[6] Ligand binding methods for analysis of ion channel structure and function

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studies. Such experiments would be nicely supplemented by isotopeenriched material. Indeed, access to an expression system such as the one described may be the only means by which structural and dynamics studies can be done at all for less abundant toxins. The 100- to 330-fold improvement in effective sample concentration obtained by I3C or 15N labeling allows measurements to be conducted at less extravagant concentrations where aggregation is minimized and eliminates the signal-to-noise problems that plagued the present study. Furthermore, natural abundance 15N relaxation studies are not feasible and so nitrogen labeling will improve the quality of relaxation data by expanding the spectral frequencies that can be monitored. NMR spectroscopy is a powerful tool that has been well utilized in the study of the structure of peptide toxins in solution. The availability of recombinant toxins opens the door to an entirely new repertoire of NMR experiments that can be brought to bear on refining this structural knowledge base and expanding it into the realm of molecular dynamics, adding new dimensionality to our understanding of the function of this important class of peptides.

[6] L i g a n d B i n d i n g M e t h o d s f o r A n a l y s i s o f I o n C h a n n e l Structure and Function

By STEEN E.

PEDERSEN,

MONICA M.

LURTZ,

and RAO V. L. PAPINENI

Introduction The nicotinic acetylcholine receptor (AChR) 1 is an ion channel that is opened by the binding of two molecules of acetylcholine on its extracellular surface.2 On prolonged exposure to acetylcholine, the channel desensitizes and acquires high affinity for acetylcholine. The equilibrium binding to the two sites appears weakly cooperative, but the two sites are distinct, as shown by the binding of various antagonists that preferentially bind one site versus the other. 3 Two subunits constitute each site: aT and ozS. The heterogeneity of the sites is primarily due to the distinct contributions of

AChR, Nicotinic acetylcholine receptor; a-BgTx, c~-bungarotoxin; DFP, diisopropyl fluorophosphonate. 2 A. Devillers-Thiery, J. L. Galzi, J. L. Eisele, S. Bertrand, and J.-P. Changeux, J. Membr. BioL 136, 97 (1993). 3 R. R. Neubig and J. B. Cohen, Biochemistry 18, 5464 (1979).

METHODS 1N ENZYMOLOGY,VOL. 294

Copyright © 1999 by Academic Press All rights of reproductionin any form reserved. 0076-6879/99 $30.00

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the 3' and ~ subunits at each site. 4 The sites are allosterically linked to a binding site located within the channel pore itself, the noncompetitive antagonist site. Binding to this site can alter the conformation in favor of either the resting conformation or the desensitized conformation, depending on the ligand. Desensitization, as induced by noncompetitive antagonists, is also marked by increased affinity for agonist binding to the acetylcholine sites. The ability of many cholinergic ligands to bind all three sites further complicates analyses of the linkage. An increased awareness of these phenomena has permitted binding to the AChR to be understood in more detail, and binding assays are finding greater use in elucidating the structure of the binding sites. In this article we describe several ligand binding techniques: radioligand binding by centrifugation assay, radioligand binding by DE-81 filter binding, and fluorescent ligand binding. In addition, we discuss how to analyze direct binding measurements, indirect binding by competition, and noncompetitive allosteric effects.

Comparison of Methods Radioligand Binding

Measuring ligand binding by radioactively labeled ligands has the advantages of high sensitivity, fewer artifacts than fluorescence, and direct determination of the amount of ligand by scintillation or gamma counting. Counting is substantially more sensitive than fluorescence: femtomoles of ligand can be directly detected whereas the limit of detection for fluorescence is near picomoles. There are some drawbacks to using radioactivity: the intrinsic health hazards, detection of/3-emission usually involves handling scintillation cocktails, and all types of radionuclei require significant effort for proper storage and disposal. Fluorescence Binding Measurements

The advantages of fluorescence measurements echo the limitations of using radioactivity. Changes in fluorescence can be followed at any time resolution that still yields a detectable signal, and the data are obtained immediately. There is usually little need for the special handling and disposal of fluorophores. A primary disadvantage of fluorescence is the lower sensitivity, which substantially limits the usable concentration range of fluorescent ligands. A second disadvantage is that the fluorescence signal 4S. E. Pedersen and J. B. Cohen, Proc. Natl. Acad. Sci. U.S.A, 87, 2785 (1990).

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must be calibrated routinely for quantitative measurements. Fluorescence yield depends on several factors: instrument optics, the fluorophore, the solution, sample geometry, and the detector. Fluorescence measurements also require a sensitive fluorescence spectrophotometer. Some instruments can be obtained for roughly the same price as a scintillation counter, though research-grade instruments may be substantially more expensive. Selection o f Ligand

A substantial number of radioactive ligands are commercially available that bind the acetylcholine binding sites. The most common is 125I-labeled a-BgTx. Tritiated or 14C-labeled ligands available include acetylcholine, epibatidine, and nicotine. For the noncompetitive site, however, there are no radioligands currently available. [3H]Phencyclidine was recently discontinued by D u P o n t / N e w England Nuclear (Boston, MA). Other ligands that have been used, such a [3H]ethidium or [3H]histrionicotoxin, must be radiolabeled through a radiolabeling service. The fluorescent ligands ethidium, quinacrine, and crystal violet are available through standard sources. Except for derivatives of a-BgTx, fluorescent ligands for the acetylcholine binding sites must be synthesized or obtained from a donor.

Methods Preparation o f Membranes

The preparation of AChR-rich membranes from Torpedo electric organ has been described in this series. 5 The procedure we follow is essentially that of Sobel et al. with some modifications. 6'7 This preparation can be conveniently scaled up to processing 2 kg of electric organ per batch with yields of several hundred milligrams of membrane protein. The membrane vesicles are near 20% purity in AChR, as assessed by the [3H]acetylcholine binding assay described later (1.5-2 nmol, acetylcholine binding sites per milligram of protein). For many of the assays, particularly the microcentrifugation assay, it is adequate to use lower specific activity membranes, and often it is desirable to do so. Therefore, we usually save a side fraction from the discontinuous sucrose fractionation which contains membranes with specific activity that vary from 0.1-1 nmol acetylcholine binding sites per milligram protein. 5 A. Chak and A. Karlin, Methods Enzymol. 207, 546 (1992). A. Sobel, M. Weber, and J.-P. Changeux, Eur. J. Biochem. 80, 215 (1977). 7S. E. Pedersen. E. B. Dreyer, and J. B. Cohen, J. Biol. Chem. 261, 13735 (1986).

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Radioligand Binding Assays The following procedure describes the microcentrifuge ligand binding assay used for routine binding measurements. It is based on procedures developed and used in Jonathan Cohen's laboratory. 3,8,9 Torpedo AChRrich membranes are diluted into HTPS (250 m M NaC1, 5 m M KC1, 3 m M CaC12, 2 m M MgCI2,0.02% NAN3,20 m M H E P E S , p H 7.0) and centrifuged for 30 min at 15 krpm (--19,000 g) in a T O M Y MTX-150 centrifuge (Peninsula Laboratories, Belmont, CA). This initial centrifugation is to remove light membranes that might not sediment during the later centrifugation step. Protein assays show that typically no more than 10-20% of the membranes are lost in this step. The pellet is resuspended by passing the membranes through a 25-gauge syringe needle several times. The membranes are then treated with 1 m M diisopropyl fluorophosphonate (DFP) for 1 hr at ambient temperature to inactivate acetylcholinesterase. DFP hydrolyzes rapidly in aqueous solution and, therefore, must be diluted from the neat liquid immediately prior to mixing with the membranes. A second 1-hr treatment with 0.1 m M DFP is then carried out and the membranes transferred to ice. Subsequent dilutions and additions are then made in the 0.1 m M D F P solution. Samples are assembled in Eppendorf-type microcentrifuge tubes and incubated for 30 rain at either 4 ° or ambient temperature. They are then centrifuged for 30 min at 15 krpm (19,000 g) in a T O M Y microcentrifuge. A sample of the supernatant is retained for counting to determine free ligand and the remainder is removed with a gel-loading pipette tip attached to an aspirator with a trap for collecting the radioactive ligand. Traces of supernatant clinging to the sides of the tubes are adsorbed by a cotton swab. The tubes are then left upside-down on the cotton swab for 15 min to drain any remaining supernatant left on the pellet. The pelleted membranes are dissolved in 100/z110% (w/v) sodium dodecyl sulfate (SDS) by shaking on a vortexer for at least 15 rain, and then transferred to a scintillation counting vial; the tube is rinsed with an additional 10/zl 10% SDS and the rinse added to the scintillation vial. The nonspecific binding is determined by parallel samples including excess carbamylcholine or o~bungarotoxin. The choice of the ligand's specific radioactivity, its concentration in the binding assays, and the concentration of binding sites must be chosen to optimize the signal with regard to the type of information desired. The concentration of binding sites is limited by the need to form a discrete pellet on centrifugation. The quality of data deteriorates if less than 50 ~g s E. K. Krodel, R. A. Beckman, and J. B. Cohen, Mol. PharmacoL 15, 294 (1979). 9S. E. Pedersen, Mol. Pharmacol. 47, 1 (1995).

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of membranes are used; using 100/xg often improves the data. Thus, the lower limit of binding site concentration is determined by the volume desired and the specific binding activity of the membranes. To minimize the concentration of binding sites, we often use a low specific activity membrane fraction in the assay (0.1-1 nmol [3H]acetylcholine binding sites per milligram protein). A typical concentration of binding sites is 20-40 nM in final volume of 1 ml. [3H]Acetylcholine Binding. To monitor the conformational changes of the acetylcholine receptors by noncompetitive antagonists, a high specific radioactivity [3H]acetylcholine ( - 3 0 Ci/mmol; available from American Radiolabeled Chemicals Inc., St. Louis, MO) can be used at a concentration substantially lower than both the dissociation constant for acetylcholine and the number of binding sites, as long as only a moderate percentage of the ligand is bound. In this way, the extent of binding is highly sensitive to the conformational equilibrium of the receptor and can be used to determine the conformational preference of the nonradioactive ligand. An example of this is shown in Fig. 1A. The increase in binding is due to the conformational effects of crystal violet that desensitizes the AChR, which is seen as higher affinity binding. At higher concentrations, crystal violet competes directly at the acetylcholine binding sites to reduce binding. Competitive binding is used to determine the affinity of a ligand that is not radioactive. Nonradioactive ligands are incubated with membranes and an excess of low specific activity acetylcholine (-100 mCi/mmol). In this case it is convenient to keep the [3H]acetylcholine concentration higher than both its KD and the binding site concentration such that the sites are saturated; 100 nM [3H]acetylcholine is typical with 20- to 40-nM binding sites. The inhibition data will yield a Kapp, the concentration at which the signal is decreased 50%. This value is most easily obtained by fitting the data to an appropriate equation using a nonlinear regression algorithm. It can then be used to calculate the KD for the inhibitor (see below). Binding to Noncompetitive Site. For [3H]phencyclidine or [3H]ethidium binding to the noncompetitive antagonist binding site, the assay is carried out as described above except that the DFP incubation steps can be omitted. A low concentration of [3H]phencyclidine is convenient for measuring either competition by other noncompetitive antagonists or measuring conformationally driven effects of agonsits or noncompetitive antagonists. Both effects can be seen in Fig. 1B where [3H]phencyclidine binding is altered by the addition of tubocurine: tubocurine binds the acetylcholine binding sites at lower concentrations, resulting in partial conversion to the desensitized conformation of the AChR, which has higher affinity for [3H]phencyclidine as seen by the increase in binding. At higher concentrations, tubocurine competes directly for binding at the noncompetitive antagonist site, producing a loss of [3H]phencyclidine binding. The complete desensiti-

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FI~. 1. Allosteric interactions detected by binding assays at low radioligand concentrations. (A) The effect of increasing crystal violet concentrations on [3H]acetylcholine binding was determined using the centrifugation assay described in the text. The assay was carried out in a 1-ml volume containing 100/~g AChR-rich membranes (18 nM acetylcholine binding sites) and 1 nM [3H]acetylcholine. The data are plotted as the ratio of the bound ligand to free ligand. Under these conditions, this value is inversely proportional to the KD. The rising phase shows that crystal violet increases the affinity of the acetylcholine binding sites for acetylcholine. The falling phase at higher concentrations reflects direct competition for binding at the acetylcholine binding sites. (B) The effect of varying concentration of tubocurine, a dtubocurarine analog, was measured by [3H]phencyclidine binding using the centrifugation assay. AChR-rich membranes (50 p~g; 200 t~l; 62.5 nM AChR) were incubated with 1 nM [3H]phencyclidine (43 Ci/mmol) and the indicated concentrations of ligand. The rising phase of binding (V) shows increased affinity for [3H]phencyclidine as a result of desensitization from tubocurine binding to the ay acetylcholine binding site. Tubocurine competitively inhibits the AChR at higher concentrations resulting in the bell-shaped curve. The direct competition by tubocurine at the noncompetitive site is further illustrated by its inhibition in the presence of 100/~M carbamylcholine (O) to block effects at the acetylcholine binding sites. Controls in the absence (T) and presence (0) of carbamylcholine illustrate the enhanced binding due to the strong desensitizing. The binding in the presence of 50/~M proadifen, a noncompetitive antagonist, is also shown (ll).

z a t i o n c a n b e s e e n b y a d d i t i o n o f a n a g o n i s t , c a r b a m y l c h o l i n e , w h i c h increases binding about 5-fold over the baseline. Assays Using 125I-Labeled o~-Bungarotoxin. 125I-Labeled-c~-bungarot o x i n is u s e d e x t e n s i v e l y f o r m e a s u r i n g b i n d i n g to t h e a c e t y l c h o l i n e r e c e p t o r . A v a r i e t y o f assays h a v e b e e n d e s c r i b e d ; t h e m o s t c o m m o n o n e r e l i e s o n

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the separation of free from bound ligand by adsorption of the A C h R to DE-81 anion-exchange filter paper. 1° We describe a variation of this assay to measure binding in physiologic buffer. It avoids the use of the detergent Triton X-100, which may contribute to desensitization of the A C h R and thereby cause artifacts when assessing the affinity of competing ligands. Because of the intrinsic high affinity of 125I-labeled ~-BgTx for the A C h R (the KD is near picomolar) and its long dissociation time (hours), competitive binding assays are not carried out at equilibrium, but rather use an initial rate assay. The assay is carried out for a limited period of time during the linear portion of the association time course. The amount of binding within this time is proportional to the free binding site concentration. Therefore a competing ligand will reduce the rate of [125I]o~-BgTx binding to the extent that is occupies the binding sites. The rate of binding is sensitive to ionic strength, 11 such that an initial rate of binding in low ionic strength buffer can be done in 1-2 min, whereas 45 min is necessary for binding in physiologic saline. The initial rate assay relies on maintaining a linear rate of binding of [125I]o~-BgTx during the course assay. This requires pseudo first-order kinetic conditions, such that only a small percentage of the added [t25I]c~-BgTx is bound and only a minor proportion of the A C h R binding sites are bound. A rule of thumb is that the maximum binding should be less than one-half of each site; that is, a quarter of the total binding acetylcholine binding sites. AChR-rich membranes are suspended to a concentration of 1-2 nM in HTPS supplemented with 0.1% bovine serum albumin (BSA) and preincubated with the competing ligand for 30 min or longer. 125I-Labeled o~-BgTx ( - 2 0 0 Ci/mmol) is then added to a final concentration of 2 nM and the reaction incubated for 45 min. The binding is stopped by dilution with four volumes of 300 n M ~-BgTx in 10 m M Tris, 0.1% (w/v) BSA, 0.1% (w/v) Triton X-100 (pH 7.4). This serves to isotopically dilute the [~25I]o~-BgTx and prevent further binding and to lower the ionic strength. The latter is necessary for binding to the DE-81 filters. A 60-/xl aliquot of each reaction is spotted on a DE-81 filter pinned to a Styrofoam rack. The filters are allowed to sit no more than a few minutes before transfer to a tray with wash buffer: 10 m M Tris, 50 m M NaC1, 0.1% Triton X-100 (pH 7.4). The filters are washed twice, in batches, for 15 min each. The length of washing is not critical. More important is the spotting of the sample onto the filters; the exact time of incubation on the filter before transfer to wash buffer is

t~ j. Schmidt and M. A. Raftery, A n a l Biochem. 52, 349 (1973). H j. Schmidt and M. A. Raftery, J. Neurochem. 23, 617 (1974).

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relatively unimportant as long as the filters remain damp. If the filters begin to dry before washing, the nonspecific binding will increase dramatically. The background binding in this assay can easily become too high; it appears to be dependent on the batch of DE-81 filters. A simple solution is to increase the amount of binding by using a higher receptor concentration, as long as the conditions for the assay listed above are still met. [125I]c~-BgTx Binding to BC3H-1 Cells. BC3H-1 cells express the mouse muscle A C h R and provide a convenient system for studying the properties of a mammalian AChR. 12,13 The binding assay can be carried out in 24well tissue culture plates. Despite the lower receptor number in these cells than are obtained from Torpedo membranes, the assay is simpler because the free [125I]a-BgTx can be washed off the cells with quite low background retention. BC3H-1 cells are maintained in Dulbecco's modified Eagle's medium ( D M E M ) with 20% fetal bovine serum, 100 units/ml penicillin, and 0.1 mg/ ml streptomycin. They are seeded (8000-12,000 cells per well) into 24-well tissue culture plates that have been precoated with gelatin (0.2% porcine gelatin, 500/zl per well, for 3 hr before plating). The cells are grown until they reach --70% confluence and then the medium is changed to Dulbecco's modified Eagle's medium with 8% fetal bovine serum, 2% horse serum, 100 units/ml penicillin, and 0.1 mg/ml streptomycin. This initiates differentiation of the cells and expression of the AChR. The cells are ready for assay after 3 days of incubation with horse serum. Like the Torpedo membrane assay, this assay relies on the initial rate of binding of [125I]a-BgTx and its slow dissociation rate. The cells are removed from the incubator and equilibrated to room temperature in a hood for 30 min. The remainder of the assay can be carried out on the bench at ambient temperature. Competing ligands are diluted in the media and then applied to the cells (350/zl) after removing the old media. The cells are incubated for 30 min with the competing ligand on a slowly rotating platform. 125I-Labeled o~-BgTx is then added in a 50-/M aliquot to a final concentration of - 2 n M and allowed to incubate for another 45 min. The solution is then aspirated off the cells and the cells washed twice with 0.7 ml Dulbecco's modified Eagle's medium. The bound [~25I]a-BgTx retained in the well is then transferred to a counting vial after dissolving the cells with 150/xl 1% Triton X-100 for 2 hr. The gelatin coating on the wells is necessary for sticking of the cells to the plates during the incubation and washing procedures, but it also slows the dissolution by Triton X-100. It is

~2S. Sine and P. Taylor, Z BioL Chem. 254, 3315 (1979). 13S. Sine and P. Taylor, J. Biol. Chem. 256, 6692 (1981).

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important to ensure that all the cells are dissolved before transferring to the counting vial. It is important to establish independently that the incubation time [12sI]a-BgTx is in the linear portion of the association rate curve. The rate of binding can be adjusted by varying the [125I]o~-BgTx concentration. As mentioned earlier, a rule of thumb is that no more than 25% of the total binding sites should be bound and only a minor portion of the [125I]a-BgTx should be bound. The total number of receptors can be determined by using longer binding time (3 hr) and higher [125I]o~-BgTx concentrations. We routinely use [~25I]a-BgTx with a specific radioactivity of 200 Ci/mmol, but higher activity [125I]o~-BgTx can also be obtained and used in this assay for higher sensitivity.

Effects of Noncompetitive Antagonists on Binding to Agonist Sites Agonists and competitive antagonists, which bind the acetylcholine binding sites, stabilize the desensitized conformation of the A C h R to varying degrees. The extent to which this occurs can be measured indirectly by examining the effect of noncompetitive antagonists on the binding of the acetylcholine site ligands. A variety of noncompetitive antagonists stabilize the desensitized conformation. We have used phencyclidine and proadifen; the former for its high solubility, low partitioning with membranes TM and well-characterized binding, and the latter for its ability to desensitize to a greater extent. 8 Fewer ligands are available that preferentially stabilize the resting conformation of the AChR. The best is tetracaine. 15 Noncompetitive ligands are usually added in competitive radioligand binding assays to a concentration near 30/zM. It is necessary to add sufficient ligand to be well above the KD of the noncompetitive ligand for the resting conformation of the A C h R (near 5/xM for proadifen and phencyclidine). However, high concentrations ( > 1 0 0 / z M ) can sometimes perturb the lipid bilayer and induce nonspecific effects. This can cause problems in obtaining good pellets in the microcentrifuge assay and can cause dissociation of the BC3H-I cells from the tissue culture dish. High concentrations of some noncompetitive antagonists also inhibit the rate of [125I]a-BgTx binding to Torpedo AChR-rich membranes. 8 The exact cause for this effect is not known but may be due to desensitization of the AChR.

14M. M. Lurtz, M. L. Hareland, and S. E. Pedersen, Biochemistry36, 2068 (1997). 15j. B. Cohen, L. A. Correll, E. B. Dreyer, I. R. Kuisk, D. C. Medynski, and N. P. Strnad, in "Molecular and Cellular Mechanisms of Anesthetics" (S. H. Roth and K. W. Miller, eds.), pp. 111-124. Plenum Publishing, New York, NY, 1986.

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F l u o r e s c e n t Ligand Binding A s s a y s Fluorescent L i g a n d s f o r A c e t y l c h o l i n e B i n d i n g Sites

Only few fluorescent ligands are available that bind the acetylcholine binding sites. A variety of fluorescent derivatives of o~-BgTx are c o m m e r cially available, 16 but are of limited use for binding assays because they do not have substantial changes in fluorescence on binding. Two agonists, dansyl-C6-choline 17 and NBD-5-acylcholine, 18 have been characterized extensively. They share the high affinity and rapid binding characteristics of acetylcholine and are excellent real-time monitors of the conformational transitions of the A C h R because their q u a n t u m yield changes substantially on binding. The change in signal is enhanced by using energy transfer from tryptophans on the A C h R to the bound ligand. Dansyl-choline 19 is an antagonist that binds with somewhat lower affinity but is useful for quantitation of receptor specific activity3,2°; it is also commercially available. 21 These ligands are useful for competitive binding assays for assessing the affinity of unlabeled ligands. Several caveats render competitive inhibition by fluorescence less useful than the radioligand assays. The concentration of receptor needed for an adequate signal is near 100 nM. For competitive inhibition it is desirable to have the ligand in excess, thus requiring several hundred n a n o m o l a r concentrations. This will increase the concentration of competing ligand required for complete inhibition. A second caveat is that m a n y competing ligands will absorb at a light of 280-290 nm, the wavelength required for excitation of these ligands. This adds the complication of having to correct for inner filter effects at higher competitor concentrations. Fluorescent L i g a n d s f o r N o n c o m p e t i t i v e Site

A variety of fluorophores bind the noncompetitive antagonist site. The best characterized ligand is ethidium bromide22; others include quinacrine, 23 decidium, 24 and crystal violet. The latter c o m p o u n d has a 200-fold increase 16R. P. Haugland, "Handbook of Fluorescent Probes and Research Chemicals." Molecular Probes, Eugene, Oregon, 1996. 17T. Heidmann and J.-P. Changeux, Eur. J. Biochem. 94, 255 (1979). 18H. Prinz and A. Maelicke, J. Biol. Chem. 258, 10263 (1983). a9j. B. Cohen and J.-P. Changeux, Biochemistry 12, 4855 (1973). 20C. F. Valenzuela, J. A. Kerr, and D. A. Johnson, J. Biol. Chem. 267, 8238 (1992). 21Sigma Chemicals, St. Louis, MO. 22j. M. Herz, D. A. Johnson, and P. Taylor, J. Biol. Chem. 262, 7238 (1987). 23H.-H. Griinhagen and J.-P. Changeux, J. Mol. Biol. 106, 517 (1976). 24D. A. Johnson, R. D. Brown, J. M. Herz, H. A. Berman, G. L. Andreasen, and P. Taylor, J. Biol. Chem. 262, 14022 (1987).

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in fluorescence yield on binding the ion channelY Ethidium fluorescence enhancement can be used to measure binding to the noncompetitive antagonist site. Titrations with competing ligands can be conveniently performed in a single cuvette to generate inhibition curves.

Fluorescent Assay for Noncompetitive Binding Fluorescent measurements on the A C h R require a good-quality fluorometer because of the scattering due to membranes. We use researchgrade instruments (SLM 8000, Rochester, NY and ISS PC1, Urbana, IL); however less expensive fluorometers are likely to be adequate. For measurements, AChR-rich membranes are sedimented in the ultracentrifuge and resuspended to 200 n M in acetylcholine binding sites in HTPS (for fluorescence measurements the sodium azide is omitted from the HTPS). Ethidium is added to a final concentration 250 n M and the agonist carbamylcholine is added to 100/xM. Carbamylcholine serves to desensitize the AChr, which improves the affinity for ethidium, and prevents binding of ethidium to the agonist sites. A 2.5- to 3-ml volume of the suspension is stirred in a 10- × 10-ram cuvette. Fluorescence is excited with 340 nm light through a visible-absorbing filter (Oriel 59152, Stratford, CT) and is measured at 595 nm through a 540-nm cuton filter (Oriel 59502). The filters improve the signal-to-noise ratio by removing stray light. To measure the affinity of a competing ligand, concentrated solutions can be titrated into the cuvette using a syringe. It is desirable to keep the additions to small volumes to avoid compensating for volume changes and to avoid affecting the equilibrium of the binding of ethidium. It is necessary to wait about 15 rain between additions in order to let the slow dissociation of ethidium come to completion. This greatly limits the speed of the assay, but many sets of data can be measured simultaneously in this way.

Analysis of Ligand Binding The object of this section is to provide some practical guides for the analysis of direct binding data and competitive binding data. The last section also discusses the use of thermodynamic cycles for interpreting conformational effects and allosteric ligand interactions. The theoretical basis and the derivation for the various equations will not be presented; they can be

25M. M. Lurtz and S. E. Pedersen, 1997 unpublished observations.

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found elsewhere. The interested reader can find more detail in a number of books and articles. 26,27A good basic primer has been published by Klotzfl 8

Analysis of Binding Isotherms Subtraction of Nonspecific Binding. To analyze binding isotherms, nonspecific binding is subtracted, and the data are then fit by a nonlinear regression algorithm to the equation for single site binding [Eq. (1)]. For the centrifugation assays described earlier, the free ligand concentration is determined directly by counting an aliquot of the supernatant. A common problem in subtracting nonspecific binding in these assays is that the free ligand concentration is not the same in parallel samples for total binding and for nonspecific binding. In this case, it is incorrect simply to subtract the nonspecific binding from the corresponding samples without inhibitor. If the nonspecific binding is linear with concentration, it can be fit to a line, and the fitted parameters used to calculate the nonspecific for each sample, using the corresponding free concentration of ligand. If the nonspecific binding is nonlinear, then the values can be fit to other functions; a hyperbolic equation often works well [B = A . L / ( L + K)]. Alternatively, the values can be manually interpolated from the nonspecific binding data. This problem is illustrated in Fig. 2. In cases where the concentrations of receptor are the same or higher than the ligand concentrations, substantial overestimates of KD values can arise from assuming the free ligand concentration to be equal to the concentration of ligand added. Further error results from directly subtracting the parallel samples that define nonspecific binding. This is a particular problem for fluorescence titration assays where it is inconvenient to determine directly the free ligand for each data point. A correction can improve the estimate: if the amount of receptor is known, then the amount of bound ligand can be estimated and subtracted from the total ligand concentration to provide a corrected free ligand concentration. Replotting the data in terms of this new concentration then gives an improved estimate for the KD. This ignores any ligand depletion from partitioning of ligand into the membrane, which may also be significant and result in severalfold errors in KD estimates. When precise determinations of the KD by fluorescence are desired, the free ligand concentration can be determined independently 26j. Wymanand S. J. Gill, "Binding and Linkage:Function Chemistryof BiologicalMacromolecules." University Science Books, Mill Valley, California, 1990. 27C. R. Cantor and P. R. Schimmel, "Biophysical Chemistry: Part III, The Behavior of Biological Macromolecules."W. H. Freeman Co., San Francisco, 1980. z8I. M. Klotz, "Ligand-Receptor Energetics:A Guide for the Perplexed." John Wiley& Sons, New York, 1997.

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1000 2000 3000 Free [~H]Ethidium (nM)

FIG. 2. Subtraction of nonspecific binding by direct determination of free ligand concentrations. AChR-rich membranes (88/xg; 200/~1; 100 nM AChR) were incubated with varying concentrations of [3H]ethidium (0.2 Ci/mmol) in the absence ( e ) and presence ( I ) of 100 /xM phencyclidine, After centrifugation of the membranes, the supernatants were counted to determine the free [3H]ethidium concentration. The nonspecific binding (111),with phencyclidine, was fit to a line. The linear parameters were then used to calculate the nonspecific component of binding using the values of free [3H]ethidium for the samples without phencyclidine. This nonspecific component was then subtracted from the binding value to give the specific binding ([Z). The specific component of binding was then fit to Eq. (1) (solid curve). Inset: Semilog plot of the specific binding illustrating the difficulty of adequately demonstrating saturability of binding data. Data that appear to level off in the linear plot do not appear to reach a well-defined plateau value when viewed in a semilog plot. However, obtaining data at higher concentrations is limited by the substantial nonspecific binding.

by removing the bound ligand by centrifugation and measuring the supernatant concentration by fluorescence or by HPLC.14 Curve Fitting. Prior to the ubiquitous use of computers, binding data were often linearized and plotted in accordance with the Scatchard equation. 29 This method is still useful for qualitative evaluation of the data, but nonlinear regression of the data is now easy to perform with commonly available programs. We routinely use Sigmaplot (SPSS, Jandel Scientific, Chicago, IL). Binding is analyzed using the equation for the binding of a ligand to a single binding site [Eq. (1)], where R L is the measured binding concentration, Ro is the total binding site concentration, L is the free ligand concentration. This equation is simply derived from the definition of the dissociation constant, KD = R . L / R L , and the mass balance equation, Ro = R + RL. Ro" L RL - L + ~

(1)

The maximum binding, R0, and the KD for binding are extracted from the fit. Most fitting routines will also supply statistical data that indicate ~-uG. Scatchard, Ann. N.Y. Acad. Sci. 51, 660 (1949).

130

PHYSICALMETHODS

[61

the quality of the fit. It is important that the data demonstrate saturability, otherwise both parameters can have substantial error. As discussed by Klotz, 28the best plot for visualizing whether the binding has reached saturation is a semilog plot of bound ligand versus the log of the ligand concentration (see Fig. 2, inset). The quality of the fit can usually be determined by comparing the best fit with the data and looking for systematic deviations. This can also be done by plotting the residuals and looking for a pattern. If the residuals are not scattered evenly about the origin, then the fit is poor. Poor fits may arise from a number of problems. If the data do not saturate, the maximum value will be poorly determined and may deviate significantly from the expected value, resulting in error in the KD as well. The data may reflect components from multiple sites, cooperativity, or heterogeneous samples that lead to a poor approximation by the single site model. If the data are presumed to bind more than one site, it must be analyzed by other equations. In the case of cooperativity between sites, the data can often be fit to the Hill equation 3° [Eq. (2)]. The value n reflects the degree of apparent cooperativity between two or more sites. In the case of positive cooperativity, the slope of the semilog plot will be steeper than for a single binding site and n > 1. For negative cooperativity or for multiple independent sites, n < 1. It is difficult to distinguish multiple independent sites from negative cooperativity among the sites by equilibrium binding. If multiple independent sites are suspected, they may also be fit to a sum of terms, each term with the same form as Eq. (1). R/~ -

R0 1 + (KD/L)"

(2)

Analysis o f Competitive Inhibition Data

Competitive inhibition to a single site can generally be fit to Eq. (3), which describes the inhibition of binding of L by increasing concentrations of I. In this equation, R L is the amount bound observed, A is the amplitude of the change in binding, Bcg is the background or nonspecific binding, and gap p is the concentration of I that produces 50% inhibition. To calculate the KI for the inhibiting ligand (i.e., dissociation constant for the inhibitor I) it is necessary to correct for the concentration of the observed ligand L using Eq. (4), where KD is the dissociation constant for L. KD must be determined independently under similar conditions. RL 3o A. V. Hill,

A + Bcg 1 + I/Kapp

J. Physiol. (Lond.) 40, iv (1910).

(3)

[61

LIGAND BINDINGTO THE A C h R

131

Ko K1 = Kapp L + K D

(4)

Competitive inhibition data must have well-defined maximum and minimum values in order to obtain reliable values for Kapp by fitting to Eq. (3): data should extend 2 orders of magnitude on either side of the Kapp. For analyzing compounds of unknown affinity, controls should be included using a known ligand at a concentration that gives complete inhibition. Then, if the data do not extend to complete inhibition, the fit can be forced to the Bcg value defined by the control inhibitor. For fitting data to the acetylcholine binding sites of the AChR, it is often necessary, as well as desirable, to fit the data to inhibition at two distinct sites and obtain a Kapp for each site. This is accomplished by fitting the data to Eq. (5), which represents inhibition to two independent sites present in equal amounts. At times, it is necessary to fit the data with no prior assumption about the relative amounts of the two sites assumed; this is described by Eq. (6). This situation occurs, for instance, with inhibition of [leSI]c~-BgTx binding by 13'-iodo-d-tubocurarine: although the two binding sites are present in equal amounts, the binding of 13'-iodo-d-tubocurarine influences the rate of [125I]o~-BgTxto the second site, and it does not appear represented in equal amplitude31:

RL

= A

RL -

[

1

1 -t-//Klapp

A1 ] + [/Klapp

+

t-

1+

l p]+Bcg I~/K2ap

(5)

+Bcg

(6)

A2 1 + I/Keapp

When attempting to distinguish binding to two sites, it is important that g2appdiffer sufficiently. The binding to two sites of equal intrinsic affinity can be nearly as well described by binding to two sites that differ 4-fold in Ko. Therefore, a separation of Klappand K2appof tenfold is often required for reliable determination of the individual constants. A good test is to run both single-site and two-site fits to the data. While there will generally be improvement in the residuals because of the increase in the number of parameters, there should be clear evidence from inspection of the graph that the two-site model provides a better fit to the data before it is interpreted as such. As a rule, the best determination of the error is to repeat the experiment. Klapp and

3~S. E. Pedersen and R. V. L. Papineni, J. Biol. Chem. 270, 31141 (1995).

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PHYSICALMETHODS

[61

Thermodynamic Cycle Analysis Thermodynamic cycles are useful tools for analyzing ligand binding when it is necessary to interpret the effects of ligand structure, receptor mutations, heterotropic allosteric effects, or conformational changes. Thermodynamic cycles simply reflect the first law of thermodynamics, the conservation of energy, and the corollary of path independence: because energy is a state function, tile difference in energy between two states is independent of the path. Scheme I shows the version for analyzing the allosteric effects of one ligand (I) on a second ligand (L). If the two states are considered to be the free receptor with unbound ligand (R + I + L) and the ternary complex ( R I L ) , then it matters not whether L binds first and then I or vice versa. The free energy of each step is proportional to the log of the equilibrium constant (AG = - R T In K). Therefore, taking each path and setting the energies equal and removing the logarithms yields KL" K{ = KI" K[. This can be rewritten K L / K [ = K I / K ~ , which says that the ratio of the binding constants for L in the absence and presence of I is the same as the ratio of the binding constants for I in the presence and absence of L. For example, if I inhibits the binding of L, then L will inhibit the binding I to the same extent. The equation also shows that if three of the constants are known, then the fourth is also determined. The scheme does not illustrate the underlying conformational changes, but they are implicit in the changes in the equilibrium constants: each constant reflects the binding to the equilibrium distribution of conformations for the receptor, which may be influenced by the presence of the second ligand. It is clear that long-range interactions between the ligands must take place, often mediated by receptor conformational changes, or else KL would simply equal K[. This cycle can be used to analyze several scenarios: the effect of varying concentrations of an allosteric ligand I on the binding of the measured ligand L, or the effect of a isotonic concentration of I on the binding affinity of L. The latter are described by Eq. (7), where the binding of L is first analyzed by Eq. (1) or by Eqs. (3) and (4), depending on whether the data are obtained by direct binding or by competitive inhibition. The K value

KL

R+L+I

.

" RL+I

K[ RI + L

.

" RLI

SCHEMEI

[6]

LIGAND BINDINGTO THE A C h R

133

obtained equals the right-hand term in the denominator of Eq. (7). If a saturating concentration of I is used, the K value reduces to KLK~/KI, which is simply equal to K{. R L = Ro

L 1 + I/K1 L+KL - 1 + I/K~

(7)

Conversely, if the radioactive (or fluorescent) ligand L is held constant and the effect of varying concentrations of I is measured, then Eq. (7) can be rearranged to give Eq. (8). The data can be fit according to Eq. (3) to yield the maximum, minimum, and Kapp. Those values can then be interpreted according to Eqs. (9)-(11). In this case, the plateau value at high concentrations of I does not reflect nonspecific binding, but rather reflects the binding of L as affected by I [Eq. (11)]. For this reason, it is important to have an independent determination of nonspecific binding using an excess of a ligand known to compete with L. This value should be substracted before the analysis. RL

Ro

1

-- (B~ - BO) p - lKq _a

Kapp =

KIK~(L +

q- B 0

KL)

(8)

(9)

LKI + KcK{

Bo B~ -

L L +KL L

(10) (11)

L + KcK[/K~ Double-Mutant Thermodynamic Cycle Analysis

The principle behind the double-mutant thermodynamic cycle analysis has been articulated by Carter et al. 32 and was outlined by Ackers and Smith 33 for the study of pairwise interactions of residues in proteins. The pairwise analysis overcomes some of the caveats of single mutation analysis on binding energetics and conformational changes. It can be used to determine whether changes in homologous ligands are independent and can be used to evaluate interactions among specific loci on ligands and receptors. 32p. j. Carter, G. Winter, A. J. Wilkinson, and A. R. Fersht, Cell 38, 835 (1984). 33G. K. Ackers and F. R. Smith, Ann. Rev. Biochem. 54, 597 (1985).

134

PHYSICALMETHODS

[61

To illustrate the method, consider ligands LI and a close analog L2, which differ by a small, discrete structural change, for example, a single methylation in d-tubocurarine. L1 and L2 bind to a receptor site, Ra. A single mutation in Ra will yield the receptor homolog Rb. If the ligand functional group does not interact with the modified receptor amino acid, then the change in affinity of the ligand will be independent of the receptor modification. If the ligand functional group does interact with the receptor amino acid residue, then the change in affinity upon modifying L1 to L2 will be dependent on whether the receptor residue is also modified. This explanation can be formalized using the thermodynamic cycle shown in Scheme II. A binding analysis is performed to measure the equilibrium dissociation constants for both L1 and L2 to both Ra and Rb. This will generate four binding constants and the corresponding free energies: AGal, AGa2, A G b l , and AGb2 ; the subscripts indicate the receptor and the ligand respectively. Each binding energy is represented at a corner of the cycle. The principle of path independence leads to the same constraints discussed above: all paths from RaLa to RbL2 must have the same energy. Therefore AAG~ + AAG2 = AAG1 + A A G b , where AAGx represents the difference between two binding energies. If the two ligand and receptor sites are independent of each other then the change in ligand binding affinities (AAGx) will be the same in each direction; i.e., AAGa = AAGb and AAG1 = AAG2. In this case, the change in binding energy caused by modifying the ligand (AAG, and A A G b ) is the same for both receptor types. Conversely, the change inbinding energy caused by mutating the receptor (AAG1 and AAG2) is the same for either ligand. If the mutated receptor residue interacts with the altered ligand site, then A A G a # A A G b and AAG1 # AAG2. However, the cyclic relationship must hold, which can be rewritten as follows: AAG~ - AAGb = AAG1 AAG2. This difference is the interaction energy and reflects the strength of the interaction. The identity of the two differences provides an internal control on the experimental measurements.

AAG

RaL 1 -

", RaL2

It...2 AAG b

RbL 1 .

, RbL 2

SCHEME II

[7]

3 - D STRUCTURE OF MEMBRANE PROTEINS

135

This type of analysis has been used to study the role of individual hemoglobin residues in conformational transitions on ligand binding. 33 It has also been applied to study the interaction of scorpion agatoxin 2 with the Shaker potassium channel and successfully revealed close electrostatic interactions. 34 This method is likely to find further use in analyzing the structures of binding sites that are inaccessible to direct structural determination. 34 p. Hidalgo and R. MacKinnon, Science 268, 307 (1995).

[7] T h r e e - D i m e n s i o n a l S t r u c t u r e o f M e m b r a n e P r o t e i n s Determined by Two-Dimensional Crystallization, Electron Cryomicroscopy, and Image Analysis By MARK YEAGER, VINZENZ

M.

UNGER, and ALOK K. MITRA

Introduction The Brookhaven Protein Data Bank now has about 5000 atomic structures available for soluble proteins. This compares with about 20 membrane protein structures, many of which are of the same class. Strategies continue to be developed for growing three-dimensional (3D) crystals of membrane proteins] 5 and recent progress has been encouraging.6,7 Nevertheless, the high-resolution structure analysis of membrane proteins is still a formidable task. In addition, no recombinant eucaryotic membrane protein has as yet been amenable to 3D crystallization. Soluble fragments of membrane proteins have been overexpressed, purified, and examined by conventional X-ray crystallography.8 10However, this approach does not allow examinat W. Kiahlbrandt, Quart. Rev. Biophysics 21, 429 (1988). 2 H. Michel, ed., "Crystallization of M e m b r a n e Proteins." C R C Press, Boca Raton, 1991. 3 F. Reiss-Husson, in "Crystallization of Nucleic Acids and Proteins: A Practical A p p r o a c h " (A. Ducruix and R. Gieg6, eds.), p. 175. I R L Press, Oxford, 1992. 4 R. M. Garavito, D. Picot, and P. J. Loll, J. Bioenerg. Biornernbr. 28, 13 (1996). 5 E. Pebay-Peyroula, G. Rumrnel. J. P. Rosenbusch, and E. M. Landau, Science 277, 1676 (1997). ~' R. M. Garavito and S. H. White, Curr. Opin. Struct. BioL 7, 533 (1997). 7 C. Ostermeier and H. Michel, Curr. Opin. Struct. Biol. 7, 697 (1997). J. Wang, Y. Yan, T. P. J. Garrett, J. Liu, D. W. Rodgers, R. L. Garlick, G. E. Tarr, Y. Husain, E. L. Reinherz, and S. C. Harrison, Nature 348, 411 (1990). '~ A. M. De Vos, M. Ultsch, and A. A. Kossiakoff, Science 255, 306 (1992).

METHODS IN ENZYMOLOGY,VOL. 294

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