 µM/3 =

1 µM


1 + (10 nM/0.5 nM) = 21Ki of the competitor = IC50/21 =

21 µM/21 = 1 µM


1 + (30 nM/0.5 nM) = 61Ki of the competitor = IC50/61 =

61 µM/61 = 1 µM

The Scatchard (Rosenthal) plotThis method was originally described by

Scatchard (1949), and was refined by Rosenthal(1967), for calculating the binding propertiesof ligands bound to proteins in solution. TheScatchard transformation is based on the occu-

pancy theory of receptor models, as previouslyshown in Equation 1.3.1.

At equilibrium, the forward and reverse re-actions are equal in velocity, and the Kd is givenas

Bmax is the total number of receptors.

By solving for [R] (Equation 1.3.18), substitut-ing into Equation 1.3.16, and rearranging, [LR]is determined as a function of the concentrationof free ligand ([L]), Kd, and Bmax (Equation1.3.19). This is equivalent to Equation 1.3.7.

As LR is the bound ligand and L is the freeligand, Equation 1.3.19 can be rewritten:

This can be rearranged to the form used in theScatchard plot.

This transformation is extensively used inanalysis of receptor binding in membranepreparations. Thus, following an equilibriumsaturation experiment, the ratio of bound/freecan be plotted versus bound (Fig. 1.3.7), with

L R LR++

−

k

k

1

1

�

Equation 1.3.15

KdL R

LR=

×[ ] [ ]

[ ]

Equation 1.3.16

Bmax [ ] [ ]= +R LR

Equation 1.3.17

[ ] [ ]maxR LR= −B

Equation 1.3.18

[ ][ ]

[ ]maxLR

L

L d

=×

+B

K

Equation 1.3.19

boundfree

free d

=××

B

Kmax

Equation 1.3.20

bound

free

bound

d d

= −B

K Kmax

Equation 1.3.21


1.3.16


Binding

the x intercept representing the maximum num-ber of binding sites (the Bmax) and the slopebeing used to determine the Kd (slope = −1/Kd).Example 3 (below) describes the data analysisused to produce this graph.

Until computers were used to facilitate thefitting of data with models using nonlinearregression methods, the Scatchard plot was thestandard way to determine the Bmax and Kd forreceptor binding sites. It has been extensivelyand justifiably criticized for its deficiencies,especially when compared to nonlinear curvefitting methods (Rodbard et al., 1980; Feldman,1983; Burgisser, 1984). Most notably, the trans-formation of the binding data produced bydividing the bound ligand by the free ligandresults in distortion, such that the upper extrem-ity of the Scatchard plot (region of low freeligand concentration) is overemphasized in alinear regression (Rodbard et al., 1980). Thisresults in a skewed determination of Bmax andKd. Other assay factors such as nonequilibrium

conditions, radioligand accumulation or degra-dation in the tissue, or receptor isomerization,are also magnified by a Scatchard transforma-tion (Ketelslegers et al., 1984; Beck and Goren,1983).

Despite these reservations, the Scatchardplot has considerable heuristic value, particu-larly for demonstrating whether the bindingdata are simple or complex in nature. Scatchardplots that are convex (i.e., the middle of the plotis curved upward relative to the extremities)indicate positive cooperativity, while concaveplots indicate negative cooperativity or bindingsite heterogeneity (Fig. 1.3.8). Cooperativityrefers to interactions between receptors uponbinding of a ligand at multiple sites (usuallyone ligand on each receptor). With positivecooperativity, ligand binding to one of the in-teracting receptors sequentially facilitatesbinding at the other(s), while in negative coop-erativity binding is progressively less avid(Monod et al., 1965; Koshland et al., 1966).

0

100

200

0 10 20 30 40 50 60

slope = – 4.309

Kd = 0.232 nM

R = 0.979

B max = 61 fmol/mg

Bound (fmol/mg)

Bou

nd/f

ree

(fm

ol/m

g/n

M)

Figure 1.3.7 Scatchard (Rosenthal) plot of the equilibrium binding of [3H]NMS to muscarinicreceptors on N1E-115 neuroblastoma cells. The data shown in Figure 1.3.1 and Table 1.3.1 wereused to construct this plot, and a full discussion is given in the text. The linear regression correlationcoefficient for this plot (R) is 0.979, the Kd value (the negative inverse of the slope) is 0.232 nM,and the Bmax (the x intercept) is 61 fmol/mg. The data in Figure 1.3.7 were normalized to mg protein,whereas the data in Figure 1.3.1 are expressed in fmol/tube specific binding.


1.3.17

Receptor Binding

Allosterism is a variant of cooperativity wherea single receptor molecule or complex containsdistinct but interacting binding sites for two ormore ligands. The seminal example of alloster-ism is that of the GABAA/benzodiazepine li-gand-gated receptor (Rabow et al., 1995).

Example 3: Scatchard analysisThis example is based on the experiment

shown in Figure 1.3.1. The untransformedbinding data are shown in Table 1.3.1. Sixconcentrations (0.06 nM to 1.4 nM) of[3H]NMS were incubated with intact N1E-115mouse neuroblastoma cells (0.5 mg tissue in a2-ml assay) at 37°C until equilibrium wasachieved (60 min). Total binding of the radio-ligand was measured in triplicate at each con-centration, and the amount of nonspecific bind-ing was determined in duplicate at each con-centration by adding 1 mM atropine to sometubes to displace the radioligand. The specificactivity of [3H]NMS was 53.5 Ci/mmol and theefficiency of the scintillation counter was 43%.

The concentrations of the radioligand used inthe assay were determined by measuring theradioactivity in two aliquots of each dilution ofstock.

First, it is necessary to calculate the factorneeded to convert cpm to fmoles of ligand.Since the specific activity of the radioligandwas 53.4 Ci/mmol and there are 2.2 × 1012

dpm/Ci, it follows that there are 53.4 × 2.2 ×1012 dpm/mmol ligand (or 117.5 dpm/fmolligand). With a 43% counting efficiency (1 dpm= 0.43 cpm), there are 50.5 cpm/fmol ligand.As an example, the results of converting totalbinding from cpm to fmol using this factor areshown in Table 1.3.1.

For each of the six points in this assay, thefree concentration of [3H]NMS is calculated bysubtracting the total radioactivity bound to thefilter from the total amount of ligand added tothe tube. For example, at the lowest ligandconcentration, 123 − 8.3 = 114.7 fmol. Thus,the lowest free concentration of [3H]NMS is114.7 fmol/2 ml, or 0.0574 nM.

100

50

020 40 60 80 1000

Bound (% B max)

Bou

nd/f

ree

(% B

/[L]

)nH = 1.5

nH = 1.0 nH = 0.5

Figure 1.3.8 Effect of allosterism or cooperativity on the appearance of binding when shown ona Scatchard (Rosenthal) plot. When multiple sites interact in negative cooperativity (nH < 1), theplot of binding is concave. When multiple sites interact with positive cooperativity (nH > 1), theScatchard transform is convex. The normal appearance of the Scatchard plot for simple bimolecularinteractions (no cooperativity; nH = 1), is the straight-line plot. Note that binding of the ligand tomultiple independent sites which exhibit different binding affinities will produce a concave Scatchardplot (apparent negative cooperativity).


1.3.18


Binding

In this calculation, nonspecific binding isconsidered to be removed from the reaction.Note that, depending on its physical or biologi-cal nature, nonspecific binding may be readilyreversible, in which case nonspecifically boundligand can be considered available for specificbinding at the target receptor. In such a case,the amount of free radioligand at each point inthe saturation curve can be calculated as thetotal ligand added minus the specific binding.

The amount of specifically bound [3H]NMSat each point is determined by subtracting thenonspecific binding from the total binding. Atthe lowest concentration of [3H]NMS used,nonspecific binding is 100 cpm, which convertsto 2.0 fmol. Specific binding is thus 8.3 − 2.0= 6.3 fmol. This value is generally normalizedto the tissue concentration: 6.3 fmol/0.5 mgtissue = 12.6 fmol/mg tissue.

Although not shown here, an alternativeprocedure for determining nonspecific bindingtakes advantage of its linearity (see BindingSpecificity). In this case, the nonspecificallybound radioligand is plotted versus the total[3H]NMS added, and linear regression is usedto derive more accurate estimates of the non-specific binding at each point. Ideally, non-spe-

cific binding would be evaluated by both meth-ods, although the latter is more involved.

In Table 1.3.2, transformations of free andbound radioligand concentrations suitable forScatchard analysis are shown. For theScatchard plot, bound/free is plotted against thespecifically bound [3H]NMS and the data areexamined for linearity (Fig. 1.3.7). In this case,the data appear to be linear since the data pointscan be fitted with a straight line. The slope ofthis line is −1/Kd in units of nM−1, with the xintercept representing Bmax, in fmol/mg tissue.For this particular plot, the slope is −4.309nM−1, which yields a Kd value of 0.232 nM. TheBmax is 61 fmol/mg tissue. Compare theScatchard plot (Fig. 1.3.7) with the plot of theuntransformed data that has not been normal-ized to the tissue concentration (Fig. 1.3.1).

The Hill plotThis analysis was originally intended to

demonstrate the number of binding sites foroxygen on hemoglobin (a protein that consistsof four subunits) and the positively cooperativenature of this binding process (Hill, 1910). Theamount of bound ligand (B) is expressed as a

Table 1.3.1 Sample Raw Data for Scatchard Analysis

Total [3H]NMS concentration Total bindinga (cpm) Nonspecificbindinga (cpm)

Average totalbinding (fmol)

0.061 nM (123 fmol/tube) 455, 395, 413 (421) 98, 101 (100) 8.3

0.12 nM (240 fmol/tube) 593, 643, 634 (623) 127, 121 (124) 12.3

0.233 nM (466 fmol/tube) 985, 942, 983 (970) 133, 144 (138) 19.2

0.47 nM (930 fmol/tube) 1250, 1249, 1332 (1277) 183, 182 (182) 25.3

0.87 nM (1747 fmol/tube) 1442, 1438, 1495 (1458) 266, 255 (261) 28.9

1.41 nM (2816 fmol/tube) 1382, 1785, 1769 (1645) 433, 442 (438) 32.6aReplicate cpm values shown, with average cpm indicated in parentheses.

Table 1.3.2 Sample Transformed Data forScatchard Analysis

Free [3H]NMS(nM)

Specificallybound [3H]NMS

(fmol/mg)

Bound/free(fmol/mg⋅nM)

0.0574 12.7 221.50.114 19.8 173.50.223 33 147.80.452 43.4 95.90.859 47.4 55.21.392 47.8 34.3


1.3.19

Receptor Binding

saturable function of the concentration of thefree ligand (F):

where n indicates the number of binding sitesand Kd′ is an amalgamation of dissociationconstants for the individual subunits, whichcan be derived mathematically. A rearrange-ment of this equation yields an expression ofbinding as the logarithm of the ratio of occu-pied sites divided by unoccupied sites. In thisequation the nomenclature has reverted to Kd,which can be viewed as the “empirical” or“observed” Kd.

A plot of this term versus the logarithm ofthe concentration of the free ligand is thus alogit-log plot, except for the use of the loga-rithm to the base 10 for the Hill plot and the useof the natural logarithm (ln) in the logit-logplot. An example of a Hill plot is shown inFigure 1.3.9 (see Example 4 below for details

on the construction of this particular plot). Then in this equation is referred to as the Hill slope,and it is often abbreviated as nH. Hill plots canalso be constructed for competition curves, inwhich case nH has a negative sign. It is notnecessary to know the Bmax to construct a Hillplot, because the data can be expressed as per-cent bound (%B) with the value on the y axisbecoming the logarithm of %B/(100 − %B). Forexample, in a competition experiment, data fora given concentration of radioligand are plottedas the logarithm of %B/(100 − %B) versus thelogarithm of the concentration of the unlabeledligand (log[D]). The displacement of a radioli-gand by an unlabeled ligand yields a Hill plotwith a negative slope. Thus, if the competitionbetween the radioligand and the unlabeledcompound is simple competitive at a singlebinding site in the preparation, then nH = −1. Inthis case, logF equals the logIC50 of the displac-ing agent at y = 0. If the equilibrium bindingconstant and the concentration for the radioli-gand are known, these values can be used in theCheng-Prusoff equation (see Equation 1.3.14)to obtain the Ki of the unlabeled ligand.

Typically, the Hill plot is used to determinethe complexity of binding. Simple bimolecularinteractions yield a Hill slope of unity. How-ever, when the absolute value of the Hill slopeis statistically different from unity it can mean

BB F

K F=

×

′ +max

n

nd

Equation 1.3.22

log log logmax

B

B Bn F K

−= −

d

Equation 1.3.23

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

–11 –10 –9 –8

slope = 0.89

x intercept = – 9.6521(0.228 nM)lo

gB

Bm

ax –

B(

)

logF (M)

Figure 1.3.9 Hill plot for the saturation binding of [3H]NMS to muscarinic receptors on N1E-115cells. The data used to make Figures 1.3.1 and 1.3.7 and Table 1.3.1 were used for this Hill plot.This is a log-log plot, in which the logarithm of the ratio of bound to unbound is plotted on the y axis,and the logarithm of the free concentration of the radioligand is plotted on the x axis. The Hill slopeis 0.89, which in this case is not significantly different from unity (P > 0.05).


1.3.20


Binding

that the simple model is not appropriate. Avalue >1 may be indicative of positive coopera-tivity, although the value of the Hill slope doesnot necessarily quantify the number of distinctligand binding sites, as Hill originally intended.With neurotransmitter receptors, the bindingisotherms of 3H-labeled antagonists commonlyyield Hill slopes of unity, while agonist bindingproduces Hill plots with slopes significantly<1.

As an example, Figure 1.3.10 shows a Hillplot of the experiment shown in Figure 1.3.3.In this case, the Hill slope is −0.25. This unusu-ally low value is a consequence of the bindingof carbachol to at least three distinct sites in theN1E-115 cells, each with a distinct bindingaffinity (0.26 nM, 0.1 µM, and 25.7 µM). Thesecells express both the m1 and m4 muscarinicreceptor subtypes (Yasuda et al., 1993), and thebinding of an agonist induces two differentaffinity states for each subtype, giving rise tovery complex competition curves (Fig.1.3.3).

If the absolute value of the Hill slope issignificantly different from unity, the Cheng-

Prusoff equation is not valid to convert an IC50

to a Kd value. Rather, the appropriate mathe-matical model and a robust fitting methodshould be used for analysis of such bindingdata. For example, the low Hill slope valuesdetermined for agonist binding to receptors thatcouple with GTP-binding proteins indicate thepresence of multiple binding states for a singlemolecular class of receptor protein, suggestinga ternary complex. Alternatively, the data mightsuggest the existence of multiple, noninteract-ing receptor subtypes, in which case a modelcontaining independent binding capacities andligand binding constants should be used. Cer-tain experimental manipulations may simplifythe analysis, including the use of preliminaryanalyses to quantify the number of each recep-tor subtype present, or the use of a GTP analogto convert the receptors to a single agonistbinding state.

Example 4: Construction of a Hill plotThe data used in the Scatchard analysis (Ta-

ble 1.3.2) can be transformed to the data shown

–10 –9 –8 –7 –6 –5 –4

1.0

0.8

0.6

0.4

0.2

0

–0.2

–0.4

–0.6

–0.8

–1.0

log[carbachol] (M)

log (

)%

B10

0 –

%B

nH = –0.25

Figure 1.3.10 Hill plot for the competition between [3H]NMS and carbachol for muscarinicreceptors on N1E-115 cells. The binding data shown in Figure 1.3.3 were used to construct thisplot. The ratio of bound/unbound in this case was expressed using percentages of maximal specificbinding (%B), rather than the Bmax (as was done in Figure 1.3.9). The absolute value of the Hillslope in this case was 0.25, which was significantly different from unity (P > 0.001). The apparentnegative cooperativity results from the binding of carbachol to three different sites on N1E-115 cellswith different affinities.


1.3.21

Receptor Binding

in Table 1.3.3. While the first three columns areself-explanatory, the Bmax determined in theScatchard plot was used in the calculations forthe final two columns.

The Hill plot is constructed by plotting thelast column on the ordinate versus the logFcolumn on the abscissa (Fig. 1.3.9). As shown,the Hill plot of a radioligand binding site satu-ration curve has a positive slope that passesthrough the value of y = 0 (when the bindingsites are 50% occupied) at the point at whichlogF = logKd. The absolute value of the Hillslope is unity if the binding is simple bimolecu-lar (nH = 1), and logF at y = 0 provides a truemeasure of logKd for the radioligand. Indeed,it is probably a more accurate method than theScatchard plot for deriving Kd, as two plots areused in the derivation. In this example, nH =0.89 and the x intercept = −9.6521, correspond-ing to a Kd of 0.228 nM, which approximatesthe value determined in the Scatchard analysis.Alternatively, instead of using the ScatchardBmax, the maximal observed binding can beused, as for the example shown in Figure 1.3.10.

The linear regression correlation coefficient(R) for this Hill plot is 0.979. Using the slopeand correlation coefficient, standard statisticalprocedures can be used to determine whetherthe slope is significantly different from unity.Computer programs such as PHARM/PCS(Tallarida and Murray, 1986) are also availablefor this purpose. In the present example, thePHARM/PCS program indicates that the slopeis not significantly different from unity (P <0.05), which can be interpreted to mean that thebinding is probably simple bimolecular. This isalso consistent with the interpretation of thedata as developed in the Scatchard plot.

Determination of Rate Constants

Dissociation rate constantFor most binding studies it is easier to de-

termine the dissociation rate constant than theassociation rate constant. This is because the

dissociation of the ligand from the receptor isusually a unimolecular process governed onlyby the off-rate, and because it is not necessaryto know the number of receptors in the assay,as is the case for determination of the associa-tion rate constant. A plot of the logarithm of theconcentration of ligand bound at time t minusthat bound at t0 versus time invariably yields astraight line for the dissociation of a ligand froma single receptor. However, if the receptor iso-merizes, it distributes into multiple forms withunique dissociation rate constants, yielding acomplex curve. This is indistinguishable fromthe situation when the ligand binds to multiplereceptors. Additional analysis is required toestablish that multiple binding states of a singlereceptor type are present (Jarv et al., 1979).

To determine the dissociation rate constant,the receptor and radioligand are incubated untilbinding equilibrium is reached. The completebinding reaction (previously shown in Equa-tion 1.3.1) is

The forward reaction is eliminated either byrapidly diluting the assay mixture to an ap-proximation of infinite volume or by addingexcess unlabeled ligand.

The rate of this reaction is modified from Equa-tion 1.3.3.

Following separation of the bound and freeradioligand, the only ligand measured is thatbound to receptor, which decreases over time.

L R L R* *++

−

k

k

1

1

�

Equation 1.3.24

L R L R* *+−

← k 1

Equation 1.3.25

− = ×−d dt k[ * ] / [ * ]L R L R1

Equation 1.3.26

Table 1.3.3 Sample Transformed Data for Constructing a Hill Plot

B (fmol/mg) F (nM) logF B/(Bmax − B) log[B/(Bmax − B)]

12.7 0.0574 −10.24 0.2629 −0.580219.8 0.114 −9.94 0.4806 −0.318233 0.223 −9.65 1.1786 0.071443.4 0.452 −9.34 2.4659 0.39247.4 0.859 −9.07 3.4853 0.542247.8 1.392 −8.86 3.6212 0.5589


1.3.22


Binding

The dissociation rate constant is then deter-mined from the slope of a plot of the logarithmof the ratio of bound ligand versus time. Thisis shown in Equation 1.3.29, which is derivedfrom Equation 1.3.26 in the following manner.Equation 1.3.26 is rearranged,

and then integrated to give

The term c is a constant of integration equiva-lent to ln[L*R0], the natural logarithm of theamount of bound ligand at t = 0, when thedissociation experiment begins. The completeequation is

where [L*Rt] is the amount of specificallybound radioligand at a given time t, [L*R0] isthe amount of specifically bound radioligandat t = 0 (i.e., at equilibrium), and k−1 is thedissociation rate constant (in units of time−1).Thus, a plot of ln([L*Rt] / [L*R0]) versus timeyields a straight line with a slope of −k−1. Whenthere are multiple states or there are multiplebinding sites that differ in their dissociation rateconstants, this plot is nonlinear and the data arebest analyzed by direct fitting to the appropriateequation (see Use of Computer Modeling Tech-niques), rather than by determining the slopesfrom the plot.

A special binding assay method that makesuse of the differential dissociation rates of ra-dioligands from a heterogeneous receptor pop-ulation is exemplified by the elegant work ofChristophe and associates (Waelbroeck et al.,1990). Muscarinic receptors are encoded byfive genes, and four of the resultant receptorsubtypes are expressed at significant levels inbrain tissue. Most antagonists, including NMS,bind with the same, or nearly the same, affinityto these receptor subtypes. However, NMS dis-sociates from muscarinic receptors with sig-nificantly differing off-rates. In a competitionbinding assay, the unlabeled ligand will com-pete more effectively with a subtype that has afaster dissociation rate. Thus, at carefully se-

lected time points, the differential dissociationof [3H]NMS can be used to reduce radioligandbinding to a particular receptor subtype to in-significance, simplifying the analysis of itsbinding to the remaining receptor populations.

Example 5: Determination of thedissociation rate constant

The binding of [3H]NMS to muscarinic re-ceptors in intact N1E-115 mouse neuroblas-toma cells at 37°C was studied in a 2-ml assayusing an isotonic physiological phosphate buff-er at pH 7.4. The assay was performed in twostages. In the first stage, [3H]NMS binding wasallowed to reach equilibrium by incubating300,000 cells/tube with 0.56 nM radioligandfor 45 min at 37°C. In the second stage, a highconcentration (10 µM) of unlabeled NMS wasadded at various times to the preequilibratedreactions to permit analysis of the dissociationof [3H]NMS over a period ranging from 30 secto 45 min. A 24-well filtration manifold wasused to separate bound from free ligand. Sincethe dissociation experiment involved a total of48 tubes, two filter strips were used. A scheduleof incubation times, NMS addition, and filtra-tion was determined so that all the reactionmixtures for one filter (24 tubes for 12 timepoints in duplicate) were filtered at once, fol-lowed 10 min later by filtration through thesecond filter (24 tubes for 12 time points induplicate). To allow all of the tubes for the 12time points to be filtered at the same time, theschedule was reversed so that the unlabeledNMS was first added to the tubes for the 45 mindissociation of [3H]NMS and last to the tubesfor 30 sec dissociation. The amount of bindingat t = 0 was determined to be 51.8 fmol/millioncells. Nonspecific binding was assessed inseparate sets of tubes and subtracted from thetotal binding to obtain the specifically bound[3H]NMS. With this protocol, the data shownin Table 1.3.4 were obtained.

The untransformed data in the center col-umn, which is the specifically bound [3H]NMSmeasured at each nonzero time point, wereplotted versus time (left column) as shown inFigure 1.3.11A. In Figure 1.3.11B, the trans-formed data in the right column were plottedversus time. These transformed data are non-linear, as would be expected if [3H]NMS dis-sociates from more than a single class of bind-ing site. A preliminary estimate for a singlevalue for k−1 could be made by fitting a straightline through the transformed data. In this case,k−1 would be 0.08 min−1. However, the data aremore properly analyzed using a computer pro-

− = ×−d k dt[ * ] / [ * ]L R L R 1

Equation 1.3.27

ln[ * ]L R = − × +−k t c1

Equation 1.3.28

ln([ * ] / [ * ]L R L Rt 0 1= − ×−k t

Equation 1.3.29


1.3.23

Receptor Binding

gram with an appropriate binding model. Otherexperiments with N1E-115 cells have shownthat they express two subtypes of muscarinicreceptors, and it is known from the literaturethat [3H]NMS dissociates from each subtypewith a different rate. Therefore, the data inFigure 1.3.11 were fitted using a computermodel of two classes of binding sites. At themajor site (79% of the total sites), k−1 = 0.114min−1, while at the less abundant site (21% ofthe total), k−1 = 0.027 min−1.

Association rate constantIn the simple bimolecular reaction between

L* and R, the rate of formation of L*R (forwardreaction from Equation 1.3.24) is second orderwith respect to the concentration of reactants. Theforward rate is modified from Equation 1.3.2.

When the receptor and radioligand are in-itially mixed, this equation describes the for-mation of L*R when [R] = [RT], the totalconcentration of receptors present. [RT] is de-termined independently by equilibrium bind-ing and by Scatchard analysis; for details, seethe Scatchard (Rosenthal) plot (above). If theconcentration of receptors is much lower thanthe concentration of radioligand ([RT] << [L]),the amount of free ligand is not appreciablyreduced by the amount of ligand bound to thereceptor, and therefore [L] is essentially a con-stant during the assay. Under these conditions,the equation is first-order with respect to recep-tor concentration at the outset of the reaction.

The slope of the line tangent to the plot ofd[L*R] versus t, at the point at which the plotpasses through the origin, can, in principle, beused to calculate the value of k+1, if [RT] isknown (Rodbard, 1973). However, because ofthe inaccuracy of determining this tangent on amanual plot, this procedure is rarely used.

As the binding reaction proceeds, a signifi-cant amount of L*R is formed and the reversereaction begins to contribute (negatively) to theamount of L*R that can be measured at anygiven time t.

Typically, k−1 is determined first (see Dissocia-tion Rate Constant, above), and k+1 is calculatedfrom the data obtained by conducting the asso-ciation experiment at several different concen-trations of [L*]. The complete equation de-scribing the association of ligand to receptor is

where [L*Req] is the concentration of ligand-receptor complexes at equilibrium and [L*Rt]is the concentration of ligand-receptor com-plexes at any time t.

A plot of the lefthand portion of Equation1.3.32 versus time yields a straight line with aslope of (k−1 + k+1[L*]). Note that [L*] isassumed to be a constant for each associationcurve. An independent determination of k−1 is

d dt k[ * ] / [ *] [ ]L R L R= × ×+1

Equation 1.3.30

d dt k k[ * ] / ( [ *] [ ]) ( [ *R])L R L R L= × × − ×+ −1 1

Equation 1.3.31

ln[ * ]

[ * ] [ * ]( [ *])

L R

L R L RL

eq

eq t−= + ×

− +k k t1 1

Equation 1.3.32

Table 1.3.4 Sample Data for the Determination of theDissociation Rate Constant

t (min) Bt(fmol/million cells) ln(Bt/B0)

45 3.4 −2.71830 6.1 −2.13720 10.7 −1.5815 14.5 −1.27310 21.3 −0.8897 27.1 −0.6485 32.5 −0.4673 39.7 −0.2672 42.3 −0.2031 48.0 −0.0770.5 49.1 −0.055


1.3.24


Binding

unnecessary when directly fitting associationdata to this equation with a computer and aniterative technique.

Example 6: Determination of theassociation rate constant

In an experiment performed in parallel withthat shown in Example 5 above, the binding of0.56 nM [3H]NMS to muscarinic receptors inN1E-115 neuroblastoma cells was studied at37°C using 300,000 cells per 2-ml assay. A

schedule of reaction initiation and terminationtimes was established so that all of the incuba-tions were terminated at the same time usingfiltration. With this protocol, the data shown inTable 1.3.5 were obtained.

Since equilibrium was attained after 10 min,the amount of binding at 60 min was taken asBeq, the amount of binding at equilibrium, andthe amount of binding at each time t (Bt) wasused to calculate the values in the righthandcolumn. The untransformed data are plotted in

A

B

5 10 15 20 25 30 35 40 450

60

50

40

30

20

10

0

–1

–2

–3

t (min)

Bou

nd [3

H]N

MS

(fm

ol/m

illio

n ce

lls)

In(B

t/B

0)

Figure 1.3.11 Dissociation of [3H]NMS from muscarinic receptors on N1E-115 cells. The radioli-gand (0.56 nM) was incubated with intact N1E-115 cells (300,000 cells/tube) for 45 min at 37°C, atwhich time equilibrium is reached. The dissociation of radioligand from the receptors was followedfor various periods of time after the addition of 10 µM NMS, and the reactions terminated by rapidfiltration. Nonspecific binding was also determined at these various times (not shown) by adding 10µM NMS to some tubes for the duration of the experiment; the nonspecific binding did not vary withtime, and it was subtracted from the total binding to obtain the specific binding, which is plotted. (A)An arithmetic plot of the time course of dissociation. (B) Plot of the natural logarithm (ln) of theamount bound at any time (t), expressed as a fraction of the amount bound at t = 0 (i.e., B0). Notethe inflection point in the lower plot is at about t =20 min.


1.3.25

Receptor Binding

Figure 1.3.12A. The transformed data (rightcolumn) are plotted in Figure 1.3.12B. Thelatter is very nearly linear; however, close ex-amination reveals nonlinearity at times earlierthan 1 min. If this early portion is ignored anda line fitted through these data, a slope of 0.43min−1 is obtained. If this slope is set equal to(k−1 + k+1[L*]), and k−1 from the major class ofsites (0.114 min−1; see Example 5) is inserted,the value for k+1 is determined to be 0.56 nM−1

min−1. Again using the k−1 for the major site,the ratio of k−1/k+1 is 0.114/0.56 = 0.204 nM.This value approximates the equilibrium bind-ing constant (Kd) determined by Scatchard orHill analysis if it is assumed that only this classof receptor is present in N1E-115 cells. Sincethe Kd determined by kinetic analysis (on- andoff-rates) is very similar to the values deter-mined with equilibrium binding (0.232 nM,0.228 nM), it appears there is only one class ofbinding sites. Although there is small percent-age of another class of muscarinic receptorbinding sites for [3H]NMS cells, their presenceis not revealed with a Scatchard plot composedof only six points. To obtain a curvilinearScatchard plot that could reliably reveal thesecond group of binding sites (19% of the total),many more data points are required from thebinding assay (typically >20).

Direct fitting of the association data shownin Figure 1.3.12 using iterative nonlinear fittingyields a k+1 value of 0.699 nM−1 min−1. A moreaccurate determination of binding parametersis possible if the data are directly fitted with amathematical model rather than being trans-formed and analyzed on a manual plot, eventhough, in this instance, the k+1 value determined

from the plot (0.56 nM−1 min−1) is similar tothe computer-derived value (0.699 nM−1 min−

1).

Use of Computer Modeling TechniquesThere are many published and commercially

available computer programs for the analysisof binding data. Most spreadsheet or graphicalprograms (e.g., Lotus) incorporate iterative fit-ting techniques for data. In many instances, theuser can formulate the mathematical model.The choice of model and the method of fittingto the data should be defensible on both bio-logical and statistical grounds. The simplesthypothesis should be selected unless there isinformation to support a more complex model(Kenakin, 1993). For example, the addition ofa third binding site to a two-site model may beinappropriate if only two sites are known toactually exist in the tissue. The addition ofparameters to a receptor-ligand binding modelalways allows a closer fit of the model to thedata to produce a lower sum-of-squared residu-als; however, the question then becomeswhether the increase in parameters has signifi-cantly reduced the variance. To permit statisti-cal discrimination between alternate models,the data must be of sufficient quality and quan-tity to permit confident assessment of modelparameters. This means the variance should beas low as experimentally possible and thereshould be a sufficient number of data points. Ameasure of variance is calculated by determin-ing the differences between the data and thefitted curve at each point, and then squaringthese differences and summing them. Variancecan be minimized by performing replicates of

Table 1.3.5 Sample Data for the Determination of theAssociation Rate Constant

t (min) Bt(fmol/million cells) ln[Beq/(Beq − Bt)]

0.5 15.5 0.311 25.4 0.583 43.4 1.385 51.6 2.207 54.9 2.92

10 57.1 4.1115 57.5 —20 61.5 —30 59.0 —45 57.6 —60 56.1 —


1.3.26


Binding

the binding assay and, up to a point, the statis-tical power may be strengthened by increasingthe number of data points in the assay.

Receptor modelsGenerally, the receptor models used in com-

puter fitting of equilibrium binding data con-tain equations that describe the binding to onesite or to multiple, noninteracting sites. Thederivation of these models and their interpreta-tion with regard to their appearance in the

Scatchard plot can be traced back at least toFeldman (1972). With the simplest model ofmultiple, independent sites (two binding sites),the Scatchard plot is concave and the tangentsto the extremities of the curve describe twomajor populations of receptors, high-affinityand low-affinity. Because these tangents aredifficult to draw accurately, the Scatchard plotshould not be used.

Examples of the more commonly encoun-tered equations are shown below with a descrip-

60

50

40

30

20

10

5 10 15 60

1

2

3

4

5

2 4 6 8 10

A

B

Bou

nd [3

H]N

MS

(fm

ol/m

illio

n ce

lls)

t (min)

t (min)

InB

eq

Beq

– B

t(

)

Figure 1.3.12 Association of [3H]NMS to muscarinic receptors on N1E-115 cells. The radioligandconcentration was 0.56 nM, 300,000 cells/tube were used, and the temperature was 37°C. Panel(A) is a plot of the untransformed specific binding measured at various times (t) after starting theincubations. The plot in panel (B) is a logarithmic transform of the ratio of the amount bound atequilibrium (Beq) to that remaining unbound (Beq − Bt) at any time (t).

Current Protocols in Pharmacology Supplement 10

1.3.27

Receptor Binding

tion of their use. While in all such cases thereis only one independent variable ([L*] or [D])and one dependent variable ([L*R]), two ormore parameters must be determined. Theseparameters are constants in the equations to besolved by the computer using the data sets(pairs of [L*], [L*R] or [D], [L*R]) to itera-tively refine parameter estimates until themodel equation best fits the data. The parame-ters are thus adjusted so that the differencesbetween the values of [L*R] actually deter-mined in the experiment and the correspondingvalues calculated from the model are mini-mized. Normally, when a computer is used todetermine binding parameters certain con-straints are applied such as allowing only non-negative values.

A common case encountered in binding ex-periments is the presence of two independentbinding sites (usually two different receptormolecules). In a saturation equilibrium bindingassay with a radioligand (L*) that distinguishestwo sites, the amount of specifically boundradioligand [L*R] is

where B1 and B2 are the capacities of the twosites (i.e., the Bmax values for each receptor),and K1 and K2 are the equilibrium bindingdissociation constants for the radioligand at therespective sites. With this equation, the inde-pendent variable is [L*], the dependent variableis [L*R], and there are four parameters to bedetermined (B1, B2, K1, and K2). If the radioli-gand recognizes both sites with the same affin-ity, then the equation simplifies to one term onthe righthand side, and only two parametersmust be determined. Conversely, if more thantwo independent binding sites are present, ad-ditional analogous terms may be added to thetwo righthand terms shown in Equation 1.3.33.Moreover, a term describing nonspecific bind-ing can be added ([L*] × KNS), in which theamount of nonspecific binding is constrainedto be linearly dependent on [L*]. With iterativecomputer-based minimization techniques, theaddition of this term is a more accurate way toobtain an estimate of the level of nonspecificbinding.

When a radioligand (L*) is competitivelydisplaced from two independent sites that bindthe radioligand with the same Kd and that also

bind an unlabeled competitor (D) with differingaffinities, the following equation is used:

where Kd refers to the dissociation constant forthe radioligand, usually determined in a sepa-rate saturation experiment, and K1 and K2 arethe two binding constants for the unlabeleddrug D at the two independent binding sites thathave respective capacities of B1 and B2. In thiscase, the independent variable is [D] and thedependent variable is [L*R]. [L*] is fixed at aknown value and this value is inserted into themodel before iterative fitting to the data. TheKd for the radioligand is determined in inde-pendent experiments by analysis of saturationcurves (either with the computer or byScatchard analysis). The six parameters on therighthand side of Equation 1.3.34 are thus re-duced to four, which can be estimated itera-tively by the computer. Constraints are appliedduring the calculation of the four parameters sothat the computer does not attempt to fit the datawith negative parameter values. An alternateform of Equation 1.3.34 uses affinity bindingconstants (the inverse of the dissociation con-stant):

in which KA, K1′, and K2′ are the affinity con-stants (expressed in liter/mol) for the radioli-gand and displacing agent, respectively.

Multiplicity of binding sites can occur in asingle receptor population if the receptorchanges conformation and consequently bindsthe ligand with a different affinity. Formally,the two binding sites are not independent be-cause they interconvert. An example of this isthe ternary complex model (DeLean et al.,1980; Wreggett and DeLean, 1984; UNIT 1.2),which describes a mechanism by which multi-ple binding sites result from the interaction ofthe agonist-receptor complex with GTP-bind-

[ * ][ *]

[ *]

[ *]

[ *]L R

L

L

L

L=

×+

+×+

B

K

B

K1

1

2

2

Equation 1.3.33

[ * ][ *]

([ *] ) ( [ ] / )

[ *]

([ *] ) ( [ ] / )

L RL

L D

L

L D

d

d

=×

+ × +

+×

+ × +

B

K K

B

K K

1

1

2

2

1

1

Equation 1.3.34

[ * ]( [ *] )

[ *] [ ]

( [ *] )

[ *] [ ]

L RL

L D

L

L D

A

A

A

A 2

=+ ×

+ × + × ′

++ ×

+ × + × ′

B K

K K

B K

K K

1

1

2

1

1

1

1

Equation 1.3.35

Supplement 10 Current Protocols in Pharmacology

1.3.28


Binding

ing proteins (Tolkovsky and Levitzki, 1981).Agonist binding to GTP-coupled receptors insitu is typically complex, with concaveScatchard plots and Hill slopes <1.0. The useof the complete ternary complex model re-quires the determination of several additionalparameters describing the interactions of recep-tor with agonist, receptor with GTP-bindingprotein, and GTP-binding protein withGTP/GDP. In most binding experiments onlysome of these parameters can be determined,while others are estimated or determined inde-pendently. Statistically, the binding data are fitequally well by models containing two inde-pendent receptors with different affinities aswith models that describe the agonist-inducedinterconversion of a single receptor into multi-ple binding states (Abramson et al., 1987). Insuch cases, use of the goodness-of-fit afterminimization does not aid in the selection ofthe most appropriate binding model. For this,additional biochemical information is required.

Iterative fitting methodsThe equations that describe equilibrium or

time-dependent radioligand binding to recep-tors are nonlinear in one or more of their pa-rameters. This means linear regression cannotbe used to determine binding parameters with-out some kind of data transformation, such as withthe Scatchard plot or the Lineweaver-Burke plot.Since data transformation can distort the esti-mates of parameters, a better approach is to fitthe nonlinear model directly to the data. This isaccomplished by computer iteration, with theoperator supplying the model and initial esti-mates of the parameters, and the computerusing an algorithm to progressively alter theparameter values to reduce variance to a mini-mum (a level usually selected by the operator).

A number of computer programs use theGauss-Newton procedure modified by the Mar-quardt-Levenberg method of approaching theminimal sum-of-squared residuals (Marquardt,1963). Examples include ALLFIT, which isused with dose-response experiments (DeLeanet al., 1978), and LIGAND, which is popularfor binding analysis (Munson and Rodbard,1980). When using an iterative fitting routine,the mathematical model is defined or selectedand the operator supplies initial estimates of theparameter values. Using numerical approxima-tions to the derivatives of the binding equationand matrices with elements determined by thenumber of data points and parameters, the com-puter calculates new parameter values which,when inserted into the model, reduce the vari-

ance between the model and the data. With eachsuch iteration the parameter values are refinedin a step-wise manner to eventually reach theminimum variance (lowest sum-of-squared re-siduals), which is defined as the point at whichsuccessive iterations do not improve the fit(reduce the minimum) by more than a certainpredetermined fraction (e.g., 0.01). This resultof iterative fitting is referred to as convergence.The number of iterations required to convergeon a solution depends on the fitting algorithm,the quality of the data, the complexity of themodel, and the accuracy of the initial parameterestimates. In some instances, the computer willseemingly iterate forever, as if it cannot con-verge. In such cases it is likely the data qualityis poor or that some data are missing. In thisregard, the data at the extremities of the bindingcurve are particularly necessary for convergence.

With actual binding data, false (“local”)minima may be determined by these iterativemethods, and the computer may provide inac-curate parameter estimates. It is important to beaware of the possibility of encountering a localminimum when evaluating a fit provided by thecomputer. The better the data (i.e., the closerthe points lie to the fitted curve) and the moredata points collected, the more powerful is themethod in finding the true (global) minimumsum-of-squared residuals and in providinggood estimates of the parameters. To assesswhether the solution is at the lowest minimumsum of squares, run the program on the dataseveral times altering the initial values for theparameters. Even when the computer con-verges on a solution in a reasonable number ofiterations, rerun the problem by inputting an-other set of estimates for the parameters todetermine whether the same, or nearly thesame, solution is given. If so, it can be assumedthat the computer is producing a reliable set ofparameter estimates.

An alternative to minimization methods us-ing differential equations is the simplex methodof Nelder and Mead (1965). A comparison ofthe methods in their application to enzymekinetics is provided by Lam and Cross (1979).An example of the use of the simplex minimi-zation is Karlsson and Neil (1989).

Statistical analysisTo mathematically define the goodness-of-

fit of the parameter estimates in a single experi-ment, computer programs sometimes providea standard deviation or standard error for theestimate of each parameter. Because the fittingmethod is nonlinear, this parameter error is


1.3.29

Receptor Binding

itself an estimate (using a linear approximation)and cannot be used in reporting the reliabilityof parameter estimates. To obtain reliable val-ues, repeated experiments must be run andstandard statistical tests must be performed onsets of parameter estimates obtained in theindependent experiments.

For a saturation experiment based on a sim-ple bimolecular equilibrium model in whichtwo parameters (Bmax and Kd) are to be deter-mined, ten data points (sets comprised of valuesof [L*] and [L*R]) determined in triplicate areusually sufficient for calculation of good esti-mates of the two parameters. In this case, thedegrees of freedom (the number of data pointsminus the number of parameters) is eight. If theexperiment is repeated several times it is usu-ally possible to obtain standard errors of 10%or less for the parameter estimates.

When the complexity of the model is in-creased as with two binding sites, more parame-ters must be estimated (four in this case). Withgood data quality, ten data points will providereliable estimates of these four parameters, al-though the estimates will be at the outer edgeof the accuracy of the methodology (with sixdegrees of freedom). With replicate assays, theestimates of the parameters will vary several-fold. In an individual assay, the confidenceintervals for the parameters (i.e., estimates ofthe possible range of parameter values, pro-vided by the iteration routine) may reach anorder of magnitude or more. The simple way toresolve this problem is to increase the numberof data points. For a two-site model, 15 to 30(or more) data points in each independent ex-periment are typically necessary. If a morecomplex model is biologically reasonable en-tailing additional parameters, and when experi-ments produce better data (lower variance andmore data sets), the more complex mathemati-cal model may be considered. In the analysisof the competition curve shown in Figure 1.3.3,it was necessary to obtain 36 data points inquadruplicate to attain statistical reliability inthe fitting of a three-site model.

For a more complex model to be justified,there should be a sufficient improvement in fitgained by adding parameters (i.e., there shouldbe a sufficient reduction in the variance). Ingeneral, for a typical binding assay with 10 to15 data points the sum of squares should bereduced several-fold. To statistically validatethe choice of the more complex model, theF-ratio test is the most appropriate (Kenakin,1993). The data are fit to each of the twoalternate models using the iterative computer

program, ensuring that the true minimum isachieved with each fit and that the parameterestimates are reasonable. The sums-of-squaredresiduals are then obtained for each model. Theformula for calculating the F-ratio (DeLean etal., 1978) is given in Equation 1.3.36,

where SSA and SSB refer to the sum-of-squaredresiduals after fitting to models A and B, anddfA and dfB are the respective degrees of free-dom (the difference between the number of datapoints and the number of parameters).

As an example, a comparison between twomodels used to account for an experiment com-prised of ten data points is shown here. ModelA has one binding site and two parameters (Kd

and Bmax). The sum-of-squared residuals (SSA)= 57, and there are 8 degrees of freedom (dfA

= 10 data points − 2 parameters). Model B hastwo binding sites and four parameters (K1, B1,K2, and B2); SSB = 21 and dfB = 10 data points− 4 parameters = 6. Using Equation 1.3.36, theF-ratio is calculated as follows:

A table providing the F-distribution for thedesired level of probability (typically, P = 5%is used) may be consulted in a textbook onstatistics. Columns correspond to the differencein degrees of freedom (dfA − dfB, in the numera-tor of Equation 1.3.36), while rows correspondto the number of degrees of freedom for the lesscomplex model (dfB, in the denominator ofEquation 1.3.36). For the above example, theF-ratio for significance at the 5% level is 10.92,shown at the intersection of the column headedby the numeral 2 and the row headed by thenumeral 6. Since the calculated value of 5.143is less than 10.92, the two-site model is notjustified at this level of probability. The im-provement in fit gained by adding two parame-ters is not statistically justified because thevariance was not sufficiently reduced. To attainsignificance, the sum of squares would need tobe reduced approximately another two-fold, orthe number of data points would need to bedoubled.

Studies using the two-independent-binding-site model have shown that with typical data

F = − −( ) / ( )

/

SS SS df df

SS dfA B A B

B B

Equation 1.3.36

F =− −

=( ) / ( )

/.

57 21 8 6

21 65143

Equation 1.3.37


1.3.30


Binding

the iterative fitting techniques can detect a mi-nor binding site with abundance as low as 10%,if the ligand binds to the two sites with a100-fold or so difference in affinity (DeLean etal., 1982). When the sites are more equal inabundance, the difference in affinity can be aslow as 10-fold without the two sites becomingindistinguishable (McKinney et al., 1985).

The Student’s t test is typically used to assesswhether there are significant differences in pa-rameter values obtained under differing condi-tions, with P < 0.05 taken as the minimal levelof significance. The t distribution is an approxi-mation of the normal (Gaussian) distribution,and tests of population differences associatedwith the normal distribution assume that thedata follows the normal curve. As Gaddum(1945) pointed out, it is essential to verifywhether the data actually follow a normal dis-tribution before using one of these tests. It isalso necessary to assume that the variance isconstant over the range of the data being ana-lyzed. For data such as those used for dose-re-sponse curves and for receptor binding, wherethe independent variable is the compound orradioligand concentration, the EC50 or Kd val-ues are not normally distributed, although theirlogarithmic transforms are (Fleming et al.,1972). Thus, the correct way to determinewhether differences between such data sets arestatistically significant is to compute the loga-rithms of the Kd values or EC50 values, obtainthe means and standard errors of the logarith-mic values of the data, and determine the levelof significance from t tables. To present themean in arithmetic form, the antilogarithm ofthe mean is used. The standard error of the meanin arithmetic form is calculated as the productof the arithmetic mean and the standard errorof the averaged logarithmic transforms (De-Lean et al., 1982). Logarithmic transforms arenot required for the statistical analysis of bind-ing capacities (Bmax).

TROUBLESHOOTINGIndividual binding assays exhibit their own

idiosyncrasies. However, there are some ge-neric guidelines that are applicable to all bind-ing assays.

Loss of specific binding. Assess radioligandpurity and possibility of degradation. Makefresh buffers and a new tissue preparation.

Ligand pharmacology changes. Assess ra-dioligand purity and possibility of degradation.Make fresh buffers and a new tissue preparation.

Total and specific binding decrease over thecourse of the assay. The assay conditions are

such that either the radioligand or the receptorpreparation are unstable over time. Include totaland nonspecific binding assay tubes at regularintervals (e.g., every 36 tubes) to correct for thedrift.

LITERATURE CITEDAbramson, S.N., McGonigle, P., and Molinoff, P.B.

1987. Evaluation of models for analysis of radi-oligand binding data. Mol. Pharmacol. 31:103-111.

Beck, J.S. and Goren, H.J. 1983. Simulation ofassociation curves and ‘Scatchard’ plots of bind-ing reactions where ligand and receptor are de-graded or internalized. J. Recept. Res. 3:561-577.

Bennett, J.P. Jr. and Yamamura, H. 1986. Neuro-transmitter, hormone, or drug receptor bindingmethods. In Neurotransmitter Receptor Binding,2nd ed. (H.I. Yamamura, S.J. Enna, and M.J.Kuhar, eds.) pp.61-90. Raven Press, New York.

Borea, P.A., Dalpiaz, A., Varani, K., Gessi, S., andGilli, G. 1996. Binding thermodynamics at A1and A2A adenosine receptors. Life Sci. 59:1373-1388.

Burgisser, E. 1984. Radioligand-receptor bindingstudies: What’s wrong with the Scatchard analy-sis? Trends Pharmcol. Sci. 5:142-145.

Cheng, Y.-C. and Prusoff, W.H. 1973. Relationshipbetween the inhibition constant (KI) and theconcentration of inhibitor which causes 50 percent inhibition (I50) of an enzymatic reaction.Biochem. Pharmacol. 22:3099-3103.

Contreras, M.L., Wolfe, B.B., and Molinoff, P.B.1986. Thermodynamic properties of agonist in-teractions with the beta adrenergic receptor-cou-pled adenylate cyclase system. I. High- and low-affinity states of agonist binding to membrane-bound beta adrenergic receptors. J. Pharmacol.Exp. Ther. 237:154-164.

Cuatrecasas, P. and Hollenberg, M.D. 1976. Mem-brane receptors and hormone action. Adv. Pro-tein Chem. 30:251-451.

DeLean, A., Munson, P.J., and Rodbard, D. 1978.Simultaneous analysis of families of sigmoidalcurves: Application to bioassay, radioligand as-say, and physiological dose-response curves.Am. J. Physiol. 235:E97-E102.

DeLean, A., Stadel, J.M., and Lefkowitz, R.J. 1980.A ternary complex model explains the agonist-specific binding properties of the adenylate cy-clase-coupled β-adrenergic receptor. J. Biol.Chem. 255:7108-7117.

DeLean, A., Hancock, A.A., and Lefkowitz, R.J.1982. Validation and statistical analysis of acomputer modeling method for quantitativeanalysis of radioligand binding data for mixturesof pharmacological receptor subtypes. Mol.Pharmacol. 21:5-16.

Ehlert, F.J., Roeske, W.R., and Yamamura, H.I.1981. Mathematical analysis of the kinetics ofcompetitive inhibition in neurotransmitter recep-


1.3.31

Receptor Binding

tor binding assays. Mol. Pharmacol. 19:367-371.

Feldman, H.A. 1972. Mathematical theory of com-plex ligand-binding systems at equilibrium:Some methods for parameter fitting. Anal. Bio-chem. 48:317-338.

Feldman, H.A. 1983. Statistical limits in Scatchardanalysis. J. Biol. Chem. 258:12865-12867.

Filer, C., Hurl, S., and Wan, Y.-P. 1989. Radioli-gands: Synthesis and handling. In ReceptorBinding. (M. Williams, P.B.M.W.M. Timmer-mans, and R.A. Glennon, eds.) pp. 105-135.Marcel Dekker, New York.

Fleming, W.W., Westfall, D.P., De La Lande, I.S.,and Jellett, L.B. 1972. Log-normal distributionof equieffective doses of norepinephrine andacetylcholine in several tissues. J. Pharmacol.Exp. Ther. 181:339-345.

Gaddum, J.H. 1945. Lognormal distributions. Na-ture 156:463-466.

Hill, A.W. 1910. The possible effects of the aggre-gation of the molecules of hemoglobin on itsdissociation curves. J. Physiol. (Lond.) 40:iv-vii.

Jacobs, S., Chang, K.-J., and Cuatrecasas, P. 1975.Estimation of hormone receptor affinity by com-petitive displacement of labeled ligand: Effect ofconcentration of receptor and of labeled ligand.Biochem. Biophys. Res. Commun. 66:687-692.

Jarv, J., Hedlund, B., and Bartfai, T. 1979. Isomeri-zation of the muscarinic receptor-antagonistcomplex. J. Biol. Chem. 254:5595-5598.

Karlsson, M.O. and Neil, A. 1989. Estimation ofligand binding parameters by simultaneous fit-ting of association and dissociation data: AMonte Carlo simulation study. Mol. Pharmacol.35:59-66.

Kenakin, T. 1993. Radioligand binding experi-ments. In Pharmacologic Analysis of Drug-Re-ceptor Interaction, 2nd ed., pp. 385-410. RavenPress, New York.

Ketelslegers, J.-M., Pirens, G., Maghuin-Rogister,G., Hennen, G., and Frere, J.-M. 1984. Thechoice of erroneous models of hormone-receptorinteractions: A consequence of illegitimate utili-zation of Scatchard graphs. Biochem. Pharma-col. 33:707-710.

Koshland, D.E., Nemthy, G., and Filmer, D. 1966.Comparison of experimental binding data andtheoretical models in proteins containingsubunits. Biochemistry 5:365-385.

Lam, C.F. and Cross, A.P. 1979. Comparative studyof parameter estimation procedures in enzymickinetics. Comput. Biol. Med. 9:145-153.

Lazareno, S. and Birdsall, N.J. 1993. Estimation ofcompetitive antagonist affinity from functionalinhibition curves using the Gaddum, Schild andCheng-Prusoff equations. Br. J. Pharmacol.109:1110-1119.

Limbird, L. 1996. Cell Surface Receptors: A ShortCourse in Theory and Methods, 2nd ed. KluwerAcademic Publishers, Boston.

Linden, J. 1982. Calculating the dissociation con-stant of an unlabeled compound from the con-centration required to displace radiolabel bind-ing by 50%. J. Cyclic Nucleotide Res. 8:163-172.

Maksay, G. 1994. Thermodynamics of gamma-ami-nobutyric acid type A receptor binding differen-tiate agonists from antagonists. Mol. Pharmacol.46:386-390.

Marquardt, D.W. 1963. An algorithm for least-squares estimation of nonlinear parameters. J.Soc. Indust. Appl. Math. 11:431-441.

McKinney, M., Stenstrom, S., and Richelson, E.1985. Muscarinic responses and binding in amurine neuroblastoma clone (N1E-115). Media-tion of separate responses by high affinity andlow affinity agonist-receptor conformations.Mol. Pharmacol. 27:223-235.

Metcalf, M.A., McGuffin, R.W., and Hamblin,M.W. 1992. Conversion of the human 5-HT1Dbserotonin receptor to the rat 5-HT1B ligand-bind-ing phenotype by Thr355Asn site directed mu-tagenesis. Biochem. Pharmacol. 44:1917-1920.

Monod, J., Wyman, J., and Changeux, J.-P. 1965. Onthe nature of allosteric transitions: A plausiblemodel. J. Mol. Biol. 12:88-118.

Motulsky, H. and Neubig, R. 1997. Analyzing radi-oligand binding data. In Current Protocols inNeuroscience (J.N., Crawley, C.R., Gerfen, R.,McKay, M.A., Rogawski, D.R., Sibley, and P.,Skolnick, eds.) pp. 7.5.1-7.5.55. John Wiley &Sons, New York.

Motulsky, H.J., Mahan, L.C., and Insel, P.A. 1985.Radioligand, agonists and membrane receptorson intact cells: Data analysis in a bind. TrendsPharmacol. Sci. 6:317-319.

Munson P.J. and Rodbard, D. 1980. LIGAND: Aversatile computerized approach for character-ization of ligand-binding systems. Anal. Bio-chem. 107:220-239.

Murphy, D.E., Schnieder, J., Boehm, C., Lehmann,J., and Williams, M. 1987. Binding of [3H]3-(2-carboxypiperazin-4-yl)propyl-1-phosphonicacid to rat brain membranes: A selective, high-affinity ligand for N-methyl-D-aspartate recep-tors. J. Pharmacol. Exp. Ther. 240:778-784.

Murphy, D.E., Hutchison, A.J., Hurt, S.D., Wil-liams, M., and Sills, M.A. 1988. Characteriza-tion of the binding of [3H]CGS 19755: A novelN-methyl-D-aspartate antagonist with nanomo-lar affinity in rat brain. Br. J. Pharmacol. 95:932-938.

Nelder, J.A. and Mead, R. 1965. A simplex methodfor function minimization. Computer J. 7:308-313.

Pang, Y.-P., Cusack, B., Groshan, K., and Richelson,E. 1996. Proposed ligand binding site of thetransmembrane receptor for neurotensin (8-13).J. Biol. Chem. 271:16060-16068.

Pellicciari, R., Marinozzi, M., Natalini, B., Costan-tino, G., Luneia, R., Giorgi, G., Moroni, F., andThomsen, C. 1996. Synthesis and pharmacologi-cal characterization of all sixteen stereoisomersof 2-(2′-carboxy-3′-phenylcyclopropyl)glycine.


1.3.32


Binding

Focus on (2S,1′S,2′S,3′R)-2-(2′-carboxy-3′-phenylcyclopropyl)glycine, a novel and selec-tive group II metabotropic glutamate receptorantagonist. J. Med. Chem. 39:2259-2269.

Rabow, L.E., Russek, S.J., and Farb, D.H. 1995.From ion currents to genomic analysis: Recentadvances in GABA-A receptor research. Syn-apse 21:189-274.

Rodbard, D. 1973. Mathematics of hormone-recep-tor interaction. I. Basic principles. Adv. Exp.Med. Biol. 36:289-329.

Rodbard, D., Munson, P.J., and Thakur, A.K. 1980.Quantitative characterization of hormone recep-tors. Cancer 46:2907-2918.

Rosenthal, H.E. 1967. Graphic method for the de-termination and presentation of binding parame-ters in a complex system. Anal. Biochem.20:525-532.

Scatchard, G. 1949. The attractions of proteins forsmall molecules and ions. Ann. N.Y. Acad. Sci.51:660-672.

Schreiber, G., Henis, Y.I., and Sokolovsky, M. 1985.Rate constants of agonist binding to muscarinicreceptors in rat brain medulla. Evaluation bycompetition kinetics. J. Biol. Chem. 260:8795-8802.

Sullivan, J.P., Decker, M.W., Brioni, J., Donnelly-Roberts, D., Anderson, D.A., Bannon, A.W.,Kang, C.-H., Adams, P., Piattoni-Kaplan, M.,Buckley, M.J., Gopalakrishnan, M., Williams,M., and Arneric, S.P. 1994. (+)-Epibatidine elic-its a diversity of in vitro and in vivo effectsmediated by nicotinic acetylcholine receptors. J.Pharmacol. Exp. Ther. 271:624-631.

Tallarida, R.J. and Murray, R.B. 1986. Manual ofPharmacologic Calculations with ComputerPrograms, 2nd ed. Springer-Verlag, New York.

Tolkovsky, A.M. and Levitzki, A. 1981. Theoriesand predictions of models describing sequentialinteractions between the receptor, the GTP regu-latory unit, and the catalytic unit of hormonedependent adenylate cyclases. J. Cyclic Nucleo-tide Res. 6:139-150.

Waelbroeck, M., Tastenoy, M., Camus, J., and Chris-tophe, J. 1990. Binding of selective antagoniststo four muscarinic receptors (m1 to m4) in ratforebrain. Mol. Pharmacol. 38:267-273.

Waelbroeck, M., Camus, J., Tastenoy, M., Lam-brecht, G., Mutschler, E., Kropfgans, M., Sper-lich, J., Wiesenberger, F., Tacke, R., and Christo-phe, J. 1993. Thermodynamics of antagonistbinding to rat muscarinic M2 receptors: An-timuscarinics of the pridinol, sila-pridinol,diphenidol and sila-diphenidol type. Br. J. Phar-macol. 109:360-370.

Weiland, G.A., Minneman, K.P., and Molinoff, P.B.1979. Fundamental difference between the mo-lecular interactions of agonists and antagonistswith the β-adrenergic receptor. Nature 281:114-117.

Wild, K.D., Porreca, F., Yamamura, H.I., and Raffa,R.B. 1994. Differentiation of receptor subtypesby thermodynamic analysis: Application toopioid receptors. Proc. Natl. Acad. Sci. U.S.A.91:12018-12021.

Williams, M. and Gordon, E. M. 1996. Drug discov-ery: An overview. In A Textbook of Drug Designand Development, 2nd ed. (P. Krogsgaard-Larsen, T. Liljefors, and U. Madsen, eds.) pp.1-34. Harwood Academic Publishers, Chur,Switzerland.

Williams, M., Deecher, D.C., and Sullivan, J.P.1995. Drug receptors. In Burger’s MedicinalChemistry and Drug Discovery, 5th ed. (M.E.Wolff, ed.) pp. 349-397. John Wiley & Sons,New York.

Wreggett, K.A. and DeLean, A. 1984. The ternarycomplex model. Its properties and application toligand interactions with the D2-dopamine recep-tor of the anterior pituitary gland. Mol. Pharma-col. 26:214-227.

Yasuda, R.P., Ciesia, W., Flores, L.R., Wall, S.J., Li,M., Satkus, S.A., Weisstein, J.S., Spagnola, B.V.,and Wolfe, B.B. 1993. Development of antiseraselective for m4 and m5 muscarinic cholinergicreceptors: Distribution of m4 and m5 muscarinicreceptors in rat brain. Mol. Pharmacol. 43:149-157.

KEY REFERENCESKenakin, 1993. See above.

A complete treatise for the advanced student.

McGonigle, P. and Molinoff, P.B. 1994. Receptorsand signal transduction: Classification and quan-titation. In Basic Neurochemistry: Molecular,Cellular, and Medical Aspects, 5th ed. (G.J.Siegel, ed.) pp. 210-230. Raven Press, New York.

An introductory treatment within the context ofneuropharmacology.

Weiland, G.A. and Molinoff, P.B. 1981. Quantitativeanalysis of drug-receptor interactions: I. Deter-mination of kinetic and equilibrium properties.Life Sci. 29:313-330.

Useful for explaining common plotting methods.

Yamamura, H.I., Enna, S.J., and Kuhar, M.J. 1985.Neurotransmitter Receptor Binding, 2nd ed. Ra-ven Press, New York.

This volume has been a standard in the field formany years and is especially useful for beginners.

Contributed by Michael McKinneyMayo Clinic JacksonvilleJacksonville, Florida


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